Applied Stress State Research Articles

Mechanical behaviour of granular materials undergoing grain dissolution

Geotechnical engineering projects are often at risk from threats related to mineral dissolution and loss of particles that constitute the matrix of the geomaterial. Moreover, the impact of climate change can exacerbate these risks by accelerating the physical processes. To address such challenges, it is a pre-requisite to understand and quantify the effect of mineral dissolution on geomechanical behaviour. A general theoretical approach to mechanical consequences of geomaterials experiencing mineral dissolution was first proposed. Following, a series of oedometer tests were conducted using mixtures of salt and sand with various salt contents to observe and characterise the effect of dissolution on the mechanical behaviour of granular materials. The dissolution of salt crystals was performed in three different stress states to observe the stress-dependent response of the material. The effect of dissolution was dependent both on the amount of dissolved salt particles and the applied stress state. The laboratory experiments and the discussion followed shares insights into the effect of grain dissolution on the mechanical behaviour of granular materials and proved the potential of the framework presented in this paper. Finally, the paper ends by discussing the engineering implications bearing in mind the climate change we are facing today.

Optimized characterization of the permanent deformation of unbound soils and granular materials considering the master curve concept

This paper presents a new method to evaluate the permanent deformation (PD) of soils and granular materials. Based on the concepts of shakedown and shift model, the PD analysis was proposed by means of master curves considering the initial 10,000 loading cycles of each applied stress state. Analogous to the superposition principle adopted in the construction of master curves for viscoelastic properties, the superposition loading cycle-magnitude of stress pair is proposed for the PD characterization of soils and granular materials. Thus, shift factors are used that provide the construction of master curves for each stress pair in an extended space of cycles. The master curves were used to predict the permanent deformation of soils and granular materials by increasing the number of cycles analyzed for each stress pair. For this, 24 different soils and granular materials were tested and analyzed to identify the influence of the loading cycles and stress state on the material behavior. The predictions provided by the proposed model were compared with those of another model currently used for flexible pavement design in Brazil. The results demonstrated the accuracy of the proposed methodology and indicated that it is possible to significantly reduce testing time than required for the PD characterization of soils and granular materials.

A Laboratory-Scale Evaluation of Smart Pebble Sensors Embedded in Geomaterials.

This paper introduces a novel approach to measure deformations in geomaterials using the recently developed 'Smart Pebble' sensors. Smart Pebbles were included in triaxial test specimens of unbound aggregates stabilized with geogrids. The sensors are equipped with an aggregate particle/position tracking algorithm that can manage uncertainty arising due to signal noise and random walk effects. Two Smart Pebbles were placed in each test specimen, one at specimen's mid-height, where a geogrid was installed in the mechanically stabilized specimen, and one towards the top of the specimen. Even with simple raw data processing, the trends on linear vertical acceleration indicated the ability of Smart Pebbles to assess the geomaterial configuration and applied stress states. Employing a Kalman filter-based algorithm, the Smart Pebble position coordinates were tracked during testing. The specimen's resilient deformations were simultaneously recorded. bender element shear wave transducer pairs were also installed on the specimens to further validate the Smart Pebble small-strain responses. The results indicate a close agreement between the BE sensors and Smart Pebbles estimates towards local stiffness enhancement quantification in the geogrid specimen. The study findings confirm the viability of using the Smart Pebbles in describing the resilient behavior of an aggregate material under repeated loading.

Grain-Scale Study of SAC305 Oligocrystalline Solder Joints: Anisotropic Elasto-Plastic Constitutive Properties of Single Crystals

Abstract This paper focuses on anisotropic elastic-plastic constitutive modeling of SAC (SnAgCu) solder grains because of their importance in modeling the behavior of oligocrystalline (few-grained) micron-scale solder joints that are increasingly common in heterogeneous integration. Such grain-scale anisotropic modeling approach provides more accurate assessment of the mechanical response of solder interconnects in terms of predicting different failure modes, failure sites, and variability in time-to-failure. Anisotropic plasticity is represented using Hill–Ramberg–Osgood (RO) continuum plasticity model, which utilizes Hill's anisotropic plastic potential along with a RO power-law plastic hardening flow rule. Mechanistically motivated empirical scaling factors are proposed to extrapolate the stress–strain response for different grain sizes/shapes and for different coarseness of microstructures within each grain (generated with different cooling rates). This scaling factor can therefore also capture the effects of microstructural coarsening due to isothermal aging. This goal is achieved by first conducting monotonic tensile and shear tests on monocrystalline and oligocrystalline SAC305 solder joints containing grains of various geometries and also intragranular microscale (dendritic and eutectic) structures of various coarseness. The grain structures are characterized for each tested specimen using electron backscattered diffraction (EBSD). The Hill–RO model constants and the empirical scaling factors are then estimated by matching grain-scale anisotropic elastic-plastic finite element models of each tested specimen to the measured stress–strain behavior, using an inverse-iteration process. Grain shape is seen to influence the sensitivity of the effective stress–strain curves to the applied stress state (i.e., to the orientation of the principal stress directions) relative to (i) the material principal directions and (ii) the geometric principal directions of grains with high aspect ratio. Limitations of the current results and opportunities for future improvements are discussed.

Effects of Stress State, Crack—γ/γ′ Phase Interface Relative Locations and Orientations on the Deformation and Crack Propagation Behaviors of the Ni-Based Superalloy—A Molecular Dynamics Study

In this study, we systematically investigate the influence of stress states, relative locations, and orientations of crack—γ/γ′ phase interfaces on the deformation and crack propagation behaviors of the Ni-based superalloy through molecular dynamics simulations. The stress state with high stress triaxiality will impede the plastic deformation process of the system, thereby promoting brittle crack propagation within the system. But the stress state of low stress triaxiality results in obvious plastic deformation and plastic crack propagation behaviors of the system. The deformation system with cracks located in both the γ and γ′ phase exhibits the slowest growth rate, regardless of applied stress states. Additionally, the deformation process demonstrates prominent plastic behavior. For the deformation system with cracks perpendicular to the γ/γ′ phase interface, the γ/γ′ phase interface will hinder the crack propagation. Our research provides interesting observations on deformation and crack propagation behaviors at an atomic level and at a nano-scale which are important for understanding deformation and fracture behaviors at a macroscopic scale for the Ni-based superalloy.

The effect of orientation on the deformation behavior of Cr2AlC

The MAX phases are a group of ternary carbides and nitrides with potential for use in advanced high temperature applications. Numerous studies have shown their main deformation mechanism to be basal plane slip, even in extreme orientations, yet the fundamentals of this mechanism and dependencies on size and applied stress state remain inconclusive. Based on similar studies in Ti3SiC2, Ti3AlC2 and Ti2AlC, the current work investigated the onset of basal plane slip as a function of loading orientation by compressing single crystal micropillars of Cr2AlC. The results suggest clear changes in the critical resolved shear stress with loading orientation (non-Schmid effects), and attempts were made to rationalize this behavior by comparison with models of dislocation activity. On this basis, it is proposed that external influences on dislocation mobility are likely the governing factor in the observed non-Schmid effects in the MAX phases.

Predicting permanent strain accumulation of unbound aggregates using machine learning algorithms

The objective of this study is to propose a machine learning-based framework for predicting the permanent strain accumulation of unbound aggregates. To develop the machine learning-based framework, material properties of 15 crushed aggregates determined at two different gradations are combined with the applied stress states on aggregate specimens during repeated load triaxial testing by considering the aggregate shear strength characteristics. Three single machine learning algorithms (K-nearest neighbor, neural network, and decision tree) and two ensemble learning algorithms (random forest and extreme gradient boosting) are used in this study. Based on the dataset obtained from 90 permanent deformation tests, hyperparameters, which are used to control the learning process, are optimized. The numerical results demonstrate that all five of the tuned machine learning models exhibit good generalization capacity and performance with the coefficient of determination exceeding 0.99. Among the five models, the extreme gradient boosting model outperforms the others, accurately predicting permanent strain accumulation even for load cycles of 10,000. The contributions of individual input features to the performance of each learning model depend on the dataset. The strength characteristics and the applied deviatoric stress are the two most important features. Therefore, the machine learning-based framework introduced in this study may be effectively used for predicting the permanent strain accumulation of unbound aggregate layer.

Twinning induced spatial stress gradients: Local versus global stress states in hexagonal close-packed materials

Length scale dependent microstructural heterogeneities serve as effective pathways in engineering materials for providing simultaneous strength-ductility enhancement. In this regard, hexagonal close-packed (hcp) materials that exhibit a combination of slip and multiple twinning modes potentially act as ideal candidates that generate heterogeneous microstructures. However, such an inhomogeneous distribution of crystallographic defects also results in build-up of spatially heterogeneous local stress gradients that can be distinct from globally applied stress state. In particular, stress fields arising at the vicinity of deformation twins and due to their interaction with grain interfaces often act as precursors to damage nucleation in most hcp metals and alloys. Hence, assessment of such local stresses and their overall impact on plasticity becomes necessary in order to understand the relationship between twinning and fracture in hcp materials. The current work utilizes commercially pure titanium (cp-Ti) as a model material to investigate the impact of twinning induced stress gradients on the local mechanical response. By means of correlative multiscale structural characterization and local stress gradient measurements, we establish a definitive relationship between applied stress vis-à-vis local stress on the local plasticity behavior ahead of a {112¯2} compression twin-grain boundary intersection in cp-Ti. Additionally, the role of twin interfacial structure for tension and compression twinning modes are experimentally determined and their corresponding impact on the local stress fields and associated twin migration mechanisms is assessed.

Microscale crack propagation in shale samples using focused ion beam scanning electron microscopy and three-dimensional numerical modeling

Reliable prediction of the shale fracturing process is a challenging problem in exploiting deep shale oil and gas resources. Complex fracture networks need to be artificially created to employ deep shale oil and gas reserves. Randomly distributed minerals and heterogeneities in shales significantly affect mechanical properties and fracturing behaviors in oil and gas exploitation. Describing the actual microstructure and associated heterogeneities in shales constitutes a significant challenge. The RFPA3D (rock failure process analysis parallel computing program)-based modeling approach is a promising numerical technique due to its unique capability to simulate the fracturing behavior of rocks. To improve traditional numerical technology and study crack propagation in shale on the microscopic scale, a combination of high-precision internal structure detection technology with the RFPA3D numerical simulation method was developed to construct a real mineral structure-based modeling method. First, an improved digital image processing technique was developed to incorporate actual shale microstructures (focused ion beam scanning electron microscopy was used to capture shale microstructure images that reflect the distributions of different minerals) into the numerical model. Second, the effect of mineral inhomogeneity was considered by integrating the mineral statistical model obtained from the mineral nanoindentation experiments into the numerical model. By simulating a shale numerical model in which pyrite particles are wrapped by organic matter, the effects of shale microstructure and applied stress state on microcrack behavior and mechanical properties were investigated and analyzed. In this study, the effect of pyrite particles on fracture propagation was systematically analyzed and summarized for the first time. The results indicate that the distribution of minerals and initial defects dominated the fracture evolution and the failure mode. Cracks are generally initiated and propagated along the boundaries of hard mineral particles such as pyrite or in soft minerals such as organic matter. Locations with collections of hard minerals are more likely to produce complex fractures. This study provides a valuable method for understanding the microfracture behavior of shales.

Phase-field study on the formation of α variant clusters induced by elastoplastic stress field around the void in titanium alloys

The formation of α variant clusters during β to α transformation under the elastoplastic stress field around a void was investigated using J2 plasticity theory and phase field simulation. Compared with elastic materials, taking an elastic–plastic phase field model in the present work, the stress fields around the void can be partially relaxed by plastic deformation, and the maximum amplitude of the stress reduces. With the increase of the void size, the selection effect on α variant clusters in titanium alloys is gradually enhanced. The variant selection is asymmetric under the conditions of applied tensile and compressive stresses, and the influence of the stress fields around the void under external shear stress is stronger. These could be predicted and confirmed by the interaction energy calculations between the stress fields around the void and α variants. Some interesting variant clusters appear, such as “windmill”, “butterfly”, and “wing” types under external tensile, compressive and shear stresses respectively. The “equilateral triangle”, “nearly parallel” and “quasi equilateral triangle” type variant clusters can form through sympathetic nucleation, given the particular α/α orientation relationship corresponding to lower energy. The ultimate microstructures of α variant clusters around a void are determined by both inter-variant and variant-external stress field interactions. The high-throughput calculations under different applied stress states would provide support for the generation and optimization of the microstructures of titanium alloys in follow-up work.

A quantitative criterion for predicting solid-state disordering during biaxial, high strain rate deformation

A criterion to predict the onset of disordering under biaxial loading based on a critical potential energy per atom was studied. In contrast to previous theories for disordering, this criterion incorporates the effects of strain rate and strain state. The strain state (or stress state) is defined by the combination of strain (or stress) magnitudes and directions that are applied to each sample during the simulation. The validity of this criterion was studied using molecular dynamic (MD) simulations of Ag conducted over a wide range of biaxial strain rates, strain configurations, and crystal orientations with respect to the applied stress state. Biaxial strains were applied in two different planes, () and (001) in eight directions in each plane. Results showed that, when larger strain rates were applied, there was a transition from plastic deformation driven by the nucleation and propagation of dislocations to disordering and viscous flow. Although the critical strain rate to initiate disorder was found to vary in the range of = 1 × 1011 s−1 to = 4 × 1011 s−1, a consistent minimum PE/atom of −2.7 eV was observed over a broad range of strain states and for both crystallographic orientations that were studied. This indicates that the critical PE/atom is a material property that can be used to predict the onset of disordering under biaxial loading. Further, the results showed that this criterion can be applied successfully even when non-uninform strain states arise in the crystal.

Kink band and shear band localization in anisotropic perfectly plastic solids

Shear-driven strain localization has been observed in a wide variety of materials and may take the form of shear bands or kink bands. Based on observations of kink bands in plastically anisotropic metallic nanolaminates and single crystal metals, we posit that, for the specific case of isochoric deformation, the kinematics of kink band formation are indistinguishable from those of plane strain shear band formation. The only distinction between shear bands and kink bands in these systems would then be that kink bands ‘lock up’ at a particular value of material rotation while shear bands may progress to arbitrarily high strains. In order to investigate whether strong material anisotropy is sufficient to arrest shear localization at a geometry that matches the classic kink band geometry, we model the development of a band of simple shear within an anisotropic perfectly plastic material. The resulting analytical model provides the stress state needed to maintain the kinematics of simple shear as a function of material anisotropy, deformation band orientation, and shear strain (or equivalently, material rotation). It is found that plastic anisotropy can promote either kink band or shear band formation depending on the loading orientation. When the deviatoric stress is positive parallel to the plane of anisotropy, shear localization may progress without bound and a shear band is produced. When the deviatoric stress is negative parallel to the plane of anisotropy, shear localization is arrested after a certain material rotation, resulting in a kink band. Examination of the requisite applied stress state during kink band formation provides an explanation for the experimentally-observed ‘lock up’ geometry. Solutions for the band boundary inclination angle are obtained and used to provide bounds on permissible band angles for both shear bands and kink bands.

On the effect of strain and triaxiality on void evolution in a heterogeneous microstructure – A statistical and single void study of damage in DP800 steel

In order to improve the understanding of damage evolution in mechanically heterogeneous microstructures, like the ones of dual-phase steels, the influence of the applied stress state is a key element. In this work, we studied the influence of the globally applied stress state on the evolution of damage in such a microstructure. Classical damage models allow predictions of damage during deformation based on considerations of the material as an isotropic continuum. Here, we investigate their validity in a dual phase microstructure that is locally dominated by its microstructural morphological complexity based on a statistical ensemble of thousands of individual voids formed under different stress states. For this purpose, we combined a calibrated material model incorporating damage formation to assess the local stress state in samples with different notch geometries and high-resolution electron microscopy of large areas using a deep learning-based automated micrograph analysis to detect and classify microstructural voids according to their source of origin. This allowed us to obtain both the continuum stress state during deformation and statistically relevant data of individual void formation. We found that the applied plastic strain is the major influence on the overall number, and therefore the nucleation of new voids, while triaxiality correlates with the median void size, supporting its proposed influence on void growth. In contrast, coalescence of voids leading to failure appears related to local instabilities in the form of shear band formation and is therefore only indirectly determined by the global stress state in that it determines the global distribution, density and size of voids.

Predicting the available work from deformation-induced α′′ martensite formation in metastable β Ti alloys

Deformation-induced α′′ martensite formation is essential to the mechanical properties of a variety of metastable β Ti alloys by extending elasticity or contributing to work-hardening during plastic deformation. Nevertheless, to date, a comprehensive analysis of the effect of β texture and applied stress state on the martensitic transformation to α′′ is still lacking. The present study therefore provides a detailed analysis of the work which is made available from the shape strain of the martensitic transformation under a variety of in-plane stress states and as a function of β crystal orientation. The available work was found to strongly depend on the applied stress state and the parent grain orientation. The shape strain of the martensitic transformation was obtained from applying the phenomenological theory of martensite crystallography. In cases where this theory was not applicable, an approximation of the shape strain by the Bain strain was found to provide a good approximation of the available work. Analysis of three different metastable β Ti alloys showed no strong effect of the alloy composition on the available work. Martensite formation from typical cold- and warm-rolling β texture components under different stress states is discussed. Cases are highlighted to show how the cold- and warm-rolling β textures can be tailored to hinder martensite formation upon subsequent industrial forming operations.

Geogrid Stabilization of Unbound Aggregates Evaluated Through Bender Element Shear Wave Measurement in Repeated Load Triaxial Testing

This paper describes the use of the bender element (BE) shear wave measurement technology for quantifying the effectiveness of geogrid stabilization of unbound aggregate materials with improved mechanical properties from repeated load triaxial testing. Crushed stone aggregate specimens were prepared with three different gradations, that is, upper bound (UB), mid-range engineered (ENG), and lower bound, according to the dense graded base course gradation specification in Illinois. The specimens were compacted at modified Proctor maximum dry densities and optimum moisture contents. Two geogrids with different triaxial aperture sizes were placed at specimen mid-height, and unstabilized specimens with no geogrid were also prepared for comparison. To measure shear wave velocity, three BE pairs were placed at different heights above geogrid. Repeated load triaxial tests were conducted following the AASHTO T307 standard resilient modulus test procedure, while shear wave velocity was measured from the installed BE pairs. After initial specimen conditioning, and at low, intermediate, and high applied stress states, both the resilient moduli and accumulated permanent strains were determined to relate to the geogrid local stiffening effects in the specimens quantified by the measured shear wave velocities. The resilient modulus and shear wave velocity trends exhibited a directly proportional relationship, whereas permanent strain and shear wave velocity values were inversely related. The enhancement ratios calculated for the geogrid stabilized over the unstabilized specimens showed significant improvements in mechanical behavior for the UB and ENG gradations, and a maximum enhancement was achieved for the engineered gradation specimens stabilized with the smaller aperture geogrid.

Influence of phase and interface properties on the stress state dependent fracture initiation behavior in DP steels through computational modeling

In dual phase (DP) steels, fracture can initiate within the ferrite phase, the martensite phase, or at the interfaces between these phases with the dominant fracture initiation mechanism expected to depend on a number of factors, including the phase and interface properties as well as the applied stress state. The present study aims to identify the links among fracture initiation behavior, phase/interface properties, and stress state in DP steels through finite element analysis using representative volume element (RVE) simulations. An idealized RVE model containing a circular martensite particle was loaded under five different stress states. The RVE model incorporated a ductile fracture criterion for ferrite, a brittle fracture criterion for martensite, and a cohesive zone model (CZM) for the ferrite/martensite interface. A parametric study was performed to determine the relative influence of fracture properties of each constituent and stress state on the failure initiation behavior, and to identify the conditions under which the fracture initiation behavior was stress state dependent.

Intrinsic ductility of random substitutional alloys from nonlinear elasticity theory

A method suitable for computing the ideal strength of random substitutional alloys is introduced. The method relies on nonlinear continuum elasticity theory and allows for the high-throughput computation of ideal strength. The method also allows for the high-throughput computation of an intrinsic ductility parameter defined for a given applied stress state as the ratio of the strain associated with the cleavage instability to the strain associated with the first shear instability. The intrinsic ductility parameter is shown to correlate well with the measured elongations to failure for elemental body-centered-cubic and hexagonal close-packed metals. Application to four high-entropy alloys indicates that the intrinsic ductility parameter describes their experimental compressions to failure well. The method is used to argue that the brittle refractory high-entropy alloy Ta-Nb-V-W-Mo could be made much more ductile through replacement of Mo with Nb. The potential for the high-throughput optimization of high entropy and chemically complex alloys is discussed.

Statistical analysis of twin/grain boundary interactions in pure rhenium

Using electron backscatter diffraction, over 1000 grain boundary/twin interactions were investigated in pure Re after uniaxial compression. Crystallographic factors such as grain boundary disorientation angle, displacement gradient tensor accommodation, and twin plane and shear vector alignment were taken into account as well as the macroscopic Schmid factor. It was found that the crystallographic relationship between coincident twin pairs at grain boundaries fall into two categories. In the first category, the twin pairs satisfied two criteria: the twin plane alignment was maximized across the boundary and the twin variant was kept constant across the boundary. In the second category, comprising approximately 5% of the characterized interactions, twin variant selection appeared to be driven by the macroscopically applied stress state, as resolved by the Schmid factor. In comparison to published results on twin/grain boundary interactions in Mg and Zr, it was found that twins transmit across grain boundaries in Re far more readily, regardless of the grain boundary disorientation angle. This is likely to be a function of the anomalously low twin boundary energy in Re as well as the difference in magnitude of the twinning-induced deformation that must be accommodated at the boundary, with the {112¯1}<1126¯> system being dominant in Re and the {101¯2}<1011¯> being dominant in Mg and Zr.

Drawing Direction Effect on Microstructure and Mechanical Properties of Twinning-Induced Plasticity Steel During Wire Drawing

The effect of drawing direction on microstructure and mechanical properties in twinning-induced plasticity (TWIP) steel during wire drawing has been investigated to improve drawability for wire rod applications. The steel wires subjected to unidirectional (UD) and reverse-directional (RD) wire drawing were analyzed. The yield and tensile strength processed by the RD were slightly higher than those by the UD, whereas the ductility and drawability have inverse features, which is totally different from the results of plain carbon steel and Al wire. Although final shear strain of wires deformed by the RD is lower than that by the UD, the RD wires had a more complex stress history and a higher texture component at the surface area, which encouraged twinning rate, resulting in fast exhaustion of ductility, finally earlier fracture of wires. In contrast to the materials deformed by mainly slip mechanism, the RD process cannot improve the ductility and drawability in TWIP steel due to the stress state dependency of twinning mechanism. Also, based on the different strengthening behaviors between pearlitic and TWIP steels during UD and RD, it is induced that microstructure and applied stress state simultaneously control the mechanical properties.

Statistical Analysis of Twin/Grain Boundary Interactions in Pure Rhenium

Using electron backscatter diffraction, over 1,000 grain boundary/twin interactions were investigated in pure Re after uniaxial compression. Crystallographic factors such as grain boundary disorientation angle and twin plane and shear vector alignment were taken into account as well as the Schmid factor. It was found that the crystallographic relationship between coincident twin pairs at grain boundaries fall into two categories. In the first category, the twin pairs satisfied two criteria: the twin plane alignment was maximized across the boundary and the twin variant was kept constant across the boundary. In the second category, twin variant selection appeared to be driven by the macroscopically applied stress state, as resolved locally by the Schmid factor. In comparison to published results on twin/grain boundary interactions in Mg and Zr, it was found that twins transmit across grain boundaries in Re far more readily,regardless of the grain boundary disorientation angle. This is likely to be a function of the anomalously low twin boundary energy in Re as well as the difference in magnitude of the twinning shear vector and the associated local stress field in the different materials systems, with the {112‾1} system being dominant in Re and the {101‾2} being dominant in Mg and Zr.