Plastic behaviour Subject

Example 2.14 A plastic is subjected to the stress history shown in Fig. 2.45. The behaviour of the material may be assumed to be described by the Maxwell model in which the elastic component = 20 GN/m and the viscous component r) = 1000 GNs/m. Determine the strain in the material (a) after u seconds (b) after 1/2 seconds and (c) after 3 seconds. 

Dynamic properties are taken to mean the results from mechanical tests in which the plastic is subjected to a deformation pattern from which the cyclic stress-strain behaviour is calculated. These do not include cyclic tests in which the main objective is to fatigue the material. 

This paper presents the combined experimental/numerical investigation of the behaviour of fluid-filled plastic containers subjected to drop impact. Drop Impact experiments were conducted on original and modified bottles. During the test, strain and pressure histories were recorded at various positions. Tests were simulated numerically using the two-system FSI model. Both solid and fluid domains remain fixed during the calculations, i.e. a small-strain analysis was performed for the solid while an Eulerian fi-ame of reference was used for the fluid. This procedure was found to be simple, stable and efficient. Numerical results agreed well with experimental data, demonstrating the capability of the code to cope with this complex fluid-structure interaction problem. 

Ductile fracture is accompanied by large deformation. In metals, there are deformations along slip planes and in specimens under test, which are subjected to tensile load, and can be observed as necking and horizontal sections of the stress-strain curves. It is also called plastic behaviour. ... 

Time-independent plastic deformation will be described in chapters 3, 6, and 8, the time-dependent plastic behaviour is subject of chapters 8 and 11. Time-dependent elastic behaviour is mainly observed in polymers, described in chapter 8. 

Yield criteria, the subject of sections 3.3.1 to 3.3.3, describe the transition between elastic and plastic behaviour for arbitrary stress states. Next, we will study flow rules that can be used to calculate how the material deforms. 

Example 2.13 A plastic which can have its creep behaviour described by a Maxwell model is to be subjected to the stress history shown in Fig. 2.43(a). If the spring and dashpot constants for this model are 20 GN/m and 1000 GNs/m respectively then predict the strains in the material after 150 seconds, 250 seconds, 350 seconds and 450 seconds. 

J7 In a tensile test on a plastic, the material is subjected to a constant strain rate of 10 s. If this material may have its behaviour modelled by a Maxwell element with the elastic component f = 20 GN/m and the viscous element t) = 1000 GNs/m, then derive an expression for the stress in the material at any instant. Plot the stress-strain curve which would be predicted by this equation for strains up to 0.1% and calculate the initial tangent modulus and 0.1% secant modulus from this graph. 

A 200 mm diameter plastic pipe is to be subjected to an internal pressure of 0.5 MN/m for 3 years. If the creep rupture behaviour of the material is as shown in Fig. 3.10, calculate a suitable wall thickness for Ae pipe. You should use a safety factor of 1.5. 

Consistency is tested on a measured volume of freshly mixed cement in the form of a cylinder. This specimen is placed between two horizontal plates using the apparatus illustrated in Figure 10.1 and subjected to a vertically applied load. The cement then flows out rapidly to form a disc. This radial flow ceases almost instantaneously because the applied stress decreases as the disc expands and rapidly reaches the yield stress, at which point outward flow ceases. This is the behaviour expected for a plastic body. 

A structure must be designed to resist gross plastic deformation and collapse under all the conditions of loading. The loads to which a process vessel will be subject in service are listed below. They can be classified as major loads, that must always be considered in vessel design, and subsidiary loads. Formal stress analysis to determine the effect of the subsidiary loads is only required in the codes and standards where it is not possible to demonstrate the adequacy of the proposed design by other means such as by comparison with the known behaviour of existing vessels. 

A different kind of time-independent behaviour is that characterized by materials known as Bingham plastics, which exhibit a yield stress rv. If subject to a shear stress smaller than the yield stress, they retain a rigid structure and do not flow. It is only at stresses in excess of the yield value that flow occurs. In the case of a Bingham plastic, the shear rate is proportional to shear stress in excess of the yield stress ... 

Subject to correct calculation of the diameters, press fitting of metal and plastic parts gives good results. Durability is conditional on the creep behaviour of the plastic. The metal... 

The strength properties of solids are most simply illustrated by the stress-strain diagram, which describes the behaviour of homogeneous brittle and ductile specimens of uniform cross section subjected to uniaxial tension (see Fig. 13.60). Within the linear region the strain is proportional to the stress and the deformation is reversible. If the material fails and ruptures at a certain tension and a certain small elongation it is called brittle. If permanent or plastic deformation sets in after elastic deformation at some critical stress, the material is called ductile. 

Figure 11.7 The behaviour of powders subjected to a compaction force fa) brittle fracture and [b] plastic deformation.

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