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Abstract

The stress-strain state analysis near the crack tip in a power-law material under mixed-mode loading conditions is investigated. By the use of the eigenfunction expansion method the stress-strain state near the mixed-mode crack tip under plane stress conditions is found. The type of the mixed-mode loading is specified by the mixity parameter, which varies from 0 to 1. The value of the mixity parameter corresponding to a mode II crack loading is equal to 0, whereas the value corresponding to a mode I crack loading is equal to 1. It is shown that the eigenfunction expansion method results in a nonlinear eigenvalue problem. The numerical solutions of the nonlinear eigenvalue problems for all values of the mixity parameter and for all practically important values of the strain hardening (or creep) exponent are obtained. It is found that mixed-mode loading of the cracked plate gives rise to a change in the stress singularity in the vicinity of the crack tip. Mixed-mode loading of the cracked plate results in new asymptotics of the stress field, which is different from the classical Hutchinson-Rice-Rosengren (HRR) stress field. The approximate solution of the nonlinear eigenvalue problem is obtained by a perturbation theory technique (artificial small parameter method). In the framework of the perturbation theory approach, a small parameter representing the difference between the eigenvalue of the nonlinear problem and the undisturbed linear problem is introduced. The asymptotic analysis carried out shows clearly that the stress singularity in the vicinity of the crack tip changes under mixed-mode loading in the case of plane stress conditions. The angular distributions of the stress and strain components (eigenfunctions) in the full range of values of the mixity parameter are given. The authors would like to acknowledge the financial support of the Russian foundation of basic research, project 13-01-97009-a.

Extraction of Fracture Mechanics Parameters From Fem Analysis: Algorithms and Procedures

“…P is the applied load, S is loading span in the SCB specimen, a is crack length, α is crack inclination angle. The semi-circular bend specimen subjected to three-point bending has received much attention in recent years for measuring the mixed mode I/II fracture resistance [16][17][18][19]. In this work, 2D FEA of semidisks with vertical crack and inclined notches is carried out using Abaqus software.…”

“…Thus, the determination of SIF still raises questions. The determination of higher order coefficients requires more accurate approaches [14][15][16][17][18][19][20][21][22][23][24].…”

Improving the Sensitivity of the Mechanoluminescence Composite through Functionalization for Structural Health Monitoring

“…Along with the presence of microcracks, the stress field in the vicinity of a microcrack is an important factor as it can reveal the fracture driving force and the crack propagation direction. 16,17 Therefore, it is necessary to develop a nondestructive method that can visualize the stress distribution around microcracks over a large area. Mechanoluminescence (ML) technologies have been proposed for detecting cracks and evaluating the stress/strain states in their vicinity.…”

“…Several nondestructive techniques have been proposed for detecting microcracks: optical transmission, , scanning acoustic microscopy, , resonance ultrasonic vibration, − luminescence imaging, , and others. , However, there are limitations in predicting the distribution of stress fields around microcracks, and the testing method can be enhanced by improving the price competitiveness, equipment management, field of view, and data processing. Along with the presence of microcracks, the stress field in the vicinity of a microcrack is an important factor as it can reveal the fracture driving force and the crack propagation direction. , Therefore, it is necessary to develop a nondestructive method that can visualize the stress distribution around microcracks over a large area.…”