Modeling the Transition between Dense Metal and Damaged (Microporous) Metal Viscoplasticity

Abstract

This article presents a physically motivated approach, which has been developed in order to describe the transition of behavior between dense metal plasticity and microporous metal plasticity in the context of dynamic plasticity and adiabatic conditions. Considering that void germination requires a certain amount of plastic deformation, a 'primary' hole nucleation criterion as well as a statistical law governing the 'secondary' hole formation kinetics has been proposed. In a consistent way, the hole nucleation criterion accounts for the accelerating effects of stress triaxiality and the delaying effects of temperature and strain rate. In addition, a modification of the GTN model was proposed, allowing for describing cavity growth under shear loading. The 3D constitutive equations were implemented as user material in the engineering finite element computation code Abaqus Õ . Numerical simulations were conducted considering a single finite element under uniaxial tensile loading and simple shear then notched cylindrical samples under remote uniaxial tensile loading. The numerical results clearly show the influence of the hole nucleation criteria on the ductile damage and failure.

Void collapse/growth in solid materials under overall shear loading

“…It must be noted that in the case where several bands are involved, one of them may be favored yielding the other to be inhibited and/or branching may occur between bands (see Fig.11b) leading to a tortuous band path -as observed experimentally, see e.g. Fig.9 of Longère et al (2012) and comments above relative to the shearcontrolled fracture of a plate specimen made of mild steel after interrupted tension loading. Cell-to-cell strain localization within 2 parallel straight bands in the direction of the layer 5 empty voids Fig.4c Cell-to-cell strain localization within 2 parallel straight bands in the direction of the layer 1 void + particle Fig.5a Cell-to-cell strain localization within 2 parallel straight bands in the direction of the layer 2 voids + particles Fig.5b Cell-to-cell strain localization within 4 parallel straight bands in the direction of the layer 8% 5 voids + particles Fig.5c Cell-to-cell strain localization within 4 parallel straight bands in the direction of the layer 1 empty void Fig.7a Cell-to-cell strain localization within 1 straight band in the direction of the layer 2 empty voids Fig.8a Void impingement within the cell and along the layer 5 empty voids Fig.9a Void impingement within the cell and along the layer 1 void + particle Fig.7b Cell-to-cell strain localization within 2 parallel straight bands in the direction of the layer 2 voids + particles Fig.8b Cell-to-cell strain localization within 1 straight band in the direction of the layer 25% 5 voids + particles Fig.9b Cell-to-cell strain localization within 2 parallel straight bands in the direction of the layer…”

“…Moreover, in the micromechanics based analysis in Siruguet and Leblond (2004), it is shown that inclusions contained within voids act as a locking mechanism which may significantly modify the yield locus (notably when compared with the ones developed by Gurson (1977) and Gologanu et al (1997) for spherical and ellipsoidal cavities, respectively) and lead to void growth under zero stress triaxiality. In this line, a model was recently proposed based on a damage related softening mechanism acting as a kinematic stress drop causing a shift of the yield locus centre, see Longère et al (2012) and Longère and Dragon (2013). It must be noted that the aforementioned micromechanical studies all (more or less explicitly)…”

Experimental and numerical aspects of ship structure failure under airblast loading

“…The damage at stake is coupled with plasticity and is supposed to occur as soon as a micro-void nucleation criterion is verified. The reader may refer to [1] for a detailed presentation of the guiding concepts of the model.…”

“…The proposed modification is based on the hypothesis of a kinematic mean stress mechanism which governs a shift of the yield locus centre towards negative stress triaxiality values along the increasing damage. The modified GTN yield locus is given, according to [1], in the form…”

“…Based on these experimental observations, a multisurface based elastic-thermo-viscoplastic model involving damage was built, intended to reproduce notably the behaviour transition between dense metal plasticity and microporous metal plasticity, see also [1]. Moreover, the modelling approach adopted here aims at palliating the incapacity of the usual elliptic, pressure dependent plasticity models, including GTN one (see [2], [3]), to describe void growth related damage under shear in a way preserving the classical meaning of the microporosity related damage.…”