The thermoelastic response of cracked polycrystals with hexagonal symmetry

ABSTRACT

The influence of a population of randomly oriented cracks on the macroscopic thermal and linear-elastic response of a hexagonal polycrystal is addressed using a self-consistent method. Coupling between micro-cracks and crystal anisotropy is taken into account through the effective medium where all inhomogeneities are embedded. In the absence of cracks, the proposed approach reduces to the self-consistent estimate of Berryman (2005). The accuracy of the present method is first assessed using numerical, Fourier-based computations. In the absence of crystal anisotropy, the estimates for the effective elastic properties are close to that obtained numerically for a homogeneous body containing disk-shaped cracks, with Boolean spatial dispersion. Various other analytical estimates and bounds, that are available for homogeneous cracked bodies, are also considered and compared to the present approach. Second, the combined role of crystal anisotropy and micro-cracks is investigated analytically, specifically when the in-plane shear modulus of the crystal becomes zero. The cracks-density percolation threshold is found to diminish abruptly in this limit. This ‘advanced’ percolation threshold is concomitant to the onset of large, weakly loaded regions surrounding cracks in strongly anisotropic crystals.

KEYWORDS:

• Cracked polycrystals
• homogenization
• thermoelasticity
• self-consistent methods
• percolation

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

F. Willot http://orcid.org/0000-0003-1544-6550

Dominique Jeulin http://orcid.org/0000-0001-6423-6926

Additional information

Funding

The financial support of the French Commissariat à l'Énergie Atomique is gratefully acknowledged.