Weight Functions Applied to Fatigue Crack Growth Analysis

Abstract

An overview is presented of studies conducted at the University of Pisa on the Weight Function technique as applied to Fatigue Crack Grown analysis. The fundamental theoretical aspects of the technique are summarised, discussing some recent methods for the determination of the Weight Function. The application of the technique to non-linear (contact) problems and to the evaluation of the crack tip stress field is also discussed. It is shown that the Weight Function method allows one to efficiently consider many crack propagation problems, some examples of which are provided. NOMENCLATURE a, a,,, a, = generic, initial and critical crack length KEXT, K, , I(,,, = stress intensity factor produced by external forces, residual stress and total value K , AK, K, = stress intensity factor in mode I (value and range) and in mode I1 N, NF = elapsed fatigue cycles, cycles to failure R = K-/K, = R-ratio u = crack opening displacement function h = weight function u, OP = stress and nominal stress

The effect of subsurface crack opening on the stress intensity factor under cyclic thermal loads

“…As shown below, the surface crack may partially close due to the compressive stresses acting near the free surface of the surface cracked plate. Adapting the idea presented by Beghini et al [21,22], the remaining open section of the surface crack is modelled as a subsurface crack. The width of the closed section of the crack is determined via the stress intensity factor value calculated for the virtual crack tip located at the end of the closed zone.…”

“…The width of the closed section of the crack is determined via the stress intensity factor value calculated for the virtual crack tip located at the end of the closed zone. Beghini et al [21,22] demonstrate that the SIF at the virtual crack tip is equal to zero, otherwise the virtual crack tip would be open or overlapping. This is concept is visualized in Figure 4.…”

Sharp evaluation of the Oore–Burns integral for cracks subjected to arbitrary normal stress field

“…The important rule of weight function in fatigue life prediction has been underlined in many papers . Usually, the crack is considered in terms of a line in a two‐dimensional body, because this assumption significantly simplifies the numerical assessments of stress intensity factors.…”

“…3 The important rule of weight function in fatigue life prediction has been underlined in many papers. [4][5][6][7] Usually, the crack is considered in terms of a line in a two-dimensional body, because this assumption significantly simplifies the numerical assessments of stress intensity factors. Accurate results can be obtained by generalising the weight function that is derived from the displacement function of Petroski and Achenbach, as suggested by Glinka and Shen.…”

A mode II weight function for subsurface cracks in a two‐dimensional half‐space

“…The weight function method has been used for SIF calculation in different problems, and it has proved to be efficient 13–17 . In fact, due to the dependence of the WF only on geometric parameters, the SIF calculation reduces to a numerical integration along the crack face of the WF multiplied by the stress acting in an uncracked body.…”