Conventional stress

Strength and Stiffness. Thermoplastic materials are viscoelastic which means that their mechanical properties reflect the characteristics of both viscous liquids and elastic solids. Thus when a thermoplastic is stressed it responds by exhibiting viscous flow (which dissipates energy) and by elastic displacement (which stores energy). The properties of viscoelastic materials are time, temperature and strain rate dependent. Nevertheless the conventional stress-strain test is frequently used to describe the (short-term) mechanical properties of plastics. It must be remembered, however, that as described in detail in Chapter 2 the information obtained from such tests may only be used for an initial sorting of materials. It is not suitable, or intended, to provide design data which must usually be obtained from long term tests. 

Conventional stress-strain curves are necessarily similar to the load-deformation curves from which they are derived. True stress-strain curves can also be derived in which the stress is based on the actual or installtaueous area of the cross-section. Such curves do not have a maximum corresponding to C, but increase continuously to the breaking load. 

The usual design procedure is to couple a specific value of design stress with a conventional stress or strain analysis of the assumed structural idealisation. The uniaxial deformation behaviour is of special importance in thin-walled pipes, circular tanks and comparable systems under simple stress. 

The shear component of the applied stress appears to be the major factor in causing yielding. The uniaxial tensile stress in a conventional stress-strain experiment can be resolved into a shear stress and a dilational (negative compressive) stress normal to the parallel sides of test specimens ofthe type shown in Fig. 11-20. Yielding occurs when the shear strain energy reaches a critical value that depends on the material, according to the von Mises yield criterion, which applies fairly well to polymers. 

There is experimental evidence, for many rubber-toughened polymers, that the rubber particles cavitate early in the deformation. The degree of cross-linking is kept relatively low in the polybutadiene phase of ABS to aid cavitation, and sometimes silicone oil is added for the same reason. Figure 4.12 shows both the conventional stress-strain curve and the volumetric strain versus tensile strain for rubber-modified polystyrene. When the polystyrene yields, the volume strain increases at a higher rate. Majority of the dilatational strain is due to cavitation in the rubber phase. 

Isochronals taken at (see Figure 4.5) after the initiation of the stress relaxation experiment, o-(f,), and at tf, a-Uf,). The diagram illustrates the transition from linear to non-linear behaviour. Note that this stress relaxation experiments, as iiiustrated in Figure 4.5. 

Fig. 6.18 Illustration of five conventional stress-strain curves of polymer materials under constant strain rates. 1 hard and brittle, 2 hard and tough, 3 hard and strong, 4 soft and tough, and 5 soft and weak...

Failure Rate and Stress Cycle Resistance. The interrelationship between the failure rate as a reliability characteristic and the conventional stress cycle resistance 5 for components under pressure—defined here as the ratio of mean endurable number of stress cycles No and design stress cycle frequency N—can be obtained from the above in the following manner. 

It is important to distinguish between the nominal stress, which is the load at any time during deformation divided by the initial cross-sectional area, and the true stress, which is the load divided by the actual cross-section at any time. The cross-section of the sample decreases with increasing extension, so the true stress may be increasing when the apparent or conventional stress or load remains constant or even decreasing. This has been discussed very well by Nadai [2] and Orowan [3]. 

Consider the conventional stress-strain curve or the load-elongation curve for a ductile material (Figure 11.2). The ordinate is equal to the nominal stress obtained by dividing the load P by the original cross-sectional area Aq ... 

Conventional stress-strain curves. In the standard tensile test the machine is programmed to move the clamps apart at a constant rate and the load generated is recorded. This test can be analysed using the BSP by assuming that at = 0 a strain programme is initiated such that (see Fig. 4.32(a))... 

In this section, discussion focuses on the interface fracture mechanics and the details of crack trajectory predictions that are possible with numerical implementation of these concepts. According to the interface fracture mechanics theory discussed in Chapter 2, a crack at the interface between the adherend and adhesive can be represented by a sub-interface crack lying a small distance (St) below the interface and the complex stress intensity factors K and K2 for the interface crack are related to the conventional stress intensity factors and Ku for the sub-interface crack as... 

This means that the cylinder will contract axially at a rate that is directly proportional to the interfacial energy and inversely proportional to the viscosity and the radius. The same result could have been obtained from a conventional stress analysis, using Laplace s equation for the radial stress (<7r = -y v o) and recognizing that there is an axial membrane stress of... 

The result with chosen as 5 is shown in Fig. 1 which compares very well with the simple stress-strain curve as given in [5] when converted into the conventional stress quantities. 

FIGURE 2.28 (a) Generalized flow curve, (b) Typical fully developed stress-strain curve as found in tough plastics under appropriate conditions. The conventional stress has been converted to the true stress. 

Recently, a new method for the determination of the shear modulus has been pro-posed It is based on the measurement of the phase velocity of an axially symmetrical dilatational mode in a gel cylinder. This method has been applied to the study of the shear modulus of polyacrylamide gels. The results obtained in the frequency range 200-2000 Hz are in very good agreement with the equilibrium values measured by conventional stress-strain methods. 

A detailed consideration of the hmit of linear viscoelasticity can be accomphshed via an analysis of the change of the slope in a stress-strain diagram. Ideally, the evaluation is based on an isochronous diagram that shows a correlation of stress to strain without superimposed time effects. Since isochronous stress-strain diagrams are hard to generate and only rarely available, conventional stress-strain diagrams can be evaluated in a good approximation. 

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