Mean Void Size Research Articles

Investigation of ductile damage in dual phase steel during tensile deformation by in situ X-ray computed tomography

In situ synchrotron radiation X-ray computed tomography (CT) is used to understand the void nucleation and growth behaviour of dual phase (DP) steel, DP800, during uniaxial tensile deformation. The voids were identified post mortem as having nucleated primarily in the (41 vol%) martensite phase. The behaviour of individual voids was found to be broadly in line with a Rice and Tracey style growth model (their volume increasing by a factor of 10), while the mean void size was broadly in line with a model that included the continuous nucleation of new voids, as well as the growth of existing voids, throughout straining. Voids tended to elongate during uniaxial (low stress triaxiality) straining, but then to dilate more isotropically as necking led to increased triaxiality. One large pre-existing void was found to elongate quicky at first, but then for growth to slow, presumably because it was not located in the highest triaxial stress (necked) region. Perhaps surprisingly the average size of the void population grows only slowly (by a factor of 2) during straining; this is because while the size of each void grows, new small voids are always being nucleated. Finally, the changes of stress triaxiality and shear stress state during tensile deformation of the square cross-section smooth tensile specimen are investigated via finite element modelling, to qualitatively assess the impact of sample geometry on void nucleation behaviour and fracture strain in the current study.

Radiological Analysis of Gentamicin Eluting Synthetic Bone Graft Substitute Used in the Management of Patients With Traumatic Bone Voids.

BackgroundManagement of traumatic bone voids has always been challenging. Gentamicin eluting synthetic bone graft substitute (Cerament-G) showed encouraging results in achieving good bone healing with a satisfactory degree of resorption when utilised as a void filler. This study aims to assess the radiological signs of Cerament-G remodelling when used for patients with traumatic bone voids.MethodsRetrospective data analysis of all patients admitted to our unit between 2015 and 2021 with traumatic bone voids who had Cerament-G applied intraoperatively as a void filler. Postoperative radiographic images of the fracture site at six weeks, three months, six months, and at the final follow-up were reviewed. The radiological signs of Cerament-G integration, percent of void healing at the final follow-up were assessed.ResultsA total of 51 patients (52 fractures) were included in the study. Among them 10 were female and 41 were male with a mean age of 42.7 (11 - 90) years. The mean void size was 6.58 cm3. Mean follow-up duration was 9.73 months. Primary fracture union was achieved in 44 (86.3%) patients. Delayed union was reported in six (11.7%) patients, while one (1.9%) patient had non-union. Twenty-seven (52%) patients had >90% of void healing with normal trabecular bone. Twenty (38.5%) patients had 50-90% void healing with normal bone. Whereas only five (9.5%) patients had less than 50% of void healing.ConclusionCerament-G used as a void filler for patients with traumatic bone void has resulted 98% fracture union rate with good signs of radiological remodelling into a trabecular bone. More than 50% void filling with new trabecular bone was reported in more than 90% of patients. Non-union was reported in only one patient.

Porous shape memory dental implant by reactive sintering of TiH2-Ni-Urea mixture.

We produced bifurcated bone-like shape memory implant (BL-SMI) with desirable tooth-root fixation capability by compact-sintering of TiH2-Ni-urea mixture. The primary constituents of the porous product were Ni and Ti. We could adjust the pores' shape, size, and interconnectivity for favorite bone ingrowth by using urea as a space holder. Without urea, we obtained an average porosity of 0.30, and a mean void size of 100 μm. With 70 vol % urea, we got 62% interconnected pores of 400 μm average size. Aging allowed us to tune the austenite-martensite transformation temperatures towards the needed body tissue arouse. Differential scanning calorimetry measured the transformation temperatures. Their austenite start, austenite peak, and austenite finish values were As = 4, Ap = 22, and Af = 34 °C, respectively. They retained functional shape recovery and superelastic effect at the body temperature. Mechanical properties, including Young's modulus of the specimens, matched well to maxilla and mandible bone tissue. The measured Young's modulus of the NiTi specimens was as low as 3.5 GPa, which decreased to ∼2.1 GPa with further porosity increase at higher space holder percentages. Superelasticity regime and low Young's modulus of the implant could potentially prevent stress-shielding from the surrounding bone tissues and give rise to secure fixation of the implant into the bone socket. Bending tests showed 0.9 mm recoverable deflection for specimens which assisted immediate self-fixation of the implant into the jaw bone cavity.

Void Formation and Strain-Induced Martensitic Transformation in TRIP780 Steel Sheet Submitted to Uniaxial Tensile Loading

This work aimed to analyze the damage behavior of cold rolled TRIP780 steel sheet submitted to interrupted uniaxial tensile tests performed along the rolling direction. The formation of voids is investigated as a function of the straining level using digital image analysis of scanning electron micrographs to obtain the measures of void density, void area fraction, void aspect ratio and mean void size. The volume fractions of both ferrite/martensite and retained austenite constituents were obtained from X-ray diffraction measurements. An abruptly decrease of retained austenite was observed at early stages of deformation followed by a slow saturation. The resulting strain-induced martensite is responsible for improving the formability of the TRIP780 as observed by instantaneous strain-hardening exponent. In the lower strain range, growth and coalescence of existing microvoids prevailed at both in-plane directions whereas nucleation of microvoids was also observed along the loading direction. Conversely, nucleation prevailed at the transverse direction in the intermediate strain range whereas growth and coalescence were predominant aligned to the loading direction. At larger strain levels, growth and coalescence of microvoids prevailed at both directions. The microvoids were initially found around inclusions and at the interface of ferrite-martensite phases and lastly also at the ferrite matrix.

Fission gas bubble identification using MATLAB's image processing toolbox

Automated image processing routines have the potential to aid in the fuel performance evaluation process by eliminating bias in human judgment that may vary from person-to-person or sample-to-sample. This study presents several MATLAB based image analysis routines designed for fission gas void identification in post-irradiation examination of uranium molybdenum (U–Mo) monolithic-type plate fuels. Frequency domain filtration, enlisted as a pre-processing technique, can eliminate artifacts from the image without compromising the critical features of interest. This process is coupled with a bilateral filter, an edge-preserving noise removal technique aimed at preparing the image for optimal segmentation. Adaptive thresholding proved to be the most consistent gray-level feature segmentation technique for U–Mo fuel microstructures. The Sauvola adaptive threshold technique segments the image based on histogram weighting factors in stable contrast regions and local statistics in variable contrast regions. Once all processing is complete, the algorithm outputs the total fission gas void count, the mean void size, and the average porosity. The final results demonstrate an ability to extract fission gas void morphological data faster, more consistently, and at least as accurately as manual segmentation methods.

Factors influencing the tangential AC breakdown strength of solid-solid interfaces

The combination of two solid dielectrics (interface) increases the risk of formation of microscopic cavities reducing the breakdown strength (BDS) of the interface considerably, particularly when the electric field has a tangential component. The main purpose of this paper is to investigate the impact of the applied contact pressure and composite elastic modulus on the tangential ac BDS of the solid-solid interfaces experimentally. In the experiments, three different contact pressures were applied using different mechanical loads with two different materials having different elastic moduli, i.e. cross-linked polyethylene (XLPE) and silicon rubber (SiR). Two rectangular prism shaped samples were placed between two vertical Rogowski shaped electrodes either in air or oil. The type of the interface (air/oil) is highlighted duly upon showing the results. Increase in contact pressure caused relatively higher increase in the tangential BDS of dry SiR-SiR (assembled in air) than that of XLPE-XLPE, revealing that elastic modulus facilitated significantly to reduce the mean void size in SiR that in turn improved the tangential BDS. Likewise, the tangential BDS of hybrid interfaces formed by XLPE-SiR specimens increased by 43% compared to that of XLPE-XLPE interface at the same pressure. Additionally, the same set of experiments assembled in oil reveals that the presence of oil enhanced the tangential BDSs around 2-3 times for all three-interface cases. Moreover, with the increase of applied pressure the tangential BDS of air-filled and oil-filled cavities tended to get significantly higher.

A study of void size growth in nonequilibrium stochastic systems of point defects

We study properties of voids growth dynamics in a stochastic system of point defects in solids under nonequilibrium conditions (sustained irradiation). It is shown that fluctuations of defect production rate (external noise) increase the critical void radius comparing to a deterministic system. An automodel regime of void size growth in a stochastic system is studied in detail. Considering a homogeneous system, it is found that external noise does not change the universality of the void size distribution function; the mean void size evolves according to classical nucleation theory. The noise increases the mean void size and spreads the void size distribution. Studying dynamics of spatially extended systems it was shown that vacancies remaining in a matrix phase are able to organize into vacancy enriched domains due to an instability caused by an elastic lattice deformation. It is shown that dynamics of voids growth is defined by void sinks strength with void size growth exponent varying from 1/3 up to 1/2.

Influence of strain path on nucleation and growth of voids in dual phase steel sheets

The objectives of this work are to describe the nucleation and growth of voids in DP600 dual phase steel sheets formed along different strain paths, and to investigate the correlation between the micro-mechanisms of damage and the forming limits. DP600 sheet specimens were stretch-formed in uniaxial, plane strain and biaxial tension using the Marciniak–Kuczynski formability test. The evolution of damage in the microstructure was correlated to the formability in each strain path by quantitatively analyzing void density, void area fraction, void aspect ratio and mean void size. Results showed that DP600 steel sheets have less formability in plane strain compared to uniaxial and biaxial tension due to the more rapid elongation and growth of voids. Moreover, the sheets safely deformed to much greater effective strains in biaxial tension due to the smaller mean void size and slower void growth. As proposed by Gurson Gurson (1977) , Tvergaard and Needleman Tvergaard and Needleman (1984) , void volume fraction is an important damage parameter. However, this work shows that void aspect ratio and mean void size also significantly influence the evolution of damage and the formability of dual phase steels.

Fractal Networks of Inter‐Granular Voids in Pressed TATB

AbstractSmall‐angle neutron scattering techniques were used to study the evolution of void morphology with pressed density of the insensitive high explosive, TATB. Samples were studied as a loose powder and as pressed pellets, ranging in density from approx. 1 to 1.804 g cm−3. Inter‐granular voids in the loose powder were randomly arranged (non‐fractal) and had a surface defined mean size of 0.66 μm. Pressing was found to induce a fractal network of voids with fractally rough interfaces. The surface‐defined mean void size of the pressed samples was between 0.21–0.33 μm over the range of densities studied and was found to increase with pressed density up to 1.720 g cm−3, decreasing thereafter. The volume fractal dimension, indicative of the void arrangement, mirrored the changes in the mean void size. No systematic change in the surface fractal dimension was found. Surface area analysis allowed the average TATB grain size within the pressed samples to be quantified. An initial decrease of the mean grain size followed by an increase with pressed density suggests that the TATB grains behave in a brittle fashion at low densities and ductile at higher pressed densities.

Effects of physical properties on one-dimensional downward smoldering of char: Numerical analysis

Smoldering combustion in a packed bed of carbonaceous material is a very complex process, where numerous physical and chemical parameters are involved. This study was conducted to examine the impact of several physical parameters on the behavior of natural downward smoldering. For that purpose, a one-dimensional homogeneous model has been developed. Due to the fact that drying, pyrolysis or oxidative degradation occurs significantly faster than carbon oxidation, only the latter phenomenon was taken into account. The model was evaluated by comparison of numerical simulation results with experimental observations. Sensitivity analysis calculations of different physical properties of the bed material with respect to smoldering time, smoldering front velocity and front temperature suggest that in future experiments special attention should be devoted to accurate determination of bed shrinkage, bulk carbon density, mean void size, oxygen diffusivity in fuel bed.

Steady-state size distribution of voids in metals under cascade irradiation

The theory of radiation damage in metallic materials predicts that under cascade-irradiation conditions the voids should approach a steady state, which is characterised by a maximum mean void size. It is shown in this paper that the steady-state concentrations of voids of different size are described by the Gaussian distribution with the maximum size mentioned above to be the most probable value. The evolution of voids towards the steady state is analysed.

The Effect of Adhesive Curing Condition on Bonding Strength in Auto Body Assembly

The bonding strength of metal-to-metal lap joining of a two-part epoxy-based adhesive employed in an automotive assembly line was investigated under different heating rates (10 to 6000°C/min), peak temperatures (room to 250°C), and holding times. The results indicate that bonding strength is controlled mainly by the peak curing temperature and the heating rate. The maximum bonding strength appears between 70 and 110°C, but the value of it depends on the heating rate. At heating rates of 10, 50, and 100°C/min, the peak strength decreases with increasing heating rate. However, a further increase in heating rate to 2000–6000°C/min resulted in higher peak bonding strength. The microstructures and fractured surfaces after shear testing were examined by a scanning electron microscope. The results revealed that many gas bubbles (voids) were formed during the adhesive curing process, and the fracture process was controlled by the link of the voids. At low heating rates (10–100°C/min), the mean void size and volume fraction increase with heating rate and peak temperature, causing the weakening of the bonding strength. However, at very high heating rates (2000–6000°C/min), the rapid hardening of the adhesive suppressed the development of gas bubbles, so that the mean void size and volume fraction were low, and the bonding strength was high. This result indicates that to effectively improve the adhesive bonding strength, both the chemical reaction (degree of cure) and physical response (gas bubble formation) need to be optimized.

Effects of chain stiffness and penetrant size on penetrant diffusion in simple polymers: deduced relations from simulation and PRISM theory

Molecular dynamics simulations in the NVT ensemble were performed for a repulsive system of bead-spring polymer chains with angle constraints. The diffusion coefficients of spherical penetrants were measured for different size penetrants as the angle constraints were varied. The scaling of the diffusion coefficient with penetrant size varies as a function of chain stiffness from liquid-like behavior to polymeric behavior. Free volume distributions were calculated from both simulation and PRISM theory. It is found that free volume distributions and mean void size are constant with chain stiffness although the diffusion coefficient changes by a factor of two. This suggests that while free volume is necessary for diffusion to occur, binary collisions and chain relaxation also play a role in determining penetrant diffusion. The relative contributions of these factors to the diffusion coefficient may change as a function of chain stiffness.

The influence of impurities on the growth of helium-induced cavities in silicon

The effects of implanted oxygen, carbon, nitrogen, and self-damage on the growth of helium-induced cavities in silicon during high-temperature annealing have been studied. Impurities and helium were implanted into silicon at room temperature. Annealing at temperatures above 1000 K converts small He-filled bubbles into larger empty voids. The mean void size after annealing for 30 min at 1173 K was significantly reduced by the presence of all three implanted impurities. In extreme cases, the mean void radius is reduced from 10 nm, for a pure He implant, to 2.8 nm in a C pre-implanted sample. On the other hand, self-ion damage, unless at or near the level sufficient to cause amorphization, does not significantly affect cavity growth during annealing. We speculate that the presence of impurities significantly reduces the movement of voids by pinning them to dislocations or impurity aggregates or by chemical reactions at the void surfaces.

Nonwoven Structure Statistics: Simulation of Effects of Fiber Crimp, Flocculation, Density and Orientation

New simulations suggest a universal relationship between the mean number of fibers per zone in a complete sampling scheme and the mean void size, independent of whether the structure is isotropic or anisotropic, contains crimped or straight fibers, randomly laid or flocculated. The mean and standard deviation turn out to be positively correlated for some network parameters, such as mean void size, density, and mean number of fiber contacts. Also, our simulations suggest that fiber crimp has a higher impact on isotropic nonwovens. As crimp is increased, isotropic structures tend to present smaller mean voids, higher mean number of fibers per zone, and higher total number of bonds per fiber, than anisotropic structures.

Evaluation of the Visual Texture and Aesthetic Appearance of Lace Patterns

Gray-scale image analysis is applied to the characterization of textural patterns of 29 kinds of lace. Five parameters extracted from the gray-level co-occurrence matrix and the fractal dimension determined from the fractal analysis of the relief of the curved surface of image gray level were measured as textural-feature parameters. Beauty, comfort, transparency, light sensation, and lacunarity of textural patterns of laces were evaluated by sensory evaluation according to the rating-scale method, and the relationship between their sensory-evaluation values and the textural-feature parameters is examined. Factor analysis shows beauty to be related to the entropy and fractal dimension; transparency and light sensation to the angular second moment, contrast, thickness, and weight; and lacunarity to the number of voids and mean void size. The beauty of textural patterns is discussed from the viewpoint of orderliness and complexity.

A probabilistic approach towards modeling the relationships between particle and pore size distributions: the multicomponent packed sphere case

A probabilistic approach that determines the distribution of the volume of the voids in packed spheres, given their size distribution, is proposed. The tetrahedron system of dense random packing is adopted, but the probability to form it is expressed in a new way, in terms of the radii, the size distribution, and the probability of pair formation of the spheres. The volume of the void within each tetrahedron is approximated by the volume of the osculatory sphere. The approach is applied to power-function, Gaussian and log-normal distributions of sphere sizes. For the power-function case, the result is a bell-shaped void size distribution, the shape of which depends upon the power-function exponent. Therefore, a fractal-like behavior of the particles does not necessarily induce a fractal-like behavior of the corresponding voids. For the two other cases, the type of the void size distribution is similar to that of the sphere size distribution. However, no similarity is found between the distributions themselves, indicating that the sphere size-void size relation is not a simple linear relationship. The void size distribution was found to be related to the standard deviation of the corresponding particle size distribution. Increasing the standard deviation leads to a broader void size distribution and increases the mean void size.

In-Situ Tem-Investigation of Stress- and Electromigration- Induced Void Formation and Growth in Passivated Al-Interconnects

ABSTRACTIn-situ TEM observations on void formation and growth have been performed in passivated Al-lines in order to collect detailed microstructural data such as void number density, void size distribution, and growth rates as a basis for modelling stress relaxation and electromigration (EM) effects.The samples were 0.5mm long lines of 200nm thick Al with different widths (0.8, 1.6 and 2.4μm) passivated with 200μm thick SiNx. Additional experimental parameters were average grain size (0.5μm to more than 3μm, i.e. nearly perfect bamboo structure in the lines), relaxation time (0.1 to 20h) and temperature (20 – 300°C) and electromigration current density (without current up to ∼2MA/cm2).Measurements without current reveal that stress induced voids– develop after a temperature step of 50°C during cooling from 450°C and above. Upon heating from RT they start shrinking at 150°C and disappear completely at 350°C.– decrease in number and total relative volume but have constant mean void size with increasing number n of temperature cycles (n < 4)– show a strong dependence of their total relative volume on the microstructure (grain size, bamboo structure) which is strongly dependent on the anealing temperature for T ≥450° C.– show growth rates during isothermal annealing which are very dependent on relaxation time and temperature.Additional measurement with an applied electrical current, i.e. during an EM-test, show that nearly all the preexisting stress-induced voids– change their shapes and positions. This is dependent on electrical current density and time. Their frequently observed motion along the line (against the electron wind) was not neccessarily stopped by so-called blocking grains, i.e. grains without boundaries parallel to the line.– slightly change their total number but nearly maintain their total relative volume which is independent of current density or time.The collected statistical microstructural data are in good agreement with macroscopic stress relaxation results by wafer curvature and X-ray diffraction and recent in-situ stress measurement during an EM-test.

Voids in Real Space and in Redshift Space

view Abstract Citations (58) References (39) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Voids in Real Space and in Redshift Space Ryden, Barbara S. ; Melott, Adrian L. Abstract Before using void statistics to compare simulations with redshift surveys, it is best to understand the behavior of the statistics as a function of the density fluctuation power spectrum and in the transformation from real space to redshift space. This is most efficiently accomplished by using two-dimensional numerical simulations of gravitational clustering, with initial power spectra of the form P(k) is proportional to k^n^. We compare the properties of voids in real space to their properties in redshift space. Both the void probability function (VPF) and the underdense probability function (RE) are enhanced in redshift space. The enhancement is greatest in the limit n = - 2. The VPF and UPF treat voids statistically and assume that two-dimensional voids are circular; we present an algorithm that detects individual voids. Voids found by this algorithm are ellipses whose enclosed density of galaxies falls below a threshold density. When voids are identified using this algorithm, the mean void size and the maximum void size both increase in going from real space to redshift space. The increase is greatest in the limit n = - 2. In redshift space, the principal axes of the largest voids in the n = 2 and n = 0 simulations show a statistically significant tendency (at the 95% confidence level) to be distributed anisotropically, relative to the line of sight from the origin to the void center. Publication: The Astrophysical Journal Pub Date: October 1996 DOI: 10.1086/177857 arXiv: arXiv:astro-ph/9510108 Bibcode: 1996ApJ...470..160R Keywords: COSMOLOGY: THEORY; GALAXIES: DISTANCES AND REDSHIFTS; COSMOLOGY: LARGE-SCALE STRUCTURE OF UNIVERSE; Astrophysics E-Print: Submitted to ApJ. 17 pages, uuencoded compressed PostScript. 14 figures available as a compressed tar file from anonymous ftp at ftp://bessel.mps.ohio-state.edu/pub/ryden/voidfigs.tar.Z full text sources arXiv | ADS |

The evolution of voids in the adhesion approximation

We apply the adhesion approximation to study the formation and evolution of voids in the universe. Our simulations-carried out using 128(exp 3) particles in a cubical box with side 128 Mpc-indicate that the void spectrum evolves with time and that the mean void size in the standard Cosmic Background Explorer Satellite (COBE)-normalized cold dark matter (CDM) model with H(sub 50) = 1 scals approximately as bar D(z) = bar D(sub zero)/(1+2)(exp 1/2), where bar D(sub zero) approximately = 10.5 Mpc. Interestingly, we find a strong correlation between the sizes of voids and the value of the primordial gravitational potential at void centers. This observation could in principle, pave the way toward reconstructing the form of the primordialpotential from a knowledge of the observed void spectrum. Studying the void spectrum at different cosmological epochs, for spectra with a built in k-space cutoff we find that the number of voids in a representative volume evolves with time. The mean number of voids first increases until a maximum value is reached (indicating that the formation of cellular structure is complete), and then begins to decrease as clumps and filaments erge leading to hierarchical clustering and the subsequent elimination of small voids. The cosmological epoch characterizing the completion of cellular structure occurs when the length scale going nonlinear approaches the mean distance between peaks of the gravitaional potential. A central result of this paper is that voids can be populated by substructure such as mini-sheets and filaments, which run through voids. The number of such mini-pancakes that pass through a given void can be measured by the genus characteristic of an individual void which is an indicator of the topology of a given void in intial (Lagrangian) space. Large voids have on an average a larger measure than smaller voids indicating more substructure within larger voids relative to smaller ones. We find that the topology of individual voids is strongly epoch dependent, with void topologies generally simplifying with time. This means that as voids grow older they become progressively more empty and have less structure within them. We evaluate the genus measure both for individual voids as well as for the entire ensemble of voids predicted by CDM model. As a result we find that the topology of voids when taken together with the void spectrum is a very useful statistical indicator of the evolution of the structure of the universe on large scales.