numero25

D. A. Hills et aliii, Frattura ed Integrità Strutturale, 25 (2013) 27-35; DOI: 10.3221/IGF-ESIS.25.05 31 1 0 I II II I K d K           , 1 1 0 II I II I I II I II G K K            (17) For this case, the stresses, instead of being given by Eq. (12), are instead given by       1  1  0 0 0 , I II ij I II ij ij r r r f f G d d                        (18) so that the direct   p x , and shearing   q x , are given by     1  1  0 0 0 0 , I II int I II r p x x x f f G G d d                           (19)     1  1  0 0 0 0 , I II r int I II r r r q x x x f f G G d d                          (20) When I K is negative and II K is positive, closure is implied through the asymptotic region. However, depending on the punch angle,  , and the coefficient of friction, f , various slip regions are implied at the edge and/or interior of the contact. To compute the implied slip extents we substitute Eq. (19) and (20) into the slip condition     q x fp x   , and solve for 0 / x d , again, denoting any boundary between stick and slip as s x , which gives 1 0 I II II II s r I I r x f f f d f f f                   (21) Figure 3 : Plots of the implied regions of slip and stick, when I K is negative and II K is positive, for punch angles of   60 , 90 ,120      , where the red line denotes the position at which the     q x fp x   condition is met, and the blue line the position at which the     q x fp x   condition is met. 60° Punch stick - slip K I ,  K II 0 1 2 3 4 x s d 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 f 90° Punch  K I ,  K II stick - slip 0 1 2 3 4 5 x s d 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 f 120° Punch  K I ,  K II stick + slip - slip 0 1 2 3 4 5 6 x s d 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 f