Evaluation of the singularity exponents and characteristic angular functions for piezoelectric V-notches under in plane and out of plane conditions

On the stress state in rectilinear anisotropic thick plates with blunt cracks

“…4. 5 shows the in-plane stresses σ yy , σ xx and σ xy over the notch edge; the agreement with Eqs (16)(17)(18) is evident. This behaviour is very similar to that exhibited by notched isotropic plates under linear elastic and elastic-plastic conditions.…”

“…1). It is worth of being underlined that in Eqs (16)(17)(18) the dependence of the stress fields according to the through-the-thickness coordinate (z-coordinate) is demanded to parameters A and B, which vary across the thickness of the plate.…”

“…The closed form solution for the elastic stress fields at the tip of a blunt crack in an isotropic material were derived by Creager and Paris 6 , and later extended to any notch opening angle by Lazzarin and Tovo, 7 for plane loadings, and by Zappalorto et al 8 and Zappalorto and Lazzarin 9 for the mode III problem. [11][12][13] The most recent advances on this topic are related to the study of the effect non-singular terms of the stress field close to a pointed V notch, 14,15 as well as materials with unconventional properties (such as angularly inhomogeneous elastic properties, 16 magneto-electro-elastic 17 and piezoelectric materials 18 ). 10 The problem of sharp and blunt V-shaped notches was also thoroughly investigated over the years by Savruk and co-workers.…”

“…10 The problem of sharp and blunt V-shaped notches was also thoroughly investigated over the years by Savruk and co-workers. [11][12][13] The most recent advances on this topic are related to the study of the effect non-singular terms of the stress field close to a pointed V notch, 14,15 as well as materials with unconventional properties (such as angularly inhomogeneous elastic properties, 16 magneto-electro-elastic 17 and piezoelectric materials 18 ).…”

“…Plot of the in-plane stress components σ xx , σ yy , σ xy along the notch edge and comparison with Eqs(16)(17)(18). Plot of the in-plane stress components σ xx , σ yy , σ xy along the notch edge and comparison with Eqs(16)(17)(18).…”