Issue34

L.P. Pook, Frattura ed Integrità Strutturale, 34 (2015) 150-159; DOI: 10.3221/IGF-ESIS.34.16 150 Focussed on Crack Paths Crack paths and the linear elastic analysis of cracked bodies L. P. Pook 21 Woodside Road, Sevenoaks TN13 3HF, United Kingdom A BSTRACT . The linear elastic analysis of cracked bodies is a Twentieth Century development, with the first papers appearing in 1907, but it was not until the introduction of the stress intensity factor concept in 1957 that widespread application to practical engineering problems became possible. Linear elastic fracture mechanics (LEFM) developed rapidly in the 1960s, with application to brittle fracture and fatigue crack growth. The first application of finite elements to the calculation of stress intensity factors for two dimensional cases was in 1969. Finite element analysis had a significant influence on the development of LEFM. Corner point singularities were investigated in the late 1970s. It was soon found that the existence of corner point effects made interpretation of calculated stress intensity factors difficult and their validity questionable. In 1998 it was shown that the assumption that crack growth is in mode I leads to geometric constraints on permissible fatigue crack paths. Current open questions are. The need for a new field parameter, probably a singularity, to describe the stresses at surfaces. How best to allow for the influence of corner point singularities in three dimensional numerical predictions of fatigue crack paths. Adequate description of fatigue crack path stability. K EYWORDS . Linear elastic analysis; Stress intensity factors; Corner point singularities; Crack paths; Finite element analysis. I NTRODUCTION he complete solution of a crack growth problem includes determination of the crack path. This review is a brief survey of the development of ideas on the linear elastic analyis of cracked bodies that are relevant to crack path determination. It is based on the author’s personal involvement over more than 50 years. The review is restricted to linear elastic, homogeneous, isotropic materials, with any yielding confined to a small region at a crack tip. The first relevant papers had been published 50 years earlier, but in the late 1950s theoretical understanding of crack growth due to fatigue and static loadings was limited. The situation changed dramatically in the 1960s with the development of fracture mechanics, which is the applied mechanics of crack growth [1]. It was realised that linear elastic fracture mechanics, based on linear elastic analyses, sufficed for the solution of many practical engineering problems. By the mid 1970s practical applications of fracture mechanics were well established. In considering practical aspects of linear elastic fracture mechanics, scales of observation need to be taken into account since the scale chosen can make a considerable difference to the appearance of an object in general, and a crack in particular [2]. Scales of observation of 0.1 mm and above are usually described as macroscopic. The linear elastic concept of stress intensity factor describes the linear elastic stress field in the vicinity of a crack tip, and is a singularity. Stress intensity factors may be used to characterise the mechanical properties of cracked test pieces in just the same way that stresses are used to characterise the mechanical properties of uncracked test pieces. The conventional notation for the position of a point relative to the crack tip, and for the stresses at T