Issue 41

A. Carpinteri et alii, Frattura ed Integrità Strutturale, 41 (2017) 175-182; DOI: 10.3221/IGF-ESIS.41.24 181 fracture propagation stress is obtained when the combined factor K eff equals the fracture toughness K Ic of the material. According to the fracture criterion we have:      3 2 cos ( / 2) 3 cos ( / 2)sin( / 2) eff I II K K K (19) where ߴ is the angle at which the crack will extend, obtained from the following expression:       2 2 1/2 tan / 2 0.25 / 0.25( / 8) II I II I K K K K (20) The effect of friction on fracture initiation is notable in Fig. 4: a strong increment in the fracture propagation stress is observed, whereas the propagation angle ߴ slightly decreases (note that the maximum value for pure Mode II would be 70.5° [13]). Figure 4 : Smooth surfaces ( ߙ =0). Fracture propagation stress q max is shown for different values of the coefficient of friction ߤ . The corresponding propagation angle ߴ is also shown . C ONCLUSIONS n this study, we describe the mixed-mode tip stress field of a crack emanating from a re-entrant corner, using the Williams solution in combination with an appropriate edge dislocation distribution along the crack line. The behaviour of a rough and frictional crack is conveniently described by an interface model where a rigid-plastic constitutive relationship between stresses and relative displacements along the crack and a slip function with non- associated flow are used. The results we have obtained clearly show that the effect of friction and roughness is remarkable. In particular, the effect of dilatancy increases the values of the (negative) Mode I stress intensity factor while it simultaneously reduces the Mode II factor when the roughness angle increases. Moreover, the fracture propagation load is strongly influenced by friction. R EFERENCES [1] Murakami, Y. (Ed.), Stress Intensity Factors Handbook, vol. 1, Pergamon Press, New York, (1987). [2] Williams, M.L., Stress singularities resulting from various boundary conditions in angular corners of plates in extension, J. Appl. Mech., 19 (1952) 526–528. [3] Churchman, C.M., Hills, D.A., The edge dislocation in a three-quarter plane. Part II: Application to an edge crack, Eur. J. Mech. A Solids, 25 (2006) 389–396. I