Surface morphological stability underlies various reliability problems of technologically important materials with applications in aerospace, microelectronics, and nanotechnology. Applied mechanical stress has been known to induce surface morphological instabilities in crystalline solid materials. Specifically, linear stability analyses have demonstrated that the competition between elastic strain energy and surface energy can cause the growth of shape perturbations from a planar surface morphology and specified the conditions for the onset of the so-called Asaro-Tiller or Grinfeld instability. In addition, numerical simulations accounting for all the important nonlinearities have addressed the surface dynamics beyond the instability onset and revealed instability mechanisms. In particular, it has been demonstrated that a planar surface of a stressed elastic solid can evolve rapidly into a cusped surface, with smooth tops and deep crack-like grooves by surface diffusion, in agreement with experimental observations. These theoretical predictions are consistent with experimental findings over a broad class of materials. However, the effects of the simultaneous action of an electric field on the surface morphological response of an electrically conducting stressed solid have not been explored systematically.

In this presentation, we report results of linear stability analysis for the morphological response of the planar surface of a stressed elastic solid that is electrically conducting under the simultaneous action of an applied electric field. Our analysis is based on a surface transport model that accounts for curvature-driven surface diffusion, surface electromigration, and stress-driven surface diffusion along with surface diffusional anisotropy. We demonstrate that proper application of an electric field can have an important effect on the dynamical response of a planar stressed solid surface that is otherwise unstable with respect to long-wavelength perturbations. Specifically, we show that application of a sufficiently strong electric field can stabilize the surface of the stressed electrically conducting solid material that would be otherwise vulnerable to surface cracking under certain thermomechanical conditions; therefore, the electric current protects the material against cracking and inhibits its damage. In addition, we report the effects on the surface morphological stability of the misorientation angle between the electric field and fast diffusion directions, as well as the effects of key material properties, such as the strength of the surface diffusional anisotropy that is temperature dependent and the material's texture that is set by the surface crystallographic orientation. We show that (a) there exists an optimum range of misorientation angles for stable morphological response, (b) the strength of the surface diffusional anisotropy can have a stabilizing effect on the surface morphological response, and (c) under given electromechanical conditions, the surface morphological response of <111>-oriented surfaces is superior to that of <100>- and <110>- oriented ones.

In addition to the linear stability analysis, we report computational results for the morphological evolution of a solid surface perturbed from an initially planar morphology under the simultaneous action of an electric field and mechanical stress. The computational predictions for the morphological evolution are based on self-consistent dynamical numerical simulations according to the fully nonlinear surface mass transport model that was employed in the stability analysis; in the simulations, the fully nonlinear model is solved self-consistently with the electric field and stress field distributions on the solid surface, as computed through a Galerkin boundary integral method, and in conjunction with a front tracking method that monitors the surface propagation. The numerical results confirm the main conclusions of the linear stability analysis. In addition, for long-wavelength perturbations, the simulations reveal a tip-splitting instability that causes the appearance of wriggles in the surface morphology. Our findings can be used toward development of systematic surface engineering strategies for improved materials reliability over a broad range of electromechanical conditions.