On the depth of cylindrical indentation of an elastic half-space for two types of displacement constraints

For cylindrical indentation of elastic half-space the relationship between the depth of indentation delta and the applied force F is nonlinear, in contrast to the linear relationship between the height of the contact zone delta_0 and the force F. While the latter is independent of the boundary conditions used to specify the rigid-body translation, the former depends on a selected datum for vertical displacement. The depth of the indentation is determined for any permissible value of the length b, which specifies the points of the free surface where the vertical displacement is required to be zero, w(b)=0. From the condition that the work of the indentation force is equal to the work of the contact pressure, it follows that the indentation is geometrically and physically possible under imposed boundary conditions w(b)=0 provided that b>=b_min. The numerical value of b_min is found to be about 10 times greater than the semi-width of the contact zone a, based on the numerical precision in fulfilling the work condition W_F=W_p. If a datum is taken to be at a point at some distance h below the load, there is an alternative closed-form expression for delta in terms of F, which involves the Poisson ratio nu. For nu=1/3, it is found that h_min is about 21a. A simple expression relating the permissible values of h and b is derived, which is linear for large values of h and b

Image force on a straight dislocation emitted from a cylindrical void

AbstractThe image force exerted by the free surface of a cylindrical circular void on a nearby straight dislocation depends on whether the dislocation has arrived at its location by the emission from the surface of the void, or by the glide from infinity. In the context of elasticity theory, in the first case, the dislocation has been created by imposing the displacement discontinuity along the cut from the free surface of the void to the center of the dislocation, and, in the second case, from the center of the dislocation to infinity. The explicit expressions for the two corresponding image forces are derived and compared. It is shown that the attraction from the free surface of the void is stronger in the first case, particularly for smaller voids. Furthermore, in the case of dislocation emitted from the surface of the void, the interaction energy depends on the cut used to impose the displacement discontinuity, but not in the case of a dislocation approaching the void from infinity. The relevance of the obtained results for the materials science problems is discussed

Determination of the belt force before the gross slip

The mechanics of belt friction before the state of gross slip is considered. The variation of the belt force within the contact region is evaluated based on the assumption of gradual growth of slip from the pull-end to the hold-end of the belt, as the pull force increases towards its Euler's value. The local pressure and friction forces exerted by the belt on the cylinder are also determined. Both flat and V-shaped belts are considered. The total pressure and friction forces are evaluated at an arbitrary stage of slip growth. They are neither proportional nor orthogonal to each other, unless the state of gross slip is reached throughout the contact range

CHAPTER 05 : FINITE STRAIN ELASTICITY

Elastic deformation does not cause irreversible rearrangement of internal structure, and the corresponding Helmholtz free energy is a function of stress and temperature only. Restricting consideration to isothermal elastic deformation (θ = 0), Eqs. (4.3.7) and (4.3.9) givė ψ = ∂ψ ∂E (n

Dislocation Burgers vector and the Peach–Koehler force: a review

Different definitions of the Burgers vector and the corresponding construction of the Burgers circuit for dislocation loops and straight dislocations, created by the displacement discontinuity imposed across different surface cuts are reviewed. This is used as a geometric background for the derivation and discussion of the Peach–Koehler expression for the energetic force exerted on a dislocation by different sources of stress. Three approaches were used and compared: (i) the classical virtual work approach of Peach and Koehler, extended to include the changes in size and shape of the dislocation loop; (ii) the potential energy approach which allows the incorporation of the effects of image stresses; and (iii) the approach based on the evaluation of the J-integral. The glide and climb components of the dislocation force are determined and discussed for continuum and lattice dislocations. Keywords: Burgers circuit, Burgers vector, Climb force, Dislocation loop, Glide force, Image stress, J integral, Osmotic force, Peach–Koehler force, Potential energy, Virtual wor