Strain limit dependence on stress triaxiality for pressure vessel steel

Transcription

1 Journal o Physics: Conerence Series Strain limit dependence on stress triaxiality or pressure vessel steel To cite this article: Y-C Deng et al 9 J. Phys.: Con. Ser View the article online or updates and enhancements. Related content - Considerations on stress triaxiality variation or P armor steel V Zichil, A Coseru, F Nede et al. - The inluence o gouge deects on ailure pressure o steel pipes N A Alang, N A Razak and M R Zuladli - Determination o Burst Pressure o API Steel Pipes using Stress Modiied Critical Strain Model N A Alang, N A Razak and A S Sulaiman This content was downloaded rom IP address on 3//18 at :4

2 Strain limit dependence on stress triaxiality or pressure vessel steel Yang-chun DENG 1, Gang CHEN, Xiao-eng YANG 1,Tong XU 1 Hubei Special Equipment Saety Inspection and Research Institute, No.35 Xudong St. Wuhan,China,4377 China Special Equipment Inspection and Research Institute, Beijing, China The corresponding author s deng_ych@16.com Abstract. In this paper, the ailure characteristics o pressure vessel materials were investigated, and measurement and analysis approaches or ductile racture strains were studied. Based on uniaxial tensile tests o notched round bar specimens, combined with inite element analyses and microscopic observations o racture surace, the relationships between the stress triaxiality actor and the ductile racture strain are proposed or three typical Chinese pressure vessel steels, 16MnR, Q35 and Cr18Ni9. The comparison o experimental racture strains with the multiaxial strain limit speciied in ASME Ⅷ- 7 shows that the strain limit criterion o ASME is suitable or carbon steels but not suitable or austenitic stainless steels or Chinese pressure vessel steels. To improve the calculation accuracy or racture strain o materials and to develop the strain limit criterion or Chinese pressure vessel materials, more experimental studies and numerical analyses on racture strain are necessary. 1. Introduction Based on many experimental results o material properties, Bridgman[1] concluded in 195 that the ductility o materials is related to the stress state and can be signiicantly improved by applying a higher pressure. In 1959, Davis and Connelly[] investigated the eect o the stress state on the racture strain o cylinders subject to internal pressure and tensile loads, and proposed the concept o stress triaxiality actor. In damage mechanics the stress triaxiality actor is a very important concept, deined as σ ( σ1 + σ + σ3) 3 m (1) TF = = σ ( σ σ ) + ( σ σ ) + ( σ σ ) where TF is the stress triaxiality actor, σ is the average stress,σ is the Mises m c 9 td 1

3 equivalent stress, σ1 σ 3 are the principal stresses. McClintock[3] in 1968, and Rice and Tracey[4] in 1969, investigated the mechanical mechanisms o the growth o a cylindrical hole and spherical hole respectively. In these two papers, they gave the quantitative relationship between the growth o holes and stress triaxiality actor, which are recognized as a milestone or the development o damage mechanics o materials. Void initiation, growth, and coalescence are three typical processes in the ductile racture o metal materials[5]. The racture strain o materials directly correlates with the critical size o voids. Hancock and Mackenzie[6], and Mackenzie[7] perormed uniaxial tension tests on the same batch o notched round bar specimens and carried out the microscopic and macromechanical analyses o the specimens with an assumption o uniorm stress and strain distributions at the notch root o the specimens. Experimental results showed that the equivalent stress dropped rapidly ater reaching a maximum value on the equivalent stress vs. equivalent strain curve. I unloading started immediately ater the maximum equivalent stress, cracks were observed rom microscopic analyses; i unloading started beore the maximum equivalent stress, discrete voids was observed. Thereore, the equivalent strain corresponding to the maximum equivalent stress was considered as the racture strain o materials. Macromechanical behaviour analyses showed that there existed a nonlinear relationship between the stress triaxiality actor and the racture strain, the bigger the stress triaxiality actor the smaller the racture strain was. Whether it is global plastic instability or local ductile racture, the ailure o materials is determined by the stress state o structures. The possibility or both ailure modes should be investigated in the prediction o the ailure mode o structures. In this paper, we present a pilot study on the ductile racture o pressure vessel materials by using three typical Chinese pressure vessel steels.. Specimens or ductile racture measurement o pressure vessel materials.1 Experimental specimens The ductile racture o materials oten occurs locally. Normally, the equivalent strain is used as a measurement o the ductility o materials, it is a material parameter related to the stress triaxiality actor but independent o specimens. Since the ductile racture under triaxial stress states is very complicated, there is no uniied conclusion made and no standard available or measuring the ductile racture strain o materials under triaxial stress states. The notched round bar tension specimen is simple, easy to test and can be used to obtain dierent stress triaxiality actors by changing the notch radius. Thereore, the tension test on the notched round bar has been widely employed by researchers as a standard method to develop the relationship o the stress triaxiality actor and the strain. Bridgman[1] made a milestone contribution to the stress analysis o notched round bar tension tests. He investigated the stress distribution o a round bar tension specimen near the neck beore racture. Bridgman s method has been widely used or the stress analysis o notched round bar tension specimens, oten reerred to as Bridgman notch specimens or the Bridgman model. In the Bridgman model, it was assumed that near the neck the specimen proile along the longitudinal direction was a circle-like shape with a diameter o R, the deormation o its cross section was uniorm with a radius o a, as shown in Fig.1. The centre o the round bar has the maximum stress triaxiality actor written as[1]

4 a R Fig.1 Diagram o the main dimensions at the neck o a Bridgman tension specimen σ m 1 a TFr = = = + ln + 1 () σ 3 R r = where a is the root radius o the notch, and R is the notch radius. With an assumption o uniorm stress and strain distributions at the cross section o the notch root, the eective strain and stress are written as ε = ln a (3) a P σ = (4) π a where ε is the eicient strain at the cross section o the notch root, a is the initial radius o the notch root beore loading, and a is the notch root radius changing with the tension load. In this paper, we employed notched round bar tension specimens to measure the equivalent strain o materials at ductile racture under triaxial stress states.. Materials o specimens Three typical pressure vessel materials were tested, 16MnR, Q35, and Cr18Ni9. The technical speciications and chemical compositions o the materials are listed in Table 1. Table 1 Speciication and chemical composition o specimens Element proportions by weight (%) Standard Material No. C Mn Si S P Ni Cr GB MnR GB6654 Q GB/T 437 Cr18Ni Six dierent notch radii were chosen:.5mm,.5mm, 1.mm, 1.5mm,.mm,.5mm and 3.mm. The root radius o the notched round bars was 4 mm. to 3 specimens were abricated or each size. 3

5 3. Experimental result analysis or ductile racture o pressure vessel materials The tension test was perormed with an MTS-88 tensile test machine under displacement controlled loading. The loading speed was.5mm/min, which was considered to be a quasic-static load, that is, the loading speed eect could be neglected[8,9]. In the test, the load was recorded, the change o the notch radius at the neck was measured by a horizontal extensometer and the length change o specimens was measured by a vertical extensometer. Since pressure vessel materials exhibit good ductility, plastic instability may still occur in a notched round bar tension test. Combined with experimental results, inite element analyses (FEAs) were used to investigate whether the ailure mode o the specimen was ductile racture. ANSYS 9., a commercial FE program, was used or all FEAs in this study. Due to the symmetry o the geometry, axisymmetric models with Plane8, an 8-node quadrilateral element type, were employed. The isotropic material with an isotropic hardening law was assumed. The arc-length method, large deormation and the Von Mises yield criterion are employed or stress and strain analyses. From notched round bar tension tests, we can directly obtain P Δ curves, where P is the tensile load and Δ is the radius reduction at the neck o specimens. Using Eqs (3) and (4), we can convert P Δ curves to equivalent stress and strain curves, σ ε. Based on FEA results rom the node o the outer surace at the neck, we can plot P Δ curves. Fig.(a) and Fig.(b) show the comparison o experimental and FEA P Δ curves or specimens with notch radius o.5mm and.mm respectively. No-notched round bar tensile tests were perormed on 3 specimens or each kind o material, and 3 true stress-strain curves were obtained or the same material. Thereore, three sets o material parameters corresponding to 3 true stress-strain curves o tensile test data were used in FEM analysis. In another words, , 1-5-1, and shown in Fig.(a) are FEM analysis results or notch radius.5mm corresponding to 3 sets o material parameters respectively, whereas 1--11, 1--1, and in Fig.(b) are results or notch radius.mm Specimen No. ls Specimen No. ls p (KN) Experiment FEM 1-5-1FEM FEM p (KN) 3 1 Experiment 1--11FEM 1--1FEM 1--13FEM Δ ( mm) (a) notch radius.5mm Δ( mm) (b) notch radius.mm Fig. Curves o P As shown in Fig.(a), the experimental curve at the earlier loading stage matches well with that rom FEAs, while the experimental curve at the late stage o loading drops much quicker than that rom FEAs. Due to the assumption o a continuous body in FEAs, the maximum value o P on FEA curves corresponds to the load at plastic instability. For 4

6 experimental specimens, the void initiation ater plastic deormation will reduce the real net cross-section area at the neck, resulting in a decrease o the load-carrying capacity o specimens. The maximum value o P on the experimental curve in Fig.(a) is less than that on the FEAs curve, that is, less than the load at plastic instability rom FEAs. In addition, value corresponding to maximum P rom test is less than that obtained rom FEAs. The reason that rom test is smaller is: during the test, beore sample met the plastic instability, ductile racture damage arising while lack o material ductility. Thereore, the ailure mechanism or the specimens with.5mm notch radius is ductile racture. Fig.(b) shows that the P Δ curve rom FEAs has a reasonable match with the experimental curve. The dierence between the experimental curve and the FEAs curve may come rom the real net cross-section area reduction at the neck due to the void initiation in the test, which cannot be considered via FEA unless damage mechanics is included in the model. value corresponding to maximum P rom test is close to that obtained rom FEAs. The two values went through a large plastic deormation process ater the maximum load, and the P curve rom the test and that rom inite element analyses are still very close, which indicates that plastic instability is reached irst beore the damage, that is the plastic instability ailure. Thereore, the ailure o the specimen with mm notch radius is plastic instability, and the experimental results rom this specimen cannot be used or ductile racture criterion studies. The optical microscopic images o the racture suraces or the two specimens are illustrated in Fig.3. Dimples are observed on the racture suraces o both specimens; these are evidence o voids beore racture. The dimple distribution o specimen with a notch radius o.5mm is very dense and linked together to orm cracks causing racture in materials; the dimple distribution o 1--1 specimen with a notch radius o.mm is relatively loose, their existence may only reduce the load-carrying capacity o materials, and the ailure o the specimen is plastic instability due to its insuicient strength. (a) 1μm (b) 1μm Fig.3 Detailed inspection o racture suraces o tensile specimens (a) notch radius.5mm (b) notch radius.mm 4. The relationship o stress triaxiality actor and strain under ductile racture Until now, although more studies are still required the Bridgman s approach is still a widely used method or calculating the equivalent strain (Eqs.(3)) and the stress triaxiality actor ( Eq. ()) in engineering applications. Using the approach described in Section 3 we investigated 5

7 the relationship o the stress triaxiality actor and the equivalent strain o materials under ductile racture by analysing more than 6 notched round bar tension tests and comparing them with FEA results. It was ound that, or 16MnR and Q35 specimens, the ailure mode was ductile racture when the notch radii o round bar specimens were less than or equal to 1.5mm, and the ailure mode o specimens was plastic instability when the notch radii o specimens were greater than 1.5mm; or Cr18Ni9 specimens, the ailure mode was ductile racture when their notch radii were less than or equal to.mm, and the ailure model was plastic instability when their notch radii were greater than.mm. By using the relationship o ε = A exp ( B TF), we obtained the relationships o the stress triaxiality actor and the equivalent strain under ductile racture or the three materials, as ollows: 16MnR: ε =.633 exp.51tf, 1.18 TF.53 ( ) Q35: ε = exp.813, 1.18 TF.53 Cr18Ni9: ε = exp.88,1. 1 TF.53 In ASME Ⅷ- 7[1] pressure vessel and boiler standard, the strain limit to protect against local ailure is introduced and written as : α sl 1 ε = ε u exp TF (5) 1+ m 3 where ε is the limiting triaxiality strain, i.e. the racture strain ε ; ε u is the uniaxial strain limit, i.e. racture strain ε which is the maximum value among, speciied u m s b elongation and speciied reduction area; is related with σ σ, or erritic steel, m =.6 ( 1 σ s σ b ) and α sl =., or austenitic stainless steel, m =.75 ( 1 σ s σ b ) and α sl =.6. Using Eq. (5), the racture strain under triaxiality stress states, ε, can be easily obtained rom a round bar uniaxial tension test by measuring σ s σ b, speciied elongation and speciied reduction area. To veriy the reliability o the strain limit, three materials, 16MnR, Q35 and Cr18Ni9, were investigated. For acilitating the comparison with experimental results, we rewrote the strain limit, Eq. 5, as ε αsl 1 ln = TF ε u 1+ m 3 (6) ε I the rewritten orm o the strain limit, Eq. (6), is plotted in the coordinates, ln ε u vs. α sl TF 13, then it is a straight line with a slope o -. Fig.4(a-c) show the comparison o 1+ m experimental results and Eq (6) or the three materials. As shown in Fig.4(a & b), the experimental curves o two erritic steels, 16MnR and Q35, are above the strain limit line deined by Eq.(6). That is, it is sae and conventional to use the strain limited speciied in ASME Ⅷ- 7 or 16MnR and Q35. Fig.4(c) shows that the experimental curve o Cr18Ni9, an austenitic material, is below strain limit line deined by Eq.(6). That is, it is not sae to use the strain limited speciied in ASME Ⅷ- 7 or Cr18Ni9. 5. Conclusion The notched round bar tension specimen can be used or the racture strain measurement o materials, but the ailure mode o specimens, such as plastic instability or ductile racture, should also be determined. Based on a large amount o experimental data rom notched round bar tension tests, combined with FEA results and microscopic observations o racture surace, the m 6

8 (a) TF 1 3 ln =.94 1/3 εu R =.944 εu -3-4 Experimental point ASME strain limit Fitting line o experiment =.87 1/3 εu (b) εu Experimental point ASME strain limit Fitting line o experiment TF 1 3 ε ln =.869 1/ 3 ε u R =.998 ln = / 3 εu (c) TF ln =.445 1/3 εu εu -3 Experimental point ASME strain limit Fitting line o experiment =.916 1/3 εu R = Fig.4 Strain limit rom experimental data and ASME strain criterion (a)16mnr (b) Q35 (c) SUS34 relationships between the stress trixaixlity actor and the strain under ductile racture or three steels commonly used in Chinese pressure vessel are proposed. The racture strains o 16MnR, Q35 and Cr18Ni9 were calculated rom the strain limit speciied in ASME Ⅷ- 7, and they were compared with experimentally measured ailure strains. It was ound that the strain limit criterion o ASME Ⅷ- 7 was sae and quite conservative or 16MnR and Q35 steel but not sae or Cr18Ni9 steel. Thereore, the 7

9 strain limit criterion o ASME Ⅷ- 7 can be used directly in carbon steels or Chinese pressure vessels, and more research will be needed beore the strain limit criterion is used or austenitic steels or Chinese pressure vessels. To improve the calculation accuracy o racture strains or dierent materials and to develop the strain limit criterion or Chinese pressure vessel materials, more experimental studies and numerical analyses on racture strain are necessary. The experimental principle, measurement method and analysis methods used in this study provided a oundation or urther studies on ductile racture o pressure vessel materials. Acknowledgments This paper is sponsored by the 11th Five-year China National Key Technology R&D Programme, No.6BAKB. Reerences [1] P.W.Bridgman, Studies in arge Plastic Flow and Fracture, First Edition,195 the McGraw-Hill Company,Inc. [] E.A.Davis and F.M.Connelly. Stress distribution and plastic deormation in rotating cylinders o strain-hardening material. Journal o Applied Mechanics, 1959,V6,No.1:5-3 [3] F.McClintockhe.A Criterion or Ductile Fracture by the Growth o Holes,Journal o Applied Mechanics,1968,35(): [4] J.R.Rice and D.M.Tracey.On the Ductile Enlargement o Voids in Triaxial Stress Fileds.Journal o the Mechanics and Physics o Solids,1969,17:1-17 [5] G.Mirone. Role o stress triaxiality in elastoplastic characterization and ductile ailure prediction. Engineering Fracture Mechanics,7,Vol.74: [6] J.Hancock and A.Mackenzie.On the mechanisms o ductile ailure in high-strength steels subjected to multi-axial stress-states. Journal o the Mechanics and Physics o Solids,1976,4: [7] A. Mackenzie J.W.Hancock D.K.Brown, On the Inluence o State o Stress on Ductile Failure Initiation in High Strength Steels, Engineering Fracture Mechanics, 1977,Vol.9: [8] O.S.Hopperstad T.Borvik et al. On the inluence o stress triaxiality and strain rate on the behaviour o a structural steel.part Ⅰ.Experiments. European Journal o Mechanics A/Solids, 3,:1-13 [9] T.Borvik O.S.Hopperstad T.Berstad. On the inluence o stress triaxiality and strain rate on the behaviour o a structural steel.part Ⅱ. Numerical stuy. European Journal o Mechanics A/Solids, 3,:15-3 [1] 7 ASME Boiler & Pressure Vessel Code,Ⅷ-Division,Alternative Rules, Rules or Construction o Pressure Vessels. 8