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Research Papers: Materials and Fabrication

# A New Computational Method for Probabilistic Elastic-Plastic Fracture Analysis

[+] Author and Article Information
Sharif Rahman

Department of Mechanical and Industrial Engineering, University of Iowa, Iowa City, IA 52242rahman@engineering.uiowa.edu

J. Pressure Vessel Technol 131(6), 061402 (Oct 01, 2009) (8 pages) doi:10.1115/1.4000159 History: Received December 26, 2008; Revised June 06, 2009; Published October 01, 2009

## Abstract

This paper presents a polynomial dimensional decomposition method for calculating the probability distributions of random crack-driving forces commonly encountered in elastic-plastic fracture analysis of ductile solids. The method involves a hierarchical decomposition of a multivariate function in terms of variables with increasing dimensions, a broad range of orthonormal polynomial bases consistent with the probability measure for Fourier-polynomial expansion of component functions, and an innovative dimension-reduction integration for calculating the expansion coefficients. Unlike the previous development, the new decomposition does not require sample points, yet it generates a convergent sequence of lower-variate estimates of the probability distributions of crack-driving forces. Numerical results, including the probability of fracture initiation of a through-walled-cracked pipe, indicate that the decomposition method developed provides accurate, convergent, and computationally efficient estimates of the probabilistic characteristics of the $J$-integral.

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## Figures

Figure 4

Probability of fracture initiation of a TWC pipe

Figure 3

A TWC pipe under four-point bending: (a) geometry and loads; (b) cracked cross section; and (c) finite element mesh

Figure 2

Probability density of the J-integral for a DE(T) specimen: (a) univariate solution for plane stress; (b) bivariate solution for plane stress; (c) univariate solution for plane strain; and (d) bivariate solution for plane strain

Figure 1

A DE(T) specimen: (a) geometry and loads; (b) finite element mesh at mean crack length; and (c) singular elements at the crack tip

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