Shear stress at yielding

Fig. 11 Calculated surface profiles of the octahedral shear stress at yield assuming a modified Von Mises criterion (a), and of the octahedral shear stress for a glass/epoxy contact under gross sliding condition (b). The grey area delimits the region at the leading edge of the contact where the octahedral shear stress is exceeding the limit octahedral shear stress at yield (a is the radius of the contact area) (from [97])...

These tests were performed using an Instron Model 8561 (single screw) machine in air and the furnace was adapted to perform four-point bend tests. The rates indicated in Fig. 2.3 relate to crosshead displacement. Figure 2.4 shows the resolved shear stress at yield for the specimens tested ate = 4.2 x 10 s above Tc at the indicated orientations. The mechanism for slip is dislocation glide, which explains the orientation dependence of yield, as seen in Fig. 2.4. Thus, the BDT temperature, Tc, of the sapphire (AI2O3) varies not only with the strain rate, but also with the crystallographic orientation of the fracture plane. 

Special attention should be paid to the fact that characterizes principally different behavior of crystalline metals compared with polymers. As it is known [3, 19], ratio (where is experimentally determined shear stress at yielding) is much higher for metals than for polymers. For five metals possessing the face-centered cubic or hexagonal lattices the following ratios were obtained = 37400 22720 (according to the data of Ref... 

Fig. 7. Decay of shear stress during steady shear at various shear rates. Determination of zero-time shear stresses or yield stresses and equiUbrium shear...

The idealization of a fixed shear stress at which a solid yields mechanically is often qualitatively correct, but yielding is perhaps better characterized as occurring over a range of stresses. For example, the x quartz does not exhibit a precursor until stresses exceed 6 GPa. Nevertheless, there is strong evidence that the yielding process begins to occur at stresses of 4 GPa [74G01]. 

Thus, for a given fluid (Ry constant), the critical radius rt is determined entirely by the pressure drop and becomes progressively larger as the pressure drop is reduced. Flow-ceases when the shear stress at the wall R falls to a value equal to the yield stress Ry. 

X is the ratio of the yield stress to the shear stress at the pipe wall. 

Clearly the Riener-Riwlin equation reduces to the Margules equation when the Bingham yield value is zero, but there is an important consequence in that it is assumed that all the material is flowing, i.e. the shear stress at the wall of the outer cylinder must be... 

Shear stress (F/A), lb.p/sq. ft. t refers to the shear stress at the wall of a round pipe (DAP/ 4L) and r< to the shear stress at the wall of a viscometer bob Yield value or yield stress of a Bingham-plastic fluid, lb.F/sq. ft. Indicator of an unspecified functional relationship... 

Active stresses exerted by smooth muscle cells appear to increase the internal stresses that exist in vessel wall. The effects of passive and active muscular contraction on the residual stress in the wall have been considered. Their results suggest that basal muscle tone, which exists under physiological conditions, reduces the strain gradient in the arterial wall and yields a near uniform stress distribution. Increased muscular tone that accompanies elevated blood pressure tends to restore the distribution of circumferential strain in the arterial wall, and to maintain the flow-induced wall shear stress at normal levels. It appears that the active stresses exerted by smooth muscle cells may balance the tension within the vessel wall in a similar manner to the way that active fibroblast tension balances the stress in the dermis. 

In general, shear stress at one location (e.g., the bob surface in a concentric cylinder viscometer) is calculated from the dimensions of the sample gap and the measured or applied torque. Shear rate is calculated at the same location from sample gap dimensions and rotational speed. By making experimental measurements over a range of speeds or torques, the flow curve (shear stress versus shear rate) of the sample can be established. Suitable mathematical treatment of the flow curve data yields the sample s constitutive equation and rheological properties. 

Indeed, the shear stress at the solid surface is txz=T (S 8z)z=q (where T (, is the melt viscosity and (8USz)z=0 the shear rate at the interface). If there is a finite slip velocity Vs at the interface, the shear stress at the solid surface can also be evaluated as txz=P Fs, where 3 is the friction coefficient between the fluid molecules in contact with the surface and the solid surface [139]. Introducing the extrapolation length b of the velocity profile to zero (b=Vs/(8vy8z)z=0, see Fig. 18), one obtains (3=r bA). Thus, any determination of b will yield (3, the friction coefficient between the surface and the fluid. This friction coefficient is a crucial characteristics of the interface it is obviously directly related to the molecular interactions between the fluid and the solid surface, and it connects these interactions at the molecular level to the rheological properties of the system. 

Strain rate of 5x10" s , while the strain rates within the epoxy surface layer are in the order of 10 s under fretting conditions. Accordingly, the values of the octahedral shear stress at the onset of yield are probably underestimated. In addition to the limited viscoelastic response of the epoxy material at the considered frequency and temperature (tan 8 = 0.005 at 25°C and 1 Hz, table I), this analysis supports the validity of a global elastic description of the contact stress environment. 

Analysis of shear stress at constant shear rate yields an average viscosity and changes in viscosity with time due to effects such as shear thinning, viscous heating and thermoset curing. 

The generic flow properties of soft particle glasses are exemplified in Fig. 17, which shows the variations of the shear stress versus the shear rate measured at steady state for microgel pastes and compressed emulsions [187]. The flow curves in Fig. 17a obtained for microgel pastes with varying particle concentration, crosslink density, salt concentration, and solvent viscosity show the same qualitative behavior a minimum shear stress, the yield stress of the material, below which the... 

The ratio between the local shear stress in the boundary layer defined by (5.246) and the shear stress at the wall given by (1.359), yields ... 

The viscometer readings are recorded at 0.5 and 1.0 r/min after 30 seconds or after the system is stable. Shear stress at zero shear is equal to two times the 0.5 r/min reading minus the reading at 1.0 r/min. The yield value is then calculated as follows ... 

Stress State at Particles. If the modifier particles consist of rubber-like material, they act as stress concentrators as in HIPS and ABS. Whereas in HIPS and related polymers the maximum stress component, aee, at the equatorial regions around the particles is responsible for initiating crazes, in polymers with a tendency to shear deformation the maximum shear stress at the particles, yielding the formation of shear bands, must be considered (see Figure 17a). But in contrast to crazes, which have a stress-concentrating ability, shear bands to not increase the stress between particles as effectively. Therefore, the formation of microvoids inside the particles is necessary as an additional mechanism to increase the stress at and between particles. To make the polymeric material between particles yield, not only is the stress concentration at particles necessary (as in craze formation), but so is the stress field between particles. 

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