Surface Of Elastic Half-plane Research Articles

Implementation of Dahl\u2019s dynamic friction model to contact mechanics of elastic solids

This study presents an analytical method for the solution of dynamic frictional contact problem between a rigid punch and an isotropic elastic solid. Rigid flat punch moves over the isotropic elastic solid at a constant subsonic speed and friction force develops based on Dahl’s friction law instead of Coulomb’s dry friction law. Dahl’s dynamic friction model is adopted since this model is one of the well-known dynamic friction models in the literature. According to this model, friction force depends only on a displacement rather than the speed of the punch since viscous effects are ignored. Influences of the parameters describing Dahl’s friction model on contact stress at slow and high speed sliding cases are examined. Analytical solution is conducted by means of Galilean and Fourier transformations. Friction force is computed numerically by the use of 4th order Runge–Kutta method for various displacements of the punch. Formulation for the contact problem is reduced to a singular integral equation and normal stress over the surface of elastic half-plane is determined. Obtained contact stresses are compared with those generated through finite element method and results display a high degree of accuracy. The influences of direction of motion, Coulomb’s coefficient of friction, pre-sliding displacement, asperity stiffness and shape factor of hysteresis loop upon contact stresses and stress intensity factors are revealed.

Initiation of parallel cracks from surface of elastic half-plane

The paper deals with the problem of initiation of thermal or shrinkage cracks from the surface of a half plane. Linear elastic fracture behavior is assumed. The initial spacing and initial stable equilibrium length of parallel equidistant cracks emanating from the surface is determined from three conditions formulated in a preceding study of penetration of sea ice plate: (1) The stress at the surface reaches a given strength limit. (2) After the initial cracks form, the energy release rate equals its given critical value. (3) The finite energy release due to the initial crack jump equals the energy needed to form the crack (according to the given fracture energy of the material or fracture toughness). The problem is reduced to a singular integral equation which is solved numerically by Erdogan's method. The results of analysis appear to be compatible with the experimental evidence on thermal cracking in glass, and appear to give also reasonable predictions for thermal cracking on top of sea ice plates and shrinkage cracking in concrete.

Initiation of parallel cracks from surface of elastic half-plane

Initiation of parallel cracks from surface of elastic half-plane