Modelling of Ductile Fracture in the Presence of Two Populations of Voids - Applications to Aluminium Alloys

2006 ◽  
Vol 519-521 ◽  
pp. 829-834 ◽  
Author(s):  
Damien Fabrègue ◽  
D. Lassance ◽  
Thomas Pardoen
Keyword(s):  
Aluminium Alloys ◽  
Volume Fraction ◽  
Micromechanical Model ◽  
Stress Triaxiality ◽  
Type Model ◽  
Void Coalescence ◽  
Element Mesh ◽  
Gurson Model ◽  
Surrounding Matrix ◽  
Void Shape

A micromechanical model has been developed in order to capture the influence of a second population of voids on the coalescence of large primary voids. FE unit cell simulations have been performed by introducing the primary voids explicitly in a finite element mesh and by using a Gurson type model for the surrounding matrix in order to reproduce the influence of the second population. These simulations have guided the development of a closed-form void coalescence model. The new coalescence condition accounts for the softening introduced by the second population by integrating the Gurson model based on an approximate solution for the stress and strain field near the surface of the primary voids. The evolution of the primary voids is modelled using an advanced Gurson model involving an evolution law for the void shape. The model is applied to the prediction of the fracture strain of 6xxx aluminium alloys measured on smooth and notched round bars. The model successfully captures, without any parameter adjustment, the variation of the ductility as a function of the stress triaxiality for various shapes of the primary particles and various volume fraction of second population.

Local Approach of Fracture in the Ductile Regime and Application to VVER Materials

2002 ◽  
Author(s):  
B. Z. Margolin ◽  
V. I. Kostylev ◽  
E. Keim ◽  
R. Chaouadi
Keyword(s):  
Finite Element ◽  
Crack Resistance ◽  
Ductile Fracture ◽  
Finite Element Simulation ◽  
Volume Fraction ◽  
Stress Triaxiality ◽  
Local Approach ◽  
Gurson Model ◽  
Element Simulation

Within the TACIS R2.06/96 project: “Surveillance Program for VVER 1000 Reactors”, sponsored by the European Commission, the local approach of fracture has been applied in the ductile regime. Two different models were applied and compared, namely Tvergaard-Needleman-Gurson versus Prometey model. The main tasks are: • perform special Local Approach experiments on smooth and notched cylindrical specimens; • predict JR-curve on the basis of the ductile fracture models; • compare two models of ductile fracture, namely, the Tvergaard-Needleman-Gurson model and the Prometey model. In this paper, the Tvergaard-Needleman-Gurson and Prometey models are briefly described. The parameters of both models were calibrated by using experimental data obtained on tensile specimens. While only smooth tensile specimens are used to calibrate the Tvergaard-Needleman-Gurson model, notched tensile in addition to smooth tensile specimens are used to calibrate the Prometey model. In the latter, standard smooth tensile specimens are used to determine the mechanical properties (the yield stress σy, the ultimate stress σu, the ultimate elongation δu, the area reduction Z) and notched cylindrical specimens to determine the strain at rupture. The numerical analysis comprises essentially two steps: • Step 1: finite element simulation of the smooth tensile specimen (determination of true stress-strain curve and critical void volume fraction for the Tvergaard-Needleman-Gurson model) and simulation of the notched cylindrical specimen up to rupture (determination of stress triaxiality for the Prometey model); • Step 2: finite element simulation of the 2T CT specimen and determination of the crack resistance behaviour in the ductile regime (J-Δa curve). It is found that both models were able to correctly predict the crack resistance behaviour of the investigated materials. The numerical and the experimental results were in very good agreement. The main difference between the two models is that the required number of calibrated parameters in the Prometey model is less than in the Tvergaard-Needleman-Gurson model but additional tests on notched specimens are required for the Prometey model.

A Stress-State Related Void Coalescence Criterion and its Validation

2010 ◽  
Vol 44-47 ◽  
pp. 2656-2660
Author(s):  
Zeng Tao Chen ◽  
Rahul Datta
Keyword(s):  
Stress State ◽  
Volume Fraction ◽  
Cell Model ◽  
Stress Triaxiality ◽  
High Strength Steels ◽  
Void Volume Fraction ◽  
Void Volume ◽  
Void Coalescence ◽  
Element Analysis ◽  
Critical Void

We propose a new critical void volume fraction (fc) criterion that identifies the onset of void coalescence based on the stress state of the material as compared to the definition of the phenomenological criterion by Tvergaard and Needleman [1], where void coalescence is predicted based merely on a constant value for critical void volume fraction. The new fc criterion is obtained using the finite element analysis of the unit cell model of clustered voids. Validation of this new criterion is done by implementing the new coalescence criterion into the Gurson-Tvergaard-Needleman (GTN) [1-3] model and simulating the ductile fracture experiment of a series of angularly notched sheet samples of dual phase (DP), advanced high strength steels (AHSS). A methodology has been devised to construct a stress triaxiality-based void coalescence criterion. Validation of the methodology has been performed using tensile tests of angularly notched samples of DP490 AHSS. Experimental data is compared with FE simulations in order to verify the dependency of void coalescence on stress triaxiality.

Void Shape and Distribution Effects on Coalescence in Elastic-Plastic Solids

1999 ◽  
Vol 578 ◽  
Author(s):  
T. Pardoen ◽  
J.W. Hutchinson
Keyword(s):  
Void Coalescence ◽  
Plastic Yielding ◽  
Gurson Model ◽  
Elastic Plastic ◽  
Void Shape

AbstractAn extended Gurson model incorporating the effects of the void shape and distribution on the growth and coalescence is proposed. The emphasis is placed on void coalescence, which is modeled as a transition from diffuse plasticity around the void to transverse localized plastic yielding in the intervoid ligament. Selected results showing the importance of correctly accounting for the void coalescence stage, as well as for the void shape and distribution effects, are presented and discussed.

scholarly journals Effects of Plastic Anisotropy and Void Shape on Full Three-Dimensional Void Growth

2018 ◽  
Vol 85 (5) ◽  
Author(s):  
Brian Nyvang Legarth ◽  
Viggo Tvergaard
Keyword(s):  
Void Growth ◽  
Volume Fraction ◽  
Plastic Anisotropy ◽  
Three Dimensional ◽  
Stress Triaxiality ◽  
Principal Stresses ◽  
Unit Cells ◽  
3D Effects ◽  
Void Shape ◽  
Transverse Stresses

Void growth in an anisotropic ductile solid is studied by numerical analyses for three-dimensional (3D) unit cells initially containing a void. The effect of plastic anisotropy on void growth is the main focus, but the studies include the effects of different void shapes, including oblate, prolate, or general ellipsoidal voids. Also, other 3D effects such as those of different spacings of voids in different material directions and the effects of different macroscopic principal stresses in three directions are accounted for. It is found that the presence of plastic anisotropy amplifies the differences between predictions obtained for different initial void shapes. Also, differences between principal transverse stresses show a strong interaction with the plastic anisotropy, such that the response is very different for different anisotropies. The studies are carried out for one particular choice of void volume fraction and stress triaxiality.

“Cavity” formation in superplastically deformed aluminium alloys

1990 ◽  
Vol 48 (4) ◽  
pp. 958-959
Author(s):  
A. Cziráki ◽  
E. Ková-csetényi ◽  
T. Torma ◽  
T. Turmezey
Keyword(s):  
Grain Boundaries ◽  
Aluminium Alloys ◽  
Superplastic Deformation ◽  
Volume Fraction ◽  
Superplastic Forming ◽  
Polished Surface ◽  
Cavity Formation ◽  
Stress Concentrations ◽  
Electron Microscopic ◽  
Commercial Aluminium

It is known that the formation of cavities during superplastic deformation can be correlated with the development of stress concentrations at irregularities along grain boundaries such as particles, ledges and triple points. In commercial aluminium alloys Al-Fe-Si particles or other coarse constituents may play an important role in cavity formation.Cavity formation during superplastic deformation was studied by optical metallography and transmission scanning electron microscopic investigations on Al-Mg-Si and Al-Mg-Mn alloys. The structure of particles was characterized by selected area diffraction and X-ray micro analysis. The volume fraction of “voids” was determined on mechanically polished surface.It was found by electron microscopy that strongly deformed regions are formed during superplastic forming at grain boundaries and around coarse particles.According to electron diffraction measurements these areas consist of small micro crystallized regions. See Fig.l.Comparing the volume fraction and morphology of cavities found by optical microscopy a good correlation was established between that of micro crystalline regions.

scholarly journals An Intrinsic Material Tailoring Approach for Functionally Graded Axisymmetric Hollow Bodies Under Plane Elasticity

2021 ◽  
Author(s):  
Hassan Mohamed Abdelalim Abdalla ◽  
Daniele Casagrande
Keyword(s):  
Optimization Problem ◽  
Volume Fraction ◽  
Minimum Principle ◽  
Equivalent Stress ◽  
Micromechanical Model ◽  
Plane Elasticity ◽  
Functionally Graded ◽  
Pontryagin Minimum Principle ◽  
Volume Fractions ◽  
Material Tailoring

AbstractOne of the main requirements in the design of structures made of functionally graded materials is their best response when used in an actual environment. This optimum behaviour may be achieved by searching for the optimal variation of the mechanical and physical properties along which the material compositionally grades. In the works available in the literature, the solution of such an optimization problem usually is obtained by searching for the values of the so called heterogeneity factors (characterizing the expression of the property variations) such that an objective function is minimized. Results, however, do not necessarily guarantee realistic structures and may give rise to unfeasible volume fractions if mapped into a micromechanical model. This paper is motivated by the confidence that a more intrinsic optimization problem should a priori consist in the search for the constituents’ volume fractions rather than tuning parameters for prefixed classes of property variations. Obtaining a solution for such a class of problem requires tools borrowed from dynamic optimization theory. More precisely, herein the so-called Pontryagin Minimum Principle is used, which leads to unexpected results in terms of the derivative of constituents’ volume fractions, regardless of the involved micromechanical model. In particular, along this line of investigation, the optimization problem for axisymmetric bodies subject to internal pressure and for which plane elasticity holds is formulated and analytically solved. The material is assumed to be functionally graded in the radial direction and the goal is to find the gradation that minimizes the maximum equivalent stress. A numerical example on internally pressurized functionally graded cylinders is also performed. The corresponding solution is found to perform better than volume fraction profiles commonly employed in the literature.

scholarly journals The Modified Void Nucleation and Growth Model (MNAG) for Damage Evolution in BCC Ta

2021 ◽  
Vol 11 (8) ◽  
pp. 3378
Author(s):  
Jie Chen ◽  
Darby J. Luscher ◽  
Saryu J. Fensin
Keyword(s):  
Growth Model ◽  
Damage Evolution ◽  
Volume Fraction ◽  
Void Nucleation ◽  
Nucleation And Growth ◽  
Void Coalescence ◽  
Hydrodynamic Simulations ◽  
Void Evolution ◽  
Void Nucleation And Growth ◽  
Nucleation Growth

A void coalescence term was proposed as an addition to the original void nucleation and growth (NAG) model to accurately describe void evolution under dynamic loading. The new model, termed as modified void nucleation and growth model (MNAG model), incorporated analytic equations to explicitly account for the evolution of the void number density and the void volume fraction (damage) during void nucleation, growth, as well as the coalescence stage. The parameters in the MNAG model were fitted to molecular dynamics (MD) shock data for single-crystal and nanocrystalline Ta, and the corresponding nucleation, growth, and coalescence rates were extracted. The results suggested that void nucleation, growth, and coalescence rates were dependent on the orientation as well as grain size. Compared to other models, such as NAG, Cocks–Ashby, Tepla, and Tonks, which were only able to reproduce early or later stage damage evolution, the MNAG model was able to reproduce all stages associated with nucleation, growth, and coalescence. The MNAG model could provide the basis for hydrodynamic simulations to improve the fidelity of the damage nucleation and evolution in 3-D microstructures.

Characterization of the vibration, stability and static responses of graphene-reinforced sandwich plates under mechanical and thermal loadings using the refined shear deformation plate theory

2021 ◽  
pp. 109963622199386
Author(s):  
Hessameddin Yaghoobi ◽  
Farid Taheri
Keyword(s):  
Shear Deformation ◽  
Volume Fraction ◽  
Plate Theory ◽  
Micromechanical Model ◽  
Sheet Thickness ◽  
Analytical Investigation ◽  
Sandwich Plates ◽  
Simply Supported ◽  
Vibration Stability ◽  
Shear Deformation Plate Theory

An analytical investigation was carried out to assess the free vibration, buckling and deformation responses of simply-supported sandwich plates. The plates constructed with graphene-reinforced polymer composite (GRPC) face sheets and are subjected to mechanical and thermal loadings while being simply-supported or resting on different types of elastic foundation. The temperature-dependent material properties of the face sheets are estimated by employing the modified Halpin-Tsai micromechanical model. The governing differential equations of the system are established based on the refined shear deformation plate theory and solved analytically using the Navier method. The validation of the formulation is carried out through comparisons of the calculated natural frequencies, thermal buckling capacities and maximum deflections of the sandwich plates with those evaluated by the available solutions in the literature. Numerical case studies are considered to examine the influences of the core to face sheet thickness ratio, temperature variation, Winkler- and Pasternak-types foundation, as well as the volume fraction of graphene on the response of the plates. It will be explicitly demonstrated that the vibration, stability and deflection responses of the sandwich plates become significantly affected by the aforementioned parameters.

Transformation Textures in Unstable Austenitic Steel

2002 ◽  
Vol 125 (1) ◽  
pp. 12-17 ◽  
Author(s):  
R. Kubler ◽  
M. Berveiller ◽  
M. Cherkaoui ◽  
K. Inal
Keyword(s):  
Martensitic Transformation ◽  
Volume Fraction ◽  
Micromechanical Model ◽  
Slip Rate ◽  
Transformation Strain ◽  
Dislocation Motion ◽  
Lattice Spin ◽  
Two Phases ◽  
The One ◽  
Elastic Plastic Materials

During the martensitic transformation in elastic-plastic materials, the local transformation strain as well as the plastic flow inside austenite are strongly related with the crystallographic orientation of the austenitic lattice. Two mechanisms involved in these materials, i.e., plasticity by dislocation motion and martensitic phase formation are coupled through kinematical constraints so that the lattice spin of the austenitic grains is different from the one due to classical slip. In this work, the lattice spin ω˙eA of the austenitic grains is related with the slip rate on the slip systems of the two phases, γ˙A and γ˙M, the evolution of the martensite volume fraction f˙ and the overall rotation rate Ω˙ of the grains. This new relation is integrated in a micromechanical model developed for unstable austenite in order to predict the evolution of the austenite texture during TRansformation Induced Plasticity (TRIP). Results for the evolution of the lattice orientation during martensitic transformation are compared with experimental data obtained by X-ray diffraction on a 304 AISI steel.

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