Mechanism Of Void Growth Research Articles

Applying x-ray microscopy and finite element modeling to identify the mechanism of stress-assisted void growth in through-silicon vias

Fabricating through-silicon vias (TSVs) is challenging, especially for conformally filled TSVs, often hampered by the seam line and void inside the TSVs. Stress-assisted void growth in TSVs has been studied by finite element stress modeling and x-ray computed tomography (XCT). Because x-ray imaging does not require TSVs to be physically cross-sectioned, the same TSV can be imaged before and after annealing. Using 8 keV laboratory-based XCT, voids formed during copper electroplating are observed in as-deposited samples and void growth is observed at the void location after annealing. We hypothesize that the mechanism generating voids is hydrostatic stress-assisted void growth. Stresses in a copper-filled TSV with a pre-existing void were simulated by finite element methods. The peaks of the hydrostatic stress and its gradient are shown to be around the edge of the void. Comparing simulated results and experimental data shows that void growth in TSVs is stress-assisted: vacancies diffuse and coalesce at the void as a result of the hydrostatic stress gradient.

A compact model for early electromigration failures of copper dual-damascene interconnects

A compact model for early electromigration failures in copper dual-damascene interconnects is proposed. The model is based on the combination of a complete void nucleation model together with a simple mechanism of slit void growth under the via. It is demonstrated that the early electromigration lifetime is well described by a simple analytical expression, from where a statistical distribution can be conveniently obtained. Furthermore, it is shown that the simulation results provide a reasonable estimation for the lifetimes.

New mechanisms of void growth in Au–Al wire bonds: Volumetric shrinkage and intermetallic oxidation

This letter examines void nucleation and coalescence in Au–Al wire bonds using high-resolution transmission electron microscopy. It is found that void formation is not only attributed to Kirkendall-type migration as conventionally believed, but also due to volumetric shrinkage and intermetallic oxidation. A volumetric shrinkage of a few percent is associated with intermetallic growth and phase transformations. Intermetallic oxidation occurs at the intermetallics/alumina interface and the migration of oxygen towards the intermetallics leads to void growth and thickening of the surrounding oxide walls.

The effect of carbon nanotubes on the fracture toughness and fatigue performance of a thermosetting epoxy polymer

Multi-walled carbon nanotubes, with a typical length of 140 μm and a diameter of 120 nm, have been used to modify an anhydride-cured epoxy polymer. The modulus, fracture energy and the fatigue performance of the modified polymers have been investigated. Microscopy showed that these long nanotubes were agglomerated, and that increasing the nanotube content increased the severity of the agglomeration. The addition of nanotubes increased the modulus of the epoxy, but the glass transition temperature was unaffected. The measured fracture energy was also increased, from 133 to 223 J/m2 with the addition of 0.5 wt% of nanotubes. The addition of the carbon nanotubes also resulted in an increase in the fatigue performance. The threshold strain-energy release-rate, G th, increased from 24 J/m2 for the unmodified material to 73 J/m2 for the epoxy with 0.5 wt% of nanotubes. Electron microscopy of the fracture surfaces showed clear evidence of nanotube debonding and pull-out, plus void growth around the nanotubes, in both the fracture and fatigue tests. The modelling study showed that the modified Halpin–Tsai equation can fit very well with the measured values of the Young’s modulus, when the orientation and agglomeration of the nanotubes are considered. The fracture energy of the nanotube-modified epoxies was predicted, by considering the contributions of the toughening mechanisms of nanotube debonding, nanotube pull-out and plastic void growth of the epoxy. This indicated that debonding and pull-out contribute to the toughening effect, but the contribution of void growth is not significant. There was excellent agreement between the predictions and the experimental results.

Atomistic insights into dislocation-based mechanisms of void growth and coalescence

One of the low-temperature failure mechanisms in ductile metallic alloys is the growth of voids and their coalescence. In the present work we attempt to obtain atomistic insights into the mechanisms underpinning cavitation in a representative metal, namely Aluminum. Often the pre-existing voids in metallic alloys such as Al have complex shapes (e.g. corrosion pits) and the defromation/damage mechanisms exhibit a rich size-dependent behavior across various material length scales. We focus on these two issues in this paper through large-scale calculations on specimens of sizes ranging from 18 thousand to 1.08 million atoms. In addition to the elucidation of the dislocation propagation based void growth mechanism we highlight the observed length scale effect reflected in the effective stress–strain response, stress triaxiality and void fraction evolution. Furthermore, as expected, the conventionally used Gurson's model fails to capture the observed size-effects calling for a mechanistic modification that incorporates the mechanisms observed in our (and other researchers') simulation. Finally, in our multi-void simulations, we find that, the splitting of a big void into a distribution of small ones increases the load-carrying capacity of specimens. However, no obvious dependence of the void fraction evolution on void coalescence is observed.

Nanovoid growth in nanocrystalline metal by dislocation shear loop emission

Experimental evidence and molecular dynamics simulations of void growth indicate that dislocation shear loop emission is a viable mechanism of void growth. Based on this mechanism, a theoretical model to describe the growth of nanovoid at triple junction of nanocrystalline metal under equal biaxial remote stress is suggested. In this model, it is proposed that emission of dislocation is caused by the interaction between applied stress and image stress introduced by existing nanovoids. The critical stress is derived for emission of dislocation by considering the effects of surface stress. Within our description, dislocations emitted from surface of nanovoid are stopped at grain boundaries and the stress field generated by arrested dislocations can prevent further dislocation emission. The maximum number of dislocations emitted from surface of nanovoid, as a representation of the nanovoid growth, is analyzed as a function of grain size.

Mechanism of Void Nucleation and Growth in bcc Fe: Atomistic Simulations at Experimental Time Scales

Evolution of small-vacancy clusters in bcc Fe is simulated using a multiscale approach coupling an atomistic activation-relaxation method for sampling transition-state pathways with environment-dependent reaction coordinate calculations and a kinetic Monte Carlo simulation to reach time scales on the order of ~10⁴ s. Under vacancy-supersaturated condition, di- and trivacancy clusters form and grow by coalescence (Ostwald ripening). For cluster size greater than four we find a transition temperature of 150 °C for accelerated cluster growth, as observed in positron annihilation spectroscopy experiments. Implications for the mechanism of stage-IV radiation-damage-recovery kinetics are discussed.

Characteristics of Hot Ductility and Fracture in Micro-Alloyed Q345B Structural Steel

Hot-ductility tests of the microalloyed Q345B structural steel were performed in a tensile machine of Gleeble-1500D at different strain rates of 1.5•10-3/s 、2.5•10-3/s and 2•10-2/s and at temperature range from 1300°C to 700°C(Δ T=100°C ), which are close to the continuous casting condition of steel. Fracture surfaces were examined using a scanning electron microscope; it was found that the hot decrease as strain rate decrease, because the void growth mechanism predominates over void nucleation, giving time for nucleation cracks to grow. The minimum ductility was found at about 800°C for the strain rates of 1.5•10-3/s and 2.5•10-3/s, and the fracture was intergranular. The steel has good plasticity in temperature range from 1200°C to 900°C which is suitable for straighten operation.

Void Nucleation Model in a Steam Turbine Material under Creep Condition

In order to establish a reliable remaining life assessment method for high temperature components in thermal power plants, it is necessary to understand the internal damage mechanism in heat resistant alloys and establish the damage prediction method. In the case of commercial heat resistant alloy used for thermal plants, nucleation, growth and coalescence of creep voids are dominant damage mechanism. So far, the void growth mechanism is well investigated and various growth models are suggested. However, rational modeling of void nucleation was remained to be difficult subject because basic mechanism has been unclear. Therefore, in this study, void nucleation behavior of a turbine rotor material under creep condition was investigated by a scanning electron microscope and development of void nucleation models was examined. Void nucleation model was developed based on the idea that creep voids nucleate by vacancy condensation at the interface between precipitated carbides and matrix on the grain boundary. In addition, consideration of creep property was included in the model via a relationship between strain and vacancy density obtained from the molecular mechanics simulation. In addition, model was expanded to predict the void number density, by a statistical treatment of the different physical property related to void nucleation in the every grain boundary. It was confirmed that the present void nucleation model can reproduce evolution of void number density.

A micro mechanical study on failure initiation of dual phase steels under tension using single crystal plasticity model

Both experimental and numerical methods were employed to investigate the mechanism of failure in dual phase steels. The tensile test was interrupted in different steps to capture the mechanism of void initiation and void growth during material failure. The results can be considered as a first report for the commercial DP800 steel. Numerical simulations, which were carried out using the real micro-structure, are able to predict the void initiation in the material. In addition, through the numerical simulation a new understanding of the deformation localization was gained. Deformation localization, which causes severely deformed regions in the material, is most probably the main source of rupture in the final stages of the failure. In the SEM micrographs of the material after failure some voids are observable which can validate the results obtained by the simulation.

Microstructural effects on ductile fracture in heterogeneous materials. Part I: Sensitivity analysis with LE-VCFEM

Abstract Ductile failure of heterogeneous materials, such as cast aluminum alloys and discretely reinforced aluminums or DRA’s, initiates with cracking, fragmentation or interface separation of inclusions, that is followed by propagation in the matrix by a ductile mechanism of void nucleation and growth. Damage localizes in bands of intense plastic deformation between inclusions and coalesces into a macroscopic crack leading to overall failure. Ductile fracture is very sensitive to the local variations of the microstructure morphology. This is the first of a two part paper on the effect of microstructural morphology and properties on the ductile fracture in heterogeneous ductile materials. In this paper the locally enhanced Voronoi cell finite element method (LE-VCFEM) for rate-dependent porous elastic–viscoplastic materials is used to investigate the sensitivity of strain to failure to loading rates, microstructural morphology and material properties. A model is also proposed for strain to failure, incorporating the effects of important morphological parameters.

A numerical study of void nucleation and growth in a flip chip assembly process

In this study, we develop mathematical models and numerical simulations of void nucleation and growth induced by the chemical reaction in the flip chip package assembly process using a no-flow underfill. During the thermal assembly process, the underfill chemically reacts to the oxidation of solders I/O on the chip, achieving interconnection between chip and substrate. The chemical reaction causes a large number of voids in the thermal reflow process. The voids have been considered as a critical defect, reducing the life of the thermal reliability. This study investigates the mechanism of void nucleation and growth based on classical bubble nucleation theory and bubble dynamics, respectively. This knowledge can provide a theoretical foundation to achieve a void-free assembly process and high reliability performance.

Molecular dynamics simulations of void growth and coalescence in single crystal magnesium

The growth and coalescence of voids in magnesium single crystals at the nanoscale have been investigated using molecular dynamics simulations and the embedded atom method. One void and two void specimens with identical initial void volume fractions were utilized to study the mechanism of void growth and coalescence. In order to study the influences of material length scale on void evolution in single crystals four specimen sizes with the same initial volume fraction of voids were considered. Investigations of the effects of temperature and strain rate were also performed. Uniaxial stress–strain curves were monitored during increasing employed strain. The simulation results show that the specimen size, loading strain rate and temperature had apparent influences on the twin or dislocation pattern, void evolution shape and uniaxial stress–strain responses, but negligible effects on the initial slopes of the uniaxial stress–strain curves. Furthermore, the nucleation stress of twin bands in orientation A – x[0 0 0 1]– y[ 1 2 ¯ 1 0 ]– z[ 1 0 1 ¯ 0 ] was much higher than that of plastic deformation in orientation B – x[ 1 2 ¯ 1 0 ]– y[ 1 0 1 ¯ 0 ]– z[0 0 0 1].

Cohesive zone laws for void growth — II. Numerical field projection of elasto-plastic fracture processes with vapor pressure

Modeling ductile fracture processes using Gurson-type cell elements has achieved considerable success in recent years. However, incorporating the full mechanisms of void growth and coalescence in cohesive zone laws for ductile fracture still remains an open challenge. In this work, a planar field projection method, combined with equilibrium field regularization, is used to extract crack-tip cohesive zone laws of void growth in an elastic–plastic solid. To this end, a single row of void-containing cell elements is deployed directly ahead of a crack in an elastic–plastic medium subjected to a remote K-field loading; the macroscopic behavior of each cell element is governed by the Gurson porous material relation, extended to incorporate vapor pressure effects. A thin elastic strip surrounding this fracture process zone is introduced, from which the cohesive zone variables can be extracted via the planar field projection method. We show that the material's initial porosity induces a highly convex traction–separation relationship — the cohesive traction reaches the peak almost instantaneously and decreases gradually with void growth, before succumbing to rapid softening during coalescence. The profile of this numerically extracted cohesive zone law is consistent with experimentally determined cohesive zone law in Part I for multiple micro-crazing in HIPS. In the presence of vapor pressure, both the cohesive traction and energy are dramatically lowered; the shape of the cohesive zone law, however, remains highly convex, which suggests that diffusive damage is still the governing failure mechanism.

The role of dislocations in the growth of nanosized voids in ductile failure of metals

Dislocations are the most important element in our understanding of the mechanical response of metals. Their postulation in 1934 led to revolutionary advances in our ability to predict the mechanical behavior of materials. The authors recently advanced a dislocation mechanism for void growth in ductile metals. This paper reviews the analytical and atomistic calculations carried out in support of this model. The emission of shear dislocation loops, nucleated at the surface of nanosized voids, is responsible for the outward flux of matter, promoting void growth. This is a new paradigm in the initiation of void growth, which was attributed to convergent vacancy diffusion or to prismatic loops by others. The analytical treatment is based on the emission of a dislocation from a void in the plane along which the shear stresses are maximum. Molecular dynamics calculations performed for different orientations of the tensile axis show how the loops generate and expand outward. These loops involve the emission of partial dislocations and are the counterpart for voids of the Ashby geometrically necessary shear loops postulated for rigid particles. This process is demonstrated for bicrystalline and nanocrystalline copper.

Constraint effects on multiple void interaction in pressure sensitive plastic solids

In this work, effects of pressure sensitive yielding and plastic dilatancy on void growth and void interaction mechanisms in fracture specimens displaying high and low constraint levels are investigated. To this end, large deformation finite element simulations are carried out with discrete voids ahead of the notch. It is observed that multiple void interaction mechanism which is favored by high initial porosity is further accelerated by pressure sensitive yielding, but is retarded by loss of constraint. The resistance curves predicted based on a simple void coalescence criterion show enhancement in fracture resistance when constraint level is low and when pressure sensitivity is suppressed.

In-situ observation of electromigration failure in AlCuSi interconnects with a passivation film

In-situ observation with an optical microscope of electromigration in a widely used Al-0.5wt%Cu-1wt%Si inter- connects was conducted to study the mechanism of void formation and transportation. In the case of an interconnect covered with a passivation film, generation of voids occurred in the cathode side around a triangle shaped notch, which was introduced to be able to detect void formation. The voids accumulated in the cathode side and moved toward the cathode end. Rupture occurred in the cathode side, which was damaged by electromigration. On the other hand, in the case of an interconnect without a passivation film, generation and accumulation of voids was observed at the tip of the notch. Growth of voids was found at the tip of the notch and the rupture occurred at this damaged region. The authors analyzed the theory of void transport by electromi- gration and stress. The experimental results are in good agreement with the theoretical results and show that electromigration is significantly influenced by the stress in the interconnection. Moreover, the mechanism of void growth was discussed to consider nucleation theory.

Internal ductile failure mechanisms in steel cold heading process

The occurrence of internal ductile failure in cold-headed products presents a major obstacle in the fast expanding cold heading (CH) industry. This internal failure may lead to catastrophic brittle fracture under tensile loads despite the ductile nature of the material. Comprehensive testing and investigation methodologies were used to this work to reveal the complicated interplay of process and material parameters contributing in the initiation and propagation of internal ductile failure in six CH quality AISI steel grades. The metallurgical and microscopic investigations showed that internal ductile failure occurs progressively by void nucleation and growth mechanisms with increasing plastic strain inside the highly localized adiabatic shear bands (ASBs). The void nucleation occurs by decohesion at second-phase particles, inclusion–matrix interfaces, grain boundaries and by particle or inclusion cracking. Therefore, the number and morphology of any inclusions and second-phase particles are key factors in material formability. The metallurgical investigations showed that under compressive loading conditions, the nature of the metal flow pattern promotes different rates of material flow around the inclusions and stringers which supports decohesion and void nucleation since the early stages of deformation. At advanced stages of deformation, the metal flow pattern contributes to the ASB localization in supporting void growth and coalescence along the band leading to narrow void sheets. All tested materials in this work experienced ductile failure by void nucleation and coalescence, forming cracks along the ASBs. The ductile failure of each material was the result of the contribution of all the mechanisms of void nucleation at the inclusion–matrix interface, second phase–matrix interface and at the grain boundaries. However, the level of contribution of each mechanism in the final ductile failure varied depending on material properties and their microstructure.

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.

Model characterization and failure analysis of welded aluminium components including process history

There is currently a high level of interest in automotive and other industries to use aluminium extrusions for lightweight structural members. The preferred joining technology is robot controlled MIG welding to provide a fast, consistent, high-quality weld. The disadvantage, however, is that the high temperature fusion process causes metallurgical transformations adjacent to the weldline in the Heat Affected Zones (HAZ), which significantly reduce mechanical properties and provide lines of weakness. Under crash loading these zones are of special concern and techniques are needed to evaluate their performance. This paper investigates reduced mechanical properties in the HAZ of welded aluminium joints and proposes a failure law suitable for practical crash simulation of automotive structures. The work has necessitated a pragmatic approach in which a compromise is sought between the true representation of the void growth and fracture mechanisms that occur on a micro-scale and the need for a simplified macro-model appropriate for large scale CPU intensive structures. Simulation tools and techniques are also presented that enable the process history of the weld manufacture to be analyzed and results of the HAZ and modified mechanical properties to be mapped to the structural model for crash or failure analysis, thus limiting the need for extensive mechanical testing. Validation studies are presented on notched butt joints and dynamically loaded sectional welded joints.