Thermally induced cracking occurs in many engineering problems such as drying shrinkage cracking of concrete, thermal shock induced fracture, micro cracking of two-phase composite materials etc. The computational simulation of such a fracture is complicated, but the use of phase-field models (PFMs) is promising as they can seamlessly model complex crack patterns like branching, merging, and fragmentation by treating the crack discontinuity as thin band of diffuse damage. Despite the success of phase-field models there are two major issues in previous PFMs of thermally induced fracture. Firstly, these models, which are mostly based on a PFM using a simple quadratic degradation function without any user-defined parameters, provide solutions that are sensitive to a length scale. Secondly, they are limited to brittle fracture only. As a solution, we extend the phase-field regularized cohesive zone model (PF-CZM) of Wu [JMPS, 103 (2017)], with a rational degradation function dependent on elasticity and fracture related material parameters, to thermoelastic solids. Furthermore, we present a monolithic BFGS algorithm to solve the three-field (displacements, phase-field and temperature) coupling equations altogether. Multiple thermally induced fracture problems, simulated within the framework of the finite element method, are presented with predictions in good agreement with previous findings and experiments. The proposed model is shown to give better performance in capturing the physics of thermally induced fracture: it provides length scale insensitive responses. And the monolithic solver is $4\sim 5$ times faster than the conventional alternating minimization solver.

热致裂纹发生在许多工程问题中，例如混凝土的干缩开裂，热冲击引起的断裂，两相复合材料的微裂纹等。这种裂缝的计算模拟很复杂，但是使用相场模型（PFM）很有希望，因为它们可以通过将裂纹的不连续性视为弥散性损伤的细带来无缝地模拟复杂的裂纹模式，例如分支，合并和破碎。尽管相场模型取得了成功，但以前的热致断裂PFM中仍然存在两个主要问题。首先，这些模型主要基于使用简单的二次退化函数而没有任何用户定义参数的PFM，提供了对长度比例敏感的解决方案。其次，它们仅限于脆性断裂。作为解决方案，我们扩展了相场正则化粘聚区模型（PF-CZMWu [JMPS，103（2017）]，具有取决于弹性和与断裂相关的材料参数的合理降解函数，以形成热弹性固体。此外，我们提出了一种整体式BFGS算法来求解三场（位移，相场和温度）耦合方程。在有限元方法的框架内模拟的多个热致裂缝问题的预测结果与先前的发现和实验吻合良好。所提出的模型在捕获热致断裂的物理特性方面表现出更好的性能：它提供了长度尺度不敏感的响应。整体求解器是$4〜5$ 比传统的交替最小化求解器快十倍。