Experimental study of the plasticity responses of TRIP780 steel subjected to strain-path changes.
The work-hardening response of TRIP780 steel subjected to strain-path changes was investigated using two-stage tension experiments. Large specimens were prestrained and then sub-sized samples were subjected to tension along various directions. The influence of strain-path changes on flow stress and work hardening performance was discussed in detail. The specific plastic work was calculated to compare the kinematic hardening behaviour after strain-path changes. The results showed that transient hardening was observed for TRIP780 sheets subjected to orthogonal strain-path change. The strain-hardening exponent (n-value) was influenced by prestraining levels and the strain path. The n-value exhibited a greater decrease under an orthogonal strain-path change. Prestraining can delay the onset of high work hardenability of TRIP steels. It is meaningful for the safety design of vehicles.
CITATION: Yu, H., He, Z., and Shen, J., "Experimental Study of the Plasticity Responses of TRIP780 Steel Subjected to Strain-Path Changes," SAE Int. J. Mater. Manf. 9(3):2016.
The production of panels in the automotive industry often involves a series of forming processes that may result in large strains and complex strain-path changes. Some investigations have shown that strain-path changes can lead to macroscopic kinematic hardening behaviour on the stress-strain curve .
There have been many studies of the kinematic hardening behaviour of metals subject to strain-path changes, such as steels [2, 3, 4], copper alloys [5, 6, 7, 8, 9] and aluminium alloys [10, 11, 12, 13, 14]. Kinematic hardening is characterized by a number of phenomena under cyclic loading, such as the Bauschinger effect, cross effects, permanent softening and work-hardening stagnation . Tarigopula et al [15, 16]. concluded that isotropic hardening was insufficient to model the hardening behaviour of dual-phase steel subjected to strain-path changes. Barlat et al [10,17]. proposed a constitutive model to describe the plastic behaviour of materials subjected to multiple strain-path changes. Achani  concluded that non-linear isotropic hardening was sufficient to describe the hardening behaviour of prestrained aluminium alloys subject to strain-path changes. Kim et al.  performed a three-stage deformation in which sheets were prestrained in the rolling direction. Prestraining was then performed at several angles to the rolling direction, and tensile specimens were cut out and tested in various directions. Butuc et al . validated the hardening model of DC06 steel under linear and complex strain paths. Nagai et al . performed 2% prestraining on ferric steels. When the strain path was changed orthogonally, the re-yield stress was lowered and the work-hardening rate at low-plastic strain increased. Cetlin et al . found that the work-hardening characteristics of AISI 420 and 304 stainless steels were dependent on strain path. Sakharov et al . performed pure tension, rolling and rolling-tension strain-path sequences on brass sheets. The results indicated that strain-path change promotes the onset of premature twinning of brass. Boer et al . designed a new testing device for investigating the complex behaviour of sheet metals under non-proportional loading. Larsson et al . studied the kinematic hardening behaviour of two high-strength steels, Docol600DP and Docol1200M, through a series of tensile and shear tests. Zang et al . characterized both the anisotropy and the hardening behaviour of mild and dual-phase steel sheets under uniaxial tension, simple shear and balanced biaxial tension strain paths. Ha et al . studied the strain-hardening responses of DP780 and EDDQ steel sheets using a tension-tension test. A significant Bauschinger effect accompanied by a transient hardening behaviour after reverse loading was found for the DP780 steel. In contrast, EDDQ exhibited stress overshooting followed by strain-hardening stagnation.
It is well known that transformation-induced plasticity (TRIP) steels are different from other high-strength steels because of the TRIP effect. Therefore, much research has concentrated on the effect of the strain path on the forming limit diagram [28, 29, 30] and finite-element simulation [31, 32, 33, 34, 35]. Kulawinski  investigated the stress-strain curves of cruciform specimens of metastable austenitic cast stainless steel under biaxial planar loading. Spencer et al . investigated the influence of strain history on the mechanical properties of austenitic stainless steel that exhibits the TRIP effect. Carbonniere et al.  compared the kinematic hardening behaviour of aluminium alloy and TRIP steel using bending-unbending and simple shear. Mendiguren et al.  concluded that the elastic behaviour of TRIP steel does not depend on strain-path changes. This conclusion seems to be different from other published results.
In this study, the work-hardening response of a cold-rolled TRIP780 steel sheet subjected to strain-path changes was investigated with two-stage uniaxial tension tests. Large specimens were prestrained to six engineering strain levels. Sub-sized dog-bone samples were machined from the gauge section along various directions. The influence of prestrain and strain-path changes on the flow stress as well as the hardening response was studied in detail. The specific plastic work was also used to determine the kinematic hardening behaviour after the strain-path changes.
2. EXPERIMENTAL PROCEDURES
The material used in this work was an uncoated cold-rolled TRIP780 steel sheet of thickness 1.4 mm and chemical composition as shown in Table 1. The austenite content was about 6%.
2.2. Example Two-Stage Uniaxial Tension
Two-stage uniaxial tension was applied to the TRIP780 steel sheet. First, large specimens were uniaxially tensioned to different strain levels along the rolling direction. Then, from the uniform-deformation domain of the prestrained large specimens, sub-sized samples were cut along the rolling direction (0[degrees]), the transverse direction (90[degrees]) and at 45[degrees] to the rolling direction, as shown in Fig. 1. The sub-sized specimens were then uniaxially tensioned until fracture occurred.
The large specimens used in this study were 537 mm long and 190 mm wide, as shown in Fig. 1. The specimen gauge section was 320 mm long and 120 mm wide. These specimens were prestrained to six engineering strain levels: 4.16%, 5.83%, 6.94%, 8.3%, 10.0% and 14.6%. The dimensions of the sub-sized samples are shown in Fig. 2. A precise Epsilon extensometer was used to measure the strain. The uniaxial tension for the large specimens was applied at a constant speed of 3 mm [min.sup.-1] in an electric loading machine with a 200 kN load cell, while the uniaxial tension for the sub-sized specimens was applied in a Zwick electric loading machine with a 100 kN load cell.
To ensure that the sub-sized samples were cut from a domain where the strain distribution was as homogeneous as possible, the stress and strain fields of the large specimens were simulated with ABAQUS/Standard software. The specimen was meshed into more than 20000 shell elements. Enforced displacement was applied at the end of the specimen. The equivalent plastic strain distribution is shown in Fig. 1, from which it can be seen that the majority of the gauge domain was subjected to homogeneously distributed strain. Therefore, the subsequent sub-sized samples that were cut from there were believed to have the same prestrain. The thickness was measured using an ultrasonic thickness gauge PX-7 and the thickness variation was found to be negligible in that region.
3. RESULTS AND DISCUSSION
3.1. Influence of Prestraining on Flow Stress
True stress-strain curves of the as-received and prestrained TRIP780 specimens are shown in Figs. 3a-3g, in which 0[degrees], 45[degrees] and 90[degrees] indicate the angle between the length direction of the sub-sized samples and the rolling direction of the sheets. In Fig. 3a, the differences among the flow stresses of the three directions in the elastic-to-plastic transition region is very small. Since there is no typical yielding platform, the stress at 0.2% offset strain is regarded as the yield stress. However, in Figs. 3b-3g, there is a prominent difference among the flow stresses in the different directions, especially in the 90[degrees] curves. They have rounder corners than the other curves, which indicate the appearance of transient hardening behaviour in the early stage. The length of the transition region increases with the prestrain. This is ascribed to the effect of strain-path change on the dislocation . After the rounder corner, the difference in flow stress tends to diminish as the plastic deformation advances, regardless of the direction, as shown in Figs. 3b-3f. This demonstrates that the flow stress curves tend to converge. Tarigopula et al. [15-16] obtained similar results for dual-phase steels, and they attributed the specific differential hardening behaviour to deformation-induced residual stresses imparted to the ferrite and martensite during prestraining.
3.2. Work-Hardening Behaviour
The n-values are calculated according to ISO10275.According to the Hollomon's equation, one can easily obtain the following expression,
ln [sigma] = ln C+n ln [epsilon] (1)
Where [sigma] and [epsilon] represent the true stress and true strain. C is the strength coefficient and n is the strain hardening exponent. From the experimental stress-strain curves, the logarithmic true stress-strain curve can be obtained. The value of the slope of the logarithmic curve can be regarded as the n-value. From the ln[sigma]~ln[epsilon] curve, during the range from 1% to fracture strain each five points are selected and the n-value can be calculated with the following equation,
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)
Where [x.sub.i] and [y.sub.i] represent the coordinates of the points.
The strain-hardening exponent (n-value) of the prestrained specimens was measured according to the ASTM-E8 standard. As shown in Figs. 4a-4g, the n-value varies with the plastic strain instead of remaining constant during plastic deformation. It first increases with plastic strain until it reaches a peak point at some plastic strain. After that, it begins to decrease. Figure 4a indicates that the n-value of the asreceived sheet increases sharply at 0-0.05 strain, which indicates that the investigated TRIP steel has a favorable initial strain hardenability. The n-value is still larger than 0.2 before the strain reaches 0.18. This illustrates that TRIP steel not only has high initial work hardenability but also has high work-hardenability duration.
Compared with the as-received sheet, the n-value of the prestrained specimens changes with the plastic strain in a different way, as shown in Figs. 4b-4g. The peak point of the n-value curve is located in the right half of the curve rather than the left half. This indicates that the prestrained steels possess later high work hardenability; that is to say, the onset of high work hardenability is delayed. This behaviour should be taken into account in the design of automotive safety parts, such as bumpers, side rails and B-pillars. These parts are commonly manufactured by a variety of stamping processes and the sheets will experience different levels of prestrain. The prestrained steels will exhibit a delayed work-hardening response to an external collision, which is meaningful for vehicle safety if this enhancement is taken into account in the initial design.
Another point that needs to be noted is that the n-value varies with the strain path. In Fig. 4a, the n-values of the three directions are very close, especially in the 0[degrees] and 45[degrees] directions. In Fig. 4b, the differences among the n-values increase, and the curve of the 90[degrees] direction is higher than the one of 0[degrees] direction during the whole plastic deformation. In Fig. 4c, the n-values of the 45[degrees] and 90[degrees] directions decrease while that in the 0[degrees] direction is almost constant.
The n-value of the 90[degrees] direction exhibits the greatest decrease with increasing prestrain. In Fig. 4g, i.e. at 14.6% prestrain, the n-value curve in the 90[degrees] direction is far below that in the 0[degrees] direction. This demonstrates that the work hardenability of the TRIP steel not only varies with the prestrain but also changes with the strain path. The n-value exhibits a large decrease for an orthogonal strain path.
3.3. Specific Plastic Work
To compare the hardening curves after strain-path change, the variation of the true stress with the specific plastic work should be determined. The specific work is calculated using Eq.(3).
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)
where [[sigma].sub.eq] and [[epsilon].sub.eq] are the equivalent stress and strain, respectively. Figures 5a, 5b and 5c show the curves of true stress versus specific plastic work for specimens subjected to different prestrains in the 0[degrees], 45[degrees] and 90[degrees] directions. These curves are compared with the curve of the as-received sheet, which was tensioned along the rolling direction. In Fig. 5a, all of the curves are obtained in the rolling direction and no strain-path changes among them. There is almost no difference among the curves after yielding, regardless of the prestrain. Therefore, prestraining without strain-path change increases the flow stress at the same work-hardening rate as the previous deformation.
In Fig. 5b, the curves of true stress versus specific plastic work were obtained by subsequent tension along the 45[degrees] direction. The length direction of the sub-sized specimens are cut along the 45[degrees] direction with the rolling direction. So there is a 45[degrees] strain-path change between the two-stage tension. The curves of the prestrained sheets are above the monotonic curve (i.e. the curve of the as-received material). This illustrates that the material yields at a higher stress and then hardens at the same rate in the reloading process. Thereafter, the curves become parallel to the curve for monotonic tension, regardless of the prestrain.
In Fig. 5c, the curves of true stress versus specific plastic work were obtained by subsequent tension along the 90[degrees] direction. The length direction of the sub-sized specimens are vertical with the rolling direction. Thus, the strain path was changed orthogonally. This figure indicates that the material yields at a lower stress and then hardens at a higher rate compared with that for monotonic tension for all levels of prestrain. This is typical transient hardening behaviour. After this transient hardening period, all the curves except that for 14.6% prestrain tend to converge with the monotonic curve. The curve for 14.6% prestrain is below the monotonic curve, and the gap between them appears to increase with increasing specific plastic work. This softening phenomenon is not observed at the other prestraining levels.
1. Transient hardening is observed in TRIP780 steel subjected to an orthogonal strain path.
2. Strain-hardening performance is affected not only by prestrain but also by the strain path. The n-value exhibits its greatest decrease under an orthogonal strain path change.
3. Prestraining can delay the onset of high work hardenability of TRIP steels. It is meaningful for the safety design of vehicles.
[1.] Bouvier S, Alves J L, Oliveira M C, et al., Modeling of anisotropic work-hardening behavior of metallic materials subjected to strain-path changes, Comp. Mater. Sci., 2005, 32:301-315.
[2.] Vincze Gabriela, Barlat Frederic, Rauch Edgar F. et al. Experiments and modeling of low carbon steel sheet subjected to double strain path changes. Metall. Mater. Trans. A, 2013, 44(10): 4475-4479.
[3.] Yen-Ju Chen, Rong-Shean Lee, Jenn-Terng Gau. Formability evaluation by novel specimen designs in sheet metal forming with two-step strain paths. J. Eng. Manufacture, 2013, 227(1):144-152.
[4.] Gonzalez D., Kelleher J.F., da Fonseca J.Q, et al. Macro and intergranular stress responses of austenitic stainless steel to 90[degrees] strain path changes. Mater. Sci. Eng. A, 2012, 546: 263-271.
[5.] Schmitt J H, Fernandes J V, Gracio J J, et al. Plastic behavior of copper sheets during sequential tension tests. Mater. Sci. Eng. A, 1991, 147: 143-154.
[6.] Fernandes J V, Vieira M F. Strain distribution in copper tensile specimens prestrained in rolling. Metall. Mater. Trans. A, 1997, 28: 1169-1179.
[7.] Vieira M F, Fernandes J V. Plastic behavior of copper sheets subjected to a double strain-path change. J. Mater. Process. Technol., 1995, 47: 261-272.
[8.] Vieira M F, Fernandes J V, Chaparro B. Yield stress after double strainpath change. Mater. Sci. Eng. A, 2000, 284: 64-69.
[9.] Wejdemann C., Poulsen H.F., Lienert U., et al. In situ observation of the dislocation structure evolution during a strain path change in copper. JOM, 2013, 65(1): 35-43.
[10.] Barlat F, Duarte J M F, Gracio J J, et al. Plastic flow for non-monotonic loading conditions of an aluminum alloy sheet sample. Int. J. Plasticity, 2003, 19:1215-1244.
[11.] Khan A S, Pandey A, Stoughton T. Evolution of subsequent yield surfaces and elastic constants with finite plastic deformation. Part II: A very high work hardening aluminum alloy (annealed 1100 Al). Int. J. Plasticity, 2010, 26, 1421-1431.
[12.] Khan A S, Pandey A, Stoughton T. Evolution of subsequent yield surfaces and elastic constants with finite plastic deformation. Part III: Yield surface in tension-tension stress space (Al 6061-T 6511 and annealed 1100 Al). Int. J. Plasticity, 2010, 26, 1432-1441.
[13.] Yoshida F, Uemori T. A model of large-strain cyclic plasticity describing the Bauschinger effect and work hardening stagnation. Int. J. Plasticity, 2002, 18,661-686.
[14.] An Y.G.. Effect of strain path changes on strain hardening of 6082 aluminium alloy. Mater. Sci. Techn., 2013, 17(3), 249-257.
[15.] Tarigopula V, Hopperstad O S, Langseth M, et al. Elastic-plastic behavior of dual-phase, high-strength steel under strain-path changes. Eur. J. Mech. A: Solids, 2008, 27, 764-782.
[16.] Tarigopula V, Hopperstad O, Langseth M, et al. An evaluation of a combined isotropic-kinematic hardening model for representation of complex strain-path changes in dual-phase steel. Eur. J. Mech. A: Solids, 2009, 28: 792-805.
[17.] Barlat F, Gracio J J, Myoung-Gyu Lee, et al. An alternative to kinematic hardening in classical plasticity. Int. J. Plasticity, 2011, 27(9):1309-1327
[18.] Achani D. Constitutive models of elastoplasticity and fracture for aluminum alloys under strain path change. Doctoral Thesis. Dept. of Structural Engineering, Norwegian University of Science and Technology (NTNU), 2006, Trondheim.
[19.] Kim K H, Yin J J. Evolution of anisotropy under plane stress. J. Mech. Phys. Solids, 1997, 45 (5), 841-851.
[20.] Butuc M C, Teodosiu C, Barlat F, et al. Analysis of sheet metal formability through isotropic and kinematic hardening models. Eur. J. Mech. A: Solids, 2011, 30(4): 532-546.
[21.] Nagai Kensuke, Shinohara Yasuhiro, Tsuru Eiji, et al. Effect of strain path change and strain aging on anisotropic work-hardening behavior in ferritic steel. J. Iron Steel Inst. Jpn., 2012, 98(6):267-274.
[22.] Cetlin P R, Correa E C S, Aguilar M T P. The effect of the strain path on the work hardening of austenitic and ferritic stainless steels in axisymmetric drawing. Metall. Mater. Trans. A, 2003, 34(3):589-601.
[23.] Sakharov N A, Fernandes J V, Vieira M F. Strain path and workhardening behavior of brass. Mater. Sci. Eng. A, 2009, 507(1-2):13-21.
[24.] Boers S H A, Schreurs P J G, Geers M G D, et al. Experimental characterization and model identification of directional hardening effects in metals for complex strain-path changes. Int. J. Solids Struct., 2010, 47 :1361-1374.
[25.] Rikard Larsson, Oscar Bjoklund, Larsgunnar Nilsson, et al. A study of high strength steels undergoing non-linear strain paths-Experiments and modeling. J. Mater. Proc. Tech., 2011, 211:122-132.
[26.] Zang S L, Thuillier S, Le Port A, et al. Prediction of anisotropy and hardening for metallic sheets in tension, simple shear and biaxial tension. Int. J Mech. Sci., 2011, 53(5):338-347.
[27.] Jinjin Ha, Myoung-Gyu Lee, Frederic Barlat. Strain hardening response and modeling of EDDQ and DP780 steel sheet under non-linear strain path. Mechanics of Materials, 2013,64: 11-26.
[28.] Paul, Surajit Kumar.Theoretical analysis of strain- and stress-based forming limit diagrams. J Strain Anal. Eng., 2013, 48(3): 177-188
[29.] Gutierrez, David, Lara, A., Casellas, Daniel, et al. Effect of Strain Paths on Formability Evaluation of TRIP Steels. Adv. Mater. Res., 2010, 89(1):214-219.
[30.] Choi K, Soulami A, Liu W, et al., Loading Path Dependence of Forming Limit Diagram of a TRIP800 Steel, Int. J. Mater. Manuf., 2011, 4(1):75-83.
[31.] Hance, B.M. Strain path effects on the flow behavior of advanced high strength steels (AHSS). International Symposium on Transformation and Deformation Mechanisms in Advanced High-strength Steels, 42nd Annual Conference of Metallurgists of CIM, Vancouver, CA, Aug 24-27, 2003
[32.] Lee Jin-Woo, Lee Myoung-Gyu, Barlat, Frederic. Finite element modeling using homogeneous anisotropic hardening and application to spring-back prediction. Int. J. Plasticity. 2012, 29:13-41.
[33.] Toros S., Polat A., Ozturk F.. Formability and springback characterization of TRIP800 advanced high strength steel. Mater. Des., 2012, 41(10):298-305.
[34.] de Souza, T., Rolfe, B.F.Understanding robustness of springback in high strength steels. Int. J. Mech.Sci., 2013, 68(3): 236-245.
[35.] Geijselaers H. J. M., Hilkhuijsen P., Bor T. C., Modeling of the austenite-martensite transformation in stainless and TRIP steels. AIP Conference Proceedings. 2013, 1532(1): 175-182.
[36.] Kulawinski D, Nagel K, Henkel S, et al. Characterization of stress-strain behavior of a cast TRIP steel under different biaxial planar load ratios. Eng. Fract. Mech., 2011, 78(8):12-23.
[37.] Spencer K, Veron M, Yu-Zhang K, et al. The strain induced martensite transformation in austenitic stainless steels Part 1- Influence of temperature and strain History. Mater. Sci. Tech., 2009, 25(1):7-17.
[38.] Carbonniere J, Thuillier S, Sabourin F, et al. Comparison of the work hardening of metallic sheets in bending-unbending and simple shear. Int. J Mech. Sci., 2009, 51(2):122-130.
[39.] Mendiguren J., Cortes F., Galdos L., et al. Strain path's influence on the elastic behavior of the TRIP700 steel. Mater. Sci. Eng. A, 2013, 560: 433-438.
[40.] Kitayama K., Tome C.N., Rauch E.F., et al. A crystallographic dislocation model for describing hardening of polycrystals during strain path changes. Application to low carbon steels. Int. J. Plasticity, 2013, 46:54-69.
This project was supported by the National Natural Science Foundation of China under grants No. 51175382 and grant by the Fundamental Research Funds for the Central Universities (20113169).
HaiYan Yu, ZeZhen He, and JiaYi Shen
Table 1. Chemical composition of the TRIP780 steel in wt-% C Si Mn Mo Al 1.70 0.59 2.50 0.08 0.47
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|Author:||Yu, HaiYan; He, ZeZhen; Shen, JiaYi|
|Publication:||SAE International Journal of Materials and Manufacturing|
|Date:||Aug 1, 2016|
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