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|Title:||AXISYMMETRICAL STRESS-DISTRIBUTION IN THE VICINITY OF AN EXTERNAL CRACK UNDER GENERAL SURFACE LOADINGS|
|Publisher:||PERGAMON-ELSEVIER SCIENCE LTD|
|Citation:||INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES, 30(18), 2567-2586|
|Abstract:||A solution is derived of the equations of equilibrium appropriate to the axisymmetric loading on the faces of a plane crack covering the outside of a circle of radius a in an infinite isotropic elastic body. Abel transforms of stress and displacement components at an arbitrary point of the solid are known in the literature in terms of the Abel transforms of the jumps of the stress and displacement components at the crack plane. Limiting values of these expressions, as we approach the crack plane from either side, are a great help in dealing with the problem The boundary conditions lead to Abel type integral equations which admit closed form solutions. The expressions for stress and displacement components on the crack plane are obtained explicitly in terms of the prescribed stress components on the crack surfaces. The surface tractions on the crack are symmetrical about the centre of the circle but not necessarily self-equilibrating. In order to illustrate the use of general formulae, some special cases of the loading functions are discussed in detail. In the first case the upper crack surface is subjected to a uniform normal stress acting over a circular ring of inner and outer radii epsilon and c, respectively, while the lower crack surface is free from tractions. In a second case the upper crack surface is subjected to a radially decaying shear load acting over a circular ring of inner and outer radii epsilon and c, respectively, while the lower crack surface is free from tractions. Also, we obtain the results for normal and shear concentrated ring loads by taking the limit as epsilon --> c while the total applied load is kept fixed. The expressions for displacement components on the crack plane are in terms of complete as well as incomplete elliptic integrals of the first and second kinds. Numerical calculations for the normal components of displacement on the crack surfaces are carried out and the results are presented|
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