Time Hardening Creep

A time hardening creep law has been used is the Nutting equation. This equation is represented here as 

The constant n can be found from the slope on the log-log scale. Take the log of Equation 2.72 and obtain 

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Findley, W.N. and Khosla, G. (1955) Application of the superposition principle and theories of mechanical equation of state, strain, and time hardening to creep of plastics under changing loads. J. Appl. Phys., 26, 821. 

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 ... 

The objective of this test method is to measure the cohesive stress and the time to failure of a crystalline polymer craze layer under rapid, uniform extension. The method is an impact variant of the Full Notch Creep test used by Fleissner [12], Duan and Williams [13], Pandya and Williams [14] and others. The specimen (Fig. 2), a square-section tensile bar, is injection moulded. At the mid-plane of the gauge length a sharp, deep circumferential notch reduces the cross-section to about one fifth of its original area. This notch plane is formed by a moulded-in, hardened steel washer. Specimens were injection moulded at 210°C into a warm (100°C) mould and air cooled to 40 C using a hold pressure of 45-50 bar. 

Additional hardened gypsum was examined with regaid to its creep behavior. Figure 4 shows the deformation time diagram of hemihydrate as a function of the citric acid addition and of the equilibrium humidity. 

For time-independent, power-hardening material (no creep) ... 

Similarly, for time-dependent, power-hardening material one that creeps), on the other hand,... 

In other words, the strain at the onset of tensile deformation instability (maximum load point) is equal to the strain-hardening exponent. For a time-dependent, power-hardening material (i.e, one that creeps), on the other hand, deformation is enhanced by creep, such that ... 

Several points in this general treatment require further comment. In the first place we have neglected interaction between dislocations, except for the multiplication equation (8.45). One might have expected A in (8.43) to depend on the dislocation density n as in metals, where such interaction impedes dislocation motion and leads to work-hardening. This does not occur in ice. Secondly, if we consider a normal creep experiment with exponential increase of strain with time. This does not occur and Cp tends to a constant. The probable explanation is that, when the dislocation density becomes high, dislocations can climb by a diffusion mechanism (Weertman, 1957) to annihilate each other after a limited amount of motion, thus maintaining n constant. 

Creep tests on structural adhesives can be divided into tests on bulk hardened adhesive specimens and tests on adhesively bonded joints. The former provides information on the mechanical properties of the adhesive rather than the joints made from them. Fig. 2.28 displays the change in creep modulus with time for a range of cold-cure epoxy adhesives(26). These curves were derived from four point bend tests on adhesive prisms loaded in accordance with Fig. 2.16 using extreme fibre stresses ranging from 0.25 to 2.0 N/mm. The curves represent the stability of the adhesive with time under... 

The impregnation of hardened concrete or mortar with polymers increases the strength of the material signifieantly forrrfold increases are not rmcommoa At the same time the material attains a more brittle character. The creep of the material is also reduced... 

As a pure metal, lead is soft and malleable with low mechanical strength. This is an advantage in some apphcations such as weatherproofing, but one consequence is that under stress the metal will easily deform to reheve that stress, or creep , and this can take place over long periods of time. Indeed, lead can aeep under its own weight, and to avoid this effect the safe tensile stress is 1.7 MN/m and in compression, 2.75 MN/m. Lead can be alloyed to improve its strength properties, and antimony was commonly used as a hardener. Pure lead is in fact rarely used. 

A prediction of the final values of shrinkage and creep is needed to determine when a state of certain stabilization is achieved. However, perfect stabilization is possible only in artificial conditions created in a laboratory, because in the natural environment the hygrothermal conditions vary and a flow of heat and moisture to and from hardened cement paste is continued indefinitely. Predictions may also concern the development in time and the rate of both processes. 

As in time-independent plastic deformation, dislocations play an important role in the time-dependent plastic deformation of metals. At the onset of creep deformation, the number of dislocations in the material usually increases, causing hardening that can be experimentally observed by the reduction in the creep rate at constant stress. However, the dislocation density cannot increase arbitrarily since recovery occurs simultaneously (see section 6.2.8), with dislocations annihilating by climb. This process becomes the easier, the closer the dislocations are. Accordingly, after some transition time, an equilibrium between the generation of additional dislocation segments by plasticity and the annihilation of dislocations by recovery will be found. This equilibrium causes the creep rate to become constant in the secondary stage. 

In some materials, the microstructure can change at elevated temperatures. For example, the particles in precipitation hardened alloys usually coarsen over time. In this case, there will be no stationary region with constant creep... 

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