Void Volume Fraction Research Articles

Damage evolution of 7075 aluminum alloy basing the Gurson Tvergaard Needleman model under high temperature conditions

Based on the Gurson-Tvergaard-Needleman (GTN) damage model, the damage evolution and ductile fracture of 7075 aluminum alloy sheets during the tensile process were predicted. First, the true stress–strain curve and micro morphology of 7075 aluminum alloy at 310 °C∼460 °C were obtained using ultra-high temperature confocal microscope with tensile and compression functions, and the damage characteristics of the fracture position of the tensile specimen were observed by Scanning Electron Microscope (SEM). Then, using the finite element reverse calibration method, the identification method of GTN damage parameters under high temperature was systematically explained and the damage characteristic parameters of 7075 aluminum alloy under high temperature (310 °C∼460 °C) were obtained. The influence of fluctuations in damage parameters on the macroscopic mechanical behavior of materials and the influence of temperature on the value of material damage variables were analyzed. Finally, the void volume fraction of 7075 aluminum alloy at 360 °C was obtained by microscopic observation and compared with the void volume fraction obtained by the finite element reverse calibration method. The results show that the effect of temperature on void volume fraction is basically the same as that of plasticity. The change of void volume fraction has a greater impact on the mechanical properties of the material. There is a small gap between the void volume fraction obtained using the microscopic observation method and the void volume fraction obtained using the finite element reverse calibration method, which verifies the accuracy of the finite element reverse calibration method.

Spallation fracture dependence on shock intensity and loading duration in single-crystal aluminum

Non-equilibrium molecular dynamics simulations were carried out to explore the effects of the shock intensity and loading duration on the spallation fracture mechanisms for single-crystal aluminum. First, the dynamic applicability of the potential function was validated by the shock Hugoniot relation. It was then found that compression waveforms ranging from triangular to rectangular closely depended on the loading duration. Coupled with atomic structural evolution, the spatio-temporal planes characterized by the density and stress well reproduced the spallation process dominated by void nucleation, growth, and coalescence. A larger shock velocity could accelerate the increase in the void volume fraction, while a larger loading duration could postpone the void nucleation but did not affect the variation trend of the void volume fraction. Based on the void morphology evolution at shock velocities of 1–3 km/s, the void volume fraction in the nucleation and growth (NAG) stages were effectively demarcated and then obtained, and the numerical values agreed closely with theoretical values calculated via the NAG model. The NAG model parameters were subsequently acquired, wherein the nucleation rate threshold and pressure sensitivity parameter were basically independent of the loading duration and shock velocity. However, they largely affected the nucleation threshold, growth threshold, and viscosity coefficient. In addition, the variation trend of the spallation strength depended on the predominance of the strain hardening and temperature softening effects. Finally, the correlation between the slope of the velocity pullback and damage rate was preliminarily discussed based on the NAG model.

A mechanistic damage model for solid oxide fuel cell ceramic materials - Part I: Constitutive modeling

A multiscale mechanistic damage model for solid oxide fuel cell (SOFC) ceramics that combines micromechanics of stiffness reduction due to material porosity change and microcracking with a continuum damage mechanics (CDM) description for the evolution of microcracks up to fracture is developed in this work. The model also accounts for volumetric swelling of the anode due to redox cycling. Porosity change and swelling during redox combined with normal operating thermomechanical loads could increase the stress, strain and damage distributions in SOFC stacks leading them to failure. The proposed model involves three governing parameters: (i) the porosity in terms of the pore or void volume fraction, (ii) material swelling magnitude prescribed at a given loading step, and (iii) the damage variable that describes microcracking caused by thermomechanical loads and swelling. Pores and microcracks in the ceramics are modeled as randomly distributed ellipsoidal inclusions with negligible stiffness by an Eshelby-Mori-Tanaka formulation combined with an inclusion orientation distribution method. Microcracking damage evolution is described by a CDM formulation. Volumetric swelling is treated in a similar way to thermal expansion in the constitutive relations. After validation and numerical checks, the damage model is used to analyze a simplified SOFC positive-electrode/electrolyte/negative-electrode (PEN) structure subjected to a redox cycle in addition to thermomechanical loads experienced during normal operation of a SOFC stack.

An atomic view on the evolution of spall damage in solid–liquid mixed aluminum at high strain rates through stretching simulations

Using the classical molecular dynamic method, we investigated the evolution of spall damage through a series of stretching simulations for solid–liquid mixed aluminum at several initial temperatures. The results show that a turning point appears before void nucleation when the initial temperature is higher than 940 K in mixed Al at a strain rate of 3 × 108 s−1. The formation mechanism of the turning point is due to the local liquid phase nucleation. The growth of the local liquid phase gradually destroys the consecutive solid phases. The lower tensile strength of liquid Al than solid Al leads to the formation of the turning point. The voids tend to nucleate in the liquid phase in mixed Al at different initial temperatures except at 940 K. The time of void nucleation will be delayed due to the melting process before void nucleation in mixed Al. A nucleation and growth (NAG) model can describe the nucleation and growth of voids very well in mixed Al at 900, 920, 960, and 980 K. By adding the criterion of liquid phase proportion, the NAG model can also well describe the void volume fraction history of mixed Al at 940 K. We clarified the micro-mechanisms of spall damage evolution in mixed Al through tension simulation. The relevant results can provide a reference for future work on spall damage studies in solid–liquid mixed metals.

Mechanical Properties of Nanoporous Metallic Ultrathin Films: A Paradigmatic Case.

Nanoporous ultrathin films, constituted by a slab less than 100 nm thick and a certain void volume fraction provided by nanopores, are emerging as a new class of systems with a wide range of possible applications, including electrochemistry, energy storage, gas sensing and supercapacitors. The film porosity and morphology strongly affect nanoporous films mechanical properties, the knowledge of which is fundamental for designing films for specific applications. To unveil the relationships among the morphology, structure and mechanical response, a comprehensive and non-destructive investigation of a model system was sought. In this review, we examined the paradigmatic case of a nanoporous, granular, metallic ultrathin film with comprehensive bottom-up and top-down approaches, both experimentals and theoreticals. The granular film was made of Ag nanoparticles deposited by gas-phase synthesis, thus providing a solvent-free and ultrapure nanoporous system at room temperature. The results, bearing generality beyond the specific model system, are discussed for several applications specific to the morphological and mechanical properties of the investigated films, including bendable electronics, membrane separation and nanofluidic sensing.

A new analytical model to predict the formation of necking instabilities in porous plates subjected to dynamic biaxial loading

In this paper, we have developed a linear stability analysis to predict the formation of necking instabilities in porous ductile plates subjected to dynamic biaxial stretching. The mechanical behavior of the material is described with the Gurson–Tvergaard–Needleman constitutive relation for progressively cavitating solids (Gurson 1977; Tvergaard 1981, 1982; Tvergaard and Needleman 1984) which considers the voids to be spherical and the matrix material isotropic with yielding defined by the von Mises (1928) criterion. The analytical model is formulated in a two-dimensional framework in which the multiaxial stress state that develops inside the necked region is approximated with the Bridgman (1952) correction factor, superimposing a hydrostatic stress state to the uniform stress field that develops in the plate before localization. As opposed to the linear stability models published so far to model dynamic necking in ductile plates, which consider the material to be fully dense and incompressible, the approach developed in this paper provides new insights into the interplay between porosity and inertia on plastic localization. In addition, the predictions of the theoretical model for the critical strain leading to necking formation have been compared with unit-cell finite element calculations performed in ABAQUS/Explicit (2019). Satisfactory quantitative and qualitative agreement has been found between the theoretical and the computational approach for loading paths ranging from plane strain tension to nearly equibiaxial tension, loading rates varying from 100 to \(10{,}000~\text {s}^{-1}\), and different values of the initial void volume fraction ranging from 0.01 to 0.1. Both analytical and finite element results suggest that the influence of porosity on necking localization increases, due to voids coalescence, as the loading rate increases and the loading path approaches equibiaxial tension. The original formulation developed in this paper serves as a basis for analytically modeling the dynamic formability of porous ductile plates, and it can be readily extended to consider more complex porous plasticity theories, e.g. constitutive models which consider the anisotropy of the material (Benzerga and Besson 2001) and/or voids with different shapes (Gologanu et al. 1993; Monchiet et al. 2008).

New insights into the role of porous microstructure on dynamic shear localization

This paper provides new insights into the role of porous microstructure on dynamic shear localization. For that purpose, we have performed 3D finite element calculations of electro-magnetically collapsing thick-walled cylinders. The geometry and dimensions of the cylindrical specimens are taken from the experiments of Lovinger et al. (2015), and the loading and boundary conditions from the 2D simulations performed by Lovinger et al. (2018). The mechanical behavior of the material is modeled as elastic-plastic, with yielding described by the von Mises criterion, an associated flow rule and isotropic hardening/softening, being the flow stress dependent on strain, strain rate and temperature. Moreover, plastic deformation is considered to be the only source of heat, and the analysis accounts for the thermal conductivity of the material. The distinctive feature of this work is that we have followed the methodology developed by Marvi-Mashhadi et al. (2021) to incorporate into the finite element calculations the actual porous microstructure of 4 different additively manufactured materials –aluminium alloy AlSi10Mg, stainless steel 316L, titanium alloy Ti6Al4V and Inconel 718– for which the initial void volume fraction varies between 0.001% and 2%, and the pores size ranges from ≈6 µm to ≈110 µm. The numerical simulations have been performed using the Coupled Eulerian-Lagrangian approach available in ABAQUS/Explicit (2016), which allows to capture the shape evolution, coalescence and collapse of the voids at large strains. To the authors’ knowledge, this paper contains the first finite element simulations with explicit representation of the material porosity which demonstrate that voids promote dynamic shear localization, acting as preferential sites for the nucleation of the shear bands, speeding up their development, and tailoring their direction of propagation. In addition, the numerical calculations bring out that for a given void volume fraction more shear bands are nucleated as the number of voids increases, while the shear bands are incepted earlier and develop faster as the size of the pores increases.

Influence of crystal orientation on stretching induced void formation in poly(4‐methyl‐1‐pentene) investigated by in‐situ small‐angle and wide‐angle X‐ ray scattering

In this work, the void formation of poly(4-methyl-1-pentene) (P4MP1) during solid-state stretching was investigated by in-situ small-angle and wide-angle X-ray scattering. By controlling the heating temperature, P4MP1 specimens with different orientation degrees were obtained. The results showed that: (1) specimens with high orientation presented hard elastic deformation behavior. Before the voids were induced, a density decrease in the amorphous phase was detected due to the extension of chain network. Once voids were formed, their longitude direction was aligned perpendicular to the stretching direction. With the increase of crystal orientation, the volume fraction of voids was greatly enlarged; (2) specimen with random orientation showed cold drawing deformation. As the Hencky strain was larger than 0.13, the void scattering was strengthened in the vertical direction whereas weakened in the horizontal direction, indicating that the longitude direction of the voids was changed to the stretching direction. With further stretching, the length of the voids was enlarged and the orientation of the voids was enhanced, but the volume fraction of the voids was reduced slightly due to the collapse of small voids. After stretching, the length and width of the void evaluated from SEM were 382 and 81 nm.

Vibration analysis of electro-magneto transversely isotropic non-local thermoelastic cylinder with voids material

The free vibrations of transversely isotropic nonlocal electro-magneto thermoelastic hollow cylinder with voids are addressed in the preview of generalized thermoelasticity. The governing equations and the constitutive relations are transformed into coupled ordinary differential equations by applying time harmonic variations. The boundary conditions of the outer and the inner surfaces of the hollow cylinder are considered to be traction free, no change in voids volume fraction and thermally insulated/isothermal temperature field. The analytical results for frequency equations are presented and validated with existing literature. To explore the free vibration analysis from the considered boundary conditions, the numerical iteration method has been generated to create data by using MATLAB software tools. The obtained analytical results are represented graphically with the assistance of numerical computations and simulations in absence/presence of magnetic field for nonlocal/local thermoelastic materials. To verify the elastic nonlocal effects in different models of thermoelasticity, the field functions are represented graphically with and without magnetic field effects. The study may find applications in the field of seismology for drilling and mining in the earth's crust appliances, lightweight armors, geophysics, acoustics, and oil prospecting etc.

Isothermal compaction-creep-recovery behavior and statistical void analysis of prepregs under various process parameters

In this study, the compaction-creep and permanent deformations of multi-layered (4, 8 and 12) glass/epoxy prepreg specimens have been investigated at different temperatures and compaction pressures, and at a constant compaction speed of 1 mm/min. The complete deformation history of specimens during compaction has been recorded from the stress-free state to the fully consolidated condition. It is noted that under similar pressure conditions, increasing the number of prepreg layers resulted in a decrease in the degree of compaction and associated creep response. At 90 °C, higher percentages of reinforcement compaction and permanent deformation were observed, due to low resin viscosity and increased resin bleed-out. X-ray computed tomography (XCT) aided geometrical models were developed to analyze the level of voiding as well as the microstructural changes in uncured specimens following the compaction-creep process. A decrease in the number of interlaminar voids and an increase in the level of intralaminar voiding was observed at higher compaction pressures and temperatures. Also, the void content in cured specimens were studied analytically. The lowest void volume fraction (VVF) was measured at 65 °C and 0.3 MPa compared to other temperatures in all layer specimens. More importantly, lower VVF was measured in 8-layer specimens than 4- and 12-layer specimens. The results highlight the importance of understanding the thermo-mechanical compaction-creep stage during the processing cycle and its effect on determining the overall void content in the resulting manufactured part.

Visualization of the damage evolution for Ti–3Al–2Mo–2Zr alloy during a uniaxial tensile process using a microvoids proliferation damage model

Abstract Understanding the damage evolution of alloys during a plastic deformation process is significant to the structural design of components and accident prevention. In order to visualize the damage evolution in the plastic deformation of Ti–3Al–2Mo–2Zr alloy, a series of uniaxial tensile experiments for this alloy were carried out under the strain rates of 0.1–10 s−1 at room temperature, and the stress–strain curves were achieved. On the other hand, the finite element (FE) models of these uniaxial tensile processes were established. A microvoids proliferation model, Gurson–Tvergaard–Needleman (GTN) damage model, was implanted into the uniaxial tensile models, and the simulated stress–strain curves corresponding to different GTN parameter combinations were obtained. Based on the simulated and experimental stress–strain curves, the GTN parameters of this alloy were solved by response surface methodology (RSM). The solved GTN parameters suggest that higher strain rate can enhance the proliferation and coalescence of microvoids. Furthermore, the uniaxial tensile tests over different strain rates were simulated using the solved GTN parameters. Then, the damage processes were visualized and evaluated. The result shows that the degradation speed of this alloy is slow at the initial stage of the tensile deformation and then accelerates once the voids volume fraction reaches a critical value.

Multiscale analysis of multi-directional composite laminates to predict stiffness and strength in the presence of micro-defects

A methodology is proposed to incorporate spatial distributions of micro-defects within a three dimensional multiscale modeling framework for Carbon Fiber Reinforced Polymer (CFRP) composites to predict stiffness and strength properties of laminates for use in structural design and in establishing nondestructive inspection protocols. Defects in both the fiber and matrix due to variations in the manufacturing process for fiber reinforced composite laminates are considered. Stochastic sampling of micro-defects based on experimental data using Ripley’s K-function is proposed. Three different laminate void volume fractions are used. Spatial statistical analysis is performed for the micro-defects, and then a methodology is presented for predicting stiffness and ultimate strength of three multi-directional composite laminates with distributions of microstructural defects. The results indicate that, in addition to the volume of micro-defects that are present, the spatial distribution of the micro-defects plays a significant role in mechanical properties of laminates, especially the ultimate strength for which a 3.62% reduction is seen in the simulations of laminates containing distributions of micro-defects. Based on these results, it is recommended that the spatial statistics of micro-defects in manufactured composites be incorporated into both design criteria and nondestructive inspection criteria for composite laminates.

Hot damage evolution in a high strength aluminum alloy during hot forming: a study using the Gurson–Tvergaard–Needleman model

The investigation on the formability of 7075-T6 aluminum alloy at elevated temperatures is significant due to its low plasticity at room temperature. Meso-Damage mechanics suggests that the growth and accumulation of micro-voids is an important factor that leads to material damage, fracture, and affects its formability. In this work, the Gurson–Tvergaard–Needleman (GTN) model was used to investigate the damage evolution of the 7075-T6 aluminum alloy during the hot forming process. The effects of different temperatures and strain rates on the formability were investigated through uniaxial hot tensile tests. The parameters of the Gurson–Tvergaard–Needleman (GTN) model were inverse-calibrated using the Central Composite Design (CCD)-Response Surface Method (RSM)-Genetic Algorithm (GA). Control variable method was used to explore the effect of each damage parameter on the fracture initiation and evolution. The results showed that the calibrated Gurson–Tvergaard–Needleman (GTN) model well predicted the high-temperature damage of the 7075-T6 aluminum alloy at 300–450 °C. Predicted necking and fracture volume fractions of voids were less than 3% error from experimental results. Initial void volume fraction (f0) had little effect on damage. Increasing void nucleation volume fraction (fN) significantly advanced the necking and fracture of the material. An increase in the critical void volume fraction (fC) and fracture void volume fraction (fF) resulted in higher peak stresses and fracture strains.

A novel method to uniquely determine the parameters in Gurson–Tvergaard–Needleman model

AbstractThe Gurson–Tvergaard–Needleman (GTN) model is promising in failure prediction as it takes the micromechanical behavior of ductile metals into consideration. However, its engineering applications have scarcely progressed due to the difficulty in determining its eight strongly coupled parameters. Taking the physical background of GTN model into consideration, a set of methods was established to determine all parameters in the GTN model. The knowledge of continuum damage mechanics was introduced to experimentally determine the development of void volume fraction through an interrupted uniaxial tensile test, by which the three parameters regarding void nucleation were analytically derived. Other parameters in the GTN model were also uniquely determined through a joint use of the chemical composition analysis, the cell model analyses, and the inverse finite element method. Reliability of this novel parameter determination method was verified through failure predictions on both cracked and un‐cracked specimens of STPT410.

The Need to Accurately Define and Measure the Properties of Particles

When dealing with powders, a fundamental knowledge of their physical parameters is indispensable, with different methods and approaches proposed in literature. Results obtained differ widely and it is important to define standards to be applied, both toward the methods of investigation and the interpretation of experimental results. The present research intends to propose such standards, while defining general rules to be respected. Firstly, the problem of defining the particle size is inspected. It was found that describing the size of a particle is not as straightforward as one might suspect. Factors of non-sphericity and size distributions make it impossible to put ‘size’ in just one number. Whereas sieving can be used for coarser particles of a size in excess of about 50 µm, instrumental techniques span a wide size range. For fine particles, the occurrence of cohesive forces needs to be overcome and solvents, dispersants and sample mixing need to be applied. Secondly, the shape of the particles is examined. By defining sphericity, irregularly shaped particles are described. Finally, the density of particles, of particle assemblies and their voidage (volume fraction of voids) and the different ways to investigate them are explored.

Ductile Damage Model Based on Void Growth Analysis for Application to Ductile Crack Growth Simulation

AbstractThis study aims to propose the damage model based on of the mechanism for ductile fracture related to void growth and to confirm the applicability of the proposed model to ductile crack growth simulation for steel. To figure out void growth behavior, elastoplastic finite element analyses using a unit cell model with an initial void were methodically performed. From the results of those analyses, it was evident that the relationships between normalized void volume fraction and normalized strain by each critical value corresponding to crack initiation were independent of stress–strain relationship of material and stress triaxiality state. Based on this characteristic associated with void growth, damage evolution law was derived. Then, using the damage evolution law, simple and phenomenological ductile damage model reflecting void growth behavior and ductility of material was proposed. To confirm the validation and application of the proposed damage model, the damage model was implemented in finite element models and ductile crack growth resistance was simulated for cracked components were performed. Then, the simulated results were compared with experimental ones and it was found that the proposed damage model could accurately predict ductile crack growth resistance and applied to ductile crack growth simulation.

Reflection of plane waves in a micropolar thermo-diffusion porous medium

The research article deals with the reflection of plane waves in a micropolar thermoelastic diffusion solid half-space with voids in the context of Lord-Shulman theory of thermoelasticity. The governing equations are formulated to obtain two velocity equations. The plane wave solution of these velocity equations indicate the existence of six plane waves, a set of four coupled longitudinal displacement waves and a set of two coupled transverse displacement wave namely coupled longitudinal displacement wave ( LD − 1 ) , coupled thermal wave ( LD − 2 ) , coupled mass diffusion wave ( LD − 3 ) , coupled longitudinal void volume fraction wave ( LD − 4 ) and coupled transverse displacement wave ( TD − 1 ) , coupled transverse micro-rotational wave ( TD − 2 ) . A reflection of the plane wave from a stress-free thermally insulated surface is studied to obtain the reflection coefficients and energy ratios of reflected waves. The reflection coefficients and energy ratios of the reflected waves are computed for a particular material and the variations of the reflection coefficients and energy ratios against the angle of incidence are shown graphically.

Numerical Study about the Influence of Superimposed Hydrostatic Pressure on Shear Damage Mechanism in Sheet Metals

It is generally accepted that the superimposed hydrostatic pressure increases fracture strain in sheet metal and mode of fracture changes with applying pressure. Void growth is delayed or completely eliminated under pressure and the shear damage mechanism becomes the dominant mode of fracture. In this study, the effect of superimposed hydrostatic pressure on the ductility of sheet metal under tension is investigated using the finite element (FE) method employing the modified Gurson–Tvergaard–Needleman (GTN) model. The shear damage mechanism is considered as an increment in the total void volume fraction and the model is implemented using the VUMAT subroutine in the ABAQUS/Explicit. It is shown that ductility and fracture strain increase significantly by imposing hydrostatic pressure as it suppresses the damage mechanisms of microvoid growth and shear damage. When hydrostatic pressure is applied, it is observed that although the shear damage mechanism is delayed, the shear damage mechanism is dominant over the growth of microvoids. These numerical findings are consistent with those experimental results published in the previous studies about the effect of superimposed hydrostatic pressure on fracture strain. The numerical results clearly show that the dominant mode of failure changes from microvoid growth to shear damage under pressure. Numerical studies in the literature explain the effect of pressure on fracture strain using the conventional GTN model available in the ABAQUS material behavior library when the mode of fracture does not change. However, in this study, the shear modified GTN model is used to understand the effect of pressure on the shear damage mechanism as one of the individual void volume fraction increments and change in mode of fracture is explained numerically.

Spall damage in single crystal tin under shock wave loading: A molecular dynamics simulation

Using molecular dynamics methods, we investigated the spall damage in single crystal tin under different shock pressures. The results show that release melting and shock melting occur when the shock velocities increase in the metallic tin. The spall strengths in the molten tin are ~1.5–2.0 GPa lower than that in solid. When release melting occurs, the spall strength drops rapidly, whereas the downtrend of the spall strength becomes gentle during shock melting. The results also show that the spall strength is affected by not only the shock pressure and phase state, but also the temperature and strain rate. By visualizing the development of spall damage, we find that it forms a spall layer in the solid. In molten tin, a cavitation region with a large volume is formed. The maximum number of voids increases with an increase in the shock pressure. The growth rate of the void volume fraction slows down after reaching the initial time of void growth at different impact pressures. We elucidated the variation trend of spall strength between solid and molten tin under different shock pressures. The relevant results can provide a reference for future studies on spall damage investigations.

Effects of void content on flexural properties of additively manufactured polymer composites

Mechanical characterizations are inevitable to the research and development in additive manufacturing (AM). Most mechanical tests for composite materials are relatively expensive, time-consuming, and challenging. Therefore, three-point flexural testing is widely adopted as it offers an easy and fast method to assess AM composite's performance. The correlations between the flexural and other mechanical properties in AM composites are, however, not understood. In this work, multiscale modeling is utilized to connect micro-scale composite properties to macro-scale flexural simulations and experiments. Two AM composite samples of continuous carbon fiber-reinforced polyetheretherketone (PEEK) are considered. The void volume fractions in these samples are ~10 and 5%, typical of the composite's AM process. First, elastic constants for the two samples, considering their porosity, are predicted via micro-mechanical finite element analysis (FEA). A test model is then constructed to carry out detailed macro-scale FEA stress analysis in flexural tests. Specifically, flexural strength of AM composites is correlated to their tensile and compressive strengths. The findings of this study can pave the way for rapid characterization, process optimization, and new materials development in AM composites.