Dilatational Strain Research Articles

Volumetric and Shear Strain Localization in Mt. Etna Basalt

AbstractTo examine the impact of preexisting weaknesses on fracture coalescence during volcanic edifice deformation, we triaxially compressed Mount Etna basalt while acquiring in situ dynamic X‐ray microtomograms and calculated the internal strain tensor fields using image correlation. Contraction localization preceded dilation and shear strain localization into the protofault zone. This onset of strain localization preceded macroscopic yielding and coincided with increases in the magnitude and volume of rock experiencing dilation, and spatial clustering of the strain populations. The exploitation of weaknesses by propagating fractures enabled the dominant shear strain to switch senses as propagating fractures lengthened along 30–60° from σ1. Scanning electron microscopy images reveal pore‐emanated fractures, and fractures linking pores. These experiments provide evidence of internal contraction preceding dilation and shear, consistent with inferences from field and laboratory observations. The transition from contraction to dilation may provide a precursory signal of volcanic flank eruption.

Compressibility, Damage, and Age-Hardening Effects of Solid Propellants Using Finite Strain Constitutive Model

AbstractIn this paper, the finite strain viscoelastic constitutive model for particulate composite solid propellants is proposed considering strain rate, large deformation/large strain, thermorheological behavior, stress softening due to microstructural damage, compressibility, and chemical age hardening. The compressible Mooney–Rivlin hyperelastic strain energy density function is used along with the standard model of viscoelasticity. To model the compressibility, the dilatational strain energy is taken as the hyperbolic function of the determinant of deformation gradient. The stress-softening phenomenon during cyclic loading (Mullin's effect) due to microstructural damage is described by an exponential function of the current magnitude of intensity of strain and its previous maximum value. The variation of material properties with time are studied using the isothermal accelerated aging technique through simulation and experimental investigation. The comparison of predictions based on the proposed model with the uniaxial experimental data demonstrates that the proposed model successfully captures the observed behavior of the solid propellants.

Active Deformation Near the Rio Grande Rift and Colorado Plateau as Inferred from Continuous Global Positioning System Measurements

AbstractWe used data from 333 continuous Global Positioning System stations, including 26 stations installed in 2006–2007 as part of a collaborative EarthScope experiment, to investigate how deformation is distributed near the Rio Grande Rift. Our previous analysis, using data from 2006 to 2010, was consistent with a nearly uniform east‐west distributed extensional strain rate of ~1.2 nε/year (nanostrain/year) along five profiles spanning a ~1,000‐km region. We built upon this analysis with additional Global Positioning System networks and longer time series of data spanning varying time ranges between 1993 and 2018. In all five east‐west profiles, extensional strain rates are higher within and west of the fault‐defined rift zone than to the east. There is an east‐to‐west increase in Central New Mexico from 0.7 ± 0.1 to 1.8 ± 0.8 nε/year that is significant at the 95% confidence level. We found elevated extensional and shear strain rates of over 10 nε/year along parts of the central Rio Grande Rift, particularly along the southeast edge of the Colorado Plateau along part of the Jemez lineament, as well as elevated dilatational strain rates and uplift above the Socorro magma body. Results from Euler pole analysis of Global Positioning System velocities for sites within the Colorado Plateau show nonrigid behavior with considerable deformation near the plateau margins and internal east‐west extension. Our results suggest the Rio Grande Rift is actively deforming in an evolving tectonic environment.

Highly reactive energetic films by pre-stressing nano-aluminum particles.

Energetic films were synthesized using stress altered nano-aluminum particles (nAl). The nAl powder was pre-stressed to examine how modified mechanical properties of the fuel particles influenced film reactivity. Pre-stressing conditions varied by quenching rate. Slow and rapid quenching rates induced elevated dilatational strain within the nAl particles that was measured using synchrotron X-ray diffraction (XRD). An analytical model for stress and strain in a nAl core–Al2O3 shell particle that includes creep in the shell and delamination at the core–shell boundary, was developed and used for interpretation of strain measurements. Results show rapid quenching induced 81% delamination at the particle core–shell interface also observed with Transmission Electron Microscopy (TEM). Slower quenching elevated dilatational strain without delamination. All films were prepared at approximately a 75 : 25 Al : poly(vinylidene fluoride) PVDF weight ratio and were 1 mm thick. A drop weight impact test was performed to assess ignition sensitivity and combustion. Stress altered nAl exhibited greater energy release rates and more complete combustion than untreated nAl, but reaction dynamics and kinetics proceeded in two different ways depending on the nAl quenching rate during pre-stressing.

Investigations of the hydrogen diffusion and distribution in Zirconium by means of Neutron Imaging

Abstract Absorbed hydrogen degrades the mechanical properties of zirconium alloys used for nuclear fuel claddings. Not only the total amount of hydrogen absorbed in the cladding tube but also the zirconium hydride orientation and its distribution influence the toughness of the material. For instance, the so-called delayed hydride cracking is caused by the diffusive re-distribution of hydrogen into the dilative elastic strain field ahead of crack tips. The paper presents in-situ and ex-situ neutron imaging investigations of hydrogen uptake, diffusion and distribution in zirconium alloys used for claddings. An overview about results of in-situ experiments studying the hydrogen uptake in strained Zircaloy-4, as well as ex-situ investigations of the diffusion of hydrogen in cold rolled Zircaloy-2 and Zr-2.5 % Nb alloy depending on temperature, rolling direction and thermal treatment and of the hydrogen re-distribution in the β-phase of Zircaloy-4 during a Three-Point-Bending-Test at 600 °C are presented.

On the Critical Driving Force for Deformation‐Induced α′‐Martensite Formation in Austenitic Cr–Mn–Ni Steels

The influence of martensite formation on the mechanical properties of an Fe–16Cr–6Ni–6Mn (concentrations in wt%) austenitic stainless steel is studied by tensile tests between −70 and 300 °C. As‐quenched martensite formation is observed at temperatures below −30 °C. Deformation‐induced martensite formation, on the other hand, is triggered below 100 °C. The temperature dependence of proof stress, tensile strength, and triggering stress for martensite formation are represented on a Stress‐Temperature‐Transformation (STT) diagram. In order to determine the critical Gibbs free energy for the formation of martensite at temperatures between and , the chemical and mechanical contributions to deformation‐induced martensite formation are determined. The chemical term is obtained from thermodynamic calculations. The mechanical term, on the other hand, is obtained by determining the mechanical energy supplied to tensile specimens to trigger martensite formation. This is done using the model proposed by Patel and Cohen. The magnitudes of shear strain () and dilatational strain (), required for the calculations, are obtained based on the martensite crystallography theory of Wechsler‐Lieberman‐Read. The sum of the chemical and mechanical contributions yields the critical driving force for the martensitic transformation. The results indicate a slight increase in the critical driving force for martensitic transformation at lower temperatures.

Dynamic In Situ Three-Dimensional Imaging and Digital Volume Correlation Analysis to Quantify Strain Localization and Fracture Coalescence in Sandstone

Advances in triaxial compression deformation apparatus design, dynamic X-ray microtomography imaging, data analysis techniques, and digital volume correlation analysis provide unparalleled access to the in situ four-dimensional distribution of developing strain within rocks. To demonstrate the power of these new techniques and acquire detailed information about the micromechanics of damage evolution, deformation, and failure of porous rocks, we deformed 3-cm-scale cylindrical specimens of low-porosity Fontainebleau sandstone in an X-ray-transparent triaxial compression apparatus, and repeatedly recorded three-dimensional tomograms of the specimens as the differential stress was increased until macroscopic failure occurred. Experiments were performed at room temperature with confining pressure in the range of 10–20 MPa. Distinct grayscale subsets, indicative of density, enabled segmentation of the three-dimensional tomograms into intact rock matrix, pore space, and fractures. Digital volume correlation analysis of pairs of tomograms provided time series of three-dimensional incremental strain tensor fields throughout the experiments. After the yield stress was reached, the samples deformed first by dilatant opening and propagation of microfractures, and then by shear sliding via grain rotation and strain localization along faults. For two samples, damage and dilatancy occurred by grain boundary opening and then a sudden collapse of the granular rock framework at failure. For the third sample, a fault nucleated near the yield point and propagated in the sample through the development of transgranular microfractures. The results confirm findings of previous experimental studies on the same rock and provide new detailed quantifications of: (1) the proportion of shear versus dilatant strain in the sample, (2) the amount of dilatancy due to microfracture opening versus pore opening when a fault develops, and (3) the role of grain boundaries and pore walls in pinning microfracture propagation and slowing down the rate of damage accumulation as failure is approached. Our study demonstrates how the combination of high-resolution in situ dynamic X-ray microtomography imaging and digital volume image correlation analysis can be used to provide additional information to unravel brittle failure processes in rocks under stress conditions relevant to the upper crust.

Spatiotemporal Correlation Between Seasonal Variations in Seismicity and Horizontal Dilatational Strain in California

AbstractWe extract significant spatially coherent strain variations from horizontal seasonal Global Positioning System (GPS) displacements in the American Southwest. The dilatational strain is largest in northern California with maximum margin‐normal contraction and extension in spring and fall, respectively, consistent with the Earth's surface going down and up at those times. The northern California signal has a phase shift with respect to that in southern California and the Great Basin. For northern and southern California the proportion of larger earthquakes are in‐phase and the aftershock productivity out of phase with the inferred Coulomb stress on the San Andreas fault system. The intensity of mainshocks is in‐phase in the north as well but not in the south. This suggests that a seasonal increase in fault‐normal extension may or may not trigger mainshocks, but when an earthquake happens at those times, they grow larger than they otherwise would, which would cause a larger stress reduction and result in fewer aftershocks.

Strain evolution in Zr-2.5 wt% Nb observed with synchrotron X-ray diffraction

The mechanical behaviour of hydrides in Zr alloy at low hydrogen concentrations continues to be the subject of research due to wide engineering application and highly complex behaviour of the Zr-H system. Significant structural differences between hydrides and α-Zr cause large dilatational strains associated with formation of the hydride precipitates in zirconium. Two hydride populations were observed to form under different strain states in the α-Zr matrix. The hysteresis of the hydrogen solubility is detected both in intensity and in strain curves for measured δ(111), α(00.2) and α{10.0} peaks. A two-dimensional analysis of α-strain was performed for the axial-hoop, hoop-radial, and axial-radial planes of Zr-2.5 wt% Nb pressure tube material. Variations in the hydrostatic and deviatoric strain components of the α-Zr with temperature were examined. In addition, a change in phase strain during a thermal excursion was considered as a sum of three cooperating components: phase thermal expansion (εT), strains associated with other phase presenting in material (ε[H] or εmatrix), and inter-granular strain within the phase caused by Type II stresses (εother).The present study broadens our understanding of strain evolution in a Zr-H system undergoing hydride dissolution and precipitation. An X-ray synchrotron diffraction technique enables the in-situ following of strain variations in differently oriented grain families during the thermal cycle. In contrast to widely reported the average strain value within the α-phase, the diffraction patterns generated with this technique allow the evaluation of the anisotropic directionality of strains in different phases in Zr-H system generated during phase transformation.

Impact ignition and combustion of micron-scale aluminum particles pre-stressed with different quenching rates

Pre-stressing aluminum (Al) particles by annealing and quenching alters dilatational strain and is linked to increased particle reactivity. The quenching rate associated with pre-stressing is a key parameter affecting the final stress state within the Al particle, with faster quenching rates theoretically favoring a higher, more desirable stress state. Micron scale Al particles are annealed to 573 K, then quenched at different rates (i.e., 200 and 900 K/min), mixed with bismuth oxide (Bi2O3), and the Al + Bi2O3 mixtures are examined under low-velocity, drop-weight impact conditions. Both quenching rates showed increased impact ignition sensitivity (i.e., between 83% and 89% decrease in ignition energy). However, the slower quenching rate showed a 100% increase in pressurization rate compared to untreated particles, while the faster quenching rate showed a 97% increase in peak pressure, indicating that these two quenching rates affect Al particles differently. Surprisingly, synchrotron X-ray diffraction data show that the 200 K/min quenched particles have a higher dilatational strain than the untreated particles or the 900 K/min quenched particles. Results are rationalized with the help of a simple mechanical model that takes into account elastic stresses, creep in the alumina shell, and delamination of shell from the core. The model predicts that Al powder quenched at 200 K/min did not experience delamination. In contrast, Al quenched at 900 K/min did not have creep but does have delamination, and under impact, delamination led to major fracture, greater oxygen access to the core, and significant promotion of reaction. Thus, the increase in quenching rate and shell-core delamination are more important for the increase in Al reactivity than pre-stressing alone.

Phase-Field Modeling of Equilibrium Precipitate Shapes Under the Influence of Coherency Stresses

Coherency misfit stresses and their related anisotropies are known to influence the equilibrium shapes of precipitates. Additionally, mechanical properties of the alloys are also dependent on the shapes of the precipitates. Therefore, in order to investigate the mechanical response of a material which undergoes precipitation during heat treatment, it is important to derive the range of precipitate shapes that evolve. In this regard, several studies have been conducted in the past using sharp interface approaches where the influence of elastic energy anisotropy on the precipitate shapes has been investigated. In this paper, we propose a diffuse interface approach which allows us to minimize grid-anisotropy related issues applicable in sharp-interface methods. In this context, we introduce a novel phase-field method where we minimize the functional consisting of the elastic and surface energy contributions while preserving the precipitate volume. Using this method we reproduce the shape-bifurcation diagrams for the cases of pure dilatational misfit that have been studied previously using sharp interface methods and then extend them to include interfacial energy anisotropy with different anisotropy strengths which has not been a part of previous sharp-interface models. While we restrict ourselves to cubic anisotropies in both elastic and interfacial energies in this study, the model is generic enough to handle any combination of anisotropies in both the bulk and interfacial terms. Further, we have examined the influence of asymmetry in dilatational misfit strains along with interfacial energy anisotropy on precipitate morphologies.

Phase stability, thermal properties and microstructure characteristics of U-15 wt.% Cr alloy

The thermal stability, thermal properties, phase transformation and microstructure characteristics of U-15 wt.%Cr alloy were investigated through a combination of calorimetry, dilatometry, x-ray diffraction and electron microscopy techniques. It is found that at room temperature, both as-cast and homogenized alloys contained metastable βm-U phase, in addition to equilibrium α-U and Cr. The electron microscopy of homogenized sample revealed fine scale nanosized dispersions of βm-U+Cr phases. The presence of metastable βm-U phase influenced the on-heating thermal stability significantly. It is found that upon heating, βm-U→α-U+Cr transformation preceded the occurrence of equilibrium α-U+Cr→β-U+Cr→γ-U+Cr transformations. The nonequilibrium βm-U→α-U conversion took place in a continuous manner. On the other hand, the transformations, α-U+Cr→β-U+Cr→γ-U+Cr occurred at distinct transformation temperatures with measurable changes in enthalpy. The calorimetry results are found to be in accord with dilatometry measurements, which showed a positive jump in the dilatational strain (Δl/lo) across α-U+Cr→β-U+Cr→γ-U+Cr transformations.

An Improved Crack Initiation Stress Criterion for Brittle Rocks under Confining Stress

The stress level associated with crack initiation is an important damage threshold in rock failure process, which can be applied in the prediction of brittle failure in tunnels. In the present study, the uniaxial and triaxial compression tests are conducted on two sets of hard sandstones, while the dilation strains and AE counts are employed to characterize the crack accumulation. The crack initiation stress is then determined through the inflection point on strain and AE curves. Furthermore, two crack initiation modes: the splitting mode for low confinements and the sliding mode for high confinements are presented by analysing the fracturing mechanism. Based on the derivation of maximum tensile stress around the rock defects, an improved crack initiation criterion is proposed to predict the σci of confined rocks. In the new criterion, the frictional components on crack surface are considered by introducing the parameter mci, which can be applied for various types of rocks as well. At last, the triaxial compression test data of different rock types are reviewed to verify the reliability and applicability of the new criterion. The results indicate that the new criterion can predict the crack initiation stress of confined rock with high accuracy.

Seasonal Nontectonic Loading Inferred From cGPS as a Potential Trigger for the M6.0 South Napa Earthquake

AbstractWe analyze crustal strain corresponding to transient continuous Global Positioning System (cGPS) horizontal displacements in Northern California, detecting a seasonal positive dilatational strain and Coulomb stress transient in the South Napa region peaking just before the 24 August 2014 M6.0 South Napa earthquake. Using data from 2007 to 2014, we show that average dilatational strain within a 500‐km2 region encompassing South Napa and northern San Pablo Bay peaks in late summer at 76 ± 17 × 10−9, accompanied by a Coulomb stress change of 1.9 ± 0.8 kPa. The situation reverses in winter, with an average dilatational strain of −51 ± 17 × 10−9 and Coulomb stress change of −1.4 ± 0.8 kPa. Within a smaller 100‐km2 area centered on the South Napa rupture, peak values are considerably higher, including a summer Coulomb stress peak of 5.1 ± 1.6 kPa. We examine regional seismicity but see no statistically significant correlation with seasonal Coulomb stressing in the declustered earthquake catalog. Using western U.S. vertical cGPS displacements, we estimate that strain from hydrologic loading explains ≤10% of the observed long‐wavelength strain and only 2–3% of peak strains around the South Napa rupture. Thermoelastic crustal strain estimated from temperature gradients between the San Francisco Bay and Sacramento Valley reaches values as high as 15% of the observed strain, but the strain patterns are not spatially consistent. Vertical deformation within the Sonoma and Napa Valley subbasins inferred from interferometric synthetic aperture radar explains large horizontal motions at nearby cGPS stations and suggests that seasonal changes in groundwater may contribute to observed strain and stress transients.

Induced fabric anisotropy of granular materials in biaxial tests along imposed strain paths

In granular materials, loading on an initially isotopic assembly usually induces particle rearrangement, and this is referred to as the induced anisotropy of fabric. A series of biaxial tests are conducted along various strain paths using DEM to investigate the evolution of the induced anisotropy. The evolution of both the overall contact network and the sub-networks (the strong and weak) are examined separately. Results of DEM simulations indicate that the evolution of the fabric deviator in the overall contact network can be described as a power function of the stress ratio prior to the peak stress ratio that depends on the imposed dilation rate. A unique fabric-stress relation is obtained for the strong sub-network, which is independent of the strain path, the initial porosity and the confining pressure. Moreover, deformation instability is observed only along dilatant strain paths, which can be related to the degradation or even collapse of a weak sub-network, even though the strong sub-network dominates the strength of the granular assembly.

Microstructural Evolution of Porosity and Stress During the Formation of Brittle Shear Fractures: A Discrete Element Model Study

AbstractBrittle fracturing in rocks is a progressive process involving changes in stress, strain, and porosity. Changes in these properties occur heterogeneously within a rock and are manifest at the grain scale, which is difficult to observe directly in the laboratory or the field. This study uses the discrete element method to show that fractures correspond to zones of generally lower stresses, higher porosity, and highly localized dilation and distortional strain. Using the discrete element method, we conducted numerical biaxial experiments at different confining pressures to probe the internal conditions of a low cohesive sandy sediment numerical analog. When compression begins, the stresses within the sandy sediment are relatively homogeneous with anastomosing stress chains. At yield stress, when the confining pressure is relatively low, multiple dilational bands start to open. At peak stress, high‐magnitude stress chains localize adjacent to the developing shear band and distortion is evident. Postpeak stress, through‐going shear fractures are fully developed. High stresses are transmitted across the fracture where porosity is low through a network of particles in contact. With increasing confining pressure, distortion is favored over dilation during deformation. Also, the number of particles that define the width of a stress chain across a shear fracture, and the steepness of the fracture, increases. Our results can be applied to understanding stress conditions of field samples, and in constraining rock property changes during reservoir modeling of fractured reservoirs.

The effect of resonance on transient microbubble acoustic response: Experimental observations and numerical simulations.

A large number of acoustic signals from single lipid-shelled Definity® (Lantheus Medical Imaging, N. Billerica, MA) microbubbles have been measured using a calibrated microacoustic system, and a unique transient characteristic of resonance has been identified in the onset of scatter. Comparison of the numerically obtained response of microbubbles with acoustic measurements provides good agreement for a soft shell that is characterized by small area dilatation modulus and strain softening behavior, and identifies time to maximum radial excursion and scatter as a robust marker of resonance during transient response. As the sound amplitude increases a two-population pattern emerges in the time delay vs the fundamental acoustic scatter plots, consisting of an initial part pertaining to microbubbles with less than resonant rest radii, which corresponds to the weaker second harmonic resonance, and the dominant resonant envelope pertaining to microbubbles with resonant and greater than resonant rest radii, which corresponds to the primary and subharmonic resonances. Consequently, a wider resonant spectrum is observed. It is a result of the strain softening nature of soft lipid shells, based on which the microbubble sizes corresponding to the above resonances decrease as the sound amplitude increases. This bares an impact on the selection of an optimal microbubble size pertaining to subharmonic imaging.

Comparison of stress-based failure criteria for prediction of curing induced damage in 3D woven composites

Several stress-based failure criteria (von Mises, dilatational strain energy density, parabolic stress and Drucker-Prager) are implemented in a numerical model of a 3D woven composite to predict initiation of damage due to cooling after curing. It is assumed that the composite is completely cured at elevated temperature and the residual stresses arise due to difference in the thermal expansion coefficients of fibers and matrix. The stresses are found by finite element analysis on the mesoscale while the effective thermoelastic properties of fiber tows are determined by micromechanical modeling. The matrix is modeled as an isotropic material with temperature dependent elastic properties and thermal expansion coefficient.Comparison of numerical simulation results with the microcomputed tomography data obtained for a one-by-one orthogonally reinforced carbon/epoxy composite shows that the parabolic stress and the dilatational strain energy criteria provide the most accurate predictions of cure-induced damage. However, the accuracy of the parabolic failure criterion is dependent on the choice of the mechanical tests used to determine the values of its two material parameters.

Local Deformation Precursors of Large Earthquakes Derived from GNSS Observation Data

Research on deformation precursors of earthquakes was of immediate interest from the middle to the end of the previous century. The repeated conventional geodetic measurements, such as precise levelling and linear-angular networks, were used for the study. Many examples of studies referenced to strong seismic events using conventional geodetic techniques are presented in [T. Rikitake, 1976]. One of the first case studies of geodetic earthquake precursors was done by Yu.A. Meshcheryakov [1968]. Rare repetitions, insufficient densities and locations of control geodetic networks made difficult predicting future places and times of earthquakes occurrences. Intensive development of Global Navigation Satellite Systems (GNSS) during the recent decades makes research more effective. The results of GNSS observations in areas of three large earthquakes (Napa M6.1, USA, 2014; El Mayor Cucapah M7.2, USA, 2010; and Parkfield M6.0, USA, 2004) are treated and presented in the paper. The characteristics of land surface deformation before, during, and after earthquakes have been obtained. The results prove the presence of anomalous deformations near their epicentres. The temporal character of dilatation and shear strain changes show existence of spatial heterogeneity of deformation of the Earth’s surface from months to years before the main shock close to it and at some distance from it. The revealed heterogeneities can be considered as deformation precursors of strong earthquakes. According to historical data and proper research values of critical deformations which are offered to be used for seismic danger scale creation based on continuous GNSS observations are received in a reference to the mentioned large earthquakes. It is shown that the approach has restrictions owing to uncertainty of the moment in the beginning of deformation accumulation and the place of expectation of another seismic event. Verification and clarification of the derived conclusions are proposed.

Full elastic strain tensor determination at the phase scale in a powder metallurgy nickel-based superalloy using X-ray Laue microdiffraction

Laue microdiffraction is used to determine the full elastic strain tensor of the γ and γ′ phases in grains of a nickel-based superalloy with a coarse-grained microstructure. A `rainbow' filter and an energy dispersive point detector are employed to measure the energy of Bragg reflections. For the two techniques, an uncertainty of ±2.5 × 10−3 Å is obtained for the undetermined crystal lattice parameter. Our measurements show that the filter method provides better confidence, energy resolution, accuracy and acquisition time. The sensitivity of each method with respect to the γ–γ′ lattice mismatch is demonstrated with measurements in samples with average precipitate sizes of 200 and 2000 nm. For the 200 nm precipitate size, the lattice mismatch is less than 2 × 10−3 Å and the dilatational strains are close to ±1.5 × 10−3 depending on the considered phase. For the 2000 nm precipitate size, the lattice mismatch is close to 8 × 10−3 Å and almost no elastic strain occurs in the microstructure.