A Temperature Dependent Constitutive Model For Fiber Reinforced Ceramic Matrix Composites

Ceramic matrix composites (Ceramic Matrix Composites: CMCs) have an excellent performancein high temperature environment, in recent years, many scholars have studied the constitutive relation,but mostly concentrated on the ambient temperature, the qusasi-static uniaxial load case. Due to thespecial application environment of CMCs, the thermal strain generated by temperature gradient cannot be ignored. So how to establish a constitutive model considered with the temperature effect mustbe solved first. Experimental results showed that at room temperature, or whether at high temperatureenvironment, the tensile and shear response of CMCs are obviously non-linear.In this paper, the material constitutive response were first studied based on the experimentalmethod, including compression test, shear test, room temperature and high temperature tensile testunder700℃,and analyzed the failure modes and failure mechanism of materials combined with thespecimen fracture surface under their experimental conditions. As the temperature increases, thetensile modulus, strength of the material and the final destruction of the failure strain has significantlyreduced, the main reason for this phenomenon is that at high temperatures the fibers to be oxidized asa result of matrix cracking. Room temperature compression test curve at lower stress levelperformance linear, nonlinear characteristics at high stress levels, but significantly higher than thetensile strength.A formulation of Helmholtz free energy with initial modulus and tangent modulus is proposed todescribe the bilinear constitutive behavior of CMCs. The Lagrange interpolation is used to describethe relations between material parameters and temperature. The effect of temperature is introducedinto the theoretical framework of continuum damage mechanics. The constitutive model is applied topredict the stress/strain curves of CMCs at room and elevated temperatures. Good agreed with theexperimental data generated and the results predicted by the continuum damage mechanics model,this demonstrates that the methods developed in this paper are effective. Finally, the calculationverified by comparing with typical example proved that the damage constitutive model in this papercan effectively simulate the material mechanical behaviors at external applied load (includingtemperature load).