The cohesive zone law represents the constitutive traction versus separation response along the crack-tip process zone of a material, which bridges the microscopic fracture process to the macroscopic failure behavior. Elucidating the exact functional form of the cohesive zone law is a challenging inverse problem since it can only be inferred indirectly from the far-field in experiments. Here, we construct the full functional form of the cohesive traction and separation relationship along the fracture process zone from far-field stresses and displacements using a physics-informed neural network (PINN), which is constrained to satisfy the Maxwell-Betti's reciprocal theorem with a reciprocity gap to account for the plastically deforming background material. Our numerical studies simulating crack growth under small-scale yielding, mode I loading, show that the PINN is robust in inversely extracting the cohesive traction and separation distributions across a wide range of simulated cohesive zone shapes, even for those with sharp transitions in the traction-separation relationships. Using the far-field elastic strain and residual elastic strain measurements associated with a fatigue crack for a ZK60 magnesium alloy specimen from synchrotron X-ray diffraction experiments, we reconstruct the cohesive traction-separation relationship and observe distinct regimes corresponding to transitions in the micromechanical damage mechanisms.

中文翻译：

---

使用物理信息神经网络的数值和实验裂纹尖端内聚区定律


内聚区定律表示沿材料裂纹尖端工艺区的本构牵引与分离响应，它将微观断裂过程与宏观失效行为联系起来。阐明内聚区定律的确切泛函形式是一个具有挑战性的逆问题，因为它只能在实验中从远场间接推断出来。在这里，我们使用物理信息神经网络 （PINN） 从远场应力和位移中构建沿断裂过程区的内聚牵引和分离关系的完整功能形式，该网络被约束以满足 Maxwell-Betti 倒易定理和互易间隙，以解释塑性变形的背景材料。我们模拟小规模屈服、模式 I 载荷下裂纹增长的数值研究表明，PINN 在逆向提取各种模拟内聚力区形状的内聚牵引和分离分布方面是稳健的，即使对于那些在牵引-分离关系中具有急剧过渡的那些也是如此。使用同步加速器 X 射线衍射实验中 ZK60 镁合金试样疲劳裂纹相关的远场弹性应变和残余弹性应变测量，我们重建了内聚牵引分离关系，并观察到与微机械损伤机制中的转变相对应的不同状态。