Some applications of Burzyński yield condition in metal plasticity

Abstract

a b s t r a c tThe classical J 2 plasticity theory is widely used to describe the plastic response of metallic materials. However, this theory does not provide satisfactory predictions for materials which exhibit pressure sen sitive yielding or plastic dilatancy. Another difficulty is the difference between the values of yield stresses in tension and compression for isotropic materials, the so called strength differential effect (SD), leading to the asymmetry of the elastic range. The Burzyń ski yield condition, proposed in 1928, can be used to overcome some of these problems. In this paper an implicit integration of the elasto plastic constitutive equations for the paraboloid case of Burzyń ski's yield condition is formulated. Also, the tangent operator consistent with the integration algorithm was developed and is presented. The proposed model was implemented in a commercial Finite Element code and different kinds of tests reported in the literature were simulated. The comparison between the numerical and experimental results shows that the plastic ity theory with the paraboloid case of Burzyń ski's yield condition describes adequately the strength dif ferential effect, which is present in many kinds of materials significant for recent applications.

Mechanical Properties Of The Ceramic Open-Cell Foams Of Variable Cell Sizes

“…The limit surface is defined by Burzyński paraboloid yield condition, Burzyński [10,11], Vadillo et al [13], Frąś et al [12], Pęcherski et al [14]. The additive decomposition of small strain tensor into elastic and inelastic part is given by following equation…”

“…In such a case the plasticity theory based on Huber-Mises-Hencky yield condition to describe inelastic behaviour of foams is not appropriate. The proper yield condition for brittle ceramic materials is related with paraboloid yield surface, (Burzyński [10,11], Vadillo et al [13], Frąś et al [12], Pęcherski et al [14]). The identification of the paraboloid yield surface requires two independent tests: tension and compression.…”

Enhanced energy conversion as a result of fluid-solid interaction in micro- and nanoscale

“…Moreover, these surface processes, in general, lead to some enhancement of energy conversion in comparison to the bulk classical transport model (Badur et al, 2015;Lemański and Karcz, 2008;Morini et al, 2011;Nakielski et al, 2015). A similar impact can be observed for porous saturated solids, when the Terzaghi principle of effective stress leads to a new situation in which the exchange of momentum and thermal energy in such continua undergo in a more complex manner (Badur et al, 2011(Badur et al, , 2015 Vadillo et al, 2011). A schematic presentation of these emergencing asspects of the modelling of fluid-solid interactions in the multiscale domain is highlighted in Fig.…”

A modified Burzynski criterion for anisotropic pressure-dependent materials

“…The Burzynski criterion for three-dimensional states of stress-and pressure-dependent isotropic materials has the following form Vadillo et al [15]:…”

“…They concluded that the Yld2000-18 yield function was the best criterion to accurately describe the yield stress and R-value directionalities of sheet metals. Vadillo et al [15] formulated an implicit integration of elastic-plastic constitutive equations for the paraboloid case of Burzynski yield condition and the tangent operator consistent with the integration algorithm was developed. Taherizadeh et al [16] developed a generalized finite-element formulation of stress integration method for nonquadratic yield functions and potentials with mixed nonlinear hardening under non-associated flow rule to analyse the anisotropic behaviour of sheet materials.…”