Plastic behaviors

A plastic material is one that shows little or no deformation up to a certain level of stress. Above this yield stress the material flows readily. Plasticity is conunon to widely different materials. Many metals yield at strains less than 1%. Concentrated suspensions of solid particles in Newtonian liquids often show a yield stress followed by nearly Newtonian flow. These materials are called viscoplastic or Bingham plastics after E. C. Bingham, who first described paint in this way in 1916. House paint and food substances like margarine, mayonnaise, and ketchup are good examples of viscoplastic materials. 

A simple model for plastic material is Hookean behavior at stresses below yield and Newtonian behavior above. For onedimensional deformations 

The model also can be written as allowing no motion below the yield stress 

This latter form is the one Bingham used in his original paper. 

To handle deformations occurring in more than one direction, eq. 2.S. 1 should be put into three-dimensional form. The only significant change required is to replace die one-dimensional yield criterion with some scalar function of the invariants of r. There are a number of yield criteria in the literature (Malvern, 1969, Sections 6.S, 6.6). The von Mises criterion, which uses the second invariant of T, is the most common. 

The plastic deformation of crystalline solids proceeds by a process of slip and/or twinning on certain crystal planes and in certain crystal directions. In metals the slip planes (denoted by ) are usually those having the highest atomic density and they are the most widely spaced. The slip directions (denoted by ) in the plane are those having the highest linear atomic density. A particular combination of slip plane and slip direction is referred to as a slip system. 

The basal plane in the hep metals Zn and Cd is the most densely packed plane and slip generally occurs in this plane and in the 1120 direction. Prismatic and pyramidal systems, in addition to the basal system, have been shown to operate at room and elevated temperatures, depending on the mode of deformation. The c/a ratio plays an important role in determining the ease with which other slip systems 

Slip Systems for a Select Group of Materials Illustrating the Effect of Bonding Type 29i,292,300 302) 

Material Crystal Nature of Slip mode (number Twin mode (number 

Macroscopically brittle at room temperature ionic contribution to bonding (charge transfer) deduced from photoelectron spectroscopy and interpretation of heats of formation the stability of these phases (high melting points, for example) attributed to the ionic and /-orbital contributions 111 110) and (110 001 slip systems operative at elevated temperatures 

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Fig. 2. Schematic stress—strain diagram, where UTS = ultimate tensile stress and (-------------) represents the demarcation between elastic and plastic behavior.

Stressing by Gutting. This method (Fig. 3e) is useful for materials that exhibit plastic behavior. 

Creep tests are ideally suited for the measurement of long-term polymer properties in aggressive environments. Both the time to failure and the ultimate elongation in such creep tests tend to be reduced. Another test to determine plastic behavior in a corrosive atmosphere is a prestressed creep test in which the specimens are prestressed at different loads, which are lower than the creep load, before the final creep test (11). 

Plastic Forming. A plastic ceramic body deforms iaelastically without mpture under a compressive load that produces a shear stress ia excess of the shear strength of the body. Plastic forming processes (38,40—42,54—57) iavolve elastic—plastic behavior, whereby measurable elastic respoase occurs before and after plastic yielding. At pressures above the shear strength, the body deforms plastically by shear flow. 

Fig. 2.5. The idealized elastic/perfectly plastic behavior results in a well defined, two-step wave form propagating in response to a loading within the elastic-plastic regime. Such behavior is seldom, if ever, observed.

A range of complex, elastic-plastic behaviors are observed experimentally they are perhaps the most widely encountered and most typical of shock behaviors, but they are perhaps the least understood of the materials responses. Unfortunately, nonspecialists seldom consider realistic elastic-plastic descriptions of shock processes. This section summarizes the very large body of information available in this area. The metallurgical mud is most viscous in this area. 

Detailed strength studies made by reloading and release of metals from high pressure provide more evidence that ideal elastic-plastic behaviors are not descriptive. An example of such a study by Lipkin and Asay [77L02] on an aluminum alloy is shown in Fig. 2.11. In this case, there is considerable... 

Release waves for the elastic-plastic regime are dominated by the strength effect and the viscoplastic deformations. Here again, quantitative study of the release waves requires the best of measurement capability. The work of Asay et al. on release of aluminum as well as reloading, shown in Fig. 2.11, demonstrates the power of the technique. Early work by Curran [63D03] shows that limited time-resolution detectors can give a first-order description of the existence of elastic-plastic behavior on release. 

The wide choice available in plastics makes it necessary to select not only between TPs, TSs, reinforced plastics (RPs), and elastomers, but also between individual materials within each family of plastic types (Chapters 6 and 7). This selection requires having data suitable for making comparisons which, apart from the availability of data, depends on defining and recognizing the relevant plastics behavior characteristics. There can be, for instance, isotropic (homogeneous) plastics and plastics that can have different directional properties that run from the isotropic to anisotropic. Here, as an example, certain... 

Sophisticated design engineers unfamiliar with plastics behavior will be able to apply the information contained in this and other chapters to applicable sophisticated equations that involve such analysis as multiple and complex stress concentrations. The various machine-design texts and mechanical engineering handbooks listed in the Appendix A PLASTICS TOOLBOX and REF-... 

The subject of transmitting motion and power by means of gears, their construction, and detail requirements are fully covered in textbooks, technical handbooks, and industrial literature of gear suppliers. The knowledge of gear fundamentals is a prerequisite for the understanding of where and how to insert the appropriate plastic behavioral information into the gear formulas so that the application results in favorable operation. 

The trend of this factor is generally consistent with plastics behaviors. However, stress-relaxation information has to be interrelated with the individual behavior of the plastics, as derived from the relaxation-test data (Chapter 2). 

Plastics behavior in fire depends upon the nature and scale of the fire as well as the surrounding conditions and how the products are designed. For example, the virtually allplastic 35 mm slide projector uses a very hot electric bulb. When designed with a metal light and heat reflector with an air circulating fan, no fire develops. Therefore, designing in this type product environment requires understanding all the variables so that the proper plastics can be used. 

Table 8-43 Plastics behavior with ultrasonic welding...

In order to understand the nature and mechanisms of foam flow in the reservoir, some investigators have examined the generation of foam in glass bead packs (12). Porous micromodels have also been used to represent actual porous rock in which the flow behavior of bubble-films or lamellae have been observed (13,14). Furthermore, since foaming agents often exhibit pseudo-plastic behavior in a flow situation, the flow of non-Newtonian fluid in porous media has been examined from a mathematical standpoint. However, representation of such flow in mathematical models has been reported to be still inadequate (15). Theoretical approaches, with the goal of computing the mobility of foam in a porous medium modelled by a bead or sand pack, have been attempted as well (16,17). 

In blast analyses, the resistance is usually specified as a nonlinear function to simulate elastic, perfectly plastic behavior of the structure. The ultimate resistance, (R ) is reached upon formation of a collapse mechanism in the member. When the resistance is nonlinear, the dynamic equilibrium equation becomes ... 

Selection of the material model is another important factor to be considered. Some programs allow the user to specify plastic moment-rotation curves for beam elements. However, the more rigorous and most widely available method of defining nonlinear material properties is to specify the stress versus strain data, Plastic behavior is approximated at the section level in the former method whereas, the latter method tracks plastic behavior at the individual integration points (fibers) through the thickness of the member. Each method has its advantages and disadvantages. 

Bar joists have adequate lateral support to prevent the top chords of the joists from laterally buckling under the loads published in the manufacturer s load tables. For required resistance higher than the load tables or for plastic behavior of the joists, additional lateral bracing may be required. Evaluations should be based on as-built dimensions and field inspections at the elements and welds. If rebound resistance is required, additional uplift bridging may be required. 

Figure 5. Stress-strain curves for SIN s exhibiting plastic behavior (ASTM D 1708) (8) 10/90 COPEN/PSN (9) 10/90 COPEUN/PSN (10) 10/90 COPUN/...

Rgure 4.9. Schematic mechanical behavior of the interface (a) elastic behavior the 2-D stress is proportional to the relative surface extension, (b) ideal plastic behavior after a narrow elastic regime the stress becomes constant and equal to standard plastic behavior in the plastic regime the stress slowly increases with the relative surface extension. (Adapted from [31].)... 

The plastic behavior necessarily follows an elastic regime that could not be probed within the explored 4> range ((/> > 70%). By integrating Eq. (4.20), the relative surface excess (S - So)/So can be calculated ... 

Craddock, J.N. and Savides. I.S. (1994). Modeling elastic-plastic behavior of metal matrix composites with reaction zones under longitudinal tension. Ini. J. Damage Mech. 3, 308-311. 

A viscometer can be used to study the yield stress and viscosity of cement pastes (Section 1.3.1). This is carried out by plotting the shear rate against shear stress as shown in Fig. 2.4 for cement pastes of various water cement ratios. These cement pastes are generally considered to exhibit Bingham plastic behavior where the yield value is the intercept on the shear stress axis and is related to cohesion, and the slope of the line is the apparent viscosity which is related to the consistency or workability of the system. The following general observations can be made ... 

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