Abstract
Within a continuum approximation, we present a thermomechanical finite strain plasticity model which incorporates the blended effects of micro-heterogeneities in the form of micro-cracks and micro-voids. The former accounts for cleavage-type of damage without any volume change whereas the latter is a consequence of plastic void growth. Limiting ourselves to isotropy, for cleavage damage a scalar damage variable [Formula: see text] is incorporated. Its conjugate variable, the elastic energy release rate, and evolution law follow the formal steps of thermodynamics of internal variables requiring postulation of an appropriate damage dissipation potential. The growth of void volume fraction [Formula: see text] is incorporated using a Gurson-type porous plastic potential postulated at the effective stress space following continuum damage mechanics principles. Since the growth of micro-voids is driven by dislocation motion around voids the dissipative effects corresponding to the void growth are encapsulated in the plastic flow. Thus, the void volume fraction is used as a dependent variable using the conservation of mass. The predictive capability of the model is tested through uniaxial tensile tests at various temperatures [Formula: see text]C, [Formula: see text]C]. It is shown, via fracture energy plots, that temperature driven ductile-brittle transition in fracture mode is well captured. With an observed ductile-brittle transition temperature around [Formula: see text]C, at lower temperatures fracture is brittle dominated by [Formula: see text] whereas at higher temperatures it is ductile dominated by [Formula: see text].
Highlights
Ductile fracture is explained by nucleation, growth and coalescence of micro-voids
A natural outcome of this formulation is irreversible volume change, i.e., plastic dilatation. This model is modified by Tvergaard and Needleman, by the introduction of void shape effects as well as acceleration in the void growth during void coalescence, to be named as Gurson– Tvergaard–Needleman porous plasticity model [Tvergaard and Needleman, 1984] and by Chu and Needleman [1980] to account for void nucleation effects along with other contributors [Tvergaard, 1981, 1982a, 1982b; Needleman and Tvergaard, 1998; Nahshon and Hutchinson, 2008; Nahshon and Xue, 2009]
Multiplicative split of the deformation gradient in elastic, plastic and thermal parts has been utilized as a basis for finite strain kinematics
Summary
Ductile fracture is explained by nucleation, growth and coalescence of micro-voids. The present work introduces a thermodynamically consistent continuum approximation of micro-void and/or micro-crack driven failure at finite strains To this end, in the spirit of Chaboche et al [2006] we blend Gurson’s porous plasticity model with Lemaitre’s continuum damage mechanics. Among various modeling attempts to the ductile-brittle transition problem in the literature [Shterenlikht, 2003; Hutter et al, 2014; Needleman and Tvergaard, 2000; Batra and Lear, 2004; Xia and Fong Shih, 1996], the most common one is based on a collective use of Gurson-type porous plasticity along with either RitchieKnott-Rice or Beremin model [Soyarslan et al, 2015; Needleman and Tvergaard, 2000; Hutter et al, 2014] These approaches suffer from the mentioned inherent weaknesses pertaining to brittle fracture models. The model framework can be exploited for fracture development under low triaxiality regimes for which Gurson’s model is known to be ineffective
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