Issue 41

J.M. Vasco-Olmo et alii, Frattura ed Integrità Strutturale, 41 (2017) 166-174; DOI: 10.3221/IGF-ESIS.41.23 172 and Dally [14] forms the basis for this process. The models are valid only for the elastic field near the crack tip singularity and hence it was necessary to identify the near-tip zone where valid experimental data could be obtained. An annular mesh (Fig. 2) was defined to establish the region from which determining the SIFs. Two parameters are fundamentals for defining the annular mesh: inner and outer radii. The inner radius was defined with sufficient extent to avoid including plastic deformation at the crack tip, while the outer radius was defined to be within the singularity dominated zone. From the calculation of the stress intensity factors, the coefficients defining the crack tip fields in the analytical models can be extracted to found the plastic zone contour. Crack tip stress fields in the analytical models depend on a set of coefficients and the coordinates of the analysed data points. Therefore, an expression as a function of the above parameters for the equivalent stress according to a yield criterion can be obtained. From this expression, an error function is defined as the difference between the equivalent stress and the yield stress of the material. Thus, plastic zone contour is found from the evaluation of the error function by analysing angle values between 0º and 360º to estimate the radius of the plastic zone. Hence the size and shape of the experimentally determined plastic zone can be compared with that found using the three different theoretical models that describe the crack tip stress and displacement fields. R ESULTS AND DISCUSSION ig. 5 shows size and shape data obtained for the plastic zone at maximum load using the von Mises yield criterion for two different crack lengths (6.42 and 9.20 mm). The white area represents the experimental plastic zone estimated from the direct method, while the dotted contours correspond to the plastic zone found for the three models by implementing the indirect method using the model coefficients. It is clear that the plastic zone size and shape predicted by the CJP model is an excellent fit to the experimental data, while the Westergaard and Williams models predict somewhat larger dimensions. Therefore, from a qualitative point of view, the CJP model seems that shows a great potential to predict the plastic zone at the crack tip. Figure 5 : Comparison between the experimental plastic zone shape and that predicted by the models using the von Mises criterion for two crack lengths, (a) 6.42 and (b) 9.20 mm at maximum load. Moreover, as indicated above the plastic zone area is evaluated for its quantification. Fig. 7 shows the evolution of both experimental and predicted plastic zone area with the crack length using the von Mises yield criterion. Again, the experimental data is in close agreement with the plastic zone area calculated from the CJP model at all crack lengths, while the predicted area using the Westergaard and Williams models is higher than the experimental results. The Westergaard model shows a progressively larger error as the crack length increases while the error in the Williams solution remains fairly constant. It can be concluded that the CJP model provides an improved prediction of the crack tip plastic zone area and shape compared with either the Westergaard or Williams models. Fig. 6 illustrates the difference that choice of yield criterion (von Mises or Tresca) would make to the experimental and CJP predictions of plastic zone area. As expected, sizes predicted using the Tresca criterion are higher, but close agreement is still observed between the experimental predictions and those provided by the CJP model. F (a) (b) green (Westergaard) cyan (Williams) yellow (CJP)