Creep parameters

The creep parameters J and y are obtained through transverse creep experiments. The initial compliance is the elastic response of the material (Equation 8.41). In general, the creep parameters J and y, and the shift factor aT may all be dependent on the cure state of the material. For the current process model the shift factor is assumed to be separable and, as such, is only temperature dependent. As a first approximation the creep parameters are represented as linear functions of the degree of cure. ... 

The values of the creep parameters (p, n and Q) identifying the superplastic behaviour of ceramic-related materials are not unique to such materials, nor to the same type of materials. As shown in the review papers, these parameters are very similar in tension as in compression in zirconia-based materials (probably the most widely studied ceramics in the widest experimental conditions), although that depends strongly on the purity of the ceramics 5,7 however, their behaviour seems to be very different in compression than in tension when an aid-sintering phase is necessary during the processing, as in silicon carbide and silicon nitride ceramics.8... 

For the sake of clarity, we will mention the reasons for the discrepancies in the creep parameters in materials for which most studies have been performed. In the case of YTZP, values of p between 1 and 3, of n between 2 and higher than 5, and of Q between 450 and 700 kJ/mol, have been reported during creep.7... 

Probably the most plausible explanation for the scatter of the creep parameters is based on a single mechanism involving GBS with a threshold stress (Oq).7,10,13 When a threshold stress is introduced into the creep equation (16.1), all the creep parameters in YTZP become n = 2, p= 2 and Q= 460 kJ/mol whatever the stress or temperature of the test. The value of this ct0 was found experimentally 13... 

As can be inferred from the equations outlined above, none of the different models can adjust the creep parameters for all the different ceramics, especially in the case of YTZP,7 explaining why there is still controversy over the accommodation process controlling superplasticity. The same conclusions can be outlined for ceramic composites, although more experimental work should be done.20,31... 

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.

Here, we note that under extensive creep conditions, C is also proportional to PV, but the proportionality factor is different from that which applies in Eqn. (9). In some specimens, the proportionality factor for C, in SSC is not appreciably different than that for the extensive creep parameter C, so that apparent correlations of experimental data in terms of C are actually correlations in terms of Ct. The important distinction arises when an attempt is made to calculate the value of the fracture parameter for use in design or life estimation. Under SSC conditions, C, can be much greater than C so that predictions based upon C in SSC will be nonconservative. 

FOUR CREEP PARAMETERS OF SIX COMMERCIAL SALAD DRESSINGS ... 

It has been found that the release of a drug may be controlled if the active compound is suspended in a carrier matrix, which is often a polymeric solution that confers viscoelastic properties to the fluid (52-54). Rates of release have been correlated either with creep parameters such a.s (7 (52) or with viscoelastic parameters, G and G" (53,54). It seems that increasing G (i.e.. the more the carrier is gd-like or viscoelastic) retards tlie laie of release of active compounds. Once more, rheology may be used to assess either the microstructure of the carrier or the rate of release by monitoring the rheological properties. 

The linear formalism implies, that for many classes of problems in deformation, solutions in the viscoelastic case can be simply obtained from elastic solutions by Laplace transform methods as for isotropic materials. Further in particularly simple cases this reduces to simple replacement of constants in elastic solutions by their time dependent analogues in creep. Most of the work of determining significant creep parameters for oriented materials falls into this latter class. 

Indentation creep parameter Cit Ctt — Relative change of indentation depth at constant test load. 

The relevant creep parameters obtained to determine AC 20 mm resistance to permanent deformation using both calculations are given in Table 7.4. The results were obtained from tests carried out at the Highway Engineering Laboratory of the Aristotle University of Thessaloniki. 

Experimental crack growth rates, da/dN, are modelled using a linear summation of cyclic and creep contributions. A good agreement is obtained using a fracture mechanics creep parameter C s(t), estimated from a reference stress approach, which continously takes into account the effects of primary and secondary creep during the tests. Detailed results will be presented at the SMIRT 14 conference (LYON, August 17-22, 1997). 

The values of the creep parameters (p, n, and Q) identifying the superplastic behavior of ceramic-related materials are not unique, neither are they similar for the same types of material. Several factors can affect these parameters, among them the... 

The case of constant density of steps modeled by Wakai is equivalent to the diffusion-controlled creep modeled by Raj and Chyung [80], and it is also consistent with terms of the stress, temperature and grain size dependence of the strain rate for interface-reactioncreep predicted by others [80]. However, in the two cases of bidimensional nucleation of step and spiral step, the creep parameters differ from those predicted by the authors cited above. In particular, for 2-D nucleation there is a divergence of the creep parameters which has been recently solved [81], considering in detail the precipitation or solution of the crystalline material at the step, which changes significantly the free enthalpy involved in the process. 

Table VI. Creep parameters for alumina-based fibers...

The creep parameters of polycrystalline YAG were derived from creep tests performed on bulk ceramic samples prepared by conditions dose to those used for the fibers. The stress exponent was dose to unity and the apparent activation energy (Equation 10) was equal to 5M kJ/mol. It has been suggested that the operative mechanism is Nabarro-Herring creep, with a rate limited by the bulk diffusion of one of the Y or AT cations [105). 

Hong K, Rastogi A, Strobl G (2004b) Model treatment of tensile deformation of semicrystalline polymers static elastic moduli and creep parameters derived for a sample of polyethylene. Macromolecules 37 10174... 

A Norton creep law seems still appropriate for die fibers. After a short transient regime, experiments with fiber-dominated creep (0 curve Figure 4, left) owed an almost constant aeep rate. Therefore new simulations with different creep parameters for fiber and matrix (Table IV) were conducted. Figure 13 shows the resulting creep curves for the diosen parameters. 

Experimental results of a quasi-unidirectional CMC revealed different creep behavior in tension and compression. Due to the porous matrix, the samples with 90° fiber orientation showed the largest creep deformation rates. In tension creep the fracture strain was 0.4-1% for 90° samples whereas in 0° fiber orientation creep strain above 8% was feasible. At the beginning of compression experiments, the absolute creep rate was highest and decreased continually. Creep parameters, i.e. temperature and stress dependencies, were deteimined in case of compression stress. Thereby, the activation energy averaged to 700 kJ/mol and the stress exponent varied with the fiber orientation from 3 to 1.9. The variation in the stress exponent was presumably caused by different stress exponents of fibers and matrix and quite likely due to the effect of matrix compaction. Latter one could be visualized by optical micrographs. 

Creep behavior of the low-melting point solders has been fully investigated [26,28,29]. Table 6 lists the steady-state creep parameters of several solders, indicating that the steady-state creep rate of Bi-Sn solder joints is smaller than similar Sn Pb solder joints, although eutectic Bi-Sn solder has a significantly lower melting point than eutectic Sn Pb solder, 139°C vs. 183°C, respectively. 

Sn-3.62Ag-l.52Cu Steady-state creep parameters measured at 20 C, 70° and 120 50... 

Where s, .is creep strain rate (1/5), T is also the absolute temperature in Kelvin, the parameters, C, - C4, in Equation (7) are the creep parameters of ANSYS (for implicit creep model, TBOPT=8), and C, Cj - C4 of Equation (8) are also the parameters of ANSYS (TBOPT=10) as shown in Table 3. 

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