Abstract At present, the analysis and interpretation of the bending response of isotropic elastic/plastic metallic materials is done based on the assumption that yielding and subsequent plastic deformation under tension and compression are the same. In this paper, we put into evidence analytically and verified through F.E. analyses that even a slight tension-compression asymmetry in yielding of isotropic pressure-insensitive materials leads to very specific behaviour under four-point bending. For this purpose, the isotropic version of Cazacu et al. [1] yield criterion is used. This yield criterion is pressure-insensitive, accounts for third-invariant effects, and involves a unique parameter k which depends solely on the ratio between the yield stress in simple tension and compression, σT/σC; k = 0 corresponding to the von Mises criterion. The theoretical analysis shows that for a material with σT σC yielding sets in at the top outer fiber. As the moment is further increased, a single plastic zone spreads into the cross section starting from the fiber where min (σT,σC) is first reached, the neutral axis being no longer located at the mid-height of the beam, but moving continuously during bending. If the applied load is sufficiently large, yielding also occurs at the other outer fiber and the plastic domain is comprised of two zones, one in tension and the other in compression. The extent of the plastic zones in tension and compression is not the same, namely the extent of each zone and the critical value of the moment when these two zones join being dictated by the tension-compression asymmetry ratio of the material. Most importantly, the stresses in the cross section during loading, and consequently the distribution of residual stresses that remain after unloading are completely different than in the case of a von Mises material. To the author's knowledge these features of the plastic response in bending, which are confirmed by F.E. analyses, have not been previously identified or reported.

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拉伸-压缩不对称对弯曲塑性响应的影响：新的理论和数值结果

摘要 目前，对各向同性弹塑性金属材料的弯曲响应的分析和解释是基于拉伸和压缩下的屈服和随后的塑性变形相同的假设进行的。在本文中，我们通过有限元分析证明并通过有限元分析验证了各向同性压力不敏感材料在屈服时即使轻微的拉压不对称也会导致四点弯曲下非常特殊的行为。为此，Cazacu 等人的各向同性版本。[1] 使用屈服准则。该屈服准则对压力不敏感，考虑了第三个不变量效应，并涉及一个独特的参数 k，该参数仅取决于简单拉伸和压缩中的屈服应力之比，σT/σC；k = 0 对应于 von Mises 准则。理论分析表明，对于具有 σT σC 的材料，屈服设置在顶部外纤维处。随着力矩的进一步增加，一个单一的塑性区扩展到从纤维开始的横截面中，首先达到 min (σT,σC)，中性轴不再位于梁的中间高度，而是连续移动弯曲过程中。如果施加的载荷足够大，则另一根外纤维也会发生屈服，塑性域由两个区域组成，一个处于拉伸状态，另一个处于压缩状态。拉伸和压缩塑性区的范围并不相同，即每个区的范围和这两个区连接的时刻的临界值由材料的拉压不对称比决定。最重要的是，加载过程中横截面的应力以及卸载后残留的残余应力分布与 von Mises 材料的情况完全不同。据作者所知，弯曲中塑性响应的这些特征已通过 FE 分析得到证实，但之前尚未发现或报告。