Model for Creep

Hart and coworkers developed a phenomenological theory of plastic deformation by using the concept of equation of state [6, 7]. The proposed deformation model consists essentially of two parallel branches (Fig. 6.10). Branch 1 represents 

Subcritical Crack Growth Creep-Controlled Crack Growth 

Deformation is obviously controlled by both the dislocation glide processes and the diffusive processes. The contribution from each process may be more, or less, at different temperatures. Hence, both branches of the phenomenological model will operate such that  

At temperatures below the homologous temperature (Thomo 0.25rmeit), however, the deformation processes are predominantly controlled by dislocation glide  

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In cellulose II with a chain modulus of 88 GPa the likely shear planes are the 110 and 020 lattice planes, both with a spacing of dc=0.41 nm [26]. The periodic spacing of the force centres in the shear direction along the chain axis is the distance between the interchain hydrogen bonds p=c/2=0.51 nm (c chain axis). There are four monomers in the unit cell with a volume Vcen=68-10-30 m3. The activation energy for creep of rayon yarns has been determined by Halsey et al. [37]. They found at a relative humidity (RH) of 57% that Wa=86.6 kj mole-1, at an RH of 4% Wa =97.5 kj mole 1 and at an RH of <0.5% Wa= 102.5 kj mole-1. Extrapolation to an RH of 65% gives Wa=86 kj mole-1 (the molar volume of cellulose taken by Halsey in his model for creep is equal to the volume of the unit cell instead of one fourth thereof). 

The proposed model for creep rupture based on the condition of maximum shear strain and the Eyring reduced time model explain the observed relations concerning the lifetime of aramid, polyamide 66 and polyacrylonitrile fibres. However, with increasing temperatures, in particular above 300 °C, chemical degradation of PpPTA also determines the lifetime. Furthermore, the model... 

The model represents a liquid (able to have irreversible deformations) with some additional reversible (elastic) deformations. If put under a constant strain, the stresses gradually relax. When a material is put under a constant stress, the strain has two components as per the Maxwell Model. First, an elastic component occurs instantaneously, corresponding to the spring, and relaxes immediately upon release of the stress. The second is a viscous component that grows with time as long as the stress is applied. The Maxwell model predicts that stress decays exponentially with time, which is accurate for most polymers. It is important to note limitations of such a model, as it is unable to predict creep in materials based on a simple dashpot and spring connected in series. The Maxwell model for creep or constant-stress conditions postulates that strain will increase linearly with time. However, polymers for the most part show the strain rate to be decreasing with time [23-26],... 

In structural ceramic composites, the principal effect considered was one of crack-face closure tractions, or cohesive forces, brought about, for instance, by bridging fibers. A rigorous evaluation of the crack tip fields where the crack faces are not traction free has not yet been attempted. However, an approximate approach for the small-scale creep case is to assume that the crack tip fields are not functionally altered by crack-face tractions, with the effect of the traction being only to introduce a zone of crack tip shielding. This allows for the development of preliminary models for creep crack growth which is inclusive of the role of crack bridging. These preliminary models predict that,... 

Figure 3-42 Mechanical Models for Creep-Compliance Data of Ice Cream Mix and Melt (Sherman, 1966).

Figure 4.31 Regions of plastic strain (dark) predicted by a model for creep of a liquid at (a) high temperature above Tg and (b) low temperature in the glassy state. At low temperature, regions of high strain accumulate into shear bands. (From Argon et al. 1995, with permission from the Journal...

The reader is referred to [ 160,161 ] for extensive reviews of creep of monolithic ceramics and ceramic composites. Models for creep of ceramic matrix composites are given in [161-163]. 

Validated models for creep damage assessment are available and these can produce estimates of time to crack initiation. High-temperature crack growth models can then be used to predict both time to failure and the nature of that event. 

Li, ]. and Dasgupta, A. 1994. Failure-mechanism models for creep and creep rupture. IEEE Trans, on Reliability 42(3) 339-353. 

I. Dutta, A Constitutive Model for Creep of Lead-Free Solders Undergoing Strain-Enhanced Microstructural Coarsening A Eirst Report, J. Electron. Mater., 2002... 

F. Masuyama, Hardness Model for Creep Life Assessment of High Strength Martensitic Steels, Kyushu Institute of Technology, Japan, 2009. 

N. C. Small, Continuum dilation model for creep analysis of ceramic nuclear fuels with applications, WAPD-TM-649, Bettis Atomic Power Labs., September, 1967. 

Use a Kelvin model for creep and show that the inflection point on the log scale plot corresponds to the creep retardation time t. Then the asymptotic time can be estimated at 3-5x even though the... 

A CONSTITUTIVE MODEL FOR CREEP LIFETIME OF PBO BRAIDED CORD... 

An Arrhenius-type phenomenological model for creep rupture, when coupled with a Weibull statistical analysis of laboratory data, provides a useful constitutive representation for the creep lifetime of braided PBO cord. This model will be useful to NASA s ULDB project, and also perhaps to other aerospace and civil engineering applications. 

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