Determination Methods of Anisotropic Coefficient R-values of Sheet Metal and Its Evolution in Subsequent Yielding

doi:10.3901/JME.2022.06.091

Abstract

Abstract: The anisotropic coefficient R-value of cold rolled sheet metal is usually used as a constant to determine the anisotropic parameters of constitutive model. In order to improve the prediction accuracy of anisotropic constitutive model, the evolution of R-values must be considered. Taking low carbon steel plate as the research object, the applicable conditions and limitations of three existing methods for determining variable R-values are compared and analysed. On this basis, a reverse solution method for variable R-values is proposed, and the analytical models under the condition of quadratic function and exponential function are given. It is revealed that the significant difference of R-values calculated by different methods is caused by the calculation error of the slope of the strain curve. Considering the in-plane anisotropy of the sheet metal, based on the principle of equal plastic work, the evolution of R-values of DC04 with plastic work and angle is given. The results show that, for low carbon steel, the evolution law of R-values show a downward trend with the increase of uniaxial tensile plastic strain. In addition, the proposed method not only has high accuracy, but also has simple expression, which is more convenient for the secondary development and application of the constitutive model considering the anisotropic evolution in subsequent yielding.

Key words: cold rolled sheet metal, uniaxial tensile, anisotropic coefficient, anisotropy, constitutive model, subsequent yielding

CLC Number:

TG301

MU Zhenkai, ZHAO Jun, YU Gaochao, HUANG Xueying, SUN Honglei. Determination Methods of Anisotropic Coefficient R-values of Sheet Metal and Its Evolution in Subsequent Yielding[J]. Journal of Mechanical Engineering, 2022, 58(6): 91-100.

References

[1] HILL R. A theory of the yielding and plastic flow of anisotropic metals[J]. Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences，1948，193(1033)：281-297.
[2] BARLAT F，LIAN K. Plastic behavior and stretchability of sheet metals. Part I: A yield function for orthotropic sheets under plane stress conditions[J]. International Journal of Plasticity，1989，5(1)：51-66.
[3] HU W. Characterized behaviors and corresponding yield criterion of anisotropic sheet metals[J]. Materials Science & Engineering A，2003，345(1-2)：139-144.
[4] ARETZ H. A non-quadratic plane stress yield function for orthotropic sheet metals[J]. Journal of Materials Processing Technology，2005，168(1)：1-9.
[5] OHASHI Y，KAWASHIMA K，YOKOCHI T. Anisotropy due to plastic deformation of initially isotropic mild steel and its analytical formulation[J]. Journal of the Mechanics & Physics of Solids，1975，23(4-5)：277-294.
[6] 李群，金淼，邹宗园，等. 基于循环拉-压试验的混合硬化模型参数确定及模型应用[J]. 机械工程学报，2020，56(2)：63-68. LI Qun，JIN Miao，ZOU Zongyuan，et al. Parameter determination and application research of mixed hardening model based on cyclic tension-compression test[J]. Journal of Mechanical Engineering，2020，56(2)：63-68.
[7] 王海波，万敏，阎昱，等. 参数求解对屈服准则的各向异性行为描述能力的影响[J]. 机械工程学报，2013，49(24)：45-53. WANG Haibo，WAN Min，YAN Yu，et al. Effect of the solving method of parameters on the description ability of the yield criterion about the anisotropic behavior[J]. Journal of Mechanical Engineering，2013，49(24)：45-53.
[8] SAVOIE J，JONAS J J，MACEWEN S R，et al. Evolution of r-value during the tensile deformation of aluminium[J]. Textures & Microstructures，1995，23(3)：149-171.
[9] CHOI Y，HAN C S，LEE J K，et al. Modeling multi-axial deformation of planar anisotropic elasto-plastic materials, part I: Theory[J]. International Journal of Plasticity，2006，22(9)：1745-1764.
[10] BARLAT F，GRACIO J J，LEE M，et al. An alternative to kinematic hardening in classical plasticity[J]. International Journal of Plasticity，2011，27(9)：1309-1327.
[11] HU H. The strain-dependence of plastic strain ratio (r_m-value) of deep drawing sheet steels determined by simple tension test[J]. Metallurgical Transactions A，1975，6(4)：945-947.
[12] HU W. Constitutive modeling of orthotropic sheet metals by presenting hardening-induced anisotropy[J]. International Journal of Plasticity，2007，23(4)：620-639.
[13] STOUGHTON T B，YOON J W. Anisotropic hardening and non-associated flow in proportional loading of sheet metals[J]. International Journal of Plasticity，2009，25(9)：1777-1817.
[14] TRUSZKOWSKI W. Influence of strain on the plastic strain ratio in cubic metals[J]. Metallurgical and Materials Transactions A，1976，7(2)：327-329.
[15] XIE Q，VAN BAEL A，AN Y G，et al. Effects of the isotropic and anisotropic hardening within each grain on the evolution of the flow stress, the r-value and the deformation texture of tensile tests for AA6016 sheets[J]. Materials Science & Engineering A Structural Materials Properties Misrostructure & Processing，2018，721(1)：154-164.
[16] ZAMIRI A，POURBOGHRAT F. Characterization and development of an evolutionary yield function for the superconducting niobium sheet[J]. International Journal of Solids & Structures，2007，44(25)：8627-8647.
[17] ROSSI M，BROGGIATO G B，PAPALINI S. Application of digital image correlation to the study of planar anisotropy of sheet metals at large strains[J]. Meccanica，2008，43(2)：185-199.
[18] LIAN J，SHEN F，JIA X，et al. An evolving non-associated Hill48 plasticity model accounting for anisotropic hardening and r-value evolution and its application to forming limit prediction[J]. International Journal of Solids & Structures，2017，151(SI)：20-44.
[19] AN Y G，VEGTER H，MELZER S，et al. Evolution of the plastic anisotropy with straining and its implication on formability for sheet metals[J]. Journal of Materials Processing Technology，2013，213(8)：1419-1425.
[20] CHOI Y，WALTER M，LEE J，et al. Observations of anisotropy evolution and identification of plastic spin parameters by uniaxial tensile tests[J]. Journal of Mechanics of Materials & Structures，2006，1(2)：303-U133.
[21] SAFAEI M，LEE M G，ZANG S L，et al. An evolutionary anisotropic model for sheet metals based on non-associated flow rule approach[J]. Computational Materials Science，2014，81(1)：15-29.
[22] YOSHIDA F，HAMASAKI H，UEMORI T. Modeling of anisotropic hardening of sheet metals including description of the Bauschinger effect[J]. International Journal of Plasticity，2015，75(SI)：170-188.