Viscoelastic plastics

A void nucleation and growth fracture model embedded in a general viscoelastic-plastic material model is representative of approaches to ductile dynamic fracture (Davison et al., 1977 Kipp and Stevens, 1976). Other approaches include employing the plastic strain as a damage variable (Johnson and Cook, 1985) so that both spall and large strain-to-failure can be treated. 

There are several ways in which the impact properties of plastics can be improved if the material selected does not have sufficient impact strength. One method is by altering the composition of the material so that it is no longer a glassy plastic at the operating temperature of the product (Chapter 6). In the case of PVC this is done by the addition of an impact modifier which can be a compatible plastic such as an acrylic or a nitrile rubber. The addition of such a material lowers the glass transition temperature and the material becomes a rubbery viscoelastic plastic with much improved impact properties. This is one of the methods in which PVC materials are made to exhibit superior impact properties. 

With plastics there are two types of deformation or flow viscous, in which the energy causing the deformation is dissipated, and elastic, in which that energy is stored. The combination produces viscoelastic plastics. See Chapter 2, MATERIAL BEHAVIOR, Rheology and Viscoelasticity, regarding their effects on fabricated products. 

We seek to nnderstand the response of a material to an applied stress. In Chapter 4, we saw how a flnid responds to a shearing stress through the application of Newton s Law of Viscosity [Eq. (4.3)]. In this chapter, we examine other types of stresses, snch as tensile and compressive, and describe the response of solids (primarily) to these stresses. That response usually takes on one of several forms elastic, inelastic, viscoelastic, plastic (ductile), fracture, or time-dependent creep. We will see that Newton s Law will be useful in describing some of these responses and that the concepts of stress (applied force per unit area) and strain (change in dimensions) are universal to these topics. 

Fig. 5a,b Schematic representation of a the tip-sample contact upon high loading b the according compliance curve. In the case of perfectly plastic response the unloading curve is identical to the vertical line intersecting with the abscissa at hmax. In general, some viscoelastic recovery occurs and the residual impression depth hy is smaller than hmax. The difference hc—hy represents the extent of viscoelastic recovery. Ap and Ae denote the dissipated and the recovered work, respectively. Ap=0 for perfect elastic behaviour, whereas Ae=0 for perfect plastic behaviour. The viscoelastic-plastic properties of the material may be described by the parameter Ap(Ap+Ae) l. The contact strain increases with the attack angle 6. Adapted from [138]... 

Abstract Grease lubrication is a complex mixture of science and engineering, requires an interdisciplinary approach, and is applied to the majority of bearings worldwide. Grease can be more than a lubricant it is often expected to perform as a seal, corrosion inhibitor, shock absorber and a noise suppressant. It is a viscoelastic plastic solid, therefore, a liquid or solid, dependent upon the applied physical conditions of stress and/or temperature, with a yield value, ao- It has a coarse structure of filaments within a matrix. The suitability of flow properties of a grease for an application is best determined using a controlled stress rheometer for the frequency response of parameters such as yield, a, complex shear modulus, G phase angle, 5, and the complex viscosity, rj. ... 

More recently, a new, viscoelastic-plastic model for suspension of small particles in polymer melts was proposed [Sobhanie et al., 1997]. The basic assumption is that the total stress is divided into that in the matrix and immersed in it network of interacting particles. Consequently, the model leads to non-linear viscoelastic relations with yield function. The latter is defined in terms of structure rupture and restoration. Derived steady state and dynamic functions were compared with the experimental data. 

This approach assumes that there is a region surrounding the crack tip with local energy dissipation. This arises from viscoelasticity, plasticity and bond rupture and can be considered the characteristic of the fracture process. For polymers the characteristic of this localized energy dissipation is considered to be independent of geometries. 

As an introduction to viscoelasticity the mechanical behavior of these viscoelastic plastics is dominated by such phenomena as tensile strength, elongation at break, stiffness, and rupture energy, which are often the controlling factors in a design. The viscous attributes of plastic melt flow are also important considerations in the fabrication of plastic products. 

By stressing a viscoelastic plastic material there are three deformation behaviors to be observed. They are an initial elastic response, followed by a time-dependent delayed elasticity that may also be fully recoverable, and the last observation is a viscous, non-recoverable, flow component. Most... 

When a viscoelastic plastic melt exits freely from a die, the exiting strand has a greater diameter than the die. The shorter the die, the more pronounced this phenomenon is. 

Sel Seltzer, R., Mai, Y.-W. Depth sensing indentation of linear viscoelastic-plastic solids A simple method to determine creep compliance. Eng. Fract. Mech. 75 (2008) 4852-4862. 

The mechanical relaxations in polymers correspond to particular mechanisms of thermally activated molecular motion and therefore to general mobility of polymer chains. Depending on their nature, polymers deform differently. Thermosetting polymers usually have little chain mobility and fail in a brittle manner. On the other hand, the chains move freely in thermoplastics and the polymer can yield or deform homogeneously at higher temperatures and behave as a viscoelastic-plastic solid [165]. 

The study of fundamental adhesion has been hampered because standard Tests of adhesion provide a result that is a complicated combination of fundamental adhesion, the physical properties of the adherend and the viscoelastic/plastic character of the adhesive (see Adhesion - fundamental and practical, Peel tests). Our understanding of adhesion has been significantly improved with the advent of mechanical devices that are able to probe the forces of adhesion under conditions that minimize all of the confounding effects of adherend, viscoelasticity, and so on. The Surface Forces Apparatus (SFA) as developed by Israelachvili and Tabor is a mechanical device that has allowed adhesion scientists to directly measure the forces of adhesion under very low rate, light loading, almost equilibrium conditions. Attention is also drawn to Atomic force microscopy. 

Sobhanie, M., Isayev, A.I., and Fan, Y. (1997) Viscoelastic plastic rheological model for particle filled polymer melts. Shed. Acta, 36 (1), 66-81. 

This superposition principle states that the response of a viscoelastic plastic to a load is independent of any other load already apphed to the plastic. Further, strain is directly proportional to apphed stress when the strains are observed at equal time intervals. The Boltzmann superposition principle quantifies creep strain as a function of stress and time at a given temperature. Constitutive equations express the relationships among stress, strain, and time [12]. 

Cell Growth. Immediately after the cells are nucleated, the pressure in the bubble is equal to the saturation pressure. Therefore, the cells expand if the polymer matrix is soft enough to undergo viscoelastic-plastic deformation. A cell expands until the final pressure inside the cell is equal to the pressure required to be in equilibrium with the surface forces and the stress in the viscoelastic cell wall. 

The problems of exact design for a viscoelastic plastic with non-linear properties are severe. For example, in Fig. 8.14(a) the stress-strain curve is linear only at the smallest strains (below 0.2 %). Most plastic parts are designed to operate at strains well above 0.2 %, and in this case exact stress analysis is impossible. In practice, a safe approximate procedure known as the pseudoelastic design method is used. The salient features of the method, which is very straightforward to apply, are as follows. 

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