Title

Inverse Method For Identifying The Underlying Crack Distribution In Plates With Random Strengths

Abstract

In the current investigation we seek to identify the underlying crack number and crack length distributions in brittle plates with a known strength distribution. The inverse problem in probabilistic fracture mechanics is defined, and the numerical procedure to solve the inverse problem is constructed. The simulation process of generating simulated plates containing simulated random cracks is elaborated. The maximum strain energy release rate criterion (Gmax) is applied to each simulated random crack to find the crack strength. The strength of the simulated plate is equated to the strength of the weakest simulated crack in the plate based on the weakest link notion. The underlying crack number and crack length distributions are obtained by minimizing the difference between the simulated plate strengths and the known plate strengths. The gamma, lognormal and two-parameter Weibull distributions are employed for the underlying crack length distribution, and are compared in order to identify the best choice. Numerical examples demonstrate that the three PDFs are all acceptable for reasons to be explained. In the appendix, the direct problem in probabilistic fracture mechanics is presented as part of the demonstration of a method for using the crack distribution identified in the inverse problem to predict the strength and the probability of fracture in a practical application.

Publication Date

12-1-2000

Publication Title

Acta Mechanica

Volume

144

Issue

3-4

Number of Pages

137-154

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1007/BF01170171

Socpus ID

0034482299 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/0034482299

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