Issue 35

Chahardehi et al, Frattura ed Integrità Strutturale, 35 (2016) 41-49; DOI: 10.3221/IGF-ESIS.35.05 43 R ESIDUAL STRESSES AND PLASTIC ZONE SIZE AHEAD OF CRACK any authors have associated the growth (and subsequent arrest) of compressive cracks to the residual stress field and the plastic zone generated at the notch due to the remote compressive loading, and the state-of-the art is reviewed in this section. Saal [19] proposed a model where the residual stresses at the notch root, generated from maximum compressive load were calculated. It was assumed that under fully compressive cyclic loading, cracks would stop growing at the boundary of the plastically deformed zone. Saal’s study was restricted to constant amplitude cyclic loading. It is different from Hubbard’s work [9], where the residual stress field in the vicinity of the notch is not released as the crack grows. Experimental work by Saal [19] showed where no tensile stress component is present, the crack stops at the elastic-plastic boundary. Fleck et al [11] used Dugdale’s strip yield model [20] and back-calculated the effective stress intensity factor range (and hence inferred the residual stresses) from crack growth test results, using Bueckner’s principle of weight function [21-22]. They found that residual stresses found by this method are greater than those calculated from Dugdale’s model [11]. Jones et al [23] suggest that since negative R-ratio effects are considered to be principally caused by crack closure, a tight crack should produce more significant crack closure and hence negative R-ratio effects. However data from their tests [23] show that results from tight cracks and notches do not significantly alter negative R-ratio effects. Assuming that the reason behind this observation by is that the extent of residual stresses due to the compressive loading remains unchanged, the work of Saal [19] may explain this phenomenon. Saal shows that the condition of a specimen with a straight cut will be a reasonable approximation of calculating the plastic zone size of any elastic-perfectly plastic notched specimen. Saal’s observation is further supported by Libatskii [24], who showed that the yield behaviour of static tensile tests of notched specimens of mild steel was very close to that described by Dugdale’s model. An important work was reported by Reid et al [25], which is the first work to report measured values of residual stress at a notch, generated by compressive loading, and to use this in the analysis of crack growth under cyclic compression. The measurement method has been explained in [26]. Furthermore, neutron diffraction was also used to obtain the residual stress field. It was found that the general shape of the stress distribution was independent of the pre-load used. Not surprisingly, the residual stress magnitude increased with the pre-load. The region of tensile stress near the uncracked notch tip increased in size with the value of the pre-load but in each case it was significantly smaller than the final crack length [26]. This contradicts the views of Gerber et al [8] and Suresh [10]. Reid et al [25] argue that it is possible for the crack tip to remain in a region of tension because the growth of a crack redistributes the original tensile stress to larger distances from the notch. A number of authors have used numerical tools to model the generated residual stress field ahead of the crack, due to the compressive loading. Among them, Zhang et al [27] developed an elastic-plastic finite element model to study the compressive stress effect on fatigue crack growth under applied tension-compression loading. Prior to this, Silva [28] had concluded that to predict fatigue crack growth behaviour under applied tension-compression loading, models based on fatigue crack closure were not suitable, and models need to be developed which are based on material’s cyclic plastic properties. The discussions above are all for fatigue crack growth. One finding worth mentioning here is by Iswanto et al [29], who found that the effect of residual stress caused by roller-working on S-N fatigue was similar to the effect of compressive mean stress. However, Chahardehi et al [30] conclude that the compressive residual stresses caused by l aser peening do not influence fatigue crack growth in the way that was previously expected, i.e. superposition of stresses is not sufficient. M ODELLING THE R- RATIO EFFECT arious authors recognized the R-ratio dependence of FCG rates, and several models have been presented to include this behaviour. Generally, equations of the Paris law type that account for the effect of R-ratio can be divided into the following three types: 1) Stress intensity factor range is defined as per the conventional definition  K=K max -K min and Paris law coefficients are dependent on R-ratio. This is the approach taken in the BS7910 : 2013 recommendation [1] and ASTM E647 [5]. M V