Crack growth, singularities and wave propagation in auxetic composite materials

Abstract

An auxetic material is a material which has a negative Poisson's ratio, so they exhibit lateral expansion upon longitudinal tensile loading, or undergo lateral contraction under longitudinal compression. Such materials can exist in cellular form, or along specific axes in certain crystals. The singularity order in a half plane consisting of two quarter dissimilar materials and the singularity at the tip of interfacial crack have been studied where the bi-material contains an auxetic material. The main goal was to investigate the effects of the auxetic behavior on the singularities. We have determined that the auxetic material has a significant effect on the singularity order. For example, the free-edge singularity can be removed for certain combinations of elastic moduli and auxetic Poisson's ratios. In general, the effects of the mismatch of elastic constants between the two materials on the singularity have been investigated and all these results will be shown in this dissertation. The effect of a single particle or inclusion on crack propagation has been studied effectively using symmetric Galerkin boundary elements and a modified quarter-point crack tip element. Typical results show that an inclusion can decrease the crack-tip stress intensity as the crack approaches an inclusion, followed by deflection of the crack. Interestingly, as the crack extends beyond the inclusion there can also be an amplification of stress intensity. These previous results have shown the great influence the presence of an inclusion may have on a crack extension behavior. Here, we examine the influence of an auxetic particle on crack growth behavior. The objective of the present study is to understand the crack extension behavior and predict the crack growth direction in materials reinforced with auxetic particles. We will show the dramatic difference in crack path as compared to particles with positive Poisson's ratio. The effects of a negative Poisson's ratio on wave propagation in elastic media are investigated numerically. Different types of elastic wave problems are taken into account. These problems are the reflection and transmission of SH-waves, and P-waves in two half-spaces and the SH-wave propagation in layered half-space. We focused on the elastic wave amplitude as a function in Poisson's ratio of this study. The results indicate a significant effect of auxetic material on wave amplitude. For example, the negative Poisson's ratio suppresses reflection and the incident wave totally transmits through the interface. Also, it reduces the value of the transmitted wave amplitude nearly to one half with compared to the incident wave amplitude. In another example, the auxetic material converts the value of amplitude from complex to real.