Over the past few decades, the phase-field method for fracture has seen widespread appeal due to the many benefits associated with its ability to regularize a sharp crack geometry. Along the way, several different models for including the effects of pressure loads on the crack faces have been developed. This work investigates the performance of these models and compares them to a relatively new formulation for incorporating crack-face pressure loads. It is shown how the new formulation can be obtained either by modifying the trial space in the traditional variational principle or by postulating a new functional that is dependent on the rates of the primary variables. The key differences between the new formulation and existing models for pressurized cracks in a phase-field setting are highlighted. Model-based simulations developed with discretized versions of the new formulation and existing models are then used to illustrate the advantages and differences. In order to analyze the results, a domain form of the J-integral is developed for diffuse cracks subjected to pressure loads. Results are presented for a one-dimensional cohesive crack, steady crack growth, and crack nucleation from a pressurized enclosure.

翻译：近几十年来，断裂相场方法因能够对尖锐裂缝几何进行正则化处理而广受青睐，其相关优势众多。在此过程中，已发展出多种考虑裂缝面压力荷载效应的模型。本研究探讨了这些模型的性能，并将其与一种相对新颖的裂缝面压力荷载纳入公式进行对比。研究表明，该新公式既可通过修改传统变分原理中的试验空间获得，也可通过假设一个依赖于主要变量率的新泛函得到。本文重点阐述了新公式与现有加压裂缝相场模型之间的关键差异。随后，利用新公式与现有模型的离散化版本开展基于模型的模拟，以展示其优势与区别。为分析结果，本文针对承受压力荷载的弥散裂缝推导了J积分的域形式。研究结果涵盖了单内聚裂缝、稳态裂缝扩展以及加压腔体内裂缝萌生等案例。