Variability in tensile ductility of a dual-phase steel is investigated using quantitative microscopy and fractography. Variability in the ductility does not correlate with the global properties such as phase volume fractions. Quantitative fractography reveals an inverse quantitative correlation between number density of the pullouts of ferrite–martensite colonies in the fracture surfaces and the ductility of corresponding tensile test specimens. Therefore, local variations in the attributes of interfaces, rather than global microstructural properties, account for a significant part of variability in ductility.

Microstructural characteristics of porous LSM/YSZ composite cathodes greatly influence the performance of solid oxide fuel cells. The triple phase boundaries, for example, account for a significant portion of the electrochemically active sites in these porous composite cathodes. Nonetheless, experimental characterization of the relevant microstructural attributes has been problematic due to lack of suitable microscopy techniques for simultaneous observations of all three phases (i.e., LSM, YSZ, and porosity) needed for identification and unbiased characterization of the triple phase boundaries. In this contribution it is shown that a combination of chemical etching and atomic force microscopy clearly reveals all three phases and the triple phase junctions in the microstructural sections. Further, stereological techniques based on the geometric probabilities of stochastic geometry enable unbiased statistical estimation of total triple phase boundary length per unit volume and other microstructural attributes from simple counting measurements performed on representative microstructural sections.

An analytical equation is derived for total triple phase boundary length per unit volume (LTPB) in an isotropic uniform random microstructure of LSM/YSZ composite cathode. The equation is applicable to YSZ and LSM particles of any convex shapes and size distributions. The equation explicitly relates LTPB to the shapes, mean sizes, coefficient of variation (a measure of the spread in a size distribution) and skewness of YSZ and LSM particle populations, and volume fractions of YSZ, LSM, and porosity. The equation is verified using available experimental data, and compared with the results of earlier simulations and models. The parametric analysis reveals that (1) non-equiaxed plate-like, flake-like, and needle-like YSZ and LSM particle shapes can yield substantially higher LTPB; (2) mono-sized YSZ and LSM powders lead to higher LTPB as compared to the powders having size distributions with large coefficient of variation; (3) LTPB is inversely proportional to the mean sizes of YSZ and LSM particles; (4) high value of LTPB is obtained at the lowest porosity volume fraction that permits sufficient connectivity of the pores for gas permeability; and (5) LTPB is not sensitive to the relative proportion of YSZ and LSM phases in the regime of interest in composite cathode applications.

Three-dimensional (3D) microstructures of TiB phase in a powder metallurgy Ti–6Al–4V–1.7B alloy processed using two different routes are reconstructed from large-area high-resolution montage serial sections. Visualizations of the 3D microstructures are used to determine the effects of the processing route on the morphology, anisotropy, and spatial distributions of TiB particles.

Cast magnesium alloys often exhibit large variability in fracture related mechanical properties such as ductility and strength. In this contribution, the variability in the tensile ductility of individually cast tensile test specimens of high-pressure die-cast AE44 Mg-alloy is examined at room temperature and at 394 K. Significant specimen-to-specimen variations in the ductility are observed at both temperatures. The variability in the ductility does not quantitatively correlate to the average volume fraction of porosity (or any other microstructural parameters) in the bulk three-dimensional microstructure. The area fraction of porosity measured in the fracture surfaces of the tensile test specimens is much larger than the average volume fraction of the porosity in the corresponding bulk microstructure. Therefore, the fracture path preferentially goes through the regions of highly localized clusters of gas and shrinkage pores. Interestingly, at both test temperatures, the percent tensile ductility e shows a quantitative correlation with the area fraction of the porosity f in the corresponding fracture surfaces, which can be represented by the following simple equation e = e0[1 − f]m, where e0 and m are empirical constants.

High-pressure die-casting is the preferred manufacturing process for cast Mg-alloy components used for numerous applications. High-pressure die-cast components usually contain micro-porosity that adversely affects their mechanical properties. In this contribution, the effects of three important process parameters, gate velocity, intensification pressure, and melt temperature on the micro-porosity distributions in high-pressure die-cast AM50 Mg-alloy are quantitatively characterized. The amounts of total porosity, gas porosity, shrinkage porosity, and pore size distributions are experimentally measured using novel digital image analysis techniques that permit quantification of both gas and shrinkage pores in an unbiased manner. The experimental data lead to the following conclusions:(1)Application of intensification pressure significantly reduces the total amount of porosity primarily via reduction in the gas porosity. The intensification pressure significantly reduces the number density and area fraction of the gas pores larger than 100 μm diameter.(2)A decrease in the gate velocity decreases the total amount of porosity predominantly via a decrease in the gas porosity and a small extent of decrease in the shrinkage porosity. The lower gate velocity uniformly decreases the number density and area fraction of gas pores of all sizes (small and large).(3)A decrease in the melt temperature also reduces the total amount of porosity primarily via reduction in the gas porosity. The lower melt temperature reduces the number density and area fraction of the gas pores larger than 30 μm.

Variability in the tensile ductility of high-pressure die-cast AM50 Mg-alloy is examined at five different test temperatures. The fracture path preferentially goes through the regions of clusters of pores. The percent ductility is correlated to area fraction of porosity in the fracture surfaces using a power law equation.

Correlation functions are useful for representation of microstructural geometry. An equation is derived for limiting behavior of direction dependent two-point correlation functions in terms of orientation distribution of the interface normals and total interfacial area. These constraints are used to identify models for correlation functions that are not physically realizable.

Metallographic evidence is presented for existence of inverse surface macro-segregation in a HPDC AM60 Mg-alloy. The process conditions that facilitate the inverse surface macro-segregation are identified, and the effects of macro-segregation on the low and high cycle fatigue behavior of the HPDC alloy are studied.

Variability in the ductility and strength of a tilt-pour-permanent-mold cast Al-alloy is examined. The variability exhibits strong correlation with the amount of oxide films and shrinkage pores in the corresponding fracture surfaces. The variability can be decreased through a reduction in the amount of these defects via better process control.

Variability in the ductility of tensile test specimens of semi solid process cast A356 Al-alloy (Al-7 wt.% Si-0.5 wt.% Mg-base alloy) is examined. The variability in the ductility does not correlate to the global average microstructural parameters such as dendrite cell size, Si particle size, and amount of porosity in the three-dimensional microstructure. Tensile fracture surfaces contain micro-defects that are essentially residues of modifiers, fluxes, grain refiners, and mold release agents: the energy dispersive analysis shows presence of elements such as O, Na, K, C, Cl, Ca, Fe, Ti, and S in these defects. The fracture path preferentially goes through the regions containing the defects. Scanning electron microscopy, quantitative fractography was used to estimate the total area fraction of such defects in the fracture surfaces of the tensile test specimens. The percent tensile ductility e shows strong quantitative correlation with the area fraction of the defects f in the corresponding fracture surfaces, which can be represented by the following simple equation.e=e0n[1−f]e=e0[1−f]nIn this equation, e0 and n are empirical constants. For the present data set, e0 is equal to 11.5% and n is equal to 41.66. Thus, the variability in the ductility can be decreased through a reduction in the amount of processing defects via better process control.

Nearest-neighbor distances (first and higher order) are an important class of spatial descriptors useful in materials science and other disciplines. These descriptors play a dominant role in microstructural evolution during recrystallization, coarsening, sintering and numerous other materials processes. In the present article, nearest-neighbor distances for mono-sized hard-core spheres in three-dimensional space are studied using computer simulations by two popular algorithms (random sequential adsorption (RSA) and equilibrium Monte Carlo method) and a simple expression (given below) is proposed for the mean values of first-, second-, and higher-order (up to sixth) nearest-neighbor distances:〈Hn〉〈Pn〉=1+2−1/6(n−1)![(4/3)π]−1/3Γ[(3n+1)/3]−1ff02n/(2n+1)where 〈Hn〉 is the mean nth nearest-neighbor distance, f is volume fraction, 〈Pn〉 is corresponding mean nearest-neighbor distance for a point process and f0 is the volume fraction for the close-packed structure (i.e., π/18 or ∼0.74). The predictions of this equation are in good agreement with the simulated results. This expression is applicable over the complete volume fraction range of 0 to π/18 (i.e., ∼0.74).

In numerous metals and alloys, ductile fracture involves void nucleation, growth, and coalescence. In this contribution, void growth has been quantitatively characterized in an extruded 6061-wrought Al-alloy as a function of stress state in notch tensile test specimens. Digital image analysis and Stereology have been used to estimate the volume fraction and three-dimensional number density of voids in a series of interrupted notch tensile test specimens where the local stress state is predominantly triaxial. Finite elements (FE) simulations have been used to compute the stress states at different locations in the specimens. The computed stress states and experimentally estimated average void volume are utilized to verify analytical void growth models. Lack of agreement between the predictions of the models and the experimental data is due to interactions between neighboring voids, which are ignored in the theoretical models, and continuous void nucleation. The following empirical damage evolution equation is obtained from the experimental data on void volume fraction expressed as % (f), and the corresponding local equivalent plastic strain (εp) and stress triaxiality (I) computed from FE simulations: f=a+b ln[εp]+cI. In this equation, a, b and c are empirical constants whose values depend on the alloy chemistry, heat treatment, and microstructure. The equation is useful only for 6061(T6) Al-alloy.

There has been increasing thrust lately on the development of lightweight cast magnesium alloy components for structural automotive and other applications. The microstructure of the high-pressure die-cast Mg alloys usually contains a fine-grained “skin” having a microstructure significantly different from that of the bulk material. Characterization of the local constitutive behavior of the skin microstructure is of interest as it can affect the overall mechanical response of the component. However, the standard mechanical tests on the macro-specimens are not useful for characterization of the local stress–strain response of the skin microstructure. In this contribution, we present a novel methodology based on a combination of micro-indentation experiments and three-dimensional (3D) finite elements based simulations that permits computation of the local stress–strain (constitutive) behavior of the skin and the interior microstructures at the length scales of 100 μm in a cast high-pressure die-cast AM60 Mg-alloy. The methodology involves development of a numerical solution to the inverse problem. The computed constitutive equations are then utilized to simulate the effect of skin thickness on the overall global mechanical response of the alloy under uniaxial compression.

Experiments have been performed to quantitatively characterize the three-dimensional (3-D) microstructural damage due to cracking of Fe-rich intermetallic particles in an Al–Mg-base extruded 5086(O) alloy as a function of strain under uniaxial compression and tension. The 3-D number density and average volume of the cracked particles are estimated using the unbiased and efficient large area disector (LAD) stereological technique. In each specimen, the two-dimensional (2-D) number fraction of cracked particles is significantly lower than the corresponding 3-D number fraction. Therefore, the conventional 2-D damage measurements considerably underestimate the true 3-D damage due to particle cracking in this alloy. Comparison of the 3-D damage data on the 5086(O) alloy and earlier data on 6061(T6) alloy reveals that at all tensile/compressive stress levels higher than the yield stress of both alloys, the 3-D number fraction of cracked Fe-rich intermetallic particles in the 5086(O) alloy is significantly lower than its corresponding value in the 6061(T6) alloy. Therefore, the 5086(O) alloy is less prone to damage progression due to particle cracking compared to the 6061(T6) alloy. In both the alloys, significant rotations of the Fe-rich intermetallic particles occur during deformation under uniaxial compression. These rotations tend to align the particles along the direction of inducedtensile stretch. The particle rotations in turn affect the progression of damage due to particle cracking. For deformation under uniaxial compression, the average volume of cracked Fe-rich particles increases with the increase in the strain. These observations are explained on the basis of the particle rotations.

Particle fracture is an important void nucleation mode in numerous alloys where fracture is governed by void nucleation and growth processes. The rotations of brittle phase inclusions/particles can facilitate particle cracking (and, therefore, void nucleation) by bringing the inclusions/particles in favorable orientations with respect to the applied/induced tensile load, thereby increasing the void nucleation rate. In this contribution, we present detailed quantitative microstructural data on the rotations of Fe-rich inclusions in a 5086 (O) Al-alloy as a function of strain and stress states. These results are compared with our earlier data on particle rotations in 6061 (T6) Al-alloy, and the differences are explained on the basis of differences in the microstructure and constitutive behavior of the two alloys.

Pressure die-cast magnesium (Mg) alloys contain both shrinkage and gas (air) microporosity. Characterization of shrinkage and (gas) air microporosity is essential for understanding microstructure–properties correlations in these alloys. In this contribution, a recently reported digital image analysis (DIA) technique has been further developed to separately quantify and characterize the attributes of shrinkage and air microporosity in AM series of cast Mg alloys. The image analysis procedure is utilized to measure the nearest-neighbor distributions of the shrinkage and gas (air) pores, and to quantify the clustering tendency of the pores. A new affinity parameter is defined to characterize the affinity of gas (air) pores to shrinkage pores and vice versa. The affinity parameters are computed from the same image analysis data.

Particle/grain size distribution is an important attribute of microstructures. However, direct estimation of three-dimensional particle/grain size distribution has never been performed in opaque material microstructures due to lack of a suitable serial sectioning technique. In this contribution, application of a montage-based efficient serial sectioning technique is presented for direct unbiased estimation of three-dimensional grain size distribution. The technique is used for estimation of three-dimensional grain size distribution of tungsten grains in a liquid phase-sintered (LPS) microstructure. It is shown that the montage-based serial sectioning technique is very efficient. It yields 25–100 times larger high-resolution three-dimensional serially sectioned volume as compared to that obtained from the same number of serial sections. The larger reconstructed microstructural volume provides sufficient number of particles/grains for a reliable estimation of detailed size distribution.

Primary Si crystals are usually present in the cast microstructures of near-eutectic, eutectic, and hyper-eutectic Al–Si base alloys. Three-dimensional digital images of individual primary Si crystals present in a permanent mold cast unmodified Al-12 wt% Si-1 wt% Ni base alloy are reconstructed using a combination of montage serial sectioning and three-dimensional digital image processing techniques. Octahedral, prismatic, and plate-like three-dimensional morphologies of the primary Si crystals are present in the microstructure. Some of the primary Si crystals contain interior regions/islands of Al-alloy that are completely enclosed in the corresponding Si crystals indicating certain variations in the crystal growth velocities during the evolution of these crystals. The boundaries of these interior regions/islands are non-faceted smooth and curved indicating re-melting of the Al-rich islands and re-dissolution of some Si near these internal boundaries in the Al-alloy as a result of the heat generated by liquid-to-solid transformation of Si away from the islands.