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Strain rate, local

If the material is perfectly plastic, i.e., if the yield function is independent of k and a, then = 0 and the magnitude of the plastic strain rate cannot be determined from (5.81). Only its direction is determined by the normality condition (5.80), its magnitude being determined by kinematical constraints on the local motion. [Pg.144]

So, for given strain rate s and v (a function of the applied shear stress in the shock front), the rate of mixing that occurs is enhanced by the factor djhy due to strain localization and thermal trapping. This effect is in addition to the greater local temperatures achieved in the shear band (Fig. 7.14). Thus we see in a qualitative way how micromechanical defects can enhance solid-state reactivity. [Pg.245]

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. [Pg.645]

According to some recent results (Sect. 5.5), the dependence of K on e and qs is more involved than suggested by Eq. (94). The dependence of K on ris is much weaker than a direct proportionality and the correct flow parameter to be used in Eq. (94) should be the local fluid kinetic energy ( v2) rather than the strain rate (e). For a constant flow geometry, however, the two variables v and e are interchangeable. At the present stage and in order not to complicate unduly the kinetic scheme, it will be assumed that the rate constant K varies with the MW and strain rate as ... [Pg.139]

Under steady-state conditions, as in the Couette flow, the strain rate is constant over the reaction volume for a long period of time (several hours) and the system of Eq. (87) could be solved exactly with the matrix technique developed by Basedow et al. [153], Transient elongational flow, on the other hand, has two distinctive features, i.e. a short residence time (a few ps) and a non-uniform flow field, which must be incorporated into the kinetics equations. In transient elongational flow, each rate constant is a strongfunction of the strain-rate which varies with time in the Lagrangian frame moving with the center of mass of the macromolecule the local value of the strain rate for each spatial coordinate must be known before Eq. (87) can be solved. [Pg.140]

First, the function e(t) computed from e(x) (Fig. 33), is divided into a number of time intervals which are sufficiently short to justify the approximation of a constant average strain-rate within each period. Only the region of space where the strain rate is significantly different from zero, i.e. from — 4r 5 x +r0 in the case of abrupt contraction flow (Fig. 33), will contribute to the degradation and needs to be considered in the calculations. The system of Eq. (87) is then solved locally using the previously mentioned matrix technique [153]. [Pg.140]

The relevance of premixed edge flames to turbulent premixed flames can also be understood in parallel to the nonpremixed cases. In the laminar flamelet regime, turbulent premixed flames can be viewed as an ensemble of premixed flamelets, in which the premixed edge flames can have quenching holes by local high strain-rate or preferential diffusion, corresponding to the broken sheet regime [58]. [Pg.64]

For fast equilibrium chemistry (Section 5.4), an equilibrium assumption allowed us to write the concentration of all chemical species in terms of the mixture-fraction vector c(x, t) = ceq( (x, 0). For a turbulent flow, it is important to note that the local micromixing rate (i.e., the instantaneous scalar dissipation rate) is a random variable. Thus, while the chemistry may be fast relative to the mean micromixing rate, at some points in a turbulent flow the instantaneous micromixing rate may be fast compared with the chemistry. This is made all the more important by the fact that fast reactions often take place in thin reaction-diffusion zones whose size may be smaller than the Kolmogorov scale. Hence, the local strain rate (micromixing rate) seen by the reaction surface may be as high as the local Kolmogorov-scale strain rate. [Pg.220]

The evaluation of viscosity is similar to the evaluation of elastic deformation except the stress in the element changes due to the local velocity gradient. The time variable is defined as the strain rate. The element changes its shape as a function of time, as long as the strain-rate-induced stress is present. Viscosity is the local slope of the function relating stress in the element to strain rate. The usual functionality is found in Fig. 3.3. The process can be visualized by a constant force on the top of the element that creates a strain rate throughout the element. This strain rate causes each molecular layer of the material to move relative to the adjacent layer continuously. Obviously the element is suspended in a continuum and material flows into and out of the geometric element. [Pg.64]

Worldwide Streptococcus pneumoniae % susceptibility to penicillin is decreasing. In some countries up to two-thirds of the clinical isolates have reduced susceptibility to penicillin or are highly resistant to this drug. Moreover, the rate of resistance to other drugs commonly used for RTI including erythromycin, tetracycline and trimethoprim-sulfamethoxazole is higher in penicillin-resistant than penicillin-susceptible strains. Monitoring local or hospital resistance patterns of pneumococci is, therefore, needed. [Pg.526]

Stress and Strain Rate The stress and strain-rate state of a fluid at a point are represented by tensors T and E. These tensors are composed of nine (six independent) quantities that depend on the velocity field. The strain rate describes how a fluid element deforms (i.e., dilates and shears) as a function of the local velocity field. The stress and strain-rate tensors are usually represented in some coordinate system, although the stress and strain-rate states are invariant to the coordinate-system representation. [Pg.17]

The test conditions of temperature, strain rate and level of strain should reflect those that will be seen in service. This might involve making tests at more than one temperature and strain rate, although modulus is relatively insensitive to strain rate. With respect to strain level, BS 903-5 points out the need to take into account the fact that local strains may be rather higher than the overall strain. When data is obtained using more than one mode of deformation, the test conditions should be consistent with respect to strain levels, strain rates etc. It is also self evident that the test pieces should be produced in the same manner and their state of cure should be equal -... [Pg.117]

At each point the local coordinate can be turned so that only one component of the strain rate vector is different from 0 y = [(U )2 + (co )2r2]1 2. In the general case the vector of velocity at each point will not coincide with the vector of the rotated system of coordinates. Equation (8) is takes for rotated base at each point and rotated in the reverse direction to bring it in register with the initial position. Thus, we get the following relationships in the cylindrical system of coordinates ... [Pg.49]

The influence of temperature and strain rate can be well represented by Eyring s law physical aging leads to an increase of the yield stress and a decrease of ductility the yield stress increases with hydrostatic pressure, and decreases with plasticization effect. Furthermore, it has been demonstrated that constant strain rate. Structure-property relationships display similar trends e.g., chain stiffness through a Tg increase and yielding is favored by the existence of mechanically active relaxations due to local molecular motions (fi relaxation). [Pg.394]

Both the Doll s and SLLOD algorithms are correct in the limit of zero-shear rate. However, for finite shear rates, the SLLOD equations are exact but Doll s tensor algorithm begins to yield incorrect results at quadratic order in the strain rate, since the former method has succeeded in transforming the boundary condition expressed in the form of the local distribution function into the form of a smooth mechanical force, which appears as a mechanical perturbation in the equation of motion (Equation (12)) (Evans and Morriss, 1990). To thermostat the... [Pg.80]


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See also in sourсe #XX -- [ Pg.122 ]

See also in sourсe #XX -- [ Pg.122 ]




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