numero25

D. Nowell et alii, Frattura ed Integrità Strutturale, 25 (2013) 1-6 ; DOI: 10.3221/IGF-ESIS.25.01 4 The experimental data is processed as described above and used to determine the stress intensity factor history for the crack. In the case of specimen CTF6, the variation of K with load, just before the overload, is shown in Fig. 4(a). It can be seen that the behaviour is quite similar to that predicted by an elastic analysis of the specimen geometry. However, there is an offset between the theoretical and experimental lines, caused by crack closure. Alternatively, this phenomenon may be thought of as a residual (negative) K caused by the residual stress (and displacement) field present. The two lines have similar slope since, once the crack is fully open at a load of approximately 0.5 kN, the behaviour is predominantly elastic, with only a small zone of cyclic plasticity close to the crack tip. Figure 4 : Variation of measured stress intensity factor with load for specimen CTF6 (a) Before the overload and (b) Immediately after the overload. Fig. 4b shows equivalent data just after the overload. A cursory inspection suggests that the behaviour appears as expected. The slope of the curve remains approximately parallel to the elastic line, and the offset has increased (perhaps as a result of the increased magnitude of residual stress resulting from the overload). However, closer inspection reveals some unexpected features. The analysis yields negative stress intensity factors, which we would not expect to be physically admissible on their own. This must mean that the relative displacement between the crack flanks is varying as -  r , where  is a positive constant. Further, this would imply that the stress field at the tip of the crack is compressive and reasonably well described by the singular Westergaard solution. One possible explanation for these observations is that the crack is being held open by the additional crack opening displacement caused by the overload. Investigation of the crack profile broadly confirms this view. As the crack propagates after the overload, the behaviour gradually returns to that which exists previously. Fig. 5 shows a similar plot of load against K taken 23,500 cycles after the overload. The negative offset is substantially reduced, although negative stress intensity factor values still exist. Moreover it is apparent that the variation is no longer linear over the range of load plotted. The deviation from linearity at lower load values is almost certainly caused by the onset of closure, which was absent immediately after the overload. The discussion above suggests that a single parameter, K , may be insufficient to fully characterize the crack tip environment, particularly under non-uniform loading conditions. An improvement can almost certainly be obtained by explicitly acknowledging the role of crack tip plasticity. A simple model has been proposed by Pommier and Hamam [11] which relies on partitioning the displacement field into elastic and plastic components. The elastic component, u el , is the usual field associated with K, whereas the plastic field, u pl , is associated with crack tip opening. To a first approximation it may be taken as that given by a unit dislocation located at the crack tip. Hence I el pl u K u u    (2) As far as the relative displacements between the crack faces are concerned, this leads to 8 ( ) 2 I y K r u r E     (3) (a) (b)