Evolution Of Void Volume Fraction Research Articles

Void growth in ductile materials with realistic porous microstructures

In this paper, we have investigated void growth in von Mises materials which contain realistic porous microstructures. For that purpose, we have performed finite element calculations of cubic unit-cells which are subjected to periodic boundary conditions and include porosity distributions representative of three additively manufactured metals. The initial void volume fraction in the calculations varies between 0.00564% and 1.75%, the number of actual voids between 14 and 5715, and the pores size from 2.3μm to 110μm. Several tests with different void sizes and positions have been generated for each of the three porous microstructures considered, and for each test we have performed several realizations with different spatial arrangement of the voids. The simulations have been carried out with random spatial distributions of pores and with clusters of the same size and different void densities. The macroscopic stress state in the unit-cell is controlled by prescribing constant triaxiality and Lode parameter throughout the loading. Calculations performed exchanging the loading directions for a given distribution of void sizes and positions have shown that the porous microstructure makes the macroscopic strain softening of the unit-cell (slightly) anisotropic. Moreover, the results obtained with the realistic porous microstructures have been compared with unit-cell calculations having an equivalent single central pore, and with calculations in which the material behavior is modeled with Gurson plasticity. It has been shown that both initial void volume fraction and spatial and size distribution of voids affect the macroscopic response of the porous aggregate and the void volume fraction evolution. Moreover, the calculations with random spatial distribution of voids have brought out that different tests of the same microstructure carry significant variations to the effective behavior of the porous aggregate, and that the interaction between neighboring pores dictates the volume evolution of individual voids, especially at higher macroscopic triaxiality. The calculations with clusters have shown that pores clustering promotes localization/coalescence due to increased interaction between the voids, which results in an increased growth rate of voids in clusters with large number of pores. Moreover, the results for the evolution of the distribution of plastic strains in the unit-cell have provided quantitative indications of the role of porous microstructure on the development of heterogeneous plastic strain fields which promote macroscopic strain softening. Namely, the accelerated growth rate of the plastic strains near the voids which indicates the onset of localization/coalescence has been shown to occur earlier as the number of voids in the microstructure increases.

A weakest link model for multiple mechanism brittle fracture — Model development and application

A multiple mechanism weakest link model for intergranular and transgranular brittle fracture is developed on the basis of experimental observations of a thermally aged low alloy steel. The model development is carried out in tandem with micro mechanical analysis of grain boundary cracking using crystal plasticity modeling of polycrystalline aggregates with the purpose to inform the weakest link model. The fracture modeling presented in this paper is carried out by using a non-local porous plastic Gurson model where the void volume fraction evolution is regularized over two separate length scales. The ductile crack growth preceding the final brittle fracture is well predicted using this type of modeling. When applied to the brittle fracture tests, the weakest link model predicts the fracture toughness distribution remarkably well, both in terms of the constraint and the size effect. Included in the study is also the analysis of a reference material.

An investigation of damage healing in high temperature compressive forming process

Damage healing in steel parts enables them to be reused again without going through the conventional metal recycling/remelting process, thus damage healing is a process with potential for reclaiming products while causing less environmental damage, that is, improving resource efficiency. In this paper, damage healing of a porous free cutting steel during a hot flat rolling process has been investigated. A UMAT subroutine incorporating damage healing models has been utilised which includes two stages: void closure and diffusion bonding. The developed UMAT subroutine captures evolution of void volume fraction (vvf) as a result of plastic compression, to model the void closure process and predict the subsequent healing time. Effects of roll gap geometry factor (RGF), initial porosity size (void volume fraction) on porosity elimination during rolling have been investigated.

Prediction of the damage and fracture of cast steel containing pores

For spatial design freedom, steel castings are widely used in bridges, airport terminals, and offshore platforms. However, different from hot-rolling technology, casting process variables, such as the casting temperature and those related to graphite spheroidization and post-heat treatment, may cause casting defects. To improve the safety and effectiveness of steel castings, a study consisting of experiments and numerical calculations is performed to investigate the effect of pores on the damage and fracture of cast steel. The chemical composition, metallography, and tomographic imaging of cast and hot-rolled steels were compared, providing a clear understanding of cast steel at the microstructure level. In addition, a complete Gurson–Tvergaard–Needleman damage model is used to predict the ductile fracture of cast steel containing pores. Good agreement is obtained between the measured and predicted tensile curves as well as between the measured and predicted void volume fraction evolution.

Molecular dynamics simulation of effect of temperature on void nucleation and growth of single crystal iron at a high strain rate

In this work, we investigate the triaxial deformation of single crystal iron at a strain rate of 5 × 10<sup>–9</sup> s<sup>–1</sup> by using molecular dynamics simulation through the embedded atomic method, and thus study the temperature effect on the void nucleation and growth, and we also discuss the applicability of nucleation and growth (NAG) model in single crystal iron. The molecular dynamics model size is 28.55 nm × 28.55 nm × 28.55 nm and contains 2 × 10<sup>6</sup> atoms. The results show that the maximum tensile stress of single crystal iron decreases with temperature increasing. The maximum tensile stress reduces 35.9% when temperature rises from 100 K to 1100 K. We find that at 100−700 K temperatures, there are two peaks in the tensile stress-time profile. To ascertain the origin of the double-peak in the stress-time profile, we compute the void volume fraction evolution. In addition, we conduct the dislocation analysis, radial distribution function analysis and common neighbor analysis. The analysis results show that the relaxation of tensile stress in the first peak of stress-time profile takes place through the structural change and the body-centered cubic crystal structure transforming into face-centered cubic crystal structure, hexagonal close packed crystal structure and other structures. We find that there are no voids’ nucleation in the first peak of stress-time profile. The second-peak of stress-time profile proceeds through the nucleation and growth of voids. And the rapid increase of the void volume fraction corresponds to the rapid decline of the tensile stress. The void volume evolution can be divided into three stages. With the increase of temperature, the double peak characteristic of the tensile stress-time profile disappears at 900−1100 K. While at 900−1100 K the nucleation and growth of voids are the only way to release the built-up stress. It is shown that the nucleation and growth of voids are more preferred at high temperature than at low temperature. The nucleation and growth of voids in single iron under high strain rate follow the NAG model. We calculate the best-fit NAG parameters at 100−1100 K, and analyze the sensitivity of NAG parameters to temperature. It is shown that the nucleation and growth threshold of the single crystal iron are much higher than those of mild steel. The results can be useful for developing the fracture models of iron at high strain rate to describe the dynamic damage on a continuum length scale.

Numerical Simulation of Collision Effect on Damage Evolution in Electromagnetic Forming of Aluminum Alloy Sheet

A numerical simulation study of collision effect on damage evolution in electromagnetic forming (EMF) was presented. EMF technology can greatly improve the forming limit of metal sheet duo to the high rate. However, collision behavior is also an important factor for the formability of sheet. Free form model and conical die model were carried out to study the effect of collision behavior on mechanical properties of Al alloy sheet. The EMF process of 1050 Al alloy sheet was analyzed and discussed by numerical analysis software LS-DYNA. The combined strategy of boundary element method and finite element method was adopted to realize the coupling calculation of electromagnetic field and structural field. Based on the GTN material model, the evolution of void volume fraction of 1050 Al sheet were calculated and analyzed. Comparing the free form model results and the die form model results, showed that the collision behavior could reduce the void volume fraction of sheet, but excessively high collision speed lead to the sheet rebound, which aggravated the damage of material and reduce the accuracy of the product. Therefore, the appropriate discharge voltage in this work was found to improve mechanical property of sheet on the premise of forming precision.

Damage Evaluation in Woven Glass Reinforced Polyamide 6.6/6 Composites Using Ultrasound Phase-Shift Analysis and X-ray Tomography

The paper proposes a new experimental methodology, based on ultrasonic measurements, that aims at evaluating the anisotropic damage in woven semi-crystalline polymer composites through new damage indicators. Due to their microstructure, woven composite materials are characterized by an anisotropic evolution of damage induced by different damage mechanisms occurring at the micro or mesoscopic scales. In this work, these damage modes in polyamide 6.6/6-woven glass fiber reinforced composites have been investigated qualitatively and quantitatively by X-ray micro-computed tomography (mCT) analysis on composite samples cut according to two orientations with respect to the mold flow direction. Composite samples are initially damaged at different levels during preliminary interrupted tensile tests. Ultrasonic investigations using C-scan imaging have been carried out without yielding significant results. Consequently, an ultrasonic method for stiffness constants estimation based on the bulk and guided wave velocity measurements is applied. Two damage indicators are then proposed. The first consists in calculating the Frobenius norm of the obtained stiffness matrix. The second is computed using the phase shift between two ultrasonic signals respectively measured on the tested samples and an undamaged reference sample. Both X-ray mCT and ultrasonic investigations show a higher damage evolution with respect to the applied stress for the samples oriented at $$45^{\circ }$$ from the warp direction compared to the samples in the $$0^{\circ }$$ configuration. The evolution of the second ultrasonic damage indicator exhibits a good correlation with the void volume fraction evolution estimated by mCT as well as with the damage calculated using the measured elastic modulus reduction. The merit of this research is of importance for the automotive industry.

An elastoviscoplastic model for porous single crystals at finite strains and its assessment based on unit cell simulations

An elastoviscoplastic model is formulated at finite strains for porous single crystals. The model extends the yield function developed by Han et al. (2013) for porous single crystals at infinitesimal strains to finite strains, incorporating the evolution of void volume fraction and strain hardening of single crystal matrix. The model is assessed through three-dimensional unit cell finite element simulations based on periodic homogenisation and loading paths with prescribed constant stress triaxiality. The unit cell simulations are performed for face-centered cubic crystals with various crystallographic orientations, stress triaxialities and initial void volume fractions, showing the competitive influence of the stress triaxiality and the crystallographic orientation on the effective behaviour and the void volume evolution. The proposed model captures the hierarchy of porous single crystal responses with respect to crystal orientation and void volume fraction. It represents a remarkable compromise between description of unit cell behaviour and tractability in the computation of structural components.

A model for ductile damage prediction at low stress triaxialities incorporating void shape change and void rotation

Ductile fracture at the high triaxiality regime is well-known to be controlled by void nucleation, growth and coalescence. However, under low stress triaxiality conditions and general three dimensional finite deformations, damage is still poorly predicted due to the complex loading state and microstructural changes under such a condition. Experimental results have revealed not only void growth, but also important void shape change and void rotation under shear-dominated loading. The ability of ductile damage models to predict both void growth with shape change and void rotation is thus crucial for complex loading applications. In the present study, a Gurson-like nonlinear homogenization-based model (namely GVAR) is proposed and compared with the constitutive models for elasto-plastic porous materials developed in Kailasam and Ponte Castañeda (1998) (VAR model) and Danas and Aravas (2012) (MVAR model). The proposed model is based on ad hoc modifications of the VAR model, to give sufficiently accurate results for void growth at both low and high stress triaxialities and keeping the functional form of the original Gurson model. The VAR and MVAR models were based on rigorous linear comparison composite (LCC) homogenization methods, which can describe the evolution of microstructure of porous materials, represented by the void volume fraction, the aspect ratios and the orientations of general ellipsoidal voids. The proposed GVAR model thus inherits these characteristics and provides a sufficiently accurate void growth formulation (and simple at the same time). In addition, the loading direction is not necessary aligned with the ellipsoidal void axes. These models are implemented in an object-oriented finite element (FE) code. The identification of model parameters and the assessment of the proposed model are then carried out via 3D periodic unit-cell computations subjected to different stress states. Comparative results show that the present model predicts relatively accurately the evolution of void volume fraction, void aspect ratios and void rotation for different initial void shapes, void volume fractions and under different stress triaxiality levels. A qualitative application to a tensile test on a notched round bar shows the efficiency of the model to predict microstructure evolution (i.e. voids volume, shape and orientation) in a real-scale model simulation. This model with few parameters to be identified is thus promising to predict damage under complex loading paths and ready to be applied to complex FE simulations.

Effect of stress triaxiality on porosity evolution in notched bars: Quantitative agreement between a recent dilatational model and X-ray tomography data

In this paper, it is shown that a micromechanically motivated macroscopic model can predict with accuracy the role of the stress state on void evolution in engineering materials. Specifically, a recent criterion that accounts for the influence of all stress invariants on the dilatational response of porous metals is used to predict porosity evolution and strength reduction in aluminum alloy AA 6016-T4. A very good quantitative agreement between the simulation results and X-ray tomography damage measurements in specimens of different notch acuities is obtained. In contrast to existing models, the void volume fraction evolution correlates very well with the X-ray data for all stress triaxialities.

Ductile damage in aluminium alloy thin sheets: Correlation between micro-tomography observations and mechanical modeling

This work deals with the characterization of ductile damage in an aluminium alloy AA6016-T4 by X-ray micro-tomography, as a function of anisotropy and triaxiality. Interrupted tensile tests on notched samples with three different geometries were performed and the void volume fraction was measured for different strain values, up to rupture. It was shown that void volume fraction evolution with the strain is rather similar at 0° and 90° to RD but at 45° to RD it shows a more rapid evolution. Moreover, for the same strain level, a higher void volume fraction was recorded for a higher triaxiality ratio. Whatever the orientation and the stress triaxiality ratio, void volume fraction values range from 5×10−4 up to 0.04. A numerical model based on Gurson–Tvergaard–Needleman constitutive equations was used to simulate the different tests. Hardening of the material was identified from macroscopic tensile test nucleation material parameters were identified by a direct method from void volume fraction evolution. It can be seen that the influence of triaxiality on void volume fraction is underestimated, though void growth is nicely predicted for the highest triaxiality ratio, for strains below 0.5. The load level was correctly predicted, except for high strain, where coalescence seems necessary to be taken into account.

Ductile Damage Analysis for Small Punch Specimens of Type 304 Stainless Steel Based on GTN Model

Abstract Based on small punch (SP) tests on Type 304 stainless steel at room temperature, a finite element (FE) model with Gurson-Tvergaard-Needleman (GTN) constitutive equations was established to analyze the ductile damage in SP specimens. Influences of the friction coefficient between SP specimen and steel ball and element size to the FE results were discussed. The evolution of void volume fraction (VVF) with time along different paths and the relation between VVF and equivalent plastic strain (PEEQ) under constant punching velocity were analyzed further by using the FE model. Good agreements between experimental results and simulation data were proved by load-displacement curves and failure locations. The numerical results show that initial crack occurs at the bottom surface about 0.86 mm away from the centre and damage localization phenomenon is extraordinarily severe in the SP specimen, and PEEQ has great effect on the evolutional rate of VVF.

An analysis of Gurson model with parameters dependent on triaxiality based on unitary cells

Abstract The Gurson model is widely used in the continuum-mechanics framework to analyse the ductile fracture process promoted by the nucleation, growth, and coalescence of voids. Further works improved the original Gurson model by introducing two parameters, q 1 and q 2 , to adjust model predictions to the numerical results of a periodic array of cylindrical and spherical voids in hardening materials. This modified model is known as the Gurson–Tvergaard (GT) model. Commonly, these parameters are considered constants or dependent only on the material-hardening properties. However, there is evidence that these parameters also depend on the triaxiality of the stress field, as well as on initial porosity. In this work, a consistent fully implicit integration of the constitutive equations of the GT model, considering the q-parameters dependent on the triaxiality and the initial porosity of the stress field, is presented, and the corresponding consistent tangent operator is proposed. The model is validated by comparing the stress–strain behaviour, as well as the evolution of void volume fraction, of a voided cell and the equivalent cell of GT material with dependent parameters. The cases considered correspond to variable triaxiality stress fields, present in non-proportional loading conditions.

Evolution of void volume fraction for simulating inner fracture defects related to in drawing of high-carbon steel wire rods

Ductile fracture occurs through the nucleation, growth and coalescence of voids. In our previous study, an evolution equation, which denotes a change in void volume fraction, and a model of void coalescence were proposed and proved to be effective in the simulation of inner fracture defects in the drawing of four types of carbon steel for machine structural use. In this study, a new evolution equation, which denotes a change in void volume fraction, is proposed for the simulation of inner fracture defects in the drawing of four types of high-carbon steel wire rod. The validities of our proposed evolution equation and model of void coalescence are clarified by comparing analytical results with experimental results.

A molecular dynamics study of void growth and coalescence in single crystal nickel

Molecular dynamics simulations using Modified Embedded Atom Method (MEAM) potentials were performed to analyze material length scale influences on damage progression of single crystal nickel. Damage evolution by void growth and coalescence was simulated at very high strain rates (10 8–10 10/s) involving four specimen sizes ranging from ≈5000 to 170,000 atoms with the same initial void volume fraction. 3D rectangular specimens with uniform thickness were provided with one and two embedded cylindrical voids and were subjected to remote uniaxial tension at a constant strain rate. Void volume fraction evolution and the corresponding stress–strain responses were monitored as the voids grew under the increasing applied tractions. The results showed that the specimen length scale changes the dislocation pattern, the evolving void aspect ratio, and the stress–strain response. At small strain levels (0–20%), a damage evolution size scale effect can be observed from the damage-strain and stress–strain curves, which is consistent with dislocation nucleation argument of Horstemeyer et al. [Horstemeyer, M.F., Baskes, M.I., Plimpton, S.J., 2001a. Length scale and time scale effects on the plastic flow of FCC metals. Acta Mater. 49, pp. 4363–4374] playing a dominant role. However, when the void volume fraction evolution is plotted versus the applied true strain at large plastic strains (>20%), minimal size scale differences were observed, even with very different dislocation patterns occurring in the specimen. At this larger strain level, the size scale differences cease to be relevant, because the effects of dislocation nucleation were overcome by dislocation interaction. This study provides fodder for bridging material length scales from the nanoscale to the larger scales by examining plasticity and damage quantities from a continuum perspective that were generated from atomistic results.

Using incremental forming to calibrate a void nucleation model for automotive aluminum sheet alloys

A novel method for the quantification of void nucleation rates in sheet material is presented. An incremental sheet forming process is employed to create large regions of homogeneous deformation, such that material density changes can then be used to quantify the evolution of void volume fraction with applied strain. This technique is employed to calibrate the void nucleation behaviour of three automotive aluminum sheet alloys (AA5182, AA5754 and AA6111) for incorporation into finite element method models which employ the Gurson–Tvergaard–Needleman (GTN) constitutive softening equations.

Inertia effects on the prediction of ductile damage

Inertia effects have some influence on ductile-damage prediction, so a static finite-element software was modified and formulated dynamically. The explicit and implicit Newmark scheme were adapted to the existing static solving method. Three ductile damage models were introduced in both the static and dynamic codes. The necking of a tensile bar is completely different under dynamic and static loading conditions. Void volume-fraction evolution is also observed during bulk forming processes such as forward extrusion and the collar test.