Open Access

ARTICLE

Evaluation of Elastic-Plastic Crack Tip Parameters using Partition of Unity Finite Element Method and Pseudo Elastic Analysis

by Raju Sethuraman¹, N.R.Rajesh²

1 Corresponding author. Department of Mechanical Engineering, Indian Institute of Technology Madras, Chennai-600036, India. e-mail: sethu@iitm.ac.in
2 Department of Mechanical Engineering, Indian Institute of Technology Madras, Chennai-600036, India.

Computer Modeling in Engineering & Sciences 2009, 39(1), 67-100. https://doi.org/10.3970/cmes.2009.039.067

Abstract

This paper presents a methodology based on Partition of Unity Finite Element Method (PUFEM) and Pseudo Elastic Analysis for solving material non-linear fracture problems within the scope of total deformation theory of plasticity. Local enrichment base functions are used to represent the asymptotic field near the crack tip and discontinuous field across the crack faces. An iterative linear elastic analysis using PUFEM is carried out for the determination of elastic-plastic crack tip stress fields by treating effective material properties as spatial field variables. The effective material parameters are defined using deformation theory and are updated in an iterative manner based on strain controlled projection method using experimental uniaxial tensile test curve. Discrete system of linear equations for the elastic-plastic analysis is obtained from the weak form of the equilibrium equation using the enriched trial function. Application of the present methodology has been illustrated considering non-linear fracture problems for the evaluation of elastic-plastic crack-tip parameters using boundary layer analysis. Ramberg-Osgood model with different hardening exponents is used to characterize the material behavior. Results of the present study for J-dominant HRR field and K dominant elastic field are compared with both the analytical and non-linear finite element solutions and found to be in very good agreement.

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Keywords

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