Pressure-dependent yield

The question of which channels account for the difference between the observed CH5 + cross-section and the CH4 + loss is illuminated by studying the isotopic system CH4-CD4. When mixtures of CH4 and CD4 were subjected to electron impact, a pressure dependent yield of CH2D+ was observed which established the reaction mechanism ... 

Kinetic examination of the methane yield shows behavior quite similar to that of methyl radical a pressure dependent yield of 0.406 molecule/100 e.v., a pressure independent yield of 0.126 molecule/100 e.v., and a rate constant ratio of kq/kf = 1.5 X 106 mole-1 cc. for the competing steps. 

Nickolaisen, S. L., S. P. Sander, and R. R. Friedl, Pressure-Dependent Yields and Product Branching Ratios in the Broadband Photolysis of Chlorine Nitrate, J. Phys. Chem., 100, 10165-10178 (1996). 

Lower values of the yield stress measured in tension compared to those measured in compression suggest that the effect of pressure, which is important for polymers, is not accounted for in this criterion. Hence, appropriate correction has to be made in order to account for the effect from external pressure. The most frequent version of pressure-dependent yield criterion is the modified von Mises criterion [20] ... 

Nickolaisen, S.L., and S.P. Sander, Pressure dependent yields and product branching ratios in the broadband photolysis of chlorine nitrate. J Phys Chem 100, 10,165, 1996. 

Figure 8.16 shows a biaxial yield contour for principal stresses a and 02 (with (73 = 0) of PVC, PC, PS, and PMMA at room temperature, normalized with the uniaxial yield stresses of these four polymers (Raghava et al. 1973). Thus, the center of the typical elliptical von Mises yield contour is displaced toward the biaxial compression quadrant characteristic of the pressure-dependent yield formalisms of Coulomb (1773) and Mohr (1900). For PC, discussed above, a model friction coefficient /if = 0.297 is obtained from eq. (8.40). In contrast, the displaced elliptical yield contour of experiments shown in Fig. 8.16 was obtained with a best fit of /if = 0.23, which gives a somewhat larger discrepancy than that for PC alone, given through eqs. (8.36) above. This could be attributed to the fact that the Oy used for normalization is itself dependent on (Tm. 

In what concerns incompressibility, several researchers stated after measuring volume variation of different polymers, that there is negligible volume variation after yielding and concluded that the normality rule, typical of associated plasticity, does not hold in case of the pressure dependent yield surfaces of polymers (Whitney and Andrews, 1967). This conclusion was confirmed by Spitzig and Richmond (1979) who showed that the associated flow rule based on a pressure sensitive yield surface leads to predictions... 

Caddell, R.M., Raghava, R.S. and Atkins, A.G. (1974) Pressure dependent yield criteria for polymers. Materials Science and Engineering, 13 113-20. 

The observed pressure dependences yield AF+ 71 for temperatures below 1000 °C, but this is progressively reduced at higher tempera-... 

The deformation or ploughing modes can also be well described for plastic and possibly even brittle fracture systems using modem numerical techniques. As with the elastomeric systems the models basically include geometric terms, such as 6, some load and various parameters such as an interface shear stress but more importantly a relatively accessible bulk deformation or dissipation property of the material. For the case of elastomers, an appropriate viscoelastic loss tangent is sufficient and for a ductile polymer some pressure dependent yield stress. There are many examples in the literature where good correlations have been obtained between a bulk mechanical test and a frictional response. Properly, it has been seen as the domain of others, perhaps polymer scientists, to seek to provide interrelationships between molecular structure and deformation dynamics and the consequent bulk material responses. 

It may be verified that oy is equal to the tensile yield stress by setting any two of the principle stresses to zero. For comparison, in pure shear, <7i = —<72 and <73 = 0, and the yield stress is ty = <7y/ /3. Moreover, it is easily seen that Eq. (59) is independent of p. In fact, most polymers do show a pressure-dependent yield stress, an observation that is attributed to their relative compressibility, so that a negative value of p significantly reduces the space available for the molecules and hence reduces their mobility. However, this can usually be accounted for by replacing Eq. (59) with Eq. (60), where S and p are materials constants [5]. 

We will see that this simple form of pressure-dependent yield criterion is more satisfactory than the Coulomb criterion when a representation is developed which includes the effects of temperature and strain rate on the yield behaviour. In physical terms, the hydrostatic pressure can be seen as changing the state of the polymer by compressing the polymer significantly, unlike the situation in metals where the bulk moduli are much larger ( 100 GPa compared... 

Further work by Adams and Coppendale (1979) considered what happens when the adhesive yields. They used a pressure-dependent yield criterion (i.e. one in which the von Mises deviatoric yield stress... 

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