Plastic instability

A ubiquitous feature accompanying large deformations in inelastic materials is the appearance of various instabilities. For example, plastic deformation may lead to shear banding, and the development of damage frequently leads to the formation of fault zones. As remarked in Section 5.2.7, normality conditions derived from the work assumption may imply stability which is too strong for such cases. Physical instabilities are likely to be associated with loss of normality and violation of the work assumption. 

Y.L. Bai, Thermo-Plastic Instability in Simple Shear, J. Mech. Phys. Solids 30, 195-207 (1982). 

If we load a material in compression, the force-displacement curve is simply the reverse of that for tension at small strains, but it becomes different at larger strains. As the specimen squashes down, becoming shorter and fatter to conserve volume, the load needed to keep it flowing rises (Fig. 8.6). No instability such as necking appears, and the specimen can be squashed almost indefinitely, this process only being limited eventually by severe cracking in the specimen or the plastic flow of the compression plates. 

We now turn to the other end of the stress-strain curve and explain why, in tensile straining, materials eventually start to neck, a name for plastic instability. It means that flow becomes localised across one section of the specimen or component, as shown in Fig. 11.5, and (if straining continues) the material fractures there. Plasticine necks readily chewing gum is very resistant to necking. 

Plastic instability is very important in processes like deep drawing sheet metal to form car bodies, cans, etc. Obviously we must ensure that the materials and press designs are chosen carefully to avoid instability. 

Hydrolytic instability or, alternatively, a tendency to revert to simple forms is shown by a number of sulphur-containing polymers. Some examples are shown in Figure 29.16 (a) plastic sulphur , (b) a polymer unstable at room temperature, (c) and (d) the (3 form of suphur trioxide. 

On its own, PVC is an extremely unstable polymer, in fact, almost certainly the least naturally stable polymer in commercial use. As Grassie has noted, Had this polymer been discovered at the present stage of development of the plastics industry, it would almost certainly have been eliminated as useless because of its general instability to all common degradative agents [2]. 

Polyvinyl chloride (p.v.c.) P.V.C. is one of the two most important plastics in terms of tonnage and shows many properties typical of rigid amorphous thermoplastics. More individually, it softens at about 70°C, burns only with difficulty and is thermally unstable. To reduce this instability, stabilisers are invariably compounded into the polymer. 

R.D. Gould, Combustion Instability of Solid Propellants Effect of Oxidizer Particle Size, Oxidizer/Fuel Ratio and Addition of Titanium Dioxide to Plastic Pro pell ants , Rept No RPE-TR-68/1, Westcott (Engl)... 

Shale stability is an important problem faced during drilling. Stability problems are attributed most often to the swelling of shales. It has been shown that several mechanisms can be involved [680,681]. These can be pore pressure diffusion, plasticity, anisotropy, capillary effects, osmosis, and physicochemical alterations. Three processes contributing to the instability of shales have to be considered [127] ... 

The plastic deformation of a member terminates with its rupture which normally occurs at the smallest section of the neck formed due to plastic instability. After being loaded into the plastic range, if the member is unloaded before plastic instability occurs then the elastic component of the strain can be recovered. This is a consequence of the atoms returning to... 

Figure 1.6 A load versus elongation diagram for a typical ductile metal, showing plastic instability.

It has been seen earlier that the condition for plastic instability can be expressed as... 

Assuming that the onset of plastic instability occurs at a fairly large value of plastic strain, one may consider the volume to remain essentially constant, so that A L = Aq L0. Differentiation gives... 

This relationship indicates that for plastic instability to occur the modulus of strain hardening, i.e., the slope of the true stress-true strain plot, should be equal to the true stress. This result is independent of any assumed functional relationship between o and s. If the relationship o = kt s " assumed to hold then one obtains... 

This relationship implies that the value of the true strain at which plastic instability sets in, i.e., necking starts to occur, is equal to the strain hardening exponent. 

The ultimate tensile strength (UTS) of a material refers to the maximum nominal stress that can be sustained by it and corresponds to the maximum load in a tension test. It is given by the stress associated with the highest point in a nominal stress-nominal stress plot. The ultimate tensile strengths of a ductile and of a brittle material are schematically illustrated in Figure 1.11. In the case of the ductile material the nominal stress decreases after reaching its maximum value because of necking. For such materials the UTS defines the onset of plastic instability. 

Storage stability Instability occurs with high temperatures or severe shock, particularly when involving containers of greater than 30 gal capacity unstable liquid. Liquid chloropicrin will attack some forms of plastics, rubber, and coatings. 

Polyvinyl chloride resin, because of its inherent thermal instability and wide range of applications, requires us to develop additive recipes based on specific application and processing requirements. Typical additive packages include stabilizers, plasticizers, waxes, processing aids, pigments, and mineral additives. 

Cyanogen bromide is moderately endothermic (AH°f (g) +50 kJ/mol, 0.47 kJ/g) and shows evidence of instability. The plastic cap of a bottle stored in a laboratory for several years on a high shelf, occasionally at 31°C, shattered and drove fragments into the shelf above [1]. This instability was confirmed, and a procedure outlined to obviate the use of the bromide in autoanalysis by generating cyanogen chloride on demand from Chloramine-T and potassium cyanide [2], A 50 wt% solution of the bromide in chloroform is a stable and convenient form for use [3], See Cyanogen chloride... 

Plastic deformation is mediated at the atomic level by the motion of dislocations. These are not particles. They are lines. As they move, they lengthen (i.e., they are not conserved). Therefore their total length increases exponentially. This leads to heterogeneous shear bands and shear instability. 

This brings us to the subject of standards. In this connection a standard is simply a sample with a known hydrogen content that is used for convenience to calibrate the overall counting efficiency of a particular setup, i.e., to determine the factor AfICalibration standards must be stable under irradiation. While plastic foils of known composition can be used if precautions are taken (Rudolph et al., 1986), their intrinsic instability makes them unsuitable. The standard used by most groups is hydrogen-implanted silicon, which has the advantages that it is easily prepared, the implanted dose can be measured to 5%, and the amount of implanted hydrogen is stable at room temperature and under MeV 15N irradiation, as discussed later. 

Slenderness considerations are of particular importance to the ductility of structural steel members, Steel, as compared to other building materials used in blast design, is considerably thinner, both in terms of the overall structure anc the components of a typical member cross section. As a result, the effect of ovcratl and local instability upon the ultimate capacity is an important consideration. Width-thickness provisions must be applied not only to the extent that a full plastic capacity can be achieved, but to the extent that higher ductility ratios can also be safely reached. The width-thickness ratios, from Table 8-1 of Seismic Provisions for Structural Steel Buildings (AISC 1992) are used for this purpose. 

Reduction of polymer flammability is of broad interest for applications ranging from plastics to textiles. For polyesters, given their inherent instability towards water at elevated temperatures, and the high temperatures of manufacture, many classes of flame-retardant (FR) agents, including most halogen-containing materials, are impractical. Phosphate esters, capable of incorporation into the polymer backbone, were pioneered by Hoechst AG, and continue to be the materials of choice [84, 85],... 

The occurrence of necking in the spin line indicates the instability of deformation and the system therefore restabilizes. Similar behavior to that shown with temperature can be observed in the presence of plasticizers. The fracture is promoted by increased stress in the case of plastic deformation. Cracks or notches at the surfaces of fibers and films are also the reason for disturbed deformation due to the more rapidly increased stress at the tips of these defect sites. 

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