Void Nucleation Stress Research Articles

Anisotropic dynamic response of AlSi10Mg fabricated via laser powder bed fusion under plate impact

The effects of structural anisotropy on dynamic yield and spallation damage of an AlSi10Mg alloy manufactured via laser powder bed fusion are investigated via plate impact experiments along the build direction (BD) and the transverse direction (TD). Free surface velocity histories are measured to deduce its dynamic mechanical properties. The as-received and postmortem samples are characterized with scanning electron microscopy, metallograpic microscopy, electron backscatter diffraction and synchrotron X-ray computed tomography. The Hugoniot elastic limit for loading along TD is about 40% higher than that along BD, given the initial 〈100〉∥BD texture. For spallation, voids prefer to nucleate at melt pool boundaries. Spall strength for loading along TD is about 18% higher than that along BD, as a result of higher critical stress for void nucleation and less nucleation sites due to the melt pool morphology. The damage evolution features are also correlated well with melt pool morphology and grain morphology within the pool interior, demonstrating the “ductile” interpool and “brittle” intrapool fracture modes for loading along BD and TD, respectively.

Probing grain boundary dependence of damage evolution under shock loading in a variety of FCC metals

This letter presents the results of a computational survey on the damage response of Ni, Al, Cu and Ag bicrystals containing various grain boundaries subjected to shock loading. Three distinct failure patterns emerge physically over the entire misorientation range, which can be correlated with the observed variations in void nucleation stresses in all the materials. The variations in damage with inclination angle for asymmetric grain boundaries bear a familiar trend similar to well established energy variations. In addition, wide variations in void nucleation stress can be related to stacking fault energy of a material.

Effect of local structure and stoichiometry on the dynamic behavior of bi-metal interfaces

Molecular dynamics (MD) simulations are performed to investigate the failure behavior of Al/Al, Al/Fe, and Al/AlFe bi-layers under high strain-rate shock loading. Additional simulations are performed to invesigate solely the tensile response of these systems and to isolate the effects of loading history on damage and failure. Specifically, the compression stage of the shock is excluded from the tensile simulations. This work shows that local structure variation, including the introduction of serrations, plays different roles in controlling damage nucleation depending on the specific loading condition. Under shock loading, the stress for void nucleation and the resulting void distribution is insensitive to an interface structure, whereas under pure tensile loading, the opposite is true, even though the strain rate is comparable. The above difference can be explained based on the corresponding change in the total deformation prior to damage nucleation under shock loading, which is missing from the pure tensile loading. Therefore, it is concluded that whether local interface structure matters under high strain-rate loading depends on the specific loading history and the stress state: the local structure variation matters only when it alters the deformation behavior, and subsequently, damage nucleation and evolution.

Associating damage nucleation and distribution with grain boundary characteristics in Ta

The effect of grain boundary (GB) characteristics (as represented by misorientation angle) on its dynamic response is investigated by sampling a large set of 185 GBs in Ta bi-crystals. These GBs encompass both ordered and disordered structures – typically referred to as metastable structures, in order to reflect the diversity in the local atomic structure observed in realistic GBs. The results reveal four distinct regimes in damage distribution and failure modes as a function of misorientation angle. The above trends also correlate with the variation in the corresponding void nucleation stress.

Characterization and micromechanical modelling of microstructural heterogeneity effects on ductile fracture of 6xxx aluminium alloys

Ductile failure of three 6xxx serie aluminium alloys has been characterized and modelled for about thirty hardening conditions each. These alloys involve relatively similar composition and volume fraction of second phase particles. The tensile mechanical properties show the expected decrease of fracture strain with increasing strength but also major differences among the different alloys with a factor ten in terms of reduction of area at fracture between best and worst case. The origin of these differences is unraveled by detailed characterization of the void nucleation, growth and coalescence process involving in situ 3D microtomography. A cellular automaton model, involving a high number of particles with distributions of position, sizes and void nucleation stress is developed to predict the fracture strain. Excellent predictions are obtained based on the same unique nucleation stress distribution versus particle size for the three alloys. The key element setting the fracture strain is the effect of particle size distribution and spatial distribution on the void nucleation and coalescence processes. The dependence of ductility on strength is properly captured as well.

Why are some Interfaces in Materials Stronger than others?

Grain boundaries (GBs) are often the preferred sites for void nucleation in ductile metals. However, it has been observed that all boundaries do not contribute equally to this process. We present a mechanistic rationale for the role of GBs in damage nucleation in copper, along with a quantitative map for predicting preferred void nucleation at GBs based on molecular dynamics simulations in copper. Simulations show a direct correlation between the void nucleation stress and the ability of a grain boundary to plastically deform by emitting dislocations, during shock compression. Plastic response of a GB, affects the development of stress concentrations believed to be responsible for void nucleation by acting as a dissipation mechanism for the applied stress.

Predicting failure stress for grain boundaries using average and local properties

Several factors can affect the failure stress of a grain boundary, such as grain boundary structure, energy and excess volume, in addition to its interactions with dislocations. In this paper, we focus on the influence of grain boundary energy, excess volume and plasticity at the boundary on the failure stress of a grain boundary, in copper from molecular-dynamics simulations. Flyer plate simulations were carried out for four boundary types with different energies and excess volumes. These boundaries were chosen as model systems to represent various boundaries observed in "real" materials. Simulations indicate that there is no direct correlation between the void nucleation stress of a boundary and either its energy and excess volume. This result suggests that average properties of grain boundaries alone are not sufficient indicators of the failure strength of a boundary. However, local boundary properties related to the ability of a grain boundary to undergo plastic deformation are better markers of its strength.

Effect of loading direction on grain boundary failure under shock loading

We investigate the effect of grain boundary inclination with respect to the loading direction on void nucleation at a boundary, using plate impact experiments on polycrystalline copper. Examination of damaged specimens reveals that boundaries perpendicular to the loading direction are an order of magnitude more susceptible to failure than those parallel to the loading direction. We investigate the mechanisms and reasons behind this experimental observation through molecular dynamics (MD) simulations, as a function of loading direction, in a copper bicrystal. Two extremes of loading directions are considered, either parallel or perpendicular to the grain boundary plane, spanning the range that grain boundaries within a polycrystalline sample will ordinarily experience under uniaxial strain conditions. Using MD simulations, we demonstrate that, during shock compression, the ability of a boundary to undergo plastic deformation is altered measurably by changing the loading direction with respect to the boundary plane. This change in the plastic response of the GB affects the development of stress concentrations believed to be responsible for void nucleation. MD simulations show that boundaries perpendicular to the loading direction do not undergo as much plastic deformation, by dislocation emission, as those parallel to the loading direction. The lack of plastic deformation at the GB, in the perpendicular loading case, can decrease the stress required for void nucleation. The MD results are consistent with experimental observations, and support the contention that plastic response of a grain boundary under shock compression can be a contributing, or even dominating, factor in determining the stress for void nucleation.

Void initiation in fcc metals: Effect of loading orientation and nanocrystalline effects

It is shown, through molecular dynamics simulations, that the emission and outward expansion of special dislocation loops, nucleated at the surface of nanosized voids, are responsible for the outward flux of matter, promoting their growth. Calculations performed for different orientations of the tensile axis, [0 0 1], [1 1 0] and [1 1 1], reveal new features of these loops for a face-centered cubic metal, copper, and show that their extremities remain attached to the surface of voids. There is a significant effect of the loading orientation on the sequence in which the loops form and interact. As a consequence, the initially spherical voids develop facets. Calculations reveal that loop emission occurs for voids with radii as low as 0.15 nm, containing two vacancies. This occurs at a von Mises stress approximately equal to 0.12 G (where G is the shear modulus of the material), and is close to the stress at which dislocation loops nucleate homogeneously. The velocities of the leading partial dislocations are measured and found to be subsonic (∼1000 m s −1). It is shown, for nanocrystalline metals that void initiation takes place at grain boundaries and that their growth proceeds by grain boundary debonding and partial dislocation emission into the grains. The principal difference with monocrystals is that the voids do not become spherical and that their growth proceeds along the boundaries. Differences in stress states (hydrostatic and uniaxial strain) are discussed. The critical stress for void nucleation and growth in the nanocrystalline metal is considerably lower than in the monocrystalline case by virtue of the availability of nucleation sites at grain boundaries (von Mises stress ∼0.05 G). This suggests a hierarchy of nucleation sites in materials, starting with dispersed phases, triple points and grain boundaries, and proceeding with vacancy complexes up to divacancies.

Damage-based finite-element modeling of tube hydroforming

Numerical simulations of straight tube hydroforming of a dual phase (DP600) advanced high strength steel were performed using a variant of the Gurson–Tvergaard–Needleman (GTN) constitutive model to account for the influence of void shape and shear on coalescence. The effect of axial-feed (end-feed) on damage development and formability is investigated for end-feed loads of zero and 133 kN. A parametric study was conducted to determine an appropriate void nucleation stress and strain and the numerical values compared with the experimental data. The calibrated GTN damage model gives good agreement with the experimentally determined burst pressure, formability and failure location with the best performance occurring for the high end-feed load.

A constitutive model for elastoplastic solids containing primary and secondary voids

In many ductile metallic alloys, the damage process controlled by the growth and coalescence of primary voids nucleated on particles with a size varying typically between 1 and 100 μm, is affected by the growth of much smaller secondary voids nucleated on inclusions with a size varying typically between 0.1 and 3 μm. The goal of this work is first to quantify the potential effect of the growth of these secondary voids on the coalescence of primary voids using finite element (FE) unit cell calculations and second to formulate a new constitutive model incorporating this effect. The nucleation and growth of secondary voids do essentially not affect the growth of the primary voids but mainly accelerate the void coalescence process. The drop of the ductility caused by the presence of secondary voids increases if the nucleation strain decreases and/or if their volume fraction increases and/or if the primary voids are flat. A strong coupling is indeed observed between the shape of the primary voids and the growth of the second population enhancing the anisotropy of the ductility induced by void shape effects. The new micromechanics-based coalescence condition for internal necking introduces the softening induced by secondary voids growing in the ligament between two primary voids. The FE cell calculations were used to guide and assess the development of this model. The use of the coalescence condition relies on a closed-form model for estimating the evolution of the secondary voids in the vicinity of a primary cavity. This coalescence criterion is connected to an extended Gurson model for the first population including the effect of the void aspect ratio. With respect to classical models for single void population, this new constitutive model improves the predictive potential of damage constitutive models devoted to ductile metal while requiring only two new parameters, i.e. the initial porosity of second population and a void nucleation stress, without any additional adjustment.

A lower bound damage-based finite element simulation of stretch flange forming of Al–Mg alloys

Numerical simulation of stretch flange forming of Al–Mg sheet AA5182 was performed using the upper and lower bound constitutive models of Gurson–Tvergaard–Needleman (GTN) and Sun and Wang, respectively. Stress and strain-controlled nucleation rules are adopted for both models. The lower bound model of Sun and Wang has been extended to include the void coalescence criterion of Tvergaard and Needleman to form the so-called Sun–Tvergaard–Needleman (STN) model. Upper and lower bound formability predictions are combined to create a predictive formability band as actual formability lies between these limits. The resulting formability predictions are compared with experimental results and an appropriate void nucleation stress and strain suggested.

Circuit-level reliability requirements for Cu metallization

Under similar test conditions, the electromigration reliability of Al and Cu interconnect trees demonstrate significant differences because of differences in interconnect architectural schemes. The low critical stress for void nucleation at the Cu and interlevel diffusion-barrier interface leads to varying failure characteristics depending on the via position and configuration in a line. Unlike Al technology, a (jL) product-filtering algorithm with a classification of separate via-above and via-below treatments is required for Cu interconnect trees. A methodology and tool for circuit-level interconnect-reliability analyses has been developed. Using data from the literature, the layout-specific circuit-level reliability for Al and dual-damascene Cu metallizations have been compared for various circuits and circuit elements. Significantly improved test-level reliability in Cu is required to achieve equivalent circuit-level reliability. Moreover, the required improvement will increase as low-k/low-modulus dielectrics are introduced, and as liner thicknesses are reduced.

Experimental characterization and modeling of the reliability of three-terminal dual-damascene Cu interconnect trees

Electromigration tests on Cu dual-damascene interconnect tree structures consisting of straight via-to-via (or contact-to-contact) lines with an extra via in the middle of the line have been carried out. Like Al-based interconnects, the reliability of a segment in a Cu-based interconnect tree strongly depends on the stress conditions of connected segments. The analytic model based on a nodal analysis developed for Al trees gives a conservative estimate of the lifetime of Cu-based interconnect trees. However, there are important differences in the results obtained under similar test conditions for Al-based and Cu-based interconnect trees. These differences are thought to be associated with variations in the architectural schemes of the two metallization systems. The absence of a conducting electromigration-resistant overlayer in Cu technology and the low critical stress for void nucleation at the Cu/interlevel diffusion barrier interface (e.g., the Cu/Si3N4 interface) leads to different failure modes between Cu and Al interconnects. As a result, the most highly stressed segment in a Cu-based interconnect tree is not always the least reliable. Moreover, the possibility of liner rupture at stressed dual-damascene vias lead to significant differences in tree reliabilities in Cu compared to Al. While an interconnect tree can be treated as a fundamental unit whose reliability is independent of that of other units in Al-based interconnect architectures, interconnect trees cannot be treated as fundamental units for circuit-level reliability analyses for Cu-based interconnects.

Probabilistic immortality of Cu damascene interconnects

We have studied electromigration short-line effects in Cu damascene interconnects through experiments on lines of various lengths L, stressed at a variety of current densities j, and embedded in different dielectric materials. We observed two modes of resistance evolution: Either the resistance of the lines remains constant for the duration of the test, so that the lines are considered immortal, or the lines fail due to abrupt open-circuit failure. The resistance was not observed to gradually increase and then saturate, as commonly observed in Al-based interconnects, because the barrier is too thin and resistive to serve as a redundant current path should voiding occur. The critical stress for void nucleation was found to be smaller than 41 MPa, since voiding occurred even under the mildest test conditions of j=2 MA/cm2 and L=10.5 μm at 300 °C. A small fraction of short Cu lines failed even at low current densities, which deems necessary a concept of probabilistic immortality rather than deterministic immortality. Experiments and modeling suggest that the probability of immortality is described by (jL2/B), where B is the effective elastic modulus of the metallization scheme. By contrast, the immortality of Al-based interconnects with shunt layers is described by (jL) if no voids nucleate, and (jL/B) if voids do nucleate. Even though the phenomenology of short-line effects differs for Al- and Cu-based interconnects, the immortality of interconnects of either materials system can be explained by the phenomena of nucleation barriers for void formation and void-growth saturation. The differences are due solely to the absence of a shunt layer and the low critical stress for void nucleation in the case of Cu.

An analysis of inclusion morphology effects on void nucleation

Deformations of a planar doubly periodic array of square elasticinclusions in an isotropically hardening elastic-viscoplastic matrixare analysed. The arrays considered have multiple inclusions per unitcell, but in each array all inclusions have the same size. Overallplane strain tension with a superposed tensile biaxial stress isimposed. A finite deformation formulation is used with a cohesivesurface constitutive relation describing the bonding between theinclusion and the matrix. A characteristic length is introduced fromdimensional considerations since the cohesive properties include thework of separation and the cohesive strength. The system analysed isused to study inclusion distribution effects on void nucleation, withthe aim of providing background for incorporating the effect ofclustering on void nucleation into phenomenological constitutiverelations for progressively cavitating plastic solids. For low valuesof the triaxiality of the imposed stress state, void nucleation occursafter extensive overall plastic straining and regular distributionshave a higher value of the void nucleation strain than randomdistributions. For larger values of stress triaxiality, where void nucleation occurs at relatively small overall plastic strains, theeffect of inclusion size dominates the effect of inclusiondistribution and smaller inclusions give rise to higher void nucleation strains. The ability of various scalar measures ofclustering to characterize the computed dependence of void nucleationon inclusion distribution is explored. Within the context of aphenomenological description of void nucleation, it is found that theeffective void nucleation stress is approximately a linear function ofthe overall hydrostatic tension with a coefficient 0.40-0.44 forregular distributions and 0.25-0.35 for random distributions.The results also suggest a possible dependence of the effective voidnucleation stress on a simple scalar measure of clustering.

Void Nucleation of Rubber Material for Seismic Isolation Due to Tension Load.

Rubber material is a most important component of seismic isolation bearing. Usually, this rubber has to be subjected to compression load, never tension because the heavy weight structure, e. g. building, is put on. Recently, the seismic isolation rubber bearing is applied to the light weight structure. On this case, the design will be considered that the bearing will be subjected to tension load because of structure tilt. Since the void nucleation due to tension affects the mechanical properties of this, it is important that the critical stress for void nucleation is to be clear. The cyclic tension tests are conducted for obtaining the variation of stress-strain relation using by thin rubber disk specimen modeled on a seismic isolation rubber bearing. After the tests specimens are cut and observed the surface configuration, especially void nucleation. Consequently, The stress-strain relation on first cyclic load has a hysteresis loop caused by void nucleation. Next, the stress distribution in the rubber disk under tension load are determined by FEM. From the comparison of experiment it is indicated that the triaxial stress is efficient for the parameter of void nucleation and the critical stress of void nucleation is determined.

Temperature-Induced Transition in Ductile Fracture Appearance of a Nitrogen-Strengthened Austenitic Stainless Steel

A nitrogen-strengthened austenitic stainless steel was tested in uniaxial tension at room temperature (295 K) and in liquid nitrogen (76 K). A transition in ductile fracture appearance from a cup-cone fracture at room temperature to shear fracture at cryogenic temperature is observed and correlated to deformation behavior and micromechanisms (void nucleation and strain localization) of fracture. The flow stresses, fracture stresses, and strain hardening rates are all higher at liquid nitrogen temperature compared to those at room temperature, and the significant increases in plastic flow stresses are accompanied by planar deformation mechanisms. At both temperatures, primary void nucleation is observed mainly at scattered, large patches of sigma phase, and initial primary void growth is associated with tensile instability (necking) in the specimen. Postuniform elongation at 295 K leads to secondary void nucleation from small, less than 1 μm in diameter, microalloy particles, leading directly to failure; the strain required for secondary void growth and coalescence is highly localized and does not contribute to macroscopic elongation. At 76 K, uniform strain increases, total strain decreases, and strain localization into shear bands between the primary voids and the surface of the neck leads directly to failure. Secondary void nucleation, growth, and coalescence are limited to shear bands and also do not contribute to the macroscopic elongation. The observations of void nucleation are characterized in terms of a continuum analysis for the interfacial stress at voidnucleating particles. The critical interfacial stress for void nucleation at the lower temperature correlates with the increased flow properties of the matrix.

The influence of nucleation criterion on shear localization in rate-sensitive porous plastic solids

The influence of the void nucleation criterion on localization in strain rate-sensitive porous plastic solids is analyzed under plane strain and axisymmetric tensile loading conditions using an infinite band model. The void nucleation process is described in terms of a void nucleation stress that depends linearly on the hydrostatic tension with a coefficient that is less than unity. Although the nucleation strain depends monotonically on the void nucleation stress coefficient, the dependence of the localization strain on this quantity is not necessarily monotonic. With the void nucleation stress coefficient fixed, there can also be a nonmonotonic dependence of the critical strain for localization on imposed strain rate.