Surface strain-rate

Fig.4. True stress-strain-strain rate surfaces for Rigidex 50 LPE at 100°C.

In the drawing process, the polymer moves across the stress-strain-strain rate surfaces of Figure 4, and any incremental change in the flow stress da with incremental... 

Figure 12.36 True stress true strain-strain rate surface for high-density polyethylene stretched at iOCPC. (Reproduced with permission from Hope, PS. and Ward, I.M. (1981) An activated rate theory approach to the hydrostatic extrusion of polymers. /. Mater. Sci., 16, 1511. Copyright (2000) Hanser Publications.)...

The use of CRDF measurements was shown by Ward and co-workers [78] to be understood in terms of the relationship of creep behaviour to plastic strain following the concept of the true stress-true strain - strain rate surface (see Section 12.6). Ward and co-workers... 

Inelastic Loading. The strain lies on the elastic limit surface = 0, and the tangent to the strain history points in a direction outward from the elastic limit surface > 0. The material is said to be undergoing inelastic loading, and k is assumed to be a function of the strain s, the internal state variables k, and the strain rate k... 

When the material is at the ultimate stress point B, inelastic loading will entail a positive strain rate, and the elastic limit surface in strain space will be moving outward. On the other hand, the stress rate at this point is zero, and the elastic limit surface in stress space will be stationary. If the material is perfectly inelastic over a range of strains, then the stress rate will be zero and the elastic limit surface in stress space will be stationary on inelastic loading throughout this range. 

The inelastic contribution to the strain rate is directed along the outward normal to the elastic limit surface in stress space. 

The normality conditions (5.56) and (5.57) have essentially the same forms as those derived by Casey and Naghdi [1], [2], [3], but the interpretation is very different. In the present theory, it is clear that the inelastic strain rate e is always normal to the elastic limit surface in stress space. When applied to plasticity, e is the plastic strain rate, which may now be denoted e", and this is always normal to the elastic limit surface, which may now be called the yield surface. Naghdi et al. by contrast, took the internal state variables k to be comprised of the plastic strain e and a scalar hardening parameter k. In their theory, consequently, the plastic strain rate e , being contained in k in (5.57), is not itself normal to the yield surface. This confusion produces quite different results. 

Since the yield function is independent of p, the yield surface reduces to a cylinder in principal stress space with axis normal to the 11 plane. If the work assumption is made, then the normality condition (5.80) implies that the plastic strain rate is normal to the yield surface and parallel to the II plane, and must therefore be a deviator k = k , k = 0. It follows that the plastic strain is incompressible and the volume change is entirely elastic. Assuming that the plastic strain is initially zero, the spherical part of the stress relation (5.85) becomes... 

Naghdi, P.M. and Trapp, J.A., On the Nature of Normality of Plastic Strain Rate and Convexity of Yield Surfaces in Plasticity, J. Appl. Mech. 62, 61-66 (1975). 

Edwards e/a/. carried out controlled potential, slow strain-rate tests on Zimaloy (a cobalt-chromium-molybdenum implant alloy) in Ringer s solution at 37°C and showed that hydrogen absorption may degrade the mechanical properties of the alloy. Potentials were controlled so that the tensile sample was either cathodic or anodic with respect to the metal s free corrosion potential. Hydrogen was generated on the sample surface when the specimen was cathodic, and dissolution of the sample was encouraged when the sample was anodic. The results of these controlled potential tests showed no susceptibility of this alloy to SCC at anodic potentials. 

If crack propagation occurs by dissolution at an active crack tip, with the crack sides rendered inactive by filming, the maintenance of film-free conditions may be dependent not only upon the electrochemical conditions but also upon the rate at which metal is exposed at the crack tip by plastic strain. Thus, it may not be stress, per se, but the strain rate that it produces, that is important, as indicated in equation (8.8). Clearly, at sufficiently high strain rates a ductile fracture may be propagated faster than the electrochemical reactions can occur whereby a stress-corrosion crack is propagated, but as the strain rate is decreased so will stress-corrosion crack propagation be facilitated. However, further decreases in strain rate will eventually result in a situation where the rate at which new surface is created by straining does not exceed the rate at which the surface is rendered inactive and hence stress corrosion may effectively cease. 

It may be felt that the initiation of a stress-corrosion test involves no more than bringing the environment into contact with the specimen in which a stress is generated, but the order in which these steps are carried out may influence the results obtained, as may certain other actions at the start of the test. Thus, in outdoor exposure tests the time of the year at which the test is initiated can have a marked effect upon the time to failure as can the orientation of the specimen, i.e. according to whether the tension surface in bend specimens is horizontal upwards or downwards or at some other angle. But even in laboratory tests, the time at which the stress is applied in relation to the time at which the specimen is exposed to the environment may influence results. Figure 8.100 shows the effects of exposure for 3 h at the applied stress before the solution was introduced to the cell, upon the failure of a magnesium alloy immersed in a chromate-chloride solution. Clearly such prior creep extends the lifetime of specimens and raises the threshold stress very considerably and since other metals are known to be strain-rate sensitive in their cracking response, it is likely that the type of result apparent in Fig. 8.100 is more widely applicable. 

Fig. 6.5. Yield strengths from flexural tests are plotted against strain rates at the surface of the samples. Tests were performed on polymers A, B, and E test temperature 23 °C. The slope of the three lines correspond to similar activation volumes v = 2 0.1 nm3...

An important aspect concerning the surface indentation mechanism is the creep effect shown by polymeric materials i.e. the time dependent part of the plastic deformation of the polymer surface under the stress of the indenter14-16. The creep curves are characterized by a decreasing strain rate, which can be described by a time law of the form... 

Based on the flame-hole dynamics [59], dynamic evolutions of flame holes were simulated to yield the statistical chance to determine the reacting or quenched flame surface under the randomly fluctuating 2D strain-rate field. The flame-hole d5mamics have also been applied to turbulent flame stabilization by considering the realistic turbulence effects by introducing fluctuating 2D strain-rate field [22] and adopting the level-set method [60]. 

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