Plasticity visco

It is very important, from one hand, to accept a hypothesis about the material fracture properties before physical model building because general view of TF is going to change depending on mechanical model (brittle, elasto-plastic, visco-elasto-plastic, ete.) of the material. From the other hand, it is necessary to keep in mind that the material response to loads or actions is different depending on the accepted mechanical model because rheological properties of the material determine type of response in time. The most remarkable difference can be observed between brittle materials and materials with explicit plastic properties. 

Burgers JM (1935) First report on viscosity and plasticity. Committee for the Study of Viscosity of the Academy of Sciences, Amsterdam de With G (2006) Structure, deformation, and integrity of materials, volume II plasticity, visco-elasticity, and fracture. Whey-VCH, Weinheim, pp 569-645 Ferry JD (1970) Viscoelastic properties of polymers, 2nd edn. Wiley, New York... 

Figure 5. Amplitude-phase characteristics of the model for visco-elasto-plastic (left column) and brittle (right column) materials 1- spectrum responses 2- TF models.

Figure 6. Location of poles and zeros for visco-elasto-plastic material (left) and brittle material (right) under loading close to fiacture.

Arutunyan N.H., Drozdov A.D., Naumov V.E. (1987) Mechanics of growing visco-elasto-plastic bodies. Nauka, Moscow (in Russian). 

Mosolov V.P., Myasnikov P.P. (1971) Variational methods in ffow theory of perfect-visco-plastic media. Moscow Univ. (in Russian). 

R.J. Clifton, On the Analysis of Elastic/Visco-Plastic Waves of Finite Uniaxial Strain, in Shock Waves and the Mechanical Properties of Solids (edited by J.J. Burke and V. Weiss), Syracuse University Press, 1971, pp. 73-119. 

Visco-plastic peel ofA-B bilayers with influxes... 

Basically, the term [fi(a /2E)Ih is the visco-plastic dissipation term and the term [1/2ctoLc/] is the intrinsic interface strength term. This equation can be further rearranged to... 

Elastic vs. viscoelastic w hen = 0, no visco-plastic deformation occurs, Eq. 4.25 gives the intrinsic strength of the interface. 

True vs. apparent strength the visco-plastic energy dissipation dominated the magnitude of the peel strength. However, little dissipation occurs if the interface becomes very weak. In other words, some influxes are necessary to produce sufficient stress to activate the viscoelastic deformation in the body of the A. 

Let us examine this relation for typical values of the A/B interface = 1 (max energy dissipation in the A layer) I = 1 (max strength of interface with influxes) E = 12,000psi (Tq = 4000 psi /t = 30 mils (10 in) Lc = 4 x lO" in. We obtain for both terms G = 20 pli (energy dissipated) + 0.08 pli (true interface strength with max influxes), or G 20 pli, which says that the measured peel strength is dominated by visco-plastic deformation processes. 

An extruder is coupled to a die, the output of which is given by (KP/ij) where P is the pressure drop across the die, i] is the visco.sity of the plastic and is a constant. What are the optimum values of screw helix angle and channel depth to give maximum output from the extruder. 

The existence of yield stress Y at shear strains seems to be the most typical feature of rheological properties of highly filled polymers. A formal meaing of this term is quite obvious. It means that at stresses lower than Y the material behaves like a solid, i.e. it deforms only elastically, while at stresses higher than Y, like a liquid, i.e. it can flow. At a first approximation it may be assumed that the material is not deformed at all, if stresses are lower than Y. In this sense, filled polymers behave as visco-plastic media with a low-molecular and low-viscosity dispersion medium. This analogy is not random as will be stressed below when the values of the yield stress are compared for the systems with different dispersion media. The existence of yield stress in its physical meaning must be correlated with the strength of a structure formed by the interaction between the particles of a filler. 

Polymers are viscoelastic materials meaning they can act as liquids, the visco portion, and as solids, the elastic portion. Descriptions of the viscoelastic properties of materials generally falls within the area called rheology. Determination of the viscoelastic behavior of materials generally occurs through stress-strain and related measurements. Whether a material behaves as a viscous or elastic material depends on temperature, the particular polymer and its prior treatment, polymer structure, and the particular measurement or conditions applied to the material. The particular property demonstrated by a material under given conditions allows polymers to act as solid or viscous liquids, as plastics, elastomers, or fibers, etc. This chapter deals with the viscoelastic properties of polymers. 

Many variables used and phenomena described by fracture mechanics concepts depend on the history of loading (its rate, form and/or duration) and on the (physical and chemical) environment. Especially time-sensitive are the level of stored and dissipated energy, also in the region away from the crack tip (far held), the stress distribution in a cracked visco-elastic body, the development of a sub-critical defect into a stress-concentrating crack and the assessment of the effective size of it, especially in the presence of microyield. The role of time in the execution and analysis of impact and fatigue experiments as well as in dynamic fracture is rather evident. To take care of the specihcities of time-dependent, non-linearly deforming materials and of the evident effects of sample plasticity different criteria for crack instability and/or toughness characterization have been developed and appropriate corrections introduced into Eq. 3, which will be discussed in most contributions of this special Double Volume (Vol. 187 and 188). 

H.D. Espinosa et al A 3-D finite deformation anisotropic visco-plasticity model for fiber composites. J. Compos. Mater. 35(5) 369-410 (2001)... 

In some cases, an extrudable and injectable paste may consist of 65% vol. ceramic powder and 35% vol. polymeric binder. In others, an extrudable paste may consist of a highly loaded aqueous suspension of clay particles such that its rheology is plastic. Hie low shear (i.e., <100 sec ) viscosity of such a paste is between 2000 and 5000 poise at ambient temperature. Highly nonlinear stress strain curves are typical of ceramic pastes, as well as time dependent thixotropy. In many cases, pastes behave like visco-elastic fluids. This complex rheological behavior of ceramic pastes has made theoretical approadies to these problems difficult. For this reason, the discussion in this chapter is limited to Newtonian fluids where analytical solutions are possible, with obvious consequences as to accuracy of these equations for non-Newtonian ceramic pastes. 

Here, is again the surface work, S is the surface energy as previously defined and is the loss function dependent on crack speed, temperature and the strain, eo, applied to the specimen. The theory gives explicitly in terms of the energy density distribution in the specimen and the plastic or visco-elastic hysteresis of the material. 

Therefore, when Jenike developed his methods to mathematically model the flow of bulk solids, he concluded that a bulk solid must be modeled as a plastic, and not a visco-elastic, continuum of solid particles (1). This approach included the postulation of a flow-no-flow criterion that states the bulk solid would flow from a bin when the stresses applied to the bulk solid exceed the strength of the bulk solid. The terms stress and strength are further discussed in this section on cohesive strength tests below. The flow properties test methods discussed are used to obtain the equipment parameters required to provide consistent, reliable flow. 

We used an elasto-plastic analysis for WC/Co and visco-elasto-plastic analysis for Cu/Ni samples. Then, the physical and mechanical properties as function of the temperature and composition were compiled from the literature or determined by mechanical tests. 

Figure 8 shows the calculated stress distribution in NiCiluNi part. The peculiar form of the curve is due to the solid solution strengthening effect that occurs while changing from a soft, pure metal to an alloy. In the pure metal layers, the thermal stresses are relaxed by visco-plastic deformation. In the adjacent layers, the yield stresses of the alloys (for example Cu-20Ni and Ni-20Cu) are higher and thus are the residual stresses. 

In figure 11, the residual stress distribution in the "NCN part obtained from the analysis is plotted against the experimental results from the electrochemical thinning method. The agreement between the results is highly satisfactory and validates the visco-elasto-plastic approach taken in the FE-analysis as well as the values of the input data. 

The consideration of thermal effects leads to the development of thermoplastic models. Furthermore also transient effects will play a role both in the barrier material and in the host rock under elevated temperature conditions. This requires an extension of the material models regarding visco-elasticity or visco-plasticity. 

Another important aspect of chalk is its time dependent behaviour. We are currently developing an elasto-visco-plastic model including suction effects. This constitutive law will be able to deal with the main issues related to chalk. 

Revil, A. 1999. Pervasive pressure-solution transfer a poro-visco-plastic model. Geophys. Res. Let., 26 pp. 255-258. 

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