Creep of particle and short fibre reinforced polyurethane rubber

Tensile stress–strain testing and creep testing have been carried out on a polyurethane rubber, at three temperatures, with and without either particulate or short fibre alumina reinforcement. A previous paper reported concerning composites with particulate reinforcement and the present work is focused on the effect of the fibres. The samples were made via a blending and extrusion process that produced a certain degree of fibre alignment (along the direction of loading). Prior milling procedures were used to produce fibres with two different ranges of aspect ratio (with averages about 10 and 16). When expressed as true stress–strain relationships, all materials exhibit approximately linear responses. The dependence of stiffness on the volume fraction and aspect ratio of the reinforcement was found to conform well to the Eshelby model predictions. Moreover, the creep behaviour of all of the materials can be captured well by a Miller–Norton formulation, using the average matrix stress predicted by the Eshelby model. A striking conclusion is that it is both predicted and observed that short fibres are much more effective in reducing the creep rate than is the case with particles.

Implementation of the self-consistent Kröner–Eshelby model for the calculation of X-ray elastic constants for any crystal symmetry

In this paper, we will report about the implementation of the self-consistent Kröner–Eshelby model for the calculation of X-ray elastic constants for general, triclinic crystal symmetry. With applying appropriate symmetry relations, the point groups of higher crystal symmetries are covered as well. This simplifies the implementation effort to cover the calculations for any crystal symmetry. In the literature, several models can be found to estimate the polycrystalline elastic properties from single crystal elastic constants. In general, this is an intermediate step toward the calculation of the polycrystalline response to different techniques using X-rays, neutrons, or ultrasonic waves. In the case of X-ray residual stress analysis, the final goal is the calculation of X-ray Elastic constants. Contrary to the models of Reuss, Voigt, and Hill, the Kröner–Eshelby model has the benefit that, because of the implementation of the Eshelby inclusion model, it can be expanded to cover more complicated systems that exhibit multiple phases, inclusions or pores and that these can be optionally combined with a polycrystalline matrix that is anisotropic, i.e., contains texture. We will discuss a recent theoretical development where the approaches of calculating bounds of Reuss and Voigt, the tighter bounds of Hashin–Shtrikman and Dederichs–Zeller are brought together in one unifying model that converges to the self-consistent solution of Kröner–Eshelby. For the implementation of the Kröner–Eshelby model the well-known Voigt notation is adopted. The 4-rank tensor operations have been rewritten into 2-rank matrix operations. The practical difficulties of the Voigt notation, as usually concealed in the scientific literature, will be discussed. Last, we will show a practical X-ray example in which the various models are applied and compared.

Internal Stress in an Alumina/Silicon Carbide Whisker Composite

The internal stress state in a Al2O3-SiC composite has been studied with X-ray diffraction and with calculations with a modified Eshelby model. The influence (on the internal stress state) of volume fraction, temperature, geometric shape, and the orientation of the silicon carbide particles are discussed. The stress tensors were measured in both the matrix and in the reinforcing phase, and the macro- and microstresses were separated for ail the components. Good agreement with the microstresses for the Eshelby model is found in all cases.Results from X-ray diffraction experiments at low temperature (45-295 K) on the coefficient of thermal expansion are also presented.