Because of the presence of second-phase particles or nanoscale particles, a term of threshold stress incorporated into the power-law creep model of some materials, such as magnesium, aluminum, and chromium alloys. The estimation of the creep crack-tip stress field for these materials is notably important to facilitate their exploitation in high-temperature structures. In the present work, a two-term asymptotic expansion of the stress field is developed to predict the creep crack-tip stress field for power-law creep materials with threshold stress. The finite element method is used to verify the accuracy of the two-term asymptotic expansion of the stress field. The simulation results reveal that the two-term asymptotic expansion of the stress field is accurate enough as an engineering method in estimating the creep crack-tip stress field. In addition, the existing estimation method of the time-dependent C-integral of C(t) can be directly implemented in power-law creep materials with threshold stress.

由于存在第二相颗粒或纳米级颗粒，因此将阈值应力这一术语合并到某些材料（例如镁，铝和铬合金）的幂律蠕变模型中。这些材料的蠕变裂纹尖端应力场的估计对于促进其在高温结构中的开发非常重要。在目前的工作中，应力场的两个项渐近扩展被开发出来，以预测具有阈值应力的幂律蠕变材料的蠕变裂纹尖端应力场。有限元方法被用来验证应力场的二项渐近展开的准确性。仿真结果表明，作为估计蠕变裂纹尖端应力场的一种工程方法，应力场的两阶段渐进扩展是足够准确的。Ç -积分的Ç（吨）可在幂律蠕变材料直接执行与阈值的应力。