Relationship between hysteresis loops and cracking evolution/closure in ceramic-matrix composites under tension-tension fatigue loading

When ceramic-matrix composites (CMCs) are under tension-tension cyclic fatigue loading, stochastic matrix cracking evolves with applied cycles and the closure of cracks occurs upon unloading. Evolution, opening, and closure of matrix cracking affect the reliability and safety of CMC components during operation. The objective of this paper is to establish the relationship between the hysteresis loops, cracking evolution, opening, and closure based on a new hysteresis constitutive model. Multiple micro damage parameters, e.g., unloading/reloading inverse tangent modulus (UITM/RITM), interface reverse slip ratio (IRSR), and interface new slip ratio (INSR), are developed to characterize the hysteresis loops with cracking evolution and closure. Upon unloading, the closure of matrix cracking decreases the UITMs and IRSR of the tension-tension fatigue hysteresis loops; upon reloading, the opening of matrix cracking increases the RITMs and IRSR of the tension-tension fatigue hysteresis loops. Experimental tension-tension fatigue hysteresis loops in different CMCs are predicted for different peak stresses and cycles. Effects of fiber volume, interface properties, peak stress, and stress ratio on ITM, IRSR, and IRSR are discussed. The developed approach can be used for cracking evolution, opening, and closure identification in CMCs.