Development of constitutive models for thin thermoelastic interphase in composite materials

Composite materials consist of two or more constituent phases with distinct geometries and physical properties. These materials incorporate reinforcements that enhance their overall thermo-mechanical performance. At the micro-mechanical scale, a distinct interphase forms between the constituent materials, characterized by its own unique set of properties. The thermo-mechanical behavior across this interphase is of critical importance, as gradients or discontinuities in these properties may lead to localized accumulations of thermal or mechanical energy and the corresponding surface fluxes. Such accumulations can serve as precursors to the initiation of micro-cracks within the composite. Under repeated cyclic loading, these micro-cracks can propagate throughout the domain, ultimately leading to structural failure. Therefore, a comprehensive understanding of the micro-mechanical behavior within the interphase is essential for optimizing the structural integrity of composite systems. However, due to the extremely small thickness of the interphase, accurately modeling its behavior and capturing variations across and within it presents a significant computational challenge. To address these difficulties, the physical interphase in the three-phase problem is replaced with an equivalent zero-thickness interface that represents the boundary between the two materials. Numerical models are then formulated across this interface to replicate the discontinuities (jumps) in thermo-mechanical fields, thereby substantially reducing the computational cost associated with direct modeling of the thin interphase domain. This research proposes two novel models that provide an effective framework for addressing the aforementioned challenges. The models are derived through asymptotic expansion with respect to the interphase thickness parameter $\epsilon$, while the state variables within the interphase are expressed using Taylor series expansions about boundary points. The proposed formulations extend and refine the classical models developed by Benveniste, offering new insights into the influence of various parameters governing property variations along the normal direction. The robustness of the proposed models is examined for thermally conductive interphases of different geometries—specifically, flat, circular, and wavy configurations, as well as for circular interphases in the settings of linear elasticity and thermo-elasticity. Their accuracy and efficiency are evaluated across a broad range of thermal and mechanical properties and curvature values. Additionally, the influence of volumetric heat sources, positioned within the interphase, is analyzed to assess its effect on model performance. The predictive capability of the proposed models is further validated by comparing with established models from the literature, and the numerical model developed in this work is found to have better approximation than the benchmark solutions.