Abstract The plastic bending of a sheet metal having tension/compression asymmetry was investigated in this work with AZ31B Mg sheets, particularly focused on its deformation behavior. With the assumptions of pure bending and rigid plasticity, analytic expressions were obtained to describe sheet bending under the plane strain condition, taking into account the movement of the neutral surface and the associated deformation histories of longitudinal fibers in the sheet. Mechanical properties associated with bending such as anisotropy, work hardening in tension and compression, and untwinning under compression-tension were characterized considering the intricate hardening nature of AZ31B Mg sheet at room temperature. With the material coefficients characterized, the analytical expressions of bending were solved incrementally by numerical procedures. The computed thicknesses were compared to the thicknesses of V-die bending tests for validation purposes. It was found that the bending formulation reflecting the tension/compression asymmetry of AZ31B Mg sheet predicts the thickness increase at the initial stage of bending numerically, in agreement with the experimental results. Besides, the thickness variation during bending was found to be significantly affected by the asymmetric R-values of AZ31B Mg sheet. These results were discussed in connection with the movement of the neutral surface, as well as the material asymmetry in tension and compression.

中文翻译：

---

具有拉伸/压缩不对称性的金属板塑性弯曲

摘要 在这项工作中使用 AZ31B 镁板研究了具有拉伸/压缩不对称性的金属板的塑性弯曲，特别关注其变形行为。在纯弯曲和刚性塑性的假设下，考虑到中性表面的运动和板中纵向纤维的相关变形历史，获得了描述平面应变条件下板弯曲的解析表达式。考虑到 AZ31B 镁板在室温下的复杂硬化性质，表征了与弯曲相关的机械性能，例如各向异性、拉伸和压缩加工硬化以及压缩拉伸下的解孪。随着材料系数的表征，弯曲的解析表达式通过数值程序逐步求解。为验证目的，将计算出的厚度与 V 型模具弯曲测试的厚度进行比较。结果表明，反映 AZ31B 镁板拉伸/压缩不对称性的弯曲公式在数值上预测了弯曲初始阶段的厚度增加，与实验结果一致。此外，发现弯曲过程中的厚度变化受 AZ31B Mg 板的不对称 R 值的显着影响。这些结果与中性表面的运动以及材料在拉伸和压缩中的不对称性有关。结果表明，反映 AZ31B 镁板拉伸/压缩不对称性的弯曲公式在数值上预测了弯曲初始阶段的厚度增加，与实验结果一致。此外，发现弯曲过程中的厚度变化受 AZ31B Mg 板的不对称 R 值的显着影响。这些结果与中性表面的运动以及材料在拉伸和压缩中的不对称性有关。结果表明，反映 AZ31B 镁板拉伸/压缩不对称性的弯曲公式在数值上预测了弯曲初始阶段的厚度增加，与实验结果一致。此外，发现弯曲过程中的厚度变化受 AZ31B Mg 板的不对称 R 值的显着影响。这些结果与中性表面的运动以及材料在拉伸和压缩中的不对称性有关。