Long-term performance of ceramic matrix composites at elevated temperatures: Modelling of creep and creep rupture

The models developed, contain explicit dependences on constituent material properties and their changes with time, so that composite performance can be predicted. Three critical processes in ceramic composites at elevated temperatures have been modeled: (1) creep deformation of composite vs stress and time-dependent creep of fibers and matrix, and failure of these components; (2) creep deformation of ``interface`` around broken fibers; and (3) lifetime of the composite under conditions of fiber strength loss over time at temperature. In (1), general evolution formulas are derived for relaxation time of matrix stresses and steady-state creep rate of composite; the model is tested against recent data on Ti-MMCs. Calculations on a composite of Hi-Nicalon fibers in a melt-infiltrated SiC matrix are presented. In (2), numerical simulations of composite failure were made to map out time-to-failure vs applied load for several sets of material parameters. In (3), simple approximate relations are obtained between fiber life and composite life that should be useful for fiber developers and testers. Strength degradation data on Hi-Nicalon fibers is used to assess composite lifetime vs fiber lifetime for Hi-Nicalon fiber composites

Fracture model with variable range of interaction

We introduce a fiber bundle model where the interaction among fibers is modeled by an adjustable stress-transfer function which can interpolate between the two limiting cases of load redistribution, the global and the local load sharing schemes. By varying the range of interaction several features of the model are numerically studied and a crossover from mean field to short range behavior is obtained. The properties of the two regimes and the emergence of the crossover in between are explored by numerically studying the dependence of the ultimate strength of the material on the system size, the distribution of avalanches of breakings, and of the cluster sizes of broken fibers. Finally, we analyze the moments of the cluster size distributions to accurately determine the value at which the crossover is observed.Comment: 8 pages, 8 figures. Two columns revtex format. Final version to be published in Phys. Rev.

Strength and reliability of fiber-reinforced composites: Localized load-sharing and associated size effects

The statistical aspects of the failure of large 3-D unidirectional fiber reinforced composites are studied numerically and analytically. A 3-D lattice Green's function model is used to calculate the stress field, damage evolution, and Failure in composites under ''Local Load Sharing'' (LLS) conditions in which the stress from broken fibers is transferred predominantly to the nearby unbroken fibers. Failure by local accumulation of a critical amount of damage, and the associated decrease in ultimate strength with increasing composite size, is explicitly demonstrated. Weakest-link statistics are then employed to investigate size effects and reliability. An intrinsic ''link'' in LLS is found which has the same Gaussian distribution function for strength as a bundle in Global Load Sharing (GLS) (no local stress concentrations) of the same size. The size of the link is found to be comparable to the critical cluster of fiber damage observed in the simulations. Then, using known results for the GLS probability distribution function, analytic asymptotic results for the strength and reliability of large composites in LLS are derived. The strength distribution shows excellent agreement with the Monte Carlo simulation results for both the median strength and high reliability tail of the distribution. The implications of these results on the expected strength and reliability of moderate-size composites components is discussed, with applications to a Ti-MMC and a SiC/SiC CMC. Finally, the application of these results to modeling of composite failure by the Finite Element Method is presented. (C) 1997 Elsevier Science Ltd

Strength and reliability of notched fiber-reinforced composites

The strength and reliability of a 3-D unidirectional fiber-reinforced composite containing an initial defect in the form of a cluster of initial fiber breaks are studied analytically and by simulation. The simulation model uses a Monte Carlo technique based on 3-D lattice Green's functions to calculate the stress field, damage evolution, and faiure in composites under ''Local Load Sharing'' (LLS) conditions in which the stress from broken fibers is transferred predominantly to the nearby unbroken fibers. Failure of ''notched'' composites, after the matrix has reached its fully cracked/yielded stare, is observed to occur by local accumulation of a critical amount of fiber damage around the notch. The decrease in tensile strength, but increasing reliability, with increasing size of the initial cluster of broken fibers is characterized. An analytic model for strength and reliability is developed which follows from the strength and reliability of un-notched composites by including, in a surprisingly simple manner, the effects of the stress concentration factor owing to the notch and the fiber pull-out stress around the notch. The model captures all of the details of the simulation results and includes the important effects of composite volume. (C) 1997 Acta Metallurgica Inc

Tensile strength of titanium matrix composites: Direct numerical simulations and analytic models

A recently-developed model for the numerical simulation of tensile stress-strain behavior in fiber-reinforced composites is used to predict the tensile strength of a metal matrix composite consisting of a Ti-1100 matrix reinforced with SCS-6 SiC fibers. Data on the as-processed fiber strengths, interfacial strength, composite size, and fiber volume fraction From Gundel and Wawner are used as input. The predicted strengths agree very well with the sample-specific values measured by Gundel and Wawner, demonstrating the accuracy of the computational model. The effects of free surfaces ina thin ply lay-up geometry are simulated as well, and show a small and surprising increased tensile strength. A modified Batdorf-type analytic model is developed which yields predictions similar to the simulated strengths for the Ti-1100 materials. The ideas and predictions of the Batdorf-type model, which is essentially an approximation to the simulation model, are then compared in more detail to the simulation-based model to more generally assess the accuracy of the Batdorf model in predicting tensile strength and notch strength vs composite size and fiber Weibull modulus. The study shows the Batdorf model to be accurate for tensile strength at high Weibull moduli and to capture general trends well, but it is not quantitatively accurate over the full range of material parameters encountered in various fiber composite systems. (C) 1998 Elsevier Science Ltd. All rights reserved