Stress analysis in a cracked strip

Cohesive modeling of crack nucleation under diffusion induced stresses in a thin strip: Implications on the critical size for flaw tolerant battery electrodes

“…Kðy; gÞ which corresponds to the axial stress at location ð0; yÞ induced by a single edge dislocation at ð0; gÞ with a unit Burgers vector in the x-direction (Fotuhi and Fariborz, 2008). The expression for Kðy; gÞ is given in Appendix C. Fig.…”

“…An alternative form of the solution has been given by Fotuhi and Fariborz (2008), which is found to be consistent with the solution given in Appendix A. Here we list the alternative solution by Fotuhi and Fariborz (2008) f þaðy=h À 1Þ cosh aðy=h À 1Þ þ 2C 1bx ½2 cosh aðy=h À 1Þ þ aðy=h À 1Þ sinh aðy=h À 1Þg; p 4l f xx2 ð0; y; g; aÞ ¼ 1 D À2A 2bx ½sinh aðy=h þ 1Þ f þ aðy=h þ 1Þ cosh aðy=h þ 1Þ þ 2C 2bx ½2 cosh aðy=h þ 1Þ þ aðy=h þ 1Þ sinh aðy=h þ 1Þg;…”

A crystal plasticity analysis of length-scale dependent internal stresses with image effects

“…However, kernel functions have been derived for some fundamental cases accounting for finiteness of domains. Some of the examples involving single dislocations or dislocation arrays include geometries such as an elastic half-space (Head, 1953;Jagannadham and Marcinkowski, 1978;Lee and Dundurs, 1973;Lubarda and Kouris, 1996b;Ma and Lin, 2001) an infinitely long strip with two parallel free surfaces (Fotuhi and Fariborz, 2008;Moss and Hoover, 1978;Nabarro and Kostlan, 1978), a straight, rigid interface separating two dissimilar half-spaces (Chou et al, 1975;Jagannadham and Marcinkowski, 1980). These kernel functions aim at providing fundamental solutions based on discrete dislocations to the problems of image fields, but may differ based on the conceptual appeal (e.g., image dislocation versus surface dislocations).…”

“…'s at free surfaces. There are some classic studies on obtaining image stress fields arising from a single dislocation hosted in a semi-infinite medium (Jagannadham and Marcinkowski, 1979;Lubarda and Kouris, 1996b), in the proximity of a bi-material interface (Chou et al, 1975;Jagannadham and Marcinkowski, 1980;Lubarda and Kouris, 1996a) and in a thin strip with two free surfaces (Fotuhi and Fariborz, 2008;Hartmaier et al, 1999;Ting, 2008). (Saada, 2008) provided a brief review on the image fields arising from planar dislocation arrays and their contribution to the plastic deformation.…”

“…The solution to (ii) is incorporated by writing an available stress function for a single dislocation in a finite medium derived using complex Fourier transform approach (Fotuhi and Fariborz, 2008), equivalently in terms of the GND density. The resulting model is applied to investigate length-scale dependent responses triggered by internal stresses-(a) strengthening under monotonic pure bending as a function of decreasing specimen thickness and (b) kinematic hardening under cyclic pure bending.…”