A STUDY OF THE MICROMECHANICAL CONSTITUTIVE BEHAVIOR OF BRITTLE CRYSTALLINE SOLIDS

A method is proposed for determination of microplastic strains in pure polycrystalline solids prior to initiation of microfracture or macroscopic yielding. The development of the theory is based upon Cottrell's classical picture of slip due to movement of dislocations and their consequent pile-up at grain boundaries. It is assumed that each grain has a single dominant slip plane, and that microplastic hardening occurs due to continuous activation of the Frank-Read sources in the crystalline grains. The orientation of the crystalline grains is assumed to be completely random and isotropic. Slip is considered to occur along the direction of maximum resolved shear stress on the slip plane. It is shown that the total microplastic strain in polycrystalline solids depends on the third power of the average grain diameter. The restraining effect of the polycrystalline aggregate is taken into account by considering Eshelby's fundamental inclusion problem. The excellent correlation that exists between the calculated and the experimentally obtained results testifies to the effectiveness of the theory.;A micromechanical theory is developed for the constitutive analysis of pure initially uncracked polycrystalline solids. The development of the theory is based upon the Zener-Stroh theory of microfracture. It is assumed that under increasingly applied stresses, a polycrystalline solid is continuously subjected to isotropic microcrack nucleation. A material constant is introduced (coefficient for isotropic microcrack nucleation), which is equal to the ratio of the microcrack density to the concentration of the nucleated microcracks, and is believed to characterize the extent of the defect structure in the polycrystalline solid. The proposed global criterion for microcrack nucleation is that the resolved shear stress on the plane of a dislocation pile-up must reach a 'nucleation stress,' which is the shear stress on the most favorably oriented slip plane in the largest grain in the polycrystalline solid. Continuous microcrack nucleation is, therefore, based upon a 'microcracking hardening' principle. It is suggested here that under uniaxial tensile loading, a Zener-Stroh microcrack is stopped at a grain boundary and undergoes interfacial displacement jumps, which contributes to the overall inelastic strains in the polycrystalline solid. It is shown that free-slipping has a significant effect on the overall inelastic strain, and that the magnitude of inelastic strain due to microcracking is proportional to the third power of the average grain diameter. Excellent agreement is found between the experimentally measured, and theoretically calculated values of the inelastic strain due to microcracking under uniaxial tensile loading.