Analytical and numerical modeling of the effective specific heat of composites
Topic(s) : Material and Structural Behavior - Simulation & Testing
Co-authors :
Efstratios POLYZOS (BELGIUM), Lincy PYL (BELGIUM)Abstract :
Effective (homogenized) properties of composite materials are used to understand their macroscopic behavior. The aim of obtaining the effective properties of a material is to replace the microstructurally complex composite with a homogeneous one with identical properties. This process finds increased application in the field of simulation since modeling high geometrical fidelity can be unachievable due to the extreme computational cost. Once the effective properties are obtained, the high geometrical fidelity is removed, and the computational cost is lowered allowing for a less time-consuming simulation.
A property that is important to be evaluated, but has received minimal attention, is the specific heat. In composite materials, effective specific heat has been regularly evaluated by volume or mass averaging. This is mentioned as the rule-of-mixture (ROM) model and it is a logical assumption for applications to composites whose properties exhibit a linear dependency on the volume (or mass) of their constituents.
Despite the fact that the effective specific heat can be evaluated, or at least estimated, using the ROM model, for composite materials this can result in inaccuracies. A uniform temperature rise in a composite, which is a structural/mechanical problem, results in zero average (over the volume) strains or stresses. Nevertheless, the values of strains and stresses locally are, in general, non-zero and depend on the material and geometric parameters of the constituents [2]. Therefore, the applicability of the ROM models should be investigated.
This work aims to derive a novel formulation of the effective specific heat for multi-phase composites that is generally applicable to composites of an anisotropic matrix with inhomogeneities of anisotropic elastic and expansion properties and of arbitrary shapes and orientations. This is accomplished in the framework of the effective field methods (EFMs) using property contribution tensors.
Two case studies are presented in this article to further investigate the applicability of the novel formulas. The first case study considers the case of overall isotropy of two particulate composites of polypropylene with copper particles (PP/Cu) (Figure 1). The second case considers two fibrous composites, a glass (GFRP) and a carbon (CFRP) fiber-reinforced epoxy composite (Figure 2). The formulas of the effective field methods are compared to the results of experiments from the open literature [2,3] and the results of finite elements (FE) models for the effective specific heat and exhibit a great agreement for almost all methods.
A property that is important to be evaluated, but has received minimal attention, is the specific heat. In composite materials, effective specific heat has been regularly evaluated by volume or mass averaging. This is mentioned as the rule-of-mixture (ROM) model and it is a logical assumption for applications to composites whose properties exhibit a linear dependency on the volume (or mass) of their constituents.
Despite the fact that the effective specific heat can be evaluated, or at least estimated, using the ROM model, for composite materials this can result in inaccuracies. A uniform temperature rise in a composite, which is a structural/mechanical problem, results in zero average (over the volume) strains or stresses. Nevertheless, the values of strains and stresses locally are, in general, non-zero and depend on the material and geometric parameters of the constituents [2]. Therefore, the applicability of the ROM models should be investigated.
This work aims to derive a novel formulation of the effective specific heat for multi-phase composites that is generally applicable to composites of an anisotropic matrix with inhomogeneities of anisotropic elastic and expansion properties and of arbitrary shapes and orientations. This is accomplished in the framework of the effective field methods (EFMs) using property contribution tensors.
Two case studies are presented in this article to further investigate the applicability of the novel formulas. The first case study considers the case of overall isotropy of two particulate composites of polypropylene with copper particles (PP/Cu) (Figure 1). The second case considers two fibrous composites, a glass (GFRP) and a carbon (CFRP) fiber-reinforced epoxy composite (Figure 2). The formulas of the effective field methods are compared to the results of experiments from the open literature [2,3] and the results of finite elements (FE) models for the effective specific heat and exhibit a great agreement for almost all methods.