T he governing field equations and boundary conditions for stress assisted diffusion are derived from basic principles of continuum mechanics and irreversible thermodynamics Attention is confined to elastic and viscoelastic material response, with emphasis on isotropy and the case of small strains It is shown that both the diffusion process and the saturation levels are stress dependent In viscoelstic materials the time-dependence of the moisture boundary condition causes the saturation level to drift with time In addition, the diffusion process becomes non-linear in stress, in spite of the linearity of the mechanical behavior

Stress Assisted Diffusion in Elastic and Viscoelastic Materials.

This paper derives the governing equations for the thermomechanical behaviour of composites. When the basic equations for the thermoelastic behaviour of solids were first derived in the nineteenth century several approximations were made. The effect of these assumptions are discussed and illustrated by the results of a simple laboratory test. The implications of this work on the analysis of impact damaged laminates are then discussed.

Thermomechanical behaviour of composites

Preexisting defects and damage under load introduce additional inhomogeneities that make analytical modeling of composite systems difficult. The non-homogeneous and/or anisotropic character of composite behavior is load time history dependent and invalidates many of the testing procedures developed for the more traditional monolithic materials. Composite specimens even though are simplified in terms of loading and geometric configuration respond inherently as structures. The relative response between any two composite systems is case-specific and has to be validated through analysis and experiment. This communication addresses a number of topics that require scrutiny in the prediction of composite material behavior and/or failure. The dominant flaw model can yield useful information in situations where subcritical material damage has a negligible influence on the energy released at incipient fracture. Analytical modeling of interface behavior between fiber and matrix or laminae is not always straightforward because load transmission from one material to another is affected by stress state in addition to being material dependent. Emphasized is the quantitative assessment of the degree of local inhomogeneity which can be measured by fluctuation of the strain energy density function, dW/dV. The local and global stationary values of dW/dV are found not only useful for identifying the sites of possible failure and yielding but also the stability of composite systems that depends on the combination of loading, geometry and material inhomogeneity. Composites being vulnerable to aggressive environmental changes can behave very differently when the moisture and temperature conditions are altered. Results are presented for a crack in T300/5208 graphite fiber laminate subjected to moisture, temperature and stress boundary conditions. These influences can, in general, be coupled and lead to failure modes that are not intuitively obvious.

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Analysis of defects and damage in composites

Moisture and/or temperature can affect the transient character of the stresses near crack-like defects with or without the additional influence of mechanical loads. Although an exhaustive amount of test data have been collected, there lacks a quantitative assessment of how the governing physical, geometric and loading parameters would interact. Without a fundamental understanding of the interaction of moisture and temperature diffusion with mechanical deformation, materials and structural components could not be expected to perform reliably. This is particularly significant to the design of performance composites that are frequently required to sustain severe moisture and temperature environments.

Moisture and Temperature Effects on the Transient Stresses Around Crack-Like Defects

Analytical treatment of coupled diffusion and deformation problems becomes unmanageable when the geometries and/or boundary conditions are complex The finite element technique as presented in Chapter 4 can again be applied No additional difficulties prevail as the governing equations for deformation coupled with diffusion are similar to those with uncoupled deformation An iteration process, however, must be adopted such that the temperature, moisture and stress field for each time increment must satisfy the equations in accordance with the specified boundary conditions Particular choice of the space and time increment for a given system requires special attention in order for the solution to converge This is resolved by resolving the time portion of the problem in the Laplace transform domain such that the space portion is evaluated by the finite element procedure

Numerical analysis of coupled diffusion and deformation problems

: A system of coupled differential equations involving moisture, temperature and stress are derived within the framework of classical thermodynamics. Analyzed are the transient character of the stress and energy density distribution around a circular cavity in a cross-ply graphite T300/5208 epoxy resin laminate assumed to behave in a quasi-isotropic manner. The laminate is stretched uniaxially such that a mutual interaction of moisture, temperature and stress depend on whether the laminate is in a state of plane strain or plane stress. Unlike the case of moisture-temperature and stress being uncoupled, the diffusion coefficients for plane strain must be distinguished from those for plane stress when stress coupling effects are included. Time-dependent numerical results are obtained from a finite element formulation and reveal that stress coupling can have a marked influence on the solution, both qualitatively and quantitatively. This is particularly significant near defects or cavities where the stress and energy state experience high elevation. The neglect of stress coupling can lead to unconservative predictions. Possible failure sites are predicted from the strain energy density criterion which assume that excessive dilation is associated with material separation while excessive distortion with yielding.

M T Shih

Papers

A Generalized Couple Theory of Hygrothermal-Elasticity: Transient Effects in Composite Laminate with Circular Cavity.