Surface cracks and boundaries

MORE (flinching) Content If they d open a crack that wide (between finger and thumb) I d be through it. (A Man for All Seasons, Robert Bolt 1960) 

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This paper compares experimental data for aluminium and steel specimens with two methods of solving the forward problem in the thin-skin regime. The first approach is a 3D Finite Element / Boundary Integral Element method (TRIFOU) developed by EDF/RD Division (France). The second approach is specialised for the treatment of surface cracks in the thin-skin regime developed by the University of Surrey (England). In the thin-skin regime, the electromagnetic skin-depth is small compared with the depth of the crack. Such conditions are common in tests on steels and sometimes on aluminium. 

At sufficiently high frequency, the electromagnetic skin depth is several times smaller than a typical defect and induced currents flow in a thin skin at the conductor surface and the crack faces. It is profitable to develop a theoretical model dedicated to this regime. Making certain assumptions, a boundary value problem can be defined and solved relatively simply leading to rapid numerical calculation of eddy-current probe impedance changes due to a variety of surface cracks. 

Submitting the main topic, we deal with models of solids with cracks. These models of mechanics and geophysics describe the stationary and quasi-stationary deformation of elastic and inelastic solid bodies having cracks and cuts. The corresponding mathematical models are reduced to boundary value problems for domains with singular boundaries. We shall use, if it is possible, a variational formulation of the problems to apply methods of convex analysis. It is of importance to note the significance of restrictions stated a priori at the crack surfaces. We assume that nonpenetration conditions of inequality type at the crack surfaces are fulfilled, which improves the accuracy of these models for contact problems. We also include the modelling of problems with friction between the crack surfaces. 

Here [ ] is the jump of a function across the crack faces and v is the normal to the surface describing the shape of the crack. Thus, we have to find a solution to the model equations of a thermoelastic plate in a domain with nonsmooth boundary and boundary conditions of the inequality type. 

Under boundary friction conditions, the exposed metal surface is extremely reactive due to mechanical activation. Exoemission occurs when a material surface is disturbed by plastic deformation, abrasion, fatigue cracking, and phase... 

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