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. 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 a similar formulation the wedging of an elastic plane is considered for a finite wedge moving at a distance from 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: the stress field singular points on the contact area (super-Rayleigh subsonic speed regime), the wave radiation (intersonic and supersonic regimes) and the fracture resistance (wedging problem). In addition to the sub-Rayleigh speed regime, where the sliding contact itself gives no contribution to the driving forces, there exists a sharp decrease in the resistance in the vicinity of the longitudinal wave speed with zero limit at this speed. (C) 2012 Elsevier Ltd. All rights reserved.
Driving forces in moving-contact problems of dynamic elasticity: Indentation, wedging and free sliding
2012
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. 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 a similar formulation the wedging of an elastic plane is considered for a finite wedge moving at a distance from 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: the stress field singular points on the contact area (super-Rayleigh subsonic speed regime), the wave radiation (intersonic and supersonic regimes) and the fracture resistance (wedging problem). In addition to the sub-Rayleigh speed regime, where the sliding contact itself gives no contribution to the driving forces, there exists a sharp decrease in the resistance in the vicinity of the longitudinal wave speed with zero limit at this speed. (C) 2012 Elsevier Ltd. All rights reserved.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
