Issue 41

A. Carpinteri et alii, Frattura ed Integrità Strutturale, 41 (2017) 175-182; DOI: 10.3221/IGF-ESIS.41.24 180 Figure 3 : Stress intensity factors as functions of the applied stresses. (a) The case of smooth surfaces, with different values of the coefficient of friction ߤ . (b) The effect of roughness is included and trends are shown for different values of the asperity angle ߙ . R ESULTS e now present the results we have obtained for the example problem in Fig. 1, consisting of an elastic punch welded to a half-space made of the same material. The elastic modulus is E = 30GPa and the Poisson coefficient is ߥ = 0.25; the fracture toughness of the material is K Ic = 1.1 MPa  m. A state of plane strain is assumed. A crack of length c = 0.2 a is present, whose surface model is described by the coefficient of friction ߤ and the constant roughness angle ߙ k . The external loading applied consists of a constant pressure p = P /2a and a shear traction q= Q/2 a which is monotonically increased in time. Fig. 3 displays the plots of the stress intensity factors as functions of the far-field shear stress. Fig. 3(a) is related to the case of smooth surfaces ( ߙ =0) , where only friction is present. We can note that the effect of friction is rather modest, anyway a slight increment of the absolute value of Mode II factor with increasing friction is observed. Fig. 3(b) plots the stress intensity factors for different values of the asperity angle ߙ . The trends show that, as the angle ߙ increases, the absolute value of Mode I stress intensity factor K I increases, while the absolute value of K II decreases (note that they are both negative). This behaviour can be explained considering the effect of dilatancy, which affects K I , and the effect of roughness, which increases the resistance to sliding displacements, therefore reducing the absolute value of K II . However, one should be careful to generalize this behaviour, which can be completely different as the coefficient of friction also increases. In this sense, more research is needed to further investigate the issue. Fig. 4 displays the dimensionless fracture propagation stress q max /p as a function of the coefficient of friction, in the case of smooth surfaces. Here, the classical mixed-mode criterion of maximum tangential stress is considered [12] and the W