Yield shear stress

If the sum of the mechanical allowances, c, is neglected, then it may be shown from equation 15 that the pressure given by equation 33 is half the coUapse pressure of a cylinder made of an elastic ideal plastic material which yields in accordance with the shear stress energy criterion at a constant value of shear yield stress = y -... 

As for the derivation of Eqs. 122,123 and 124 only the transitions 1—>2 have been counted, these equations do not describe recovery processes, where the transitions 2 —>1 are important as well. These approximations have been made for convenience s sake, but neither imply a limitation for the model, nor are they essential to the results of the calculations. Equation 124 is the well-known formula for the relaxation time of an Eyring process. In Fig. 65 the relaxation time for this plastic shear transition has been plotted versus the stress for two temperature values. It can be observed from this figure that in the limit of low temperatures, the relaxation time changes very abruptly at the shear yield stress Ty = U0/Q.. Below this stress the relaxation time is very long, which corresponds with an approximation of elastic behaviour. 

The transition from ideal elastic to plastic behaviour is described by the change in relaxation time as shown by the stress relaxation in Fig. 66. The immediate or plastic decrease of the stress after an initial stress cr0 is described by a relaxation time equal to zero, whereas a pure elastic response corresponds with an infinite relaxation time. The relaxation time becomes suddenly very short as the shear stress increases to a value equal to ry. Thus, in an experiment at a constant stress rate, all transitions occur almost immediately at the shear yield stress. This critical behaviour closely resembles the ideal plastic behaviour. This can be expected for a polymer well below the glass transition temperature where the mobility of the chains is low. At a high temperature the transition is a... 

Pure shear tests are often performed with torsional bars or flexural tests with very close spans, or using grooved tensile specimens (Fig. 12.2a). They provide the shear yielding stress, ry, which can be related to ay using yielding criteria (see below). 

At low temperatures the theoretical maximum shear yield stress in most glassy polymers is... 

Octahedral shear yield stress in the absence of hydrostatic stress cth- Hydrostatic stress... 

Fig. 20a—d. Surface stress profiles for polytertbutylstyrene [PTBS], poly(styrene-26% acrylonitrile) [PSANl] and poly(styrene-65% methylmethacrylate) [PSMMAj. The stress at the craze tip S, is plotted vs. Ve in d. The value of the shear yield stress Y of polycarbonate is indicated... 

Physical aging (annealing the glass at temperatures close to, but below, the glass transition temperature) is known to raise the shear yield stress Its effects... 

Some of the most important early experimental observations were of transitions from the quasi-brittle crazing deformation mode to the ductile shear deformation mechanisms with changes in the experimental conditions, such as temperature and strain rate, as well as in polymer variables, such as polymer backbone architecture, blend composition, crosslinking and physical aging state of the polymer glass. One of the strengths of the model of craze growth outlined above is that it allows one to make sense out of some experimentally observed craze-to-shear transitions that had previously defied explanation . The idea behind this explanation is quite simple One writes an expression for the shear yield stress, viz ... 

It is usual to assume that the shear yield stress has the same temperature dependence and strain rate dependence as the flow stress of the polymer in the active zone of the craze, i.e., n, = n, and in fact usually one go even further and sets How-... 

One of the great successes of the craze growth model is that it predicts a transition from scission-dominated crazing to shear deformation as the strand density of the network is increased. While the shear yield stress is essentially unaffected by dian ... 

Fig. 11a. A summary of the dominant mode of plastic deformation observed in crosslinked PS films as a function of the strand density v and the temperature at which the deformation was carried out. The open squares, half-filled squares and filled squares represent crazing only, crazing plus shear, and shear only, respectively (From Ref. courtesy of J. Mat. Sci. (Chapman and Hall), b The temperature dependence of the shear yield stress Oy and the crazing stress S (for two values of v)...

Fig. 13. Crazing stress versus temperature for a 1,800,000 molecular weight PS deformed at a rate of 4.1xl0" s . A second-order polynomial fit is drawn through the data. Also shown, as a dashed line, is a linearly decreasing shear yield stress (From Ref. courtesy J. Polymer Sci.-Polymer Phys. Wiley))...

Figure 7.19 Shear yield stress versus square of the zeta potential for the dispersions described in Fig. 7-18 at particle volume fractions (p = 0.184 and 0.213, or mass percentages of 57.0% and 61.4%. The zeta potential was obtained at low (p from the dynamic mobility. (From Leong et al. 1993, reproduced by permission of The Royal Society of Chemistry.)...

Equation (14.11) can be compared with Eq. (14.9), which corresponds to the Tresca criterion. According to Eq. (14.9) the shear yield stress is one-half the tensile yield stress, whereas Eq. (14.11) predicts that the shear yield stress is 1 /VI times the tensile yield stress. 

In equation (1), Tocto corresponds to the shear yield stress under zero pressure and a is a pressure coefficient, which quantifies the yield stress sensitivity to pressure. Such a yield criterion has previously been shown to hold for epoxy resins under a wide range of pressure, temperature and strain rate conditions [10, 11]. The two parameters, Tocto and a were found to be 44 MPa and 0.173 respectively from the uniaxial and plane strain compression results reported in table I. 

For the evaluation of the rheology of the silica dispersions, different test methods were applied (a) a shear rate-controlled relaxation experiment at = 0.5 s (conditioning), 500 s (shear thinning), and 0.5 s (relaxation) to evaluate the apparent viscosity, the relaxation behavior, and thixotropy (b) shear yield-stress measurements using a vane technique introduced by Nguyen and Boger [5] (c) low deformation dynamic tests at a constant frequency of 1.6 s in a stress range of ca. 0.5 - 100 Pa. All samples contained 3 wt% of fumed silica. 

Commonly, the thickening of liquids by hydrophilic silica is explained by the formation of H-bonds between the silanol groups of silica particles [6]. According to this model, the stability of silica gels in styrene and toluene, two fluids with comparable dielectrical properties, should be more or less identical. Figure 2 depicts the shear yield-stress experiments using the vane geometry of HDK N20 in styrene and toluene. 

Subbanna, M., Pradip, and Malghan, S.G., Shear yield stress of flocculated alumina-zirconia mixed suspensions Effect of solid loading, composition and particle size distribution, Chem. Eng. Sci., 53, 3073, 1998. 

Johnson. S.B. et al... The binding of monovalent electrolyte ions on a-alumina. IL The shear yield stress of concentrated suspensions. Langmuir, 15, 2844, 1999. 

---