On the separation of stress-induced and texture-induced birefringence in acoustoelasticity

Abstract

In this paper we develop a simple micromechanical model of a prestressed polycrystalline aggregate, in which the texture-induced and stress-induced anisotropies of the aggregate are precisely defined; here the word 'texture' always refers to the texture of the aggregate at the given prestressed configuration, not to that of a perhaps fictitious natural state of the aggregate. We use this model to derive, for a prestressed orthotropic aggregate of cubic crystallites, a birefringence formula which shows explicitly the effects of the orthotropic texture on the acoustoelastic coefficients. From this formula we observe that, generally speaking, we cannot separate the total birefringence into two distinct parts, one reflecting purely the influence of stress on the birefringence, and the other encompassing all the effects of texture. The same formula, on the other hand, provides for each material specific quantitative criteria under which the 'separation of stress-induced and texture-induced birefringence' would become meaningful in an approximate sense

Stress-dependent second-order grain statistics of polycrystals

“…To arrive at N, the stress-dependent effective elastic modulus for a single crystallite was defined as C eff , which is homogenized in order to define the analogous tensor hC eff i. hC eff i is the stress-dependent effective elastic modulus tensor for a stressed polycrystal. The definition of N differs from the previous definition in Turner and Ghoshal 17 by making use of the constitutive stress/strain relation developed by Man and co-workers and Huang et al [31][32][33][34][35][36][37] This constitutive relation introduces the initial stress r, which is valid for residual or mechanically induced stresses.…”

“…The characterization of the stress-dependence in N was first given by Turner and Ghoshal 17 and later demonstrated experimentally by Kube et al 18,19 The present theory utilizes a more commonly used elastic constitutive relation, [31][32][33][34][35][36][37] which is valid for both residual and mechanical stresses. This constitutive relation leads to different stress-dependent elastic properties than those given by Turner and Ghoshal.…”

“…(A5) in Appendix A]. 17 The theory is divided into two sections, which result in the outcome of an expression for the stress-dependent eighth-rank covariance tensor N. Section II A follows from the theory of acoustoelasticity developed by Man and coworkers and Huang et al [31][32][33][34][35][36][37] In this treatment, a constitutive relation for elastic media containing an initial stress is employed in order to derive equations of motion for a smallamplitude harmonic plane wave. A stress-dependent Christoffel equation follows from the equation of motion, which is applicable to materials belonging to any crystallographic symmetry group.…”

“…Thus, the possible complex plastic deformation processes that led to the initial state of stress are of no concern. A number of models for acoustoelasticity [32][33][34][35][36][37] related closely to the formalism of Man and Lu 31 followed. Due to the advantage of its applicability to materials having residual stresses, we adopt their form of the constitutive relation valid for polycrystalline materials with an initial stress 33,37 …”

Stress-dependent ultrasonic scattering in polycrystalline materials

“…26 The derivation of N was based on the constitutive relation derived by Man and co-workers, which is valid for both residual and mechanical stresses. [27][28][29][30][31][32] The components of N were shown to be quadratic with respect to the magnitude of the components of the Cauchy stress tensor, e.g., N…”