Creep conditioning

Leaderman [1] was the first worker to emphasize that specimens must be cyclically conditioned at the highest temperature of measurement in order to obtain reproducible measurements in creep and recovery. Each cycle consists of application of the maximum load for the maximum period of loading, followed by a recovery period after unloading of about 10 times the loading period cycling must be continued until reproducibility is obtained. 

Leaderman [1] was the first worker to emphasise that specimens must be cyclically conditioned at the highest temperature of measurement in order to obtain reproducible 

Mechanical Properties of Solid Polymers, Third Edition. I. M. Ward and J. Sweeney. 

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Utilizing the constitutive law (1.5), the other model of a plate under the creep condition follows ... 

Let C be a bounded domain with smooth boundary T, <3 = x (0, T). Our object is to study a contact problem for a plate under creep conditions (see Khludneva, 1990b). The formulation of the problem is as follows. In the domain Q, it is required to find functions w, Mij, i,j = 1,2, satisfying the relations... 

We proceed with an investigation of the contact problem for a plate under creep conditions. We know that for every fixed / G L Q) there exists a unique solution w,M satisfying (2.35)-(2.37). Let G L Q) be a given element and F c (Q) be a closed convex and bounded set. We introduce the cost functional... 

We continue the investigation of the contact problem for a plate under creep conditions. In this section the case of both normal and tangential displacements of the plate is considered. 

Plate with a crack under the creep condition... 

The contact problem for a rod under creep conditions is considered in this section. Our goal is to prove an existence theorem. We use the notations of the preceding sections. For convenience, introduce the notations... 

Khludnev A.M. (1993b) Contact elastoplastic problem for a rod under the creep condition. In Nonlinear Math. Prob. in Industry, Math. Sci. and Appl. 1, 311-319. 

Khludnev A.M. (1996c) On equilibrium problem for a plate having a crack under the creep condition. Control and Cybernetics 25 (5), 1015-1029. 

Analogous to the arguments of small-scale yielding in linear elastic fracture mechanics, small-scale creep conditions (i.e., the situation where the size of the creep zone ahead of the fatigue crack tip is small compared to the characteristic dimensions of the test specimen, including the size of the crack and that of the uncracked liagment) can be assumed to exist when... 

Crack Tip Fields Under Nonlinear Creep Conditions... 

In the 1980s there was significant progress in the understanding of crack tip stresses and strains under creep conditions an excellent review of research up to 1986 is found in Riedel s book.3 This relatively rapid progress has possibly been due to the developments of previous decade in time-dependent... 

For long times, extensive creep conditions are reached, in which case the amplitude C(t) is replaced by C. The transition from SSC to extensive creep under constant load condition is... 

It is important to keep in mind that this transition time is an estimate based on a stationary crack analysis and that only when crack growth behavior is measured at times very much larger than tT can extensive creep conditions be reasonably assumed. In many cases, Eqn. (6) underestimates the transition time a better estimate may be the time when the creep strain equals the elastic strain in the far field.35,42... 

Here, we note that under extensive creep conditions, C is also proportional to PV, but the proportionality factor is different from that which applies in Eqn. (9). In some specimens, the proportionality factor for C, in SSC is not appreciably different than that for the extensive creep parameter C, so that apparent correlations of experimental data in terms of C are actually correlations in terms of Ct. The important distinction arises when an attempt is made to calculate the value of the fracture parameter for use in design or life estimation. Under SSC conditions, C, can be much greater than C so that predictions based upon C in SSC will be nonconservative. 

Under extensive creep conditions, the crack is engulfed by the creeping solid and the appropriate fracture parameter is C. In order to calculate the strain, e(r), ahead of the crack tip, one starts with the HRR-field pertinent to a static crack, Eqn. (4), and calculates the strain rate from the material law, Eqn. (2). The strain then follows from time integration of the strain rate. Under these assumptions, Riedel3 calculated the crack growth rate by taking into account the contribution to the strain at distance, r, from the current crack tip due to prior periods of crack extension, and showed that for sufficiently large crack extensions... 

D. E. Hawk and J. L. Bassani, Transient Crack Growth under Creep Conditions, J. Mech. Phys. Solids, 34(3], 191-212 (1986). 

J. L. Bassani and D. E. Hawk, Influence of Damage on Crack-Tip Fields under Small-Scale-Creep Conditions, Int. J. Fract., 42,157-172 (1990). 

For a comparison of the stress bases between Division 2 and other codes see Table 4-1. Allowable stresses stop at 800°F. Additional committee work is necessary before the effect of plastic deformation under creep conditions can be assessed well enough to develop adequate design rules for higher temperatures. It is believed that provisions in the area of toughness (brittle fracture) represent quite a step forward. The temperature of -20°F is no longer significant. A basic requirement is that adequate notch toughness be provided at all temperatures for all materials. 

Corrugated-pipe designs shown in Fig. 9-8b behave structurally as an intermediate between a bellow s joint and straight pipe They are also intermediate in price and require tie-rod support to keep the corrugations from straightening out under creep conditions. Such expansion designs are limited to short-expansion, straight-line requirements. 

The four-parameter model provides a crude quahtative representation of the phenomena generally observed with viscoelastie materials instantaneous elastie strain, retarded elastic strain, viscous flow, instantaneous elastie reeovery, retarded elastie reeovery, and plastic deformation (permanent set). Also, the model parameters ean be assoeiated with various molecular mechanisms responsible for the viscoelastic behavior of linear amorphous polymers under creep conditions. The analogies to the moleeular mechanism can be made as follows. 

The affirmation of the importance of the welded joints in questions regarding reactor lifetime especially during creep conditions which must lead to an increased R D effort bzised on the methods adapted to their local aspect and multi-materials. 

Two engineering parameters are commonly used to rank the behavior of materials under creep conditions (constant temperature and applied uniaxial stress) the minimum strain rate and the time to rupture. The first parameter is related to the useful life of components susceptible to shape-change in service (in heat engines, for example), while the second estimates the time-dependent failure probability. 

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