Fluctuating stress

A proposal based on Onsager s theory was made by Landau and Lifshitz [27] for the fluctuations that should be added to the Navier-Stokes hydrodynamic equations. Fluctuating stress tensor and heat flux temis were postulated in analogy with the Onsager theory. Flowever, since this is a case where the variables are of mixed time reversal character, tlie derivation was not fiilly rigorous. This situation was remedied by tlie derivation by Fox and Ulilenbeck [13, H, 18] based on general stationary Gaussian-Markov processes [12]. The precise fomi of the Landau proposal is confimied by this approach [14]. 

For convenience, in the previous sections it has been arranged so that the mean stress is zero. However, in many cases of practical interest the fluctuating stresses may be always in tension (or at least biased towards tension) so that the mean stress is not zero. The result is that the stress system is effectively a constant mean stress, a superimposed on a fluctuating stress a a- Since the plastic will creep under the action of the steady mean stress, this adds to the complexity because if the mean stress is large then a creep rupture failure may occur before any fatigue failure. The interaction of mean stress and stress amplitude is usually presented as a graph of as shown in Fig. 2.76. 

A very wide sheet of grp which is known to contain intrinsic defects 1 mm long, is subjected to a fluctuating stress which varies from 0 to 80 MN/m. How many cycles would the sheet be expected to withstand if it is made from (a) chopped strand mat (CSM) and (b) woven roving (WR) reinforcement. The crack growth parameters C and n, and the critical stress intensity factors, Kc, for these materials are... 

Dynamic stress The varying or fluctuating stress occurring in a structural member as a result of dynamic loading. 

A metal s resistance to fatigue is markedly reduced in a corrosive environment. Many welded structures are subjected to fluctuating stresses which, with the superimposed tensile residual stress of the joint, can be dangerous. In addition to this a welded joint is a discontinuity in an engineering structure containing many possible sites of stress concentration, e.g. toe or root of the joint, weld ripple. 

The cyclic load (or strain) is usually a sinusoidal function, but triangle or square functions may be used. It is characterized by its frequency, [Pg.390]

Any unit, structure, or component that is subject to vibration, or any other fluctuating stress in presence of a corrosive environment. 

Any grade of steel can be subject to corrosion fatigue when operating under conducive fluctuating stress and corrosive conditions. 

Debonding (also called dewetting) is one mechanism of the failure of filler reinforced composites which are subjected to either continuous stress or fluctuating stresses. Debonding may also be used as a method of production for some of the materials discussed in Section 7.3. 

The memory equation contains fluctuating stresses and, like (z,y) in (lid), is calculated in mode coupling approximation using (10a) giving ... 

Equation (12B.1) describes the response if a prescribed fluctuating stress 0-22 is imposed, but it can be used to answer a related question if a... 

The lack of correlation between the fluctuating stress tensor and the fluctuating heat flux in the third expression is an example of the Curie principle for the fluctuations. These equations for fluctuating hydrodynamics are arrived at by a procedure very similar to that exhibited in the preceding section for diffusion. A crucial ingredient is the equation for entropy production in a fluid... 

The process of progressive localized permanent stmctural change occurring in a material subjected to conditions that produce fluctuating stresses and strains at some point or points that may culminate in cracks, complete fracture or thermal softening after sufficient number of fluctuations [Borders et al., 1946]... 

FATIGUE - The phenomenon leading to fracture under repeated or fluctuating stresses having maximum value less than the ultimate strength of the material. 

The maximum allowable mean stress is a-y, which is the yield stress for the material. The maximum allowable fluctuating stress, the endurance limit o, can be calculated from the ultimate stress of the material, (Ty,. The rotating beam endurance limit cr is calculated from (ry, as follows ... 

Maximum fluctuating stress a material can endure for infinite number of cycles - determined firom the S-N diagram. Function the part or assembly was originally designed and manufactured to perform. 

Permanent structural changes that occur in a material subjected to fluctuating stress and strain, which cause decay of mechanical properties. See S-N diagram. The ability of a material to plastically deform before fracturing in constant strain amplitude and low-cycle fatigue tests. See S-N diagram. ... 

Plot of stress, S, vs. number of cycles, N, required to cause failure of similar specimens in fatigue test. Data for each curve on the S-N diagram are obtained by determining fatigue life of a number of specimens subjected to various amounts of fluctuating stress. The stress axis may represent stress amplitude, maximum stress, or minimum stress. A log scale is usually used, especially for the N-axis. 

Flex fatigue is a term that is commonly used in the testing of elastomers. Flex fatigue is the result of a rubber fracturing after being subjected to fluctuating stresses. 

Radicals can be created by impurities (catalyst residues). Thermal fluctuations, stresses at high temperatures and the attack by oxygen molecules itself can all result in radical formation. UV radiation has a considerable impact. Radicals are created without UV radiation only extremely infrequently under normal conditions. Oxidation therefore progresses very slowly. Only at high temperatures does radical formation and oxidative reaction mechanisms get considerably accelerated, for example under conditions prevailing during polyethylene processing. 

Actually, machine parts or components, for reasons of simplification, are often designed for static operation only, although a fluctuating stress pattern may be expected. Therefore, instead of a static stress, pressures whose amplitudes and frequencies are subject to fluctuations will occur. These may be displayed with the help of stress-time functions. Given the above-described conditions, components subjected to dynamic stresses will fail earlier than those under static stresses. The following is meant to show how examinations of components in such cases may be conducted with maximum expediency. 

The fracturing of an elastomer after being subjected to fluctuating stresses is known as flex fatigue. 

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