The steady-state solution for an elastic half-plane under a moving frictionless smooth indenter of arbitrary shape is derived based on the corresponding transient problem and on a condition concerning energy fluxes. The resulting stresses and displacements are found explicitly starting from their expressions in terms of a single analytical function. This solution incorporates all speed ranges, including the super-Rayleigh subsonic and intersonic speed regimes, which received no final description to date. Next, under similar formulation the wedging of an elastic plane is considered for a finite wedge moving at a distance of the crack tip. Finally, we solve the problem for such a wedge moving along the interface of two elastic half-planes compressed together. Considering these problems we determine the driving forces caused by the main underlying factors: stress field singular points on the contact area (the super-Rayleigh subsonic speed regime), the wave radiation (intersonic and supersonic regimes) and the fracture resistance (the wedging problem). It was found that in addition to the sub-Rayleigh speed regime, where a the contact sliding itself gives no contribution to the driving forces, there exists a sharp decrease in the resistance in a vicinity of the longitudinal wave speed with zero limit at this speed.
Driving forces in moving-contact problems of dynamic elasticity: indentation, wedging and free sliding
BRUN, MICHELE
2012-01-01
Abstract
The steady-state solution for an elastic half-plane under a moving frictionless smooth indenter of arbitrary shape is derived based on the corresponding transient problem and on a condition concerning energy fluxes. The resulting stresses and displacements are found explicitly starting from their expressions in terms of a single analytical function. This solution incorporates all speed ranges, including the super-Rayleigh subsonic and intersonic speed regimes, which received no final description to date. Next, under similar formulation the wedging of an elastic plane is considered for a finite wedge moving at a distance of the crack tip. Finally, we solve the problem for such a wedge moving along the interface of two elastic half-planes compressed together. Considering these problems we determine the driving forces caused by the main underlying factors: stress field singular points on the contact area (the super-Rayleigh subsonic speed regime), the wave radiation (intersonic and supersonic regimes) and the fracture resistance (the wedging problem). It was found that in addition to the sub-Rayleigh speed regime, where a the contact sliding itself gives no contribution to the driving forces, there exists a sharp decrease in the resistance in a vicinity of the longitudinal wave speed with zero limit at this speed.
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