# A Method for Calculating Residual Strength of Crack Arrest Hole on Tungsten-Copper Functionally Graded Materials by Phase-Field Gradient Element Combined with Multi-Fidelity Neural Network

## TL;DR

This paper introduces a new computational method to assess the residual strength of tungsten-copper graded materials after crack arrest hole drilling.

## Contribution

The novelty lies in combining phase-field gradient elements with a multi-fidelity neural network to improve crack modeling accuracy.

## Key findings

- Gradient finite elements provide smoother transitions in stress and damage fields compared to conventional elements.
- The Miehe decomposition scheme better captures complex crack paths than the Amor model.
- The method improves residual strength prediction accuracy by 39.07% to 44.05%.

## Abstract

This study develops a computational framework for evaluating the residual strength of tungsten-copper functionally graded materials following crack-arrest hole drilling. The proposed methodology features two pivotal innovations: First, a phase-field isoparametric gradient elements is established through representing the gradient effect within the finite element stiffness matrices, incorporating both Amor and Miehe elastic energy decomposition schemes to address tension-compression asymmetry in crack evolution. Second, a multi-fidelity neural network strategy is integrated with the gradient phase-field element to mitigate characteristic length dependency in residual strength predictions. Comparative analyses demonstrate that the gradient finite element achieves smoother field transitions at element interfaces compared to conventional homogeneous elements, as quantified in both stress and damage fields. The Miehe decomposition scheme outperforms the Amor model in capturing complex crack trajectories. Validation against the average strain energy criterion indicates the present approach enhances residual strength prediction accuracy by 39.07% to 44.05%, establishing a robust numerical tool for damage tolerance assessment in graded materials.