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采用能描述非均质性的具有内部长度的梯度塑性理论推导了颈缩区域的非均匀的塑性拉伸应变。描述了颈缩区域的外形轮廓,并计算了当颈缩区域的体积保持不变时的颈缩区域的塑性伸长。由于外形轮廓已被确定,因而导出了真应力的表达式。目前得到的关于真应力-真应变曲线解析解的优越性在于:所需要的参数具有明确的物理意义,如:采用软化模量描述脆性;采用弹性模量描述弹性;采用特征长度描述材料的非均质性;模型中含有标定长度可用于研究结构的尺寸效应等。将目前得到的解析解与前人通过实验得到的钛及Ti-6Al-4V 的真应力-真应变曲线进行了对比,验证了本文考虑微小结构效应及局部化颈缩的真应力-真应变曲线的解析解。另外,还发现Ti-6Al-4V 的脆性及非均质性要高于商业纯钛。前人试验发现的局部化带在2 种材料内部的传播速度的差异可以通过它们具有不同的脆性得到解释。
The non-uniform plastic tensile strain of the necking region is deduced using an internally-lengthable gradient plastic theory that describes heterogeneity. Describes the contour of the necked area and calculates the plastic elongation of the necked area when the volume of the necked area remains constant. Since the contour has been defined, the true stress expression is derived. At present, the superiority of the analytic solution of true stress-true strain curve lies in that the required parameters have definite physical meanings, such as: using the softening modulus to describe the brittleness; using the elastic modulus to describe the elasticity; using the characteristic length to describe the material's non- Homogeneity; the model contains the calibration length can be used to study the size effect of the structure and so on. The analytical solutions obtained at present are compared with the true stress-strain curves of titanium and Ti-6Al-4V obtained by the predecessors, and the true stress-true strain curves of microstructure effects and localized necking are considered in this paper. Analytic solution. In addition, Ti-6Al-4V was also found to have higher brittleness and heterogeneity than commercial pure titanium. Differences in the rate of propagation of the localized bands within the two materials found by previous experiments can be explained by their different brittleness.