Three-dimensional analysis of micro-residual stresses in fibrous composites based on the energy method: a study including interphase effects

In polymer composites, thermal residual stresses arise due to the mismatch of the thermal expansion coefficients of the fiber and matrix. Polymer composites generally consist of three phases: fiber, matrix, and the interphase. In this article, to study the effects of the interphase on residual stresses, a three-dimensional energy-based closed-form solution is developed. Residual stresses are assumed variable along longitudinal and radial directions, and two Airy stress functions are introduced. By considering the interphase region, in comparison with the perfect bonding conditions, thermal residual stresses decrease. The longitudinal residual stress distribution is sensitive to the interphase thickness. The maximum axial stress occurs at the fiber mid-length and decreases by increasing the interphase thickness. The maximum fiber–interphase and interphase–matrix interfacial shear stresses vary by increasing the interphase thickness, whereas their position is approximately unchanged. An increase in the interphase thickness leads to a decrease of the shear stress concentration factor near the fiber ends. For different magnitudes of bonding efficiency, the interfacial radial stresses are zero at the maximum fiber length. Although, the interphase region has a minor effect on the interfacial radial stresses, it has a significant effect on the maximum interfacial radial stresses at the fiber ends.