Abstract:
The body deformation in terms of a planar layer weakened by a cut is considered. As the radius of curvature of the cut tends to zero at the maximum free-energy point, the cut transforms into a mathematical cut. The use of classical conditions for determining the elastic limit leads to the formation of plastic regions under an arbitrarily small external load. To solve this problem, the free energy flow through a cutout arc section is introduced as the product of the free energy density at the point of its maximum and a linear parameter. The free energy flow is represented by the sum of the volumetric- and shape-change energy flows. The energy flow of the shape change is limited by the elastic limit as a result of the accepted generalized condition of reversible deformation. When moving to technological cutouts, converting this condition into the Mises criterion allows one to obtain the threshold length of the linear parameter. For bodies with technological cutouts, the external load corresponding to the elastic limit depends on the curvature radius. For crack-like notches with radii of curvature varying from a threshold value to zero, the external load is constant. Based on the known asymptotic solutions, the external loads corresponding to the elastic limit are obtained using a threshold linear parameter.
Keywords:free energy flow, ultimate elastic load, strip with a cut.
Fulltext:
PDF file (555 kB)