Residual strength at -40 o C of a pre-cracked cold-formed rectangular hollow section made of ultra-high-strength steel - An engineering approach

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2 Theme Days of the HRO Design Forum Holiday Club Tampere Spa, Tampere This Programme is co-funded by the European Union, the Russian Federation and the Republic of Finland Residual strength at -40 o C of a pre-cracked cold-formed rectangular hollow section made of ultra-high-strength steel - An engineering approach Väsytyskuormitetun UHSS-rakenneputken äärikestävyys alhaisissa käyttölämpötiloissa T. Nykänen 1, T. Björk 1, H. Mettänen 1, A. V. Ilyin 2, M. Koskimäki 1 1 Lappeenranta University of Technology, Laboratory of Steel Structures, P.O. Box 20, FIN Lappeenranta, Finland; 2 Structural integrity department FSUE CRISM Prometey Saint-Petersburg, , Russia timo.nykanen@lut.fi, timo.bjork@lut.fi, heli.mettanen@lut.fi, victorm@crism.ru, matti.koskimäki@lut.fi Tuesday, August 13, 2013 Design Forum of optimized welded structures (HRO)

3 Experimental program Material properties of the S960 QC steel Basic chemical composition limits (wt%) and carbon equivalent values C max Si max Mn max P max S max Ti max CEV typical CEV max CEV = C+Mn/6+(Cr+Mo+V)/5+(Cu+Ni)/15 Tensile properties of S960 QC steel Condition, orientation Rp 0.2 [MPa] R m [MPa] A 5 [%] As-delivered LT As-delivered TL Artificially aged 250 o C/30 min TL Rectangular hollow section, 5 mm, LT, -40 o C

4 True stress-strain plot at -40 o C and +20 o C from laboratory data 4

5 Fracture resistance curves for ductile fracture for cold-formed steel - To simulate a welded structure, a single weld bead was welded around the bottom corners of the section (GMAW + Union X96 wire Æ 1 mm) - The fracture mechanics tests were carried out using two small pre-fatigued single edge bend (SE(B)) specimens of the dimensions 5 x 10 x 55 mm and 4.7 x 20 x 80 mm, both without side grooves and pre-fatigued with a/w = The J-R curve determination was done according to ASTM E specifications and new recommendations. 5

6 Specimen, test set up and procedures - W x H x B x L = 135 x 180 x 5 x1820 mm. - Four point bending. - Clad welds around the bottom corners of the section. - Two tests were carried out in which the beam was cyclically loaded at +20 o C to produce a fatigue crack that penetrated the whole bottom flange; then in the final stage, at -40 o C, the fatigue crack gradually grew into the web until the critical size was reached. - In another two tests, the crack was grown to a certain length at +20 o C, and then the beam was subjected to a quasi-static bending load at -40 o C until final failure occurred. - One preliminary quasi-static test had been done at +20 o C. - In all cases, the pre-cracks were introduced by sawing the bottom rounded corners of the profile before the fatigue process. - Sub-zero temperatures were achieved by circulating a coolant inside the test specimens. Crack starting point and laboratory test arrangement. L = 1820 mm and l = 400 mm 6

7 Experimental results Direct results crack lengths - Crack length was not monitored during the fatigue tests. However, in quasi-static tests, pictures were taken after the fatigue process and before the specimens were broken with quasistatic loading. Estimated crack lengths are shown below. Under cyclic loading, the cracks did not propagate evenly in the webs; therefore, the crack lengths were not the same in both webs before the final breaking test. After Before Crack before and after the final quasi-static fracture test 7

8 Direct results test records at final stage before fracture Load vs. load-line displacement behaviour of the beam under four point bending loading at the final stage in quasi-static and fatigue tests Specimen #1 Specimen #2 Specimen #4 Specimen #3 Specimen #5 8

9 Critical crack lengths - The critical crack lengths were determined indirectly based on the change in stiffness of the beam as the crack grew. Two methods were utilized: Secant stiffness method - non-linear elastic behavior Elastic unloading stiffness method - incremental plasticity theory - First, the stiffness of the beam was calculated as a function of load and crack length. Then, using the load vs. load-line displacement records, the stiffness was determined as corresponding to the critical load, F cr,. Finally, the stiffness was compared to the calculated stiffness values in order to find the critical crack length, a exp. The determination of crack lengths could be based on load-point displacements as well. 9

10 - Computations were made using Abaqus/CAE Because of its symmetry, only a quarter of the profile was modeled. A threedimensional model was used. The finite element mesh was filled with parabolic hexahedral and wedge elements. - The mesh consisted of three layers of finite elements distributed throughout the thickness of the specimen. The element layers were of the same thickness. - The profile was modeled using finite elements and nodes. - The analyses were geometrically non-linear in all cases. - In the model, the stress strain curve was approximated as linear up to yield stress, and the power hardening law from yield stress at -40 o C. - The different behavior of the deformed corners was taken into account. - All models were similar apart from the crack tip mesh, which was modified to correspond to the different crack lengths. - Because the loading rig was not included in the model, the calculated stiffness values were corrected in order to take into account the stiffness of the bending rig (k = kn/mm). The maximum correction was approximately 2-3%. A typical finite element mesh used in calculations 10

11 The critical crack lengths based on k sec and k unl and from the pictorial estimated crack lengths, a, before the final quasi-static fracture test Specimen F cr [kn] a exp_sec [mm] a exp_unl [mm] a [mm] # # # # #

12 Assessment procedure J-integral The fitted J mean and J max values as a function of force F and crack length a J c 1 c 2 c 3 c 4 c 5 c 6 c 7 c 8 c 9 c 10 mean max ( ) c 2 1+ ca 2 + ca 3 + cfc5 4 = c 9 J a,f c ca ca cf a[mm], F [kn] and J [N/ mm] J mean as a function of the force F and crack length a The small circles are the results of calculations, which were used to fit the surface. 12

13 Instability and resistance curve - Generally, the crack resistance curve illustrates the energy released in the presence of the defined crack extension size. In ductile material, it can represent the total amount of work to create the new plastic zone on the crack tip plus the work required for the initiation, growth and coalescence of micro voids. - According to the energy criterion, during crack propagation, resistance energy must be satisfied. If the amount of applied energy is less than that of resistance energy, the crack may tear and stop. If the applied energy is more than the resistance energy, instability will occur. - The tangential curve drawn to the resistance curve defines both a unique crack size and extension at the instability point. Fracture instability will then occur when: ì J=JR ï ídj dj ï = î da da R Determination of critical crack length, acr = a 0 + ac 13

14 Comparison between predicted and experimental results Specimen #1 was not analyzed separately at + 20 o C FEM limit load Limit design R p0.2, R m Comparison of predicted and measured critical loads at -40 o C as a function of crack length at fracture. 14

15 Ductile-tearing analysis with the J-based FAD - Alternative method Crack size a ( a,f) 0 ( Δ ) ( a,f) æ R ö m L = 0.5 max ç 1+ r è R e ø Force F mat 0 FAD Curve: J I 0 r 0 Flimit ( 0) KJ 0 Assessment : limit 0 1 -ν ( Δ ) R 0 ( Δa) 1-ν 2 2 ( a,f 0 ) ( ) F K L r( a,f) = K ( a,f) = a a,f K = F KI( a + Δ a) 0 L r( Δa) = K r ( Δa) = F a + a K a K a = J J E E K I - linear analysis K J - non-linear analysis mat ( Δ ) 4Mpl ( a) F limit ( a) =, H - R ³ a ³ R L-l ì æ Bö 2 2 ü ï( W -2R) Bç n( a) - + ( n( a) - R) B+ ( H -a -n( a) ) Bï è 2 ø ï ï M ( a) =R 3 pl p0.2 í ér3 ( ) ù ý ï 1 - R-B 2 é 4 + πr2 -π ë û ( R-B) ù ï ï ë û é ( ) ù ï ï π R2 - R-B î ë û ïþ H -a R W -2R 1 2 n ( a) = éπr2 -π( R-B) ù Bë û Anderson, T. L. (2005) Fracture Mechanics, Fundamentals and Applications, 3 th Ed., Taylor & Francis Group. 15

16 Conclusions Based on the present investigation of the residual strength of a pre-cracked cold-formed rectangular hollow section, made of S960 QC steel and loaded in pure bending, the following main conclusions can be drawn: At room temperature and at -40 C, the fracture resistance (J-R) tests indicated overall ductile behavior. Large-scale tests showed that brittle cleavage fracture will not become the dominant fracture mode at -40 o C in the hollow section beam construction studied. The mean trend resistance curve at -40 o C was based on data derived from small pre-fatigued SE(B) specimens without side grooves. The predicted critical loads based on J mean were approximately 6.5% smaller than the experimentally derived critical loads; the predicted critical loads based on J max were approximately 10.1% smaller than the experimentally derived critical loads. When side-grooved specimen data were utilized, the estimates based on fracture mechanics tests using small-scale SE(B) specimens were clearly conservative. The predicted critical loads of these were approximately 26% smaller than those predicted with a resistance curve derived from specimens without side grooves. The predictions reasonably matched the test results in spite of the at-slant transition, although in 3-D analysis, the crack was modeled as a at, straight-through crack. After a simple limit load analysis (without strain hardening) at -40 o C, the calculated plastic limit loads were within -4.0 to 7.7% as compared to the experimental critical loads. 16

17 Source material Björk, T. (2005) Ductility and ultimate strength of cold-formed rectangular hollow section joints at sub-zero temperatures. Doctoral thesis, Lappeenranta University of Technology, Lappeenranta, Finland. Zerbst, U., Heinimann, M., Donne, C. D. and Steglich, D. (2009) Fracture and damage mechanics modelling of thin-walled structures An overview. Eng. Fract. Mech. 76, Newman, J. C., Jr., James, M. A. and Zerbst, U. (2003) A review of the CTOA/CTOD fracture criterion. Eng. Fract. Mech. 70, Nevasmaa, P., Karjalainen-Roikonen, P., Laukkanen, A., Nykänen, T., Ameri, A., Björk, T., Limnell, T. and Kuoppala, J. (2010) Fracture characteristics of new ultra-high-strength steel with yield strengths MPa. 4/4/2013. Ruukki, Research Centre. Raahe, Finland. 27/5/2013. Kielce University of Technology, Faculty of Mechatronics and Machine Building, Al lecia P.P.7, Kielce, Poland. 24/5/2013. ASTM E (2011) Standard test method for measurement of fracture toughness. American Society for Testing and Materials. Xian-Kui, Z. and Joyce, J. A. (2012) Review of fracture toughness (G, K, J, CTOD, CTOA) testing and standardisation. Eng. Fract. Mech. 85, Landes, J. D. (2006) Evaluation of ASTM J initiation procedure using the EURO fracture data set. J. Test. Evaluat. 34, Wallin, K. (2007) Specimen size limitation in J-R curve testing standards versus reality. J. ASTM Int. 4(9) [paper ID: JAI100978]. Zhou, D. W., Xu, W. G. and Smith, S. D. (2009) R-Curve Modeling with Constraint Effect, Structural Integrity Technology Group, TWI Ltd, Cambridge, UK, Paper presented at 12th International Conference on Fracture, July 12-17, 2009, Ottawa, Canada. Abaqus/CAE - Dassault Systèmes. 10/4/2013. Wardle, G. (2002) A Study of Specimen Size Effects on the Initiation Toughness and Tearing Resistance of an A533B-1 Steel, in Small Specimen Test Techniques: Fourth Volume, ASTM STP 1418, Sokolov, M. A., Landes, J. D. and Lucas, G. E., Eds, ASTM International, West Conshohocken, PA. 17

18 Thank you Acknowledgements This work was supported by Rautaruukki Corporation, FIMECC Ltd. and the LUT/ENPI Project. The authors would like to thank all their coworkers for their contribution to the completion of this research work.