Analytical solution for fatigue crack propagation of an embedded elliptical crack
Source abstract
Abstract
Fatigue crack propagation of an embedded elliptical crack under a uniform cyclic loading is investigated using Paris law. The goal of this paper is to analytically integrate a pair of nonlinear differential equations derived from Paris law applied at two points on the crack front where the crack front intersects with the major and minor semi-axes of an elliptical crack. An analytical integration is successfully achieved by creating an intermediate differential equation for an eccentricity of an ellipse, k, which is also a modulus of an elliptic integral. This is believed to be the first non-trivial exact analytical solution for fatigue crack propagation of a 3D crack. As an application of the exact analytical solution, the error of the finite difference solution is also investigated. It is found that there is a “universal” error curve for the finite difference solution of a fatigue crack problem.
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Research context
OpenAlex topics: Fatigue and fracture mechanics · Numerical methods in engineering · Material Properties and Failure Mechanisms
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References (22)
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