Isotropic creep, equation

An attempt to predict the buckling time was made using the isotropic creep equation with Mises stress potential as outlined above for the plastic liner in the warpage problem. 

In the derivation of equations 24—26 (60) it is assumed that the cylinder is made of a material which is isotropic and initially stress-free, the temperature does not vary along the length of the cylinder, and that the effect of temperature on the coefficient of thermal expansion and Young s modulus maybe neglected. Furthermore, it is assumed that the temperatures everywhere in the cylinder are low enough for there to be no relaxation of the stresses as a result of creep. 

For isotropic homogeneous porous media (uniform permeability and porosity), the pressure for creeping incompressible single phase-flow may be shown to satisfy the LaPlace equation ... 

By careful analysis of extensive creep and constant strain-rate data from PET and creep data from isotropic PP and PMMA, Brereton showed that eqn. (19) could be usefully written as an integral equation... 

In a follow-up of the integral equation approach Croll made a preliminary study of the non-linear creep behaviour of the same oriented PET sheet in other orientations, and also of amorphous and crystallised isotropic PET. He discovered that whereas for the oriented material at 0 = 90° and for the amorphous isotropic sheet, the creep modulus versus stress graphs were linear, as suggested by eqn. (22), a more complicated form of non-linearity was evident both for the oriented material at 6 = 45° and 0°, and for the highly crystalline isotropic material. An example of this is shown schematically in Fig. 22 where the creep modulus/stress graph for oriented PET sheet in tension at 0 = 0°, can be seen to have three distinct regimes. 

Equation 30 shows that the yield stress is both rate and temperature dependent, hence it captures some important features of yield in polymers. For example, Figure 10 (44) shows a plot of ax/T (or aJT in the notation of Reference (44)) as a function of log strain rate and, as predicted by equation 30, a linear relationship is seen at each temperature. It is worth noting that the Eyring equation (typically in the form of two activated processes acting in parallel) has been successfiilly applied not only to the yield behavior of polsrmers but also to the creep rupture behavior of isotropic and oriented polymers (45- 8). 

Unified Plasticity Model The time-independent plastic deformation and fee time-dependent creep deformation arise from fee same fundamental mechanism of dislocation motion. Hence, a constitutive model which captures both of these deformation mechanisms is desirable. Such a constitutive model is referred to as a unified plasticity model. A commonly-used unified plasticity model is the Anand s model. This is a rate-dependent phenomenological model (Ref 17 and 18). There are two basic characteristics of fee Anand s model. First, no explicit yield criterion is specified, and second, a single internal state variable (ISV) s, the deformation resistance, represents the isotropic resistance to inelastic strain hardening. Anand s model can represent fee strain rate and temperature sensitivity, strain rate history effects, strain hardening, and fee restoration process of dynamic recovery. Equation 9 shows the functional form of fee flow equation that accommodates fee strain rate dependence on the stress ... 

Table III lists the material properties of the components. Fibers and matrix were considered as isotropic, and in a first step the Norton-equation for steady state creep was assumed. Because of missing parameters for compression creep, tension creep data for the fibers were adapted from elsewhere The data for the matrix was estimated as follows. Based on the experimental results for the 0° and 90 fiber orientation the overall creep rate for the matrix was chosen higher and the stress exponent lower than for the fibers.

Unified equations that couple rate-independent plasticity and creep [114] are not readily available for SOFC materials. The data in the hterature allows a simple description that arbitrarily separates the two contributions. In the case of isotropic hardening FEM tools for structural analysis conveniently accept data in the form of tabular data that describes the plastic strain-stress relation for uniaxial loading. This approach suffers limitations, in terms of maximum allowed strain, typically 10 %, predictions in the behaviour during cycling and validity for stress states characterised by large rotations of the principal axes. 

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