A weak interface model with a predefined traction-separation relationship (denoted as the cohesive zone law), when embedded in a bulk solid, is oftentimes adopted to simulate the crack advancement and thus determine the crack resistance under either monotonic or cyclic loading conditions. To-date, various types of loading-unloading irreversibility and hysteresis are only presumed in the cohesive zone law for fatigue crack growth, but without any direct determination from experimental measurements. Using a fine-grained Mg alloy and synchrotron X-ray diffraction (S-XRD) measurements with a sub-millimeter beam, in situ lattice strain mapping can be obtained with the needed resolution to cover both the “messy” process zone as modeled by the cohesive zone law and the “clean” process zone caused by plastic deformation. We extend our previously developed nonlinear field projection method, and create trial elastic fields from the S-XRD-measured elastic strain fields at different loading levels when choosing the fully unloaded state as the new reference. From the Maxwell-Betti's reciprocal theorem, we reconstruct a mechanistic cohesive zone law for fatigue cracks, where the reciprocity gap is governed by the residual stress field at the fully unloaded state. Combining our inverse approach with S-XRD measurements, it is discovered that the fatigue-crack cohesive zone exhibits a bilinear unloading and reloading behavior that is distinctively different than all prior works. This particular form suggests the origin of irreversibility be primarily from crack-surface oxidation and the hysteresis from dislocation plasticity in surrounding grains.

中文翻译：

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疲劳裂纹的机械内聚区定律：非线性场投影和原位同步加速器 X 射线衍射 （S-XRD） 测量


当嵌入块状固体中时，通常采用具有预定义牵引-分离关系的弱界面模型（表示为内聚区定律）来模拟裂纹进展，从而确定单调或循环载荷条件下的抗裂性。迄今为止，各种类型的加载-卸载不可逆性和磁滞仅在内聚区定律中假设为疲劳裂纹扩展，而没有通过实验测量直接确定。使用细晶粒镁合金和同步加速器 X 射线衍射 （S-XRD） 和亚毫米光束进行测量，可以获得具有所需分辨率的原位晶格应变映射，以覆盖由内聚区定律建模的“杂乱”工艺区和由塑性变形引起的“干净”工艺区。我们扩展了之前开发的非线性场投影方法，并在选择完全卸载状态作为新参考时，从 S-XRD 测量的不同载荷水平的弹性应变场创建试验弹性场。根据 Maxwell-Betti 倒易定理，我们重建了疲劳裂纹的机理内聚区定律，其中倒易间隙由完全卸载状态下的残余应力场控制。将我们的逆向方法与 S-XRD 测量相结合，发现疲劳裂纹内聚区表现出双线性卸载和重新加载行为，这与之前的所有工作都截然不同。这种特殊形式表明不可逆性的起源主要是由于裂纹表面氧化和周围晶粒中位错塑性的滞后。