Mechanical Behaviour of Cold-Formed Hollow Structural Section Material

Transcription

1 Mechanical Behaviour of Cold-Formed Hollow Structural Section Material by Min Sun A thesis submitted in conformity with the requirements for the degree of Doctor of Philosophy Graduate Department of Civil Engineering University of Toronto Copyright by Min Sun 2014

2 Mechanical Behaviour of Cold-Formed Hollow Structural Section Material Abstract Min Sun Doctor of Philosophy Graduate Department of Civil Engineering University of Toronto 2014 In this thesis, the static and dynamic properties of cold-formed Rectangular Hollow Sections (RHS) produced by different manufacturing techniques (direct-forming versus continuousforming; heat-treated versus non-heat-treated) were studied comparatively for the first time. The aim of this research was to quantify the effects of different manufacturing processes on the mechanical behaviour of RHS such that the implications of using RHS with different production histories can be better appreciated during the design of structures made of RHS and their welded joints. The static properties of seven cold-formed RHS specimens were investigated by performing tensile coupon tests, stub column tests, and residual stress measurements. Analytical column curves were generated to reflect their compression behaviour, based on the experimental results. It was found that, in general, the static properties of a direct-formed RHS are midway between those of its continuous-formed and continuous-formed plus heat-treated counterparts. The Charpy V-notch (CVN) impact toughness properties of six RHS specimens were studied via 378 CVN coupons. For RHS with different cross-sectional geometries and produced by different methods, complete CVN toughness-temperature curves of the flat face and the corner were compared to quantify the decrease of notch toughness from the flat face to the ii

3 corner due to uneven degrees of cold-forming. It was also found that heat treatment in accordance with Canadian standards for Class H finishing does not provide improvement in the CVN toughness. The high strain rate properties (compressive and tensile) of four RHS specimens manufactured by different cold-forming methods were examined by performing a total of 166 split Hopkinson pressure/tension bar tests at strain rates ranging from 100 to 1000 s -1. Their dynamic yield stresses were compared to their static yield stresses, to characterize the strength enhancement of cold-formed RHS under such loading rates, which can be used in the blast- or impact-resistant design of RHS members. iii

4 Acknowledgements First and foremost I would like to thank Professor Jeffrey Packer for his guidance and expertise. I appreciate the countless hours he has invested in this thesis as well as in my professional and personal development. I would like to thank Professor Kaiwen Xia for his technical support in the split-hopkinson pressure/tension bar test program and Professor Michael Seica for his expertise in high strain rate loadings and dynamic structural design. I am also grateful to the discussions and motivation generously offered by my friends Dr. Michael Simpson, David Ruggiero, Paolo Calvi, Giorgio Proestos, Drew Cheung, Martin Walker, Tarana Haque, Elena Nuta, Matthew McFadden, Stephen Perkins, and many officemates and research group members. Financial support has been provided by the Natural Sciences and Engineering Research Council of Canada (NSERC), Explora Foundation, the Ontario Graduate Scholarship program and the University of Toronto. Appreciation is extended to Bull Moose Tube and Atlas Tube for providing the RHS members. I am grateful to the staff of the Department of Civil Engineering s Structural Testing Facilities Giovanni Buzzeo, John MacDonald, Renzo Basset and Xiaoming Sun for their help with the experiments. Also, I would like to thank Sheng Huang for his help in using the split-hopkinson pressure/tension bar apparatus in the Department s Impact and Fracture Laboratory. Finally, I would like to express my profound appreciation to my family, in particular my wife Yang Yang, for their love, encouragement and patience. iv

5 Table of Contents Abstract Acknowledgements Table of Contents List of Tables List of Figures Notation ii iv v viii xi xviii Chapter 1 Introduction Background Scope of research 4 Chapter 2 Static Properties Summary Background RHS specimens and geometric measurements Experimental investigation Tensile coupon tests Stub column tests Longitudinal residual stress measurements Results and discussions Tensile stress-strain behaviour and ductility around the cross-section Compressive stress-strain behaviour of the entire cross-section Longitudinal residual stresses around the cross-section Column model 30 Chapter 3 Charpy V-Notch Impact Toughness Summary Background 39 v

6 3.3 Effects of chemical composition on material CVN impact toughness Toughness anisotropy in HSS Effect of rolling direction of base plate Effect of notch orientation of CVN coupon CVN toughness in pertinent HSS product standards ASTM A [ASTM 2013a] ASTM A [ASTM 2013b] CAN/CSA G /G [CSA 2013] EN 10219:2006 [CEN 2006a; CEN 2006b] and ISO [ISO 2011] CVN toughness in international design standards Correlation of CVN toughness to fracture mechanics AASHTO [AASHTO 2007] CSA S16-09 [CSA 2009] EN :2005 [CEN 2005] Previous toughness investigations on cold-formed products RHS specimens and chemical compositions Experimental investigation Results and discussions Effects of chemical composition Effects of cold-forming and heat-treatment 67 Chapter 4 High Strain Rate Behaviour Summary Background Previous investigations RHS specimens Experimental investigation Tensile coupon tests SHPB tests Background Compressive SHPB tests 84 vi

7 Tensile SHPB tests Results and discussions Strength increase factor Dynamic increase factor 92 Chapter 5 Conclusions 96 References 101 Appendix A Geometric Measurements and Static Properties 108 A.1 Geometric measurements 108 A.2 Tensile coupon test results 110 A.3 Stub column test results and determination of maximum longitudinal compressive residual stresses 114 A.4 Measured longitudinal residual stresses 118 A.5 Analytical compressive stress-strain curves based on column models 123 Appendix B Calculations for Analytical Charpy Transition Temperatures 126 B.1 Derivation of equations in Figure 3.7 for determination of ε eff in the bent region of HSS [Feldmann et al. 2012] 126 B.2 Calculation of analytical T cf -values in Table 3.10 based on the approach proposed by [Feldmann et al. 2012] using measured cross-sectional dimensions 129 Appendix C Split-Hopkinson Pressure Bar Test Results 144 vii

8 List of Tables Table 2.1 List of RHS specimens 8 Table 2.2 Nominal and measured dimensions of RHS specimens 10 Table 2.3 Measured cross-sectional area of flat faces and corners 12 Table 2.4 Key tensile coupon test results 13 Table 2.5 Full-sectional tensile properties 16 Table 2.6 Key stub column test results 18 Table 2.7 Comparison of full-sectional tensile and compressive properties 18 Table 2.8 Key longitudinal residual stress measurement results 24 Table 3.1 Chemical requirements in ASTM A500 [ASTM 2013a] 42 Table 3.2 Charpy V-notch test acceptance criteria for coupons with different sizes [ASTM 2009] 45 Table 3.3 Maximum permissible value of element thickness for S355 steel [CEN 2005] 47 Table 3.4 Maximum permissible value of element thickness for S355 steel Table 2.1 of EN :2005 extended [Feldmann et al. 2012] 53 Table 3.5 Chemical compositions of RHS specimens and effects of chemical elements on the CVN toughness of low-carbon structural steel [Roe and Bramfitt 1990; Maranian 2010] 56 Table 3.6 Cutting locations and orientations of CVN coupons 57 Table 3.7 CVN test results: (a) full-sized coupons; (b) sub-sized coupons 59 Table 3.8 Normalized upper-shelf energy (KV us ), ductile-to-brittle transition temperature (DBTT) and nil-ductility temperature (NDT) of all RHS specimens 65 viii

9 Table 3.9 Measured cross-sectional dimensions 69 Table 3.10 Comparison of T cf -values obtained from experiment results and T cf -values estimated based on the approach proposed by [Feldmann et al. 2012] using measured cross-sectional dimensions 69 Table 4.1 DIF y and DIF u values for various structural steels under low pressure explosion [Gilsanz et al. 2013] 72 Table 4.2 SIF y and SIF u values for RHS specimens 80 Table 4.3 DIF y values for RHS specimens under compression loading ( = 100 s -1 ) 93 Table 4.4 DIF y values for RHS specimens under compression loading ( = 1000 s -1 ) 93 Table 4.5 DIF y values for RHS specimens under tension loading ( = 100 s -1 ) 93 Table 4.6 DIF y values for RHS specimens under tension loading ( = 1000 s -1 ) 93 Table 4.7 DIF y values for RHS specimens under flexural loading ( = 100 s -1 ) 93 Table 4.8 DIF y values for RHS specimens under flexural loading ( = 1000 s -1 ) 94 Table A.1 Measured thickness and corner radius of RHS 152x152x12.7 & Domex (DF19) 108 Table A.2 Measured thickness and corner radius of RHS 152x152x Table A.3 Normalized measured longitudinal residual stresses in DF12, CF12 and CFH Table A.4 Normalized measured longitudinal residual stresses in DF24, CF24 and CFH Table A.5 Calculation of residual force in DF Table A.6 Calculation of residual force in CF Table A.7 Calculation of residual force in CFH Table A.8 Calculation of residual force in DF ix

10 Table A.9 Calculation of residual force in CF Table A.10 Calculation of residual force in CFH Table C.1 Key compressive SHPB test results (F = flat face; C = corner) 148 Table C.2 Key tensile SHPB test results (F = flat face; C = corner) 154 x

11 List of Figures Figure 1.1 Cold-forming processes: (a) direct-forming; (b) continuous-forming 2 Figure 1.2 Flat rollers used in direct-forming process 3 Figure 1.3 Concave rollers used in continuous-forming process 3 Figure 2.1 Thickness and corner radius measurement locations 9 Figure 2.2 Difference between measured and nominal thickness (mm) 9 Figure 2.3 Normalized corner radii for all RHS specimens: (a) outside corner radii; (b) inside corner radii 10 Figure 2.4 Measurement of corner area 11 Figure 2.5 Average elongations of tensile coupons at failure 14 Figure 2.6 Comparison of typical tensile coupon test results from different RHS: (a) flat coupons; (b) corner coupons 14 Figure 2.7 Comparison of typical flat and corner tensile coupon test results from the same RHS: (a) DF24; (b) CF24; (c) CFH24 15 Figure 2.8 Stub column test setup: (a) before testing; (b) after testing 17 Figure 2.9 Normalized compressive stress-strain curves from stub column tests: (a) RHS152x152x12.7; (b) RHS152x152x Figure 2.10 Relationship between unloading stress and in-situ longitudinal residual stress 21 Figure 2.11 Locations of strain gauges for longitudinal residual stress measurement: (a) strain gauges on RHS 152x152x12.7 and RHS 152x152x6.35; (b) strain gauges on one inside surface of RHS 152x152x Figure 2.12 Normalized longitudinal residual stresses: (a) RHS 152x152x12.7; (b) RHS 152x152x xi

12 Figure 2.13 Example (DF24) of determination of maximum longitudinal compressive residual stress based on stub column test result 29 Figure 2.14 Comparison of maximum compressive longitudinal residual stresses obtained from residual stress measurements and stub column test results 29 Figure 2.15 Illustration of discretized cross-section column model 32 Figure 2.16 Comparisons of overall compressive stress-strain curves from stub column tests and column models: (a) CF12; (b) CF24 34 Figure 2.17 Analytical column curves: (a) RHS 152x152x12.7; (b) RHS 152x152x Figure 2.18 Comparison with column curves as per CSA S16-09, AISC and EN :2005 for direct-formed RHS: (a) DF12 (RHS 152x152x12.7); (b) DF24 (RHS 152x152x6.35) 36 Figure 2.19 Comparison with column curves as per CSA S16-09, AISC and EN :2005 for continuous-formed RHS: (a) CF12 (RHS 152x152x12.7); (b) CF24 (RHS 152x152x6.35) 37 Figure 2.20 Comparison with column curves as per CSA S16-09, AISC and EN :2005 for continuous-formed plus heat-treated RHS: (a) CFH12 (RHS 152x152x12.7); (b) CFH24 (RHS 152x152x6.35) 38 Figure 3.1 Approximate relationship between the CVN energy-temperature curve and the fracture behaviour of a steel component [adapted from Sedlacek et al. 2008] 40 Figure 3.2 Variation in CVN impact energy with temperature for carbon steels of varying carbon content [adapted from Roe and Bramfitt 1990] 43 Figure 3.3 Variation in CVN impact energy with temperature for 0.30% carbon steels of varying manganese content [adapted from Roe and Bramfitt 1990] 43 Figure 3.4 Determination of maximum plastic strain due to cold-bending [adapted from Sedlacek et al. 2008] 48 xii

13 Figure 3.5 Change of Charpy V-notch impact energy due to cold-forming, for S355J2 steel [adapted from VDEh 1992] 49 Figure 3.6 Change of T 27J -temperature due to cold-forming, for S355J2 steel [adapted from VDEh 1992] 50 Figure 3.7 Determination of ε eff in the bent region of HSS [adapted from Feldmann et al. 2012] 54 Figure 3.8 Cutting locations and orientations of CVN coupons: (a) full-sized coupons; (b) sub-sized coupons 57 Figure 3.9 CVN impact test setup 58 Figure 3.10 Illustration of tanh function 60 Figure 3.11 CVN impact energy-temperature curves for DF12 61 Figure 3.12 CVN impact energy-temperature curves for CF12 61 Figure 3.13 CVN impact energy-temperature curves for CFH12 62 Figure 3.14 CVN impact energy-temperature curves for DF24 62 Figure 3.15 CVN impact energy-temperature curves for CF24 63 Figure 3.16 CVN impact energy-temperature curves for CFH24 63 Figure 3.17 Change of DBTT from flat face to corner for all RHS specimens 64 Figure 3.18 Change of NDT from flat face to corner for all RHS specimens 64 Figure 3.19 Normalized KV us (J/cm 2 ) for all RHS specimens 65 Figure 4.1 DIF y values at various strain rates for ASTM A36 and A514 steels in [adapted from DOD 2008] 73 Figure 4.2 Typical stress-strain curves for steel and dynamic design stress [adapted from DOD 2008] 74 xiii

14 Figure 4.3 Relationships between DIF y and strain rate based on previous investigations at intermediate strain rate level (test strain rate up to 10 s -1 ) 77 Figure 4.4 Relationships between DIF y and strain rate based on previous investigations at high strain rate level (test strain rate up to 2500 s -1 ) 78 Figure 4.5 Schematic diagram of compressive SHPB apparatus 80 Figure 4.6 Photograph of compressive SHPB apparatus 81 Figure 4.7 Typical strain gauge data from a compressive SHPB test 81 Figure 4.8 Schematic diagram of tensile SHPB apparatus 83 Figure 4.9 Determination of dynamic yield stress 84 Figure 4.10 Determination of strain rate 84 Figure 4.11 Compressive and tensile SHPB samples 85 Figure 4.12 Cutting location and orientation of compressive and tensile SHPB samples 85 Figure 4.13 Typical compressive SHPB test results 86 Figure 4.14 Compressive DIF y values of DF12 (12.7 mm thick RHS) 87 Figure 4.15 Compressive DIF y values of CF12 (12.7 mm thick RHS) 87 Figure 4.16 Compressive DIF y values of DF24 (6.35 mm thick RHS) 88 Figure 4.17 Compressive DIF y values of CF24 (6.35 mm thick RHS) 88 Figure 4.18 Schematic diagram of tensile SHPB sample 89 Figure 4.19 Tensile SHPB sample after test 90 Figure 4.20 Typical tensile SHPB test results 90 Figure 4.21 Tensile DIF y values of DF12 (12.7 mm thick RHS) 91 Figure 4.22 Tensile DIF y values of CF12 (12.7 mm thick RHS) 91 xiv

15 Figure A.1 Tensile coupon test results for DF19 (RHS 152x152x7.95, high strength, direct-formed) 110 Figure A.2 Tensile coupon test results for DF12 (RHS 152x152x12.7, regular strength, direct-formed) 110 Figure A.3 Tensile coupon test results for DF24 (RHS 152x152x6.35, regular strength, direct-formed) 111 Figure A.4 Tensile coupon test results for CF12 (RHS 152x152x12.7, regular strength, continuous-formed) 111 Figure A.5 Tensile coupon test results for CFH12 (RHS 152x152x12.7, regular strength, continuous-formed plus heat-treated) 112 Figure A.6 Tensile coupon test results for CF24 (RHS 152x152x6.35, regular strength, continuous-formed) 112 Figure A.7 Tensile coupon test results for CFH24 (RHS 152x152x6.35, regular strength, continuous-formed plus heat-treated) 113 Figure A.8 Stub column test results for DF19 (RHS 152x152x7.95, high strength, direct-formed) 114 Figure A.9 Stub column test results for DF12 (RHS 152x152x12.7, regular strength, direct-formed) 114 Figure A.10 Stub column test results for DF24 (RHS 152x152x6.35, regular strength, direct-formed) 115 Figure A.11 Stub column test results for CF12 (RHS 152x152x12.7, regular strength, continuous-formed) 115 Figure A.12 Stub column test results for CFH12 (RHS 152x152x12.7, regular strength, continuous-formed plus heat-treated) 116 Figure A.13 Stub column test results for CF24 (RHS 152x152x6.35, regular strength, continuous-formed) 116 xv

16 Figure A.14 Stub column test results for CFH24 (RHS 152x152x6.35, regular strength, continuous-formed plus heat-treated) 117 Figure A.15 Comparisons of overall compressive stress-strain curves from stub column tests and column models for DF Figure A.16 Comparisons of overall compressive stress-strain curves from stub column tests and column models for DF Figure A.17 Comparisons of overall compressive stress-strain curves from stub column tests and column models for CF Figure A.18 Comparisons of overall compressive stress-strain curves from stub column tests and column models for CFH Figure A.19 Comparisons of overall compressive stress-strain curves from stub column tests and column models for CF Figure A.20 Comparisons of overall compressive stress-strain curves from stub column tests and column models for CFH Figure C.1 Dynamic compressive stress-strain curves for flat face of DF12 (RHS 152x152x12.7, regular strength, direct-formed) 144 Figure C.2 Dynamic compressive stress-strain curves for corner of DF12 (RHS 152x152x12.7, regular strength, direct-formed) 144 Figure C.3 Dynamic compressive stress-strain curves for flat face of CF12 (RHS 152x152x12.7, regular strength, continuous-formed) 145 Figure C.4 Dynamic compressive stress-strain curves for corner of CF12 (RHS 152x152x12.7, regular strength, continuous-formed) 145 Figure C.5 Dynamic compressive stress-strain curves for flat face of DF24 (RHS 152x152x6.35, regular strength, direct-formed) 146 Figure C.6 Dynamic compressive stress-strain curves for corner of DF24 (RHS 152x152x6.35, regular strength, direct-formed) 146 xvi

17 Figure C.7 Dynamic compressive stress-strain curves for flat face of CF24 (RHS 152x152x6.35, regular strength, continuous-formed) 147 Figure C.8 Dynamic compressive stress-strain curves for corner of CF24 (RHS 152x152x6.35, regular strength, continuous-formed) 147 Figure C.9 Dynamic tensile stress-strain curves for flat face of DF12 (RHS 152x152x12.7, regular strength, direct-formed) 152 Figure C.10 Dynamic tensile stress-strain curves for corner of DF12 (RHS 152x152x12.7, regular strength, direct-formed) 152 Figure C.11 Dynamic tensile stress-strain curves for flat face of CF12 (RHS 152x152x12.7, regular strength, continuous-formed) 153 Figure C.12 Dynamic tensile stress-strain curves for corner of CF12 (RHS 152x152x12.7, regular strength, continuous-formed) 153 xvii

18 Notation f ds Dynamic design stress for tension, compression and bending f dv Dynamic design stress for shear f dy Measured dynamic yield stress, or predicted dynamic yield stress f du Predicted dynamic ultimate strength f y Measured static yield strength f y,avg Average of yield strengths of tensile coupons f y,nom Nominal yield strength f u Measured static ultimate strength f u,avg Average of ultimate strengths of tensile coupons f u,nom Nominal ultimate strength l s Length of compressive SHPB sample q Cowper-Symonds parameter r i Inside corner radius of RHS, or inside radius of CHS r i,avg Average of measured inside corner radii of RHS r o Outside corner radius of RHS r o,avg Average of measured outside corner radii of RHS t Measured wall thickness of RHS t avg Average of measured wall thicknesses of RHS t nom Nominal wall thickness of RHS A Cross-sectional area, or curve fitting coefficient in Eq. 3-4 xviii

19 A b Cross-sectional area of pressure bar A s Cross-sectional area of compressive SHPB sample, or cross-sectional area of the test region of tensile SHPB sample B Measured external width of RHS, or curve fitting coefficient in Eq. 3-4 B avg Average of measured external widths of RHS B nom Nominal external width of RHS C Curve fitting coefficient in Eq. 3-4, or Cowper-Symonds parameter C b Longitudinal elastic wave speed in pressure bar CF CFH CHS CVN DBTT Continuous-forming Continuous-forming and stress-relieved Circular hollow section(s) Charpy V-notch Ductile-to-brittle transition temperature ( C) DCF Degree of cold-forming (%) DF DIF y DIF u E F HSS Direct-forming Dynamic increase factor for yield stress = measured dynamic yield stress / measured static yield stress Dynamic increase factor for ultimate strength = measured dynamic ultimate strength / measured static ultimate strength Young s modulus Ratio of flat face area to total cross-sectional area of RHS Hollow structural section(s) I E Effective moment of inertia xix

20 KV Energy absorbed by the CVN coupon (J) KV us Upper-shelf energy (J) L NDT P Length of RHS Nil-ductility temperature ( C) Compression load R 2 Coefficient of determination RHS Rectangular hollow section(s) R y Ratio of the expected yield stress to the specified minimum yield stress SHPB SHTB SIF y Split-Hopkinson pressure bar Split-Hopkinson tension bar Strength increase factor for yield stress = measured static yield stress / nominal yield stress SIF u Strength increase factor for ultimate strength = measured static ultimate strength / nominal ultimate strength T Temperature ( C) T 27J Temperature ( C) at which the energy absorbed by the CVN coupon is 27 J σ b Bending component of theoretical unloading surface stress σ in Theoretical unloading stress on the inside surface of RHS σ m Membrane component of theoretical unloading surface stress σ out Theoretical unloading stress on the outside surface of RHS σ p Proportional limit xx

21 σ rs Longitudinal residual stress σ rs,in Longitudinal residual stress on the inside surface of RHS σ rs,out Longitudinal residual stress on the outside surface of RHS σ(t) Stress-time history of SHPB sample ε eff Average value of the plastic strain (%) in the net section of the CVN coupon ε max Plastic strain (%) on the surface of HSS ε(t) ε i (t) ε r (t) ε t (t) ε Strain-time history of SHPB sample Incident wave in the pressure bar Reflected wave in the pressure bar Transmitted wave in the pressure bar Strain rate T cf Shift of CVN energy-temperature curve ( C) due to cold-forming xxi

22 Chapter 1 Introduction 1.1 Background Hollow Structural Sections (HSS) have become an increasingly popular building material since their introduction in the 1950s due to their torsional rigidity, high compression strengthto-weight ratio and aesthetic form. HSS are manufactured around the world by either hotforming (a hot-finishing or seamless process) or, more commonly, by cold-forming. Hotformed HSS have superior mechanical properties compared to their cold-formed counterparts, but they are either unavailable in much of the world or prohibitively expensive. With coldformed HSS, depending on the amount of cold-working, the mechanical properties are sometimes substantially different from those of the base material. Thus, experimental tests and numerical analyses have been conducted extensively in the past to investigate the effect of cold-forming on the structural behaviour of HSS and their welded joints, thereby encouraging the use of HSS by design engineers. Although elliptical shapes are available, HSS are predominantly available in two shapes: circular and rectangular (including square). Among different shapes, Rectangular Hollow Sections (RHS) are often preferred to Circular Hollow Sections (CHS) due to the ease of fabrication at the connections. Internationally, there are two common manufacturing methods for cold-formed RHS: directforming and continuous-forming. For both methods, the coil strip is progressively cold-bent into the desired shape by passage through a serious of pressure rollers, during which the rollers introduce a controlled amount of cold-bending (depending on the sizes of the used rollers) to the coil strip, thus the mechanical properties are theoretically consistent in the longitudinal direction of the RHS product. However, some gradual variation in the longitudinal direction will occur for both production methods in practice due to the location of the final RHS member relative to the position in the hot-rolled coil material from which it was made. The direct-forming process is illustrated in Figure 1.1(a) and includes: (1) roll-forming a coil strip directly into an open section with the desired rectangular shape; and (2) joining the edges of the open section by welding to form a closed rectangular shape. The continuousforming process is illustrated in Figure 1.1(b) and includes: (1) roll-forming a coil strip first into a circular open tube; (2) joining the edges of the open tube by welding to form a closed 1

23 circular shape; and (3) flattening the circular tube walls to form the desired rectangular shape. Figure 1.2 shows the flat rollers used in the direct-forming process to form the coil into a rectangular tube directly. Figure 1.3 shows the concave rollers used in the continuousforming process to form the coil into a circular tube before further flattening it into a rectangular tube. (a) (b) Figure 1.1 Cold-forming processes: (a) direct-forming; (b) continuous-forming Although the appearance of the sections can be similar, the mechanical behaviours of RHS produced by different cold-forming methods can be substantially different. For direct-formed RHS, the cold-working is concentrated at the four corners, thus the flat faces (not containing the weld) of the final RHS product have similar properties to the coil material. For 2

24 continuous-formed RHS, the entire cross-section contains high degrees of cold-working, thus the final RHS product has higher yield and ultimate strengths and lower ductility compared to the coil material. The implications of using RHS produced by different cold-forming methods (i.e. different mechanical behaviours) are often not fully appreciated. Thus, in this thesis, the static and dynamic properties of cold-formed RHS produced by different manufacturing techniques (direct-forming versus continuous-forming; heat-treated versus non-heat-treated) were studied comprehensively. Figure 1.2 Flat rollers used in direct-forming process Figure 1.3 Concave rollers used in continuous-forming process 3

25 1.2 Scope of research The main aim of this thesis has been to determine experimentally how different manufacturing techniques (direct-forming versus continuous-forming; heat-treated versus non-heat-treated) affect the static and dynamic properties of cold-formed RHS. The static properties of the RHS specimens were investigated by performing tensile coupon tests, stub column tests, and residual stress measurements. The dynamic properties of the RHS specimens were investigated by performing Charpy V-notch (CVN) tests, Split-Hopkinson Pressure Bar (SHPB) tests and Split-Hopkinson Tension Bar (SHTB) tests. The main parameters considered include: (1) various cross-sectional geometries, which correspond to different degrees of cold-forming; and (2) different static yield strengths, as steel with higher static yield strength is in general less susceptible to cold-forming and high strain rate effects. Since cold-forming increases yield and ultimate strengths but decreases ductility of steel, theoretically there is a larger cross-sectional variation (i.e. flat face versus corner) of mechanical properties in a direct-formed RHS than that in its continuous-formed counterpart. For all RHS specimens, the static tensile stress-strain behaviour and ductility of the flat face and the corner were measured locally through tensile coupon tests. Using the measured flat face and corner areas, the full-sectional tensile properties of the RHS specimens with different production histories are determined and compared. Column strengths are influenced by the magnitude and distribution of residual stresses. In the Canadian steel structures design standard [CSA 2009], a single column curve is used for the determination of column strengths of cold-formed non-stress-relieved HSS (Class C), regardless of the cold-forming methods. A more favourable column curve is used for the cold-formed stress-relieved HSS (Class H). However, due to a lower overall residual stress level, theoretically a direct-formed RHS (Class C) should have a more favourable column behaviour than its continuous-formed counterpart (Class C). In this study, the overall compressive behaviours of the RHS specimens with different production histories were investigated both experimentally (through stub column tests and longitudinal residual stress measurements) and analytically (through discretized cross-section column models). For the assessment of RHS for notch toughness, steel product standards normally require testing of Charpy V-notch (CVN) coupons taken longitudinally in the flat face (away from the weld seam) of the RHS, which is questionable since the corner in general has lower notch toughness due to uneven degrees of cold-forming. Thus, when selecting RHS for notch 4

26 toughness, it is preferable to specify the corner as an alternate measuring location, or to consider the deterioration from the flat face to the corner if the notch toughness was measured in the standard location (flat face). In this study, by performing CVN tests, the notch toughness decrease from the flat face to the corner of RHS specimens with different production histories is quantified (in terms of degree of cold-forming) and expressed as a transition temperature shift ( T cf ). Also, steel product standards are in general ambiguous about the sampling orientation (i.e. notch orientation) of full-sized CVN coupons (10x10 mm) from HSS, which in fact affects the test results. Hence, the effect of notch orientation is investigated in this study as well. For blast- or impact-resistant design of steel structures, it is important to use realistic properties of steel under high strain rate. In particular, the substantial rise in yield stress under high strain rate may have important effects on the dynamic behaviour of a steel structure. Since investigations on the high strain rate properties of cold-formed HSS are scarce, by performing split-hopkinson pressure/tension bar tests at strain rates from 100 to 1000 s -1, the local dynamic yield stresses (compressive and tensile) of the flat face and the corner of the RHS specimens were measured. Using the measured flat face and corner areas, the fullsectional dynamic yield stresses are determined and compared to the corresponding static yield stresses to characterize the dynamic yield stress enhancements (compressive and tensile) of RHS specimens with different production histories. A secondary aim of this thesis has been to compare the experimental and analytical results with the respective design rules and recommendations for cold-formed hollow sections, in international design specifications for steel structures, with a view to improving current design practice with hollow sections. 5

27 Chapter 2 Static Properties 2.1 Summary This chapter compares the static properties of a total of seven cold-formed RHS manufactured by different methods: (1) direct-forming, (2) continuous-forming, and (3) continuous-forming plus stress-relieving by heat treatment. The static properties compared are: (1) tensile stress-strain behaviour and ductility around the cross-section, (2) compressive stress-strain behaviour of the entire cross-section, and (3) longitudinal residual stress around the cross-section. The maximum values of longitudinal compressive residual stresses estimated from the stub column test results are used to check the accuracy of the longitudinal residual stress measurements from strips. Finally, the measured longitudinal residual stress gradients are incorporated into column models to study the column behaviour of RHS with different production histories. 2.2 Background It is well known that cold-forming causes strain hardening of the steel material, hence its yield and ultimate strengths increase while its ductility decreases. Early investigations on the corner properties of cold-formed steel shapes [Chajes et al. 1963; Karren 1967; Karren and Winter 1967] have shown that, for steel shapes cold-bent from the same virgin steel, values of yield strength are larger for smaller inside radius-to-thickness ratios since they correspond to larger degrees of cold-forming. Based on these investigations, equations have been developed and adopted by AISI S [AISI 2007], using the material properties of the virgin steel and the bending radius as input, for estimation of the average yield strength of the coldformed section. Of particular interest, similar investigations have been conducted on coldformed RHS [Davison and Birkemoe 1983; Key et al. 1988; Zhao and Hancock 1992; Key and Hancock 1993; Wilkinson and Hancock 1997; Guo et al. 2007; Gardner et al. 2010]. These studies revealed that, depending on the cross-sectional geometry, the mechanical behaviours of the flat face and the corner are sometimes substantially diverse due to the different degrees of cold-forming. Also associated with cold-forming is the generation of residual stress. For the purpose of compression member design, residual stress in the longitudinal direction is much more influential than that in the transverse direction. The effect of longitudinal residual stress on the compression behaviour of a steel member is to cause premature yielding, leading to a loss 6

28 of stiffness and a reduction in load-carrying capacity. In previous investigations on the compression behaviour of cold-formed RHS [Davison and Birkemoe 1983; Key et al. 1988; Key and Hancock 1993; Gardner et al. 2010], the measured longitudinal residual stresses are commonly considered as two components. The first is the membrane component (tensile or compressive depending on the measuring location), which is the mean value of the measured longitudinal residual stress and occurs uniformly through the wall thickness. The second is the bending component, which is the deviation from the mean value. Due to the existence of the longitudinal residual stress, tensile coupons cut from the tube walls may exhibit both axial deformation and curvature, corresponding to membrane and bending residual stresses respectively. It can be concluded from these investigations that the compression behaviour of cold-formed RHS is mostly affected by the bending residual stress, while the membrane residual stress plays a minimal role. Although the effects of cold-forming on the mechanical properties of cold-formed RHS have been studied in the past, direct comparisons between RHS produced by different methods are scarce. Since RHS of similar cross-sectional geometry may exhibit different structural behaviours due to different strain histories and thermal actions experienced during production, in this chapter the mechanical properties of RHS manufactured in North America by: (1) direct-forming, (2) continuous-forming and (3) continuous-forming plus stress-relieving by heat treatment are compared through a series of investigations. 2.3 RHS specimens and geometric measurements In this study, continuous-formed square hollow section specimens with different B nom /t nom ratios are selected since the B nom /t nom ratio is a good indicator of the overall amount of coldforming contained in the cross-section. The conclusions and recommendations based on the test results of the square hollow section specimens apply to rectangular hollow sections as well since the overall amount of cold-forming in a rectangular cross-section can be estimated based on the average external width-to-wall thickness ratio, or conservatively based on the smaller external width-to-wall thickness ratio. On the other hand, the overall amounts of cold-forming contained in the cross-sections of direct-formed RHS with different B nom /t nom ratios are similar. For comparison purpose, the direct-formed square hollow section specimens were chosen to have the same cross-sectional dimensions as the continuous-formed ones. 7

29 The nominal sizes and manufacturing standards for the seven RHS examined are summarized in Table 2.1. Each section is denoted by a section number in which the prefix DF, CF, or CFH distinguishes the section by its manufacturing method, where DF = direct-formed; CF = continuous-formed; and CFH = continuous-formed and subsequently stress-relieved by heat treatment in accordance with Canadian standards for Class H finishing (heated to a temperature of 450 C or higher, followed by cooling in air) [CSA 2013]. The number after the prefix is the B nom /t nom ratio of the RHS specimen. Table 2.1 List of RHS specimens RHS ID Nominal sizes B nom /t nom Manufacturing standard / grade DF19 152x152x7.95 mm 19 N/A (Domex) DF12 152x152x12.7 mm 12 CAN/CSA-G /G Gr. 350W Class C DF24 152x152x6.35 mm 24 CAN/CSA-G /G Gr. 350W Class C CF12 152x152x12.7 mm 12 CAN/CSA-G /G Gr. 350W Class C CFH12 152x152x12.7 mm 12 CAN/CSA-G /G Gr. 350W Class H CF24 152x152x6.35 mm 24 CAN/CSA-G /G Gr. 350W Class C CFH24 152x152x6.35 mm 24 CAN/CSA-G /G Gr. 350W Class H The two sets of RHS, (1) DF12, CF12 and CFH12, and (2) DF24, CF24, and CFH24, with each set having the same nominal dimensions and including one direct-formed, one continuous-formed and one continuous-formed plus stress-relieved RHS, enabled the effects of different cold-forming methods and heat treatment to be directly compared. The inclusion of DF19 (direct-formed, thin-walled, high-strength RHS) enabled a comparison of its mechanical properties with the other RHS with different wall thicknesses and strength properties. Also, the effect of residual stresses due to direct-forming could be further demonstrated, in conjunction with DF12 and DF24. Prior to testing the specimens, each RHS was subject to careful geometrical measurement. For each specimen, the external widths of all four sides, the thicknesses at 16 different locations, and the outside and inside corner radii of all four corners of the section were measured. The measurement locations of thickness and corner radius are shown in Figure 2.1. For corner radius measurement, the cross-section of each specimen was scanned and input into AutoCAD so that three-point arcs could be drawn to fit the outside and inside surfaces of all corners, and the corner radii were then determined by measuring the radii of these arcs. The thickness and corner radius of all measured locations of the RHS specimens are listed in Appendix A.1. 8

30 weld seam Figure 2.1 Thickness and corner radius measurement locations The differences between the measured and nominal thickness for all RHS are shown in Figure 2.2. The averages of measured width and thickness (B avg and t avg ) are compared to the nominal values (B nom and t nom ) in Table 2.2. The measured outside and inside corner radii (r o and r i ) of all RHS specimens are normalized to their corresponding t avg in Figure 2.3(a) and (b), respectively. The averages of measured outside and inside corner radii (r o,avg and r i,avg ) are compared to their corresponding t avg in Table 2.2. The dimensions of CF12 and CFH12 are the same since they were cut from the same tube. Similarly, CF24 and CFH24 have the same dimensions as well DF19 DF12 DF24 CF12 & CFH12 CF24 & CFH24 Figure 2.2 Difference between measured and nominal thickness (mm) 9

31 Table 2.2 Nominal and measured dimensions of RHS specimens RHS ID B nom (mm) t nom (mm) B avg (mm) B avg / B nom t avg (mm) t avg / t nom r o,avg / t avg r i,avg / t avg DF DF CF12 & CFH DF CF24 & CFH r o /t avg DF19 DF12 DF24 CF12 & CFH12 CF24 & CFH24 (a) r i /t avg DF19 DF12 DF24 CF12 & CFH12 CF24 & CFH24 (b) Figure 2.3 Normalized corner radii for all RHS specimens: (a) outside corner radii; (b) inside corner radii 10

32 According to Figure 2.2, there are considerable variations in thickness around the crosssection of the RHS examined. Particularly, for DF24, a small notch near the weld seam was found such that the local wall thickness was lower than the other locations around the section. As can be seen in Table 2.2, for all RHS specimens, the B avg /B nom ratios range from to 1.010, and the t avg /t nom ratios range from to 1.038, both of which are within permitted tolerance ranges for ASTM A500 (± 1% for external width for RHS with a nominal external width 140 mm; ±10% for wall thickness for all RHS) [ASTM 2013a]. However, CF24/CFH24 have an average measured thickness below CSA [CSA 2013] tolerance (±5% for wall thickness for all RHS), and this product was supposed to conform to this manufacturing standard (see Table 2.1). Although the average outside corner radius-to-thickness ratios (r o,avg /t avg ) for all seven RHS, ranging from 1.89 to 2.31, are within the typical scatter previously found for cold-formed sections in North America [Packer and Frater 2005], there is quite a variation of both outside and inside corner radii (r o and r i ) around the measured sections, as can be seen in Figure 2.3(a) and (b). The corner at location 3 of CF12/CFH12 is much flatter than the others. For the corner at location 7 of DF12, the inside surface was severely cold-bent to a very small r i /t avg value of 0.42, which is likely to cause the local mechanical properties to be quite different from other parts of the section. Figure 2.4 Measurement of corner area The cross-sectional areas of the flat faces and corners of all RHS specimens were measured by scanning the cross-sections and inputting them into AutoCAD. It is assumed that the cross-sectional area remains the same in the longitudinal direction of the RHS specimens. The calibration and area measurement of a typical corner is shown in Figure 2.4. In order to ensure the accuracy of the AutoCAD measurements, the total cross-sectional areas of all RHS specimens were also determined by weighing the stub column (further discussion about stub 11

33 columns can be found in Section 2.4.2), using a steel density of 7850 kg/m 3 [CISC 2010]. The measured cross-sectional areas are listed in Table 2.3. The areas measured using both methods are consistent. It can be seen that as the B nom /t nom ratio increases, the ratio of corner area to total cross-sectional area of RHS decreases. Thus, as the B nom /t nom ratio increases, the influence of the corner on the full-sectional behaviour of RHS (tensile or compressive) becomes smaller. Table 2.3 Measured cross-sectional area of flat faces and corners Cross-sectional area (mm 2 ) Measured by Measured in AutoCAD weighing stub column RHS ID B nom /t nom Flat face Corner Total Corner/total Total DF % 6678 CF12 & CFH % 6565 DF % 4662 DF % 3549 CF24 & CFH % Experimental investigation Tensile coupon tests The tensile stress-strain behaviour and ductility around the cross-sections of the investigated RHS specimens were obtained through tensile coupon tests. For each RHS, three flat tensile coupons (from locations 1, 5 and 13 in Figure 2.1) and two corner coupons (from locations 3 and 7 in Figure 2.1) were machined and tested in accordance with ASTM A370 [ASTM 2009]. The tensile coupons tended to become curved after being cut from the RHS due to the release of longitudinal residual stress. Prior to each test, one end of the curved coupon was clamped by the universal testing machine. Using a prying bar, the curved coupon was straightened by force, predominantly elastically (i.e. the coupon would go back to the curved shape if the prying bar was removed), such that the other end of the coupon could be clamped by the machine. During tests, the curved coupons were thus restored to their original straight shape so that their in-situ tensile behaviours could be studied. The tensile stress-strain curves of all coupons are shown in Appendix A.2. The key test results from the tensile coupon tests are summarized and compared to the nominal values in 12

34 Table 2.4. The yield stresses are determined by the 0.2% strain offset method. The average elongations of the flat coupons and corner coupons at failure are shown in Figure 2.5. Comparisons of typical flat and corner tensile coupon test results from different RHS are shown in Figures 2.6 and 2.7. Using Eq. 2-1 and the measured flat face and corner areas in Table 2.3, the full-sectional tensile properties of the RHS specimens are determined in Table 2.5. ( ) (2-1a) ( ) (2-1b) where F is the ratio of flat face area to total cross-sectional area of RHS RHS ID Table 2.4 Key tensile coupon test results f y,nom (MPa) f y,avg (MPa) Flat face (f y,avg -f y,nom ) /f y,nom f y,avg (MPa) Corner (f y,avg -f y,nom ) /f y,nom DF % % DF % % DF % % CF % % CFH % % CF % % CFH % % RHS ID f u,nom (MPa) f u,avg (MPa) Flat face (f u,avg -f u,nom ) /f u,nom f u,avg (MPa) Corner (f u,avg -f u,nom ) /f u,nom DF19 N/A 779 N/A 807 N/A DF % % DF % % CF % % CFH % % CF % % CFH % % 13

35 Stress (MPa) Stress (MPa) 40% 30% 20% 10% 0% DF19 DF12 DF24 CF12 CFH12 CF24 CFH24 Flat coupon Corner coupon Figure 2.5 Average elongations of tensile coupons at failure (a) Strain DF24 CF24 CFH24 (b) Strain DF24 CF24 CFH24 Figure 2.6 Comparison of typical tensile coupon test results from different RHS: (a) flat coupons; (b) corner coupons 14

36 Stress (MPa) Stress (MPa) Stress (MPa) (a) Strain Flat face Corner (b) Strain Flat face Corner (c) Strain Flat face Corner Figure 2.7 Comparison of typical flat and corner tensile coupon test results from the same RHS: (a) DF24; (b) CF24; (c) CFH24 15

37 RHS ID B nom /t nom Table 2.5 Full-sectional tensile properties Area (mm 2 ) Flat face f y,avg (MPa) Area (mm 2 ) Corner f y,avg (MPa) Entire cross-section Area (mm 2 ) f y,avg (MPa) f y,avg difference between flat face and entire cross-section DF % DF % DF % CF % CFH % CF % CFH % RHS ID B nom /t nom Area (mm 2 ) Flat face f u,avg (MPa) Area (mm 2 ) Corner f u,avg (MPa) Entire cross-section Area (mm 2 ) f u,avg (MPa) f u,avg difference between flat face and entire cross-section DF % DF % DF % CF % CFH % CF % CFH % Stub column tests The overall compressive stress-strain behaviour of the investigated RHS specimens and the influence of longitudinal residual stress were determined by stub column tests. The stub columns were machined and tested in accordance with internationally accepted criteria [Ziemian 2010]. For all stub columns, both ends were machined flat, parallel and normal to the tube axis. As per [Ziemian 2010], the lengths of the stub columns were chosen to be at least three times the nominal width of the RHS specimens but no more than 20 times the corresponding radius of gyration. The former was to ensure that the stub columns were sufficiently long to contain the same initial residual stress pattern as a much longer member cut from the same stock. The latter was to ensure that the stub columns could resist the yield load (i.e. Af y ). During testing, each stub column was instrumented with 5 mm long strain gauges at the midheight of each tube face and Linearly Varying Differential Transformers (LVDTs) to ensure 16

38 proper alignment. The criterion for acceptable alignment is for the variation between strains on any stub column face, relative to the average strain, to be less than 5% [Ziemian 2010]. This requirement is stipulated to ensure concentric, uniform compression over the crosssection of the stub column. The alignment of each specimen was checked at 25% and 50% of the expected yield load as per [Ziemian 2010]. All specimens were tested in an MTS machine with a compression capacity of 4800 kn. The loading rate of all specimens was kept quasistatic to preclude any dynamic influence on the test results. The tests were continued after the ultimate load until the load dropped to approximately 80% of the yield load. Figure 2.8 shows a typical stub column test setup. Local inelastic buckling (a) (b) Figure 2.8 Stub column test setup: (a) before testing; (b) after testing All stub columns failed by local inelastic buckling (squashing) of the RHS walls near the ends due to restraint from the platens. The average compressive stress over the cross-section was determined by dividing the compression load by the cross-sectional area in Table 2.3 (measured by weighing the stub columns), and the average strain over the cross-section was determined by dividing the end shortening by the initial length of the specimen. The compressive stress-strain curves of all stub columns (up to an average strain of 0.015) are 17

39 shown in Appendix A.3. The key test results from all stub column tests are summarized in Table 2.6. The overall compressive yield strength is determined by the 0.2% strain offset method. The Young s modulus values were determined based on the average strain gauge data in the elastic range. The overall compressive properties are compared to the overall tensile properties in Table 2.7. The compressive stress-strain curves obtained from the stub column tests for RHS with 12.7 mm nominal wall thickness (DF12, CF12 and CFH12) and 6.35 mm nominal wall thickness (DF24, CF24 and CFH24) are normalized by their overall compressive yield strengths (f y ) for comparison in Figure 2.9(a) and (b), together with their proportional limits. The proportional limit was determined by fitting a straight line to the elastic portion of the stress-strain curve. The point from which the stress-strain curve starts to deviate from the straight line is identified as the proportional limit (i.e. the stress is no longer proportional to the strain). Table 2.6 Key stub column test results RHS ID L (mm) A (mm 2 ) E (GPa) f y (MPa) f u (MPa) σ p (MPa) σ p / f y DF % DF % DF % CF % CFH % CF % CFH % Table 2.7 Comparison of full-sectional tensile and compressive properties RHS ID B nom /t nom Tensile (MPa) f y,avg Compressive (MPa) Tensile / compressive Tensile (MPa) f u,avg Compressive (MPa) Tensile / compressive DF DF DF CF CFH CF CFH Note: There are differences between the full-sectional tensile and compressive properties because the fullsectional tensile properties were calculated based on local tensile properties obtained from tensile coupon tests. 18

40 1.2 1 Stress / f y Respective Proportional Limits Strain DF12 CF12 CFH12 (a) Stress / f y Respective Proportional Limits Strain DF24 CF24 CFH24 (b) Figure 2.9 Normalized compressive stress-strain curves from stub column tests: (a) RHS152x152x12.7; (b) RHS152x152x

41 2.4.3 Longitudinal residual stress measurements The longitudinal residual stress around the cross-section of the investigated RHS specimens was measured using the sectioning technique, which has been commonly used by researchers for the determination of residual stress in all types of steel shapes including hollow sections [Davison and Birkemoe 1983; Key et al. 1988; Key and Hancock 1993; Gardner et al. 2010; Jiao and Zhao 2003]. The procedures of the sectioning technique are as follows: (1) Attach strain gauges to the outside and inside surfaces of the examined section in the longitudinal direction. (2) Cut the examined section into longitudinal strips. During cutting, these steel strips will exhibit both axial deformation and curvature due to the membrane and bending components of the unloading stress as shown in Figure 2.10(b) and (c). (3) Measure the changes in strains on the outside and inside surfaces of the steel strips. (4) Convert the measured changes in strains to the unloading surface stresses, σ out and σ in, so that theoretical through-thickness unloading stress due to sectioning, as shown in Figure 2.10(a), can be determined. The opposite of the measured unloading stress, as shown in Figure 2.10(d), is a good indicator of the magnitude of the in-situ surface longitudinal residual stress. As shown in Figure 2.10(a), (b) and (c), the measured unloading stress equals the algebraic sum of the membrane and bending components. It shall be noted that, for illustration purposes, the membrane component is assumed to be compressive in Figure 2.10(b). According to previous investigations on hollow sections [Davison and Birkemoe 1983; Key et al. 1988; Key and Hancock 1993; Gardner et al. 2010; Jiao and Zhao 2003], the membrane component can be either tensile or compressive, depending on the measuring location. Generally, the magnitude of the membrane component is much smaller than that of the bending component. Previous investigations [Davison and Birkemoe 1983; Key et al. 1988; Key and Hancock 1993; Gardner et al. 2010; Jiao and Zhao 2003] have also revealed that, for hollow sections, the measured unloading stress in Figure 2.10(a) is always compressive on the outside surface and tensile on the inside surface. In other words, the in-situ longitudinal residual stress is tensile on the outside surface and compressive on the inside surface. 20

42 A limitation of the sectioning technique is that the measured unloading stress is only an approximation of the in-situ longitudinal residual stress. It has been shown [Davison and Birkemoe 1983; Key and Hancock 1993] that a block sectioned from a cold-formed RHS still contains compressive longitudinal residual stress on the outside surface and tensile longitudinal residual stress on the inside surface (Figure 2.10(f)). That is, the measured σ out and σ in values are in fact the difference between the in-situ state and the final block state, rather than the in-situ longitudinal residual stress itself. As shown experimentally by [Davison and Birkemoe 1983], for RHS containing a high level of longitudinal residual stress (i.e. with the maximum value approaching the yield stress), the measured σ out and σ in values may sometimes exceed the corresponding yield stress. It was also found in this study that the measured σ out and σ in values at some locations of the two continuous-formed RHS (CF12 and CF24) exceeded their corresponding yield stresses. σ out = σ b + σ m σ m σ b Outside surface t / 2 t / 2 σ in = σ b + σ m σ m σ b Inside surface (a) Measured unloading strain x E σ out (b) Membrane component (assume compressive) σ rs,out (c) Bending component Outside surface t / 3 t / 2 t / 3 t / 3 t / 2 σ in (d) Opposite of measured unloading strain x E σ rs,in (e) In-situ longitudinal residual stress (assumed) Inside surface (f) Longitudinal residual stress in released block (e.g. [Davison and Birkemoe 1983]) Figure 2.10 Relationship between unloading stress and in-situ longitudinal residual stress 21

43 In this chapter, the relationship between the measured values and the in-situ values suggested by [Davison and Birkemoe 1983] was adopted. This suggested in-situ through-thickness distribution, as shown in Figure 2.10(e), was later shown both experimentally [Weng and White 1990] and analytically [Quach et al. 2006] to be representative of the throughthickness longitudinal residual stress distribution associated with large plastic bending deformations. In this model, using the measured unloading surface stress data as input, the insitu longitudinal residual stresses on the outside and inside surfaces (σ rs,out and σ rs,in ) at an arbitrary point on the RHS can be determined by Eqs. 2-2 and 2-3, which were derived from graphs in [Davison and Birkemoe 1983]. σ rs, out 9σ b σ m (2-2) 13 in which σ b is the bending component of the measured theoretical unloading stress on the outside surface (compressive and hence negative), as shown in Figure 2.10(c), and σ m is the membrane component of the measured theoretical unloading stress on the outside surface (either tensile or compressive depending on the measuring location around the crosssection), as shown in Figure 2.10(b). σ rs,in 9σ 13 b σm (2-3) in which σ b is the bending component of the measured theoretical unloading stress on the inside surface (tensile and hence positive), as shown in Figure 2.10(c), and σ m is the membrane component of the measured theoretical unloading stress on the inside surface (either tensile or compressive depending on the measuring location around the crosssection), as shown in Figure 2.10(b). Since the residual stress increase due to heat input from welding is very local, it is not considered in this study. A total of 18 strain gauges were mounted on the RHS with nominal dimensions of 152x152x12.7 mm (DF12, CF12 and CFH12) to monitor the unloading strains in the longitudinal direction (half on the outside surface and half on the inside surface). For 22

44 comparison purpose, 26 strain gauges were mounted on the RHS with nominal dimensions of 152x152x6.35 mm (DF24, CF24 and CFH24). Due to physical constraints, these strain gauges were mounted at a section located 60 mm away from the end of the RHS rather than the mid-length of the RHS. According to previous research [Jiao and Zhao 2003], residual stress values at this location would be reasonably close to those at the mid-length of the RHS. The strain gauge locations are shown schematically in Figure 2.11(a) and photographically in Figure 2.11(b). 35 mm 35 mm 35 mm 35 mm 24 mm 24 mm 24 mm 24 mm 24 mm 24 mm strain gauge 6 strain gauge weld seam 8 weld seam RHS 152x152x RHS 152x152x (a) (b) Figure 2.11 Locations of strain gauges for longitudinal residual stress measurement: (a) strain gauges on RHS 152x152x12.7 and RHS 152x152x6.35; (b) strain gauges on one inside surface of RHS 152x152x

45 The procedures for the determination of the longitudinal residual stresses in the examined RHS are as follows: (1) After initial readings, cuttings were made around each strain gauge and small blocks with strain gauges on both sides were taken from each RHS. The differences between the strain gauge readings before and after the cutting were recorded as the unloading strains; (2) The theoretical unloading stresses (σ out and σ in ) were obtained by multiplying the unloading strains by Young s modulus (E in Table 2.6). It was found that the unloading stress at some locations of the two continuous-formed Class C RHS (CF12 and CF24) exceeded their corresponding average compressive yield strengths (f y in Table 2.6); (3) Calculate σ m and σ b, using the relationship illustrated in Figure 2.10(a), (b) and (c); and finally (4) Calculate the σ rs,out and σ rs,in, using Eqs. 2-2 and 2-3. The calculated σ rs,out and σ rs,in values around the cross-section of all examined RHS are normalized by their corresponding average compressive yield strength (f y in Table 2.6) and listed in Appendix A.4, in which the tensile residual stress on the outside surface is positive and the compressive residual stress on the inside surface is negative. These values are plotted here in Figure 2.12(a) and (b). The averages of the normalized values (σ rs,out /f y and σ rs,in /f y ) are listed in Table 2.8. The normalized maximum longitudinal compressive residual stresses (max. compressive σ rs /f y ) for all RHS specimens, determined from Figure 2.12, are also listed in Table 2.8. RHS ID B nom / t nom Table 2.8 Key longitudinal residual stress measurement results Average of σ rs,out / f y (tensile) Average of σ rs,in / f y (compressive) Max. compressive σ rs / f y (from residual stress measurements) Max. compressive σ rs / f y (from stub column test results) DF % 37.6% 60.2% 52.0% DF % 28.1% 56.7% 48.9% CF % 60.0% 91.1% 74.5% CFH % 24.5% 37.2% 31.0% CF % 47.4% 74.9% 61.5% CFH % 16.1% 28.5% 17.1% 24

46 1 0.5 σ rs / f y Outside surface of DF12 Outside surface of CF12 Outside surface of CFH12 Inside surface of DF12 Inside surface of CF12 Inside surface of CFH12 (a) σ rs / f y Outside surface of DF24 Outside surface of CF24 Outside surface of CFH24 Inside surface of DF24 Inside surface of CF24 Inside surface of CFH24 (b) Figure 2.12 Normalized longitudinal residual stresses: (a) RHS 152x152x12.7; (b) RHS 152x152x

47 2.5 Results and discussions Tensile stress-strain behaviour and ductility around the crosssection As can be seen in Table 2.4, the spread between the actual yield strength (f y,avg ) and the minimum specified value (f y,nom ) is sometimes substantial, up to 38% for the flat face and 76% for the corner. For RHS specimens with regular yield strength (DF12, DF24, CF12, CFH12, CF24, CFH24), there is generally a significant variation between the flat face and corner in yield and ultimate strengths due to the uneven degrees of cold-forming around the crosssection. For the RHS specimen with a high yield strength (DF19), such variation is minor, which suggests that steel material with such a chemical composition is less sensitive to coldworking. For the effects of cold-forming and heat treatment on the ductility around the RHS crosssection, it can be seen from Figure 2.5 that: (1) The flat face is much more ductile than the corner for all direct-formed RHS (DF19, DF12 and DF24). This is because the flat face was not severely cold-formed during production. (2) For the continuous-formed RHS with B nom /t nom ratio of 12 (CF12), the ductility difference between the flat face and corner is minor. However, for the continuous-formed RHS with B nom /t nom ratio of 24 (CF24), such difference becomes obvious again. This is because, as discussed previously, the steel plate is roll-formed into a circular section before reverse bending it into a rectangular section during the continuous-forming process. Previous research [Feldmann et al. 2012] suggested that the amount of cold-working at the flat face of the continuous-formed rectangular section is proportional to the thickness-to-radius ratio of the circular section. Since the thickness-to-radius ratio of the circular section used to form CF12 is approximately twice that of CF24, the amount of cold-working at the flat face of CF12 is approximately twice that of CF24. In other words, the cold-working gradient around the cross-section (i.e. flat face versus corner) of CF12 is smaller than that of CF24. Thus, the ductility difference between the flat face and the corner of CF12 is smaller than that of CF24. (3) Heat treatment is effective in bringing back the ductility of the cold-formed RHS (CFH12 versus CF12, and CFH24 versus CF24). For the effects of cold-forming and heat treatment on the tensile stress-strain behaviour around the RHS cross-section, it can be seen from Figure 2.6(a) and (b) that: 26

48 (1) The tensile stress-strain behaviour of the flat face of the direct-formed RHS is similar to that of the continuous-formed-stress-relieved RHS, wherein there is a clear yield point. (2) The tensile stress-strain behaviour of the corner of the direct-formed RHS is similar to that of the continuous-formed RHS, wherein there is no clear yield point (i.e. the material starts to yield at a relatively early stage). For full-sectional tensile properties, it can be seen in Table 2.5 that: (1) For all RHS specimens, the f y,avg differences between flat face and entire cross-section are in general larger than the f u,avg differences. This is because, for low carbon structural steel, as the amount of cold-working increases, the yield strength increases dramatically, while the ultimate strength increases moderately [Roe and Bramfitt 1990]. This is confirmed by the results in Table 2.5. Due to uneven degrees of cold-working, generally there are large yield strength differences between the flat face and corner of the RHS specimens. On the other hand, the ultimate strength differences between the flat face and the corner are moderate. (2) For RHS with B nom /t nom ratio of 12 (DF12, CF12 and CFH12), the corners contribute approximately 25% of the total cross-sectional area, thus the corner effect is obvious. Since the cold-forming gradient in DF12 is larger than those in CF12 and CFH12, DF12 has a larger f y,avg difference between flat face and entire cross-section (10%) than CF12 and CFH12 (7% and 5% respectively). (3) For RHS with B nom /t nom ratio of 24 (DF24, CF24 and CFH24), although the cold-forming gradient in DF24 is larger than those in CF24 and CFH24, since the corners only contribute approximately 11% of the total cross-sectional area, the f y,avg differences between flat and entire cross-section for DF24, CF24 and CFH24 are small and similar (4%, 5% and 3% respectively). It can be seen that the corner effect becomes less obvious as the B nom /t nom ratio increases from 12 to Compressive stress-strain behaviour of the entire cross-section Theoretically, the corners and their nearby regions of both direct-formed and continuousformed RHS should contain similar amounts of longitudinal residual stress which are primarily influenced by the corner bending radius. The flat face of direct-formed RHS likely contains a low level of longitudinal residual stress, since it experiences a small amount of cold-work during the direct-forming process. The flat face of continuous-formed RHS likely 27

49 contains a high level of longitudinal residual stress due to the high degree of cold-forming during the continuous-forming process. According to Table 2.6, the proportional limit-to-overall compressive yield strength ratios (σ p /f y ) for the three direct-formed RHS (DF19, DF12 and DF24) are very similar, regardless of the dimensional differences. However, for the two continuous-formed RHS (CF12 and CF24), a relatively larger difference in the σ p /f y ratios was observed. This is because, for continuous-formed RHS, as the B nom /t nom ratio increases, the overall degree of cold-forming to the cross-section decreases, leading to a lower level of longitudinal residual stress. It can be seen in Figure 2.9(a) and (b) that: (1) For RHS with a low width-to-thickness ratio (B nom /t nom = 12), the compressive stressstrain behaviour of the direct-formed RHS is midway between those of its continuous-formed and continuous-formed-stress-relieved counterparts. (2) For RHS with an intermediate width-to-thickness ratio (B nom /t nom = 24), the difference in compressive stress-strain behaviour between the direct-formed RHS and the continuousformed non-stress-relieved RHS becomes smaller Longitudinal residual stresses around the cross-section Before analysing the longitudinal residual stresses measured using the sectioning technique, the maximum value of the longitudinal compressive residual stress in all RHS specimens was estimated using the stub column test results. These maximum values were used to check the accuracy of the longitudinal residual stress measurements. Since the stub columns tested have very low global slenderness ratios and non-slender crosssections, their capacities are achieved when all fibres reach the yield stress. The presence of longitudinal residual stress in the cross-section implies that some fibres are in a state of residual compression. Under compression load, these fibres will yield before others, leading to a loss in column stiffness. Thus, the maximum value of the longitudinal compressive residual stress within the section can be estimated by evaluating the difference between the proportional limit stress and the yield stress. An example (DF24) is shown in Figure As can be seen in this figure, the maximum longitudinal compressive residual stress in DF24 is approximately 50% of its yield stress. Using this method, the maximum longitudinal 28

50 Stress (MPa) f rom residual stress measurements compressive residual stress values for all RHS specimens are determined and shown in Appendix A.3, and are listed in Table Yield stress = 470 MPa Maximum longitudinal compressive residual stress = 230 MPa 200 Proportional limit = 240 MPa Strain Figure 2.13 Example (DF24) of determination of maximum longitudinal compressive residual stress based on stub column test result 100% CF12 Max. compressive σrs / f y 75% 50% 25% CF24 DF12 DF24 CFH12 CFH24 0% 0% 25% 50% 75% 100% Max. compressive σ rs / f y f rom stub column test results Figure 2.14 Comparison of maximum compressive longitudinal residual stresses obtained from residual stress measurements and stub column test results Credence was given to the accuracy of the longitudinal residual stress measurement since: 29

51 (1) The maximum values of the longitudinal compressive residual stress measured using the sectioning technique are in general consistent with those estimated based on the stub column test results. The comparison is shown in Figure (2) Assuming the through-thickness longitudinal residual stress distribution in Figure 2.10(e), the residual forces (integral of residual stress over the cross-sectional area) in all RHS are below 5% of their corresponding yield load, thus adequate equilibria were attained. The calculations of residual forces in the cross-section of the RHS specimens are shown in Appendix A.4. For each RHS specimen, since the residual stress measurement was performed on half of the cross-section, it is assumed that the residual stress on the other half of the crosssection is the same. Thus, the bending moment resulting from the bending component of the residual stress (i.e. Figure 2.10(e) minus Figure 2.10(b)) at a certain location is balanced by that at the symmetrical location of the cross-section. Also, the bending component results in zero axial force. Hence, the residual force in the cross-section equals the integral of the membrane component (i.e. Figure 2.10(b)) over the cross-sectional area. It can be seen in Figure 2.12(a) and (b) that: (1) For all RHS, the maximum longitudinal residual stresses were found between the centrelines of the flat faces and the corners, which is in good agreement with the measurements reported by other researchers [Davison and Birkemoe 1983; Key et al. 1988; Key and Hancock 1993; Gardner et al. 2010]. (2) The continuous-formed RHS (CF12 and CF24) contain the highest level of longitudinal residual stress. The longitudinal residual stress in continuous-formed-stress-relieved RHS (CFH12 and CFH24) is not only the lowest but also the most uniform around the crosssection, due to the heat treatment. The magnitude of the longitudinal residual stress in the direct-formed RHS (DF12 and DF24) is mid-way between those of its continuous-formed and continuous-formed-stress-relieved counterparts. According to Table 2.8, as the B nom /t nom ratio increases, the average longitudinal residual stress level decreases for all three types of RHS (DF24 versus DF12, CF24 versus CF12, and CFH24 versus CFH12) Column model In this section, the measured longitudinal residual stress gradients were incorporated into column models to study the column behaviour of RHS with different production histories. 30

52 Column behaviour models are commonly based on the tangent modulus theory or the maximum strength theory [Davison and Birkemoe 1983]. In this section, the tangent modulus theory, considering the column strength of a perfectly straight member, was used. The initial crookedness of the column was deemed of minor significance in this study because HSS has a reputation for very high levels of straightness in practice. The column behaviour was simplified to a bifurcation problem, and the tangent modulus bifurcation load (P) of a centrally loaded, perfectly straight, pin-ended column of length L was calculated as: 2 π EI E P (2-4) 2 L where E is the Young s modulus and I E is the effective moment of inertia of the cross-section at a certain load stage. The following assumptions were made when applying the tangent modulus theory: (1) The stress-strain state in any longitudinal fibre at a certain load stage is independent of that in any other longitudinal fibre, and it is constant along the member length; (2) The residual stress varies around the cross-section perimeter and through the wall thickness of the member but is constant in any longitudinal fibre along the member length; (3) Only the longitudinal residual stress is considered. The interaction with transverse residual stress is ignored; (4) Strain hardening of the material is not considered; (5) For simplification, the corner radius is ignored and a box section is used in the calculation. Comparing to the actual section with corner radius, the simplified box section ignoring corner radius has a slightly larger cross-sectional area since it overestimates the corner area. However, since the cross-sections of all RHS specimens contain much more flat face than corner (i.e. the percentages of corner areas are small), the impact of this assumption on the column model results was found to be very minor. For each of the RHS specimens, a discretized cross-section column model was built, using the material properties listed in Table 2.6 (i.e. E and f y ). As illustrated in Figure 2.15, the model contained the through-thickness longitudinal residual stress distribution as shown in Figure 2.10(e), with the σ rs,out and σ rs,in values as shown in Figure 2.12(a) and (b) around the cross-section. The discretized cross-section column models were subjected to uniform strains. The applied buckling load (P) and the effective moment of inertia (I E ) corresponding to a 31

53 t / 3 t / 3 t / 3 certain applied strain were determined and used to solve for the buckling length (L) under this buckling load using Eq Outside surface = σ rs,out (tensile) Layer 1 Corresponding magnitude of longitudinal residual stress Layer 2 Layer 3 Layer 4 Layer 5 Layer 6 Layer 7 Layer 8 Layer 9 Layer 10 Layer 11 (compressive) Inside surface = σ rs,in Figure 2.15 Illustration of discretized cross-section column model The analytical stress-strain relationships of the cross-section column models were compared to the stub column test results and shown in Appendix A.5. Typical comparisons are shown in Figure 2.16(a) and (b). The maximum stresses for the model stress-strain curves are the f y values listed in Table 2.6, since strain hardening of the material was not considered. The analytical stress-strain curves (pre-yielding) generated by the tangent modulus column models were found to agree with the stub column test results well. Thus, further credence is given to the longitudinal residual stress measurements and the following deductions. 32

54 The normalized analytical column curves of the RHS with the same nominal dimensions but different production histories are compared in Figure 2.17(a) and (b). The data points on the normalized analytical column curves correspond to those in the analytical compressive stressstrain curves in Figure 2.16 (i.e. the same applied strain level up to the yield point). It can be seen in Figure 2.17(a) that for the three RHS 152x152x12.7, the column behaviour of the direct-formed RHS (DF12) is closer to that of its heat-treated continuous-formed counterpart (CFH12). On the other hand, Figure 2.17(b) shows that for the three RHS 152x152x6.35, the column behaviour of the direct-formed RHS (DF24) is closer to that of its non-heat-treated counterpart (CF24). Figures show the comparisons between the analytical column curves with the respective column curves for cold-formed and cold-formed stress-relived (CSA Class H) hollow sections, omitting any resistance or partial safety factor, for CSA S16-09 [CSA 2009], AISC [AISC 2010b], and Eurocode 3 curve c [CEN 2010]. It can be seen that (1) the two direct-formed RHS specimens have analytical column curves close to the CSA Class H curves; (2) among different design curves, the CSA Class C curves give the best predictions for the column behaviours two non-heat-treated continuous-formed RHS specimens; and (3) all design curves are conservative in predicting the column behaviours of the two heat-treated continuous-formed RHS specimens. One must bear in mind, however, that the column design curves in various codes/specifications have further conservatisms and safety factors included, and relative comparisons between production methods are better evaluated from Figure 2.17 than Figures 2.18 to

55 Stress (MPa) Stress (MPa) Strain CF12 stub column test results CF12 column model results (a) Strain CF24 stub column test results CF24 column model results (b) Figure 2.16 Comparisons of overall compressive stress-strain curves from stub column tests and column models: (a) CF12; (b) CF24 34

56 P/Af y L (m) DF12 CF12 CFH12 (a) P/Af y L (m) DF24 CF24 CFH24 (b) Figure 2.17 Analytical column curves: (a) RHS 152x152x12.7; (b) RHS 152x152x

57 P/Af y L (m) DF12 Class C CSA S16-09 Class H CSA S16-09 AISC EN :2005 curve c (a) P/Af y L (m) DF24 Class C CSA S16-09 Class H CSA S16-09 AISC EN :2005 curve c (b) Figure 2.18 Comparison with column curves as per CSA S16-09, AISC and EN :2005 for direct-formed RHS: (a) DF12 (RHS 152x152x12.7); (b) DF24 (RHS 152x152x6.35) 36

58 P/Af y L (m) CF12 Class C CSA S16-09 Class H CSA S16-09 AISC EN :2005 curve c (a) P/Af y L (m) CF24 Class C CSA S16-09 Class H CSA S16-09 AISC EN :2005 curve c (b) Figure 2.19 Comparison with column curves as per CSA S16-09, AISC and EN :2005 for continuous-formed RHS: (a) CF12 (RHS 152x152x12.7); (b) CF24 (RHS 152x152x6.35) 37

59 P/Af y L (m) CFH12 Class C CSA S16-09 Class H CSA S16-09 AISC EN :2005 curve c (a) P/Af y L (m) CFH24 Class C CSA S16-09 Class H CSA S16-09 AISC EN :2005 curve c (b) Figure 2.20 Comparison with column curves as per CSA S16-09, AISC and EN :2005 for continuous-formed plus heat-treated RHS: (a) CFH12 (RHS 152x152x12.7); (b) CFH24 (RHS 152x152x6.35) 38

60 Chapter 3 Charpy V-Notch Impact Toughness 3.1 Summary This chapter compares the Charpy V-notch (CVN) impact toughness of a total of six coldformed RHS manufactured by different methods: (1) direct-forming, (2) continuous-forming, and (3) continuous-forming plus stress-relieving by heat treatment. A total of 378 CVN coupons were tested and complete CVN toughness-temperature curves were generated for the flat face, corner and weld seam regions of the RHS specimens. For RHS with different crosssectional geometries and produced by different methods, the CVN toughness-temperature curves of the flat face and the corner were compared to quantify the decrease of notch toughness from the flat face to the corner due to uneven degrees of cold-forming, which can be used by structural designers for the choice of steel material to avoid brittle fracture for RHS structures. 3.2 Background The selection of steel for toughness, as specified by international steel product standards and design specifications, normally requires CVN impact testing of the material. A required toughness is commonly expressed in terms of the test temperature (e.g. 20 C) at which a minimum CVN impact energy value (e.g. 34 J/cm 2, which is 27 J for a standard full-sized CVN coupon) shall be achieved. As detailed in ASTM A370 [ASTM 2009], a CVN impact test is a dynamic test in which a notched coupon is struck and broken by a single mechanical impact in a specially designed apparatus. The measured test value is the energy consumed to break the coupon at the testing temperature. Testing temperatures other than room temperature are often specified in product standards. For steel products, the CVN test most commonly uses a standard full-sized (10x10x55 mm) rectangular beam-type coupon with a machined notch of specified geometry (2 mm deep). By plotting the energy absorbed by the coupons as a function of the testing temperatures, as shown in Figure 3.1 [Sedlacek et al. 2008], an energy absorption versus temperature transition curve can be produced. At temperatures in the upper shelf, CVN coupons normally fracture in a ductile manner, absorbing relatively large amounts of energy. At temperatures in the lower shelf, CVN coupons normally fracture in a brittle manner, absorbing considerably less energy. Within the transition range, the fracture is generally a mixture of both ductile and brittle fractures. The approximate relationship between the CVN 39

61 energy-temperature curve and the fracture behaviour of a steel component is also illustrated in Figure 3.1 [Sedlacek et al. 2008]. CVN Energy (J/cm 2 ) Lower shelf NDT Transition region DBTT Upper shelf Room temperature 34 Temperature( C) σ σ σ ε Figure 3.1 Approximate relationship between the CVN energy-temperature curve and the fracture behaviour of a steel component [adapted from Sedlacek et al. 2008] ε ε There are various methods for the determination of the transition temperature [Roe and Bramfitt 1990; Barsom and Rolfe 1999; Sedlacek et al. 2008; ASTM 2009]. As shown in Figure 3.1, in this study the Ductile-to-Brittle Transition Temperature (DBTT) is defined as the temperature corresponding to half of the upper-shelf energy value [Barsom and Rolfe 1999]. The 34 J/cm 2 temperature, commonly defined as the beginning of the lower-shelf region in international steel product standards, is defined as the Nil-Ductility Temperature (NDT) in this study. Below the NDT, the material is considered to be brittle under impact loading [Sedlacek et al. 2008]. The modern design of structures made of cold-formed HSS and their welded joints is largely dependent on the redistribution of stress in the inelastic range. Thus, the selection of HSS for CVN toughness is critical if low temperature or dynamic loading is a design consideration. For RHS, previous research [Kosteski et al. 2005] has shown that the CVN toughness around the cross-section is sometimes highly heterogeneous due to the uneven degree of coldforming. However, for the assessment of notch toughness of RHS, steel product standards [CEN 2006a; CEN 2006b; ISO 2011; ASTM 2013b; CSA 2013] normally require testing of Charpy V-notch (CVN) coupons taken longitudinally from one of the flat faces not containing the weld. This tends to lead to the most optimistic notch toughness result for the cross-section. As discussed previously, there are two common manufacturing methods 40

62 internationally for cold-forming RHS: direct-forming and continuous-forming. For directformed RHS, the cold-working is concentrated at the four corners only. For continuousformed RHS, the entire cross-section may contain high degrees of cold-working. Thus, it can be expected that there is a larger variation of CVN toughness between the flat face and the corner of direct-formed RHS than for continuous-formed RHS, as cold-forming reduces the CVN toughness of steel [Sedlacek et al. 2008]. Failures of cold-formed RHS members due to cracking in the corners have been reported around the world. During the 1994 Northridge, California earthquake, there were incidents involving damage to RHS bracing (including local buckling, tearing of steel at corners and complete rupture of braces) due to cracking initiated from the corner as a result of low CVN toughness [Maranian 2010]. Thus, the use of cold-formed RHS for low temperature or dynamic applications is questionable if the selection of the member is based on the CVN toughness at the flat face only, as required by international standards [CEN 2006a; CEN 2006b; ISO 2011; ASTM 2013b; CSA 2013]. Hence, there is a need to incorporate the CVN toughness differences between the flat face and other locations around the RHS, for various member types and sizes, so that the selection of RHS can be based on better judgement. In this study, CVN tests were performed on coupons taken from various locations around the cross-sections of six RHS specimens with different production histories, to investigate the effects of different coldforming methods and heat treatment. 3.3 Effects of chemical composition on material CVN impact toughness The control of chemical composition is one of the methods to obtain the desired mechanical properties of structural steels. Product standards normally specify the ranges or limits of chemical elements which are considered necessary for the proper production of steel materials covered by the scope of the standards. For example, the chemical requirements for cold-formed HSS produced to ASTM A500 [ASTM 2013a] are shown in Table 3.1. Low-carbon structural steels, commonly referred to as mild steels, normally have up to 0.25% carbon, 0.4% - 0.7% manganese, 0.1% - 0.5% silicon and some residuals of sulphur, phosphorus, and some other elements. They are not deliberately strengthened by alloying elements other than carbon and contain manganese for sulphur stabilization and silicon for 41

63 deoxidation, thus their yield strengths cannot be increased beyond approximately 690 MPa without significant loss in toughness and ductility [Roe and Bramfitt 1990]. Although the effects of a single chemical element on the mechanical properties of steel are sometimes influenced by the effects of other elements, for simplification, the common elements and their effects on the CVN toughness of steel are usually discussed individually. Table 3.1 Chemical requirements in ASTM A500 [ASTM 2013a] Composition, % Element Grade A, B, and D Grade C Heat Analysis Product Analysis Heat Analysis Product Analysis Carbon, max Manganese, max Phosphorus, max Sulphur, max Copper, min The CVN impact energy temperature curves for carbon steels of varying carbon content, and 0.30 % carbon steels of varying manganese content are shown in Figures 3.2 and 3.3, respectively [Roe and Bramfitt 1990]. As can be seen in Figure 3.2, for the steels investigated, the increasing carbon content (from 0.11% to 0.80%) increases the transition temperature (from -46 C to 150 C) and decreases the upper-shelf energy (from 204 J to 33 J) primarily as a result of the increased strength. Despite the importance of strength, CVN toughness must also be considered when selecting a structural steel, thus a compromise has to be made. Manganese is the principal element for increasing toughness in carbon structural steels. As can be seen in Figure 3.3, for the steels investigated, the increasing manganese content (from 0.30% to 1.55%) decreases the transition temperatures (from 36 C to -23 C) while its effect on the upper-shelf energy is less obvious (increased from 128 J to 141 J). For applications involving exposure to low temperatures ranging from 0 C to -200 C, low-carbon and highnickel steels are typically used. The effect of nickel content is to reduce the ductile-to-brittle transition temperature, therefore improving the toughness of the steel material at low temperature. Phosphorous is generally considered an impurity but sometimes is added for atmospheric corrosion resistance. It increases the strength and hardness of steel but significantly decreases its ductility and toughness. Silicon is primarily a deoxidizing agent and it tends to reduce steel ductility. Sulphur is considered an impurity which significantly reduces the fracture toughness of steels. It is necessary to keep sulphur content low, which is usually done by adding manganese to form manganese sulphides. However, the MnS 42

64 Absorbed energy (J) Absorbed energy (J) inclusion may increase the susceptibility of the steel to lamellar tearing [Roe and Bramfitt 1990]. Investigations on the effects of these chemical elements on the CVN toughness of various steels have been brought together in ASM Handbook Vol. 1 [Roe and Bramfitt 1990] Temperature ( C) 0.11% C 0.20% C 0.31% C 0.41% C 0.49% C 0.60% C 0.69% C 0.80% C Figure 3.2 Variation in CVN impact energy with temperature for carbon steels of varying carbon content [adapted from Roe and Bramfitt 1990] Temperature ( C) 1.55% Mn 1.01% Mn 0.39% Mn 0.30% Mn Figure 3.3 Variation in CVN impact energy with temperature for 0.30% carbon steels of varying manganese content [adapted from Roe and Bramfitt 1990] 43

65 3.4 Toughness anisotropy in HSS Effect of rolling direction of base plate Steels can acquire strongly anisotropic microstructures as a result of rolling, leading to the anisotropy of mechanical properties, particularly notch toughness [Roe and Bramfitt 1990]. For as-rolled low carbon steel plate, previous research [Puzak et al. 1952] has shown that CVN coupons taken parallel to the rolling direction have better impact toughness than those taken perpendicular to the rolling direction. Similarly, for cold-formed RHS, previous research [Kosteski et al. 2005; Stranghöner et al. 2010] found that CVN coupons taken from the flat face (not containing the weld) in the longitudinal direction of the RHS absorb greater amounts of energy then their transverse counterparts. This is because the rolling direction of the steel plate, which is later used to form the RHS, is the same as the longitudinal direction of the tube Effect of notch orientation of CVN coupon For as-rolled low carbon steel plate, previous investigations [Puzak et al. 1952; Roe and Bramfitt 1990] have shown that CVN coupons with notches lying in the plane of the plate surface tend to absorb greater amounts of energy than those with notches perpendicular to the plate surface. However, the temperature range over which the ductile-to-brittle transition occurs is the same, regardless of notch orientation. For cold-formed RHS, such comparison is scarce, and most previous investigations have used CVN coupons with notches lying in the plane of the RHS surface [Kosteski et al. 2005; Puthli and Herion 2005; Stranghöner et al. 2010; Ritakallio 2012; Stranghöner et al. 2012]. Thus, it is also desirable to study the effect of different notch orientations within RHS. 3.5 CVN toughness in pertinent HSS product standards ASTM A [ASTM 2013a] The prime American standard for cold-formed HSS [ASTM 2013a] has no notch toughness requirement, and within its scope it states that products manufactured to this specification may not be suitable for those applications such as dynamically loaded elements in welded structures, etc., where low-temperature notch-toughness properties may be important. Although cold-formed HSS with a notch toughness grade is not commonly produced in North America, this has not inhibited its widespread use for all structural applications [Kosteski et al. 2005; Packer et al. 2010]. 44

66 3.5.2 ASTM A [ASTM 2013b] This recent American standard was developed to include cold-formed HSS in dynamically loaded structures. For the preparation of CVN test coupons, it refers to ASTM A370 [ASTM 2009] which specifies that the CVN coupon be taken longitudinally from one of the flat faces not containing the weld. When the tube wall thickness is greater than or equal to 11 mm, standard full-sized coupons (10x10 mm) shall be tested and conform to a minimum CVN impact energy of 34 J at 4 C. When the material is less than 11 mm thick, the largest feasible standard sub-sized coupons shall be tested. Standard sub-sized test coupon sizes are 10x7.5 mm, 10x6.7 mm, 10x5 mm, 10x3.3 mm and 10x2.5 mm. It is specified that the notch shall be made on the narrow face of the standard sub-sized coupon so that the notch is perpendicular to the 10 mm wide face [ASTM 2009]. When sub-sized coupons are tested, the minimum CVN impact energy requirement is to be modified according to Table 3.2, in which the required impact energy for acceptance is proportional to the net cross-sectional area (i.e. the area of notched cross-section) of CVN coupons with various sizes. Table 3.2 Charpy V-notch test acceptance criteria for coupons with different sizes [ASTM 2009] Size (mm) Charpy V-notch test acceptance criteria for full-sized coupon (J) 10x Size (mm) Equivalent Charpy V-notch test acceptance criteria for sub-sized coupon (J) 10x x x x x CAN/CSA G /G [CSA 2013] This Canadian structural steel product standard specifies minimum CVN requirements (20 J, 27 J, or 34 J for full-sized specimens) for notch tough base material with different grades (Grade AT, QT or WT), according to four standard temperature categories (0 C, -20 C, - 30 C or -45 C). For the preparation and testing of both full-sized and sub-sized CVN coupons, the Canadian standard also refers to ASTM A370 [ASTM 2009] EN 10219:2006 [CEN 2006a; CEN 2006b] and ISO [ISO 2011] In Europe, cold-formed HSS is most commonly produced to Grade S255J2H as per EN This standard and grade guarantees a minimum CVN impact energy of 27 J at -20 C 45

67 from full-sized CVN coupons taken either longitudinally or transversely, at the discretion of the manufacturer, from one of the flat faces not containing the weld. For HSS with wall thickness less than 10 mm, EN [CEN 2006a] specifies that the CVN impact test shall be carried out using sub-sized coupons of depth less than 10 mm, but not less than 5 mm, and the minimum CVN energy requirement shall be reduced in direct proportion to the actual net cross-sectional area of the coupon compared to that of a full-sized CVN coupon. ISO has the same requirements as EN CVN toughness in international design standards Correlation of CVN toughness to fracture mechanics Although the CVN impact test is used worldwide across many industries to indicate the ductile-to-brittle transition of steel materials, the CVN test results cannot be directly applied in structural design since the potential for brittle fracture of a steel component depends on multiple factors: (1) steel strength, (2) material thickness, (3) loading rate, (4) minimum service temperature, (5) material toughness and (6) type of structural element [Roe and Bramfitt 1990]. Thus, correlations of the CVN impact toughness of steel material to the fracture toughness of a steel component have been developed using fracture mechanics, and design criteria based on these correlations have been adopted by international specifications such as the AASHTO bridge design specification [AASHTO 2007], CSA S16 [CSA 2009], and EN [CEN 2005] to minimize failure of steel components subjected to dynamic loading. For different service temperatures, these specifications require minimum values of CVN impact energy at certain testing temperatures AASHTO [AASHTO 2007] The AASHTO bridge design specification [AASHTO 2007] has CVN impact energy requirements for three service temperatures zones, including Zone 1: -18 C and above; Zone 2: -18 C to -34 C; and Zone 3: -35 C to -51 C. For different service temperature zones, different minimum CVN impact energy values are required for steel plates manufactured as per various ASTM standards. For example, a carbon steel ASTM A36 plate (thickness less than 102 mm) would require 34 J for full-sized CVN coupons at the following CVN test temperatures: 21 C for Zone 1; 4 C for Zone 2; and -12 C for Zone 3. The effect of coldforming is not explicitly considered in this specification. 46

68 3.6.3 CSA S16-09 [CSA 2009] In Annex L of the Canadian steel structures design standard [CSA 2009], the required notch toughness to prevent brittle fracture is expressed in terms of different testing temperatures (from 20 C to -75 C) and a minimum CVN impact energy (20 J or 27 J) for four different service temperature ranges (above 0 C, 0 C to -30 C, -30 C to -60 C, and below -60 C). In general, for notch tough steel material, plates are more readily available than shapes [CSA 2009]. Due to this limited availability of notch tough steel sections, the Canadian standard permits steel which is not specifically designated as notch-tough (e.g. cold-formed HSS) to be substituted if the minimum CVN impact energy requirement is satisfied. For the preparation and testing of both full-sized and sub-sized CVN coupons, the Canadian standard also refers to ASTM A370 [ASTM 2009]. Similar to the AASHTO specification [AASHTO 2007], the effect of cold-forming is not explicitly considered in the Canadian standard EN :2005 [CEN 2005] The design rules for the selection of material for fracture toughness given in EN [CEN 2005] are related to welded structures made by plates and rolled sections [Sedlacek et al. 2008; Feldmann et al. 2012]. Table 2-1 of EN [CEN 2005] gives the maximum permissible values of element thickness to avoid brittle fracture depending on the following parameters: (1) steel grade and T 27J (temperature for a full-sized CVN coupon to absorb an impact energy of 27 J), (2) service temperature and (3) stress level for the design situation. Part of the table, for S355 steel with a design stress level of 0.75f y, is shown as Table 3.3. Table 3.3 Maximum permissible value of element thickness for S355 steel [CEN 2005] Steel grade S355 Sub -grade Charpy test energy Stress level: σ/f y = 0.75 Service temperature ( C) at T ( C) J min Maximum permissible thickness (mm) JR J J K2,M,N ML,NL Since Table 2-1 of EN [CEN 2005] is for non-cold-formed steel, to account for the reduction of toughness from the cold-forming of plates, EN specifies that the tabulated values may be used by altering the service temperature by deducting T cf ( C) (i.e. 47

69 the maximum permissible element thickness decreases as the degree of cold-forming increases), where T cf = 3 x DCF (3-1) in which DCF = degree of cold-forming (%), and T cf = adjustment for the degree of coldforming ( C). The method for determination of DCF is not included in EN [CEN 2005]. It was recommended in the Commentary and Worked Examples to EN [Sedlacek et al. 2008] that DCF due to cold-bending can be calculated using Eq [Sedlacek et al. 2008] suggest that T cf equals zero for DCF 2% and T cf is constant (45 C) for DCF 15%. The development and validity range of Eq. 3-1 are further discussed in Section 3.7. DCF = ε max 0.02 (3-2) in which ε max is the maximum plastic strain (%) on the surface of the bent region, which can be calculated using Figure 3.4. Determination of maximum plastic strain ε max 1 ε max r i t ε max = t 2r i + t r i Determination of ε eff Figure 3.4 Determination of maximum plastic strain due to cold-bending [adapted from Sedlacek et al. 2008] 3.7 Previous toughness investigations on cold-formed products As documented by the German Iron and Steel Institute (VDEh) [VDEh 1992], early investigations on the effect of cold-forming on the toughness of various steels were conducted by performing German DVM-notch impact tests on pre-strained (constant through thickness) steels. It was concluded that, for pre-strain up to 10%, the T 27J -temperature (for 48

70 Energy (J) full-sized 10x10 coupons) increases linearly as the pre-strain increases, and a 10% pre-strain leads to an increase in the transition temperature of approximately 30 C for various types of steel materials. For S355J2 steel, which is the grade most commonly used to produce coldformed HSS in Europe, CVN impact tests were performed. The changes in CVN impact energy and T 27J -temperature with various degrees of cold-forming (i.e. pre-straining) are shown in Figures 3.5 and 3.6, respectively. It can be seen that both changes become insignificant with a degree of cold-forming (DCF) higher than 15% [VDEh 1992]. The design rule in EN [CEN 2005] for the reduction of toughness due to cold-forming of steel plates (i.e. Eq. 3-1) was developed based on these investigations [VDEh 1992]. However, it shall be noted that the pre-strains applied in the above research were constant through the thickness of the coupons, while for HSS the through-thickness strain input during production is non-uniform Temperature ( C) DCF=0 DCF=5% DCF=7% DCF=10% DCF=15% DCF=20% DCF=30% Figure 3.5 Change of Charpy V-notch impact energy due to cold-forming, for S355J2 steel [adapted from VDEh 1992] For research on the notch toughness of cold-formed hollow sections, an early investigation by [Dagg et al. 1989] studied the CVN toughness difference between coupons sampled from the flat face (not containing the weld) and the corner of Australian cold-formed RHS 203x203x9.5 and RHS 76x76x6.3. Sub-sized 5 x 10 mm CVN coupons were machined in the 49

71 T 27J ( C) longitudinal direction of the RHS and notched on the narrow face so that the notch was perpendicular to the RHS surface. Little difference was observed between the energytemperature results of CVN coupons sampled from the flat face versus the corner for both RHS, regardless of cross-sectional geometry. Although there was no information regarding the cold-forming method used to produce the above RHS specimens, it is likely that the two tubes were continuous-formed as this is the normal production method in Australia % 5% 10% 15% 20% 25% 30% 35% Degree of cold-forming Figure 3.6 Change of T 27J -temperature due to cold-forming, for S355J2 steel [adapted from VDEh 1992] Later, [Soininen 1996] also conducted an investigation on the CVN toughness of cold-formed European RHS with different cross-sectional geometries. All tubes were continuous-formed. The CVN coupons were sampled from the following locations and delivery states: (1) base material with CVN coupons longitudinal and transverse to the rolling direction of the coil; (2) flat face of the RHS with CVN coupons longitudinal and transverse to the rolling direction of the coil; (3) longitudinal and transverse from the flat face of the RHS after artificial ageing at 250 C for 30 minutes; and (4) longitudinal from the corner of the RHS, in the delivery condition and after artificial ageing at 250 C for 30 minutes. For RHS with wall thickness more than 10 mm, full-sized CVN coupons were made. For RHS with wall thickness less than 10 mm, sub-sized CVN coupons were made using the full wall thickness. All notches 50

72 were made perpendicular to the plane of the RHS surfaces. The 34 J/cm 2 -temperatures (e.g. 27 J for full-sized 10x10 mm coupon with a notch depth of 2 mm) were determined based on the CVN test results. It was reported that the transverse coupons had, on average, 19 C higher 34 J/cm 2 -temperatures both in the base material and in the flat face of the RHS, compared to the longitudinal coupons. The average 34 J/cm 2 -temperatures of longitudinal coupons from the flat face and corner of the RHS were 15 C and 23 C higher than those of longitudinal coupons from the base material. Similar to [Dagg et al. 1989], [Soininen 1996] reported a relatively small difference (8 C) between the average 34 J/cm 2 -temperatures of the flat face and corner of the tested RHS. One of the principal conclusions of [Soininen 1996] was that in order to fulfil a certain Charpy toughness requirement in the finished cold-formed RHS, at a certain temperature, the base material had to fulfil the same notch toughness at a temperature at least 30 C lower. However, as discussed previously, for continuous-formed RHS the plate is first bent into a circular tube before further flattening it into the rectangular shape, thus the degree of coldforming to the flat face decreases as the wall slenderness (B nom /t nom ) ratio increases, and the differences in the mechanical behaviours between the flat face and corner become larger as the B nom /t nom ratio of the tube increases. Hence, it is not logical to average the transition temperatures for RHS with different cross-sectional geometries. The Australian and Finnish RHS specimens studied in the above investigations are not necessarily representative of those produced in other parts of the world. Thus, [Kosteski et al. 2005] conducted a study of the CVN toughness of various RHS manufactured in North America, South America, and Europe. The specimens included hot-formed RHS, cold-formed RHS, and stress-relieved cold-formed RHS. CVN impact tests were performed on CVN coupons with different orientations (longitudinal versus transverse), different cross-section location (flat face, corner, and weld seam), and different notched face exposures (interior face of RHS versus exterior face). In total, 557 CVN coupons were tested. All coupons had the notch parallel to the tube surface. It was found by [Kosteski et al. 2005] that: (1) hot-formed RHS has excellent CVN toughness at all locations around the cross-section and in both the longitudinal and transverse directions; (2) the European cold-formed RHS generally have better CVN toughness than the North American ones; (3) for cold-formed RHS, there is little improvement in CVN toughness achieved by stress-relieving the section by heat treatment according to CSA Class H requirements [CSA 2013]; and (4) for cold-formed RHS, transverse CVN coupons from the weld regions have a particularly poor CVN toughness. 51

73 Thus, [Kosteski et al. 2005] concluded that to guarantee high values of inherent toughness at any location or orientation in the cross-section, hot-formed RHS are more reliable. The excellent CVN toughness of hot-formed RHS has again been demonstrated by [Stranghöner et al. 2012]. Although European cold-formed HSS produced to EN10219 [CEN 2006a; CEN 2006b] in general exhibit good toughness properties [Kosteski et al. 2005; Ritakallio 2012; Ritakallio 2013], limits in applying the toughness-related rules for the choice of steel material in EN [CEN 2005] to cold-formed HSS still constitute barriers to their utilization. According to [Feldmann et al. 2012], the design rules in EN [CEN 2005] may not be sufficient for the specific case of cold-formed HSS due to the high degrees of coldforming since the design rules in EN are related to welded structures made by plates and rolled section (i.e. not severely cold-formed). Also, Eq. 3-1 is limited by the following factors: (1) the linear relation only applies to DCF-values below 15%; and (2) it assumes an equal distribution of degree of cold-forming across the thickness of the material since, as discussed at the beginning of this section, the equation was developed based on the notch impact test results of uniformly pre-strained specimens, while in the case of coldforming of HSS by bending the strain distribution varies over the cross-section and contains both tensile and compressive strains. In order to include cold-formed HSS in the rules for the choice of steel to avoid brittle fracture in EN [CEN 2005], an amendment was proposed by [Feldmann et al. 2012], in which an approach was developed to consider the reduction in material toughness in the bent areas of HSS due to the cold-forming process. For the degradation of these toughness properties an appropriate temperature shift ΔT cf was derived for both circular and rectangular hollow sections. In order to guarantee the proper application of this temperature shift, Table 2.1 in EN (part of which is shown as Table 3.3 in this thesis) was extended to lower temperatures down to -120 C. Part of the extended table, for S355 steel with a design stress level of 0.75f y, is shown here as Table 3.4. It was suggested by [Feldmann et al. 2012] that: (1) since the extended table is intended for structural components made of steel plate and rolled sections (i.e. non-cold-formed steels), it could be used without a temperature shift when determining the maximum permissible wall thickness of hot-formed HSS, since it is 52

74 believed that the toughness properties in the flat face and corner of hot-finished HSS are close to its base material. Table 3.4 Maximum permissible value of element thickness for S355 steel Table 2.1 of EN :2005 extended [Feldmann et al. 2012] Steel grade S355 Steel grade S355 Sub-grade Stress level: σ/f y = 0.75 Charpy energy Service temperature ( C) at T ( C) J min Maximum permissible thickness (mm) JR J J K2,M,N ML,NL Sub-grade Charpy energy Service temperature ( C) at T ( C) J min Maximum permissible thickness (mm) JR J J K2,M,N ML,NL Note: Values based upon slightly different parameters to Table 3.3. (2) when determining the maximum permissible wall thickness of structural components made of cold-formed HSS, the extended table could be used with a shift of the service temperature to allow for the reduction in material toughness due to cold-forming (i.e. the maximum permissible thickness decreases as the degree of cold-forming increases). The shift in service temperature of the structural component is considered to be the same as the shift of the T 27J -temperature due to cold-forming. It is assumed by [Feldmann et al. 2012] that the effect of coiling and uncoiling of the base material is minor, hence the steel plate used for production of cold-formed HSS is considered to be in a non-cold-formed state. Thus, the degree of cold-forming contained in the crosssection of the CVN coupon can be estimated based on the cross-sectional dimensions of the cold-formed HSS and the sampling location of the CVN coupon. Similar to Eq. 3-1, for the reduction of toughness from cold-forming plates into HSS, Table 3.4 can be used by altering the service temperature by deducting T cf ( C), where: 53

75 T cf = 3 x ε eff 45 C (3-3) in which ε eff = the average value of the plastic strain (%) in the net section of the CVN coupon, with the longitudinal position taken adjacent to the surface of the HSS, which is the most severely cold-worked region; and T cf = adjustment for the degree of cold forming ( C). The temperature shift is limited to 45 C since, as discussed previously, T cf equals zero for DCF 2% and T cf is constant for DCF 15% [Sedlacek et al. 2008]. Determination of maximum plastic strain ε max 1 ε max r i t ε max = t 2r i + t r i Determination of ε eff t (mm) Plastic strain distribution ε eff ε max t t ε max 1 10 t max ε max < t 10 t ε t 2 20 t max t max ε max < t <10 ε max t 20 Note: The shaded areas represent the cross-section of a CVN coupon Figure 3.7 Determination of ε eff in the bent region of HSS [adapted from Feldmann et al. 2012] For cold-formed Circular Hollow Sections (CHS), T cf was calculated by assuming that: (1) tensile and compressive strains have equal effects on toughness; and (2) the effect of unequal 54

76 strain distribution over the net cross-section of the CVN coupon is equivalent to the effect of the mean strain-value of that distribution, ε eff, which can be determined based on the geometry of the cross-section and the sampling location of the CVN coupon, using Figure 3.7. The derivations of the equations in Figure 3.7 are shown in Appendix B.1. As a conclusion from the calculation method, [Feldmann et al. 2012] suggested that for CHS with external radius-to-thickness ratio greater than 16, the cold-forming effects may be neglected, and the maximum T cf may be taken as 20 C. For cold-formed RHS, ε eff needs to be determined based on the corner geometry only since it is the most severely cold-worked area. Following the same assumptions as CHS, ε eff can be determined using Figure 3.7. Based on the relationship between the inside radius and the wall thickness for RHS corners according to EN [CEN 2006b], the conclusion from this approach is that, for cold-formed RHS, the temperature shift ΔT cf is about 35 C for wall thickness 16 mm and 45 C for wall thickness > 16 mm. This conclusion is consistent with the experimental results (all RHS specimens are continuous-formed) reported by [Feldmann et al. 2012] and has been implemented in reference tables [Puthli and Packer 2013]. However, as stated in the JRC report [Feldmann et al. 2012], since the tests have been carried out mainly with HSS made of EN S355J2H material, the conclusions refer to this material type only (i.e. are not necessarily applicable to HSS produced in North America). It can be seen from the above studies that research on the effects of cold-forming and heat treatment on the CVN impact toughness of North American cold-formed RHS is still insufficient and none of the previous investigations have included direct-formed RHS. 3.8 RHS specimens and chemical compositions In this chapter, CVN impact tests were performed on RHS specimens DF12, DF24, CF12, CFH12, CF24, and CFH24 in Table 2.1. The chemical compositions of the six RHS specimens are listed in Table 3.5. The chemical analysis (Optical Emission Vacuum Spectrometric Analysis) was performed at Acuren Group Inc. (2421 Drew Road, Mississauga, Ontario, L5S 1A1). The effects of the listed chemical elements on the CVN toughness of lowcarbon structural steel, according to [Roe and Bramfitt 1990; Maranian 2010] are also shown in Table

77 Chemical elements and the effects of high amounts on CVN toughness of low-carbon structural steel Note: + + = increases it significantly, + = increases it moderately, = decreases it significantly, = decreases it moderately, ~ = has a negligible effect Chemical analysis results (% by weight) Table 3.5 Chemical compositions of RHS specimens and effects of chemical elements on the CVN toughness of low-carbon structural steel [Roe and Bramfitt 1990; Maranian 2010] Nominal sizes 152x152x12.7 mm 152x152x6.35 mm C RHS specimen DF12 CF12 & CFH12 DF24 CF24 & CFH Si Mn P S < Cr ~ Mo Ni Al Cu ~ Nb Ti + <0.005 <0.005 <0.005 <0.005 V + < <0.005 <0.005 Sn < <0.005 As Zr + <0.005 <0.005 <0.005 <0.005 Ca <0.001 Sb B + < < < < Experimental investigation The objective of the CVN impact test program was to generate the complete toughnesstemperature transition curves for CVN coupons sampled from various cross-section locations (flat face, corner and weld seam) with different coupon orientations (longitudinal and transverse) and notch face exposures (in the plane of, and perpendicular to, the RHS surface), for the six North American RHS. The cutting locations and orientations of the CVN coupons are summarized in Table 3.6, and illustrated in Figure 3.8. For the three RHS with a nominal wall thickness of 6.35 mm (DF24, CF24 and CFH24), 162 sub-sized coupons (10x3.3x55 mm) with notch perpendicular to the RHS surface were made since, as specified in ASTM A370 [ASTM 2009], due to the fact that the width of the subsized coupon is reduced, the sub-sized coupon has to be notched on the narrow side to have enough cross-sectional area. As discussed in Section 3.4.2, it has been shown by previous investigations [Puzak et al. 1952; Roe and Bramfitt 1990] that different notch orientations 56

78 result in different CVN energy absorption levels but the same DBTT. For the three RHS with a nominal wall thickness of 12.7 mm (DF12, CF12 and CF12), 216 full-sized coupons (10x10x55 mm) were made as per ASTM A370 [ASTM 2009] with notches lying in the plane of the RHS surface as most of the previous investigations [Kosteski et al. 2005; Puthli and Herion 2005; Stranghöner et al. 2010; Ritakallio 2012; Stranghöner et al. 2012] used CVN coupons with such notch orientations. Table 3.6 Cutting locations and orientations of CVN coupons Location Full-sized coupons Sub-sized coupons A Flat face not containing the weld, Flat face not containing the weld, longitudinal, notch facing outside surface longitudinal, notch through thickness B Corner, longitudinal, notch facing Corner, longitudinal, notch through outside surface thickness C Flat face containing the weld, transverse, Flat face containing the weld, transverse, notch facing outside surface notch through thickness D Corner, longitudinal, notch facing inside surface N/A A A weld seam weld seam D C (a) B Figure 3.8 Cutting locations and orientations of CVN coupons: (a) full-sized coupons; (b) sub-sized coupons B C (b) B The CVN coupons from DF12, CF12 and CFH12 were tested using a Riehle pendulum impact tester with a 325 J direct-reading scale. The CVN coupons from DF24, CF24 and CFH24 were tested using a Tinius Olsen pendulum impact tester with a 406 J directreading scale. Before testing, 20 self-verification coupons (10 low-energy ones and 10 highenergy ones) supplied by the National Institute of Standards and Technology (NIST) were 57

79 used to check the calibrations of both testing machines and the results were consistent with the expected values provided by NIST. For DF12, CF12 and CFH12, the CVN specimens were cooled by a freezer and an additional thermometer was used to ensure the accuracy of the desired testing temperatures for the CVN specimens. For DF24, CF24 and CFH24, the specimens were thermally conditioned in a dry ice-methanol liquid coolant mixture for a sufficiently long time before being tested. A thermometer was used to monitor the temperature of the dry ice-methanol mixture. The dry ice, which has an ambient temperature of C, was proportioned by trial and error in the methanol bath to achieve the desired testing temperatures for the CVN specimens. The test setup is shown in Figure 3.9. Figure 3.9 CVN impact test setup The CVN impact tests were performed in accordance with ASTM A370 [ASTM 2009]. Prior to the tests, the coupons and the tongs for handling coupons were held in the conditioning medium for a sufficiently long time (at least 5 minutes in liquid media and 30 minutes in gaseous media as per ASTM A370 [ASTM 2009]) to ensure that the intended testing temperature was reached in both of them. During the tests, the coupon was carefully centered in the anvil and the pendulum was released to break the coupon. For all tests, the pendulum was released within 5 seconds after removing the coupon from the conditioning medium. 58

80 Table 3.7 CVN test results: (a) full-sized coupons; (b) sub-sized coupons (a) Energy absorption (J) for full-sized CVN coupons (10x10x55 mm) RHS DF12 CF12 CFH12 Temperature ( C) A flat B corner C weld D corner A flat B corner C weld D corner A flat B corner Note: CVN coupons from the flat face (location A) of DF2 did not fully break at 20 C, 10 C, 0 C and -10 C C weld D corner (b) Energy absorption (J) for sub-sized CVN coupons (10x3.3x55 mm) RHS DF24 CF24 CFH24 Temperature ( C) A flat B corner C weld A flat B corner C weld A flat B corner C weld

81 KV (J) Three replicate specimens were tested at each target temperature. All test results are listed in Table 3.7. The test results in Table 3.7 are normalized and plotted against the testing temperatures in Figures CVN coupons from the flat face (location A) of DF12 did not fully break at 20 C, 10 C, 0 C and -10 C, therefore the Riehle testing machine capacity (325 J / 0.8 cm 2 = 406 J/cm 2 ) was used to plot these points Results and discussions The evaluation of the data in Figures is performed by using Eq. 3-4, a hyperbolic tangent tanh function commonly used for assessment of CVN data [Feldmann et al. 2012]. Research has shown that among different curve fitting methods, the tanh function gives the best approximation of the mean of the CVN data in the upper-shelf, the lower-shelf and the transition regions [Cao et al. 2012]. As shown in Figure 3.10, the tanh function is a convenient S-shaped curve whereby the point of contra-curvature (KV = half of upper-shelf energy) can be taken to represent the DBTT. [ ] (3-4) where KV is the absorbed energy (J), T is the temperature ( C), and A, B and C are fitting coefficients. KV = A [1 + tanh T B C ] Upper-shelf e x tanhx = ex e x + e x where x = T B C DBTT Lower-shelf T ( C) Figure 3.10 Illustration of tanh function Curve-fitting is performed using a non-linear least squares method. The best fit lines for the groups of data are shown in Figures As shown in Figure 3.11, some data points for location C (weld) of DF12 have very low CVN toughness possibly due to very small welding defects, which are inherent in welding processes. The four circled data points were considered as outliers and were not used when determining the best fit line. The normalized 60

82 Normalized Energy (J/cm 2 ) Normalized Energy (J/cm 2 ) upper-shelf energy (KV us ), DBTT and NDT for all flat face and corner curves were determined and shown in Table 3.8 and Figures A (flat) B (corner) C (weld) D (corner) Possibly due to very small welding defects Temperature ( C) Figure 3.11 CVN impact energy-temperature curves for DF A (flat) B (corner) C (weld) D (corner) Temperature ( C) Figure 3.12 CVN impact energy-temperature curves for CF12 61

83 Normalized Energy (J/cm 2 ) Normalized Energy (J/cm 2 ) 400 A (flat) B (corner) C (weld) D (corner) Temperature ( C) Figure 3.13 CVN impact energy-temperature curves for CFH A (flat) B (corner) C (weld) Temperature ( C) Figure 3.14 CVN impact energy-temperature curves for DF24 62

84 Normalized Energy (J/cm 2 ) Normalized Energy (J/cm 2 ) 400 A (flat) B (corner) C (weld) Temperature ( C) Figure 3.15 CVN impact energy-temperature curves for CF A (flat) B (corner) C (weld) Temperature ( C) Figure 3.16 CVN impact energy-temperature curves for CFH24 63

85 NDT ( C) DBTT ( C) 0 A (flat) B (corner) D (corner) DF12 CF12 CFH12 DF24 CF24 CFH24 Figure 3.17 Change of DBTT from flat face to corner for all RHS specimens 0 A (flat) B (corner) D (corner) DF12 CF12 CFH12 DF24 CF24 CFH24 Figure 3.18 Change of NDT from flat face to corner for all RHS specimens 64

86 Normalized Kvus (J/cm 2 ) A (flat) B (corner) D (corner) DF12 CF12 CFH12 DF24 CF24 CFH24 Figure 3.19 Normalized KV us (J/cm 2 ) for all RHS specimens Table 3.8 Normalized upper-shelf energy (KV us ), ductile-to-brittle transition temperature (DBTT) and nil-ductility temperature (NDT) of all RHS specimens KV us (J/cm 2 ) DF12 A (flat) B (corner) D (corner) DBTT ( C) NDT ( C) KV us (J/cm 2 ) DBTT ( C) NDT ( C) KV us (J/cm 2 ) DBTT KV us (J/cm 2 ) CF12 ( C) A (flat) B (corner) D (corner) DBTT ( C) NDT ( C) KV us (J/cm 2 ) DBTT ( C) NDT ( C) KV us (J/cm 2 ) DBTT KV us (J/cm 2 ) CFH12 ( C) A (flat) B (corner) D (corner) DBTT ( C) NDT ( C) KV us (J/cm 2 ) DBTT ( C) NDT ( C) KV us (J/cm 2 ) DBTT ( C) NDT ( C) NDT ( C) NDT ( C) 65

87 KV us Table 3.8 (continued) DF24 A (flat) B (corner) DBTT NDT KV us DBTT NDT (J/cm 2 ) ( C) ( C) (J/cm 2 ) ( C) ( C) CF24 A (flat) B (corner) KV us DBTT NDT KV us DBTT NDT (J/cm 2 ) ( C) ( C) (J/cm 2 ) ( C) ( C) CFH24 A (flat) B (corner) KV us DBTT NDT KV us DBTT NDT (J/cm 2 ) ( C) ( C) (J/cm 2 ) ( C) ( C) N/A* N/A* N/A* * N/A = not available, because no coupons were machined from location D of the DF24, CF24 and CFH Effects of chemical composition As discussed previously, for the same nominal size, the corners and their nearby regions of both direct-formed and continuous-formed RHS should theoretically contain similar amounts of cold-working which are primarily influenced by the corner bending radius. Hence, in order to study the effects of chemical composition on the CVN toughness of RHS, the corner test results of RHS specimen DF12 (152x152x12.7 mm) were compared to those of CF12 (152x152x12.7 mm), and the corner test results of DF24 (152x152x6.35 mm) were compared to those of CF24 (152x152x6.35 mm), to exclude the effect of cold-forming. According to the effects of chemical elements on the CVN toughness of low-carbon structural steel shown in Table 3.5 [Roe and Bramfitt 1990; Maranian 2010], it can be deduced based on the test results that: (1) As can be seen in Figures , the corners of CF12 and DF12 have similar CVN toughness properties, including DBTT, NDT and KV us. Comparing the chemistry of CF12 and DF12 in Table 3.5, although CF12 has a much higher silicon content than DF12 (0.353% versus 0.052%), the detrimental effect of silicon is offset by the relatively higher contents of the beneficial elements in CF12 than those in DF12, including manganese (0.871% versus 0.715%), nickel (0.173% versus 0.068%), and vanadium (0.034% versus <0.005%). 66

88 (2) As discussed previously, the carbon content has the most significant effect on the CVN toughness of steel. As can be seen in Table 3.5, the carbon content of DF24 (0.058%) is much lower than that of CF24 (0.182%), hence the DBTT and NDT of the corner of DF24 is much lower than those of CF24 in Figures 3.17 and 3.18, which is consistent with the findings in Figure Effects of cold-forming and heat-treatment For the effects of cold-forming and heat-treatment on the CVN toughness of RHS, the following deductions were made based on the test results: (1) Comparing CF12 to CFH12, and CF24 to CFH24 in Figures , it can be seen that stress-relieving the section by heat treatment in accordance with Canadian standards for Class H finishing [CSA 2013] results in little, if any, change in the DBTT, NDT and KV us, which is consistent with the test results by [Kosteski et al. 2005]. (2) For CF12 and CFH12 in Figures 3.17 and 3.18, it can be seen that for thick-walled continuous-formed RHS (B nom /t nom = 12), the DBTT and NDT of the flat face are not significantly different than those of the corner, which is consistent with the test results by [Soininen 1996; Kosteski et al. 2005], as the whole cross-section is severely cold-formed during production. (3) For CF24 and CFH24 in Figures 3.17 and 3.18, it can be seen that for the thin-walled continuous-formed RHS (B nom /t nom = 24), the DBTT and NDT of the flat face are approximately 15 C and 20 C lower than those of the corner, since the amount of coldforming to the flat face decreases as the B nom /t nom ratio increases during the continuousforming process, leading to better CVN toughness. (4) For DF12 in Figures 3.17 and 3.18, it can be seen that for the thick-walled direct-formed RHS (B nom /t nom = 12), the DBTT and NDT of the flat face are approximately 20 C and 30 C lower than those of the corner. The spread is larger compared to its continuous-formed counterparts (CF12 and CFH12) because theoretically the flat face of DF12 was not coldformed during the direct-forming process. (5) For DF24 in Figures 3.17 and 3.18, it can be seen that for the thin-walled direct-formed RHS (B nom /t nom = 24), both the DBTT and NDT of the flat face are approximately 40 C 67

89 lower than those of the corner. Again, the spread is larger compared to its continuous-formed counterparts (CF24 and CFH24). (6) As shown in Figure 3.19, the CVN coupons with notch lying in the plane of the RHS surface (DF12, CF12 and CFH12) result in much higher normalized KV us -values than those with notch perpendicular to the RHS surface (DF24, CF24 and CFH24), which is consistent with previous investigations on as-rolled steel plate [Puzak et al. 1952; Roe and Bramfitt 1990]. (7) Figures show that the weld seam region has the lowest CVN toughness around the cross-section for all RHS specimens tested. Thus, for dynamically loaded connections, fabricated from cold-formed HSS, it is preferable to keep the weld seam region away from the connecting face, as suggested by [Kosteski et al. 2005]. Using the measured cross-sectional geometries of the six RHS specimens listed in Table 3.9, the analytical T cf -values from the flat face to the corner due to the extra amount of coldforming were determined and are listed in Table 3.10, using the approach proposed by [Feldmann et al. 2012]. The equations in Figure 3.7 were slightly modified for the calculation since the CVN coupons in this study were taken at the mid-thickness of the tube wall. For the continuous-formed RHS specimens (CF12, CFH12, CF24, CFH24), the temperature shift from the coil plate to the flat face and the temperature shift from the coil plate to the corner were both determined, and the difference between the two temperature shifts was taken as the analytical T cf -value from the flat face to the corner due to the extra amount of cold-working. For the direct-formed RHS (DF12 and DF24), the temperature shift from the coil plate to the corner was taken as the T cf -value from the flat face to the corner. The calculations for all the analytical T cf -values are shown in Appendix B.2. The analytical T cf -values for the all six RHS specimens are compared to the experimentally obtained T cf -values (i.e. difference between DBTTs (or NDTs) of the flat face and the corner) in Table It can be seen that, for the RHS specimens investigated in this study, the approach proposed by [Feldmann et al. 2012] gives safe estimations for the thick-walled RHS (DF12, CF12 and CFH12), but unsafe estimations for the thin-walled RHS (DF24, CF24 and CFH24). This (unsafe) difference is probably because [Feldmann et al. 2012] assumed a linear relationship between T cf and ε eff (i.e. T cf = 3 x ε eff within the range of validity). However, for DF24, CF24 and CFH24, the calculated ε eff -values are very small due to their high B nom /t nom ratio = 24, thus the calculated T cf -values in Table 3.10 are small. It is possible that the linear relationship in [Feldmann et 68

90 al. 2012], which was developed based on the test results of European RHS, does not apply to North American RHS. For DF24 in Table 3.10, the experimental T cf -values are very large, exceeding the recommended value of 35 C in [Feldmann et al. 2012], because DF24 was direct-formed, while [Feldmann et al. 2012] assumes that all RHS are continuous-formed. Table 3.9 Measured cross-sectional dimensions A (flat) B (corner) D (corner) RHS t (mm) t (mm) r i (mm) t (mm) r i (mm) DF12 Not used* CF12 & CFH DF24 Not used* CF24 & CFH N/A** * The wall thicknesses of the flat face of DF12 and DF24 are not used for the calculation of T cf. ** N/A = not applicable. No coupons were machined from location D of the DF24, CF24 and CFH24, thus the wall thickness and inside corner radius are not included in the table. Table 3.10 Comparison of T cf -values obtained from experiment results and T cf -values estimated based on the approach proposed by [Feldmann et al. 2012] using measured crosssectional dimensions Based on experimental results T cf for DBTT from A (flat) to B (corner) T cf for NDT from A (flat) to B (corner) DF12 Based on [Feldmann et al. Based on experimental results 2012] T cf from A T cf for DBTT T cf for NDT (flat) to B from A (flat) to from A (flat) to (corner) D (corner) D (corner) Based on [Feldmann et al. 2012] T cf from A (flat) to D (corner) 17 C 28 C 45 C (safe) 21 C 26 C 44 C (safe) CF12 Based on experimental results Based on [Feldmann et al. 2012] Based on experimental results Based on [Feldmann et al. 2012] T cf for DBTT from A (flat) to B (corner) T cf for NDT from A (flat) to B (corner) T cf from A (flat) to B (corner) T cf for DBTT from A (flat) to D (corner) T cf for NDT from A (flat) to D (corner) T cf from A (flat) to D (corner) -7 C -8 C 14 C (safe) 8 C 10 C 18 C (safe) CFH12 Based on experimental results T cf for DBTT from A (flat) to B (corner) T cf for NDT from A (flat) to B (corner) Based on [Feldmann et al. 2012] T cf from A (flat) to B (corner) Based on experimental results T cf for DBTT from A (flat) to D (corner) T cf for NDT from A (flat) to D (corner) Based on [Feldmann et al. 2012] T cf from A (flat) to D (corner) -14 C -14 C 14 C (safe) 8 C -7 C 18 C (safe) 69

91 Table 3.10 (continued) DF24 Based on Based on experimental results [Feldmann et al. 2012] T cf for DBTT T cf for NDT T cf from A from A (flat) to from A (flat) to (flat) to B B (corner) B (corner) (corner) 38 C 37 C 7 C (unsafe) CF24 Based on Based on experimental results [Feldmann et al. 2012] T cf for DBTT T cf for NDT T cf from A from A (flat) to from A (flat) to (flat) to B B (corner) B (corner) (corner) 15 C 19 C 6 C (unsafe) CFH24 Based on Based on experimental results [Feldmann et al. T cf for DBTT from A (flat) to B (corner) T cf for NDT from A (flat) to B (corner) 2012] T cf from A (flat) to B (corner) 10 C 15 C 6 C (unsafe) * N/A = not available. No coupons were tested from location D of the DF24, CF24 and CFH24, thus the T cf - values from location A to location D were not calculated. N/A* N/A* N/A* 70

92 Chapter 4 High Strain Rate Behaviour 4.1 Summary This chapter compares the high strain rate properties of four cold-formed RHS specimens manufactured by two different methods: direct-forming versus continuous-forming. Their compressive and tensile dynamic properties were obtained by performing 128 split- Hopkinson pressure bar tests and 38 split-hopkinson tension bar tests respectively. The test strain rates ranged from 100 to 1000 s -1 and the dynamic yield stresses were compared to the corresponding static yield stresses, to characterize the strength enhancement of cold-formed RHS under such loading rates. For simplification and consistency purposes, in this chapter the abbreviation SHPB is used for both split-hopkinson pressure bar and split-hopkinson tension bar. 4.2 Background Recently, blast and impact loadings have been taken into consideration for the design of critical infrastructure. For structures under these severe loadings, their responses at high strain rates from 100 to 1000 s -1 are often sought [Malvar and Crawford 1998; Paik and Thayamballi 2003; Luecke et al. 2005; Razaqpur et al. 2009; Astaneh-Asl 2010]. It is estimated that the strain rates on the World Trade Centre steels, due to the aircraft impacts, were up to 1000 s -1 [Luecke et al. 2005]. For blast- or impact-resistant design of steel structures, Strength Increase Factors (SIF y ) are commonly used to consider the difference between the nominal static yield stress and the probable static yield stress, and Dynamic Increase Factors (DIF y and DIF u ) are commonly used to consider the dynamic increase of yield stress and ultimate strength. According to AISC Steel Design Guide 26 [Gilsanz et al. 2013], for steel grades of 345 MPa or less, the average yield stress of steels currently produced is approximately 10% larger than the nominal yield stress specified by the American Society for Testing and Materials (ASTM) specification. Hence, for blast design the nominal yield stress would be multiplied by a SIF y of For higher grades this average is claimed to be smaller than 5%, so no factor is used on those grades. Ultimate strength is not factored in any case. The same suggestions are given in [DOD 2008; ASCE 2010; ASCE 2011; CSA 2012]. It should be noted that the SIF y value of 1.10 is intended for non-cold-formed steels. For cold-formed hollow sections, the ratio between the actual yield stress and the nominal value is typically higher. For example, SIF y is 71

93 taken as 1.4 (R y factor) for cold-formed hollow sections in the AISC Seismic Provisions for Structural Steel Buildings [AISC 2010a]. The mechanical properties of steel material vary with strain rate. Compared to the static values normally used in design, the properties vary for dynamic loading as follows: (1) the yield stress increases substantially; (2) the ultimate strength increases slightly; and (3) both modulus of elasticity and the elongation at rupture remain nearly constant [Luecke et al. 2005; Gilsanz et al. 2013]. Thus, DIF y and DIF u are commonly used to consider the increases in yield stress and ultimate strength due to blast loading [Gilsanz et al. 2013; DOD 2008; ASCE 2010; ASCE 2011; CSA 2012]. The DIF y and DIF u values for various structural steels suggested by [Gilsanz et al. 2013] are listed in Table 4.1. The values are based on an average strain rate of 0.1 s -1 which is characteristic of low pressure explosions. It can be seen in Table 4.1 that the ultimate strengths of various steels are in general less sensitive to the strain rate effect, compared to the yield stresses. Similar constant DIF y and DIF u values, independent of the strain rate, are given in [DOD 2008; ASCE 2010; ASCE 2011; CSA 2012]. If the strain rate can be determined, UFC [DOD 2008] recommends that the DIF y for strain rates up to 100 s -1, for ASTM A36 and A514 steels, be determined using Figure 4.1. Another important effect of high strain rate on steel members is that the cross-section classification, and hence member behaviour, may be affected. The yield strength increase from the static to the dynamic value may cause a downgrading of cross-section classification, for example changing a section from compact to slender [Liew 2008]. Table 4.1 DIF y and DIF u values for various structural steels under low pressure explosion [Gilsanz et al. 2013] ASTM specifications Bending / Shear DIF y Tension / Compression DIF u A A A A446/A A A

94 ASTM A36 ASTM A514 plate thickness 63.5 mm ASTM A514 plate thickness > 63.5 mm DIF y Strain rate (s -1 ) Figure 4.1 DIF y values at various strain rates for ASTM A36 and A514 steels in [adapted from DOD 2008] Based on the expected ductility ratio (ratio between the maximum displacement and the elastic displacement) or the expected support rotation angle (tangent angle at the support formed by the maximum beam deflection), it is suggested by AISC Steel Design Guide 26 [Gilsanz et al. 2013] that the dynamic design stress for tension, compression and bending (f ds ) can be calculated as follows, for non cold-formed steel: For ductility ratio 10 or support rotation angle 2 degrees, ( ) (4-1) For ductility ratio > 10 or support rotation angle > 2 degrees, (4-2) where (4-3) The dynamic design stress for shear is given as:. (4-4) 73

95 Stress The dynamic design stress for tension, compression and bending (f ds ), calculated using Eqs. 4-1 and 4-2, is illustrated in Figure 4.2, for hot-formed (or hot-finished) steel. As can be seen, Eq. 4-2 considers the strain hardening effect when the expected ductility ratio (i.e. the damage allowed in the structural member) is large. f du f u f dy f ds = f dy f ds = f dy + (f du f dy )/4 f y Quasi-static strain rate High strain rate Dynamic design stress (f ds ) Strain corresponding to a ductility ratio = 10 Strain corresponding to a ductility ratio = 20 (incipient failure of member) Strain Figure 4.2 Typical stress-strain curves for steel and dynamic design stress (adapted from DOD 2008) It should be noted that the constant DIF y and DIF u values suggested by the above design guides and technical manuals are in general intended for low pressure explosions (for strain rates in the order of 10-1 s -1 ). Thus, they may not be accurate for blast loading in close proximity or impact loading where the strain rate may be much higher (in the order of 10 2 to 10 3 s -1 ). 4.3 Previous investigations The effect of strain rate on the mechanical properties of steels, particularly yield strength, has long been a subject of interest to researchers. It was found that the yield strength of steel increases as the strain rate increases. This is because as the material dislocation velocity 74

96 increases, cross slip becomes increasingly difficult and the flow stress at any given strain increases, thus increasing the yield strength of steel [Davis 2004]. Early research on the influence of strain rate on the yield stresses of three structural steels (ASTM A36 and A441 steels and one quenched and tempered steel) was conducted by [Rao et al. 1966]. Tensile coupons were tested quasi-statically and dynamically to obtain the experimental results. The measured static tensile yield stresses of the steels tested ranged from 238 MPa to 778 MPa. The dynamic test strain rates were up to 1.4 x 10-3 s -1. Based on 189 tests on A36 steel, 39 tests on A441 steel and 29 tests on the quenched and tempered steel (Q-T), Eqs. 4-5 to 4-7 were established to describe the relationships between DIF y and strain rate for the three tested steels. The equations are functions of the strain rates only. (4-5) (4-6) (4-7) Later, the mechanical properties of various steels at different strain rates were studied by [Soroushian and Choi 1987]. Dynamic test results on structural steels, reinforcing bars and deformed wires were collected. All tests (approximately 60 tests based on the number of data points in the publication figure) were performed in tension. The measured static tensile yield stresses of the steels tested ranged from 180 MPa to 684 MPa. The dynamic test strain rates were up to 10 s -1 and Eq. 4-8 was established for prediction of the DIF y. The equation is a function of both the strain rate and the actual static yield stress (in MPa) of the steel. ( ) (4-8) The effects of cold-working and strain rate on the mechanical properties of three types of sheet steels were investigated by [Kassar and Yu 1992]. The three sheet steels were designated 35XF, 50XF and 100XF. The numbers 35, 50 and 100 distinguish the three sheet steels by their nominal yield stresses (100 ksi = 689 MPa, 50 ksi = 345 MPa, and 35 ksi = 241 MPa). A total of 124 tensile coupons and 54 compressive coupons were tested. The measured static tensile yield stresses of the steels tested ranged from 227 MPa to 950 MPa, and the measured static compressive yield stresses ranged from 206 MPa to 853 MPa. For the tension tests, the specimens were subjected to uniform cold stretching of 2% and 8% before testing. By comparing the dynamic yield stresses (obtained from tests at a strain rate of 1 s -1 ) 75

97 to the static yield stresses (obtained from tests at a strain rate of 1x10-4 s -1 ), the dynamic increases in yield stress for the three steels tested in tension were: 12 29% for the 241 MPa (nominal yield stress, same for the following) steel, 4 15% for the 345 MPa steel, and 4% for the 689 MPa steel, while the dynamic increases in yield stress for the three steels tested in compression were: 24 33% for the 241 MPa steel, 9 10% for the 345 MPa steel, and 7% for the 689 MPa steel. For tension tests with different amounts of cold stretching, the strainrate sensitivity decreased as the amount of prior cold stretching increased. Comparing the average value of the measured static tensile yield stresses (in the non-cold-stretched condition) and the measured dynamic tensile yield stresses under different strain rates, three equations were established for prediction of dynamic yield stress for the three tested sheet steels. The three original equations in [Kassar and Yu 1992] are herein divided by the corresponding average value of the measured static tensile yield stress (in the non-cold-stretched condition), and are shown as Eqs. 4-9 to 4-11 so that they can be used for prediction of the DIF y. (4-9) (4-10) (4-11) Recently, [Filiatrault and Holleran 2001] studied experimentally the uniaxial tensile behaviours of reinforcing steel bars under various combinations of earthquake-level strain rates (quasi-static to 0.1 s -1 ) and temperatures typical of summer and winter conditions in cold urban regions (+20 C to -40 C). A total of 36 coupons were machined from a single reinforcing bar with a nominal yield stress of 400 MPa. The test results revealed that, when the strain rate increased from quasi-static (80x10-6 s -1 ) to 0.1 s -1 and the temperature dropped from +20 C to -40 C, the yield stress and ultimate strength increased by 22% and 12% respectively. Using Eqs. 4-5 to 4-11, for various steels in the above investigations the relationships between DIF y and test strain rates, together with extrapolations beyond the test strain rates, are shown in Figure 4.3. It was suggested by [Kassar and Yu 1992] that Eqs. 4-9 to 4-11 could be used for strain rates beyond the test strain rates. However, since there is no test data to justify this suggestion, the accuracy of the extrapolations is unknown. It can be seen in Figure 4.3 that the sensitivities for various steels to the strain rate effect are quite different, thus it is hard to establish a single equation to describe the DIF y versus strain rate relationship 76

98 for various steels. Nevertheless, there is a strong correlation of the DIF y to the logarithm of the strain rate. DIF y A36 in [Rao et al. 1966] A441 in [Rao et al. 1966] Q-T in [Rao et al. 1966] [Soroushian and Choi 1987], fy=350 MPa 35XF in [Kassar and Yu 1992] 50XF in [Kassar and Yu 1992] 100XF in [Kassar and Yu 1992] E Strain rate (s -1 ) Figure 4.3 Relationships between DIF y and strain rate based on previous investigations at intermediate strain rate level (test strain rate up to 10 s -1 ) Investigation into the dynamic strength increase for steel reinforcing bars at higher strain rates, up to 225 s -1, was conducted by [Malvar and Crawford 1998]. The static and dynamic tensile behaviours were studied for reinforcing bars satisfying ASTM A615, A15, A432, A431, and A706, with the nominal yield stresses ranging from 290 to 710 MPa. The test results revealed that, under dynamic loading, the yield stresses of these rebars increase by up to 60% for strain rates of up to 10 s -1, and up to 100% for strain rates of 225 s -1. Based on the experimental data, [Malvar and Crawford 1998] proposed Eqs and 4-13 that give DIF y and DIF u as functions of the strain rate and the measured static yield stress, f y (MPa). These two equations have been adopted by CSA S [CSA 2012] for prediction of the dynamic strength increase of rebar. (4-12) 77

99 (4-13) Recently, in order to study the aircraft impact and the resulting damage to the World Trade Center (WTC), [Luecke et al. 2005] investigated the dynamic properties of the WTC steels for strain rates up to 2500 s -1. Test coupons (tensile and compressive) were machined from perimeter column steels and core column steels (welded box sections, rolled wide flange sections and spandrel plates). The nominal yield stresses of the examined steels ranged from 248 MPa to 621 MPa. Based on the experimental data, [Luecke et al. 2005] proposed a modified Cowper-Symonds [Cowper and Symonds 1957] model for prediction of DIF y of various steels under high strain rates. Since the original equations are in ksi (unit-dependent), they are modified hereby as Eqs and 4-15 where f y is in MPa. (4-14) (4-15) DIF y [Malvar and Crawford 1998], fy=300 MPa [Malvar and Crawford 1998], fy=350 MPa [Malvar and Crawford 1998], fy=400 MPa [Luecke et al. 2005], fy=300 MPa [Luecke et al. 2005], fy=350 MPa [Luecke et al. 2005], fy=400 MPa E Strain rate (s -1 ) Figure 4.4 Relationships between DIF y and strain rate based on previous investigations at high strain rate level (test strain rate up to 2500 s -1 ) 78

100 Using Eqs to 4-15, the relationships between DIF y and strain rate suggested by [Malvar and Crawford 1998; Luecke et al. 2005] are shown in Figure 4.4. Similar to Figure 4.3, Figure 4.4 also indicates that the sensitivities for different steels to the strain rate effect are quite different. Based on Figures 4.3 and 4.4, it can be seen that the DIF y values in Table 4.1, which are intended for low pressure explosion (strain rates in the order of 10-1 s -1 ), may be too conservative for blast loading in close proximity or impact loading (strain rates in the order of 10 2 to 10 3 s -1 ). Since (1) test results on structural steel properties under high strain rate are still highly insufficient [Astaneh-Asl 2010], (2) the high strain rate behaviours of various types of steels are quite different, and (3) previous investigations are mostly on non-cold-formed steels, there is a need to investigate the high strain rate behaviour of cold-formed hollow structural sections, especially as these are favoured for building columns. 4.4 RHS specimens In this chapter, the dynamic compression and tensile behaviours (at strain rates ranging from 100 to 1000 s -1 ) of four RHS specimens (DF12, DF24, CF12 and CF24 in Table 2.1) are examined by SHPB tests. The dynamic test results are compared to the static tensile coupon test results to characterize the strength enhancement of cold-formed RHS under such high strain rate loading. 4.5 Experimental investigation Tensile coupon tests The SIF y and SIF u values around the cross-sections of the investigated RHS specimens were obtained through tensile coupon tests. For each RHS, five tensile coupons (three from three different flat faces and two from two different corners) were machined and tested quasistatically in accordance with ASTM A370 [ASTM 2009] (see Chapter 2). The static yield stresses are determined by the 0.2% strain offset method. The averages of the measured static yield stresses (f y,avg in Table 2.4) and the averages of the measured static ultimate strengths (f u,avg in Table 2.4) are compared to the nominal values (f y,nom and f u,nom ), and the SIF y and SIF u values are listed in Table

101 Table 4.2 SIF y and SIF u values for RHS specimens Flat face Corner RHS ID SIF y = f y,avg /f y,nom SIF u = f u,avg /f u,nom SIF y = f y,avg /f y,nom SIF u = f u,avg /f u,nom DF DF CF CF Avg SHPB tests Background Testing using SHPB apparatus is the most common method of determining the high strain rate behaviour of engineering materials. The determination of the high strain rate behaviour of a material being tested using SHPB, whether it is loaded in compression or tension, is based on the same principles of one-dimensional elastic wave propagation within the pressure loading bars. The detailed historical background and principles of SHPB apparatus can be found in the ASM Handbook Volume 8 [Gray 2000]. Sample sandwiched between bars Striker bar Incident bar Transmitted bar Gas gun Strain gauge Strain gauge Figure 4.5 Schematic diagram of compressive SHPB apparatus While there is no universal standard design for SHPB apparatus, all facilities share common design elements [Gray 2000]. The University of Toronto compressive SHPB apparatus used in this study is shown schematically in Figure 4.5 and photographically in Figure 4.6. It consists of two cylindrical bars (incident bar and transmitted bar), a gas gun and a striker. Strain gauges are mounted on both bars to measure the elastic strains. During a compressive 80

102 Strain SHPB test, the sample (usually a cylinder) is sandwiched between the incident bar and the transmitted bar. The elastic strains measured in the bars are used to determine the stress-strain relationship of the examined material. The bars used in the SHPB apparatus are made of high strength steel since the yield strength of the selected pressure bar material determines the maximum stress attainable within the sample material, given that the pressure bars must remain elastic. Figure 4.6 Photograph of compressive SHPB apparatus Incident wave Transmitted wave Reflected wave Time (s) Figure 4.7 Typical strain gauge data from a compressive SHPB test 81

103 The compressive SHPB test starts with accelerating the striker, from the gas gun towards the incident bar. At impact, a compressive strain wave (incident wave), ε i (t), is created within the incident bar which travels towards the sample. At the boundary between the incident bar and the sample, part of the pulse reflects as a tensile strain wave (reflected wave), ε r (t), back into the incident bar while the rest transmits as a compressive strain wave (transmitted wave), ε t (t), into the specimen and eventually the transmitted bar [Gray 2000]. The strain-time histories of the two bars recorded by the strain gauges can be analysed to extract the compressive stresstime curve and the compressive strain-time curve for the sample tested. These data can then be combined to obtain the rate-dependent compressive stress-strain relationship of the tested material. Typical strain gauge data from a compressive SHPB test is shown in Figure 4.7. Note that for calculation purpose the three waves are truncated so that they start from the same time. During a test, there are time delays between the waves due to the distance between the strain gauges. According to one dimensional elastic wave propagation theory [Gray 2000], the dynamic compressive stress-time history and the dynamic compressive strain-time history (σ(t) and ε(t)) of the sample can be determined using Eqs and σ ε (4-16) ε ε (4-17) where A b and A s are the cross-sectional areas of the bars and the sample, respectively, l s is the length of the cylinder sample and C b is the longitudinal elastic wave speed in the pressure bar. The longitudinal elastic wave speed in the pressure bar (C b ) can be determined by striking the pressure bars with no sample. It is the result of dividing the distance between the two strain gauges by the time difference between the starting points of the incident wave and transmitted wave. C b equalled 4790 m/s in this study. The principles for the tensile SHPB test are similar to those for the compressive SHPB test. The most commonly used tensile SHPB test method uses a dumb-bell-shaped sample threaded directly into the ends of the incident and transmitted bars. A tensile force can be generated by direct impact on a flange at the end of the incident bar, using a hollow striker 82

104 tube accelerated along the incident bar from a gas gun [Gray 2000]. The tensile SHPB apparatus used in this study is shown schematically in Figure 4.8. In the tensile SHPB test, the incident, reflected and transmitted waves recorded by the strain gauges are in the opposite directions to those in the compressive SHPB test, as shown in Figure 4.7. Data analysis for the tensile SHPB test is essentially identical to that of the compressive SHPB test. The same equations (Eqs and 4-17) can be used to determine the dynamic tensile stress-time history and the dynamic tensile strain-time history. Sample threaded into bars Hollow striker bar Incident bar Transmitted bar Gas gun Strain gauge Strain gauge Figure 4.8 Schematic diagram of tensile SHPB apparatus In the SHPB test of steel material, the elastic region of the test result (tensile or compressive) is commonly considered non-reliable, since Eqs and 4-17 assume that the sample is in force equilibrium, while at strains below the yield point this assumption is not valid [Luecke et al. 2005; Gray 2000]. Thus, in this study the test results were analysed as follows: (1) Truncate the data at the elastic region. (2) Fit a straight line to the yield plateau and determine the dynamic yield stress using the 0.2% strain offset method, as illustrated in Figure 4.9. (3) Fit a straight line to the strain-time curve for determination of the average strain rate experienced by the sample, as illustrated in Figure

105 Strain Stress (MPa) Intercept = 762, Slope = E Dynamic yield stress = 775 MPa Strain Figure 4.9 Determination of dynamic yield stress Strain rate = Slope = 858 s Time (s) Figure 4.10 Determination of strain rate Compressive SHPB tests The dynamic compressive stress-strain behaviours of all the RHS specimens, under high strain rates from 100 to 1000 s -1, were obtained by compressive SHPB tests. The selection of 84

106 sample size is dependent on the strain rate desired. The compressive SHPB sample sizes in this study were selected following ASM Handbook Volume 8 [Gray 2000], which suggests a cylinder sample with length-to-diameter ratio from 0.5 to 1.0. The diameters of the samples in this study were made almost the full wall thickness of the RHS specimens to ensure measurement of the bulk properties of the RHS specimens. Tensile SHPB sample Compressive SHPB samples Figure 4.11 Compressive and tensile SHPB samples weld seam Figure 4.12 Cutting location and orientation of compressive and tensile SHPB samples Cylinder samples with length of 5 mm or 10 mm and a diameter of 10 mm were machined from the RHS specimens with nominal thickness of 12.7 mm (DF12 and CF12). Cylinder samples with length of 2.5 mm or 5 mm and a diameter of 5 mm were machined from the RHS specimens with nominal thickness of 6.35 mm (DF24 and CF24). In both cases, the longer samples were intended for strain rates from s -1, and the shorter samples 85

107 Stress (MPa) were intended for strain rates from s -1. Typical compressive SHPB samples are shown in Figure The cutting location and orientation of the compressive samples are illustrated in Figure The circular surface of the compressive sample is normal to the longitudinal direction of the RHS specimen. For all four RHS specimens, a total of 128 compressive SHPB samples were tested. During the compressive SHPB test, the loading direction is normal to the circular surface of the cylinder sample (i.e. in the longitudinal direction of the RHS specimen), since RHS is usually loaded longitudinally (under compression, tension or flexural loading). As discussed above, Eqs and 4-17 are valid when the sample is in force equilibrium. Thus, in this study the pulse shaping technique suggested by ASM Handbook Volume 8 [Gray 2000] was used to modify the pulse shape of the incident wave through the placement of a copper disk at the front of the incident bar. The aim was to obtain dynamic equilibrium in the sample at an earlier stage of a test such that the data would be valid at an earlier strain Strain rate = 135 s -1 Strain rate = 577 s -1 Strain rate = 987 s Strain Figure 4.13 Typical compressive SHPB test results Typical dynamic compressive stress-strain curves are shown in Figure 4.13 and the full set is given in Appendix C. Using the procedures illustrated in Figures 4.9 and 4.10, and Eqs and 4-17, the dynamic compressive yield stresses at the flat faces and corners of the RHS specimens were determined. The compressive DIF y values, obtained by dividing the dynamic compressive yield stresses by the corresponding static yield stresses (obtained from testing the tensile coupon machined from the same location), are shown in Figures It is 86

108 assumed in this study that at the location where the tensile coupon was machined (flat face or corner) the local static compressive yield stress equals the local static tensile yield stress. Key compressive SHPB test results are listed in Appendix C. 2.8 Flat face Corner 2.4 DIF y Flat face: C=2318, q=2.83 R 2 = Corner: C=5931, q=1.92 R 2 = Strain rate (s -1 ) Figure 4.14 Compressive DIF y values of DF12 (12.7 mm thick RHS) 2.8 Flat face Corner DIF y Flat face: C=1997, q=0.46 R 2 =0.838 Corner: C=2271, q=0.48 R 2 = Strain rate (s -1 ) Figure 4.15 Compressive DIF y values of CF12 (12.7 mm thick RHS) 87

109 2.8 Flat face Corner 2.4 DIF y Corner: C=118552, q=10.65 R 2 = Flat face: C=11494, q=5.96 R 2 = Strain rate (s -1 ) Figure 4.16 Compressive DIF y values of DF24 (6.35 mm thick RHS) 2.8 Flat face Corner 2.4 DIF y 2.0 Flat face: C=3427, q=9.59 R 2 = Corner: C=70926, q=12.43 R 2 = Strain rate (s -1 ) Figure 4.17 Compressive DIF y values of CF24 (6.35 mm thick RHS) Tensile SHPB tests The dynamic tensile stress-strain behaviours of RHS specimens DF12 and CF12 under high strain rates from 100 to 1000 s -1 were obtained by tensile SHPB tests. No tensile samples 88

110 d=8 mm were made from RHS specimens DF24 and CF24 since the tube walls are too thin (nominal thickness = 6.35 mm). In this study, the dumb-bell-shaped sample with threads on both ends suggested by ASM Handbook Volume 8 [Gray 2000] was used, as shown in Figure The cross-section of the test region of the tensile SHPB sample is circular with a diameter of 5 mm. A schematic diagram of the tensile SHPB sample is shown in Figure mm A 12 mm 12 mm B 2.5 mm A B d=12 mm d=5 mm Section A-A Section B-B Figure 4.18 Schematic diagram of tensile SHPB sample The longitudinal direction of the tensile sample is the same as that of the mother tube, such that during the tensile SHPB test the samples are loaded in the longitudinal direction of the RHS specimen. The cutting location and orientation of the tensile samples are illustrated in Figure Similar to the compressive SHPB tests, during the tensile SHPB tests pulse shaping was achieved using copper disks, with the selection of pulse shapers based on experience [Gray 2000]. By trial and error, best test results were achieved by placing two copper disks at the symmetrical locations on the impact surface of the flange with the striker bars in this study. A photograph of a typical tensile SHPB sample after testing is shown as Figure Typical dynamic tensile stress-strain curves are shown in Figure 4.20 and the full set is given in Appendix C. Similar to the compressive SHPB tests, using the procedures illustrated in Figures 4.9 and 4.10, and Eqs and 4-17, the dynamic tensile yield stresses at the flat faces and corners of the RHS specimens were determined. The tensile DIF y values, obtained by dividing the dynamic tensile yield stresses by the corresponding static yield stresses 89

111 Stress (MPa) (obtained from testing the tensile coupon machined from the same location), are shown in Figures 4.21 and Key tensile SHPB test results for 38 samples are listed in Appendix C. Figure 4.19 Tensile SHPB sample after test Strain rate = 265 s -1 Strain rate = 496 s -1 Strain rate = 888 s Strain Figure 4.20 Typical tensile SHPB test results 90