Viscoplastic materials

Viscoelasticity of metal This subject provides an introduction on the viscoelasticity of metals that has no bearing or relationship with viscoelastic properties of plastic materials. The aim is to have the reader recognize that the complex thermodynamic foundations of the theory of viscoplasticity exist with metals. There have been developments in the thermodynamic approach to combined treatment of rheologic and plastic phenomena and to construct a thermodynamic theory non-linear viscoplastic material that may be used to describe the behavior of metals under dynamic loads. 

As a result of simultaneous introduction of elastic, viscous and plastic properties of a material, a description of the actual state functions involves the history of the local configuration expressed as a function of the time and of the path. The restrictions, which impose the second law of thermodynamics and the principle of material objectivity, have been analyzed. Among others, a viscoplastic material of the rate type and a strain-rate sensitive material have been examined. 

Tanaka et al. (1971) have used a two-element mechanical model (Figure 8-32) to represent fats as viscoplastic materials. The model consists of a dashpot representing the viscous element in parallel with a friction element that represents the yield value. 

Figure 8-32 Mechanical Model for Foods as Viscoplastic Materials. Source From M. Tanaka, et al., Measurement of Textural Properties of Foods with a Constant Speed Cone Penetrometer, J. Texture Studies, Vol. 2, pp. 301-315, 1971.

Keywords Crack tip plasticity Elastic-viscoplastic material Crazing Cohesive surface Fracture... 

The toughening observed in Fig. 11 with increasing loading rate is quite surprising from a standard fracture mechanics point of view on the fracture of viscoplastic materials increasing the loading rate results in less energy dissipated by plasticity and a more brittle response is expected (if the failure process is assumed to be rate independent). One could also invoke a failure... 

It was found that both Newtonian and Carreau liquids always gave radially uniform films at sufficiently long spinning times even for initially non-uniform film thickness profiles. Power-law and viscoplastic materials gave highly non-uniform films even for initially uniform film thickness profiles. Since all the polymer solutions of interest in microelectronic applications can be described by non-Newtonian Carreau viscosity equation it can be concluded that uniform polymer thin films can be produced by the SCD process. 

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. 

Figure 5 Schematic illustration of the behavior of elastic, elastoplastic, and viscoplastic materials. A loading-unloading sequence is shown in (A) and (B), whereas stress relaxation following straining past the yield point is depicted in (C). (A) Elastic. (B) Elastoplastic. (C) Viscoplastic.

Viscoplastic materials, therefore, share many features with elastoplastic materials but, in addition, exhibit a dependence on the rate of straining. Again, a decomposition of the total strain is convenient, this time into elastic and viscoplastic parts (i.e., e = where e and are the elastic and viscoplastic strains, respectively). In analogy with the elastoplastic case, the boundary of the elastic region may be specified in terms of a yield function. However, whereas the region outside the yield surface was inadmissible in the elastoplastic case, the stress is allowed to lie outside the yield surface in the viscoplastic one. Hence, straining beyond the yield point generally results in the creation of an excess (or extra) stress o that decays toward zero with time, typically as (38)... 

Smol skii, B. M., Shul man, Z. P., and Gorislavets, V. M., Rheodynamics and Heat Transfer in Nonlinear Viscoplastic Materials, Nauka i Tekhnika, Minsk, 1970 [in Russian],... 

Kletschkowski, T., Schomburg, U., and Bertram, A., Endochronic Viscoplastic Material Model for Filled VTTE, Mechanics of Materials, 34 795-808 (2002)... 

It is interesting to note that a viscoplastic material also displays an apparent viscosity which decreases with increasing shear rate. At very low shear rates, the apparent viscosity is elFectively infinite at the instant immediately before the substance yields and begins to flow. It is thus possible to regard these materials as possessing a particular class of shear-thinning behaviour. 

The term false body has been introduced to describe the thixotropic behaviour of viscoplastic materials. Although the thixotropy is associated with the build-up of structure at rest and breakdown of structure under shear, viscoplastic materials do not lose their solid-like properties completely and can still exhibit a yield stress, though this is usually less than the original value of the virgin sample which is regained (if at all) only after a long recovery period. 

The selection of a suitable rotary positive-displacement pump for a viscoplastic material has been discussed by Steffe and Morgan [1986]. 

By virtue of its yield stress, a viscoplastic material in an unsheared state will support an immersed particle for an indefinite period of time. In recent years, this property has been successfiilly exploited in the design of slurry pipelines, as briefly discussed in section 4.3. Before undertaking an examination of the drag force on a spherical particle in a viscoplastic medium, the question of static equilibrium will be discussed and a criterion will be developed to delineate the conditions under which a sphere will either settle or be held stationary in a liquid exhibiting a yield stress. 

The question of whether or not a sphere will settle in an unsheared viscoplastic material has received considerable attention in the literature [Chhabra and Uhlherr, 1988 Chhabra, 1993a]. For the usual case where the sphere is acted upon by gravity, it is convenient to introduce a dimensionless group, Y, which denotes the ratio of the forces due to the yield stress and due to gravity. Neglecting munerical constants, the simplest definition of Y is To... 

A vertical tube whose lower end is sealed by a movable plate is filled with a viscoplastic material having a yield stress of 20 Pa and density llOOkg/m. Estimate the minimum tube diameter for this material to flow under its own weight when the plate is removed. Does the depth of the material in the tube have any influence on the initiation of flow ... 

De Angehs F. (2012)—On the structural response of elasto/viscoplastic materials subject to time-de-pendent loadings, Structural Durability Health Monitoring, Vol. 8, No. 4, pp. 341-358. 

Kletschkowski T., U. Schomburg, and A. Bertram. 2002. Endochronic viscoplastic material models for filled PTFE. Mech Mater 34 795-808. 

Finite element calculations using a viscoplastic material law show good correlation between the calculated stresses and the located AE events... 

Fig. 8.7. Mechanical models of viscoelastic and viscoplastic materials, built as systems containing spring and dashpot elements...

Ghoneim and Chen(33) developed a viscoelastic-viscoplastic law based on the assumption that the total strain rate tensor can be decomposed into a viscoelastic and a viscoplastic component. A linear viscoelasticity model is used in conjunction with a modified plasticity model in which hardening is assumed to be a function of viscoplastic strains as well as the total strain rate. The resulting finite-element algorithm is then used to analyze the strain rate and pressure effects on the mechanical behavior of a viscoelastic-viscoplastic material. 

FIGURE 59.6 A typical creep strain versus time curve for viscoplastic materials. The curve shows that creep strain starts out as a non-linear curve, becomes steady for a significant period, and then increases significantly into tertiary creep. Most of the life of a solder joint is spent in the primary and secondary creep strain range of the curve. 

Several models for viscoplastic materials are contained in the expression... 

Many of the materials described as viscoplastic also exhibit time-dependent effects associated with a change in structure. This behavior is characterized by a reversible decrease in shear viscosity with time under isothermal conditions. Materials that fit this description are called thixotropic and one can describe them using the same constitutive equation suggested for incompressible viscoplastic materials. However now the modulus, Eq. 155, evolves with time through the gel strength F and the characteristic time k. Evolution equations are supplied in the... 

For viscoplastic materials the rheograms (i.e. plots of shear stress x versus strain rate dU/dy) are very often approximated by the Bingham model, a straight line of the form... 

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