Effect of loading condition and stress state on damage evolution of silicon particles in an Al-Si-Mg-Base cast alloy

Damage evolution of Si particles in a Sr modified cast A356(T6) Al alloy is quantitatively characterized as a function of strain under tension, compression, and torsion. The fraction of damaged Si particles, their size distributions, and orientation distribution of particle cracks are measured by image analysis and stereological techniques. Silicon particle cracking and debonding are the predominant damage modes. Particle debonding is observed only under externally applied tensile loads, whereas particle cracking is observed under all loading conditions. The relative contributions of Si particle debonding and fracture to the total damage strongly depend on stress state and temperature. For all loading conditions and stress states studied, the average size of damaged Si particles is considerably larger than the bulk average size. The rate of damage accumulation is different for different loading conditions. At a given strain level, Si particle damage is lowest under compression and highest under torsion. The anisotropy of the damage is highly dependent on the deformation path and stress state. Under uniaxial tension, the cracks in the broken Si particles are mostly perpendicular to the loading direction, whereas in the compression test specimens they are parallel to the loading direction. The Si particle cracks in the torsion and notch-tension test specimens do not exhibit preferred orientations. The quantitative microstructural data are used to test damage evolution models.     

Damage by eutectic particle cracking in aluminum casting alloys A356/357

The strain dependence of particle cracking in aluminum alloys A356/357 in the T6 temper has been studied in a range of microstructures produced by varying solidification rate and Mg content, and by chemical (Sr) modification of the eutectic silicon. The damage accumulates linearly with the applied strain for all microstructures, but the rate depends on the secondary dendrite arm spacing and modification state. Large and elongated eutectic silicon particles in the unmodified alloys and large π-phase (Al₉FeMg₃Si₅) particles in alloy A357 show the greatest tendency to cracking. In alloy A356, cracking of eutectic silicon particles dominates the accumulation of damage while cracking of Fe-rich particles is relatively unimportant. However, in alloy A357, especially with Sr modification, cracking of the large π-phase intermetallics accounts for the majority of damage at low and intermediate strains but becomes comparable with silicon particle cracking at large strains. Fracture occurs when the volume fraction of cracked particles (eutectic silicon and Fe-rich intermetallics combined) approximates 45 pct of the total particle volume fraction or when the number fraction of cracked particles is about 20 pct. The results are discussed in terms of Weibull statistics and existing models for dispersion hardening.     

Anisotropy of intermetallic particle cracking damage evolution in an Al-Mg-Si base wrought aluminum alloy under uniaxial compression

Particle cracking is an important damage mode in numerous engineering alloys having anisotropic microstructures. In this contribution, cracking of anisotropic Fe-rich intermetallic particles in an extruded 6061 (T651) Al-alloy is quantitatively characterized as a function of compressive strain for two loading directions. The Fe-rich intermetallic particles rotate when a compressive load is applied parallel to the extrusion direction, which in turn affects the particle cracking process. At low compressive strains, the number fraction of cracked Fe-rich particles is higher in specimens loaded perpendicular to the extrusion axis as compared to that in specimens loaded parallel to the extrusion axis. However, the reverse is true at the high strain levels. These differences in damage evolution are explained on the basis of particle rotations and microstructural anisotropy.     

Effect of strain rate on damage evolution in a cast Al-Si-Mg base alloy

An important aspect of damage evolution in cast Al-Si-Mg base alloys is fracture/cracking of Si particles. This microstructural damage is quantitatively characterized as a function of strain rate in the range 10⁻⁴ to 3.7 × 10⁺³, at an approximately constant uniaxial compressive strain level (20 to 25 pct). It is shown that the fraction of damaged silicon particles, their average size, and size distribution do not vary significantly with the strain rate, and at all strain rates studied, larger Si particles are more likely to crack than the smaller ones. However, the stress-strain curves are sensitive to the strain rate. These observations have implications for modeling of deformation and fracture of cast components under high strain rate crash conditions.     

SiC particle cracking in powder metallurgy processed aluminum matrix composite materials

Particle cracking is one of the key elements in the fracture process of particulate-reinforced metal-matrix composite (MMC) materials. The present study quantitatively examined the amount of new surface area created by particle cracking and the number fraction of cracked particles in a series of SiC-reinforced aluminum-matrix composite materials. These composite materials were fabricated by liquid-phase sintering and contained 9 vol pct of 23, 63, or 142 μm SiC. The matrix properties were varied by heat treating to either an underaged or peak-aged condition. In general, the new surface area created by particle cracking (S _v ) and the number fraction of cracked particles (F_no) were linearly dependent on the local strain along the tensile specimen. Multiple cracks were frequently observed in the composites containing large particles. It was found that the new surface area created by particle cracking per unit strain was higher for the case of high-strength matrices and was not systematically affected by particle size within the range studied. The number fraction of cracked particles was affected by both particle size and matrix strength. A higher number fraction of particles cracked in the composites reinforced with large particles and with high matrix yield strengths. These results are interpreted in terms of the size of the particle defects, which is a function of particle size, and the critical flaw size necessary to crack a given particle, which is a function of the stress on the particle. The new surface area created by cracking and the fraction of cracked particles were related and are in good agreement for the large and medium sized particles.     

Fracture at elevated temperatures in a particle reinforced composite

The tensile fracture behavior of a cast and extruded 2014 aluminum alloy metal matrix composite (MMC) reinforced with 10, 15, and 20 vol.% aluminum oxide particles was investigated as a function of temperature between 100 and 300°C and hold time, and compared with the unreinforced alloy. In addition, the effect of aging condition was investigated in a 15 vol.% composite tested at 200°C. At lower temperature the composites have higher yield strength and UTS than the unreinforced material, and both decrease with increasing temperature. At higher temperatures all the materials have similar strength levels. The elongation is lower in the composites, decreasing with increasing level of reinforcement and increasing with increasing temperature, except at the highest temperature where all the composites are about the same. The microstructural damage in the composites also varies with temperature: particle fracture dominates at lower temperatures and interparticle voiding is the main damage feature at elevated temperatures. The time at temperature, and hence the degree of overaging, has little effect on the observed trends in the composite, in contrast with the unreinforced material where the density of voids decreases with increasing hold times. The transition temperature where the major damage changes from particle cracking to interparticle voiding increases with volume fraction and particle size, and decreases with overaging. The cracked particle density and void density both increase with strain, and the highest rate of increase occurs in the overaged material. In general, the tendency for particle cracking is reduced and for interparticle voiding is increased by any factor which permits accomodation of strain by the matrix, such as lower volume fraction of particles, small particle size, nonclustered particle distribution, and matrix softening from underaging or overaging.     

Damage due to fracture of brittle reinforcements in a ductile matrix

A micromechanical model is developed for brittle particle reinforced metal matrix composites sustaining damage. A composite with uniformly distributed damage is modelled by a three-phase damage cell consisting of a cracked particle in a cylindrical matrix cell embedded in an undamaged composite cylinder. The fraction of broken particles to all particles is taken as the ratio of the broken-particle/matrix cell volume to the whole damage cell volume. Systematic analysis is carried out for aligned spherical and cylindrical particles in an elastic-perfectly plastic matrix subject to tensile loading normal to the plane of particle cracks. The influence of damage evolution paths on the composite stress-strain behavior is investigated. Results are given for the effects of damaged particle percentage, total particle volume fraction and particle shape on the overall composite limit flow behavior. Significant reduction in composite limit flow stress may occur if most of the particles are broken. For composite with spherical reinforcement, the reduction is found to be linearly dependent on the percentage of damaged particles.     

Yield criteria and strain-rate behavior of Zr57.4Cu16.4Ni8.2Ta8Al10 metallic-glass-matrix composites

We have examined the yielding and fracture behavior of Zr_57.4Cu_16.4Ni_8.2Ta₈Al₁₀ metallic-glass-matrix composites with a small volume fraction (∼4 pct) of ductile crystalline particles under quasi-static uniaxial tension and compression and dynamic uniaxial compression. The yield stress of the composite is the same for quasi-static tension and compression, consistent with a von Mises yield criterion. The measured average angle between the shear bands and the loading axis in quasi-static compression is 47±2 deg, significantly larger than the value of ∼42 deg typically reported for single-phase metallic glasses. Finite element modeling (FEM) shows that the measured value is consistent with both the von Mises criterion (48±4 deg) and the Mohr-Coulomb criterion (46±5 deg). The fracture surface angles, however, are 41±1 deg (compression) and 54±2 deg (tension), in good agreement with observations of single-phase metallic glasses. At low strain rates (<10⁻¹ s⁻¹), the yield stress is independent of strain rate, while at higher strain rates (>10⁰ s⁻¹), the failure stress decreases with increasing strain rate, which again is similar to the behavior of single-phase glasses. These results indicate that while the presence of the particles has a significant effect on the yield behavior of the composites, the fracture behavior is largely governed by the properties and behavior of the amorphous matrix.     

Plastic deformation behavior of aluminum casting alloys A356/357

The plastic deformation behavior of aluminum casting alloys A356 and A357 has been investigated at various solidification rates with or without Sr modification using monotonic tensile and multi-loop tensile and compression testing. The results indicate that at low plastic strains, the eutectic particle aspect ratio and matrix strength dominate the work hardening, while at large plastic strains, the hardening rate depends on secondary dendrite arm spacing (SDAS). For the alloys studied, the average internal stresses increase very rapidly at small plastic strains and gradually saturate at large plastic strains. Elongated eutectic particles, small SDAS, or high matrix strength result in a high saturation value. The difference in the internal stresses, due to different microstructural features, determines the rate of eutectic particle cracking and, in turn, the tensile instability of the alloys. The higher the internal stresses, the higher the damage rate of particle cracking and then the lower the Young’s modulus. The fracture strain of alloys A356/357 corresponds to the critical amount of damage by particle cracking locally or globally, irrespective of the fineness of the microstructure. In the coarse structure (large SDAS), this critical amount of damage is easily reached, due to the clusters of large and elongated particles, leading to alloy fracture before global necking. However, in the alloy with the small SDAS, the critical amount of damage is postponed until global necking takes place due to the small and round particles. Current models for dispersion hardening can be used to calculate the stresses induced in the particles. The calculations agree well with the results inferred from the experimental results. This article is based on a presentation given in the symposium “Dynamic Deformation: Constitutive Modeling, Grain Size, and Other Effects: In Honor of Prof. Ronald W. Armstrong,” March 2–6, 2003, at the 2003 TMS/ASM Annual Meeting, San Diego, California, under the auspices of the TMS/ASM Joint Mechanical Behavior of Materials Committee.     

Deformation and damage mechanisms of zinc coatings on hot-dip galvanized steel sheets: Part II. Damage modes

Zinc-based coatings are widely used for protection against corrosion of steel-sheet products in the automotive industry. The objective of the present article is to investigate the damage modes at work in three different microstructures of a zinc coating on an interstitial-free steel substrate under tension, planestrain tension, and expansion loading. Plastic-deformation mechanisms are addressed in the companion article. Two main fracture mechanisms, namely, intergranular cracking and transgranular cleavage fracture, were identified in an untempered cold-rolled coating, a tempered cold-rolled coating, and a recrystallized coating. No fracture at the interface between the steel and zinc coating was observed that could lead to spalling, in the studied zinc alloy. A complex network of cleavage cracks and their interaction with deformation twinning is shown to develop in the material. An extensive quantitative analysis based on systematic image analysis provides the number and cumulative length of cleavage cracks at different strain levels for the three investigated microstructures and three loading conditions. Grain refinement by recrystallization is shown to lead to an improved cracking resistance of the coating. A model for crystallographic cleavage combining the stress component normal to the basal plane and the amount of plastic slip on the basal slip systems is proposed and identified from equibiaxial tension tests and electron backscattered diffraction (EBSD) analysis of the cracked grains. This analysis requires the computation of the nonlinear stress-strain response of each grain using a crystal-plasticity constitutive model. The model is then applied successfully to other loading conditions and is shown to account for the preferred orientations of damaged grains observed in the case of plane-strain tension.     

Effect of Stress Triaxiality on the Flow and Fracture of Mg Alloy AZ31

The microscopic damage mechanisms operating in a hot-rolled magnesium alloy AZ31B are investigated under both uniaxial and controlled triaxial loadings. Their connection to macroscopic fracture strains and fracture mode (normal vs shear) is elucidated using postmortem fractography, interrupted tests, and microscopic analysis. The fracture locus (strain-to-failure vs stress triaxiality) exhibits a maximum at moderate triaxiality, and the strain-to-failure is found to be greater in notched specimens than in initially smooth ones. A transition from twinning-induced fracture under uniaxial loading to microvoid coalescence fracture under triaxial loading is evidenced. It is argued that this transition accounts in part for the observed greater ductility in notched bars. The evolution of plastic anisotropy with stress triaxiality is also investigated. It is inferred that anisotropic plasticity at a macroscopic scale suffices to account for the observed transition in the fracture mode from flat (triaxial loading) to shear-like (uniaxial loading). Damage is found to initiate at second-phase particles and deformation twins. Fracture surfaces of broken specimens exhibit granular morphology, coarse splits, twin-sized crack traces, as well as shallow and deep dimples, in proportions that depend on the overall stress triaxiality and fracture mode. An important finding is that AZ31B has a greater tolerance to ductile damage accumulation than has been believed thus far, based on the fracture behavior in uniaxial specimens. Another finding, common to both tension and compression, is the increase in volumetric strain, the microscopic origins of which remain to be elucidated.     

Plastic flow of a tungsten-based composite under quasi-static compression

A micromechanics study is carried out on the plastic flow of a tungsten “heavy alloy” under uniaxial compression. The alloy-composed of a continuous tungsten phase in a tungsten-nickel-iron “matrix”—is modeled as a dual-phase composite, with the tungsten phase approximated by aligned, uniformly distributed and equal-sized particles. The stress-strain behavior of each phase is assumed to be power-law hardening of the Ramberg-Osgood type. Stress-strain curves of the composite under uniaxial compression are computed numerically using several cell models representing different tungsten particle shapes. It is found that the overall stress-strain behavior of the composite is essentially independent of the particle shape. However, the character of the local plastic deformation changes dramatically with the inclusion geometry. Two simple formulae are given that approximate the overall flow behavior of the composite in terms of the tungsten volume fraction and the behavior of the individual phases.     

Acoustic emission from particulate-reinforced metal matrix composites

A systematic study of the effect of microstructural parameters on the fracture behaviour of silicon carbide particle reinforced aluminium matrix composites has been carried out. Acoustic emissions have been monitored during tensile testing, giving the size and number of emmissions as a function of strain. This has been shown to be simply related to the rate of void nucleation at the reinforcing phase. Both particle fracture and particle/matrix decohesion mechanisms can be detected. Void nucleation was observed from the onset of plastic deformation and a linear relationship between damage initiation rate and strain was found. The rate of emission increased with reiforcing particle size and volume fraction but was independent of matrix alloy composition and heat treatment. These results show that the failure strain of particulate metal matrix composites is not controlled solely by the onset of void nucleation at the reinforcing phase. Local failure processes in the matrix are shown to promote void coalescence and dominate the ductility. However, suppression of void nucleation at the particles increases the ductility. It is suggested that a critical number of fractured particles is required before failure.     

Applied Stress Affecting the Environmentally Assisted Cracking

Stress corrosion cracking (SCC) is affected by the mode of applied stress, i.e., tension, compression, or torsion. The cracking is measured in terms of initiation time to nucleate a crack or time to failure. In a simple uniaxial loading under tension or compression, it is observed that the initiation time can vary in orders of magnitude depending on the alloy and the environment. Fracture can be intergranular or transgranular or mixed mode. Factors that affect SCC are solubility of the metal into surrounding chemical solution, and diffusion rate (like hydrogen into a tensile region) of an aggressive element into the metal and liquid metallic elements in the grain boundaries. Strain hardening exponent that affects the local internal stresses and their gradients can affect the diffusion kinetics. We examine two environments (Ga and 3.5 pct NaCl) for the same alloy 7075-T651, under constant uniaxial tension and compression load. These two cases provide us application to two different governing mechanisms namely liquid metal embrittlement (7075-Ga) and hydrogen-assisted cracking (7075-NaCl). We note that, in spite of the differences in their mechanisms, both systems show similar behavior in the applied K vs crack initiation time plots. One common theme among them is the transport mechanism of a solute element to a tensile-stress region to initiate fracture.     

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.     

Isotropic and kinematic hardening in a dispersion-strengthened aluminum alloy

The room temperature mechanical behavior of a dispersion strengthened aluminum alloy was examined in tension, compression, and in fully reversed loading. The alloy, 8009, is characterized by a high volume fraction of 50–100 nm dispersoid (25%) and 0.5 mm grain size. In tension, 8009 exhibits low strain to UTS and large post uniform elongation; in compression, near steady state deformation is observed after 2–3% strain. The Bauschinger effect was quantified as a function of prestrain in the forward direction. The experimental reverse loading curves were compared to those expected for ideal isotropic hardening and ideal K1 type kinematic hardening. The alloy exhibits nearly pure kinematic hardening of the K1 type. Based on the microstructure and the fully reversed loading behavior, the monotonic deformation behavior is explained.     

Effect of the Type of State of Stress on the Stress Relaxation in Titanium Nickelide

The stress relaxation in titanium nickelide specimens subjected to strain controlled uniaxial tension under martensitic anelasticity conditions at a given rate and the limited creep effect observed at the stages of stress controlled steplike loading are studied. The rheonomic properties of a shape memory alloy are found to depend on the type of state of stress, and they are more pronounced in tension than in compression. A simple model is develop to describe the detected effects.     

Void Nucleation and Growth in Dual-Phase Steel 600 during Uniaxial Tensile Testing

Commercial dual-phase (DP) steel in sheet form and comprised of ferrite, martensite, and bainite was subjected to uniaxial tension up to fracture. The damage characteristics were studied through extensive quantitative metallography and scanning electron microscope (SEM) observations of polished sections and fracture surfaces of failed specimens. The observed void nucleation mechanisms include nucleation at the martensite/ferrite interface or triple junction (most predominant), nucleation due to the cracking of martensite particles, and nucleation at the inclusions. The void characteristics in terms of area fraction, void density, void size ranges, and void orientations were analyzed as a function of thickness strain from various regions of the different uniaxial tensile test specimens taken to fracture. The damage analysis suggests that the void nucleation occurs during the entire deformation process with an almost constant rate and this rate reduces before fracture. A nucleation strain of 0.15 has been estimated for this material.     

Aspects of fracture in particulate reinforced metal matrix composites

The tensile deformation and fracture behaviour of the aluminium alloy 6061 reinforced with SiC has been investigated. In the T4 temper plastic deformation occurs throughout the gauge length and the extent of SiC particle cracking increases with increasing strain. In the T6 temper strain becomes localised and particle cracking is more concentrated close to the fracture. The elastic modulus decreases with increasing particle damage and this allows a damage parameter to be identified. The fraction of SiC particles which fracture is less than 5%, and over most of the strain range the damage controlling the tensile ductility can be recovered, indicating that other factors, in addition to particle cracking are important in influencing tensile ductility. It is suggested that macroscopic fracture is initiated by the SiC particle clusters that are present in these composites as a result of the processing. The matrix within the clusters is subjected to high levels of triaxial stress due to elastic misfit and the constraints exerted on the matrix by the surrounding particles. Final fracture is then produced by crack propagation through the matrix between the clusters.     

New Model for the Analysis of Size-Scale Effects on the Ductility of Reinforced Concrete Elements in Bending

The well-known cohesive crack model describes strain localization with a softening stress variation in concrete members subjected to tension. An analogous behavior is also observed in compression, when strain localization takes place in a damaged zone and the stress reaches the compression strength with surface energy dissipation. In the present paper, we propose the new concept of overlapping crack model, which is analogous to the cohesive one and permits us to simulate material interpenetration due to crushing. The two aforementioned elementary models are merged into a more complex algorithm able to describe both cracking and crushing growths during loading processes in reinforced concrete members. A numerical procedure based on elastic coefficients is developed, taking into account the proposed constitutive laws in tension and compression. With this algorithm, it is possible to effectively capture the flexural behavior of reinforced concrete beams by varying the reinforcement percentage and/or the beam depth.