Tensile instabilities

In this chapter we show that k = Oy/2, and use k to relate the hardness to the yield strength of a solid. We then examine tensile instabilities which appear in the drawing of metals and polymers. 

Figure 3. Tensile flow curves of pure aluminium matrix composites, reinforced with angular (A) and polygonal (P) alumina particles (see Fig. 2), of diameter given in pm by the legend of the curves. The 10 and 5 pm angular particle reinforced composites fail before tensile instability is reached.

Consider a ligament at the crack tip, with a current cross-sectional area A and true stress a, the load P carried by this ligament would be P = a A. At maximum load at the onset of tensile instability), the change in load would be zero i.e.,... 

Hutchinson, J. W. and Obrecht, H. (1977) Tensile instabilities in strain rate dependent materials, in Fracture 1977, edited by Taplin, D., Waterloo, ON University of Waterloo Press, Vol. 1, pp. 101-116. 

In the SPH simulation, when the material is in a state of tensile stress, the particle motion may become unstable, leading to the so-called tensile instability. One can add an artificial pressure (Monaghan 2000) to stabilize the simulation. 

An approximate sketch of the stress-strain diagram for mild steel is shown in Fig. 2.8(a). The numbers given for proportional limit, upper and lower yield points and maximum stress are taken from the literature, but are only approximations. Notice that the stress is nearly hnear with strain until it reaches the upper yield point stress which is also known as the elastic-plastic tensile instability point. At this point the load (or stress) decreases as the deformation continues to increase. That is, less load is necessary to sustain continued deformation. The region between the lower yield point and the maximum stress is a region of strain hardening, a concept that is discussed in the next section. Note that if true stress and strain are used, the maximum or ultimate stress is at the rupture point. 

The elastic-plastic tensile instability point in mild steel has received much attention and many explanations. Some polymers, such as polycarbonate, exhibit a similar phenomenon. Both steel and polycarbonate not only show an upper and lower yield point but visible striations of yielding, plastic flow or slip lines (Luder s bands) at an approximate angle of 54.7° to the load axis also occur in each for stresses equivalent to the upper yield point stress. (For a description and an example of Luder s band formation in polycarbonate, see Fig. 3.7(c)). It has been argued that this instability point (and the appearance of an upper and lower yield point) in metals is a result of the testing procedure and is related to the evolution of internal damage. That this is the case for polycarbonate will be shown in Chapter 3. For a discussion of these factors for metals, see Drucker (1962) and Kachanov (1986). 

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. 

Deliberately oriented polystyrene is available in two forms filament (mono-axially oriented) and film (biaxially oriented). In both cases the increase in tensile strength in the direction of stretching is offset by a reduction in softening point because of the inherent instability of oriented molecules. 

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. 

Since for liquids ry is of the order of 2 x 109 dyn/cm3, Sps must be of the order of 7,000 V/micron by this mechanism. Schultz and Wiech suggest that filaments of liquid may first be formed by Rayleigh instability from which are torn finer drops by local electrostatic stresses exceeding the tensile strength. 

Sirotyuk (ref. 25) found that the complete removal of solid particles from a sample of water increased the tensile strength by at most 30 percent, indicating that most of the gas nuclei present in high purity water are not associated with solid particles. Bernd (ref. 15,16) observed that gas phases stabilized in crevices are not usually truly stable, but instead tend to dissolve slowly. This instability is due to imperfections in the geometry of the liquid/gas interface, which is almost never exactly flat (ref. 114). Medwin (ref. 31,32) attributed the excess ultrasonic attenuation and backscatter measured in his ocean experiments to free microbubbles rather than to particulate bodies this distinction was based on the fact that marine microbubbles in resonance, but prior to ultrasonic cavitation (ref. 4), have acoustical scattering and absorption cross sections that are several orders of magnitude greater than those of particulate bodies (see Section 1.1.2). 

In summary, my view is that the fundamental cause for superplasticity is electronic in origin which has to do with the probability curves for the formation of compounds. This in turn creates the instability of the compounds and results in the ultra small grain size. Then, on the application of tensile stress, the plastic deformation is purely mechanical and has nothing to do with electrons. This is completely different from that observed in the normal plasticity as described above. The cause and mechanism for super-plasticity and normal plasticity are therefore fundamentally different. The phenomenon of superplasticity therefore can be viewed stepwise as follows ... 

Fig. 3 Schematic representation of various types of failure associated with the mechanical instability of a film deposited on a substrate, (a) cracking of a thin film subjected to residual tensile stress, (b) plastic deformation of the substrate at the end of the crack, (c) deviation of the crack at the interface, (d) cracking of the substrate, (e) detachment and buckling (formation of a blister from an interface defect) of a film subjected to residual compressive stress, and (f) deviation of the crack through the thickness of the film (flaking).

As with UV light, heat tends to oxidize polymers. The symptoms are embrittlement, melt flow instability, loss of tensile properties and discolouration. The mechanism of stabilization is therefore to prevent oxidatimi or to mitigate its effects. Plastics, particularly thermoplastics, also require stabilization protection against degradation from heat during processing or in use. 

Processing Stability. Despite its improved properties, the polymer based on PPG 2000 was found to be impractical because of instability at processing temperatures. Retention of the polymer melt at 204°C. in the barrel of an injection molding machine for times as short as 10 minutes gave molded parts with reduced tensile strength and loss of impact resistance. Ineffectiveness of antioxidants and nitrogen blankets in preventing this breakdown indicates that it is thermal and not oxidative. 

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