Void Spacing Research Articles

Analysis of the geometry dependence of fracture toughness at cracking initiation by comparison of circumferentially cracked round bars and SENB tests on Copper

In the first part of the paper, the use of circumferentially cracked round bars (CRB geometry) for characterizing fracture toughness of a ductile material, namely copper, is assessed experimentally through a comparison with the single edge notched bend (SENB) geometry. The J(R) curve method with multiple-specimens was applied, but, as unstable cracking appeared very early in the CRB specimen, an engineering definition of fracture toughness was not pertinent. Unloaded specimens were analyzed metallographically to determine the CTOD at physical cracking initiation. The fracture toughness measured using the CRB geometry was 50% larger than using the SENB geometry. The second part of the paper aims at justifying this difference of fracture toughness at cracking initiation. Finite element simulations revealed a slightly higher constraint in the SENB specimens. The main difference between the two specimen geometries lies in a 50% larger extension of the finite strain zone with respect to the CTOD in the case of the SENB specimens. Based on the observation that, in the studied material, the critical CTOD is one order of magnitude larger than the void spacing, we conclude that the geometry dependence of the fracture toughness is caused by the difference in the finite strain zone extension rather than by a stress triaxiality effect.

Ductile fracture of materials with high void volumefraction

In the present paper, axisymmetric cell models containing one or two voids and athree-dimensional cell model containing two voids have been used to investigate void size andspacing effect on the ductile fracture in materials with high initial void volume fraction. They areperformed for round smooth and round notched specimens under uniaxial tension. The examplematerial used for comparison is a nodular cast iron material GGG-40 with initial void volumefraction of 7.7%. The parameters considered in this paper are void size and shape foraxisymmetric cell models containing a single void, and void distribution pattern foraxisymmetric and 3D cell models containing two voids of different sizes. The results obtainedfrom these cell models by using FEM calculations are compared with the Gurson model, theGurson–Tvergaard–Needleman model, the Rice–Tracey model and the modified Rice–Traceymodel. It can be stated that the influence of void size and void spacing on the growth in volumeof voids is very large, and it is dependent on the distribution of voids. Using non-uniform voiddistribution, the results of axisymmetric cell models can explain how a void can grow in anunstable state under very low stress triaxiality at very small strain as observed in experiments.Calculations using cell models containing two voids give very different results about the stableand unstable growth of voids which are strongly dependent on the configuration of cell model.

A Numerical Test of Air Void Spacing Equations

Air void spacing equations have been proposed in the literature by a number of authors: Powers; Philleo; Attiogbe; and Pleau and Pigeon. Each proposed spacing equation attempts to characterize the true “spacing” of entrained air voids in concrete. While efforts have been made to correlate these spacing equation calculations to freeze-thaw performance, no test has been performed to assess the geometrical accuracy of these spacing equations. Herein is a computerized accuracy test of these proposed spacing equations. A computer model of air void systems is used, and various “spacings” are measured in the model system. The results of these measurements are then compared to the appropriate spacing equation prediction, along with equations developed by Lu and Torquato.

Nonlocal effects on localization in a void-sheet

For a nonlocal damage model it is expected that the characteristic material length relates to the damage mechanism. In the case of ductile fracture the most relevant length scales would be the average void radius or spacing. Cell model computations representing a single row of voids in an infinite solid under plane strain conditions are here used to compare with predictions of a nonlocal version of a porous ductile material model. Both the critical strain for the onset of plastic flow localization and the slope of the stress-strain curve in the post-localization range are compared, and it is found that both of these are affected by the value of the material length in the nonlocal model. Comparison with predictions of the void-sheet cell model are carried out for an inclined row of voids, leading to shear band failure, as well as a row of transversely aligned voids. For shear bands the material characteristic length scales with the void radius, whereas for transversely aligned voids the scaling is with the void spacing.

Volume Fraction of Protected Paste and Mean Spacing of Air Voids

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An experimental model of the growth of neighboring voids during ductile fracture

We have examined aspects of the strain-induced growth behavior of pairs of neighboring voids using a macroscopic model consisting of a uniaxial tensile specimen containing pairs of opposing blind-end holes. Experimental measurements have been made of the thinning behavior of the inter-hole ligament for hole-ends spaced initially 0.5 D, 1.0 D, and 2.0 D apart, where D is the hole diameter. These results indicate that deformation causes the interhole ligament to thin at a rate which increases with increasing strain and decreasing hole spacing. When compared to predictions of the growth of isolated voids (based on the Rice-Tracey analysis [1,5]), our results indicate void interaction effects accelerate ligament thinning and become pronounced with decreasing void spacing (≤ 1.0 D) and increasing applied strain (ε 1≥ 0.2) even in uniaxial tension.

Frost resistant concrete

There are two basic frost durability problems: internal cracking due to freezing and thawing cycles, and surface scaling, generally due to freezing in the presence of deicer salts. Although there are still parts of the problem which are not perfectly well understood and warrant further investigation, particularly with respect to the differences between laboratory tests and field exposure, the way to make concrete resistant to freezing and thawing cycles is very well known. It is simply to ensure that the hardened concrete has an adequate system of entrained air voids. Field experience as well as laboratory data has shown very conclusively that internal cracking due to frost in properly air-entrained concretes is almost non-existent. Scaling due to freezing in the presence of deicer salts is a much more complex problem than internal cracking for many reasons, but probably mainly because it is related to the microstructure of the very surface layer or ‘skin’ of concrete. Properly air-entrained and properly cured well-designed Portland cement field concretes are generally quite resistant to deicer salt scaling, but scaling still sometimes occurs unexpectedly after only a few years. Research in this area is therefore required. The ability of the commonly used deicer salt scaling tests to predict the performance of concrete under normal field exposure conditions must also be particularly investigated. In addition, research is needed to better understand the process of the formation of large air voids in air-entrained concrete, since the dosage of air-entraining admixtures is based on the total volume of air in the mixture and small dosages that yield an adequate air volume often do not yield an adequate air void spacing factor (and thus adequate frost protection).

Surface reactions during water atomizing and sintering of austenitic stainless steel : T. Tunberg, L. Nyborg (Chalmers University of Technology, Gothenburg, Sweden). PowderMetall., vol 38, no 2, 1995, 120–130

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.

密着完了時間予測アルゴリズム 固相拡散接合予測支援システムに関する研究 第２報

The algorithm for predicting the intimate contact process in the solid state diffusion bonding has been developed. The numerical model proposed in our previous study (Part 1) was updated to predict the void shrinkage process in the final stage of bonding.The influence of dispersion of void spacing on the contacting process was examined based on the calculated results. The plural measurements of surface profiles was performed to estimate the variation of the bonding process. The distribution of void spacing estimated by the overlap method was also examined. It was useful to take into account the largest void spacing and the largest void volume for the prediction of the final stage. The algorithm was verified experimentally. It was indicated that the algorithm predicts the time taken to attain the full contact.

確率統計論的解析を適用した接合過程ばらつき推定アルゴリズム 固相拡散接合予測支援システムに関する研究 第３報

An algorithm for estimating the bonding process variation is developed to establish the selection system for the optimal solid state bonding conditions. The bonding process variation (dispersion) due to surface roughness is discussed by applying the statistical analysis. The distributions of void spacing and void volume are estimated by the overlap method which was proposed in our previous paper (part 1). The standard deviations are calculated from the distributions. The numerical calculations are performed by taking into account the standard deviations. Also, the hazard rate is newly introduced to comprehend the bonding dispersion. Experimental bonding tests suggest that the algorithm developed in the present study can predict the bonding process variation.

接合中の空隙間隔分布推定手法と密着過程予測モデルの試作 固相拡散接合予測支援システムに関する研究 第１報

接合中の空隙間隔分布推定手法と密着過程予測モデルの試作 固相拡散接合予測支援システムに関する研究 第１報

Ductile crack growth—II. Void nucleation and geometry effects on macroscopic fracture behavior

Many metals that fail by void growth and coalescence display a macroscopically planar fracture process zone of one or two void spacings in thickness; outside this region, the voids exhibit little or no growth. A finite element model of this mode of failure was described in Part I of this paper [ J. Mech. Phys. Solids, 43, 233–259 (1995)]. A row of void-containing cell elements is placed on the symmetry plane ahead of the initial crack. The cells incorporate the softening characteristics of hole growth and dependence on stress triaxiality. These cells are embedded within a conventional elastic-plastic continuum. Under increasing strain, the voids grow and coalesce to form new crack surfaces, thereby advancing the crack. Parametric studies reveal that the important microstructural parameters in the model are D and f 0, characterizing the spacing and the initial volume fraction of voids on the fracture plane. Using this model, Xia et al. [J. Mech. Phys. Solids, 43, 389–413 (1995)] have successfully predicted details of the load, displacement and crack growth histories—collectively referred to as the macroscopic fracture behavior—of four specimen geometries, which give rise to significantly different crack tip constraints under fully plastic conditions. Here we study the quantitative effects of void nucleation by a stress and strain criterion on the macroscopic fracture behavior. This behavior is compared with predictions using a similar volume of voids present from the very beginning. Geometry effects on macroscopic fracture behavior under contained and fully yielded conditions are discussed for the three-point-bend specimen and the center-crack-panel loaded in tension. Here the objective is to show the connection between the crack growth resistance and the fracture environment, namely, the constraint ahead of the crack tip and the tensile stress on the fracture plane.

Frost Resistance of Roller-Compacted High-Volume Fly Ash Concrete

Laboratory investigations were performed to design four high-volume fly ash roller-compacted concrete mixtures. The amount of fly ash was fixed at 63% of the total cementitious material. Two mixtures (one air-entrained and one non-air-entrained) had a cementitious material content of 12% (as a proportion of the total mass of dry materials), and two mixtures (one air-entrained and one non-air-entrained) had a cementitious material content of 15%. The apparatus used to prepare the cylindrical specimens required for the tests was specifically designed for this purpose. In this apparatus, the concrete is placed in a cylindrical mold that is vibrated laterally while a longitudinal compressive force is applied to the concrete. Each mixture was tested for strength, absorption, permeability, determination of the air-void characteristics, and frost resistance. The frost resistance of air-entrained concretes (tested according to Procedure A of ASTM Standard C 666) was found to be very good, irrespective of the cementitious material content. These concretes contained only a small number of irregularly shaped compaction air voids. The value of the air-void spacing factor was 250 ± 5 μm for the air-entrained concretes, and only slightly higher at 309 μm and 393 μm for the non-air-entrained concretes. The latter concretes also showed adequate frost resistance. Notwithstanding these conditions, the use of air entrainment is recommended for roller-compacted, high-volume fly ash concretes.

A computational approach to ductile crack growth under large scale yielding conditions

Mode I crack initiation and growth under plane strain conditions in tough metals is computed using an elastic-plastic continuum model which accounts for void growth and coalescence ahead of the crack tip. The material parameters are the Young's modulus, yield stress and strain hardening exponent of the metal, along with the parameters characterizing the spacing and volume fraction of voids in material elements lying in the plane of the crack. For a given set of these parameters and a specific specimen, or component, subject to a specific loading, relationships among load, load-line displacement and crack advance can be computed with no restrictions on the extent of plastic deformation. Similarly, there is no limit on crack advance, except that it must take place on the symmetry plane ahead of the initial crack. Suitably defined measures of crack tip loading intensity, such as those based on the J-integral, can also be computed, thereby directly generating crack growth resistance curves. In this paper, the model is applied to five specimen geometries which are known to give rise to significantly different crack tip constraints and crack growth resistance behaviors. Computed results are compared with sets of experimental data for two tough steels for four of the specimen types. Details of the load, displacement and crack growth histories are accurately reproduced, even when extensive crack growth takes place under conditions of fully plastic yielding.

Ductile crack growth-I. A numerical study using computational cells with microstructurally-based length scales

Many metals which fail by a void growth mechanism display a macroscopically planar fracture process zone of one or two void spacings in thickness characterized by intense plastic flow in the ligaments between the voids; outside this region, the voids exhibit little or no growth. To model this process a material layer containing a pre-existing population of similar sized voids is assumed. The thickness of the layer, D, can be identified with the mean spacing between the voids. This layer is represented by an aggregate of computational cells of linear dimension D. Each cell contains a single void of some initial volume. The Gurson constitutive relation for dilatant plasticity describes the hole growth in a cell resulting in material softening and, ultimately, loss of stress carrying capacity. The collection of cells softened by hole growth constitutes the fracture process zone of length l 1. Two fracture mechanism regimes can be identified corresponding to l 1 ≈ D and l 1 ⪢ D. The connection between these mechanisms and fracture resistance is discussed. Finite element calculations have been carried out to determine crack growth resistance curves for plane strain, mode I crack growth under small scale yielding. A row of voided cells is placed on the symmetry plane ahead of the initial crack. These cell elements are embedded within a conventional elastic-plastic continuum. Under increasing load, the voids in the cells grow and coalesce to form a new crack surface thereby advancing the crack. Resistance curves are calculated for crack growth exceeding many multiples of D. The parameters affecting fracture resistance are discussed emphasizing the roles of microstructural parameters and continuum properties of the material. The effect of crack tip constraint on fracture resistance is examined under small scale yielding by way of the T-stress. As a final application, resistance curves for a deep and a shallow crack bend bar are computed. These are compared with experimental data.

Loss of freeze–thaw durability of concrete containing accelerating admixtures

Rapid freeze–thaw durability tests on air entrained concrete mixes containing a proprietary nonchloride accelerating admixture or CaCl2 show that although early age compressive strength acceleration is achieved, the freeze-thaw durability is reduced when compared with the durability of control concretes of similar mix proportions, but without accelerating admixtures. Although the compressive strength gains were accelerated in mixes containing either the proprietary accelerating admixture or CaCl2, the tensile strengths at 28 days were similar for mixes with and without the admixtures.Petrographic analyses showed air contents and air void spacing factors in concretes with accelerating admixtures, either nonchloride or CaCl2, to be similar to the air systems in the control concrete, though more air entraining agent was required with the mixes containing accelerating admixtures. Local aggregates as well as aggregates from three alternate sources were used. Test results did not show any significant differences in durability on the basis of aggregate source.As the larger reduction measured in freeze–thaw durability for concrete mixes containing either chloride or nonchloride accelerating admixtures could not be attributed to either a deficient air void system in the cured concrete or inferior aggregate, it is believed that the cause is some characteristic or a hydration product in the cement paste microstructure produced by accelerated hydration. Key words: concrete, durability, freeze–thaw testing, strength acceleration, admixtures, air void system.

Void/Bridged-Crack Interactions and Their Implications for Defect Coalescence

Void-crack interactions with crack bridging play an important role in the determination of rupture failure modes of composite materials. In this paper, an integral equation approach is developed to study the behavior of systems containing multiple in teracting voids and cracks with a general form of crack bridging. The formulation is based on a superposition technique that decompose the interacting voids and cracks into a number of subproblems, each involving only a single void or single crack. The integral equations are fully non-singular and thus can be solved effectively with a Gauss integra tion scheme. Numerical examples are given in order to study the effects of bridging, bridg ing anisotropy, void size, and void spacing, among others, on the crack-tip behavior. The influence of void-crack interactions on the fracture path are also investigated. For a material containing doubly periodic collinear holes arranged with offsets in subsequent rows, it is found that the fracture path can be formed either by the coalescence of the holes in a row or by the coalescence of the holes across neighboring rows, depending on the ratio of vertical to horizontal void spacing.

Ductile fracture by the growth and coalescence of microvoids of non-uniform size and spacing

A two-dimensional plane strain model of void growth and coalescence in a rigid/plastic solid, containing void sizes and spacings which can be highly non-uniform, is developed to investigate the effects of non-uniform distributions of void-nucleating particles on the ductility of a metal. The theoretical void-growth strains to ductile fracture for a wide variation in void diameters and spacings show that, for a given volume fraction of voids, the minimum ductile-fracture strain occurs when the voids are of uniform size and spacing. For the same volume fraction of voids, greatly increased ductility is likely to be achieved when the void sizes and spacings are highly non-uniform and the sub-cell volume fractions are also non-uniform.

Fracture mechanisms in constrained Ni interlayers

The process of void growth and coalescence during the fracture of thin diffusion bonded Ni interlayers has been studied by tensile testing and metallographic examination. The tensile strength increased nonlinearly with the interlayer diameter-to-thickness ( D/ T) ratio. Fracture occurred in the Ni on a plane near and parallel to, the steel interface. The fracture surface dimple size increased with D/ T. The increasing failure stress and dimple size with D/ T was similar to that observed in other types of constrained interlayer. The size of the void nucleation sites in the Ni was determined by means of an expression developed for void coalescence through a mechanism of localized plastic instability. The observed changes in the void size and spacing with increasing D/ T are a consequence of the increased triaxial tensile stress in highly-constrained ductile interlayers.

Mean Spacing of Air Voids in Hardened Concrete

In this study geometric probability concepts and stereological principles are used to derive an equation for the mean spacing of air voids in hardened concrete. The equation is presented and it is shown that the input paramerers for the equation are the same as those obtained from the standard air-void system analysis of hardened concrete. The equation is valid for all values of paste-to-air ratio. The mean spacing yields a better estimate of the actual spacing of the air voids in hardened concrete than the standard spacing factor.