Void Evolution Research Articles

Computational simulation of voids formation and evolution in Kirkendall effect

An important phenomenon of Kirkendall effect is the presence of voids that formed during diffusion, which may crack the mechanical properties. In this paper, a cellular automaton (CA) based model is developed to simulate the voids formation and evolution process of Kirkendall effect. Firstly, this paper derives the critical radius of voids nucleation and the nucleation rate. Secondly, this paper derives the growth rate of Kirkendall voids, and the relationship between the movement of interface plane and the growth rate of voids. According to the formulas derived from this paper, the number of voids and the average radius of voids can be inferred by observing the shift velocity of interface plane between the different metals. Theoretical analysis is helpful for the fundamental understanding of the underlying mechanisms of Kirkendall voids, and is helpful for the study on suppressing the formation of Kirkendall voids. Thirdly, this paper presents a numerical simulation on Kirkendall voids formation and evolution process based on cellular automaton, which provides an intuitive visual process of Kirkendall voids growth and the movement of interface plane.

From suppressed void growth to significant void swelling in NiCoFeCr complex concentrated solid-solution alloy

Void swelling can result in dimensional instability and undermine the safe operation of nuclear reactors. Current strategies to inhibit void swelling mainly focus on enhancing defect absorption and recombination by introducing high-density defect sinks. Complex concentrated solid-solution alloys (CSAs), including high-entropy alloys, can withstand severe radiation damage due to their inherent chemical complexity without interfaces. However, the underlying mechanisms for void suppression in CSAs are far from clear. In this research, we studied the void evolution with respect to irradiation depths, doses, and temperatures in equiatomic NiCoFeCr under 3 MeV Ni ion irradiations. At relatively low doses (16 and 54 displacements per atom, dpa), voids form mainly outside of the ion-damaged region, and void formation in the peak damage region is suppressed, leading to negligible swelling. However, with further increase of dose (86 up to 250 dpa), significant void growth occurs in the peak damage region and extended dislocation lines dominate instead of short dislocation lines and loops formed at lower doses. From 500 to 700 °C, the dislocation density decreases while dislocations grow. Although the overall void swelling increases dramatically from 500 to 580 °C at 54 dpa, void growth in the peak damage region is still suppressed. The transition from suppressed void growth to significant void swelling is attributed to dislocation evolution and local chemical inhomogeneity (enrichment of Fe/Cr in the matrix) at higher doses. Our study shows that controlling element diffusion and defect evolution through tuning chemical complexity can further enhance the swelling resistance of CSAs.

Semi-Implicit Numerical Strategy for Implementing a Nonlocal Finite-Deformation Gurson Model for Glassy Polymer Using Finite Element Analysis

Post-peak strain softening for some thermoplastic resins often leads to localized deformation with plastic flow instability, spurious energy dissipation, and numerical solutions with mesh dependency using finite element analysis (FEA) due to the lack of a length scale. This paper introduces the nonlocal integral theory with a length scale into the Gurson model to capture objective void evolution and shear bands for glassy polymer under quasi-static loading. Nonlocal numerical technique using the finite-deformation Gurson model is developed, where the nonlocal implicit stress return algorithm and the nonlocal consistent tangent stiffness are presented in the corotational configuration by performing nonlocal averaging on the void volume fraction in a semi-implicit way. The numerical strategy is implemented by combining the finite element software ABAQUS-UMAT, USDFLD, and UEXTERNALDB subroutines. For plane tension problem, the developed nonlocal numerical technique circumvents mesh dependency well by studying the void growth, the evolution of shear bands, and the load responses.

Effect of MnS inclusions on plastic deformation and fracture behavior of the steel matrix at high temperature

The effect of MnS inclusions on the plastic deformation and fracture behavior of a steel matrix at high temperature was studied. The macroscopic mechanical properties of the material were analyzed using high-temperature uniaxial tensile testing. Numerical simulations were performed by combining the response surface method and finite element simulations. The Gurson–Tvergaard–Needleman damage parameters and the void growth accelerating factor (k) were obtained at different temperatures. Through the fracture analysis and microstructure analysis of the samples at different temperatures, the reasons that affect the macro mechanical properties of the materials are obtained. At 900 °C–1200 °C, there was a large difference in strength and toughness between steels with and without MnS inclusions. The strength of the materials was determined by both the stress intensification caused by the MnS inclusions and stress softening due to dynamic recrystallization (DRX). The plasticity of the materials was jointly determined by the MnS inclusions promoting void initiation and growth, and the DRX inhibiting void growth and coalescence. Moreover, the accelerating factor of void growth (k) reflected the comprehensive effect of MnS and temperature on the evolution of voids in the matrix.

Pseudo-elastic cavitation model: part I\u2014finite element analyses on thin silicone adhesives in fa\xe7ades

This study investigates the structural behavior of adhesive bonds of glass and metal using thin, structural silicones in heavily constrained applications. This special type of connection may lead to triaxial stress conditions under axial loading, which can lead to dilatation failure due to the abrupt growth of cavities (cavitation effect). Cavitation failure leads to significant stress softening and loss of stiffness; however, it increases connection’s ductility. These material deformations should be considered when designing glass-metal connections. Therefore, a constitutive model is developed to account for cavitation in hyperelastic materials. The volumetric component of the model is equipped with a non-linear Helmholtz free energy function that accounts for isotropic void growth under hydrostatic loading. An energy coupling term is then added that numerically explicates strain energy under isochoric deformation, while also guaranteeing physical material behavior. The energy contribution is calculated internally by analysing the geometric evolution of inherent voids. The extended volumetric–isochoric split enables one to numerically calculate heavily constrained silicone joints under arbitrary deformation modes. Three-dimensional finite element calculations on uniaxial tension, bulge, and pancake tests validate the constitutive model. All experiments could be validated with one set of material parameters through numerical simulations. The numerical calculations were robust and efficient without any underlying mesh dependencies.

A New Electron Backscatter Diffraction-Based Method to Study the Role of Crystallographic Orientation in Ductile Damage Initiation

The third generation of advanced high strength steels shows promising properties for automotive applications. The macroscopic mechanical response of this generation can be further improved by a better understanding of failure mechanisms on the microstructural level and micro-mechanical behavior under various loading conditions. In the current study, the microstructure of a multiphase low silicon bainitic steel is characterized with a scanning electron microscope (SEM) equipped with an electron backscatter diffraction detector. A uniaxial tensile test is carried out on the bainitic steel with martensite and carbides as second phase constituents. An extensive image processing on SEM micrographs is conducted in order to quantify the void evolution during plastic deformation. Later, a new post-mortem electron backscatter diffraction-based method is introduced to address the correlation between crystallographic orientation and damage initiation. In this multiphase steel, particular crystallographic orientation components were observed to be highly susceptible to micro-void formation. It is shown that stress concentration around voids is rather relaxed by void growth than local plasticity. Therefore, this post-mortem method can be used as a validation tool together with a crystal plasticity-based hardening model in order to predict the susceptible crystallographic orientations to damage nucleation.

Temperature-induced nanostructural evolution of hydrogen-rich voids in amorphous silicon: a first-principles study.

The paper presents an ab initio study of temperature-induced nanostructural evolution of hydrogen-rich voids in amorphous silicon. By using large a-Si models, obtained from classical molecular-dynamics simulations, with a realistic void-volume density of 0.2%, the dynamics of Si and H atoms on the surface of the nanometer-size cavities were studied and their effects on the shape and size of the voids were examined using first-principles density-functional simulations. The results from ab initio calculations were compared with those obtained from using the modified Stillinger-Weber potential. The temperature-induced nanostructural evolution of the voids was examined by analyzing the three-dimensional distribution of Si and H atoms on/near void surfaces using the convex-hull approximation, and computing the radius of gyration of the corresponding convex hulls. A comparison of the results with those from the simulated values of the intensity in small-angle X-ray scattering of a-Si/a-Si:H in the Guinier approximation is also provided, along with a discussion on the dynamics of bonded and non-bonded hydrogen in the vicinity of voids.

Radiation-Induced Swelling and Precipitation in Fe ++ Ion-Irradiated Ferritic/Martensitic Steels

The radiation responses of two newly developed ferritic/martensitic steels, FC92-B and -N, were tested in comparison to reference alloys HT9 and Gr.92. Ion irradiations on the steels were performed up to 480 dpa at 475 °C using 3.5-MeV Fe++ ions with a helium pre-implantation of 1 appm/dpa. Void swelling and M2X precipitation were characterized using FE-TEM and EDS. Swelling resistance was the greatest in FC92-N, which showed suppressed void nucleation and growth. The swelling rate in FC92-N was determined as 0.007 %/dpa, indicating that FC92-N did not reach the steady-state swelling regime with void nucleation behavior. The least swelling-resistant alloy was HT9 with a swelling rate of 0.038 %/dpa. Cr-rich carbide, M2X, was observed in only 9Cr-FC92 series; however, its formation did not depend on radiation damage. This exceptional M2X evolution in FC92 series may be attributed to B and N alloying, which resulted in suppressed M23C6 carbide formation during metallurgical production and sequentially high C contents in the alloy solution of FC92 series. A narrower range (800 nm) of M2X evolution compared to that of cavity formation (1,000 nm) indicates that radiation-induced precipitation (RIP) is sensitive to the injected interstitial effect. Precipitation-induced Cr depletion and preferential interstitial outward sinking to the free surface synergistically modified local chemical composition before void evolution and led to double-peak swelling by locally forming a low-alloyed zone. This study provides the first experimental evidence that RIP modifies the swelling–depth profiles and in turn, determines double-peak swelling in ion-irradiated steels.

Prediction of Ductile Damage in the Process Chain of Caliber Rolling and Forward Rod Extrusion

Many metal forming processes involve several steps, which influence the shape and properties of the final component. The previous manufacturing process of the semi-finished component influences the properties of extruded components. The authors analyze the evolution of damage and voids in the sequence of caliber rolling to cold forward rod extrusion. The analysis is performed with the help of a variant of the Lemaitre model, microstructural analysis of the void area fraction and density measurements. The numerical analysis of this process chain makes use of a fully three-dimensional simulation approach. Even though the damage distribution is non-axisymmetric in caliber rolling, the distribution is almost axisymmetric after cold forward extrusion. The shoulder opening angle in extrusion is varied to compare model predictions with experiments. The decrease in density is largest for the largest shoulder opening angle and smallest for the smallest shoulder opening angle. The simulations agree qualitatively well with the experiments in term of the measured void area fraction and the density changes. The quantitative comparison reveals differences of one to two orders of magnitude.

Semi In-Situ Observation on Void Formation in Electromigrated Sn-Ag Film and its Prediction by Random-Walk Simulation

In this study a thin metallic film composed of Sn-3.5Ag (wt.%) was subjected to a current density of 7.77×104 A/cm2 at room temperature, in order to test the ability of existing models of electromigration (EM) to predict the nucleation and evolution of voids generated by the resulting atomic migration. The computer simulation used to compute the coupled current distribution, thermal distribution and atomic migration problems relied on a Random Walk (RW) method that has not previously been applied to this problem but is particularly well suited to modelling a domain which is undergoing changes due to the formation of voids. Comparison of the experimental results and computer simulations provide proof of concept that the RW method can be successfully applied to this class of problem, but also that imperfections in the film can lead to deviations from the predicted patterns.

In situ observation of void evolution in 1,3,5-triamino-2,4,6-trinitrobenzene under compression by synchrotron radiation X-ray nano-computed tomography.

The formation and development of voids in 1,3,5-triamino-2,4,6-trinitrobenzene crystals under compression were characterized in situ by X-ray nano-computed tomography. Benefiting from high spatial resolution (30 nm) and excellent imaging contrast, the X-ray nano-computed tomography images revealed the presence of a small fraction of inhomogeneous structures in the original crystal (volume ratio ∼1.2%). Such an inhomogeneity acts as a nucleation of voids and produces stress concentration during compression, which leads to continuous growth of the voids under loading. Meanwhile, the results further reveal that the developing voids are not isotropic: voids with higher surface roughness and irregular structures are easier to break and form new micro-voids. These new voids with higher irregular structures are weaker and easier to break into smaller ones compared with the originals, leading to the development of voids along these weak zones. Finally large voids form. The experiments allow direct investigation of void formation and development, which helps in studying the mechanisms of void development and energetic materials deterioration during manufacturing and transporting.

Structural and mechanical properties of densified (Li2O)0.2(SiO2)0.8 glasses: A molecular dynamics simulations study

Molecular dynamics (MD) simulations have been carried out to study the structural and mechanical properties of densified (Li2O)0.2(SiO2)0.8 glasses under uniaxial tension. Fractions of SiOx(x = 4−6) and LiOy(y = 3−8) units change with the density. There is a relationship between the changes in Qn species and in SiOx unit with increasing density. The sample of 2.28 g cm−3 exhibits brittle behavior, at which fraction of SiO4 units is almost maintained and the breakages of LiO bonds cause the transformation of LiOy units from higher- to lower- fold Li coordination. Big-voids are formed during the tension process. LiO voids play important roles in the evolution and coalescence of voids causing the crack propagation. The densified samples of 2.96 and 3.81 g cm−3 exhibit ductile behavior, at which the transformations of SiOx and LiOy occur. Shear transformation zones (STZs) and shear bands (SBs) are formed during plastic deformation.

Damage-induced performance variations of cold forged parts

Abstract Forming processes play a key role in the manufacturing of metal components. They allow for the economical production of geometrical shapes with reproducibly high quality. Strain hardening and residual stresses affect the performance of the produced parts. These factors are controllable and can even be utilized to increase the performance of the component. This, however, does not apply to damage. Damage in metals describes the decrease of the load-bearing capacity due to the appearance and evolution of voids. The aim is to analyse, predict, and control the evolution of damage in cold forging, to allow for a production of cold forged components with a defined, load-adapted performance. It was investigated numerically to what extent the load path, which is responsible for the damage evolution, is affected in cold forging. Subsequently, the effect of load path changes on the product performance was determined experimentally in the region of the central axis where the load path is affected most by the extrusion parameters. Hereby, a correlation between the occurring triaxiality during forming and the product performance by means of number of cycles to failure in multi-step fatigue tests, impact energy and Young’s modulus was observed.

A viscoplastic model for void growth under dynamic loading conditions

We present a dynamic theoretical viscoplastic model of voids subjected to external dynamic tensile loadings. The material viscosity and temperature are factors that are considered in the dynamic evolution of voids in viscoplastic materials. We focus on the thermal effect; the temperature affects the thermal softening of the material strength and also the material viscosity. Viscous flow is the dominant growth mechanism under high stresses and rates based on the results of the calculations for dynamic void growth predictions. The factors are independently studied, and the correlations are systematically analyzed.

A void evolution-based damage model for ductile fracture of metallic materials

A modified damage model is developed for describing ductile fracture of metallic materials by introducing damage variables with respect to porosity. Based on the geometric characteristics of the void deformation process, modified governing equations of void evolution are proposed to reduce the dependence of micro parameters. A transformed variable is introduced to incorporate the porosity into continuum damage mechanics. The numerical predictions are compared with experimental results for AISI-1095, AISI-1090 and AISI-1045 steel.

Shock deformation and spallation of Cu bicrystals with (1 1 1) twist grain boundaries

The shock deformation and spallation of Cu bicrystals with (111) twist grain boundary (GB) of different misorientation angles are investigated by using molecular dynamics simulations. The selected GBs include low angle (LAGB), near twin (NTGB) and intermediate angle (IAGB) twist GBs, and the shock direction is along the GB normal. It is demonstrated that the bicrystals are of lower Hugoniot elastic limit than single crystal, as the twist GBs provide dislocation sources for deformation. At the shock compression stage, GB plasticity at the LAGBs and NTGBs is initiated via reaction and dissociation of GB dislocations, and can be triggered by elastic shock wave more readily than that at the IAGBs, on which dislocation emission is homogeneous and irrelevant to initial GB dislocations. At the tension stage, the incipient spall for different twist GBs occurs at an identical shock strength, but is of different details in dislocation and void evolutions. With varying shock strength and misorientation angle, spall strength of the Cu bicrystals depends on whether GB plasticity is produced at the compression stage, and the values are consistent with that of Cu single crystal under similar shock loading conditions.

Towards a digital twin for mitigating void formation during debulking of autoclave composite parts

High-performance polymeric composites are increasingly used in the design of aircraft structural components; however, susceptibility to manufacturing irregularities, including porosity/voids, remains a primary challenge delaying the implementation of advanced composites in modern aircraft. Voids may be precursors to structural damage significantly affecting structural integrity and remaining useful life of the aircraft. High-performance aerospace composite parts are commonly manufactured from resin-saturated pre-impregnated plies of uncured material laid-up over a rigid tool and consolidated and cured in an autoclave. In many applications, especially in thick and curved composite sections common in aerospace designs, autoclave consolidation alone is not sufficient to remove the air, or bulk, that might have been entrapped within the laminate during the layup process. Vacuum consolidation, or “debulking”, has been a standard practice extensively used by manufacturers to reduce the amount of bulk prior to autoclave curing. The debulking process typically takes a long time and requires intensive manual operations. The underlying physical principles governing the formation and evolution of voids during these early stages of the manufacturing process are not yet well understood, and controlling parameters remain largely determined empirically or based on prior experience. Driven by the need to improve such understanding, there has been a recent interest in using newly available high-fidelity non-destructive inspection (NDI) techniques, such as X-ray Computed Tomography, for in situ observations of composites internal structure during the early stages of manufacturing. In situ observations are allowing researchers to identify the driving mechanisms involved during defect formation and develop improved predictive models. The objective of this work is to show that high-fidelity NDI data and new developments in numerical modeling can be combined to create a Digital Twin for mitigation of void formation in composite parts. In particular, X-ray CT data is used to extract bulk content and distribution in uncured carbon-epoxy curved-beam specimens after manual layup, and such information is transferred into a finite element (FE) model for simulation of debulking. The FE model uses a fracture-based approach that relies on pore-pressure cohesive zone modeling recently proposed for the discrete representation of entrapped air pockets in uncured resin-saturated prepregs. Preliminary results support a promising ability of the Digital Twin concept for optimizing the debulking process of autoclave composites towards mitigating void formation.

Efficient characterization tools for deformation-induced damage at different scales

In modern multiphase materials, damage initiation and growth during plastic deformation is a commonly observed and technologically relevant process. To reliably assess the state of damage in a specimen or, ultimately, a formed product, precise and comparable damage quantification is required. Furthermore, the key to understanding the initiation and evolution of voids in such materials is the characterization of the initiating microstructural mechanisms in a statistically relevant way over a large number of damage sites. In this work, we present the results of large-scale scanning electron microscopy methods for automated damage recognition and analytical characterization, together with a concept for joining the available void size statistics to micromechanical experiments such as micro-cantilever tests. These tests are able to determine a critical crack length for various types of void initiation processes, leading to an improved understanding of the consequences of ductile damage evolution and void growth, and their subsequent interaction leading to material failure. In this way, a framework for quantification and high-resolution characterization of damage mechanisms is constructed, enabling new insights on damage evolution in forming processes.

Competition between plasticity- and void-based dynamic damage behaviors of single crystal HCP-Zr by considering the high strain rate and temperature

Spall dynamic damage has been extensively investigated in ductile metals with weak mechanical anisotropies, such as copper, iron, and aluminum. However, the fracture of stronger anisotropic metals, especially those with HCP structures, remains far less understood. In this work, the void evolution, including nucleation, growth, and coalescence, in single crystal HCP-zirconium at triaxial ultra-strain rates was investigated using molecular dynamics modeling. The internal pressure, microstructural evolution, and void evolution dynamics under various strain rates and temperatures were examined to reveal two competitive mechanisms, i.e., the competition between the dislocation and void evolution and the competition between the structural phase transformation and void evolution. The results showed that at the initial stage of void nucleation, the dislocations and voids exhibited interacted. However, when voids began to grow exponentially, they moved toward the dense dislocation direction and reduced the space for dislocation growth. In addition, the change in the pressure peak was caused by the sequence between the structural phase transformation and void nucleation under the strain rate strengthening effect and temperature softening action. When the void creation was ahead of the structural phase transformation, the pressure dropped once with only one peak. Contrarily, when the void nucleation lagged behind the structural phase transformation, two peaks appeared in the pressure–strain profile. The findings of this study are expected to be useful for the development of a fracture model that accounts for the effects of high strain rates and temperatures on the dynamic damage behavior across multiple scales.

A void evolution model accounting for stress triaxiality, Lode parameter and effective strain for hot metal forming

Large numbers of voids inevitably exist in the metal ingot due to non-equilibrium solidification. Forging is an important technique to eliminate such internal defects and obtain sound products. However, the research regarding void evolution mechanisms are currently not sufficient to direct the technological design in practical engineering because of the lack of suitable void evolution model, especially in terms of complex stress states. On the basis of a large number of numerical computations, the effect of Lode parameter on the void volume evolution rate is firstly investigated, and then incorporated together with the stress triaxiality T, effective strain Ee and Norton exponent n into a newly proposed void evolution model. At the scale of representative volume element (RVE), the prediction of void evolution calculated from the new model has achieved better accuracy than other analytical models comparing with the simulation results. Radial forging test for rectangular cross-section billet is carried out to verify the accuracy of the proposed void evolution model. Paired screw threads are used to introduce pre-fabricated voids and then embedded into the billet for measuring void volume variation and the distribution of strain around void during forging. The comparison of void evolution between the experimental and analytical solutions also shows that the prediction of void relative volume change by the proposed model is more accurate than those by other models.