Creep modeling

Creep modeling A stress-strain diagram is a significant source of data for a material. In metals, for example, most of the needed data for mechanical property considerations are obtained from a stress-strain diagram. In plastic, however, the viscoelasticity causes an initial deformation at a specific load and temperature and is followed by a continuous increase in strain under identical test conditions until the product is either dimensionally out of tolerance or fails in rupture as a result of excessive deformation. This type of an occurrence can be explained with the aid of the Maxwell model shown in Fig. 2-24. 

Table 1 Constants for Four-Element Creep Model...

The power law approximation of the voltage current characteristic for superconductors above Ic has been known for some time (64). Such studies have been made in Y-Ba-Cu-O (65) with results similar to those shown in Figure 16. The value of n in V In has been found to decrease as the magnetic field is increased, and of course becomes ohmic above Hc2. Another representation of the current voltage data is shown in Figure 17 from Enpuku et al. (66), log V vs 1/T for increasing currents (above critical). The expected near straight line arises from the flux creep model of Tinkham for T/Tc 1. 

Figure 12 Ratio of flux creep rate S(T) to the magnetization at 1 second MQ(T) versus temperature. S and MQ are obtained by fitting data such as those in Figure 11 using Eq. (13). The slope of the dashed line corresponds to an effective flux pinning potential U = 83 meV according to a simple thermally activated flux creep model which yields Eq. (14).

The solution-precipitation creep model was first proposed by Raj and Chyung 32 they assumed two cases ... 

Comparison with the creep model mentioned above gives (Bland, 1960)... 

Fig. 13.104 shows that the creep rate calculated as a function of the initial modulus agrees well with the experimental data of a series PpPTA. This creep model has been confirmed for PpPTA fibres up to a stress of 2 GPa (Baltussen and Northolt, 2001). 

This review is intended to focus on ceramic matrix composite materials. However, the creep models which exist and which will be discussed are generic in the sense that they can apply to materials with polymer, metal or ceramic matrices. Only a case-by-case distinction between linear and nonlinear behavior separates the materials into classes of response. The temperature-dependent issue of whether the fibers creep or do not creep permits further classification. Therefore, in the review of the models, it is more attractive to use a classification scheme which accords with the nature of the material response rather than one which identifies the materials per se. Thus, this review could apply to polymer, metal or ceramic matrix materials equally well. 

B. Voight-Kelvin (Creep) Model Superposition Principles... 

Numerical simulation of stress distribution In the process of stress simulation, the front, back and bottom of the model are fixed, and each of the left and right boundary of the model are exerted the horizontal compression in 5.2 MPa, then simulate the horizontal stress distribution station along the seam after the fold formation by using the creep model, the result of which is shown in figure 3. 

These measurements show also the correlation between swelling and in-pile creep according to the theory of stress-induced preferential absorption (SIPA) and the creep model proposed by Gittus. 

The scheme also assumes that the redistribution of the secondary phase changes the size distribution of cavities within the material, which is supported by experimental observations [23,46], Final proof of the cavitation creep model is the fact that Eq. (2) fits the experimental data over a wide range of stresses for both SN 88 and NT 154. Thus, the model shovm in Figure 13.16 provides an understanding of the overall creep behavior of silicon nitride. Cavitation is the main creep mechanism in silicon nitride, and in other similarly bonded ceramics. 

In the absence of cavitation, creep in vitreous-bonded materials would occur by S-P, wherein material dissolves from one side of the grain and deposits on another [48, 49]. No definitive studies have been made to date that support the dislocation creep models in which the grains of silicon nitride deform by dislocation motion. Studies of deformed silicon nitride grains have provided no evidence of the types of dislocation pileup that should be present in order for this type of mechanism to be active [50]. 

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. 

When using the creep model for duplex microstructure, as developed by French et al. [98], it is possible to fabricate a composite with a defined creep resistance that will control the grain size, the width of the layers, and the compression axis. In the case of isostrain, where the strain and strain rate are the same for each phase, and assuming the creep equation in a compact form as, e = Ajo the stress for this configuration, o, is given as ... 

Although it is possible to introduce non-linear visco-elastic models, the second common approach is to utilize existing metals creep models. There are a number of models and all express the creep strain rate as a function of stress and other parameters. Popular forms are given below for primary and secondary creep, respectively. 

Merry and co-workers [5] used an axisymmetric tension test to perform constant stress tests and compare the creep response of new and old HDPE geomembranes. A 36-h constant stress creep test was performed on new HDPE using a temperature range of 2-53 °C and stresses ranging from 2-15 MPa. Excess material was then stored in a laboratory for an additional seven years, after which time tests on old geo-membranes were performed. Because the experimental results could not be compared directly, an adaption of the Singh-Mitchell creep model for soil, which is a rate process equation. 

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