Thermal stress analysis of unidirectional fiber reinforced composites

Abstract

Composite materials are widely used in temperature fluctuating environments, which make these materials highly prone to cracking. The cracking phenomenon is a result of high thermal stresses that are generated by the mismatch in properties of the composite constituents, particularly the mismatch in the thermal expansion coefficient. The main objective of this study is to understand the micromechanics of such a phenomenon. The problem has been investigated using the finite element method (FEM). The analyses were performed utilizing 3-D prism and axisymmetric models. Hexagonal fiber packing of unidirectional composites was considered. The dimensions of the models were assumed such that the models could provide sufficient information on the behavior near the free surface as well as the interior of fiber composites. Properties of the constituents were considered to be temperature dependent. The elasto-plastic and visco-elastic characteristics of the materials were also included. The transient thermal analysis of the models showed that, for most practical applications, the temperature gradient in the composite constituents has minor effects on the stresses generated. Therefore, several stress analyses were performed assuming a uniformly changing temperature throughout the composite. The elastic analysis of thermal stresses and deformations showed high radial and hoop stress concentrations occurring at the fiber end on the free surface. This is contrary to the shear-lag theorem, which assumes that these stress components are negligible. An overlapping hypothesis, based on the deformation of the fiber and matrix, is proposed to explain such high radial and hoop stresses. Using regular FEM elements, it was concluded that the stresses are singular in nature. The stress singularity was numerically investigated and found to be of the type r ⁻ᵅ with α being dependent on the material properties but having a value close to 1/3. The elasto-visco-plastic behavior of composites was also analyzed. Large plastic strains were localized at the fiber end even for a small temperature change. Creep effects that were significant at elevated temperatures brought about some stress relaxation during the manufacturing process. Thermally induced stress concentration in composites can be controlled, to some extent, by changing the geometry of the free surface. The analysis of such effects indicated that reduction of the contact angle between the fiber and the matrix on the fire surface reduced the high radial and hoop stress magnitudes. Also, the influence of covering the free surface of the composite with a thin layer of matrix-like material was studied. The magnitudes of the radial and hoop stress components were substantially reduced. The case when the cover and the composite are made in separate stages (two-stage covering), was also studied. Based on the analysis, effective and practical ways of applying the cover are recommended. To verify the effects of the covering process, experiments were conducted on large-scale laboratory-made composite samples. The samples with the free surface covered with a thin layer of matrix-like material showed no trace of cracking or fiber/matrix debonding even after 1000 thermal cycles. On the other hand, in the samples without cover, exposed to identical thermal cycling, numerous matrix cracks and extensive fiber/matrix debonding were observed.