Steady-state creep rate

In this Section, the secondary stage of creep, steady-state creep will be considered. In this stage, the creep rate seems to be constant... 

Boltzmann s constant, and T is tempeiatuie in kelvin. In general, the creep resistance of metal is improved by the incorporation of ceramic reinforcements. The steady-state creep rate as a function of appHed stress for silver matrix and tungsten fiber—silver matrix composites at 600°C is an example (Fig. 18) (52). The modeling of creep behavior of MMCs is compHcated because in the temperature regime where the metal matrix may be creeping, the ceramic reinforcement is likely to be deforming elastically. 

Fig. 18. Steady-state creep rate as a function of appHed stress for silver matrix (0) and tungsten fiber—silver matrix composites (A) at 600°C. To convert...

In the steady-state creep regime of ceramics, almost aU creep mechanisms fit a strain rate dependence of the form (18) ... 

We saw in the last chapter that the rate of steady-state creep, 55, varies with temperature as... 

Steady-state creep rate (s ), for ai applied tensile stress cr of 200iVINm- ... 

Like metals, ceramics creep when they are hot. The creep curve (Fig. 17.4) is just like that for a metal (see Book 1, Chapter 17). During primary creep, the strain-rate decreases with time, tending towards the steady state creep rate... 

A well-known example of this time-temperature equivalence is the steady-state creep of a crystalline metal or ceramic, where it follows immediately from the kinetics of thermal activation (Chapter 6). At a constant stress o the creep rate varies with temperature as... 

Above 0.5 ceramics creep in exactly the same way that metals do. The strain-rate increases as a power of the stress. At steady state (see Chapter 17, eqn. 17.6) this rate is... 

Star-shaped polymer molecules with long branches not only increase the viscosity in the molten state and the steady-state compliance, but the star polymers also decrease the rate of stress relaxation (and creep) compared to a linear polymer (169). The decrease in creep and relaxation rate of star-shaped molecules can be due to extra entanglements because of the many long branches, or the effect can be due to the suppression of reptation of the branches. Linear polymers can reptate, but the bulky center of the star and the different directions of the branch chains from the center make reptation difficult. 

Creep curves of Si3N4 at high temperatures generally consist of three regimes transient, steady-state, and accelerated creep, similar to metals. The creep rate under tensile stresses is some orders of magnitude higher than under compression [412, 416]. 

In the initial stage, known as primary creep, the strain rate is relatively high, but slows with increasing strain. The strain rate eventually reaches a minimum and becomes near-constant. This is known as secondary or steady-state creep. This stage is the most understood. The characterized creep strain rate , typically refers to the rate in this secondary stage. The stress dependence of this rate depends on the creep mechanism. In tertiary creep, the strain-rate exponentially increases with strain [1-9]. 

Alloy Formula Steady state creep rate (h-1) Rupture [time (h)] Creep rupture ductility (%)... 

Fig. 5.2 Comparison of creep behavior and time-dependent change in fiber and matrix stress predicted using a 1-D concentric cylinder model (ROM model) (solid lines) and a 2-D finite element analysis (dashed lines). In both approaches it was assumed that a unidirectional creep specimen was instantaneously loaded parallel to the fibers to a constant creep stress. The analyses, which assumed a creep temperature of 1200°C, were conducted assuming 40 vol.% SCS-6 SiC fibers in a hot-pressed SijN4 matrix. The constituents were assumed to undergo steady-state creep only, with perfect interfacial bonding. For the FEM analysis, Poisson s ratio was 0.17 for the fibers and 0.27 for the matrix, (a) Total composite strain (axial), (b) composite creep rate, and (c) transient redistribution in axial stress in the fibers and matrix (the initial loading transient has been ignored). Although the fibers and matrix were assumed to exhibit only steady-state creep behavior, the transient redistribution in stress gives rise to the transient creep response shown in parts (a) and (b). After Wu et al 1...

After a long period of time, the composite will approach a steady-state condition, with no further change occurring in the fiber and matrix stress (cr, = 0). From Eqn. (2b), and with ai ss = (eitJAl)l,n the creep rate of the composite approaches a steady-state value ec>ss (= eiss), which is determined by the condition... 

In Fig. 5.4a and b, the initial creep rate of each phase (Eqn. (7)) is represented by the intersection of the monolithic creep curve for that phase and the elastic stress and strain (vertical line). After initial loading, the total strain rate (elastic + creep) of each phase, which remains equal to the total strain rate of the composite (for compatibility), decreases. The only exception arises if ki 0 = 2,0 (= c,o), so that ec 0 = c ss (see Fig. 5.4c). In this instance, the initial condition matches the steady-state condition—the composite strain rate remains unchanged. The applied stress for this condition is given by... 

Fig. 5.4 (a, b and c) Initial and final (steady-state) strain rate of a hypothetical composite as a function of normalized stress. The dashed lines represent the creep rate of the constituents, (b) and (c), which detail the two framed regions in Fig. 5.4(a), show the transient paths of the stress and strain rate for the composite and its constituents for the two corresponding stress regimes cr and a<. The dashed lines in (b) and (c) show the creep rate of the constituents (excluding the elastic components), which follow the monolithic creep behavior of each phase the total strain rate of the composite and the constituents must remain equal. 

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