Issue 35

L. C. H. Ricardo et alii, Frattura ed Integrità Strutturale, 35 (2016) 456-471; DOI: 10.3221/IGF-ESIS.35.52 458 where K max and K min are the maximum and the minimum stress intensity factors, respectively. In the crack propagation curve, the linear part represents the Paris - Erdogan law, when plotting the values of  K vs da/dN in logarithmic scale. Fatigue crack initiation and growth under cyclic loading conditions is controlled by the plastic zones that result from the applied stresses and exist in the vicinity (ahead) of a propagating crack and in its wake or flanks of the adjoining surfaces. For example, the fatigue characteristics of a cracked specimen or component under a single overload or variable amplitude loading situations are significantly influenced by these plastic zones. In modelling the fatigue crack growth rate this is accounted by the incorporation of accumulative damage cycle after cycle and should include plasticity effects. During the crack propagation the plastic zone should grown and the plastic wake will have compressive plastic zones that can help to keep the crack close. Prediction of the fatigue behaviour of structural components subjected to overloads and variable amplitude loading requires an estimation of the plastically affected regions ahead of the crack-tip. One of the most widely used plasticity models in fatigue is the Dugdale’s yield strip model [16] In this model the plastically affected zone (r y or r p ) is assumed to be small as shown Fig. 1. Figure 1 : Elastic and Elastic-Plastic Zone Sizes. Hairman & Provan [17] discuss the problems pertaining to fatigue loading of engineering structures under single overload and variable amplitude loading involving the estimation of plasticity affected zones ahead of the crack tip. The models of Irwin [6,7] and Dugdale [16] give an idea of the size of the plastic zone but not of its shape. The size, in general, is estimated as a circle of certain diameter (r y or r p ) obtained on the basis of reasoning given in the above models for crack- tip-plasticity. In these models the effect of the shape of the plasticity affected zones is not taken into account. To obtain a better idea of the plastic zone shape, the components of stress in the radial and circumferential directions of a mode-1 type of loading were derived using an eigenfunction expansion method developed by Williams [18] and with a modification to take into consideration crack-tip blunting. The resulting equations are:       1 3 5cos cos , , 4 2 2 2 1 3 3cos cos , , 4 2 2 2 1 3 sin sin , , 4 2 2 2 rr r r K T f r r K f r r K f r r                                                                                                                 (5) The first terms in Eq. (5) represent the singular terms as r  0 and are, therefore, dominant near the crack-tip. The second term in Eq. (5) arises from a consideration of higher power terms. This term is known as the T-stress, it is not singular as r  0 but it can affect the elastic-plastic crack-tip stress state. The third terms arise as a contribution from crack-tip blunting and are not given in Williams [18]. The contribution of crack-tip blunting has been discussed in Rolfe –