Stress threshold

Creep. The creep characteristic of plastic foams must be considered when they are used in stmctural appHcations. Creep is the change in dimensions of a material when it is maintained under a constant stress. Data on the deformation of polystyrene foam under various static loads have been compiled (158). There are two types of creep in this material short-term and long-term. Short-term creep exists in foams at all stress levels however, a threshold stress level exists below which there is no detectable long-term creep. The minimum load required to cause long-term creep in molded polystyrene foam varies with density ranging from 50 kPa (7.3 psi) for foam density 16 kg/m (1 lb /ft ) to 455 kPa (66 psi) at foam density 160 kg/m (10... 

Sufficient tensile stress. Sufficiency here is difficult to define since it depends on a number of factors such as alloy composition, concentration of corrodent, and temperature. In some cases, stresses near the jdeld strength of the metal are necessary. In other cases, the stresses can be much lower. However, for each combination of environment and alloy system, there appears to be a threshold stress below which SCC will not occur. Threshold stresses can vary from 10 to 70% of yield strength depending on the alloy and environment combination and temperature (Fig. 9.6). 

Figure 9.6 Threshold stresses of two types of stainless steel in boiling 42% magnesium chloride solution. Reprinted with permission of American Society for Metals from Metals Handbook, vol. 10, 8th ed., Metals Park, Ohio, 1974, p. 210.)...

G.T. Gray III and P.S. Follansbee, Influence of Peak Pressure and Pulse Duration on the Substructure Development and Threshold Stress Measurements in Shock-loaded Copper, in Impact Loading and Dynamic Behavior of Materials (edited by C.Y. Chiem, H.-D. Kunze, and L.W. Meyer), Deutsche Gesellschaft fuer Metall-kunde, Germany, 1988, 541 pp. 

Two examples of path-dependent micromechanical effects are models of Swegle and Grady [13] for thermal trapping in shear bands and Follansbee and Kocks [14] for path-dependent evolution of the mechanical threshold stress in copper. 

The mechanical threshold stress has a straightforward micromechanical interpretation for pure materials... 

The mechanical threshold stress determines the applied stress necessary for substantial thermal activation. The quantity = 7.0 eV for OFE... 

The variation of r and f through 3.0 GPa and 5.4 GPa shock waves is shown in Fig. 7.7 [38]. This figure shows clearly that the shock-wave path is in the dislocation drag regime (r > f). The mechanical threshold stress f increases from 10 MPa to 80 MPa in the 5.4 GPa shock thus from (7.37)... 

Figure 7.7. Shear stress and mechanical threshold stress for 3.0 GPa and 5.4 GPa shock waves in copper.

The lone remaining aspect of this topic that requires additional discussion is the fact that the mechanical threshold stress evolution is path-dependent. The fact that (df/dy)o in (7.41) is a function of y means that computations of material behavior must follow the actual high-rate deformational path to obtain the material strength f. This becomes a practical problem only in dealing with shock-wave compression. 

P.S. Follansbee and U.F. Kocks, A Constitutive Description of the Deformation of Copper Based on the Use of the Mechanical Threshold Stress as an Internal State Variable, Acta Metall. 36, 81-93 (1988). 

D.L. Tonks and J.N. Johnson, Shock-Wave Evolution of the Mechanical Threshold Stress in Copper, in Shock Compression of Condensed Matter (edited by S.C. Schmidt, J.N. Johnson, and L.W. Davison), Elsevier Science, Amsterdam, 1990, pp. 333-336. 

The above-mentioned models differ in the relation that is derived between the rate of pull-out of the individual chain and the crack velocity. These models also differ in their interpretation of the threshold stress and the threshold toughness (Go). Also, V is expected to be dependent on the configuration of the connector chain at the interface. The value of v when connector chain crosses the interface just once is higher than the value when the chain forms multiple stitches, even though Go is not altered. When the chain forms multiple stitches, the block and tackle effect ensures that the viscous processes dominate even at lower velocities, and V is reduced by a factor of N from the value obtained from the single crossing case. These models are discussed by Brown and coworkers [45,46]. 

As shown in Fig. 4.9, these studies provide evidence that the breakdown was characterized by a fixed threshold stress of 11 GPa and a fixed threshold field of 2.8 X 10 Vm Once the threshold stress is exceeded, the conduction is controlled by the field and is independent of the stress. The threshold field is in reasonable agreement with the field of 7 x 10 V m below which a recovery from breakdown is observed when the field decreases due to the... 

It appears that the observed breakdown must be explained in terms of the transient behavior of stress-induced defects even though the stresses are well within the nominal elastic range. In lithium niobate [77G06] and aluminum oxide [68G05] the extent of the breakdown appears to be strongly influenced by residual strains. In the vicinity of the threshold stress, dielectric relaxation associated with defects may have a significant effect on current observed in the short interval preceding breakdown. 

Clearly the variables that may influence or the threshold stress for initially plain specimens, and hence the susceptibility to stress-corrosion cracking, are P and rj, i.e. 

The implications of a significant role for strain rate are wider than the obvious one that stress corrosion should only occur over a restricted range of strain rates. Thus, in constant load tests, since cracks will continue to propagate only if their rate of advancement is sufficient to maintain the crack-tip strain rate above the minimum rate for cracking, it is to be expected that cracks will sometimes stop propagating, particularly below the threshold stress. Such non-propagating cracks are indeed observed below the thres-hold . Moreover, in constant-load or constant-strain tests, the strain rate diminishes with time after loading, by creep exhaustion if the stress remains sensibly constant, and it is found that the stress-corrosion results are sensitive to the relative times at which the stress and electrochemical... 

Fig. 8.13 Effect of carbon content of annealed mild steels upon threshold stress for cracking...

For normal commercial-quality mild steels in the annealed or normalised conditions in which they are almost invariably used, various workers have shown that the carbon content of the steel is the major factor determining intergranular cracking susceptibility. Figure 8.13 shows the threshold stresses for a series of commercial mild steels of different carbon contents caused to crack in boiling 4n NH4NO3. The trend of the result suggests... 

Fig. 8.2S Long-time constant-load tests demonstrating a distinct stress-corrosion cracking threshold stress in the case of a straight l3Cr martensitic SS as opposed to a nickel-bearing SS...

Crack Initiation and the Threshold Stress intensity Factor Range... 

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