On the onset of necking in the tensile test
On the onset of necking in the tensile test
复制标题
DOI：
10.1016/j.ijplas.2003.05.004
复制
发表时间：
2004-04
影响因子：
9.8
通讯作者：
K. S. Havner
中科院分区：
文献类型：
--
作者：
K. S. Havner
在拉伸试验中研究（多晶）棒材的颈缩时，考虑了宏观材料特性中非常小的不均匀性。采用简单的一维模型（即仅沿着杆的长度发生空间变化），相应地，随着载荷的增加，横截面积的不均匀性的演变（直至最大值）也很小。不均匀性由随位置略有变化的单个模量表示，但始终具有相同的无量纲形式的应力-应变曲线。导出了一个超越方程，将最弱和最强部分的应变与其各自的材料强度联系起来。结果表明，在众所周知的 Considère 应变（对应于最大载荷）下，最小截面处的面积减小仅略大于最强截面处的面积减小，但其随后者应变的变化率是无穷大。因此，该分析给出了颈缩快速增加的理想化表示，颈缩通常是由实验中的最大负载引起的。在扩展附录中，对理论上均质材料棒的传统情况进行了审查和重新分析，包括考虑速率依赖性。
A very small inhomogeneity in macroscopic material properties is considered for the investigation of necking of a (polycrystalline) bar in the tensile test. A simple, one-dimensional model is adopted (i.e. spatial variation only along the bar's length), corresponding to which the evolving nonuniformity of cross-sectional area with increasing load, up to the maximum, also is small. The inhomogeneity is represented by a single modulus varying slightly with position, but with the same dimensionless form of the stress–strain curve throughout. A transcendental equation is derived that relates the strains at the weakest and strongest sections to their respective material strengths. It is shown that, at the well known Considère strain (corresponding to the maximum load), the decrease in area at the minimum section is only a little greater than at the strongest, but its rate of change with the latter strain is infinite. The analysis thus gives an idealized representation of the rapid increase in necking that typically ensues from the maximum load in experiments. In an extended Appendix the traditional case of a bar of theoretically homogeneous material is reviewed and reanalyzed, including consideration of rate-dependence.