Hysteresis constitutive model of C/SiC composites considering probabilistic matrix fragmentations

In this paper, a new micromechanical hysteresis loop constitutive model of C/SiC composites with different interphases was developed considering the probabilistic-statistical matrix fragmentation process. The lengths of matrix fragmentation were divided into three types, that is, long matrix fragments (LMFs), medium matrix fragments (MMFs), and short matrix fragments (SMFs). The distributions of the LMFs, MMFs, and SMFs with increasing tensile stress were determined using the probabilistic-stochastic model by assuming the two-parameter matrix strength distribution. The micro stress field of the LMFs, MMFs, and SMFs upon unloading and reloading was obtained and adopted to determine the corresponding stress-strain relations. The interaction of matrix fragmentation lengths, especially for the LMFs with large debonding energy (LDE) and SMFs, was considered in the closed-form constitutive model and hysteresis-based inverse tangent modulus (ITMs) damage parameter. Synergistic effects of the fiber volumes, peak stresses, and interface debonding energy on the interface damage state, mechanical hysteresis loops, and related ITMs with small debonding energy and LDE were also analyzed. Comparisons of the mechanical hysteresis loops using the new hysteresis models considering matrix stochastic fragmentation and hysteresis models considering constant matrix fragmentation were also discussed. Experimental cyclic tensile hysteresis loops and unloading/reloading ITMs of C/(PyC)/SiC and C/(PyC+SiC)/SiC composites with different interphase thickness (i.e., t = 300, 600, 1000, and 2000 nm) were predicted using the developed constitutive model. Evolution of the unloading/reloading interface slip ratio was analyzed for different tensile peak stresses.