Stress drop

Many fibrous composites are made of strong, brittle fibres in a more ductile polymeric matrix. Then the stress-strain curve looks like the heavy line in Fig. 25.2. The figure largely explains itself. The stress-strain curve is linear, with slope E (eqn. 25.1) until the matrix yields. From there on, most of the extra load is carried by the fibres which continue to stretch elastically until they fracture. When they do, the stress drops to the yield strength of the matrix (though not as sharply as the figure shows because the fibres do not all break at once). When the matrix fractures, the composite fails completely. 

Many properties are temperature dependent. For example up to 100°C the yield stress drops with temperature at a faster rate than does the yield stress of polypropylene however, it retains some strength up to 160°C. 

In a constant strain-rate experiment, the rapid multiplication of dislocations following the yield point can produce more mobile dislocations than are necessary to maintain the imposed strain-rate and consequently the stress drops. The deformation will continue at a constant stress provided any decrease in u is compensated by an increase in iom, or vice versa. However, in general, the stress rises with increasing strain. The slope (dajdt) of the stress-strain curve is determined by the competition between two dislocation processes namely, work-hardening and recovery, which we now consider briefly. 

Glass transition temperature Secondary transition Extension ratio Maximum extension ratio Craze intensification stress Craze initiation stress Tensile strength Compressive yield stress Drop in after yielding A measure of strain softening Test frequency... 

The plots show that in both cases the craze stress S (x) is almost constant (quoted a,) along the craze, and is about 40% lower for the toluene gas graze. Again, comparison with liquid solvent crazes show that in liquids the craze stress drops to much lower values that in the low pressure solvent vapor. 

When a co-current vapor flow is present, the basic nature of this flow does not change, but the details differ because of the thinning of the liquid film by interfacial shear stress. Dropping the convective terms we can write the Navier-Stokes equations for steady film flow as follows ... 

For the purpose of designing machine parts, one can imagine a simple stress profile as in Figure 13.1b, with a vertical step or infinite gradient da Jdx but if one is interested in chemical details at the interface, it is prudent to consider the possibility that the profile may actually be as in Figure 13.1c—with a strong but not infinite gradient. As will be shown later in this chapter, the width over which the main stress-drop extends is measured in nanometers or perhaps micrometers. 

These are rather natural-seeming results and l/K can be thought of as measures of the resistance in material 1 to any kind of motion. If, in this sense, material 1 is more inert or resistant than material 2, it is reasonable to expect that the stress-drop across the neighborhood of the interface will be mainly in material 1, i.e., Aj will be larger than Aj. 

Also included in Table I are the true fracture stress (of) calculated from the cross section of the fractured specimen, and the fracture strain (ef). The fracture stress dropped significantly, from 171 MPa for LLDPE to 100 MPa and 35 MPa for 10% and 25% PS, respectively. The fracture stress of the 37.5% PS blend was even lower, 8.5 MPa, but was still higher than the oy value of 5.9 MPa, so the blend deformed in a ductile manner. The blend with 50% PS fractured in a quasi-brittle manner at a stress of 7.0 MPa, which was slightly lower than cry for this composition. The large decrease in Of with increasing PS concentration was consistent with debonded PS particles that were not load-bearing during plastic deformation. 

Figure 11.16. (a) General shapes of the stress-strain curves of ductile thermoplastics. Some such polymers manifest a very distinct post-yield stress drop, while many others do not. (b) For comparison, the general shape of the stress-strain curve is shown for a very brittle material. 

When a cell (fc, 1) fails, the stress drops in this cell to the arrest stress... 

While it is obvious that the mean stress drop (At) (r — t ) controls the mean stress (r) on the fault, it has also been found that the spatial distribution of the stress drop has significant influence on the FS distribution. In [61], it is demonstrated that the degree of spatial disorder of the stress... 

Evaluation of the wall region eddy viscosity has been facilitated by the fact that the shear stress remains essentially constant across the wall layer. On a flat plate with uniform free-stream conditions, the shear stress drops less than 10 percent from its wall value across the wall layer. The equation governing low-speed flow on a flat plate in the absence of a pressure gradient is... 

After the yield point at cTy = 29 MPa, the neat PP (51 wt% crystalline in this case) exhibits a small but significant true stress drop followed, for strain larger than about 0.3, by a progressive (although moderate) hardening. 

High temperatures induce a more ductile mechanical behaviour. The heated specimen exhibited a higher shear strength. This effect is slightly more important for samples initially normally consolidated than for overconsolidated ones. At large strain when the critical state is reached the deviator stress drops and has almost the same value as for samples tested at ambient temperature. 

Figure 6. Approximation on temperature distribution in order to estimate the stress drop caused by cooling.

Note that this stress drop Act occurs in hydrostatic manner in the circular region with radius d (see Figure 6). Namely the normal stress component in any direction decreases uniformly anywhere in that region by Aa... 

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