In this paper, the influence of plasticity graded property and thermal boundary conditions have been investigated on the fracture parameter, i.e. J-integral using the extended finite element method. A complete computational methodology has been presented to model elasto-plastic fracture problems with geometrical and material nonlinearities. For crack discontinuity modeling, a partition of unity enrichment concept was employed with additional mathematical functions like Heaviside and branch enrichment for crack discontinuity and stress field gradient, respectively. The modeling of the stress–strain relationship of the material is implemented using the Ramberg–Osgood material model and geometric nonlinearity is modeled using an updated Lagrangian approach. The isotropic hardening and von-Mises yield criteria are considered to check the plasticity condition. The elastic predictor–plastic corrector algorithm is employed to capture elasto-plastic stress in a cracked domain. The variation in plasticity properties for plastically graded material is modeled by exponential law. Furthermore, the nonlinear discrete equations are numerically solved using a Newton–Raphson iterative scheme. Various cracked problem geometries subjected to thermal (adiabatic and isothermal conditions) and thermo-mechanical loads are simulated for stress contours and J-integrals using the elasto-plastic fracture mechanics approach. A comparison of the results obtained using extended finite element method with literature and the finite element analysis (FEA) package shows the accuracy and effectiveness of the presented computational approach. A component-based problem, i.e. a Brazilian disc subjected to thermo-mechanical loading, has been solved to show the adaptability of this work.

本文研究了塑性梯度性能和热边界条件对断裂参数J的影响。-使用扩展有限元方法的积分。已经提出了一种完整的计算方法来对具有几何和材料非线性的弹塑性断裂问题进行建模。对于裂纹不连续性建模，采用了单元富集概念的分区，并分别使用了其他数学函数，例如Heaviside和分支富集，分别用于裂纹不连续性和应力场梯度。使用Ramberg-Osgood材料模型对材料的应力-应变关系进行建模，并使用更新的Lagrangian方法对几何非线性进行建模。考虑各向同性硬化和von-Mises屈服准则来检查塑性条件。弹性预测器-塑性校正器算法用于捕获裂纹域中的弹塑性应力。塑性梯度材料的塑性特性变化是通过指数定律建模的。此外，使用牛顿-拉夫森迭代方案对非线性离散方程进行数值求解。模拟了应力（等温和等温条件）和热机械载荷作用下的各种裂纹问题几何形状的应力轮廓和使用弹塑性断裂力学方法进行J积分。使用扩展有限元方法与文献以及有限元分析（FEA）软件包所获得的结果进行了比较，结果表明了所提出的计算方法的准确性和有效性。解决了基于组件的问题，即承受热机械载荷的巴西圆盘，以显示这项工作的适应性。