The influence of martensite shape,concentration, and phase transformation strain on the deformation behavior of stable dual-phase steels

A continuum model is developed to examine the influence of martensite shape, volume fraction, phase transformation strain, and thermal mismatch on the initial plastic state of the ferrite matrix following phase transformation and on the subsequent stress-strain behavior of the dual-phase steels upon loading. The theory is developed based on a relaxed constraint in the ductile matrix and an energy criterion to define its effective stress. In addition, it also assumes the martensite islands to possess a spheroidal shape and to be randomly oriented and homogenously dispersed in the ferrite matrix. It is found that for a typical water-quenched process from an intercritical temperature of 760 °C, the critical martensite volume fraction needed to induce plastic deformation in the ferrite matrix is very low, typically below 1 pct, regardless of the martensite shape. Thus, when the two-phase system is subjected to an external load, plastic deformation commences immediately, resulting in the widely observed “continuous yielding” behavior in dual-phase steels. The subsequent deformation of the dual-phase system is shown to be rather sensitive to the martensite shape, with the disc-shaped morphology giving rise to a superior overall response (over the spherical type). The stress-strain relations are also dependent upon the magnitude of the prior phase transformation strain. The strength coefficienth and the work-hardening exponentn of the smooth, parabolic-type stress-strain curves of the dual-phase system also increase with increasing martensite content for each selected inclusion shape. Comparison with an exact solution and with one set of experimental data indicates that the theory is generally within a reasonable range of accuracy. Formerly Visiting Professor, Department of Mechanical and Aerospace Engineering, Rutgers University     

Performance of a Three-Dimensional Hvorslev–Modified Cam Clay Model for Overconsolidated Clay

It is well established that critical state soil mechanics provides a useful theoretical framework for constitutive modeling of soil. Most of the critical state models, including the popular modified Cam clay (MCC) model, predict soil behavior in the subcritical region fairly well. However, the predictions for heavily overconsolidated soils, in the supercritical region, are not so satisfactory. Furthermore, the critical state models were developed from triaxial test data and extension of these models into three-dimensional (3D) stress space has not been investigated thoroughly. In the present work, experiments were carried out to obtain stress–strain behavior of overconsolidated soil in triaxial compression, extension, and plane strain conditions. A novel biaxial device has been developed to conduct the plane strain tests. The experimental results were used to formulate Hvorslev–MCC model which has MCC features in the subcritical region and Hvorslev surface in the supercritical region. The model was generalized to 3D stress space using the Mohr–Coulomb failure criterion. A comparison of the model predictions with test results has indicated that the Hvorslev–MCC model performs fairly well up to the peak supercritical point, during which deformations are fairly uniform and the specimens remain reasonably intact. Limitations of this simple model in predicting postpeak localization are also discussed. The model’s predictions for volumetric response in different shear modes seem to agree reasonably well with test results.     

State Pressure Index for Modeling Sand Behavior

The effort to model sand behavior within the framework of critical-state soil mechanics would benefit from a state variable that relates the current void ratio and mean pressure of the soil to its void ratio and mean pressure at the critical state. In this paper we propose a state pressure index, Ip, which is defined as the ratio of the current mean pressure to the mean pressure at the critical state that corresponds to the current void ratio. Using this state pressure index, a bounding surface hypoplasticity model for sand is modified so that the phase transformation and failure stress ratios both depend on Ip and merge into the critical-state stress ratio at failure. The Ip dependency introduced enables use of a single set of model constants in modeling sand behavior for various initial confining pressures and densities under both undrained and drained conditions. Dilatancy, strain softening, and strain hardening are simulated for both loose and dense sands. Simulations from the modified model are compared with results of laboratory tests of drained and undrained triaxial compression.     

Effect of Particle Shape on Interface Behavior of DEM‐Simulated Granular Materials

This paper presents a detailed computational investigation of the effect of particle shape on the interface shear behavior of granular materials. The discrete element method (DEM) using clusters to model rough particles is used, expanding the procedure introduced in an earlier paper by Jensen et al. [1]. Seven new cluster shapes (i.e., particle configurations) of varying degrees of roughness are presented herein, and numerical experiments simulating ring shear tests are made using these clusters. From these simulations, the effect of particle shape on void ratio (e) and interface angle of friction between soil and structure surface (δ) is reported. Particle shape characteristics include roundness, angularity, and surface roughness. The results of numerical simulations using the newly formed cluster shapes are in very good qualitative agreement with laboratory tests. Simulation results showed that the void ratio of a particle mass increased as the angularity or roughness of the particles increased. They also showed an increase in interface shear strength between perfectly round DEM particles and the more angular cluster shapes, but no systematic correlations with the various definitions of particle shape parameters was found. It may be necessary to use greater accuracy in modeling the size and shape distributions of a natural medium to further investigate the influence of particle shape on interface friction. The simulations also successfully reflected the relationship between interface friction angle and structure surface roughness as demonstrated in recent physical experiments. The simulations comparing initially “dense” media to initially “loose” media demonstrated behavior that is similar to the behavior of a natural sandy soil observed in experiments.     

Numerical Modeling of Nonhomogeneous Behavior of Structured Soils during Triaxial Tests

The nonhomogeneous behavior of structured soils during triaxial tests has been studied using a finite element model based on the Structured Cam Clay constitutive model with Biot-type consolidation. The effect of inhomogeneities caused by the end restraint is studied by simulating drained triaxial tests for samples with a height to diameter ratio of 2. It was discovered that with the increase in degree of soil structure with respect to the same soil at the reconstituted state, the inhomogeineities caused by the end restraint will increase. By loading the sample at different strain rates and assuming different hydraulic boundary conditions, inhomogeneities caused by partial drainage were investigated. It was found that if drainage is allowed from all faces of the specimen, fully drained tests can be carried out at strain rates about ten times higher than those required when the drainage is allowed only in the vertical direction at the top and bottom of the specimen, confirming the findings of previous studies. Both end restraint and partial drainage can cause bulging of the triaxial specimen around mid-height. Inhomogeneities due to partial drainage influence the stress–strain behavior during destructuring, a characteristic feature of a structured soil. With an increase in the strain rate, the change in voids ratio during destructuration reduces, but, in contrast, the mean effective stress at which destructuration commences was found to increase. It is shown that the stress–strain behavior of the soil calculated for a triaxial specimen with inhomogeneities, based on global measurements of the triaxial response, does not represent the true constitutive behavior of the soil inside the test specimen. For most soils analyzed, the deviatoric stress based on the global measurements is about 25% less than that for the soil inside the test specimen, when the applied axial strain is about 30%. Therefore it can be concluded that the conventional global measurements of the sample response may not accurately reflect the true stress–strain behavior of a structured soil. This finding has major implications for the interpretation of laboratory triaxial tests on structured soils.     

Effects of bond strength on densification and flow of powder compacts

Abstract

Plastic flow surfaces for metal and metal/composite powder compacts with variable cohesive strength are derived using the Beltrami total strain energy criterion, modified to permit asymmetric yielding. The present theory thus includes the domains of both soil mechanics and powder metallurgy, covering both granular and porous microstructures of varying bond strengths over all possible densities. A quantitative theory of the expansion of non-bonded particle compacts under certain combinations of applied shear stress and pressure is given. Physical models of the failure mechanisms are provided, their applicability depending on the particle interface strength. If the particle interface lacks strength, the flow surface is identical to that of the ‘critical state’ criterion of soil mechanics. The flow ellipse lies entirely within the negative pressure domain and failure occurs at the particle interface by various mechanisms including frictional slip. At the other extreme, if the particle interfaces are as strong in shear as the particles, failure occurs by plastic shear of the particles and the flow ellipse is centred at the origin. Density–stress and density–aspect ratio maps are shown which define these domains. Theoretical predictions compare well with the results of data compiled from the literature as well as data from tests performed in this study on cold pressed Al and Al/SiC powder compacts.     

Cracking in γ-TiAl due to high speed particle impact

Cracking due to small particle impacts on prospective γ-TiAl blades in jet turbine engines has been studied experimentally and theoretically. Flat rectangular specimens of two γ-TiAl alloys, with edges chamfered to resemble the taper of blades, were subjected to small particle impacts. The forms of damage observed resembled those revealed by earlier studies using specimens that were cast closely to the shape of blade leading edges. Numerical simulations of the impact events were carried out using finite element analysis, using uniaxial stress-strain behavior that was obtained in compression at high strain rates. A criterion for cracking is proposed that requires critical levels of plastic strain and tensile stress. Predictions of crack extent that were based on such a combined criterion were found to be in the range of observations. The predictive methodology, together with information on the fatigue strength of various damage states, potentially offers designers the opportunity to examine the risk associated with small particle damage on contemplated blades.     

Role of Initial State, Material Properties, and Confinement Condition on Local and Global Soil-Structure Interface Behavior

Difficulty in predicting the transfer of load from a structural element to the surrounding soil has limited the reliability of geotechnical design and performance. The remaining uncertainty in load transfer mechanics is primarily due to the localized nature of the mechanism. This study examines localized soil-structure interaction through a series of monotonic direct interface shear tests. Parameters investigated include relative density, particle angularity, particle hardness, surface roughness, normal stress, and normal stiffness. The soil-structure interface behavior is quantified in terms of the local two-dimensional displacement and strain distributions within the test specimens using particle image velocimetry. In addition, the localized zone of soil adjacent to the structural surface within which shear and volumetric strains occur is quantified. The relative density of the soil, and the relationship between particle characteristics (angularity and hardness) and surface roughness are shown to have the greatest effect on local interface behavior, followed by confining stress and stiffness conditions.     

Possibility of Postliquefaction Flow Failure due to Seepage

This study examines the postliquefaction flow failure mechanism, in which shear strain develops due to seepage upward during the redistribution of excess pore water pressure after an earthquake. The mechanism is addressed as both a soil element and a boundary value problem. Triaxial tests that reproduce the stress state of a gentle slope subjected to upward pore water inflow were performed, with the results showing that shear strain can increase significantly after the stress state reaches the failure line. In addition, when subject to equivalent volumetric strain, shear strain is considerably larger in loose sand conditions than in dense sand. Compared with consolidated and drained test results, the dilatancy coefficient β, which indicates the rate of dilation, is the same as that obtained from pore water inflow tests. Torsional hollow cylinder tests were also performed to ascertain the limit of dilation of sand specimens. It was found that the β values are nonlinear in behavior. In addition, a postliquefaction flow failure mechanism based on one-dimensional consolidation theory and shear deformation behavior as a result of pore water inflow is proposed.     

Yield, Strength, and Critical State Behavior of a Tropical Saturated Soil

The paper reports laboratory investigations carried out on a tropical soil profile to study its compressibility, strength, critical state and limit state conditions, and their variation with depth. The soil profile comprises a reddish lateritic layer (horizon B) underlain by a saprolitic soil (horizon C) from which a number of block samples were taken. A series of isotropic and anisotropic compression tests, and drained and undrained triaxial tests, were conducted on specimens sampled at depths between 1.0 and 7.0 m, and also in the exposed saprolitic soil. Special triaxial tests, with the pore pressure increased to induce failure, were performed to investigate the failure at low stress levels. On this basis a tensile cutoff on the failure envelope was defined. In order to assess the influence of the natural soil structure, drained and undrained triaxial tests were carried out on compacted samples obtained from depths of 1.0 and 5.0 m. Higher strength parameters were measured for the horizon C soil, which is consistent with its lower clay content. A nonlinearity in the critical state line in q:p′ stress space was identified, but linear regression was used to obtain critical state parameters. The limit state curves for soils from horizon B are centered on the hydrostatic axis, but limit state curves for horizon C suggested anisotropic behavior.     

Particle size determination of a flocculated suspension using a light-scattering particle size analyzer

Microscopy is a useful and direct method for measuring the particle size of a suspension because, in addition to the particle size and size distribution, it provides visual detection of the shape and state of aggregation of the particles in the suspension. However, this method suffers from the shortcomings of being tedious and time consuming. In this study, a light-scattering particle size analyzer was used to determine the particle size and size distribution of a flocculated suspension. The sonication of the sample prior to and during measurement was found to be critical in ensuring that data are representative of the size distribution of the primary particles of the suspension. The light-scattering results were further confirmed by data generated using a polarized light microscope equipped with an image analyzer.     

Metallurgical factors affecting the crack growth resistance of a superalloy

During creep loading of IN-792, grain boundary morphology in conjunction with grain size strongly affected crack propagation. Compositional variations and fabrication techniques showed no significant effect. A primary requirement for materials to be used in gas turbine engine discs is satisfactory resistance to crack growth resistance in the 650 to 760°C range. Both conventional smooth and machine notched stress-rupture samples and dead weight loaded fatigue precracked fracture toughness specimens were evaluated in this study. Creep fractures took place by grain boundary cracking followed by rapid transgranular fractures. Composition variations had only very slight effects on crack propagation. Materials hot worked from castings had the same properties as those made by powder metallurgy techniques. The primary factors influencing the crack growth behavior were the grain size and grain shape. Increasing grain size markedly improved the toughness. By slow cooling through the gamma prime solvus a serrated grain boundary structure was developed that also improved the cracking resistance. Earlier creep fracture toughness studies have shown that the slow crack growth behavior can be described by a critical strain model in which the crack propagation is controlled by the yield strength, grain size, and a critical strain parameter. The present results are consistent with this model, with serrated grain boundaries introducing a four-fold increase in the critical strain parameter over that of smooth grained material.     

Shear Behavior of AA6061 Aluminum in the Semisolid State Under Isothermal and Nonisothermal Conditions

The shear behavior of a 6061 aluminum alloy was studied in the semisolid state at large solid fractions. The tests were carried out either at constant temperature after partial solidification (i.e., isothermal shear tests) or during solidification at low cooling rate (i.e., nonisothermal shear tests). In isothermal conditions, results show that (1) the mechanical behavior depends on the volume fraction of the solid phase present in the sample at the temperature of the test, (2) there is a critical solid fraction corresponding to the coalescence of the solid grains beyond which shear stress increases very sharply with increasing solid fraction, and (3) the mushy alloy exhibits viscoplastic behavior with a strain-rate-sensitivity parameter close to about 0.17. In nonisothermal conditions, results show that stress increases continuously with decreasing temperature whatever the strain rate. However, at high strain rate, it was observed that cracks developed when the solid fraction approaches 1, leading to a slower stress increase compared to that observed at low strain rate. Finally, modeling of this behavior is carried out by considering a cohesion parameter of the solid phase, which depends on solid fraction and strain rate.     

Effect of Particle Grading on the Response of an Idealized Granular Assemblage

The effects of particle-size distribution on a granular assemblage’s mechanical response were studied through a series of numerical triaxial tests using the three-dimensional (3D) discrete-element method. An assemblage was formed by spherical particles of various sizes. A simple linear contact model was adopted with the crucial consideration of varying contact stiffness with particle diameter. Numerical triaxial tests were mimicked by imposing axial compression under constant lateral pressure and constant volume condition, respectively. It was found that an assemblage with a wider particle grading gives more contractive response and behaves toward strain hardening upon shearing. Its critical state locates at a lower position in a void ratio versus mean normal stress plot. Nevertheless, no obvious difference in the critical stress ratio was shown. Model constants in a simple but efficient phenomenologically based granular material model within the framework of critical-state soil mechanics were calibrated from the numerical test results. Results show that some model constants exhibit linear variation with the coefficient of uniformity whereas others are almost independent of particle grading. This investigation provides an opportunity to better understand the implications and meanings of model constants in a phenomenologically based model from the microscale perspective.     

The deformation of particle reinforced metal matrix composites during temperature cycling

Superplasticity during temperature cycling of particle reinforced metal matrix composites has been studied over a range of reinforcement sizes and volume fractions. Above a critical volume and thermal cycle amplitude, the mean strain per cycle is proportional to stress and approximately proportional to cycle amplitude. For a given thermal cycle the constant of proportionality with respect to stress increases with reinforcement fraction to a maximum at around 30%; it then decreases with further increase in reinforcement. Transmission electron microscopy revealed no characteristics dislocation substructure; even after 90% strain the material was indistinguishable from its undeformed state. The experimental results confirm an internal plastic flow model for the phenomenon rather than an enhanced creep. A model of the process derived from the Lévy-Von Mises equations predicts both the effect of thermal cycle amplitude the MMC microstructure on the enhanced creep rate.     

Simulation of Upward Seepage Flow in a Single Column of Spheres Using Discrete-Element Method with Fluid-Particle Interaction

The interaction between soil particles and pore water makes the behavior of saturated and unsaturated soil complex. In this note, upward seepage flow through a granular material was idealized using a one-column particle model. The motion of the individual particles was numerically simulated using the discrete-element method taking the interaction with the fluid into account. The fluid behavior was simulated by the Navier-Stokes equation using the semi-implicit method for pressure-linked equation. This approach has already been applied in powder engineering applications. However, there are very few studies that have used this approach in geotechnical engineering. This note first describes the qualitative and quantitative validation of this method for hydraulic gradients below the critical one by comparing the results with an analytical solution. Then, the ability of the method to simulate the macroscale behavior due to the interaction between particles and pore water at hydraulic gradients exceeding the critical hydraulic gradient is discussed.     

Quantitative characterization of three-dimensional damage evolution in a wrought Al-alloy under tension and compression

Three-dimensional (3-D) microstructural damage due to cracking of Fe-rich intermetallic particles is quantitatively characterized as a function of strain under compression and tension in an Al-Mg-Si base wrought alloy. The 3-D number fraction of damaged (cracked) particles, their average volume, average surface area, and shape factor are estimated at different strain levels for deformation under uniaxial tension and compression. It is shown that, depending on the type of loading, loading direction, particle shape, and microstructural anisotropy, the two-dimensional (2-D) number fraction of the damaged particles can be smaller or larger than the corresponding true 3-D number fraction. Under uniaxial tension, the average volume and surface area of cracked particles decrease with the strain. However, the average volume and surface area of the cracked particles increase with the increase in the compressive strain, implying that more and more larger elongated particles crack at higher and higher stress levels, which is contrary to the predictions of the existing particle cracking theories. In this alloy, the damage development due to particle cracking is intimately coupled with the particle rotations. The differences in the damage evolution under tension and compression are explained on the basis of the differences in the particle rotation tendencies under these two loading conditions.     

Sydney Soil Model. I: Theoretical Formulation

In this paper a theoretical study of the behavior of structured soils, including both clays and sands, is presented. A new model, which is referred to as the “Sydney soil model,” is formulated within the framework of critical state soil mechanics. In the proposed model, the mechanical behavior of soil is divided into two parts, that at a reference state and that attributed to the influence of soil structure. The reference state behavior is formulated according to the soil properties at the critical state of deformation, based on the concept of plastic volumetric hardening. The effects of structure are captured in the model by incorporation of the additional voids ratio that arises owing to the presence of soil structure. The formulation is generalized to include both isotropic compression and general shearing. In part?I of this paper, a new theoretical framework for modeling structured soil behavior and the formulation of the proposed Sydney soil model are introduced. In part?II of this paper, the Sydney soil model is employed to simulate the behavior of clays and sands, including calcareous clays and sands subjected to both drained and undrained shearing, and the performance of the model is evaluated.     

Contraction, Dilation, and Failure of Sand in Triaxial, Torsional, and Rotational Shear Tests

The response of a saturated fine sand (Nevada sand No. 120) with relative density Dr ≈ 70% in drained and undrained conventional triaxial compression and extension tests and undrained cyclic shear tests in a hollow cylinder apparatus with rotation of the stress directions was studied. It was observed that the peak mobilized friction angle for this dilatant material was different in undrained and drained tests; the difference is attributed to the fact that the rate of dilation is smaller in an undrained test than it is in a drained test. Consistent with the findings of others, the material is more resistant to undrained cyclic loading for triaxial compression than for triaxial extension. In rotational shear tests in which the second invariant of the deviatoric stress tensor is held constant, the shear stress path (after being normalized by the mean normal effective stress) approached an envelope that is comparable but not identical in shape to a Mohr-Coulomb failure surface. As the stress path approached the envelope, the shear end deviatoric strains continued to increase in an unsymmetrical smooth spiral path. During the rotational shear tests, the direction of the deviatoric strain-rate vector (deviatoric strain increment divided by the magnitude of change in Lode angle) was observed to be about midway between the deviatoric stress increment vector and the normal to a Mohr-Coulomb failure surface in the deviatoric plane. The stress ratio at the transition from contractive to dilative behavior (i.e., “phase transformation”) was also observed to depend on the direction of the stress path; therefore this stress ratio is not a fundamental property. Results from torsional hollow cylinder tests with rotation of stress directions are presented in new graphical formats to help understand and interpret the fundamental soil behavior.     

Laboratory Study of Loose Saturated and Unsaturated Decomposed Granitic Soil

Weathered soils are used extensively as fill materials in slope construction in tropical and subtropical cities such as Hong Kong. The mechanical behavior of loose decomposed fill materials, particularly in the unsaturated state, has not often been investigated and is not yet fully understood. The objective of this study was to understand the mechanical behavior of loose unsaturated decomposed granitic soil and to study the effects of the stress state, the stress path and the soil suction on the stress–strain relationship, shear strength, volume change, and dilatancy via three series of stress path triaxial tests on both saturated and unsaturated specimens. It was found that loose and saturated decomposed granitic soil behaves like clean sands during undrained shearing. Strain-softening behavior is observed in loose saturated specimens. In unsaturated specimens sheared at a constant water content, a hardening stress–strain relationship and volumetric contractions are observed in the considered range of net mean stresses. The suction of the soil contributed little to the apparent cohesion. The angle of friction appeared to be independent of the suction. In unsaturated specimens subjected to continuous wetting (suction reduction) at a constant deviator stress, the volumetric behavior changed from dilative to contractive with increasing net mean stress and the specimen failed at a degree of saturation far below full saturation. It was revealed that the dilatancy of the unsaturated soil depends on the suction, the state, and the stress path.