<p>Cohesive zone failure models are widely adopted to simulate fatigue crack propagation under cyclic loading. However, accumulative damage in the form of plastic strain induced by fatigue crack growth proposes an insurmountable challenge to the calibration of the models’ parameters. In this paper, we develop a simple method to extract these variables for any testing specimens. We extend the previously developed field projection method (FPM) to reconstruct the crack-tip interfacial tractions and separations from far-field elastic strain information provided by the experiment, at different loading stages during a single fatigue loading cycle, in the steady-state fatigue crack growth regime. We exploit in situ synchrotron X-ray diffraction to provide the high-resolution elastic strain mapping around the fatigue crack tip. Considering the reference material configuration to be at the end of each fatigue cycle where the material is fully unloaded, the deformation of the material within that specific cycle can then be treated as linear elastic. Therefore, the stress field can be calculated directly based on linear elastic constitutive law plane strain conditions. Additionally, the displacement field can be obtained by using the&nbsp;finite element B matrix (gradient of shape function)&nbsp;and applying the principle of superposition on the residual elastic strain. With the unknown tractions expressed in terms of a Fourier series, we can then extract the field projected traction coefficients from experimentally derived stress and displacement data. The corresponding separation distribution is determined by subsequently imposed the calculated traction in a finite element mesh subjected to the calculated boundary displacements. We successfully apply&nbsp;this method to construct the cohesive zone law for fatigue from the experimental neutron diffraction results for ZK60 Mg alloy. This material is fabricated by an extrusion process with a T5 temper condition. The samples are prepared with the loading direction parallel to the normal direction (ND) and extruded direction (ED) on the ED-ND plane. The experiment set up closely follows the procedure outlined by the American Society of Testing and Materials (ASTM). Four loading and three unloading levels are selected to measure the diffraction patterns by azimuthally averaging the ring pattern over ±5° with respect to the loading and crack growth direction using General Structure Analysis System (GSAS) II software. From the diffraction data, we find&nbsp;that the gradual increase of the applied stress levels leads to a progressively increased lattice strain field around the fatigue crack tip, and a reverse compressive residual stress zone at the crack tip is observed at a low load level. Applying FPM, we notice the traction rapidly increases from zero to reach a peak cohesive traction before decreases&nbsp;towards a constant traction value along the crack interface. Furthermore, at the same applied load, the unloading distribution profiles show a decrease in traction and increase in distribution compared to loading distribution profiles, which indicates a loss of stress carrying capacity, suggesting that FPM quantitatively captures the irreversible damage associated with fatigue even after a single loading and unloading cycle. Moreover, we overall observe a triangular cohesive shape over different loads in addition to the linear loading, bilinear unloading cohesive response across various material points along the crack-face. This response is notably different from 'Neumann’s linear elastic constant unloading', and 'linear unloading towards the origin' model. This result demonstrates the effectiveness of the proposed method which has notable engineering and micromechanics applications.</p>

Cohesive Zone Law for Fatigue Crack Growth in Magnesium Alloy

Paper Proceedings: https://asmedigitalcollection.asme.org/IMECE/IMECE2021/volume/85543

ASME 2021 International Mechanical Engineering Congress and Exposition (IMECE2021)

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