Void Nucleation Rate Research Articles

Integrated model for simulating Coble creep deformation and void nucleation/growth in polycrystalline solids - Part I: Theoretical framework

This study proposes an integrated model for simulating Coble creep deformation and void nucleation/growth in a 3D polycrystalline solid. Part I of the paper provides a theoretical framework for the proposed model. A representative volume element approach is employed to predict the effects of 3D polycrystalline morphology. The model comprises two distinct but interconnected stages: deformation and void nucleation/growth. The deformation stage of the proposed model comprises two sub-models: grain boundary (GB) migration and GB diffusion. The void nucleation/growth stage is composed of three consecutive calculations: void nucleation, void growth, and postprocessing. The process simulated in the void nucleation/growth stage is driven by relative GB velocity of the respective GBFs and diffusional fluxes between adjacent GBFs, which are provided from the deformation stage. The void nucleation rate is quantified using the relative GB velocity, and the initial void size is determined based on the stability condition for void existence derived from Helmholtz free energy. The void growth rate is evaluated by the atomic diffusion on the GBF and the surface of each void.

Effect of Carbon on Void Nucleation in Iron.

The study reports the significance of carbon presence in affecting void nucleation in Fe. Without carbon, void nucleation rates decrease gradually at high temperatures but remain significantly high and almost saturated at low temperatures. With carbon present, even at 1 atomic parts per million, void nucleation rates show a low-temperature cutoff. With higher carbon levels, the nucleation temperature window becomes narrower, the maximum nucleation rate becomes lower, and the temperature of maximum void nucleation shifts to a higher temperature. Fundamentally, this is caused by the change in effective vacancy diffusivity due to the formation of carbon-vacancy complexes. The high sensitivity of void nucleation to carbon comes from the high sensitivity of void nucleation to the vacancy arrival rate in a void. The void nucleation is calculated by first obtaining the effective vacancy diffusivity considering the carbon effect, then calculating the defect concentration and defect flux change considering both carbon effects and pre-existing dislocations, and finally calculating the void nucleation rate based on the recently corrected homogeneous void nucleation theory. The study is important not only in the fundamental understanding of impurity effects in ion/neutron irradiation but also in alloy engineering for judiciously introducing impurities to increase swelling resistance, as well as in the development of simulation and modeling methodologies applicable to other metals.

Orientation-dependent multi-spall performance of monocrystalline NiTi alloys under shock compression

The primary objective of this work was committed to large-scale non-equilibrium molecular dynamics modeling for the investigation on multiple spall performance, microstructural evolutions, and melting state of NiTi alloys along three typical crystal orientations. We discovered that there was a single-wave structure present in the [100] orientation, whereas elastic-plastic two-wave structures were found in [110] and [111], exhibiting a significant anisotropy in elastic-plastic wave velocity. Compared to [110] and [111] orientations, multi-spallation was more likely to be generated in the [100] direction. During accumulative dynamic damage, there was also a strong sensitivity of void evolution to orientation. For [100], voids tended to be densely distributed in the material and exhibited a strip-shaped manner. In contrast, a more scattered void distribution was observed for the other two orientations, showing a flaky pattern. Interestingly, dislocations in the spall region were almost annihilated before approaching void nucleation. According to void statistics, the peak number of voids, void nucleation rate, and spall region size were identified to be in a good uniformity along [110], [100], and [111]. For all the cases, the samples experienced partial melting in the released state and were followed by a recovery of structural order degree. However, there was an insignificant anisotropy in the melting state for each crystal orientation during multi-spallation.

Microstructural evolution in doped high entropy alloys NiCoFeCr-3X (X=Pd/Al/Cu) under irradiation

Commonly studied equatomic single-phase FCC high entropy alloys based on 3d transition metals like NiCoFeCr do not provide adequate strength and radiation resistance at high doses for nuclear structural applications. In the current study, the major alloying effects like lattice distortion, ordering and clustering tendencies were investigated by adding low concentration of Pd, Al, or Cu respectively to study the doping effects on the ion irradiation response of NiCoFeCr alloy. The alloys were irradiated with 3 MeV Ni2+ ions at 500 °C to a fluence of 1 × 1017/cm2 at a beam flux of approximately 2.8 × 1012 ions/cm2/s. The microstructural evolution upon irradiation i.e., formation of dislocation networks, radiation induced segregation and precipitation, and void formation were studied in detail. Post-irradiation characterization results showed that a Pd addition leads to a high void nucleation rate but controlled void growth, which may be attributed to increased lattice distortion. In Al added HEA, our microstructural analysis indicates that radiation induced ordered L12 precipitates do not affect void swelling significantly. Cu addition led to Cu precipitation that drastically suppressed dislocation density and void swelling of the alloy. Additionally, a model was developed to qualitatively describe the trend in void swelling of typical FCC alloys under ion irradiation. This model was able to qualitatively explain the suppression and reappearance of void swelling in ion irradiated alloys that generally occurs near the region with peak implanted ion concentration.

Coupling effect between electromigration and joule heating on the failure of ball grid array in 3D integrated circuit technology

Ball Grid Array (BGA) packaging method has been widely used in microelectronic devices, and electromigration (EM) in BGA is a crucial reliability issue, determining the performance of the products. Herein, we report a new failure mode induced by a coupling effect of EM and Joule heating in BGA structure. The test sample consists of a roll of 500 μm-BGA solder joints with upper and lower Cu under-bump-metallization (UBM) of different thicknesses, 16 μm, and 68 μm, respectively. Open failures of the thinner cathodic Cu UBM at the contacting area with solder joint were observed under four different EM conditions (130 °C-3000 A/cm2, 160 °C-2300 A/cm2, 160 °C-3000 A/cm2, and 160 °C-4600 A/cm2). Infrared (IR) results reveal the temperature at the thinner Cu UBM is higher than that in the solder joint as well as at the thicker Cu UBM. Simulation results elucidate the current density at the contacting area is about 22 times higher than the average density in the solder joint, so the effect of current crowding can be very serious in the failure site. Furthermore, severe current crowding and Joule heating promote the nucleation rate of voids at the joint location, which can further increase the current density and temperature, leading to a positive feedback effect until an open failure occurs in the circuitry. Our analysis enables the discussion of a coupling failure mode of EM and Joule heating in BGA, and provides a valuable guide of device design against EM failure in consumer electronic products.

Computational modeling of tension behaviors of metal matrix composites with particle network architecture

Rigid powders as the second phase in the conventional metal matrix composites (MMCs) are usually uniform and random, but recently powders dispersed with some special architectures to form configuration composites would yield a remarkable enhancement in the stiffness, strength and toughness as well. In this work, FE investigation was performed on tension behaviors of MMCs with network architectures to understand their dependences on particle volume fraction, particle size, network thickness and morphology. With the aid of the Gurson’s porous metal plasticity theory, the void nucleation rate acted as an internal state variable to monitor the development of micro-cracks in the metal matrix. The impedance effect of particle network architectures on the propagation of micro-cracks was interpreted in stark contrast to that in uniform MMCs, whereby their particular strengthening and toughening mechanisms were clarified. The present study would be helpful to the guidance in designing advanced MMCs with superior comprehensive properties.

On the theory of void nucleation in irradiated crystals

The theory of void nucleation in irradiated materials is critically analysed and further developed. It is shown that the existing theory overestimates the rate of empty void nucleation in ion-irradiated steels by several orders of magnitude and therefore requires revision for an adequate interpretation of ion bombardment tests. To extend the nucleation model to the conditions of reactor neutron irradiation, it is modified to take into account the effect of void stabilisation by transmutation gas (He) in steels or by fission gases (Xe, Kr) in fuels. It is shown that the presence of gas atoms in a solid solution strongly reduces the free energy of void formation, but does not affect the number of void nucleation sites, which is determined by the concentration of vacancies in the irradiated material. The model developed for nucleation of small gas filled voids (bubbles) is further modified to adequately consider their further growth, stabilisation (due to athermal resolution of gas atoms) and generation of a new population of larger bubbles. The obtained analytical expression for the nucleation rate is applied to a simplified analysis of experimental data on neutron irradiation of stainless steel in PWRs and FRs. For a more accurate analysis of these tests, it is recommended to implement the new model in a fuel performance code, additionally taking into consideration the migration and coalescence of small bubbles.

Dislocation-dominated void nucleation in shock-spalled single crystal copper: Mechanism and anisotropy

Large-scale molecular dynamics simulations are conducted on single crystal copper along eight representative orientations to investigate dislocation-dominated void nucleation during shock loading and spall failure, including mechanisms and anisotropy. Spall strength estimated from free surface velocity decreases in the order of group I ([001]), group IV ([012] and [011]), group III ([122] and [123]) and group II ([114], [112] and [111]), respectively, in good agreement with anisotropy of spall strength in previous experiments and simulations. A lower spall strength is statistically associated with a higher void nucleation rate and a higher density of stable immobile dislocations (1/6〈110〉 and 1/3〈100〉) formed before void nucleation. Stable immobile dislocation plays a key role in void nucleation. The formation of stable immobile dislocations requires three conditions: high resolved shear stress for activating mobile dislocations, two or more main slip planes for dislocation reaction, and high angle between activated slip directions for high stability of immobile dislocations. Based on crystal elastic–plastic theory, resolved shear stress on all slip systems is calculated to analyze orientation effects on the three conditions. The three conditions can be fulfilled by group II orientations, but cannot by group I, III, and IV orientations, leading to anisotropy in void nucleation and spall strength.

The Modified Void Nucleation and Growth Model (MNAG) for Damage Evolution in BCC Ta

A void coalescence term was proposed as an addition to the original void nucleation and growth (NAG) model to accurately describe void evolution under dynamic loading. The new model, termed as modified void nucleation and growth model (MNAG model), incorporated analytic equations to explicitly account for the evolution of the void number density and the void volume fraction (damage) during void nucleation, growth, as well as the coalescence stage. The parameters in the MNAG model were fitted to molecular dynamics (MD) shock data for single-crystal and nanocrystalline Ta, and the corresponding nucleation, growth, and coalescence rates were extracted. The results suggested that void nucleation, growth, and coalescence rates were dependent on the orientation as well as grain size. Compared to other models, such as NAG, Cocks–Ashby, Tepla, and Tonks, which were only able to reproduce early or later stage damage evolution, the MNAG model was able to reproduce all stages associated with nucleation, growth, and coalescence. The MNAG model could provide the basis for hydrodynamic simulations to improve the fidelity of the damage nucleation and evolution in 3-D microstructures.

A microstructural and damage investigation into the effect of coiling temperature on the low temperature impact behaviour of an HSLA structural steel

ABSTRACT An HSLA grade of structural steel was hot rolled using a coiling temperature of 500°C (CT500) or 540°C (CT540). As expected, the lower coiling temperature resulted in a more refined ferrite grain structure and a more dispersed distribution of smaller pearlite grains and carbides which formed along grain boundaries. Instrumented Charpy V-notch (CVN) tests were conducted and the CT500 material resulted in a higher ductile-brittle transition temperature, which was unexpected for the more refined microstructure. Damage evolution was characterized from the tested CVN specimens and revealed that a higher initial void/inclusion content for CT500 resulted in elevated void area fraction and void density values near the fracture surface of this material. Also, the refined distribution of carbides contributed to the higher void nucleation rate of CT500, which ultimately reduced the low temperature impact performance of this material.

Homogenized Modeling of Anisotropic Impact Damage in Rolled AZ31B with Aligned Second-Phase Particles

Magnesium is attractive for ballistic applications due to its high specific strength, but is not widely used due to its lower ductility as compared to other traditionally used materials (e.g. aluminum, titanium, and steel). Additionally, the behavior of magnesium is highly complex and is not well understood due to its HCP crystal structure and significant anisotropy. This work builds on direct numerical simulations (DNS) of rolled AZ31B magnesium with explicitly modeled second-phase particles subject to high strain rate uniaxial tension. The second-phase particles are preferentially aligned along the rolling direction, which induces anisotropies in void nucleation rates and void coalescence as a function of loading orientation. We propose a straightforward approach to account for these damage anisotropies in an anisotropic extension of the Gurson–Tvergaard–Needleman (GTN) homogenized damage model. The resulting anisotropic GTN model is calibrated against the uniaxial tension stress–strain responses predicted from DNS calculations for seven different loading orientations. The calibrated anisotropic GTN model is utilized to probe orientation effects in ballistic simulations. Two ballistic cases are conducted: (i) magnesium plate impacted with a steel sphere and (ii) magnesium plate impacted with a steel plate. The results quantify the degree to which preferential alignment of second-phase particles degrades the ballistic performance along the normal direction. This degradation is significant for a spherical impactor case, but fairly insensitive under plate impact. Consequently, the spall strength of rolled AZ31B is fairly insensitive to particle alignment.

Free volume and internal structural evolution during creep in model amorphous polyethylene by Molecular Dynamics simulations

All-atom Molecular Dynamics (MD) simulations were employed to investigate the structural and free volume evolution (correlated with damage) during creep of model amorphous polyethylene (PE) at various applied stress states (tension, shear, compression), stress levels (10–200 MPa), and temperatures (175–325 K). The Modified Embedded-Atom Method for saturated hydrocarbons is applied to show that the phenomenological macroscale creep response of PE can be captured through MD simulations. The model adequately predicts the three classical stages of creep (primary, secondary, and tertiary) and provides detailed insight into the underlying molecular mechanisms. The calculated glass transition temperature (Tg) was found to be very close to the experimental Tg. Simulations were performed at temperatures below Tg (175 K) to above Tg (325 K) and demonstrate that the transition from glassy to rubbery state is reflected in the chain dynamics and damage evolution. Under all the stress states and temperatures simulated, the evolution of void volume, nucleation, growth, and coalescence are shown to directly correlate with specific stages of the creep response and the underlying chain dynamics within each stage. A correlation between the steady-state creep rate and steady-state void nucleation rate is found, suggesting that secondary creep is heavily driven by void nucleation, while tertiary creep is driven by void growth and coalescence.

Using micro-computed tomography and scanning electron microscopy to assess the morphological evolution and fractal dimension of a salt-gypsum rock subjected to a coupled thermal-hydrological-chemical environment

Abstract It is well known that salt-gypsum evaporites play a significant role in controlling the physio-mechanical performance of the earth's upper mantle as well as forming extensive “halokineticˮ structures that are directly linked to lithologic hydrocarbon reservoirs and petroleum accumulation. Under many geological conditions, hot saline groundwater frequently intrudes into salt-gypsum evaporite sequences. However, relatively little is known regarding the micromechanical behaviour of salt-gypsum in these saline environments, and this behaviour governs the macro-mechanical behaviour and the overall deformation. In this study, we examine the microstructural evolution of salt-gypsum and its weakening mechanisms under varied brine conditions (or coupled thermal-hydrological-chemical environments). A series of laboratory tests, including scanning electron microscopy and micro-computed tomography (MCT), were conducted to study how the petrographic characteristics, including porosity, pore size distribution and fractal dimension, evolved. In total, 81 specimens were prepared and then soaked in brines of 3 different concentrations and at 3 different temperatures. The results showed the following: 1) after brine treatment, the MCT slices of the specimens generally contained four areas: a residual porous skeleton area, an undissolved area, a cracked area and an interface area. 2) For a given concentration, the porosity and fractal dimensions of the specimens gradually increased with temperature, while for a given temperature, the porosity and fractal dimension tended to decrease as the brine concentration increased. 3) Because the nucleation or initiation rate of new voids was slower than the growth and coalescence rate of the original voids, the proportion of 0–1 μm pores gradually decreased over time. However, the proportion of 5 to + ∞ μm pores gradually increased over time. To study the effects of each factor and the interactions between them on the response variables (porosity and fractal dimension), 2 × 2 and 2 × 3 factorial designs were employed to assess the brine concentrations and temperatures. The results verify that the water temperature significantly weakened the salt-gypsum, while the chlorine ions had a much weaker effect.

Damage identification parameters of dual-phase 600–800 steels based on experimental void analysis and finite element simulations

In this work, the damage behavior of cold-rolled zinc-coated dual-phase steel sheets 600 and 800 grades was evaluated by means of standard uniaxial tensile testing, microstructural characterization and finite element modeling. The void formation in both steels was investigated as a function of the plastic strain level from digital image processing of scanning electron micrographs to quantify the average void size and to determine the corresponding measures of void density, void area fraction and void aspect ratio. Based on the void analysis and the experimental uniaxial tensile test data, a four-step procedure is proposed to identify the parameters of the Gurson–Tvergaard–Needleman (GTN) damage model. Bearing in mind the non-uniqueness of the GTN model parameters, 3D finite element simulations using a single element and an 1/8 symmetry uniaxial tensile specimen model were performed in a systematic manner to investigate the role of both nucleation and failure parameters on the uniaxial behavior. At low straining levels, most of the void initiated by debonding of globular aluminum-oxide inclusions identified by EDS in both dual-phase steels. At higher straining levels, the void density evolution is found to be more pronounced in DP600 steel owing to the faster void nucleation rate at the ferrite grain boundaries. A good agreement between predictions and experimental load-elongation is achieved allowing for the identification of the full set of GTN damage model parameters of both DP600 and DP800 steels. The proposed damage calibration of dual-phase steels can be very helpful in simulations of practical sheet metal forming processes.

Deformation, diffusion and ductility during creep – continuous void nucleation and creep-fatigue damage

It is shown that the assumption of unit (negative) slope in the well known Monkman–Grant plot of time to failure against minimum creep rate is too restrictive. By acknowledging observed slopes in the range 0.8–1, a ductility–strain-rate relation is deduced where ductility decreases with reducing strain rate. This in turn has implications for the ductility exhaustion method as applied during stress relaxation in the dwell period of low cycle fatigue tests of austenitic steels at elevated temperature. The simple method is used to calculate the cyclic creep damage in typical tests on austenitic steels in the region 550–650 °C and is compared to other calculations as employed in the R5 high temperature assessment procedure. The assumption of a uniform nucleation rate of grain boundary voids with creep strain goes some way to predicting the slope of the ductility–strain-rate relation. Both the ‘unconstrained’ and ‘constrained’ (lower shelf) regions of void growth are discussed.

Impact specimen geometry on T23 and TP347HFG steels behaviour during steam oxidation at harsh conditions

Ferritic T23 steel and austenitic TP347HFG steel have been studied with an emphasis on understanding the impact of specimen geometry on their steam oxidation behaviour. The selected materials were tested over a wide range of temperatures from 600 to 750°C. The tests were carried out in 100% steam conditions for 1000 hours. The tests indicated that the ‘curved-shaped’ specimens show slower mass gain, scale ticking and void nucleation rates than ‘bridge-shaped’ specimens (with flat and convex surfaces combined). Furthermore, a bridge TP347HFG sample showed the formation of lower amount of flaky oxide at 750°C.

Ductile damage model for metal forming simulations including refined description of void nucleation

We address the prediction of ductile damage and material anisotropy accumulated during plastic deformation of metals. A new model of phenomenological metal plasticity is proposed which is suitable for applications involving large deformations of workpiece material. The model takes combined nonlinear isotropic/kinematic hardening, strain-driven damage and rate-dependence of the stress response into account. Within this model, the work hardening and the damage evolution are fully coupled. The description of the kinematics is based on the double multiplicative decomposition of the deformation gradient proposed by Lion. An additional multiplicative decomposition is introduced in order to account for the damage-induced volume increase of the material. The model is formulated in a thermodynamically admissible manner. Within a simple example of the proposed framework, the material porosity is adopted as a rough measure of damage.A new simple void nucleation rule is formulated based on the consideration of various nucleation mechanisms. In particular, this rule is suitable for materials which exhibit a higher void nucleation rate under torsion than in case of tension.The material model is implemented into the FEM code Abaqus and a simulation of a deep drawing process is presented. The robustness of the algorithm and the performance of the formulation is demonstrated.

Enhanced Electromigration Resistance of Pb-Free Solders by Using Cu/Sn Composite Structure

This study employs a unique composite structure consisting of alternating Cu/Sn columns with different spacing to realize the electromigration resistance in Pb-free solders. Pure Sn and Cu/Sn composite structures were designed and current stressed by 1 × 104 A/cm2 at 80°C. The results show that the samples with a composite structure exhibited better electromigration resistance than those with a pure Sn structure. In addition, no void formation and no hillock appeared in the Cu/Sn composite structures with 20 μm of Cu column specimen after electromigration test for 1600 h. We proposed that this improved electromigration resistance in the composite samples is mainly because the current density in the current crowding region of Sn was reduced and the rate of void nucleation in the composite samples was effectively hindered by the introduction of Cu columns. Moreover, the void propagation rate was also lowered as a result of the better electromigration resistance of Cu columns.

Plastic behavior of aluminum in high strain rate regime

The aim of this experiment was to study the plastic response of Al to dynamic loading at high strain rates. Dynamic loading was applied by direct laser ablation of the sample with pulse width of 3 ns long. The free surface velocity histories of shock loaded samples, 60-310 μm thick at room temperature, and 150 μm thick with initial temperature from 293 to 893 K, have been recorded using a line velocity interferometer for any reflections (VISAR) system. The line VISAR could measure free surface velocity profile with high temporal resolution (∼100 ps). The measured amplitudes of the elastic precursor waves have been approximated by power functions of the propagation distance with the power index of 0.581, and these data have been converted into relationships between the shear stress at Hugoniot elastic limit and the initial plastic strain rate. The peak longitudinal elastic stress and the strain rate meet a power law dependency with the power index of 0.44. Samples were recovered for post-shot metallographic analysis. The metallographic analysis leads to the conclusion that the spall strength of preheated aluminum is determined more by the rate of void nucleation rather than its growth.

On the Use of Infrared Thermography for Analysis of Fatigue Damage in Ti6Al4V-Welded Joints

The present work is aimed at comparatively studying fatigue damage evolution of a pulsed Nd:YAG laser beam-welded (LBW) joint and the base metal (BM) of Ti6Al4V alloy subjected to cyclic loading. To reveal crack nucleation and propagation during the fatigue process, in situ fatigue was generated using infrared measurement methods. The results indicate that the rate of damage accumulated in the LBW joint was higher than in the BM specimens during a fatigue test, which decreased the fatigue life of the LBW joint. This observation is attributable to the LBW joint fusion zone microstructure, which has a higher void nucleation and growth rate compared with the BM microstructure.