Void Growth In Metals Research Articles

Secondary void interactions under shear in thin porous sheets

A compressive stress state decreases the mechanism of void growth in metals. However, in reality, void sheets are evidenced on the fracture surface of metallic shear-compression specimens. The prevailing stress state in the gauge is in contrast to the features observed on the fracture surface. This work examines the mechanical fields in the surroundings of a void under shear as a realization of the mechanical behavior of a ligament between coalescing voids. It is shown that the presence of secondary voids in the surroundings of one primary void reduces the average triaxiality in the cell and homogenizes its distribution; thus, it can be surmised to be mechanically favored. This paper examines this point from a micromechanical perspective utilizing the periodic unit cell method with a single void in its center as a reference case to be compared with other configurations of voids distributed in the cell. It is hypothesized that nucleated voids grow and promote nucleation and growth of voids around them – a mechanism to describe void sheet formation as a positive feedback loop process. The effect of extra secondary voids on the mechanical fields is examined and correlated to their size and location with respect to the existing primary void.

Shear impossibility: Comments on “Void growth by dislocation emission” and “Void growth in metals: Atomistic calculations”

Recently it was proposed that voids in crystals could grow by emission of shear dislocation loops [V.A. Lubarda, M.S. Scheider, D.H. Kalantar, B.A. Remington, M.A. Meyers, Acta Materialia 52 (2004) 1397–1408]. Even more recently, this proposal was ostensibly supported by molecular simulations of voids in strained single crystals [S. Traiviratana, E.M. Bringa, D.J. Benson, M.A. Meyers, Acta Materialia 56 (2008) 3874–3886]. The purpose of this comment is to dispute this recent assertion as unfounded.

Response to “Shear Impossibility—Comments on ‘Void Growth by Dislocation Emission’ and ‘Void Growth in Metals’”

We thank the authors of Ref. [1] for their comments and interest in our work [2–6]. We agree that the emission of shear loops on one single shear plane cannot lead to void growth. However, our simulations suggest that coordinated shear on non-parallel planes can lead to void growth/shrinkage [3–5]. Detailed descriptions of this process are still being worked out and represent an exciting area for future research. Thus, there seem to be two separate dislocation mechanisms operating either sequentially or simultaneously: shear and prismatic loop emission. Whereas prismatic loops are well known and have been extensively documented, the postulation of “special” shear loops is novel. The authors [1] have correctly pointed out that special restrictions need to be applied to these shear loops, something not mentioned in Refs. [2–6]. On the subject of shear impossibility, the authors [1] bring some good points in their comments of our papers. Indeed, the closed loop emitted from the surface of the void does not by itself expand the void. This is obvious from our papers, in which we considered a growth of a cylindrical void by emission of an edge dislocation [2], and a collapse of the void by an emission of an opposite-signed edge dislocation [5]. Thus, if both (positive and negative) dislocations were emitted (which is a 2-D counterpart of a dislocation loop), no net effect on the void growth would take place. Void growth takes place by the outward transfer of the material, which is possible even in an incompressible case due to the outward movement of the remote boundary of the body (the plastically deformed region around the void is surrounded by an elastically deformed region). Eq. (1) of the Comments on our papers [1] nicely states that the net amount of added material associated with the crea-

Statistically informed dynamics of void growth in rate dependent materials

An inherently rate dependent material model is used to model the nucleation and growth of voids in metals, leading to spall fracture. Intrinsic material rate dependence introduces a third time scale in addition to those introduced by rates of nucleation and growth. Material rate dependence does increase the spall strength of metals, but it is not nearly as important as local inertia in doing so.

Void growth in metals: Atomistic calculations

Molecular dynamics simulations in monocrystalline and bicrystalline copper were carried out with LAMMPS (Large-scale Atomic/Molecular Massively Parallel Simulator) to reveal void growth mechanisms. The specimens were subjected to tensile uniaxial strains; the results confirm that the emission of (shear) loops is the primary mechanism of void growth. It is observed that many of these shear loops develop along two slip planes (and not one, as previously thought), in a heretofore unidentified mechanism of cooperative growth. The emission of dislocations from voids is the first stage, and their reaction and interaction is the second stage. These loops, forming initially on different {1 1 1} planes, join at the intersection, if the Burgers vector of the dislocations is parallel to the intersection of two {1 1 1} planes: a 〈1 1 0〉 direction. Thus, the two dislocations cancel at the intersection and a biplanar shear loop is formed. The expansion of the loops and their cross slip leads to the severely work-hardened region surrounding a growing void. Calculations were carried out on voids with different sizes, and a size dependence of the stress threshold to emit dislocations was obtained by MD, in disagreement with the Gurson model which is scale independent. This disagreement is most marked for the nanometer sized voids. The scale dependence of the stress required to grow voids is interpreted in terms of the decreasing availability of optimally oriented shear planes and increased stress required to nucleate shear loops as the void size is reduced. The growth of voids simulated by MD is compared with the Cocks–Ashby constitutive model and significant agreement is found. The density of geometrically necessary dislocations as a function of void size is calculated based on the emission of shear loops and their outward propagation. Calculations are also carried out for a void at the interface between two grains to simulate polycrystalline response. The dislocation emission pattern is qualitatively similar to microscope observations.

A parametric-experimental study of void growth in superplastic deformation

Abstract Substantial void growth in metals constitutes a problem in many industrial operations that utilize superplastic deformation. This is because of the likelihood of material failure due to such growth. Hence, there is a need to study void growth mechanisms in an effort to understand the parameters governing it. In this work, numerical and experimental studies of void growth, and the parameters that affect it, in a superplastically deforming (SPD) metal have been performed. In the numerical studies, using the finite-element method, a 1×2 sized thin plate (i.e. plane stress conditions) of a viscoplastic material with pre-existing holes has been subjected to a constant extension rate. The experimental studies were performed under similar conditions to the numerical ones and provided for qualitative comparison. The parameters affecting void growth in SPD are: m (the strain-rate sensitivity), void size (i.e. diameter) and the number (density) of existing voids. The results showed that increased m values produced strengthening and decreased the rate of void growth. In addition, larger initial void size (or, equivalently, a larger initial void fraction) had the effect of weakening the specimen through causing accelerated void growth. Finally, multiple holes had the effect of increasing the metal ductility by reducing the extent of necking and its onset. This was realized through diffusing the plastic deformation at the different hole sites and reducing the stress concentration. The numerical results were in good qualitative agreement with the experiment and suggested the need to refine existing phenomenological void growth models to include the dependence on the void fraction.

Plasticity and ductile fracture damage: Study of void growth in metals

The kinetics of internal deterioration by void growth around a spherical inclusion is studied as coupled with inelastic deformation. The void growth is described by the rate of a second-order damage tensor φ, whose definition supposes an appropriate averaging process over a statistically significant representative volume (the “unit cell”). The correlation between the damage tensor rate and the plastic deformation rate is established on the basis of results from auxiliary solutions of model boundary value problems for cavity growth in an infinite body. These results are properly adapted to the finite cell case. The damage tensor definition and the hypothesis on the microscopic pointwise displacement field within the cell constitute the basis of a method proposed for setting up the damage evolution equation quantifying the void growth process. The method has the advantage of being flexible enough so that the more refined approximations for a microscale displacement field can be adjusted to increase the accuracy of void growth description. Nevertheless, even starting from the simple Rice-Tracey-like microscopic velocity approximation, by applying the present method one can arrive at the tensorial damage kinetics relation which expresses the important features of the phenomena under consideration in a quantified manner. Thus, the relations obtained in this paper have the general form ·φ = ·φ(·E (p), φ, k ) and indicate the following effects: 1. (i) The damage rate as coupled with the macroscopic plastic strain rate Ė (p) depends on the actual damage state (φ); 2. (ii) it is affected by an initial inclusion size and spacing (viz. the presence of a scale factor k in the kinetics equations); 3. (iii) there is no coaxiality between strain rate and damage-rate tensors in the general case. Some exemplary situations are presented; relevant examples are developed.

The effect of cyclic pulsed temperature on void growth in metals during irradiation

The analysis of Brailsford and Bullough on radiation-produced point defect transport to lattice sinks and the analysis of Ghoniem and Kulcinski of pulsed radiation have been extended to include the effects of radiation-induced temperature oscillations. We have already shown in earlier papers that these temperature pulses enhance void growth if the ambient temperature is below the peak swelling temperature and, conversely, decrease void growth when the ambient temperature is above the peak swelling temperature. When the temperature pulses were suppressed, no difference was seen between void growth under steady and pulsed irradiation. In this paper, we show that the same effects on void growth can be obtained by superposing externally-produced temperature pulses on material under steady irradiation. Calculations have been done for aluminum and molybdenum for sinusoidal temperature pulses of many amplitudes and frequencies.

An analytical approach to void growth in metals under intense radiation pulsing

An analytical approach to void growth in metals under intense radiation pulsing

The effect of damage rate on void growth in metals

The rate theory formulation of void growth was utilized to analyze the effects of damage rate on metal swelling. In particular, the swelling behavior of 316 SS was modeled as a function of temperature, over a range of displacement damage rates between 10 −6dpa/s and 10 −3dpa/s. Detailed analysis of the rate processes for point defect annihilation, migration, and loss to sinks indicated that small vacancy loops limit void growth at high damage rates. The reduction of void growth rates by vacancy emission from voids was found to be shifted towards higher temperature at higher displacement rates. In effect, the peak swelling temperature as well as the upper cutoff temperature for swelling are increased as the displacement rate is increased. The influence of constant or rate dependent nucleation conditions on the final swelling was investigated and it was shown that the initial microstructure before the growth stage essentially determines the peak swelling temperature. When appropriate empirical expressions for void and loop densities were used, the final peak swelling temperature shift agrees reasonably well with experimental data.

The use of the fully dynamic rate theory to predict void growth in metals

Abstract A Fully Dynamic Rate Theory (FDRT) has been used in the computer code TRANSWELL to analyze the response of metals during steady-state and pulsed irradiations. This paper correlates the FDRT with experimental data on void growth in metals. It is shown that the theory is successful in predicting the swelling behavior of different metals over a wide range of temperatures, dose rates, bombarding particles and irradiation time structures. Swelling of 316 stainless steel, Aluminum and Nickel bombarded with heavy ions, neutrons, and electrons at dose rates varying from 10−6 to 10−1 dpa/second is studied for both steady-state and pulsed irradiations.

The use of the high voltage electron microscope to simulate fast neutron-induced void swelling in metals

Electron irradiation with the beam of a high voltage electron microscope can be used to produce void growth in metals, simulating the effect of high dose neutron irradiation. The advantages of the technique are the high dose rate, the relative simplicity of electron irradiation and the ability to make observations during irradiation. Problems of determining the vacancy creation rate are discussed. Secondary displacements are not important for 1 MeV electron irradiation of nickel or iron. In nickel, voids are nucleated if implanted gas atoms are present, but pre-existing vacancy clusters are not necessary. The void concentration is reduced near incoherent boundaries, the effective denuded layer thickness in nickel being 0.06 μm at 330 °C and 0.13 μm at 390 °C. Similar denuded layers occur near surfaces, constituting a serious problem of working with thin foil specimens. Studies of void growth behaviour are illustrated by results for stainless steel and for nickel. The roles of the moving dislocations and the surfaces are discussed. Comparisons of swelling versus dose curves with neutron irradiation work suggest that collision cascades are not an important factor. Thermal annealing of voids is not important in nickel at 540°C or below, but radiation-enhanced diffusion effects can occur.

The Growth and Stability of Voids in Irradiated Metals

AbstractA model has been developed to describe the kinetics of void growth in metals during irradiation which explicitly includes the presence of both migrating interstitials and vacancies. It is clear that void growth can occur only when an excess flux of vacancies arrives at the void surface and this can be achieved by taking into account the preferred drift of the interstitials to the dislocation sinks as a result of the long-range size effect interaction. Results of numerical calculations of the vacancy and interstitial average concentration in stainless steel and molybdenum irradiated under typical fast reactor conditions are presented, and these are used to calculate void growth rates as a function of temperature. It is shown that the void growth rate goes through a maximum when plotted against temperature and this is consistent with the experimental swelling data. During the early stages of irradiation, when the number of point defects arriving at voids is negligible compared with those being lost ...

Growth of voids in metals during diffusion and creep

A study has been made of the thermodynamic conditions under which voids may grow from suitable nuclei in a metal by a mechanism of vacancy aggregation under the influence of stress and vacancy supersaturation. The results are applied to the intergranular void formation observed during creep experiments and also void formation during Kirkendall diffusion. In the case of creep it is postulated that nuclei may grow into voids by receiving stress-motivated vacancy currents from nearby grain boundary sources. In the case of Kirkendall diffusion it is first shown that the development of stress in the diffusion zone depends directly upon the existence of a vacancy supersaturation. The roles of vacancy supersaturation and stress in producing voids are then discussed individually. It is concluded that there is sufficient vacancy supersaturation present to produce voids within grains if nuclei of reasonable size are present. The effect of stress in the absence of large stress concentrations is probably to increase the equilibrium vacancy concentrations at sinks within the grains thereby diverting extra vacancies into voids. Void formation at grain boundaries, where the vacancies are maintained near equilibrium, is explained as a result of stress.