Steady state creep

Creep. The phenomenon of creep refers to time-dependent deformation. In practice, at least for most metals and ceramics, the creep behavior becomes important at high temperatures and thus sets a limit on the maximum appHcation temperature. In general, this limit increases with the melting point of a material. An approximate limit can be estimated to He at about half of the Kelvin melting temperature. The basic governing equation of steady-state creep can be written as foUows ... 

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...

Table 3. Steady-State Creep for Alpha-Silicon Carbides...

Steady-state creep did not occur at these experimental conditions. 

Fig. 5. Tensile elongation vs time demonstrating creep behavior of ceramics. Section I is primary creep II, secondary or steady-state creep III, tertiary...

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

For straight metal pipe under internal pressure the formula for minimum reqiiired w thickness is applicable for D /t ratios greater than 6. Tme more conservative Barlow and Lame equations may also be used. Equation (10-92) includes a factor Y varying with material and temperature to account for the redistribution of circumferential stress which occurs under steady-state creep at high temperature and permits slightly lesser thickness at this range. 

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... 

This is then replaced by a period of steady state creep which, depending on the temperature and stress level, takes up the greatest part of the creep life. 

Nere- Xf is the weight-average molecular weight of the blend, and Afwl is the weight-average molecular weight of component /. The steady-state creep compliance 7, of the blend is... 

The variation of creep with time as a function of both load and temperature is illustrated in Figure 5.44. Arrhenius-type relationships have been developed for steady-state creep as a function of both variables such as... 

Fig. 5.14. Reduced compliance vs molecular weight for undiluted polystyrenes of narrow molecular weight distributions. Symbols are O from creep recovery (163), Cr from G (w) (192), O- from flow birefringence (180), (X from (189), 9 from G (a>) (M>105 only) (124), jO extrapolated from steady state creep (191), -O from stress relaxation (165), and...

Fig. 5.16. Reduced compliance vs cMw for solutions and undiluted samples of cis-polyisoprene. Symbols are undiluted samples from steady state creep (166, 196), undiluted samples from Nt (197), and O solutions extrapolated from steady state creep (196)...

Nixon, R.D., Koester, D.A., Chevacharoenkul, S. and Davis, R.F. Steady-state creep of hot-pressed SiC whisker-reinforced silicon nitride , Composites Sci. Tech., 37 (1990) 313-328. 

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 (%)... 

J. R. Porter, Observations of Non-Steady State Creep in SiC Whisker Reinforced Alumina, in Whisker- and Fiber-Toughened Ceramics, eds. R. A. Bradley, D. E. Clark, D. C. Larsen, and J. O. Stiegler, ASM International, Metals Park, OH, 1988, pp. 147-152. 

R. D. Nixon, D. A. Koester, S. Chevacharoenkul, and R. F. Davis, Steady State Creep of Hot Pressed SiC Whisker Reinforced Silicon Nitride, Comp. Sci. Tech., 37, 313-328 (1990). 

To illustrate a key point concerning the creep behavior of fiber-reinforced ceramics, the primary creep behavior of the constituents was purposely omitted in the above analysis. As shown in Fig. 5.2, even though it was assumed that the constituents undergo only steady-state creep, a protracted transient creep... 

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...

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