Equivalent plastic strain

The formulation above is assumed to hold for temperatures up to the glass transition Tg. For T > Tg, most studies found in the literature focus on the description of the molten state [14] due to its practical importance, while little attention is paid to the response of glassy polymers in the rubbery state, near Tg. For strain rates larger than 1 s 1, the mechanical response of the molten material is non-Newtonian for most polymers and described by r = qym, where q and m are material parameters. We assume that this non-Newtonian response prevails as soon as Tg is exceeded. Hence, within the same framework as used below Tg, the equivalent plastic strain rate (Eq. 3) is replaced by... 

For T < Tg, the viscoplastic model used here accounts for intrinsic softening upon yielding followed by progressive orientational hardening. Rate dependent flow is taken to be governed by Argon s formulation [5] of the equivalent plastic strain rate... 

The internal variables of the model are the frictional angles (for compression paths). (for extension paths) and the cohesion c, which are related to the equivalent plastic strain. 

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... 

In eqs. (8.42) we recall that the dilatancy factor depends on f, the liquid-like-material fraction, which increases with increasing plastic strain -f (or e ) from a low value cp- of around 0.05 at -f= 0 in the annealed structure to = 0.5 in the flow state through the strain-softening range and remains stationary after that. In the stress-strain relationship all plastic strains are represented as the true equivalent plastic strain sP, where we recall that... 

Figure 9.28 shows the stress train eurves of a whole eomplement of deformation modes with all flow stresses normalized with tq, giving the dependenees of e/ro, the normalized global equivalent deviatorie shear resistances, on Se, the global equivalent plastic strain. The predieted stress strain eurve for plane-strain eompression agrees well with the data points of the Gal ski et al. experiments. We note that the predicted response for uniaxial tension is also elose to the predietion for plane-strain compression and that these two, as examples of irrotational flow, differ markedly from the simple shear results and also from the experimental results and the predictions for uniaxial compression, in comparison with the experimental results of Bartczak et al. (1992b). 

We found that the equivalent plastic strain generated by the TCE mismatch among Si-die, substrate, potting compound and PWB drastically decreases... 

Figure I Three-dimensional elastoplastic solid in free flight. Sequence of deformed configurations in the early stages of the motion with the distribution of the equivalent plastic strain a, obtained with the EDMC scheme.

Fig. 3.14. Plastic strain in a necked tensile test specimen. The maximal deformation occurs within the necking region in the centre of the specimen. The used measure for the plastic strain is the equivalent plastic strain which provides a quantitative measure for the total plastic deformation (cf. section 3.3.5)...

To take hardening into account, we need to find a quantity that can describe the deformation history of the material. This quantity has to increase during plastic deformation, regardless of the deformation orientation, for, in general, any plastic deformation causes hardening. A frequently used quantity is the so-called equivalent plastic strain To define this strain, we need... 

Since the equivalent plastic strain rate defined this way is positive for all plastic strain rates, the equivalent plastic strain increases for any plastic deformation, regardless of the deformation orientation. 

The equivalent plastic strain is calculated from the equivalent plastic strain rate eiq by integrating ... 

The equivalent plastic strain rate for the case [Pg.105]

If the plastic response remains essentially isotropic, then there must be an equivalent plastic strain measure, having the form of some function of the principal values of the plastic strain rate tensor, such that the Mises stress times the equivalent plastic strain rate is the local rate of plastic work per unit volume of material. In terms of the principal plastic strain rates e, 2 3, this equivalent plastic strain rate is defined as... 

The most commonly adopted isotropic yield function is the von Mises yield function which depends on stress only through the equivalent stress (7p. If the accumulated equivalent plastic strain , which is a nonnegative measure of the history of plastic deformation, is adopted as a particular choice of the history parameter then... 

The other two principal plastic strain rates are then equal to each other with values eP = eP = ffP for deformation without volume change. The equivalent plastic strain rate is = eP. The product = creP is... 

In order to simplify the exposition, we consider that the process is isothermic, and we assume that the evolution of the internal structure can be described with the aid of a scalar-hardening parameter (the density of dislocations or the equivalent plastic strain) and of an internal tensorial parameter (back stress). These restrictions are eliminated in the authors... 

Fig. 25 Contour plots of the equivalent plastic strain (PEEQ) in the connection at different drift levels SC-WHPl (left) and SC-WHP2 (right)...

Equivalent plastic strain in adhesive layer of a single lap joint subjected to tensile loading using an elasto-plastic material model... 

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