Elastostatic field distributions in polycrystals and cracked media

ABSTRACT

This work addresses the problem of the reconstruction of the local fields distribution occurring in heterogeneous linear elastic solids. The constitutive heterogeneities are crystals and cracks. Through comparisons with FFT computations, it is shown that self-consistent estimates together with an assumption of normal distribution at the phase scale provide an accurate description of the elastostatic field histograms in polycrystals without cracks. In the case of inter and transgranular cracks, full-field FFT simulations indicate that the field histograms present van Hove singularities. Their natures are determined analytically in the low-density regime, in the case of an homogeneous medium containing cracks.

KEYWORDS:

• Polycrystals
• cracked media
• field fluctuation
• self-consistent methods
• micromechanics
• Van Hove singularities

Acknowledgments

The authors thank J.-B. Gasnier for helping with the data in Figure 11. F.W. thanks D. Leguillon for letting him know about references [49,50] and Y.-P. Pellegrini for helpful discussions.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

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

Additional information

Funding

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