Void Area Fraction Research Articles

Analysis of fracture limit curves and void coalescence in high strength interstitial free steel sheets formed under different stress conditions

Void formation, which is a statistical event, depends on inhomogeneities present in the microstructure. The analysis on void nucleation, their growth and coalescence during the fracture of high strength interstitial free steel sheets of different thicknesses is presented in this article. The analysis shows that the criterion of void coalescence depends on the d-factor, which is the ratio of relative spacing of the ligaments (δd) present between the two consecutive voids to the radius of the voids. The computation of hydrostatic stress (σm), the dominant factor in depicting the evolution of void nucleation, growth and coalescence and the dimensional analysis of three different types of voids namely oblate, prolate and spherical type, have been carried out. The ratio of the length to the width (L/W) of the oblate or prolate voids at fracture is correlated with the mechanical properties, microstructure, strains at fracture, Mohr’s circle shear strains and Triaxiality factors. The Lode angle (θ) is determined and correlated with the stress triaxiality factor (T), ratio of mean stress (σm) to effective stress (σe). In addition, the Void area fraction (Va), which is the ratio of void area to the representative area, is determined and correlated with the strain triaxiality factor (To).

Effect of annealing temperature on void coalescence in 5086 aluminium alloy formed under different stress conditions

In this paper, the influence of annealing temperature on formability, fracture behavior, void nucleation, its growth, and coalescence are studied. The voids and fracture behavior are studied as a function of various void parameters, namely δd-factor (ligament thickness between consecutive voids), d factor (ratio of δd and radius of the void), void area fraction (Va) and L/W ratio (ratio of length to width of the void). The L/W ratio of the oblate or prolate voids at fracture is correlated with the mechanical properties, microstructure, minor strain at fracture (e2), Mohr’s circle shear strains, stress, and strain triaxiality factors. The Lode factor (θ) is determined and correlated with the Stress triaxiality factor (T), which is the ratio of mean stress (σm) to effective stress (σe). In addition, the Void area fraction (Va), which is the ratio of void area to the representative sample area, is determined correlated with the Strain triaxiality factor (To). It is found that the sheets annealed at 300°C, possesses better formability due to lower d-factor, higher \( \overline n \) and \( \overline r \)-values, greater void area fraction and lower L/W ratio of void accommodating more plastic deformation.

Effect of Voids on Thermomechanical Durability of Pb-Free BGA Solder Joints: Modeling and Simulation

The effect of process-induced voids on the durability of Sn–Pb and Pb-free solder interconnects in electronic products is not clearly understood. Experimental studies have provided conflicting ambiguous conclusions, showing that voids may sometimes be detrimental to reliability, but they may sometimes even increase the reliability of joints, depending on the size and location. Because of the higher level of process-induced voids in Pb-free solders, this debate is more intensified in Pb-free joints. This study presents finite element analysis (FEA) of the influence of void size, location, and spacing on the durability of Pb-free solders. A three-dimensional, global-local, viscoplastic FEA is conducted for a CTBAG132 assembly under thermal cycling. The displacement result of the global FEA at the top and bottom of the critical ball is used as the boundary condition in a local model, which focuses on the details of a single ball of the CTBGA package under temperature cycling. Parametric study is conducted to model a solder ball with voids of different sizes and locations. The maximum void area fraction modeled is from 1% to 49% of the ball area. An energy-partitioning model for cyclic creep-fatigue damage is used to estimate the damage and to monitor the trends as the size and location of voids are varied. Potential sites for maximum damage and crack initiation are identified. FEA results show that as void size increases up to about 15% of the area fraction of the ball, durability increases. For voids bigger than that, the durability starts to decrease. This study also confirms that as voids are located closer to the damage initiation site and the propagation path, their lifespan decreases.

Estimation of Creep Damage for the Components of Mod. 9Cr-1Mo Steel. 3rd Report, Creep Damage Assessment for Seam Weld in Internally Pressurized Pipe.

In order to establish the assessment method of creep damage for high temperature piping components made of modified 9Cr-1Mo steel with seam weld, subjected to internal pressure, the internal pressure creep tests and FEM stress analysis were done for cylinders with seam weld. In internal pressure creep tests, the creep rupture occurred at fine grained heat affected zone (F. G. HAZ), caused by cracking originated from the formation of voids. The correlation between void area fraction and creep damage was obtained. The morphology of voids were quite similar to that observed in welded joint specimens in uni-axial creep tests. Stress distribution of seam weld cylinder under internal pressure creep showed the higher circumferential stresses in F. G. HAZ where creep rupture occurred. The distribution of circumferential stress and creep damage calculated by using circumferential stress along specimen thickness were quite similar to that of void area fraction in internal pressure creep test. The creep damage in seam weld pipe under internal pressure creep could be estimated by the observation of void area fraction in F. G. HAZ.

Estimation of Creep Damage for the Components of Mod. 9Cr-1Mo Steel. 4th Report. Creep Damage Assessment for Circular Seam Welded Joint in Internally Pressurized Pipe.

In order to establish the assessment method of creep damage for high temperature piping components made of mod. 9Cr-1Mo steel with circular seam welded joint, the internal pressure creep tests and FEM stress analysis were done. Internal pressure creep tests showed the creep rupture occurred in the coarse grained heat affected zone (C. G. HAZ), caused by cracking originated from the formation of voids on grain boundaries. The void parameters such as void area fraction, density of void population and A parameter correlated well with time fraction in internal pressure creep tests. Vickers hardness decreased with creep times and correlated well also with time fraction of internal pressure creep tests. Stress distribution of cylinder with circular seam welded joint under internal pressure creep showed the maximum circumferential stress in C. G. HAZ where creep rupture occurred. The distribution of circumferential stress and creep damage calculated by using circumferential stress along specimen thickness were quite similar to that of void area fraction. The creep damage of circular seam welded joint under internal pressure creep could be estimated by the observation of void and the FEM stress analysis.

Evolution and Distribution of Surface Voids Affecting Char Burning Rates at Diffusion-Limited Conditions

Research has indicated that the accurate calculation of char burning rates at diffusion-limited conditions requires consideration of the effects of voids (gaps in the continuous surface of burnable material that are deeper than their surface radius) on the particle burning area. Experimentally, void area distributions as a function of void size can be quantified using scanning electron microscopy and digital processing of quenched char particle images. Modeling void area distributions is problematic, even assuming voids behave as pores, because of initial surface imperfections and effects of combustion on surface morphology. This work examines the effects of factors that affect general pore formation for their effect on voids larger than 1 μm, such as heterogeneous combustion, devolatilization, and particle size and how these factors influence the calculation of diffusion limited burning rate from temperature and image data. Void distributions were predicted using an established pore distribution model, with and without the effects of pore combination. Results indicate that void distributions roughly follow expected pore behavior through devolatiltzation, but not after ignition, with void area fraction increasing with increasing coal volatile content and particle heating rate, but not significantly affected by oxygen concentration or initial particle size. Further, analytical pore models provide reasonable approximations for void distributions in the calculation of particle burning rates from temperature and image data.

Refinement of the Accuracy of Residual Life Assessment Based on the Generation and Growth Behavior of Creep Voids for Boiler Welded Zone.

Currently, in order to evaluate the residual life of a welded area of an actual boiler, the Void Area Fraction is usually measured at the evaluation points. The residual life is calculated from the life fraction Master curve prepared in the laboratory. But since such Master curves are obtained from a series of partially completed creep tests and since the effects of temperature, stress, and weld-heat-affected-zone structure have not been satisfactorily examined, a lower limit of 99% of the data band has been adopted for safety. In order to achieve high-accuracy evaluations, differences in creep void generation and growth processes resulting from differences in heat, stress, and weld-heat-affected zone structure were observed in detail. As a result, the method described below is proposed as a high-accuracy method of Residual Life Asessment. (1) Clarification of damage evaluation position. a. Evaluate the coarse-grained areas of the circumferential joints of pipes subject to internal pressure. b. Evaluate the fine-grained areas of the longitudinal joints of pipes subject to internal pressure, longitudinal joints of elbows, and circumferential joints of pipes subject to system stress. (2) Use of Different Master curves for the evaluation positions. Use the different Master curves (which was conventionally a single curve) for the HAZ fine grain section and the coarse grain section. The Void Area Fraction method is appropriate for the HAZ fine grain section, and is not appropriate for the coarse grain section.

Imaging damage evolution in a small particle metal matrix composite

It is difficult to study effectively microstructural damage in metal matrix composites (MMCs) due to artefacts arising from traditional metallographic sample preparation techniques. The sectioning and imaging capabilities of the focused ion beam (FIB) microscope provide an excellent method for studying damage accumulation in MMCs. The capabilities of the FIB system have been used to carry out a study of damage evolution in a powder-processed/hot-extruded Al2080/SiCp MMC. Microvoid damage is found to be preserved accurately during FIB sectioning, allowing measurements of the fraction of decohered particles and the void area fraction. These microscopic damage measurements are correlated with the macroscopic damage parameter, D, as determined by density measurements. Using transmission electron microscopy, the evolution of dislocation structures at the SiC-matrix interfaces has been examined. A previously unreported decohesion mechanism has been observed.

Basic investigation for life assessment technology of modified 9Cr–1Mo steel

In order to develop life assessment techniques for aged components made of modified 9Cr–1Mo steel, specimens were artificially deteriorated by aging, creep and fatigue tests at elevated temperatures, and associated changes in the microstructure and mechanical properties were examined. It was observed that aging resulted in formation of Laves phase causing a decrease in toughness. The creep damage in base metal could be correlated with decrease in hardness, while creep damage in weldments could be correlated with the area fraction and density of creep voids. Creep rupture in weldments occurred in the fine-grained heat affected zone by the formation and growth of creep voids. The fatigue damage in base metal correlated to the maximum length of a crack among micro-cracks initiated during fatigue cycles.

Detection of Micro-Voids by Evaluation for Attenuation Coefficient of Ultrasonic Waves Using Electromagnetic Acoustic Resonance Method on SUS 304 Fabricated by Hot Isostatic Press.

It was evaluated creep damage by Electromagnetic Acoustic Resonance (EMAR), Noise Energy Method and Supersonic Spectroscopy (First Moment) Method on SUS 304 fabricated by Hot Isostatic Press (HIF) at 1050°C. Attenuation coefficient of electromagnetically excited acoustic wave in HIP has been investigated with frequency between 1.1 MHz and 5.4 MHz. Attenuation coefficient of the shear wave of as low as 2.5×10-4/μs at 1.1 MHz has been detected by reducing diffraction loss and the loss due to transmission of the ultrasonic wave to the electromagnetic acoustic transducer through the mechanical contact. The attenuation coefficient increases in proportion with frequency up to 5.4 MHz on the samples (specimen) fabricated with the pressure of 170 MPa. On the other hand, on the samples (specimen) fabricated with pressure lower than 80 MPa, the attenuation coefficient increases rapidly above 4 MHz. The void area fraction has been found to increase as the pressure decreases, which may be responsible for the rapid increment of the ultrasonic attenuation of the samples (specimen) fabricated with pressure lower than 80 MPa. As a result, it was clear that EMAR is more sensitive one to detect creep voids than the other methods. So We hope it is possible to use the actual facilitles in future.

Estimation of the lifetime of Al/Ni-plated material for wet-seal area in molten carbonate fuel cells

Al/Ni-plated material, which is produced by electroplating of Ni and Al on a stainless-steel substrate followed by heat-treating at 750°C, has been investigated for the wet-seal material. In order to estimate the lifetime of the material, Type A and Type B were prepared, and immersion test in molten carbonate and heating test in air at various temperatures were carried out. Results of this study are summarized as follows. Two types of Al/Ni-plated material showed a good corrosion resistance against the molten carbonate at 650°C in 70% air/30% CO2 for 14 500 h. In the accelerated heating test, Al concentration in the Al–Ni layer kept nearly constant after 10 000 h, but voids were observed at the Al–Ni layer/the substrate interface. It was found that the growth rate of void, which was calculated from the area fraction of voids observed at each temperature, was proportional to temperature. The log k decreased linearly with 1/T, where k was a constant of the growth rate of voids. It was suggested that the lifetime of the Al/Ni-plated material is expected to be more than 40 000 h at 650°C in molten carbonate.

Replication Technique for Microscopic Examination of Microstructures Etched by Penning Discharge Micro-Sputtering.

A combination of penning discharge micro sputtering techniques and non destructive replication method have been applied for etching an austenitic stainless steel SUS 316 H after creep and rupture testing. The micro-sputtering produced clear and reproducible microstructures so that grain boundaries, creep voids, carbides and σ phase precipitates were readily characterized. The replica taken from the specimen surface after micro-sputtering were observed by optical and scanning electron microscopes. Several factors during replica sampling such as an adherence between replica film and specimen surface, expansion and contraction of the film and so on, which can affect a quality of resulting microstructures, were examined and the sampling procedures were improved. Optimizing the conditions of replica sampling, clear microstructures as good as those by conventional chemical etching were obtained and the A parameter and area fraction of creep voids were quantitatively evaluated for analysis of microstructural degradation during creep.

Microstructural evolution and superplastic deformation behavior of fine grain 5083Al

The microstructural evolution during superplastic deformation of a fine grain Al-4.7 pct Mg alloy (5083Al) has been studied quantitatively. Starting from an average grain size of 7 µm, grain growth was monitored in this alloy both under static annealing and with concurrent superplastic deformation at a high test temperature of 550°C. Grain size was averaged from measurements taken in longitudinal, transverse, and thickness directions and was found to grow faster during concurrent superplastic deformation than for static annealing. A grain growth law based on an additive nature between time-based and strain-based growth behavior was used to quantify the dynamics of concurrent grain growth. The extent of void formation during deformation was quantified as the area fraction of voids on L-S planes. This void fraction, referred to as the cavity area percent, was recorded at several levels of strain for specimens deformed at two different strain rates. A constitutive equation incorporating this grain growth data into the stress-strain rate data, determined during the early part of deformation, was generated and utilized to model the superplastic tensile behavior. This model was used in an effort to predict the stress-strain curves in uniaxial tension under constant and variable strain rate conditions. Particular attention was paid to the effects of a rapid prestrain rate on the overall superplastic response and hardening characteristics of this alloy.

Uniformity Evaluation of Cohesionless Specimens Using Digital Image Analysis

Nonuniformity within specimens of granular materials is considered to be one of the major reasons for the dependence of the observed static/dynamic response during laboratory testing on the method of preparation. In this paper, a resin-impregnation/digital image analysis method to examine the uniformity of cohesionless specimens at microscopic, macroscopic, and global scales is described. The approach relies on the equivalence between volume fraction and the expected value of area fraction where the area fraction of voids on two-dimensional sections is obtained using a computer-based digital image analysis system. A sampling strategy which allows porosity variations in the vertical direction as well as in the radial direction of the specimen to be examined is proposed. The method is illustrated with the results of measurements performed on a typical specimen and shows that a much larger amount of nonuniformity exists when the soil is examined at a microscopic level. A statistical procedure to evaluate the accuracy of a volume-fraction measurement using areal analysis is also described. The proposed method offers much promise for examining the uniformity of specimens accurately and efficiently.

Study on Highly Accurate Evaluation of Creep Void Area Fraction Rate by Use of Image Processing Technique.

For life extension of fossil power plants, one of the most important subjects is to evaluate creep damage in high-temperature components such as boilers and turbines. A creep void area fraction rate method, by which damage is evaluated based on visible information from a material texture image, is a useful method with applicability to damage detection in actual plants. In this study, an evaluation system for creep void area fraction rate assisted by an image-processing technique was newly developed. It was ascertained that the developed system enabled efficient and objective evaluation with the same accuracy as the conventional manual method. Statistical properties of creep void distribution were studied using data acquired with the system. The relation between measurement conditions and evaluation accuracy was examined, and reasonable measurement conditions were proposed.

Transport and reaction in evolving, disordered composites-II. Coke deposition in a catalytic pellet

We present a model for transient diffusion and reaction occurring in a single, spherical pellet undergoing deactivation by coke deposition. The assumption and limitations are similar to those of Part I. The solid morphology is assumed to be completely disordered throughout the process and is represented by a site-percolation model. The emphasis of this work is on the pore-plugging phenomenon, although the active-site poisoning is accounted for in conventional terms. We study the influence of process parameters, such as Damköhler number and selectivity, on the pore plugging process for both the parallel and series mechanisms. Special attention is paid to the effect, on the same process, of various morphological parameters such as accessible void area fraction, accessible void volume fraction, accessible intermaterial area density and the effective diffusivity factor. Some of these morphological features are critical in the modeling of catalyst deactivation under diffusion control.

Application of McClintock's ductile fracture model by the growth of holes to the tensile straining of some spheroidized steels under superimposed hydrostatic pressures

Quantitative metallography performed on three spheroidized steels under tensile loading has provided data of void initiation and growth up to fracture. In the present article an attempt is made to explain the experimental results on the basis of a model due to McClintock for the growth of isolated cylindrical holes under an applied stress system. The model had been modified to permit continuous nucleation of voids throughout the deformation, and this is consistent with the experimental observations. The model ignores the size, shape and distribution effects of the second-phase particles and does not account for the local stress conditions which will govern the onset of nucleation. In spite of these shortcomings, it is demonstrated that the predicated area fraction of voids as a function of strain shows excellent correlation with the experimental observations. Furthermore, the model provides a qualitative account of the actual growth of voids and provides a realistic assessment of the influence of hydrostatic pressure on void initiation and their morphology during continuing deformation.

Void formation in INCONEL MA-754 by high temperature oxidation

Subsurface void formation in oxide dispersion strengthened MA-754 caused by high temperature oxidation was investigated at temperatures of 1100, 1150, and 1200 °C for times of 1, 10, 50, and 100 hours. Material exposed at 1200 °C was examined using microprobe, SEM, and optical microscopy techniques. After exposure in air at 1200 °C for 100 hours, chromium depletion by as much as 10 wt pct was observed near the surface, and voids of various sizes up to 15 µm in diameter were found to depths of 300 µm. The fraction of voids increases with exposure time and, with the exception of anomalous values near the surface, decreases with depth. The maximum area fraction of voids observed was approximately 8 pct. Correlation of the void area fraction profile with the measured chromium depletion through a diffusion analysis shows that void formation is due to vacancy injection. Similar void formation in Ni-Cr alloys without oxide dispersions suggests that void formation is not dependent upon the presence of oxide dispersions. The diffusion coefficient for chromium in MA-754 at 1200 °C was computed from microprobe data to be 4 × 10-10 cm2 per second.

The nucleation and growth of voids in a material containing a distribution of grain-boundary particles

Void growth is analysed when a grain boundary contains a distribution of second phase particles. The rate of void growth is determined by the ease with which material can plate out around the particles or the rale at which the material surrounding the particles can deform by power-law creep. At low applied stresses, stress is concentrated onto the particles which can act as nucleating sites for new cavities. The stress at a particle is a function of its size, and increases as the area fraction of voids increases. A new cavity can nucleate once this stress reaches a critical value, and because materials contain a distribution of particle sizes, nucleation occurs continuously during the course of an experiment.