Title

Extreme value probabilistic model for brittle plates with random cracks under multiaxial loads

Abstract

Several authors (Shih (1980), Tryon (1995)) have discussed the application of probabilistic fracture mechanics (PFM) to gas turbine structures, but in general terms. The literature contains many PFM models, most of which assume that plates contain cracks with random strengths. Catastrophic fracture occurs at the weakest crack, implying a probability distribution for the strength of the plates. Criteria from fracture mechanics, which take account of crack number, length and orientation, are not applied explicitly in such models. In contrast, a few models have assumed the presence of cracks with random lengths and orientations, and have explicitly applied fracture criteria. The ensuing strength distributions for the plates depend on the parameters of the crack length distribution, on the fracture criteria, and on the plate size. However, the models have several limitations, including: (1) a probabilistic formulation which depends on large numbers of long cracks being present in the plates; (2) uniaxial loading; and (3) simplified fracture criteria. Recently, under the restriction of uniaxial loading, the authors have introduced a conditional probability model based on a cell concept, leading to a distribution which is applicable without restrictions on crack number or length. In the present study, the formulation is extended to the general case of biaxial loading and torsion (Mode III). Expressions for the mean and variance of the strength are derived in terms of plate size, the crack length distribution, the fracture criteria and ratios of the applied loads. Scaling relations are computed and presented.

Publication Date

12-1-1997

Publication Title

American Society of Mechanical Engineers, Pressure Vessels and Piping Division (Publication) PVP

Volume

356

Number of Pages

59-64

Document Type

Article

Personal Identifier

scopus

Socpus ID

0030658150 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/0030658150

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