Issue 41

F. Berto, Frattura ed Integrità Strutturale, 41 (2017) 475-483; DOI: 10.3221/IGF-ESIS.41.59 478 Figure 2 : Plate geometry. Figure 3 : Overall view of finite element mesh. Detail of finite element mesh at outer surface and at crack tip. R ESULTS rack surface stresses, τ yz and τ xy (Fig. 1) were extracted from the finite element results at distances, s , from the plate surfaces of 0 mm, 0.25 mm, 1 mm and 2 mm. Results for t/a = 1, plotted on logarithmic scales, are shown in Figs. 4-6. Results for other values of t/a are generally similar, but with some differences in detail. When the plot is a straight line its slope is - λ . Values of λ taken from straight line plots are shown in Tabs. 1 and 2. Where no value is shown the plot could not be regarded as a straight line. For s = 0.25 mm, 1 mm and 2 mm λ calculated from τ xy is close to the theoretical value of 0.5 for a stress intensity factor singularity (Tab. 1). Hence, realistic values of K II can be calculated. For s = 0 mm the value of λ has a maximum for t/a = 0.25, and decreases as t/a increases. The values of λ are all significantly less than the theoretical value of 0.598 for a corner point singularity. Realistic values of K II can probably be calculated for t/a > 2. Realistic values of K III can be calculated from τ yz for s = 1 mm and 2 mm. The results for s = 0 mm (Fig. 4) show that τ yz is slightly lower than τ xy for small x , and decreases as x increases. Realistic values of K III cannot be calculated. The presence of finite values of τ yz , linked to finite values of K III , appears because of the appearance of mode I disclinations, which are rotations about the y axis. Differentiating the expression for the displacement U z gives the amount of this rotation which increases towards the crack tip, with a concomitant increase in τ yz at a surface. This accounts qualitatively for the observed distributions of τ yz at a surface. C