This paper presents a multi-temporal series high-accuracy numerical manifold method (NMM) for fracture analysis of solid materials under highly time-dependent thermal loadings. In the present method, the framework of NMM is used to perform space discretization of the thermo-mechanical coupling system, due to its advantages in accurately calculating field variables and describing discontinuity. An explicit direct integration scheme based on the precise time step integration method (or PTSIM scheme for short) is constructed for discretization in the time domain. In the present PTSIM scheme, the time-dependent thermal loadings are expressed by means of the basic function in a polynomial form. Highly accurate calculation of the response matrix for the load item is achieved by introducing the exponential transfer matrix. The results of stability, error and convergence analyses indicate that the proposed method is unconditionally stable and convergent. The superior advantages of present method are firstly verified by one example for transient thermal analysis, then four numerical examples with different time-dependent thermal boundary conditions and crack configurations are used for fracture analysis. The results show that the present method is unconditionally stable and time-independent, and high-accuracy can be achieved even for highly time-dependent thermal loadings and large time-step sizes.

本文提出了一种多时间序列高精度数值流形方法 (NMM)，用于在高度依赖于时间的热载荷下对固体材料进行断裂分析。在本方法中，NMM 的框架被用于对热-机械耦合系统进行空间离散化，因为它在精确计算场变量和描述不连续性方面具有优势。构建了基于精确时间步长积分方法（或简称PTSIM 方案）的显式直接积分方案，用于时域离散化。在当前的 PTSIM 方案中，与时间相关的热载荷通过多项式形式的基本函数表示。载荷项响应矩阵的高精度计算是通过引入指数传递矩阵实现的。稳定的结果，误差和收敛性分析表明所提出的方法是无条件稳定和收敛的。首先通过一个瞬态热分析算例验证了本方法的优越性，然后利用四个具有不同瞬态热边界条件和裂纹配置的数值算例进行断裂分析。结果表明，本方法无条件稳定且与时间无关，即使对于高度依赖于时间的热载荷和大时间步长，也可以实现高精度。然后使用具有不同瞬态热边界条件和裂纹配置的四个数值示例进行断裂分析。结果表明，本方法无条件稳定且与时间无关，即使对于高度依赖于时间的热载荷和大时间步长，也可以实现高精度。然后使用具有不同瞬态热边界条件和裂纹配置的四个数值示例进行断裂分析。结果表明，本方法无条件稳定且与时间无关，即使对于高度依赖于时间的热载荷和大时间步长，也可以实现高精度。