Perturbation method for solving the nonlinear eigenvalue problem arising from fatigue crack growth problem in a damaged medium |
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Authors: | LV Stepanova SA Igonin |
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Institution: | Department of Mathematical Modelling in Mechanics, Samara State University, Samara 443011, Russia |
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Abstract: | An analytical solution of the nonlinear eigenvalue problem arising from the fatigue crack growth problem in a damaged medium in coupled formulation is obtained. The perturbation technique for solving the nonlinear eigenvalue problem is used. The method allows to find the analytical formula expressing the eigenvalue as the function of parameters of the damage evolution law. It is shown that the eigenvalues of the nonlinear eigenvalue problem are fully determined by the exponents of the damage evolution law. In the paper the third-order (four-term) asymptotic expansions of the angular functions determining the stress and continuity fields in the neighborhood of the crack tip are given. The asymptotic expansions of the angular functions permit to find the closed-form solution for the problem considered. |
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Keywords: | Nonlinear fracture mechanics Nonlinear eigenvalue problem Cyclic loading Crack growth in a damaged medium Perturbation method Analytical solution |
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