As surface cracks may cause potential failure for engineering structures, it is of vital significance to carry out the fracture assessment for cracked structures. The crack driving force in the form of -integral is an important input parameter in fracture assessment. This paper focuses on the determination of -integral for surface cracked plates under biaxial loading. A method for predicting the -integral based on the deep neural network (DNN) is proposed to estimate -integral efficiently and accurately. Firstly, extensive three-dimensional (3D) elastic–plastic finite element (FE) analysis is conducted to compute the -integral along the crack front for developing a FE -integral datasets containing 1600 cases. Various crack aspect ratios, crack depth ratios, strain hardening exponents, ratios of the loading perpendicular to the crack plane to yield stress, and biaxial ratios, are strategically considered. Secondly, DNN models for predicting the -integral are constructed and trained according to the obtained datasets by FE analysis. Then, the evaluation criteria for DNN models and the grid search method are utilized to determine the optimal DNN model structure. Finally, test cases are employed to verify the feasibility and prediction accuracy of the determined DNN model. Based on validation results, the determined DNN model exhibits sufficiently accurate prediction performance. This research provides an idea for engineering applications, through building software based on continuously optimized DNN models, the -integral for surface cracked plates under biaxial loading can be accurately and efficiently predicted for performing fracture assessments.

中文翻译：

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基于深度神经网络的双轴载荷下表面裂纹板 J 积分预测方法

由于表面裂纹可能导致工程结构潜在失效，因此对裂纹结构进行断裂评估具有重要意义。 -积分形式的裂纹驱动力是断裂评估中的重要输入参数。本文重点研究双轴加载下表面裂纹板的β积分的确定。提出一种基于深度神经网络（DNN）的β积分预测方法，以高效、准确地估计β积分。首先，进行广泛的三维 (3D) 弹塑性有限元 (FE) 分析来计算沿裂纹前沿的 积分，以开发包含 1600 个案例的 FE 积分数据集。策略性地考虑了各种裂纹纵横比、裂纹深度比、应变硬化指数、垂直于裂纹平面的载荷与屈服应力的比率以及双轴比。其次，根据有限元分析获得的数据集构建和训练用于预测积分的DNN模型。然后，利用DNN模型的评价标准和网格搜索方法来确定最佳的DNN模型结构。最后利用测试用例验证所确定的DNN模型的可行性和预测精度。根据验证结果，确定的 DNN 模型表现出足够准确的预测性能。该研究为工程应用提供了思路，通过构建基于不断优化的DNN模型的软件，可以准确、高效地预测双轴加载下表面裂纹板的积分，以进行断裂评估。