Deformation viscoelasticity, viscoplasticity

Effect of Scratch Velocity and Temperature. Another frequently investigated experimental parameter on the effect of scratch behavior of materials is the scratching rate or the scanning velocity. Since polymers are viscoelastic-viscoplastic in nature, the importance of scratching rate lies in its ability to change the strain and strain rate at the interface of the sample and the indenter and thus alters the deformation mode. The relationship between velocity and coefficient of fiction will depend on the relaxation state of the surface concerned, especially for nanoscratch (21,56,57,63-65). It was shown that rate and temperature interplay to affect nanotribological behavior of polymer films (57). 

Although, for computational wear analyses purposes, the UHMWPE viscoelastic/viscoplastic deformations may play a very important role in the wear phenomenon, this type of behavior has been scarcely considered in the literature [139]. Moreover the crack initiation from a notch in UHMWPE is a complex phenomenon that is governed by the viscoelastic fracture theory [140]. In brief, the importance of considering the viscoelatic/viscoplastic behavior of UHMWPE for medical application has been further emphasized by recent research. 

The creep and recovery behaviour of an UHMWPE was studied in the region of small xmiaxial deformations by Zapas and Crissman [152]. These results are used to illustrate the capability of the Schapery model to represent the viscoelastic/viscoplastic behaviour of UHMWPE. Creep and recovery experiments were carried out on specimens under creep stresses in the range 1-8 MPa. In Figure 7.9 are plotted the creep compliances obtained, showing to be stress dependent above 1 MPa. Using the appropriate values for the model parameters, the strain under creep and creep-recovery loading conditions were very well captured as shown in Figure 7.10. 

Petrie and Ito (84) used numerical methods to analyze the dynamic deformation of axisymmetric cylindrical HDPE parisons and estimate final thickness. One of the early and important contributions to parison inflation simulation came from DeLorenzi et al. (85-89), who studied thermoforming and isothermal and nonisothermal parison inflation with both two- and three-dimensional formulation, using FEM with a hyperelastic, solidlike constitutive model. Hyperelastic constitutive models (i.e., models that account for the strains that go beyond the linear elastic into the nonlinear elastic region) were also used, among others, by Charrier (90) and by Marckmann et al. (91), who developed a three-dimensional dynamic FEM procedure using a nonlinear hyperelastic Mooney-Rivlin membrane, and who also used a viscoelastic model (92). However, as was pointed out by Laroche et al. (93), hyperelastic constitutive equations do not allow for time dependence and strain-rate dependence. Thus, their assumption of quasi-static equilibrium during parison inflation, and overpredicts stresses because they cannot account for stress relaxation furthermore, the solutions are prone to numerical instabilities. Hyperelastic models like viscoplastic models do allow for strain hardening, however, which is a very important element of the actual inflation process. 

If the solid does not shows time-dependent behavior, that is, it deforms instantaneously, one has an ideal elastic body or a Hookean solid. The symbol E for the modulus is used when the applied strain is extension or compression, while the symbol G is used when the modulus is determined using shear strain. The conduct of experiment such that a linear relationship is obtained between stress and strain should be noted. In addition, for an ideal Hookean solid, the deformation is instantaneous. In contrast, all real materials are either viscoplastic or viscoelastic in nature and, in particular, the latter exhibit time-dependent deformations. The rheological behavior of many foods may be described as viscoplastic and the applicable equations are discussed in Chapter 2. 

The deformation behavior of many pharmaceutical materials is time-dependent and the nature of this time dependency is often related to the mechanism of compaction for a given material. It is thought that time dependency or speed sensitivity arises from the viscoelastic or viscoplastic characteristics of a material. In contrast, studies have shown that brittle materials are much less speed dependent that ductile materials because yielding and fragmentation are not as dependent on the rate of compression. It is also believed that the particle size and size distribution of the powder or granules have an important role in the speed sensitivity due to the fact that this property affects the predominant mechanism of deformation (6,58-60). 

Visoelastic/viscoplastic materials The distinguishing mark of viscoelastic and viscoplastic materials is a response that depends on the rate of straining. Viscoelastic and viscoplastic strains are, however, not equivalent since the former is completely recoverable, whereas the latter is not. In other words, the undeformed configuration is eventually recovered when a viscoelastic material is unloaded, whereas a permanent deformation may persist for viscoplastic materials. 

The key point in the rheological classification of substances is the question as to whether the substance has a preferred shape or a natural state or not [19]. If the answer is yes, then this substance is said to be solid-shaped otherwise it is referred to as fluid-shaped [508]. The simplest model of a viscoelastic solid-shaped substance is the Kelvin body [396] or the Voigt body [508], which consists of a Hooke and a Newton body connected in parallel. This model describes deformations with time-lag and elastic aftereffects. A classical model of viscoplastic fluid-shaped substance is the Maxwell body [396], which consists of a Hooke and a Newton body connected in series and describes stress relaxation. 

Fluoropolymers, as well as other thermoplastics, exhibit a complicated nonlinear response when subjected to loads. The behavior is characterized by initial linear viscoelasticity at small deformations, followed by distributed yielding, viscoplastic flow, and material stiffening at large deformations until ultimate failure occurs. The response is further complicated by a strong dependence on strain rate and temperature, as illustrated in Fig. 11.1. It is clear that higher deformation rates and lower temperatures increase the stiffness of the material. 

The DNF model incorporates the experimentally observed characteristics by using a micromechanism-inspired approach in which the material behavior is decomposed into a viscoplastic response, corresponding to irreversible molecular chain sliding due to the lack of chemical crosslinks in the material, and atime-dependent viscoelastic response. The viscoelastic response is further decomposed into the response of two molecular networks acting in parallel the first network (A) captures the equilibrium response and the second network (B) the time-dependent deviation from the viscoelastic equilibrium state. A onedimensional rheological representation of the model framework and a schematic illustrating the kinematics of deformation are shown in Fig. 11.6. 

In this constitutive framework, the total deformation gradient F is decomposed into viscoplastic and viscoelastic components F = F F. The viscoelastic deformation gradient acts on both the equilibrium network A, and on the time-dependent network F = F = F. The Cauchy stress acting on network A is given by the eight-chain representa-... 

With 10% pre-strain, which is about 3% higher than the yield strain, a tendency similar to 30% pre-strain is observed. Therefore, as long as the pre-strain is over the yield strain, a certain amount of shape fixity can be realized. Of course, as the pre-strain increases, the shape fixity ratio also increases. For example, at the zero stress relaxation time, the shape fixity is about 62.5% for the 10% pre-strain level, which is lower than the corresponding shape fixity of 73% for the 30% pre-strain level. It is also observed that the shape fixity with 10% pre-strain plateaus earlier than that with 30% pre-strain as the stress relaxation time increases, possibly due to less viscoelastic and viscoplastic deformation with the lower pre-strain level. 

As discussed in Chapter 3, pseudo-plastic deformation is the key for cold-programmed thermosetting SMP to display shape memory functionality. Therefore, the deformation includes both plastic/viscoplastic and elastic/viscoelastic deformation. The thermomechanical cycle also includes thermal deformation. Based on Figure 4.5, the deformation gradient F can be multiplicatively decomposed into thermal Fj and mechanical Fm, which are further decomposed into plastic F and elastic F, as follows ... 

Both the elastic and the plastic behaviour of polymers are time-dependent even at room temperature polymers are thus viscoelastic and viscoplastic. In this section, we discuss the time-dependent deformation behaviour phenomenologically and explain how thermal activation of relaxation processes causes the time-dependence of deformation. 

As we already saw, in reality, the behaviour of a polymer is never purely viscoelastic. There is always an instantaneous elastic contribution to the deformation (without any time-dependence) and, at elevated temperatures, a plastic deformation which is irreversible. Similar to the elastic properties, the plastic properties of a polymer also strongly depend on time. Thus, polymers are viscoplastic i. e., they creep. ... 

The time-dependence of deformation renders the parameters measured in simple tensile tests (see section 3.2) much less important than they are in metals, for instance. Although they do describe the behaviour at short-termed loads, time-dependent parameters obtained, for example, from isochrones -have to be used to design polymer components. Viscoelastic and viscoplastic effects can be neglected only if strains and loading times both are small. 

At aU technically relevant temperatures, polymers deform by creep. To describe the time-dependence of plastic deformation, we again exploit equation (8.3). In contrast to the viscoelastic deformation, there is no restoring force in viscoplasticity. Equation (8.3) is thus used to describe the dashpot element connected in series in the four-parameter model from figure 8.7(b). 

If we load a polymer cyclically with a non-zero mean stress, the viscoelastic and viscoplastic deformation causes an increase of the strain. 

---