Load histories

It is important to note that the state determined by this analysis refers only to the pressure (or normal stress) and particle velocity. The material on either side of the point at which the shock waves collide reach the same pressure-particle velocity state, but other variables may be different from one side to the other. The material on the left-hand side experienced a different loading history than that on the right-hand side. In this example the material on the left-hand side would have a lower final temperature, because the first shock wave was smaller. Such a discontinuity of a variable, other than P or u that arises from a shock wave interaction within a material, is called a contact discontinuity. Contact discontinuities are frequently encountered in the context of inelastic behavior, which will be discussed in Chapter 5. 

Contact discontinuity A spatial discontinuity in one of the dependent variables other than normal stress (or pressure) and particle velocity. Examples such as density, specific internal energy, or temperature are possible. The contact discontinuity may arise because material on either side of it has experienced a different loading history. It does not give rise to further wave motion. 

For statie design to be valid in praetiee, we must assume situations where there is no deterioration of the material strength within the time period being eonsidered for the loading history of the produet. With a large number of eyelie loads the material will eventually fatigue. With an assumed statie analysis, stress rupture is the meehanism of failure to be eonsidered, not fatigue. The number of stress eyeles in a problem eould... 

Some typieal load histories for meehanieal eomponents and systems are shown in Figure 4.21. The load (dead load, pressure, bending moment, ete.) is subjeet to variation in all eases, rather than a unique value, the likely shape of the final... 

Figure 4.21 Typical load histories for engineering components/systems...

A key problem in experimental load analysis is the translation of the data yielded from the measurement system (as represented by the load histories in Figure 4.21) into an... 

Figure 4.47 shows a typieal load history (in Newtons foree) measured experimentally during the operation of a similar produet in serviee. It is also antieipated that the... 

Figure 4.47 Typical load history during operation of the foot pedal...

Occasionally, materials are tested in tension by applying the loads in increments. If this method is used for plastics then special caution is needed because during the delay between applying the load and recording the strain, the material creeps. Therefore if the delay is not uniform there may appear to be excessive scatter or non-linearity in the material. In addition, the way in which the loads are applied constitutes a loading history which can affect the performance of the material. A test in which the increments are large would quite probably give results which are different from those obtained from a test in which the increments were small or variable. 

The simplest theoretical model proposed to predict the strain response to a complex stress history is the Boltzmann Superposition Principle. Basically this principle proposes that for a linear viscoelastic material, the strain response to a complex loading history is simply the algebraic sum of the strains due to each step in load. Implied in this principle is the idea that the behaviour of a plastic is a function of its entire loading history. There are two situations to consider. 

Fig. 8.3. The yield of shock-synthesized zinc ferrite is found to be strongly dependent on the early loading history. This characteristic is thought to be an indication of shock modification on subsequent chemical reaction.

The first assumption involved in using the Boltzmann superposition principle is that elongation is proportional to stress, that is, compliance is independent of stress. The second assumption is that the elongation created by a given load is independent of the elongation caused by any previous load. Therefore, deformation resulting from a complex loading history is obtained as the sum of the deformations that can be attributed to each separate load. 

Several criticisms of these parameters have recently been pointed out. First, they have no specific association with a material plane (i.e., they are scalar parameters), despite the fact that cracks are known to nucleate on specific material planes. With traditional parameters it is difficult to account for the effects of crack closure under compressive loading. Traditional parameters have not been successful at unifying experimental results for simple tension and equibiaxial tension fatigue tests. Finally, a nonproportional loading history can always be constmcted for a given scalar equivalence parameter that holds constant the value of the scalar parameter, but which results in cyclic loading of material planes. For such histories, scalar parameters incorrectly predict infinite fatigue life. 

There are two superposition principles that are important in the theory of Viscoelasticity. The first of these is the Boltzmann superposition principle, which describes the response of a material to different loading histories (22). The second is the time-temperature superposition principle or WLF (Williams, Landel, and Ferry) equation, which describes the effect of temperature on the time scale of the response. 

The first category is traditional in the solid rocket industry, and variations on this approach have been many and diverse. The second category is appealing its generality and possible mathematical rigor but has been hampered in its development by experimental difficulties. Until recently, however, most failure relationships have been based on a single loading history or first stretch conditions. 

Clark, J.F., Simpson, H.J., Bopp, R.F., and Deck, B. (1992) Geochemistry and loading history of phosphate and silica in the Hudson estuary. Estuar. Coastal Shelf Sci. 34, 213-233. 

To investigate the control factors of welded component s fatigue behaviour, and use the analytical methods for estimating the total fatigue life of welds subjected to variable-amplitude loading histories and surface treatments, in order to find some possible methods to improve the fatigue strength. 

After a time increment dt, the local stresses in the fibers and matrix can be updated to obtain (tr,-, e e,)t at any time t+ dt. Using this information, the composite stress, strain, and strain rate (ac, ec, ec), can be obtained from the constituent parameters (iterative computation, the creep behavior of the composite and constituents can be predicted for any loading history, including cyclic creep. 

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