Void Spacing Research Articles

A Multiscale Analysis of Void Coalescence in Nickel

An internal state variable void coalescence equation developed by Horstemeyer, Lathrop, Gokhale, and Dighe (2000, Theor. Appl. Fract. Mech., 33(1), pp. 31–47) that comprises void impingement and void sheet mechanisms is updated based on three-dimensional micromechanical simulations and novel experiments. This macroscale coalescence equation, developed originally from two-dimensional finite element simulations, was formulated to enhance void growth. In this study, three-dimensional micromechanical finite element simulations were employed using cylindrical and spherical void geometries in nickel that were validated by experiments. The number of voids, void orientation, and void spacing were all varied and tested and simulated under uniaxial loading conditions. The micromechanical results showed excellent agreement with experiments in terms of void volume fractions versus strain and local void geometry images. Perhaps more importantly, the macroscale internal state variable void coalescence equation did not require a functional form change but just a coefficient value modification.

On ductile fracture initiation toughness: Effects of void volume fraction, void shape and void distribution

This paper studies the effects of the initial relative void spacing, void pattern, void shape and void volume fraction on ductile fracture toughness using three-dimensional, small scale yielding models, where voids are assumed to pre-exist in the material and are explicitly modeled using refined finite elements. Results of this study can be used to explain the observed fracture toughness anisotropy in industrial alloys. Our analyses suggest that simplified models containing a single row of voids ahead of the crack tip is sufficient when the initial void volume fraction remains small. When the initial void volume fraction becomes large, these simplified models can predict the fracture initiation toughness ( J Ic) with adequate accuracy but cannot predict the correct J– R curve because they over-predict the interaction among growing voids on the plane of crack propagation. Consequently, finite element models containing multiple rows of voids should be used when the material has large initial void volume fraction.

The characteristics of air void and frost resistance of RCC with fly ash and expansive agent

In order to assure the outer concrete of Longtan dam in China possesses excellent of frost resistance, the losses of strength, mass and air void characteristics of roller compacted concrete (RCC) containing fly ash, superplasticizer and a novel MgO-bearing expansive agent (HNM) were studied using the freezing–thawing method ASTM C666. The results show that there is a linear correlation between strength and mass losses in RCC subjected to cycles of freezing and thawing. There is a relationship between the air void spacing factor and the frost resistance of RCC. However, for RCC containing fly ash and superplasticizer a spacing factor of 0.25 mm is not necessary. Using a water:binder ratio of 0.48 in RCC containing 50% fly ash and 8% HNM a durability factor of over D 300 can be achieved provided the spacing factor is less than 0.4 mm.

Anisotropic ductile fracture: Part I: experiments

Deformation and fracture are investigated at room temperature in steel through tension and compression tests. Round smooth bars and cylinders are used to characterize the deformation behavior while round notched bars are used to explore stress state and specimen orientation effects on fracture. The microstructure is characterized to infer initial average values of porosity, void aspect ratio and void spacing ratio, all three playing a key role in the fracture process. Interrupted tests are used to determine the spatial distribution of those variables after crack extension thus providing a basis for comparison at the micro-scale with theoretical predictions. All damage stages are found to be inherently anisotropic, including void nucleation and crack propagation. An important finding of this investigation is that, in quantitative modeling of ductile fracture, any void growth model should be supplemented by a physically motivated void coalescence model.

Calculating liquid transport into high-performance concrete during wet freeze/thaw

A method for calculation of the liquid transport into high-performance concrete (HPC) during wet freeze/thaw exposure is proposed. This transport, or pumping effect, which is larger than absorption above 0 °C, is in the present calculation assumed to be caused by diffusion of water from the wet surface, through hardened cement paste (HCP) where water in nonfreezable, to large voids with very low vapour content. Saturated flow is assumed between the wet concrete surface and the active voids. Cranks solution for stationary transport into a hollow sphere of mean radius r̄ is combined with Powers spacing factor. The shell thickness is the mean void spacing factor ( L̄). The flow into voids was calculated (“good” vs. “bad” void system) for various maximum possible moisture potentials between wet surface, saturated HCP and active void (at 263 K and 1 atm; Δ p=saturation pressure=260 Pa or Δ v=moisture content=0.00215 kg/m 3 in void, etc.). Realistic voids and diffusivity were used. The calculation fits with liquid uptake measured in wet freeze/thaw of HPC with exposed surface equal to the surface of the active voids. The lower the void content, the lower is the pumping effect. Nonstationary transport, further experiments and simulations are discussed briefly.

The three-dimensional analysis for diffusive shrinkage of a grain-boundary void in stressed solid

As atoms migrate along void surface and grain-boundary driven by various thermodynamic forces, the grain-boundary void changes its shape and volume. A rounded void may become unstable and collapse. The void instability is an outcome of the competition between the variation in the elastic energy stored in the stressed solid, the void surface and grain-boundary energies. In this article, the instability conditions and the equilibrium shape of a gas-filled grain-boundary void are first determined, and then an explicit expression for the shrinkage rate is derived as a function of the void spacing, the applied stress, the internal pressure built up by the gas filled in the void as well as relevant material parameters.

Mode I fracture of sheet metal

The perceived wisdom about thin sheet fracture is that (i) the crack propagates under mixed mode I & III giving rise to a slant through-thickness fracture profile and (ii) the fracture toughness remains constant at low thickness and eventually decreases with increasing thickness. In the present study, fracture tests performed on thin DENT plates of various thicknesses made of stainless steel, mild steel, 6082-O and NS4 aluminium alloys, brass, bronze, lead, and zinc systematically exhibit (i) mode I “bath-tub”, i.e. “cup & cup”, fracture profiles with limited shear lips and significant localized necking (more than 50% thickness reduction), (ii) a fracture toughness that linearly increases with increasing thickness (in the range of 0.5– 5 mm ). The different contributions to the work expended during fracture of these materials are separated based on dimensional considerations. The paper emphasises the two parts of the work spent in the fracture process zone: the necking work and the “fracture” work. Experiments show that, as expected, the work of necking per unit area linearly increases with thickness. For a typical thickness of 1 mm , both fracture and necking contributions have the same order of magnitude in most of the metals investigated. A model is developed in order to independently evaluate the work of necking, which successfully predicts the experimental values. Furthermore, it enables the fracture energy to be derived from tests performed with only one specimen thickness. In a second modelling step, the work of fracture is computed using an enhanced void growth model valid in the quasi plane stress regime. The fracture energy varies linearly with the yield stress and void spacing and is a strong function of the hardening exponent and initial void volume fraction. The coupling of the two models allows the relative contributions of necking versus fracture to be quantified with respect to (i) the two length scales involved in this problem, i.e. the void spacing and the plate thickness, and (ii) the flow properties of the material. Each term can dominate depending on the properties of the material which explains the different behaviours reported in the literature about thin plate fracture toughness and its dependence with thickness.

Grain boundary versus transgranular ductile failure

The competition between intergranular and intragranular fracture is investigated using a bilayer damage model, which incorporates the relevant microstructural features of aluminium alloys with precipitate free zones (PFZ) nearby the grain boundary. One layer represents the grain behaviour: due to precipitation, it presents a high yield stress and low hardening exponent. The other layer represents the PFZ which has the behaviour of a solid solution: it is much softer but with a much higher strain hardening capacity. In both layers, void growth and coalescence is modelled using an enhanced Gurson-type model incorporating the effects of the void aspect ratio and of the relative void spacing. The effects on the ductility (i) of the flow properties of each zone, (ii) of the relative thickness of the PFZ, and (iii) of the particles spacing and volume fraction in the PFZ are elucidated. Comparisons are made with experimental data. Based on the previous analysis, qualitative understanding of trends in the fracture toughness of aluminium alloys can be gained in order to provide a link with the thermal treatment process.

Micromechanics-based model for trends in toughness of ductile metals

Relations between fracture toughness and microstructural details have been calculated for ductile materials based on a dilatational plasticity constitutive model that has recently been proposed. The model generalizes the Gurson model to account for both void growth and coalescence with explicit dependence on void shape and distribution effects. Based on a small scale yielding formulation of crack growth, toughness trends are determined as a function of yield stress, strain-hardening, initial porosity, void shape and spacing as well as void spacing anisotropy. Distinctions are drawn between the engineering fracture toughness, which is typically associated with 0.2 mm of crack growth, and the theoretical toughness based on coalescence of the crack tip with the first void ahead of it. Comparison with one set of experimental data for a steel is made for which a fairly complete characterization of the microstructure is available.

Abatement of shocks during disruption of porous thick-liquid blankets in HYLIFE-type inertial fusion chambers

The dispersion and control of liquid kinetic energy and momentum are a major issue after the explosion of targets in an inertial fusion energy (IFE) thick-liquid chamber. For HYLIFE-type IFE chambers the desired repetition rate for shots varies from 5 to 10 Hz—a rate much too fast for natural gravity clearing of liquid debris. The impulse load delivered by a single shot generates enough kinetic energy in disrupted liquid material to do significant damage to surrounding solid structures. However, carefully designed jet arrays with regular void spacing can diffuse and dissipate kinetic energy that could damage adjacent structures, and rapidly moving, oscillating jets can dynamically clear the chamber center. A brief theoretical and mathematical background is given for this method of shock abatement, using the current Berkeley jet array experiment as a representative geometry.

Characteristics of water- and gas-atomised SS powders for MIM

Given the complexity of the laser-material interactions prevalent in powder bed fusion additive manufacturing, the need for tight control of alloy composition in the metal powder feedstock is leading to the use of specific gases during atomization. These changes in atomization gas also impact powder flow and packing. In order to identify the magnitude of this impact, two nitrogen atomized and one argon atomized 316 L austenitic stainless steel powders with similar size distributions were characterized using traditional powder characterization tools and rotating drum and annular shear rheological tools. While the traditional characterization tools and particle size measurements did not differentiate between the powders, these rheological tools allowed connections between the particle morphologies and rheological properties and powder performance to be identified. In particular, the argon atomized powders displayed higher aspect ratios, which translate into more spherical morphologies, and improved flow, defined by lower avalanche angles, when tested in the rotating drum. On the other hand, these differences in flow properties were not captured in the corresponding basic flow and specific energy measurements made with the annular shear tools. Variations in the powder packing properties and internal powder porosity in the different powder lots decreased the powder mass and introduced increased uncertainty in the force and torque measurements. The void spacing between loosely packed powders was also measured and showed how changes in particle size distribution and morphology impacted both packing density and permeability. Larger void spacing produced higher permeability values, indicating greater gas flow through the loosely packed powder.

Low-pressure deposition of cubic boron nitride

Fracture is the main cause of degradation and capacity fading in lithiated silicon during cycling. Experiments on the fracture of lithiated silicon show conflicting results, and so mechanistic models can help interpret experiments and guide component design. Here, large-scale K-controlled atomistic simulations of crack propagation (R-curve KI vs. Δa) are performed at LixSi compositions x=0.5,1.0,1.5 for as-quenched/relaxed samples and at x=0.5,1.0 for samples created by discharging from higher Li compositions. In all cases, the fracture mechanism is void nucleation, growth, and coalescence. In as-quenched materials, with increasing Li content the plastic flow stress and elastic moduli decrease but void nucleation and growth happen at smaller stress, so that the initial fracture toughness KIc≈1.0MPam decreases slightly but the initial fracture energy JIc ≈ 10.5J/m2 is similar. After 10 nm of crack growth, the fracture toughnesses increase and become similar at KIc≈1.9MPam across all compositions. Plane-strain equi-biaxial expansion simulations of uncracked samples provide complementary information on void nucleation and growth. The simulations are interpreted within the framework of Gurson model for ductile fracture, which predicts JIc=ασyD where α ≃ 1 and D is the void spacing, and good agreement is found. In spite of flowing plastically, the fracture toughness of LixSi is low because voids nucleate within nano-sized distances ahead of the crack (D ≈ 1nm). Scaling simulation results to experimental conditions, reasonable agreement with experimentally-estimated fracture toughnesses is obtained. The discharging process facilitates void nucleation but decreases the flow stress (as shown previously), leading to enhanced fracture toughness at all levels of crack growth. Therefore, the fracture behavior of lithiated silicon at a given composition is not a material property but instead depends on the history of charging/discharging. These findings indicate that the mechanical behavior (flow and fracture) of lithiated Si must be interpreted within a fully rate- and history-dependent framework.

A Model for Shrinkage of a Spherical Void in the Center of a Grain: Influence of Lattice Diffusion

A model is presented to describe a spherical void shrinkage at the center of a quasi-spherical grain dominated by lattice self-diffusion. The model is based on the difference in chemical potential between the spherical void surface and the grain boundary interface. The quantitative calculations for pure iron predicted that only small, micron-sized spherical voids could be wholly healed within hours at high temperature. The spherical void shrinkage process can be greatly promoted with an increase in temperature, which depends strongly on crystal lattices, particularly the initial radius of the spherical void and the grain size. The time to eliminate a spherical void with an identical radius within grains is close to that for grain boundaries, while different shrinkage processes were undergone, at fixed temperatures, and related to spherical void size, void spacing, and the grain size.

Damage and size effect during superplastic deformation

Abstract Superplastic forming is a valuable metal working technique because of the extreme ductility that can be achieved. However, it is limited in application due to the presence of small voids that grow and coalesce during the forming process, often causing premature failure. In order to understand and control this phenomenon accurate constitutive models must be developed which account for void parameters that affect the macroscopic behavior of the material. This paper looks specifically at the effect of void size and spacing on the ductility and flow stress of viscoplastic materials. Based on the gradient-dependent theory of plasticity, a model is proposed that accounts for size effects by incorporating strain gradient terms into a continuum based constitutive equation. Both experimental testing and finite element (FE) modeling were performed on Pb–Sn, tensile specimens with small holes drilled in them in random patterns. The experimental tests indicate that a decrease in void size results in an increase in ductility. The FE results demonstrate that the gradient terms strengthen the material by diffusing the strain in areas of high strain concentration and delay failure by slowing void growth. In addition, the model predicted an increase in ductility and flow stress with decreasing void size.

Crack growth predictions by cohesive zone model for ductile fracture

For crack growth by a ductile failure mechanism, the fracture process zone is represented in terms of special interface elements in the crack plane ahead of the crack. A porous ductile material model is used in the interface elements to represent the growth of voids to coalescence. In relation to the finite element mesh, the initial width of the interface is taken to be zero, but the traction separation relations represented by the interface are based on assuming an interface width of the order of the void spacing. The tangential stresses inside the interface are determined by the requirement of compatibility with the surrounding material in the tangential direction. Some comparison with predictions based on related crack growth models is used to discuss the performance of the special cohesive zone model presented here.

Some findings on the usefulness of image analysis for determining the characteristics of the air-void system on hardened concrete

This paper discusses the usefulness of image analysis techniques in order to assess the characteristics of the air-void system in concrete. Test results indicate that such a technique can correctly assess the air-void characteristics as defined in ASTM C 457 Standard test method. However, the accuracy of the test results is not significantly improved as compared with the manual technique and the image analysis method must be very carefully validated before being used as a routine procedure. Test results also indicate that the image analysis technique failed to correctly assess the size-distribution of air voids and, for that reason, this technique cannot be used to provide a better estimate of the real spacing of air voids than the commonly used ASTM C 457 spacing factor.

An extended model for void growth and coalescence

A model for the axisymmetric growth and coalescence of small internal voids in elastoplastic solids is proposed and assessed using void cell computations. Two contributions existing in the literature have been integrated into the enhanced model. The first is the model of Gologanu–Leblond–Devaux, extending the Gurson model to void shape effects. The second is the approach of Thomason for the onset of void coalescence. Each of these has been extended heuristically to account for strain hardening. In addition, a micromechanically-based simple constitutive model for the void coalescence stage is proposed to supplement the criterion for the onset of coalescence. The fully enhanced Gurson model depends on the flow properties of the material and the dimensional ratios of the void-cell representative volume element. Phenomenological parameters such as critical porosities are not employed in the enhanced model. It incorporates the effect of void shape, relative void spacing, strain hardening, and porosity. The effect of the relative void spacing on void coalescence, which has not yet been carefully addressed in the literature, has received special attention. Using cell model computations, accurate predictions through final fracture have been obtained for a wide range of porosity, void spacing, initial void shape, strain hardening, and stress triaxiality. These predictions have been used to assess the enhanced model.

Finite-element simulation of the diffusivegrowth of grain boundary voids

A finite-element method is formulated to simulate the diffusive growth of thegrain boundary voids. Two rate processes, grain boundary diffusion and surfacediffusion, are concomitant. In the finite-element method, the surfacediffusion and the grain boundary diffusion are coupled by boundary conditionsat the triple point of the void surface and the grain boundary. Finite-elementsimulations show that the void growth is controlled by the relative magnitudeof the grain boundary and surface diffusion coefficients, the applied tensilestresses and the void spacing. When the surface diffusion process is theslower process, as occurring in the case of highly applied tensile stress andsmall void space, the voids grow in a crack-like manner. Otherwise, the voidsremain rounded during growth.

Analysis of Stress-Strain Relationship in Materials Containing Voids by Means of Plastic Finite Element Method

Applying the finite element method in two dimensions, an analysis is performed to derive the stress-strain relationship of material containing voids in matrix, and which is subjected to large deformation. The conditions assumed for the analysis are applicability of continuum body mechanics, Mises yield criterion, J2 flow theory, power work-hardening, plane stress in two-dimensional system and uniform cyclically recurring void distribution. Taking as example a case of material presenting 0.3 work-hardening, it is indicated from the analysis that:- —With voids arrayed in square lattice, total elongation would be little affected by change in void size; —With a void spacing in lattice of 10 fim, a uniform elongation 12–14% should be obtained in a wide range of void sizes from 0.01 to 8.0 μm; —Tensile strength should start to lower at a void areal fraction of around 1%; —A sharply lowered uniform elongation of a level far below 1% should be presented by material of low work-hardening exponent. The severe decline of ductility seen with 316 stainless steel upon neutron irradiation at temperatures around 600 K is interpreted as resulting from a combination of low work-hardening and the presence of voids in matrix.

Analysis of Stress-Strain Relationship in Materials Containing Voids by Means of Plastic Finite Element Method.

Applying the finite element method in two dimensions, an analysis is performed to derive the stress-strain relationship of material containing voids in matrix, and which is subjected to large deformation. The conditions assumed for the analysis are applicability of continuum body mechanics, Mises yield criterion, J2 flow theory, power work-hardening, plane stress in two-dimensional system and uniform cyclically recurring void distribution. Taking as example a case of material presenting 0.3 work-hardening, it is indicated from the analysis that:- —With voids arrayed in square lattice, total elongation would be little affected by change in void size; —With a void spacing in lattice of 10 fim, a uniform elongation 12–14% should be obtained in a wide range of void sizes from 0.01 to 8.0 μm; —Tensile strength should start to lower at a void areal fraction of around 1%; —A sharply lowered uniform elongation of a level far below 1% should be presented by material of low work-hardening exponent. The severe decline of ductility seen with 316 stainless steel upon neutron irradiation at temperatures around 600 K is interpreted as resulting from a combination of low work-hardening and the presence of voids in matrix.