Creep mismatch ratio

Fig. 5.3 Schematic showing the changes in strain rate and elastic/creep strains of the individual constituents that occur during creep of a composite, (a) Strain rate versus time, (b) strain rate versus in situ stress acting in the fibers and matrix. In both plots, the shadowed portions show the elastic strain components, which compensate the creep rate mismatch of the individual phases, such that the total creep rates of the constituents remain equal. The creep mismatch ratio (CMR) is discussed in Section 5.2.4. After Wu and Holmes.31...

Initial and Final Creep Mismatch Ratio At low temperatures, or during rapid loading, the stress in the fibers and matrix can be estimated from a simple rule-of-mixtures approach this gives the elastic stress distribution between the fibers and matrix. During creep, the stress distribution is time dependent and is influenced by both the initial elastic stress distribution and the creep behavior of the constituents. Immediately after applying an instantaneous creep load (i.e., at t = 0+), the CMR, =0+ can be found by substituting ef0 = Af (E/ Ec)a-C nf and emfi = Am (Em/Ec)[Pg.176]

For times between these two extremes, the creep mismatch ratio is time dependent and can be determined using Eqns. (4) and (5) and an iterative process. Since, in general, CMR +1, time-dependent load redistribution between the fibers and matrix is a general phenomenon that occurs in all fiber-reinforced ceramics. 

The in situ creep mismatch ratio CMR, can provide a quantitative estimate of the driving force for load transfer between constituents. However, it is a rather complicated function of the stress redistribution processes. In order to indicate the basic characteristics of stress redistribution, it is convenient to directly compare the intrinsic (unconstrained) creep rates using the initial elastic stress experienced by the constituents. From Eqn. (12),... 

Suppose that one conducts a series of experiments to determine the stress and temperature dependence of creep behavior for the fibers and matrix these experiments would provide curves such as those shown schematically in Fig. 5.6a and b. Conducting these experiments over a range of temperatures and stresses would provide a family of curves that could be combined to provide a relationship between strain rate, stress, and temperature. Such a temperature and stress dependence of constituent intrinsic creep rates, together with the intrinsic creep mismatch ratio, is schematically illustrated in Fig. 5.6c. In this plot, the creep equations for the two constituents at a given temperature and stress are represented by planes in (1 IT, logo-, logs) space, with different slopes, described by <2/> Qm and ny, nm. The intersection of the two planes represents the condition where CMR = 1, which separates temperature and stress into two regimes CMR< 1 and CMR> 1. 

Fig. 5.6 Relationship between the creep rate of a composite and the stress and temperature dependence of the creep parameters of the constituents.31 (a) Temperature dependence of constituent creep rate, (b) Stress dependence of constituent creep rate, (c) Intrinsic creep rate of constituents as a function of temperature and stress illustrating the temperature and stress dependence of the creep mismatch ratio. In general, load transfer occurs from the constituent with the higher creep rate to the more creep-resistant constituent, (d) Composite creep rate with reference to the intrinsic creep rate of the constituents. The planes labeled kf and em represent the intrinsic creep rates of the fibers and matrix, respectively.

For the other extreme of an exceedingly long time, the creep rate mismatch ratio approaches unity ... 

Influence of Creep Rate Mismatch Ratio on Microstructural Damage Mode... 

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