Creep rate stress dependence

Mosedale et al. were the first to publish useful fast flux irradiation creep data on cladding materials (86). They showed that the irradiation creep rate in solution treated 316 stainless steel is approximately proportional to stress and neutron flux at temperatures of about 250°C. Theoretical studies have predicted a creep rate stress dependence of a power less than 2 and a negative temperature dependence, i.e., at lower temperatures a faster creep rate (77). Claudson has observed such behavior with temperature and has suggested that a creep rate proportional to exp(—0.0027T), where T is in kelvins, should fit both solution treated and cold worked stainless steels. 

As shown in Fig. 5.4, for stresses far away from a (either a-c cr or crc a ), the initial creep behavior (stress dependence) of the composite is determined primarily by the constituent having the higher creep rate. On the other hand, the final creep behavior of the composite is governed by the constituent with the lower creep rate. For applied creep stresses close to o, a gradual change in creep stress exponent n occurs from rii to n2 (or vice versa). 

For material produced in the 1970s with a mean, but strongly scattered, grain aspect ratio of around 35, dislocation creep dominated at stresses > 60 MPa (stress exponent = 25), as can be seen in Fig. 3.1-188. For material produced 20 years later with a similar grain aspect ratio of 31, a stress exponent of 1.2 was found in the stress regime from 30 to 80 MPa, indicating a diffusion-controlled creep process [1.214]. The evaluation of the strain rate/stress dependence of the values... 

The linearisation of the creep curves, by representing in double logarithmic co-ordinates the variation of deformation with time can be done applying the method developed by B.W. Chery and D.F. Kindles [887], i.e. of overlapping of the stress vs. time, for the prediction of the polymers behaviour to creep for long periods of solicitation. In the case of the vitreous polymers, the creep rate can depend, in certain conditions, only by the applied stress and instantaneous deformation. 

The creep rate occurring depends on the stress and the temperature. 

In diffusion creep, atoms diffuse along the grain boundaries from zones with compression stress to zones with tensile stress. This creep mechanism is very slow and is activated with low stress levels and high temperatures. The creep rate also depends on the diffusion length the atoms have to travel and thus on the grain size. Diffusion creep does not play an important role in solder joints of electronic assemblies because of its slowness. 

Here, is the effective viscosity that is affected by the volume fraction of the phase, f. The intrinsic viscosity that is independent of the volume fraction is denoted as ri . The strain rate, which is same as the creep rate, is dependent upon the shear stress and the effective viscosity. 

Another aspect of plasticity is the time dependent progressive deformation under constant load, known as creep. This process occurs when a fiber is loaded above the yield value and continues over several logarithmic decades of time. The extension under fixed load, or creep, is analogous to the relaxation of stress under fixed extension. Stress relaxation is the process whereby the stress that is generated as a result of a deformation is dissipated as a function of time. Both of these time dependent processes are reflections of plastic flow resulting from various molecular motions in the fiber. As a direct consequence of creep and stress relaxation, the shape of a stress—strain curve is in many cases strongly dependent on the rate of deformation, as is illustrated in Figure 6. 

The dependence of creep rate on applied stress a is due to the climb force the higher CT, the higher the climb force jb tan 0, the more dislocations become unlocked per second, the more dislocations glide per second, and the higher is the strain rate. 

The predicted strain variation is shown in Fig. 2.43(b). The constant strain rates predicted in this diagram are a result of the Maxwell model used in this example to illustrate the use of the superposition principle. Of course superposition is not restricted to this simple model. It can be applied to any type of model or directly to the creep curves. The method also lends itself to a graphical solution as follows. If a stress is applied at zero time, then the creep curve will be the time dependent strain response predicted by equation (2.54). When a second stress, 0 2 is added then the new creep curve will be obtained by adding the creep due to 02 to the anticipated creep if stress a had remained... 

Dynamic loading in the present context is taken to include deformation rates above those achieved on the standard laboratorytesting machine (commonly designated as static or quasi-static). These slower tests may encounter minimal time-dependent effects, such as creep and stress-relaxation, and therefore are in a sense dynamic. Thus the terms static and dynamic can be overlapping. 

It can be shown that for o>2 GPa a constant transition density function I=I0 yields almost the same stress dependence of the creep rate as the linear function. Therefore, in order to keep the calculations tractable we derive the lifetime of a fibre by applying the same density transition function as was used in the calculation of the dependence of the strength on the load rate, viz. I(U)=IQ on the interval [U0, Um and I(U)=0 elsewhere. This results for the shear strain of a domain in... 

In the initial stage, known as primary creep, the strain rate is relatively high, but slows with increasing strain. The strain rate eventually reaches a minimum and becomes near-constant. This is known as secondary or steady-state creep. This stage is the most understood. The characterized creep strain rate , typically refers to the rate in this secondary stage. The stress dependence of this rate depends on the creep mechanism. In tertiary creep, the strain-rate exponentially increases with strain [1-9]. 

Background At elevated temperatures the rapid application of a sustained creep load to a fiber-reinforced ceramic typically produces an instantaneous elastic strain, followed by time-dependent creep deformation. Because the elastic constants, creep rates and stress-relaxation behavior of the fibers and matrix typically differ, a time-dependent redistribution in stress between the fibers and matrix will occur during creep. Even in the absence of an applied load, stress redistribution can occur if differences in the thermal expansion coefficients of the fibers and matrix generate residual stresses when a component is heated. For temperatures sufficient to cause the creep deformation of either constituent, this mismatch in creep resistance causes a progres-... 

Fig. 5.2 Comparison of creep behavior and time-dependent change in fiber and matrix stress predicted using a 1-D concentric cylinder model (ROM model) (solid lines) and a 2-D finite element analysis (dashed lines). In both approaches it was assumed that a unidirectional creep specimen was instantaneously loaded parallel to the fibers to a constant creep stress. The analyses, which assumed a creep temperature of 1200°C, were conducted assuming 40 vol.% SCS-6 SiC fibers in a hot-pressed SijN4 matrix. The constituents were assumed to undergo steady-state creep only, with perfect interfacial bonding. For the FEM analysis, Poisson s ratio was 0.17 for the fibers and 0.27 for the matrix, (a) Total composite strain (axial), (b) composite creep rate, and (c) transient redistribution in axial stress in the fibers and matrix (the initial loading transient has been ignored). Although the fibers and matrix were assumed to exhibit only steady-state creep behavior, the transient redistribution in stress gives rise to the transient creep response shown in parts (a) and (b). After Wu et al 1...

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