Effect Of Void Size Research Articles

Plastic deformation of [001]-oriented single-crystal iron under shock compression: Effects of void size

The thermomechanical behavior of materials is known to be sensitive to preexisting defects in their microstructure. In this paper, non-equilibrium molecular dynamics simulations have been used to investigate the effects of the microvoid size on the plastic deformation in single-crystal iron shock-compressed along the [001] crystallographic direction. The higher the microvoid radius, the faster the kinetics of dislocations. Thus, as the microvoid radius increases, the plastic activity evolves from a regime where the deformation is dominated by twin activities to a regime where both twin and dislocation activities play an essential role and then to a regime where the deformation is dominated by dislocation slip. Furthermore, in both defect-free and defective initial crystal states, the elastic precursor wave is observed to decay with propagation distance, resulting in a constitutive functional dependence of the yielding pressure, σE, on the plastic deformation rate, ε˙p. In the regime where both deformation twinning and dislocation slip play important roles, the constitutive behavior is consistent with the original Swegle–Grady model and is in overall agreement with experimental data and thermomechanical simulations.

Atomic-scale investigation on the mechanical behaviors of the γ′/γ′′ co-precipitates compounds in Ni-based superalloys

The γ′/γ′′ co-precipitation strategy entails excellent mechanical properties for Ni-based superalloys, but the deformation mechanism of γ′/γ′′ co-precipitates Ni-based superalloys at atomic-scale remains unclear. In this work, we studied the effect of loading rate, void size, and temperature on the mechanical behaviors of γ′-Ni3Nb/γ′′-Ni3Nb co-precipitates via molecular dynamic (MD) simulations. The simulation results show that the tensile load rate 1×109 s−1 is critical for the free-void γ′/γ′′ co-precipitates. When the loading rate exceeds 1×109 s−1, a transition occurs in the deformation mechanism, leading to a rapid increase in tensile strength and a subsequent reduction in flow stress until it eventually vanishes (1.35 GPa→0.98 GPa→0 GPa). The presence of voids at the interphase boundary significantly reduces the material's strength, with this weakening effect becoming more pronounced as the void radius increases. Furthermore, the voids facilitate the easier penetration of dislocations into the γ′ and γ′′ precipitated phases along the void peripheries through the interphase boundary. The study also reveals that the trends in Young’s modulus and yield stress for both pre-void and void-free models are similar with increasing temperature, with Young’s modulus decreasing as temperature rises. Notably, at elevated temperatures, γ′′ precipitated phase transitions occur within the γ′/γ′′ co-precipitates, and the yield stress is maximum at 800 K. This study provides valuable insights into the mechanical behavior of γ′/γ′′ co-precipitates and the weakening effects of atomic-scale voids in Ni-based superalloys.

Void-induced mechanisms in tensile behavior of nickel-based single crystal superalloys

Void defects significantly impact the tensile properties of nickel-based single crystal superalloys. In this work, the dynamic response of void-included nickel-based single crystal superalloys under tensile loading was studied using molecular dynamics method. The effects of porosity and void size on the tensile behavior and the evolution of internal defects were explored from a microscopic perspective. The results indicate that the presence of voids promotes the development of internal dislocation defects and atomic phase transitions, especially in the initial stage of plastic deformation. The tensile strength decreases with increasing porosity. Plastic deformation and atomic phase transitions typically initiate between voids and continue until complete fracture, with shear strains and dislocation defects continuously concentrating around the voids. Notably, some HCP defect atoms distant from voids revert to FCC phase atoms during the tensile process, leading to a decrease in dislocation density. Additionally, the mode of fracture in the porous model is shear fracture, with shear strain and dislocation defects remaining at the fracture surface after complete fracture. The effects of void size on the tensile strength are relatively small. As the void size decreases, the shear strain bands in the models become more regular and the dislocation density decreases. However, the impact of small-sized voids on the material becomes increasingly evident with further stretching.

Effect of void size and position on mechanical properties of nanotwinned metals under cyclic loading

Effect of void size and position on mechanical properties of nanotwinned metals under cyclic loading

Forming limit and failure characterization of as-received and bi-axial prestrained Cu-Cr-Zr-Ti alloy sheets in the context of multistage forming

The characterization of forming limit utilizing Cu-Cr-Zr-Ti alloy sheets during the multistage forming process is imperative for successfully fabricating thrust chamber liners used in satellite launch vehicles. Therefore, the present work studies the effect of prestrain on the forming limit and failure behaviour of this alloy under different deformation paths. A stretch-forming setup was utilized to induce 8% equi-biaxial prestrain (EBP), and subsequently, these prestrained specimens were deformed till the onset of failure using the same setup. After prestraining, a shift in the failure strains was observed in the principal strain space, whereas it was found to be absent in the polar effective plastic strain, principal stress and effective plastic strain-stress triaxiality loci. The cup height along different deformation paths was marginally decreased in the prestrained specimens because of the reduction in failure strains, and the fracture occurred in the prestrained region. Further, failure analysis revealed intergranular cracks in the specimens deformed along plane strain and uniaxial deformation paths due to the presence of micron-size Cr-rich precipitates along grain boundaries. However, intergranular and transgranular cracks were present in the prestrained specimens, which were deformed equi-biaxially similar to the as-received specimens. The presence of nano-size Cr-rich precipitates inside the grains acted as nucleation sites for voids during equi-biaxial stretching, leading to transgranular cracks. It was also observed that failure in the prestrained and as-received specimens occurred at a similar effective plastic strain value due to the combined effect of void density and void size. Based on experimental observations, it was inferred that the forming limit of Cu-Cr-Zr-Ti sheets under a two-stage forming process was primarily affected by the presence of micro and nano-size Cr-rich precipitates.

Three-Dimensional Meso-Structure-Based Model for Evaluating the Complex Permittivity of Asphalt Concrete.

Microwave heating is an emerging alternative pretreatment method for road maintenance in cold seasons. The thermal behavior of asphalt pavement under microwave heating is mainly determined by the complex permittivity of the asphalt mixture. In this study, an innovative approach for calculating the complex permittivity of an asphalt mixture based on a three-dimensional meso-scale heterogeneous structure was proposed. A series of experiments was conducted to verify the accuracy of this approach. The effect of porosity, void size, moisture content and aggregate gradation on the complex permittivity for an asphalt mixture were computationally analyzed based on the validated approach. Moreover, the applicability of commonly used classical dielectric models was analyzed. The classical Lichtenecker-Rother (LR) dielectric model was modified on the basis of simulation data for various conditions. The results showed that the real part of the complex permittivity decreased with the increase in porosity. Some sudden change in the imaginary part of the complex permittivity was observed within the frequency range from 2.6 GHz to 3.9 GHz. A larger air void size would lead to a larger frequency at which sudden change occurs. The real part and imaginary part of the complex permittivity tend to be smaller when more coarse aggregates are replaced with fine aggregates. Both the real part and the imaginary part of the complex permittivity increase with higher moisture content due to the stronger dielectric property of water. Each 1% increase in moisture content would lead to about a 3~4% increase in the real part of the complex permittivity. The determination coefficients R2 for the real part and the imaginary part of the complex permittivity fitted by the modified Brown model were the maximum values, which were 0.922 and 0.980, respectively. The method presented in this study is useful for transportation agencies to optimize microwave heating during winter maintenance.

Probabilistic fatigue strength assessment of cross-ply laminates: Exploring effects of manufacturing defects through a two-scale modeling approach

The study presents a two-scale modeling approach allowing for an efficient fatigue strength evaluation on a macro scale considering a micro-mechanical defect characterization of a Carbon Fiber Reinforced Polymer (CFRP) material. The modeling approach integrates a macro model with the effective elastic properties from micro-mechanical simulations considering voids. This enables the analysis of defects’ influence on material fatigue strength using a probabilistic weakest link approach. A CFRP laminate with a cross-ply layup was investigated. Two simulation case studies demonstrate the effect of void content and size on the characteristic fatigue strength. An experimental investigation was conducted testing the laminates in tension–tension fatigue verifying the predicted numerical behavior. The numerical models identify a difference in the characteristic fatigue strength consistent with the fatigue test results. It is numerically concluded that the investigated CFRP material’s fatigue strength is affected by the presence of voids and even with only a slight difference in the global void volume fraction a scatter in fatigue strength is identified.

Void size, shape, and orientation effects in shear-dominated void coalescence across scales

In a stress state dominated by shear, pre-existing voids rotate, elongate, and close up to form micro-cracks, which interact through void coalescence and eventually may cause a complete loss of load-carrying capacity. The mechanism sets apart void coalescence in shear from that under tensile-dominated stress states, and the present work demonstrates that gradient strengthening affects the macroscopic strain at the onset of plastic flow localization leading to coalescence. Despite that zero or limited void growth develop in shear, a severe heterogeneous plastic straining develops near the void, which generates large plastic strain gradients accompanied by densities of Geometrically Necessary Dislocations (GNDs) in addition to the Statistically Stored Dislocations (SSDs) that controls conventional strain hardening. The GNDs lead to additional micron scale strengthening, and the present work investigates their effect on the plastic flow localization leading to void coalescence in shear by modeling voids embedded in a gradient-enhanced matrix material, thus revisiting the early work by Tvergaard (2008), which was carried out in a conventional scale independent setting. The Fleck–Willis gradient theory is assumed to govern the matrix surrounding the voids such that a material length parameter enters the analysis. Increasing the length parameters while keeping the void volume fraction and intervoid distance constant corresponds to diminishing the material microstructure. The results show that (i) voids with the minor axis in the direction of the shear (denoted “prolate”), give the highest ductility mainly due to the larger intervoid ligament; (ii) both the initial relative void size and the initial void orientation have strong effects on material ductility across the scales; (iii) the initial void orientation plays a fundamental part in the void deformation mechanism and the plastic field that develops prior to coalescence; (iv) the ductility increases substantially when down-scaling the microstructure where the gradient strengthening intensifies (corresponding to increasing the material length parameter). Throughout, fitting functions for the average shear angle at the onset of plastic flow localization are suggested, with respect to the relative void size, the initial void orientation, and the intrinsic material length parameter, to bring out the dependencies and facilitate using the unit cell results in continuum models.

Efficient computational framework for image-based micromechanical analysis of additively manufactured Ti-6Al-4V alloy

The increase in additively manufactured (AM) Ti-6Al-4V alloys in high-performance industrial applications has necessitated the development of robust computational models that can aid in their qualification and certification. Physics-based micromechanical models, relating the AM-processed material microstructure and defect state with the overall material response and life, can play an important role in reducing uncertainty in component behavior and increasing acceptance. Motivated by this need, the present paper develops a novel image-based crystal plasticity finite element model (CPFEM) for efficient micromechanical simulation of the additively manufactured Ti-6Al-4V alloy, whose Widmanstätten microstructure is characterized by 12 HCP α lath variants in the parent β grain. A unique feature of this work is the creation of an efficient crystal plasticity framework for the parent β grain polycrystalline ensembles with parametric representation of the α lath statistics of size, shape, orientation, and crystallography. This statistical representation is expected to significantly enhance its efficiency over models that represent each α lath explicitly in the microstructure. Defects in the form of voids are represented at two scales. The smaller voids in the microstructure are manifested as porosity or void volume fraction distribution in the crystal plasticity model. Larger voids are represented explicitly in the statistically equivalent microstructural volume element (SEMVE) model. The models are built from experimentally acquired electron back scatter diffraction (EBSD) and micro-focus X-ray computed tomography (XCT) images and calibrated and validated with mechanical testing data. This paper extends the developments in Pinz et al. (2022) through the development of a special self-consistent boundary condition in the context of a concurrent model to overcome limitations of periodicity boundary conditions. The concurrent model embeds the SEMVE in a homogenized exterior domain represented by a rate-dependent isotropic plasticity model. Parametric studies are conducted to comprehend the effect of void size, shape and orientation on the overall material response.

Dynamic Characterization of Hexagonal Microstructured Materials with Voids from Discrete and Continuum Models.

The mechanical response of materials such as fiber and particle composites, rocks, concrete, and granular materials, can be profoundly influenced by the existence of voids. The aim of the present work is to study the dynamic behavior of hexagonal microstructured composites with voids by using a discrete model and homogenizing materials, such as micropolar and classical Cauchy continua. Three kinds of hexagonal microstructures, named regular, hourglass, and skew, are considered with different length scales. The analysis of free vibration of a panel described as a discrete system, as a classical and as a micropolar continuum, and the comparison of results in terms of natural frequencies and modes show the advantage of the micropolar continuum in describing dynamic characteristics of orthotropic composites (i.e., regular and hourglass microstructures) with respect to the Cauchy continuum, which gives a higher error in frequency evaluations for all three hexagonal microstructured materials. Moreover, the micropolar model also satisfactorily predicts the behavior of skewed microstructured composites. Another advantage shown here by the micropolar continuum is that, like the discrete model, this continuum is able to present the scale effect of microstructures, while maintaining all the advantages of the field description. The effect of void size is also investigated and the results show that the first six frequencies of the current problem decrease by increasing in void size.

Effect of void size and Mg contents on plastic deformation behaviors of Al–Mg alloy with pre-existing void: Molecular dynamics study

The plastic deformation properties of cylindrical pre-void aluminum–magnesium (Al–Mg) alloy under uniaxial tension are explored using molecular dynamics simulations with embedded atom method (EAM) potential. The factors of Mg content, void size, and temperature are considered. The results show that the void fraction decreases with increasing Mg in the plastic deformation, and it is almost independent of Mg content when Mg is beyond 5%. Both Mg contents and stacking faults around the void affect the void growth. These phenomena are explained by the dislocation density of the sample and stacking faults distribution around the void. The variation trends of yield stress caused by void size are in good agreement with the Lubarda model. Moreover, temperature effects are explored, the yield stress and Young’s modulus obviously decrease with temperature. Our results may enrich and facilitate the understanding of the plastic mechanism of Al–Mg with defects or other alloys.

Simulation and experiment analysis of relationship between voids and permeability of composites

Due to the significant weight reduction advantage, aerospace composite tanks have become the focus of international competition of spacecraft. However, the permeation of small molecules at low temperature caused by the internal voids of composites is one of the key technical problems which restrict the engineering application of composite tanks. In this study, a combination of theoretical research and experimental research was adopted. By changing the curing pressures of the composites’ autoclave process, laminates with different porosities were prepared and tested for low-temperature permeability. Based on the grayscale processing and median filtering methods, a permeability prediction model with the true voids morphology of composite materials was established. Based on the random medium theory, the random voids model of composites was built to study the effect of void size and shape on the permeability of laminates. The results showed that the finite element analysis of composites, permeability based on the real voids morphology model was in good agreement with the experimental results, which proved the feasibility of this method. The permeation rate of laminates increased with the raised of porosity, and the internal porosity of the laminates could be diminished by improving the curing pressure so as to reduce the permeation of the composite components. Under the condition of a certain porosity, the laminates with small, stripe voids had a higher permeation rate than the laminates with large, circular voids.

Effective yield criterion for a porous single crystal accounting for void size effects

The growth of sub-grain voids in crystalline materials is affected by plastic anisotropy as well as void size effects. In this paper, an effective yield criterion is derived for a porous single crystal using homogenization theory and limit analysis. A two dimensional planar model of a single crystal containing a random distribution of cylindrical voids is assumed. The effective yield criterion is derived using plastic limit load analysis of a hollow cylindrical representative volume element, containing a concentric cylindrical void in a single crystalline matrix. A conventional strain gradient plasticity model with an embedded material length scale is assumed for the matrix, in order to account for the void size dependence of yielding. The yield loci and void growth rates predicted by the model under plane strain conditions are validated by comparison with numerical results obtained using finite elements, as well as prior analytical results for the special case of size independent matrix behavior. The model predictions for the size dependence of the yield stress as well as void growth under proportional loading conditions are discussed with reference of known results from experiments and lower scale dislocation dynamics simulations.

A numerical study of a size-dependent finite-element based unit cell with primary and secondary voids

Aluminium alloys contain various types of intermetallic particles with different sizes, such as constituent particles and dispersoids. The main mechanism of ductile fracture in these materials is assumed to be nucleation of voids around the constituent particles, which grow during plastic deformation and eventually coalesce, resulting in material failure. The role of the dispersoids is less certain, but they are assumed to contribute in the last stages of the ductile fracture process. While the constituent particles are in the range of a couple of microns, the size of dispersoids is normally one order of magnitude smaller. To disclose the possible effects of the dispersoids on the ductile fracture process in aluminium alloys, this paper presents a numerical study of a finite-element based unit cell, which consists of a single spherical void embedded in a matrix material represented by a porous plasticity model with void size effects. Accordingly, the single, primary void of the unit cell is assumed to have nucleated on a constituent particle, whereas the matrix porosity is assumed to account for secondary, smaller voids nucleated on dispersoids. The effects of the intrinsic length scale of the matrix material on the void growth and coalescence are studied for a range of stress states, while the initial primary and secondary void volume fractions are kept constant. The secondary voids have a substantial effect on the behaviour of the unit cell when their size is large compared to the intrinsic material length scale, but they were not found to influence the growth of the primary void. Instead, the growth of the secondary voids promotes strain softening and influences the coalescence process of the primary voids, which gradually changes mode from internal necking to loss of load-carrying capacity of the inter-void ligament.

A multiscale modeling for predicting the thermal expansion behaviors of 3D C/SiC composites considering porosity and fiber volume fraction

Coefficients of thermal expansion (CTEs) are an essential design criterion of the three-dimensional carbon fiber reinforced SiC matrix composites (3D C/SiC). Representative volume element (RVE) models of microscale, void/matrix, and mesoscale developed in this work were used to investigate the CTEs of these composites. A coupled temp-displacement steady-state analysis step was created for assessing the thermal expansions behaviors of the composites by applying periodic displacement and temperature boundary conditions. Three RVE models of cuboid, hexagonal and fiber random distribution were respectively established to comparatively study the influence of fiber package pattern on the CTEs at microscale. Similarly, the effects of different void size, locations, and shapes on the CTEs of the matrix are comparatively analyzed by the void/matrix models. The prediction results at mesoscale corresponded closely to the experimental results. The effect of the porosities on the CTEs was studied by the void/matrix RVE models. The voids were effective in lowering the CTE of the 3D C/SiC composites. Furthermore, the effect of fiber volume fractions on the CTE were also taken into consideration. Equal in-plane and out-of-plane CTEs were realized by selecting appropriate fiber volume fractions for the different directions. The multiscale models developed in this work can be used to predict the thermal expansion behaviors of other complex structure composites.

Prediction of forming limits for porous materials using void-size dependent model and bifurcation approach

The scientific literature has shown the strong effect of void size on material response. Several yield functions have been developed to incorporate the void size effects in ductile porous materials. Based on the interface stresses of the membrane around a spherical void, a Gurson-type yield function, which includes void size effects, is coupled with the bifurcation theory for the prediction of plastic strain localization. The constitutive equations as well as the bifurcation-based localization criterion are implemented into the finite element code ABAQUS/Standard within the framework of large plastic deformations. The resulting numerical tool is applied to the prediction of forming limit diagrams (FLDs) for an aluminum material. The effect of void size on the prediction of FLDs is investigated. It is shown that smaller void sizes lead to an increase in the ductility limits of the material. This effect on the FLDs becomes more significant for high initial porosity, due to the increase of void-matrix interface strength within the material.

The Influence of Solder Void on IGBT Temperature

The void in solder layer is the main factor that causes bad heat dissipation of IGBT (Insulated Gate Bipolar Transistor) module. Based on the seven-layer structure of IGBT, this article established a three-dimensional finite element model of IGBT module packaging structure and carried out its thermal analysis, then had a study on the effect of welding layer void on the temperature of IGBT chip. The overall distribution of IGBT module with or without solder hole is compared, meanwhile the article analyzed the effects of void type, size, shape, number and distribution on the temperature distribution of IGBT chips. The results show that the void in the solder layer of the chip has a great influence on the temperature of the chip. The influence of penetrating voids on chip temperature is greater than that of non-penetrating voids, the bigger the single hole is, the higher the temperature of IGBT chip. Voids of the same shape have greater influence on chip temperature at edge and corner positions than those inside the welding layer. The more concentrated the distribution of multiple holes, the higher the chip’s temperature. Therefore, in order to improve the reliability of IGBT, it is necessary to avoid voids in the chip welding layer during the packaging process.

Mathematical modeling of closure behavior for a centrally elliptical void in thick slab

To investigate the evolution behavior of a centrally elliptical void in thick slab during rolling, a critical criterion for closing a central elliptical void is established through the energy analysis. According to the condition of volume constancy, a triangular velocity field embedding an elliptical void is established. Based on the velocity field, the minimum value of rolling energy rate, composed of shear energy rate and cracking energy rate, is calculated. According to the balance principle of energy rate, the expression of relative stress factor is obtained. Then, a mechanical criterion for void closure is derived from the basis of extreme condition, and the effects of void size, aspect ratio, geometrical shape parameter, thickness-to-radius ratio, and the relative reduction on the void closure are analyzed. Several rolling processes with different elliptical voids under seven aspect ratios are simulated by the finite element method (FEM), and the evolution characteristic of the void is revealed. The analytical results based on the mechanical criterion and those by the FEM are compared. It is shown that the two prediction results are in good agreement, and a flat void is easier to be closed than a sharp one. Also, the simulated rolling force and torque are obtained through the FEM model, and the comparison result confirms the validity of the upper bound solution. Finally, a rolling experiment with a prefabricated void is carried out to check the reliability of the closure criterion, and a good consistence is also found. In addition, the shortage of the present investigation based on 2D simulation for assessing the mechanical criterion is discussed as a prospect of the future research.

Mechanical Behavior of Concrete Pavement considering Void beneath Slabs and Joints LTE

Dowel bars are arranged between two slabs of jointed plain concrete pavements to transfer load between them. The looseness of these dowel bars leads to the decrease of the load transfer efficiency (LTE). Meanwhile, repeated vehicle load can result in void near the joints. In this paper, the behaviors of concrete pavement under the effect of void size and joint stiffness were studied by using ABAQUS software. The FEA model was calibrated for different element parameters based on mesh convergence analysis and validated by comparison with previous studies. The voids beneath slabs were considered in this study, including the loaded slab and unloaded slab. The different effects of base course modulus on the stress of loaded slab are also analysed. It is concluded that the results show that the void size and joint stiffness affect the stress of the loaded plate. Smaller void size and larger joint stiffness will lead to the maximum stress located at the bottom of the loaded slab, and the void size has little effect on the stress of the loaded slab. Otherwise, the larger void size will cause larger stress. The effect of base modulus on stress is similar.

Optimizing size and distribution of voids in phenolic resins through the choice of catalyst types

ABSTRACTPhenolics are widely used for over a century in different industries due to their chemical resistance and thermomechanical properties. However, the presence of voids in phenolic resins has negative effects on the mechanical properties and a conventional approach is to avoid these by utilizing very long cure cycles. Our alternative approach investigates the tailoring of void size and distribution to achieve a better balance between processing time and mechanical properties. Therefore, we produced phenolic resin with a void‐free microstructure by a long cure cycle as a reference. To alter the void size and distributions, we utilized different catalysts and a short cure cycle to obtain phenolic resins and test their flexural properties with respect to the reference. We investigated the fracture surfaces of all materials by SEM, FTIR and compared results to finite element modeling that confirmed the effects of different void size and distributions on the mechanical properties. © 2019 The Authors. Journal of Applied Polymer Science published by Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2019, 136, 48249.