Plastic deformation onset

Viscosity has been replaced by a generahzed form of plastic deformation controlled by a yield stress which may be determined by compression e)meriments. Compare with Eq. (20-48). The critical shear rate describing complete granule rupture defines St , whereas the onset of deformation and the beginning of granule breakdown defines an additional critical value SVh... 

For most practical purposes, the onset of plastic deformation constitutes failure. In an axially loaded part, the yield point is known from testing (see Tables 2-15 through 2-18), and failure prediction is no problem. However, it is often necessary to use uniaxial tensile data to predict yielding due to a multidimensional state of stress. Many failure theories have been developed for this purpose. For elastoplastic materials (steel, aluminum, brass, etc.), the maximum distortion energy theory or von Mises theory is in general application. With this theory the components of stress are combined into a single effective stress, denoted as uniaxial yielding. Tlie ratio of the measure yield stress to the effective stress is known as the factor of safety. 

The onset of plastic deformation in a material under load is called yielding [60]. In contrast to the experiments described in the previous sections, yielding causes a permanent deformation, i.e. a deformation that remains after the load is removed. The effects of crosslinks on the yield behaviour of polymers are demonstrated by three experiments ... 

Plastic deformation is the permanent change in shape of a specimen due to applied stress. The onset of plastic deformation is seen as curvature in the stress—strain curve. Plastic deformation is important because it allows pharmaceutical excipients and drugs to establish large true areas of contact during compaction that can remain on decompression. In this way, good, intact, tablets can be prepared. 

Several groups tried to unravel whether the cavitation occurs before or after the onset of plastic deformation. Real-time small angle X-ray scattering [162] and light scattering [163,164] techniques were used to study the deformation of... 

Fig. 44. Comparison of theoretical predictions and experimental results for the lowering of yield strength, oy and stress at the onset of extensive plastic deformation, obtained from...

Various models 1-2,42 43) have been proposed to describe the extent and shape of the localised plastic deformation zone at the crack tip. From these models one may define a parameter known as the crack opening displacement, 5, (see Fig. 16) and the value of 5,c for the onset of crack growth is given by... 

Constant-load SCC tests have been shown to be more severe than constant-deflection tests. Under a constant load, stress increases as the cross-section is reduced by cracking or corrosion. However, this condition produces decreasing stress when deflection is fixed. It has been suggested that SCC threshold stress is associated with the onset of plastic deformation, that is, the elastic limit of the alloy. The elastic limit is difficult to measure unambiguously, however, the stress at which 0.2% plastic deformation occurs is generally used. 

A high pr value indicates that there will be a high volume reduction of the product due to particle rearrangement. The constant A has been shown to be equal to the reciprocal of the mean yield pressure required to induce plastic deformation. A larger value for A (low yield pressure) indicates the onset of plastic deformation at relatively low pressure, a sign that the material is more compressible. 

FCP tests of PS samples parallel and perpendicular to the injection molding direction were performed in comparison to material that was compression-molded from granules [76]. To minimize the effect of a plastic deformation possibly induced by precracking with a razor blade, the precrack was extended for a minimum of 2 mm by fatigue loading before onset of the experiment. 

Solidification and deformation processes are very seldom used to fabricate bulk articles from ceramics and other materials with low ductility and malleability. These substances are brittle and suffer fracmre before the onset of plastic deformation. Additionally, ceramics normally have exceedingly high melting points, decompose, or react with most cm-cible materials at their melting temperatures. Many ceramics are worked with in powder form since the products of most solid-state chemical syntheses are powders. Fabricating a bulk part from a powder requires a consolidation process, usually compaction followed... 

Figure 5.2. Stress vs. strain curves for various polymers around its glass-transition temperature. The maximum in the curve that occurs at Tg is referred to as the yield point (onset of plastic deformation).

Several methods, as described in the preceding section, have been used to acquire information relative to the onset of the initial localized plastic deformation under alternating loading. Figure 5 is a plot of reflected light intensity vs. cycles for a transparent PS sample tested at 21 Hz at a stress amplitude of 17.2 MPa The number of cycles, N., to initiate the craze, as determined from the first jump in intensity over background, is about 5,000 cycles and the cycles to fracture, N, is about 11,000. In later sections, the ratio of to Np which in this example is about 0.45, is shown to be a function of both stress amplitude and frequency. 

Fig. 20a. Tensile strain at the onset of plastic deformation in PC as a function of temperature for samples having a molecxdar weight of 30,000 (O) and 150,000 ( ) . b Plot of the extension ratio in the crazes as a function of temperature for the same samples described in a...

Fig. 23. Tensile strain at onset of plastic deformation in PES as a function of temperature for samples having a molecular weight of47.000 Prior to deformation the samples were physically aged at 200 Cfor 1 hour ( ),4hours ( land 70hours (O)...

The onset of plastic deformation in ABS copolymer can be seen as a thermally and stress activated process. In that framework, the Eyring equation can be written in terms of strain rate and temperature as... 

From the standpoint of a stress-strain curve, the constitutive behavior discussed in the previous section corresponds to a limited range of loads and strains. In particular, as seen in fig. 2.10, for stresses beyond a certain level, the solid suffers permanent deformation and if the load is increased too far, the solid eventually fails via fracture. From a constitutive viewpoint, more challenges are posed by the existence of permanent deformation in the form of plasticity and fracture. Phenomenologically, the onset of plastic deformation is often treated in terms of a yield surface. The yield surface is the locus of all points in stress space at which the material begins to undergo plastic deformation. The fundamental idea is that until a certain critical load is reached, the deformation is entirely elastic. Upon reaching a critical state of stress (the yield stress), the material then undergoes plastic deformation. Because the state of stress at a point can be parameterized in terms of six numbers, the tensorial character of the stress state must be reflected in the determination of the yield surface. 

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