材料期刊网

基于多晶体黏塑性自洽方法, 建立了金属板材的Lankford 系数(r值)、屈服应力和屈服面的计算模型. 以fcc多晶体为例, 模拟分析了理想织构组分对宏观各向异性的影响. 模拟结果表明, 具有Cube和Goss织构的板材, 其r值在45°附近最小, Cube织构的r值具有对称性, 而Goss织构90°的r值远大于0°的r值; 具有Cu, Bs和S织构的板材, 其最大r值均出现在45°附近, 0°和90°的r值均具有一定的不对称性. 各理想织构的单轴拉伸屈服应力呈现出与^r值相对应的变化规律, 屈服面的形状也表现出相应的变化. 上述模拟结果与Taylor--Bishop--Hill (TBH) 模型以及唯象方法的计算结果定性符合.

The macroscopic anisotropies, which are caused primarily by crystallographic textures, have significant effects on the formability of metal sheets and were extensively investigated experimentally and theoretically. Among the numerous theoretical investigations, the phenomenological approach is based on the classical theory of plasticity, in which the plastic behavior of metals is assumed to be well described by analytical functions proposed by Hill, Hosford and Barlat etc.. Because of its simplicity, the phenomenological approach is widely used in finite element method for plastic forming analysis, but this method lacks direct connection between textures and the revealed anisotropies. An alternative is the Taylor--Bishop--Hill (TBH) model which adopts the crystal plastic theory and explicitly takes the crystallographic textures into account, and thus can be used to analyze the anisotropic phenomena on a physical basis. However, implementation of the TBH model into the analysis of industrial forming process is a real tedious task, needing large amount of computational skill and computer resources. Besides, the TBH polycrystalline model does not satisfy the stress equilibrium condition between grains. The viscoplastic self--consistent (VPSC) model for polycrystalline is also a crystal plastic scheme, but it satisfies both strain compatibility and stress equilibrium conditions. In this study, mathematical models for the Lankford coefficient (r value), uniaxial tensile yield stress and yield locus were established based on the polycrystalline VPSC scheme. The effects of ideal crystallographic textures on the macroscopic anisotropy of fcc materials were analyzed. The results show that the minimum r values of Cube and Goss textures appear at an angle of about 45° from the rolling direction (RD), the r values of Cube at 0° and 90° are both approximately equal to unity whereas the r value of Goss at 90° is much higher than that of 0°. For the Cu, Bs and S textures, their maximum r values appear at the angle of about 45° from RD, and their r values of 0° and 90° present some asymmetries. The uniaxial tensile yield stresses of these ideal textures exhibit corresponding characteristics to their r values and the shape of yield locus also varies accordingly. The simulation results are in agreement qualitatively with those of TBH model and phenomenological theory.