Interaction integral method for computation of crack parameters K–T – A review

Highlights

• Origin, development and implementation of the I-integral are critically reviewed.

• A comprehensive review on determining key fracture parameters is presented.

• Overview of extensions, advantages and limitations of the I-integral is provided.

• Further studies on multi-field, atomic-scale and non-classical cracks are required.

Abstract

A critical overview of past research on the interaction integral (I-integral) method is presented. The I-integral is the two-state mutual energy release rate decided by a designable auxiliary field and the actual field. Due to the designability of the auxiliary field, the I-integral has been used extensively in extracting the individual stress intensity factors (SIFs) and the T-stress of a crack in single materials or at a bi-material interface. The practical implementation of the I-integral mainly experienced three periods. 1) In the last quarter of the twentieth century, the path-independent I-integral was developed for homogeneous materials subjected to static, dynamic and/or thermal loading. 2) In the 2000 s, the domain-form I-integrals were discussed to deal with inhomogeneous materials. 3) In the past decade, the domain-independent I-integral (DII-integral) was proposed for multi-interface materials. After that, we review the I-integrals for functional materials and the extensions of the I-integral to some new fracture problems. Subsequently, diverse practical applications are introduced. Various research works demonstrate that the I-integral is a most accurate and reliable approach to extracting the individual SIFs and T-stress for the materials obeying linear constitutive law or the materials with limited nonlinear effect. Finally, the advantages, limitations, and future issues of the I-integral method are discussed.