Equivalent strain

Figure 6.1. Stress-strain behavior of shock-loaded copper compared to the annealed starting condition illustrating an enhanced flow stress following shock-wave deformation compared to quasi-static deformation (based on an equivalent strain basis).

Many other ion-molecule reactions involving highly unsaturated hydrocarbon ions and neutral olefins or the equivalent strained cycloalkanes have been studied by mass spectrometry98. For example, we may mention here the addition of ionized cyclopropane and cyclobutane to benzene radical cations giving the respective n-alkylbenzene ions but also isomeric cyclodiene ions such as ionized 8,9-dihydroindane and 9,10-dihydrotetralin, respectively. Extensive studies have been performed on the dimerization product of charged and neutral styrene4. 

To understand the capability of this technique to produce deformed structures, it is useful to compare the strain induced by ECAE with equivalent strains produced during conventional metal-forming processes. A reduction in area during an ideal extrusion, Re, produces a strain 8re that is equal to the ratio of the areas, Aq/Aj. Table 7.5 compares the strain for N ECAE passes with the equivalent reduction in area needed to produce the same strain in an ideal extrusion. After eight... 

TABLE 7.5 Equivalent Strains for ECAE and Ideal Extrusion ... 

The metalloregulatory protein arsR was overexpressed in Escherichia coli and resulted in both elevated levels of arsenite bioaccumulation leading to severe reduction in cellular growth (Kostal et al, 2004), and the efficacy of this strain at low arsenic levels. Equivalent strains overexpressing PC synthase genes and arsR could be developed to have arsenic hypertolerant strains with higher bioaccumulation, valuable for the bioremediation of arsenic. 

Such a wavelength will neither grow nor shrink. The fastest growing wavelength is just Aj = /3 A For a material with a non-Newtonian flow law of the form E = Epia/np), where ct and e are the equivalent stress and equivalent strain rate in tension and and Ep are material parameters, d Jo/dx is computed to be... 

In Eqs. (43) and (44), H is the channel height in which the meniscus convolutes (or in our case the craze tip opening displacement), % the surface energy of the solid polymer, the equivalent inelastic deformation rate, a non-linear extensional viscosity coefficient, and n a strain rate exponent in the non-linear connection between the equivalent deformation resistance and the equivalent strain rate. The last four quantities are taken to be related by a non-linear constitutive law that is... 

Quasi-static Young s modulus measured by Hertzian indentation (b) Data taken from ref [5] (c) Measured by Dynamic Mechanical Thermal Analysis (D.M.T.A) at 1 Hz (T is taken as the temperature of the maximum in tan 5) (d) (7y and Oy are the yield stress under uniaxial and plane strain compression, respectively, for an equivalent strain rate of 5x10" s" (see ref... 

For comparison of different experiments the concepts of equivalent strain and strain efficiency are discussed. 

Key words Severe plastic deformation, strain path, fragmentation, geometric recovery, strain efficiency, equivalent strain... 

Figure 1. Relative increase of boundary area as a function of strain for a cubic grain deformed by different techniques. (

If we want to discuss the efficiency of various techniques to produce SPD structures, we should compare samples that have experienced equivalent strains. 

Equivalent Strain Under Uniaxial Stress and in Simple Shear... 

The conventional definition of equivalent strain is based on the proposition that samples should be compared on which the same amount of plastic work has been spent. For comparison of two specimens deformed in compression and torsion this would read... 

For a discussion of SPD without change of strain path a rough estimate of equivalent strains using, e.g., a =2 may be reasonable. Caution is necessary when strain is accumulated with changing strain path. This is so because there is no reason to believe that the total plastic work put into a material is a sufficient measure to determine its microstructure (for a more detailed discussion, see [10]). 

For a comparison of the efficiency of different SPD techniques to produce such structures the traditional concept of equivalent strain based on equal mechanical work is problematic, especially when strain is accumulated in steps with varying strain path where geometric recovery must be taken into account. 

Therefore, a temperature correction was applied to flow stress under such conditions. For each value of equivalent strain, the temperature increase was calculated using the following relationship ... 

The entering material presents the initial yield stress Yq. During die-through, diameter reduces and, at the same time, the average equivalent strain and true stress increase, according to material yielding phenomenon. If the material temperature does not increase sensibly, a simple power law can be assumed ... 

Material Flow Rule Cutting processes of metallic materials involve highly complex interactions between plastic material behavior, strain rate, temperature, and material microstructure. Even in conventional cutting, very high equivalent strain rates of approximately 10 s are... 

The different terms in the model assume that the flow stress curve is independently affected by equivalent plastic strain, equivalent plastic strain rate, and temperature. In this model, the temperature is influenced at high equivalent strain rates due to the adiabatic deformation. As a result of the complex interrelations between the material law parameters, the existing approaches show major... 

It is important to note that in the expressions in eqs. (3.32)-(3.36) the shear rate is to be considered as a scalar-average deviatoric rate, which is related to a reference tensile equivalent strain rate by... 

Fig. 9.29 Predicted (WAXS) crystallographic textures of the (002) and (200) plane normals of HDPE in plane-strain compression, viewed from the flow direction (FD), after various equivalent strains of (a) = 0.8 and (b) = 1.3 (from Lee et al. (1993a) courtesy of...

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