Stress exponent

Fig. 4.5 Comparison of flexural creep of whisker-reinforced A1203 with that of whisker-free aluminum oxide. A sharp increase in the stress exponent is observed at the higher stresses for the whisker-reinforced materials tested at 1400°C. Figure from Ref.

Results on other composite materials are similar to those obtained by Morrell and Ashbee.56 Creep asymmetry has been demonstrated for two grades of siliconized silicon carbide,35,60,61 SiC whisker-reinforced silicon nitride,53 HIPed silicon nitride,29 and vitreous-bonded aluminum oxide.29 Again, stresses required to achieve the same creep rate were at least a factor of two greater in compression than in tension. In two grades of siliconized silicon carbide,35,58-61 the stress exponent changed from 4 at creep rates below... 

Fig. 4.6 Temperature-compensated creep plot for tension and compression on a glass-ceramic. Data are compensated by an Arrhenius correction to 700°C. Data from Ref. 56 were replotted. The curves are least square fits of quadratic polynomials to the data. An increase in the stress exponent of the creep data is clearly indicated.

More recently, Yoon and Chen68 developed a theory to predict the deformation behavior of particulate composites. Their theory treats the case of rigid particles embedded in a nonNewtonian matrix. The relative deformation rate, e/k0, is related to the volume fraction of particles, , the creep stress exponent of the matrix, n, and the stress concentration factor, k, of the inclusion in the matrix ... 

Solution-precipitation theory cannot be used to justify creep asymmetry or high tensile stress exponents for ceramic matrix composites. The theory suggests that creep is symmetric in stress and that the stress exponent is equal to 1. Justification of creep asymmetry by solution-precipitation would require other parameters in Eqn. (4) to depend on the sign of the applied stress. A nonlinear dependence on stress would be required. Diffusion and devitrification may play a role in this regard however, the data needed to support this possibility have yet to be obtained. 

In this paper, the importance of particle and whisker reinforcement to creep and creep rupture behavior of ceramics is discussed. Particle and whisker additions generally increase both the fracture toughness and creep resistance of structural ceramics. These additions also act as nucleation sites for cavities. Cavities form preferentially in tensile specimens. This results in a creep asymmetry, in which composites creep faster in tension than in compression. As a consequence of cavitation, the stress exponent for creep in tension 6-10,... 

As shown in Fig. 5.4, for stresses far away from a (either a-c cr or crc a ), the initial creep behavior (stress dependence) of the composite is determined primarily by the constituent having the higher creep rate. On the other hand, the final creep behavior of the composite is governed by the constituent with the lower creep rate. For applied creep stresses close to o, a gradual change in creep stress exponent n occurs from rii to n2 (or vice versa). 

S.2.3.2 Parametric Studies Influence of Constituent Moduli and Creep-Stress Exponents on Composite Creep Behavior... 

Fig. 5.5 Effect of changing the elastic modulus ratio and constituent creep stress exponents on the total strain rate of a 1-D composite subjected to tensile creep loading.31 In both (a) and (b), the dashed lines represent the composite behavior, and the thin solid lines the constituent behavior. In the calculations, it was assumed that the creep load was applied instantaneously.

The stress and temperature dependence of the composite creep rate is governed by the values of the activation energies and stress exponents of the constituents. The initial stress and temperature dependence of composite creep rate is governed by the values of n and Q for the constituent which has the higher creep rate the final stress and temperature dependence is governed by the values of n and Q for the constituent with the lowest creep rate. This is illustrated in Fig. 5.6d, which compares the stress and temperature dependence of the constituent creep rate with the initial and final creep behavior of the composite. 

Of particular interest in the present chapter is the effect of test atmosphere on creep and creep damage mechanisms. While there are undoubtedly several factors that can promote creep cavitation and contribute to the observed changes in stress exponent and activation energy, the fact remains that the strain rates are substantially higher in air than in inert atmospheres, as shown in Fig. 8.12. This phenomenon is a direct consequence of the topotactic oxidation reaction of SiC whiskers exposed at the surface. As described by Porter and Chokshi,38 and subsequently by others,21,22 at high temperatures in air, a carbon-condensed oxidation displacement reaction occurs in which graphitic carbon and silica are formed at the whisker interface via... 

As mentioned above, for a creep stress exponent, n<3, the crack tip stress field for a continuously growing crack is the applied A -field. For this case, based on the model of Purushothaman and Tien48 the crack growth rate is, for strain-controlled failure,... 

Usually, creep deformation of ice single crystals is associated to a steady-state creep regime, with a stress exponent equal to 2 when basal glide is activated . In the torsion experiments performed, the steady-state creep was not reached, but one would expect it to be achieved for larger strain when the immobilisation of the basal dislocations in the pile-ups is balanced by the dislocation multiplication induced by the double cross-slip mechanism. 

For large samples of pure tungsten at temperatures >2200 °C (0.65 7] ), the stress exponent n = 5 and A// = 585kJ-mol . This activation enthalpy is similar to that of self-diffusion in tungsten. It was therefore assumed that under these conditions the deformation of the grains by dislocation climb or glide processes is the rate-controlling reaction [1.63]. 

At this point, several comments are in order. First, we note that we have recovered an expression for the strain rate which jibes with the empirical result presented in eqn (11.3). In this case, the stress exponent is unity. 

Figure 5. Procedure for determining the threshold stress in the composite at 423 and 473 K using a stress exponent of n = 3.

Figure 10. Stress exponent n derived from the slope of the log vs. log. o plot for (a) Ti5Si3 and (b)TiSi2.

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