An Atlas of Asymptotically Singular Stress Fields in Axisymmetric Fiber Push-Out Model

Abstract

Abstract Extracting fiber-matrix interface properties from single fiber push-out experimentation results requires careful micro-mechanical modeling. The axisymmetric concentric cylinder model is widely used to determine stress and damage state in the fiber, matrix, and at the interface. Several mechanics models developed for analyzing this model recognize the existence of asymptotically singular local regions for analyzing the stress fields in fiber push-out, but a comprehensive description of the nature of these stress fields and estimates for the regions of their influence is not available. Early work by Zak has shown that plane strain singularities which are separable in radial and angular directions dominate in the axisymmetric model at regions close to the point of singularity. Later efforts characterized the power of the radial singularity and angular variations of the singular stress fields in the model. In this paper the qualitative and quantitative nature of the singular stress fields, their regions of dominance, and scaling of the stress intensity with applied load for several fiber-matrix interface conditions are described. The presented results are obtained using a local-global matching technique which uses combined asymptotic and finite element methods to determine the stress fields in the local regions. The results are presented for both edge/corner singularities and for crack tip singularities in the model. The fiber radius and fiber volume fraction are considered as the geometric parameters. The material mismatch effects are considered using a wide spectrum of Dundurs mismatch parameters. Several interface conditions including perfectly bonded, partially cracked, debonding with frictional sliding of the crack tips and the oscillatory bi-material singularities are considered. Two different loading conditions, namely the thermal residual stresses and the push-in displacement loads are considered. The paper focuses on the local stress fields as determined by the first and second (when singular) terms of the asymptotic expansion and their scaling with applied loading. The paper provides an atlas of the nature of the stress singularities (power of the stress singularity, mode mixity, the angular variation, and region of dominance) and the approximate stress intensity factors in the model for the two loading types for most practical fiber-matrix combinations, interface frictions and model geometric parameters.