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.
Gradient-dependent plasticity having characteristic length reflecting heterogeneity was used to deduce analytically non-uniform plastic strain in necked zone, and the external shape of the zone was described because the plastic strain and the plastic extension of the zone regardless of change of volume of the zone was calculated. In addition, the true stress was deduced because the minimum sectional area in the zone can be determined according to the external shape. The advantage of the present analytical results for true stress and true strain curve is that the related parameters have specific physical meanings,such as softening modulus describing brittleness, elastic modulus considering elasticity, characteristic length reflecting the heterogeneity, the gauge length involved in the present model to study the geometrical size effect. Comparisons of the existing experimental results for titanium and Ti-6Al-4V and the present analytical results were carried out and the new model considering microstructures and localized necking was verified. It is found that the brittleness and heterogeneity of Ti-6Al-4V are higher than those of CP titanium. The differences of the propagation velocity of the localized band in two kinds of materials are explained in terms of the different brittleness.
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