Stress field

About: Stress field is a research topic. Over the lifetime, 11926 publications have been published within this topic receiving 226417 citations.

The elastic stress field produced by a point force in a cubic crystal

Abstract: Fredholm in 1900 gave a solution in principle for the displacements generated by a point force at the origin in an infinite elastic solid. Eshelby in 1955 gave an approximate solution of the dilation for the triple force at the origin with no moment. Eshelby and Leibried gave expressions which converge only when The present calculation uses Fredholm's work to provide a Fourier expansion of displacement which converges for all stable cubic crystals. The convergence of the series giving the displacement due to a point force is very slow for lithium which is on the verge of a phase change Detailed calculations of stress fields have been made for aluminium and copper. It is noted that for Cu a contribution of additional terms besides that given by Eshelby appears in the angular dependence of dilatation for the triple double force but for Al the dilatation is in close agreement with Eshelby's result. The elastic interaction energies of two triple double force interstitials and of two single double for...

Fracture analysis in the conventional theory of mechanism-based strain gradient (CMSG) plasticity

Abstract: In a remarkable series of experiments, Elssner et al. (1994) and Korn et al. (2002) observed cleavage cracking along a bimaterial interface between Nb and sapphire. The stress required for cleavage cracking is around the theoretical strength of the material. Classical plasticity models fall short to reach such a high stress level. We use the conventional theory of mechanism-based strain gradient plasticity (Huang et al., 2004) to investigate the stress field around the tip of an interface crack between Nb and sapphire. The tensile stress at a distance of 0.1 μm to the interface crack tip reaches 13.3σY, where σY is the yield stress of Nb. This stress is nearly 4 times of that predicted by classical plasticity theory (3.6σY) at the same distance to the crack tip, and is high enough to trigger cleavage cracking in materials and interfaces. This is consistent with Elssner et al.'s (1994) and Korn et al.'s (2002) experimental observations.

The orientation dependence of elastic strain energy in cubic crystals and its application to the preferred orientation in titanium nitride thin films

Abstract: Elastic strain energy under some conditions provides the major contribution to the total energy of a film growing on a substrate from condensing vapour. Polycrystalline films grown with intrinsic stress induced by energetic bombardment are expected to show orientations which minimize total energy. Even for a cubic crystal in a non-hydrostatic stress field the energy is a function of the relative orientation of the stress field and the crystallographic axes. The Gibbs free energy is minimized under constant stress and temperature conditions at thermal equilibrium. In this paper we derive expressions for the Gibbs free energy of a cubic crystal in uniaxial and biaxial stress fields and find the conditions under which it is a minimum. The sign of the expression is the quantity which determines the behaviour of a cubic crystal and if negative, predicts that the [111] direction of the crystal will align with the principal stress of a uniaxial stress field and will lie normal to the plane of principal stresses in a biaxial stress field. Experimental evidence is presented which shows that titanium nitride, TiN, which has a negative value of , obeys these predictions. If is positive, then the [100] direction of the crystal obeys the above rules rather than the [111] direction.