Micromechanical prediction of ultimate strength of transversely isotropic fibrous composites

This series of papers reports a new, general, and unified micromechanical model for estimating the three-dimensional mechanical properties of a composite made from two constituent materials, i.e., continuous fiber and matrix. The present paper addresses the application of the model to rubber-based composites, with a focus on prediction of the entire stress-strain response characteristic of a composite having an elastomer matrix constituent material. For this purpose, an accurate constitutive theory has been developed for any incompressible rubber-like material. Its incremental stress-strain relationship at any given level is simply correlated by a load-dependent compliance matrix, similar to Hooke's law. The theory is consistent in that when the involved material parameters, i.e., the load-dependent Young's modulus and Poisson's ratio, are determined using a single type of test data such as uniaxial tension data, it is then able to predict precisely the material responses to other types of deformation con...

A Unified Micromechanical Model for the Mechanical Properties of Two Constituent Composite Materials. Part IV: Rubber-Elastic Behavior

A three-dimensional (3D) finite element (FE) analysis of the stress concentration factor (SCF) around a broken fibre in a model composite has been performed. This model composite consisted of a planar array of five carbon fibres positioned in the centre of an epoxy tensile bar. Two cases were considered, namely the case of perfect fibre/matrix adhesion and the case of poor fibre/matrix adhesion. For the case of perfect fibre/matrix adhesion, a parametric study was performed to study the influence of the inter-fibre spacing, matrix plasticity, and the ratio of the matrix modulus (Em) to the fibre modulus (Ef) on the stress concentration around a fibre break. It was found that the SCF increases with an increase of the ratio Em/Ef, an increase of the matrix yield stress, and a decrease of the inter-fibre spacing. For the case of poor fibre/matrix adhesion, a parametric study was performed to study the influence of the debonded length and the coefficient of friction on the SCF. It was found that the SCF increases with a decrease of the debonded length and an increase of the coefficient of friction. More importantly, the results of the FE analysis were validated against experimental results obtained with Raman spectroscopy. In this validation three matrix systems with varying mechanical behaviour and two carbon fibres with different levels of fibre/matrix adhesion were considered. In general, good agreement between the experimental stress situation and the calculated stress situation of the fibres in the model composite was found. At relatively small inter-fibre spacings, however, the FE analysis predicts SCFs slightly lower than experimentally measured.

Failure phenomena in two-dimensional multi-fibre model composites: 5. A finite element study

The mechanics of composite strength evolution

Simultaneous fiber-failure (SFF) model that determines tensile strengths for various systems of unidirectional composites comprehensively is presented. The SFF derives the strength of unidirectional composites as a function of the single-fiber strength distribution, interfacial shear strength, and matrix strength. The point of the SFF is that a fiber group which is considered to be experiencing simultaneous fiber failures triggered by neighboring fiber failures is assumed to fail when the weakest fiber in the fiber group fails. We discuss a method to determine the magnitude of the fiber group for various systems of composites on a basis of whether a crack located near a bi-materials interface penetrates into another material or deflects along the interface. The SFF is established by integrating the magnitude of the simultaneous fiber failures into the conventional Global load sharing model.

A Comprehensive Model for Determining Tensile Strengths of Various Unidirectional Composites

A micromechanics model has been developed to predict the tensile strength of unidirectional composites. The local stresses are calculated using shear lag analysis, including the effects of interfacial debonding. The tensile strength of the composite is estimated by considering the accumulation of fiber fractures as a function of applied load. A new parameter called ‘efficiency’ of the interface is introduced to account for the effectiveness of load transfer from the matrix to the fiber. A simple scheme is described to estimate this efficiency parameter η using the experimentally measured tensile stiffness in the concentric cylinders model. It is postulated that the interface can be completely characterized by two parameters: interfacial shear strength τi and efficiency of the interface η. Results indicate that the interfacial strength and efficiency can be optimized to maximize the tensile strength of a unidirectional composite. The proposed model was used to predict tensile strength of three different sets of materials that possessed carefully tailored interphase variations. The predicted tensile strengths agree well with the experimental data. The predicted failure modes in these material systems are also consistent with experimental observations.

Suresh Subramanian

Papers

Tensile Strength of Unidirectional Composites: The Role of Efficiency and Strength of Fiber-Matrix Interface