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Second-order approximation to the crack trajectory equation

✍ Scribed by E. Viola; A. Piva


Publisher
Elsevier Science
Year
1986
Tongue
English
Weight
440 KB
Volume
24
Category
Article
ISSN
0013-7944

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✦ Synopsis


According to an approach recently proposed [5], this analysis includes the second-order approximation in order to obtain the deviation of the extended crack tip from the original direction. The dependence of the curvature on the crack path upon the inplane stress fields and the derivatives of the stress intensity factors with respect to the original crack length is shown. In particular, the analysis indicates that, for some values of the above-mentioned parameters, an asymptote perpendicular to the original crack direction occurs which specifies the unstable behaviour of the crack path. In addition, the asymptotic crack path behaviour is obtained to the same order of approximation when stability is assumed.


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Approximate solution (with error bounds)
✍ James G. Taylor πŸ“‚ Article πŸ“… 1978 πŸ› Elsevier Science 🌐 English βš– 851 KB

## Two approximations are developed to the solution of an important nonlinear, nonautonomous second-order differential equation that arises in various fields of science and technology such as operations research, mathematical ecology and epidemiology. The origin of the second-order differential equa