Elastic stress field ahead of a crack like notch and critical misfit strain energy density as a local elastic fracture criterion

Abstract

<span style="font-size:11.0pt;line-height:115%; font-family:" calibri","sans-serif";mso-ascii-theme-font:minor-latin;mso-fareast-font-family:="" "times="" new="" roman";mso-fareast-theme-font:minor-fareast;mso-hansi-theme-font:="" minor-latin;mso-bidi-font-family:arial;mso-ansi-language:en-us;mso-fareast-language:="" en-us;mso-bidi-language:ar-sa"="">An analytical solution for the elastic stress field ahead of a fictitiously yielding notch has been presented. The derived expressions are valid only inside the elastic volume of material, behind the imaginary plastic zone. The results given are useful for a plane strain situation when the notch is fully loaded; taking the fictitious plastic zone size dimension on the crack extension plane as unity, The numerical results of elastic stresses show that there is a misfit on the crack extension plane. This weak discontinuity has been allowed to remain hypothetically at the fictitiously yielded-unyielded boundary. An avalanche of dislocations by reverse slip mechanism is seen to occur on the crack extension plane, before the onset of fracture, due to the sudden release of a mismatch load at a critical misfit elastic strain energy density, This misfit elastic strain energy density on the crack extension plane has maxima first at 0.2⁰ and then again at 0.6⁰ flank opening angles. Thus, the paper shows that a critical misfit elastic strain energy density should be the local fracture nucleation criterion for an elastic solid.</span>