The present paper continues the discussion in Part I. Model and Formulation. Based on the theory proposed in Part I, the formulae predicting stiffness moduli of the composites in some typical cases of whisker orientations and loading conditions are derived and compared with theoretical representatives in literatures, experimental measurement and commonly used empirical formulae. It seems that (1) with whisker reinforcing and matrix hardening considered, the present prediction is in well agreement with the experimental measurement; (2) the present theory can predict accurate moduli with the proper pre calculated parameters; (3) the upper bound and lower bound of the present theory are just the predictions of equal strain theory and equal stress theory; (4) the present theory provides a physical explanation and theoretical base for the present commonly used empirical formulae. Compared with the microscopic mechanical theories, the present theory is competent for modulus prediction of practical engineering composite in accuracy and simplicity. [WT5”HZ]
Based on study of strain distribution in whisker reinforced metal matrix composites, an explicit precise stiffness tensor is derived. In the present theory, the effect of whisker orientation on the macro property of composites is considered, but the effect of random whisker position and the complicated strain field at whisker ends are averaged. The derived formula is able to predict the stiffness modulus of composites with arbitrary whisker orientation under any loading condition. Compared with the models of micro mechanics, the present theory is competent for modulus prediction of actual engineering composites. The verification and application of the present theory are given in a subsequent paper published in the same issue
Rock experiment results indicate that the load/unload response ratio (LURR) of rocks expressed via strain energy may have singular or negative value after the stress in the rock reaches its maximum before rock failure or when the rock goes into the strain-weakening phase. The universality of this phenomenon is discussed. Expressed via strain or strain energy and the travel time of P wave, the variation form of the reciprocal of LURR during the process of rock failure preparation is derived. The results show that after a sharp decrease the reciprocal of LURR reaches its minimum when the main fracture of the rock is about to appear. This feature can be taken as an indication that the rock main fracture is impending.
A material model, whose framework is parallel spring-bundles oriented in 3-D space, is proposed. Based on a discussion of the discrete schemes and optimum discretization of the solid angles, a 3-D network cell consisted of one-dimensional components is developed with its geometrical and physical parameters calibrated. It is proved that the 3-D network model is able to exactly simulate materials with arbitrary Poisson ratio from 0 to 1/2, breaking through the limit that the previous models in the literature are only suitable for materials with Poisson ratio from 0 to 1/3. A simplified model is also proposed to realize high computation accuracy within low computation cost. Examples demonstrate that the 3-D network model has particular superiority in the simulation of short-fiber reinforced composites.
Aimed at brittle composites reinforced by randomly distributed short-fibers with a relatively large aspect ratio, stiffness modulus and strength, a mesoscopic material model was proposed. Based on the statistical description,damage mechanisms, damage-induced anisotropy, damage rate effect and stress redistribution, the constitutive relation were derived. By taking glass fiber reinforced polypropylene polymers as an example, the effect of initial orientation distribution of fibers, damage-induced anisotropy, and damage-rate effect on macro-behaviors of composites were quantitatively analyzed. The theoretical predictions compared favorably with the experimental results.
