Theoretically the overall CTE value of certain composite material can be calculated by the rule of mixture but there are always some variations between the results of the rule of mixture , the experimental test and that of Turner (1989) equation
∝c = Vp (CTE of reinforcement) +Vm (CTE of matrix)
Where ∝c is the overall CTE of the composite and Vp and Vm are the volume fractions of the reinforcement and the matrix respectively within the composite. However the interaction between the reinforcement and the matrix and the formation of a third inter-compound layer between them, whether the composite is in-situ or ex-situ and the percentage of the pores in the composite drift the results from their theoretical calculations.
Turner equation
∝c= (∝m Km Vm+ ∝p Kp Vp)/(Km Vm+Kp Vp )
Where: ∝c ∝m and ∝p are the CTE of the composite, the matrix and the particulates respectively. Km and KP are the bulk modules of the matrix and the particulates respectively.
Theoretically the overall CTE value of certain composite material can be calculated by the rule of mixture but there are always some variations between the results of the rule of mixture , the experimental test and that of Turner (1989) equation
∝c = Vp (CTE of reinforcement) +Vm (CTE of matrix)
Where ∝c is the overall CTE of the composite and Vp and Vm are the volume fractions of the reinforcement and the matrix respectively within the composite. However the interaction between the reinforcement and the matrix and the formation of a third inter-compound layer between them, whether the composite is in-situ or ex-situ and the percentage of the pores in the composite drift the results from their theoretical calculations.
Turner equation
∝c= (∝m Km Vm+ ∝p Kp Vp)/(Km Vm+Kp Vp )
Where: ∝c ∝m and ∝p are the CTE of the composite, the matrix and the particulates respectively. Km and KP are the bulk modules of the matrix and the particulates respectively.
Scale transition models such as Mori-Tanaka estimates or the classical thermoelastic Eshelby-Kröner self-consistent model can enable you to predict the CTE of complex composites in a more reliable way than rules of mixture.
see the link below for a paper where the self-consistent model is compared to measurements of CTE as a function of the temperature in Al-SiC (50%-50%) composite.
http://www.iut-sn.univ-nantes.fr/servlet/com.univ.collaboratif.utils.LectureFichiergw?CODE_FICHIER=1317992740003&ID_FICHE=677684
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