Strain Rate Direction Research Articles

A fabric-based sand plasticity model with reversal surfaces within anisotropic critical state theory

The paper describes the formulation and capabilities of a new constitutive model that accounts for the effects of fabric anisotropy on the response of granular materials under monotonic loading. It is developed within the framework of bounding surface plasticity in conjunction with the concept of (stress) reversal surfaces, i.e., the use of the last stress reversal point as projection center for defining the image stress on the bounding surface. A key constitutive ingredient is the fabric anisotropy variable A, relating the fabric tensor to the plastic strain rate direction, that acquires the value A = 1 as the third requirement for critical state according to the anisotropic critical state theory. This A is used in the definition of dilatancy, the plastic modulus and the evolution equation of the fabric tensor, thus simulating experimental results that show more dilative and stiff response when the loading is applied along the direction of the fabric. Model performance is verified against a large database of monotonic shearing tests on samples of Toyoura sand prepared with three different methods, as well as similar tests on samples whose (initially horizontal) deposition plane was rotated by up to 90 degrees. All simulations are performed with a single set of constants, thus validating the efficiency of the model to account for density, stress level and, most importantly, fabric anisotropy effects on the monotonic shearing response. The paper shows that considering dependence of strength and dilatancy on Lode angle θ and state parameter ψ does not suffice for simulating fabric anisotropy effects on sand response. It ends with a discussion of how fabric effects on sand response are more pronounced under undrained, versus drained conditions.

Autoignition-controlled flame initiation and flame stabilization in a reacting jet in crossflow

This paper describes an analysis of the mechanisms of autoignition-controlled flame initiation and flame stabilization in a nonpremixed jet in crossflows, using simultaneous high-speed (10 kHz) tomographic particle image velocimetry, OH-PLIF and line-of-sight flame emissions. Measurements are conducted on a turbulent, transverse, reacting propane jet issued into a crossflow generated by combustion of natural gas at an equivalence ratio of 0.4 with the crossflow velocity of 10 m/s, the crossflow temperature of 1350 K and the jet momentum flux ratio of 41. While several prior studies have analyzed the lifted character of the flame in similar configurations, we show that several dynamic processes precede the leading edge of the lifted diffusion flame, including formation and evolution of “autoignition kernels”, “flame kernels” and “flame fragments”. “Autoignition kernels”, i.e., discrete compact reaction zones with the peak hydroxyl (OH) fluorescence intensity below that of the diffusion flame, initiate preferably at bulges along the jet periphery where the strain rates and the scalar dissipation rates are lower. The autoignition kernel grows in both size and the OH-fluorescence intensity as it convects downstream. An autoignition kernel transitions into a propagating flame kernel, which quickly gets distorted and elongated in the direction of the principal expansion strain rate to form a flame fragment. Neighboring flame fragments merge with each other and with the downstream diffusion flame via edge-flame propagation. Merging of upstream flame fragments with the downstream diffusion flame results in an upstream advancement of the diffusion-flame front. The diffusion flame front is intrinsically unsteady because of the rather random formation and evolution of autoignition kernels, flame kernels and flame fragments, presumably due to the stochastic velocity, the strain rate and mixture-fraction oscillations.

Strain rate and flame orientation statistics in the near-wall region for turbulent flame-wall interaction

Flame–wall interaction (FWI) in premixed turbulent combustion has been analysed based on a counter-flow like configuration at the statistically stationary state. For the present configuration, the two FWI sub-zones, i.e the influence zone and the quenching zone, can be identified from the DNS results. Detailed analysis of the important quantities, such as the flame temperature, flame–wall distance, wall heat flux, flame curvature and dilatation (including the flame normal and tangential strain rates), and some orientation relations between the flame normal and the principal strain rate directions, have been reported, together with the physical explanations. All these statistical results are determined by the relative strengths of the wall heat flux, thermal expansion and the flame–turbulence interaction.

Plastic flow of thin-walled tubes under nonlinear tension-torsion loading paths and an improved pseudo-corner model

The elastoplastic deformation behaviors of thin-walled tubes made of pure aluminum and steel were measured under various tension–torsion combined loadings. The ratio between the displacement and rotation of a grip was held constant for the linear-loading experiment. In the nonlinear-loading experiments, a specimen was subjected to uniaxial tension followed by the simultaneous application of tension and torsion. It was determined that the associated flow rule predicts the plastic flow behaviors observed in the experiments with sufficient accuracy, provided that the specimen was subjected to linear loadings. Meanwhile, under nonlinear loadings, the plastic flow behaviors were markedly dissimilar to those in the linear loadings, and the direction of plastic flow rotated toward the direction of the stress/strain rate. By analyzing the experimental results, a linear relationship between the plastic flow direction and strain rate direction was determined. Therefore, the experimental data demonstrated that the stress state and the strain rate direction are essential parameters characterizing a plastic flow rule. Eventually, a pseudo-corner model capable of reproducing experimentally observed plastic deformation behavior was proposed.

Upper crustal anisotropy from local shear-wave splitting and crust-mantle coupling of Yunnan, SE margin of Tibetan Plateau

The upper crustal anisotropy of Yunnan area, SE margin of Tibetan Plateau, is investigated by measuring the shear wave splitting of local earthquakes. The mean value of the measured delay times is 0.054 s and far less than that from Pms splitting analysis, indicating that the crustal anisotropy is contributed mostly from mid-lower crust. The fast polarization directions are mostly sub-parallel to the maximum horizontal compression directions while the stations near fault zones show fault-parallel fast polarization directions, suggesting both stress and geological structure contribute to the upper crust anisotropy. Comparing fast polarization directions from shear wave splitting of local earthquakes and Pms, large angle differences are shown at most stations, implying different anisotropy properties between upper and mid-lower crust. However, in southwestern Yunnan, the fast polarization directions of Pms and S-wave splitting are nearly parallel, and the stress and surface strain rate directions show strong correlation, which may indicate that the surface and deep crust deformations can be explained by the same mechanism and the surface deformation can represent the deformation of the whole crust. Therefore, the high correlation between surface strain and mantle deformation in this area suggests the mechanical coupling between crust and mantle in southwestern Yunnan. In the rest region of Yunnan, the crust-mantle coupling mechanisms are supported by the lack of significant crustal anisotropy with NS fast polarization directions from Pms splitting. Therefore, we conclude that the crust and upper mantle are coupled in Yunnan, SE margin of Tibetan Plateau.

Mechanical properties of high-density TRIP steel honeycomb structures with varying cell profiles under different loading conditions

As the mechanical properties of honeycomb structures are influenced by several parameters, detailed analysis is necessary before their potential application in transportation industry components. Previous Finite Element Model (FEM)-based numerical analysis demonstrated that variation in cell geometry affects the achievable strength level and, thus, the energy absorption capability. According to this FEM study, the Kagome geometry – an ordered sequence of hexagons and triangles – exhibits properties that are particularly promising when compared to the square-celled structures investigated to date. When the load is applied parallel to the channel axis (the out-of-plane direction), the increment of strength is comparatively low, whereas in the in-plane direction (loading orthogonal to the channel axis), the dissipated specific energy can reach almost double that of the square-celled structure. In this study, the results of static and dynamic compression tests – performed in the out-of-plane and in-plane modes – are presented to examine the influence of strain rate and loading direction on the characteristic deformation stages of squarecelled and Kagome structures. Particular attention is paid to deformation induced martensite formation in the cell wall material, indicating the TRansformation Induced Plasticity (TRIP) effect as a function of applied cell geometry, strain rate and loading direction.

Accurate relocation of seismicity along the North Aegean Trough and its relation to active tectonics

The tectonics of northern Aegean are affected by the westward push of Anatolia and the gravitational spreading of the Aegean lithosphere that promote transtensional deformation in the area. This regime is also responsible for the creation of a series of pull-apart basins, collectively known as the North Aegean Trough. This work accurately relocates a total of 2300 earthquakes that were recorded along the North Aegean Trough during 2011–2016 by stations of the Hellenic Unified Seismic Network (HUSN) and strong-motion sensors. Absolute locations for these events were obtained using a nonlinear probabilistic algorithm and utilizing a minimum 1D velocity model with station corrections. The hypocentral depth distribution of these events shows a peak at 8km diminishing gradually down to 20km. A systematic overestimation of hypocentral depths is observed in the routine locations provided by the National Observatory of Athens where the majority of events appear to be deeper than 15km. In order to obtain more accurate relative locations these events were relocated using the double-difference method. A total of 1693 events were finally relocated with horizontal and vertical uncertainties that do not exceed 0.11km and 0.22km respectively. Well-defined clusters of seismicity can be observed along the Saros and Sporades basins as well as the Kassandra and Sithonia peninsulas. These clusters either occur along the well-known NE-SW strike-slip faults bounding the basins, or along normal faults whose strike is perpendicular to the regional minimum stress axis. Locking depth along the North Aegean Trough is found to be remarkably stable between 13 and 17km. This is likely a consequence of simultaneous reduction along the SW direction of heat flow (from 89 to 51mW/m2) and strain rate (from 600 to 50nstrain/yr) whose opposite effects are canceled out, precluding any sharp changes in locking depth.

A plastic flow rule representing corner effects predicted by rate-independent crystal plasticity

Elastoplastic responses of rate-independent polycrystals are simulated under linear and various nonlinear strain paths, and the influence of the loading condition on the plastic flow behavior is investigated. It is observed that the shear components of elastoplastic tangent moduli start decreasing when the plastic deformation occurs, and the direction of the plastic flow depends on the direction of the stress/strain rates. A phenomenological plastic flow rule capable of reproducing these behaviors is developed. The flow rule relates the direction of plastic strain rate to the direction of strain rate, and yields the reduction of shear modulus after plastic yielding. The proposed constitutive model is then integrated into a finite element program, and the plane strain tension and pure bending are analyzed. The advantage of the proposed flow rule for simulating the occurrence of a shear band is demonstrated.

Influences of high strain rate, low temperature, and deformation direction on microstructural evolution and mechanical properties of copper

Step-wise deformations are applied to pure copper along uniaxial direction or multiaxial directions in three conditions of speed and temperature: static and room temperature, dynamic and room temperature, or dynamic and low temperature. Through examinations of total 36 deformation stages, the influences of strain rate, temperature, and deformation direction on microstructural evolution and mechanical properties are investigated. According to the results, the deformation mechanism at extreme conditions (high strain rate and low temperature) changes from only dislocation slip to dislocation slip and deformation twinning. Although deformation-direction change has no significant effect on the final mechanical properties and total dislocation densities measured from X-ray diffraction results, the evolutions of grain-boundary misorientation and geometrically necessary dislocations (GNDs) are clearly influenced. The trend of microstructural evolution, i.e. larger grain size and lower GND densities by multi-axial deformation than the uniaxial case, is reversed when twinning occurred. Based on the results, we suggest four evolution models: uniaxial or multi axial cases with dislocation slip, or with dislocation slip and deformation twining. Even if the homogenous and almost fully twinned microstructure producing improved mechanical strength was obtained by applying the extreme deformations, poor ductility of the processed specimen were observed.

SANISAND-Z: zero elastic range sand plasticity model

The theory of zero purely elastic range in stress space within the framework of bounding surface plasticity is applied to sand constitutive modelling. The yield surface shrinks to zero and becomes identical to the stress point itself, and plastic loading occurs for any direction of the stress ratio rate on which the loading and plastic strain rate directions now depend, rendering the model incrementally non-linear. The simplicity of the conceptual structure of the model is particularly attractive as it consists of only one surface, the bounding/failure surface, and the stress point itself in the stress ratio π-plane. The image stress point on the bounding surface is defined analytically in terms of the direction of the rate of the stress ratio, with the latter being inside, on, or outside the surface, so that the model can address consistently hardening, softening and critical state response. An updating scheme of the initial value of stress ratio at unloading–reloading events is proposed in order to avoid the overshooting phenomenon. The model follows the basic premises of the SANISAND family of models that unify the description for any pressure and density within critical state theory. The simulating capabilities of the model are shown to be comparable with those of classical models with very small yield surfaces, and additional simulations of unorthodox loading paths such as rotational shear are successfully compared with experimental data.

Effects of equivalence ratio variations on turbulent flame speed in lean methane/air mixtures under lean-burn natural gas engine operating conditions

Direct numerical simulations (DNS) of turbulent premixed methane/air flames are carried out to investigate the effects of equivalence ratio on the turbulent flame speed in lean mixtures. Turbulent flames are simulated as statistically stationary following a Lagrangian framework using an inflow–outflow configuration. The inflow velocity is dynamically adjusted at run-time to stabilize the flame brush location within the computational domain. Linear forcing is applied inside the unburned mixtures to maintain the turbulent intensities at desired levels. For the same turbulence properties, several equivalence ratios near the lean limit are selected and it is shown that the normalized turbulent flame speed is a function of the equivalence ratio. Velocity and length scales of the imposed turbulence are then selected in such a way that the Karlovitz and Damköhler numbers remain constant for flames of different equivalence ratios. Simulations are run for more than 80 eddy turnover times and the turbulent flame speed is derived by averaging the inflow velocity. The results show that equivalence ratio does not have an explicit effect on the normalized turbulent flame speed above the lean limit. Analysis of flame surface area shows that surface wrinkling generated by eddies of different scales is not affected by variation in equivalence ratios when the Karlovitz and Damköhler numbers are fixed. Furthermore, flame surface generated by large-scale eddies is independent of the Karlovitz and Damköhler numbers. Examining the flame surface statistics, it is shown that the flame surface normal is preferentially parallel to the most compressive strain rate direction for all equivalence ratios.

Investigation on anisotropic behavior of spruce mechanical properties under medium strain rate loading conditions

Medium strain rate (100 s-1~102 s-1) compression experiments were performed on spruce using high-speed loading equipment (INSTRON). Loading was conducted in the axial, radial, tangential and included angle directions, respectively. Angles of 15°, 30°, 45°, 60°, 75° between loading direction and grain are taken into account in radial and tangential sections. The experimental results indicate spruce yield strength decreases when loading varies from axial to radial or tangential direction. The plastic phase of stress versus strain curve changes from ‘plastic softening’ to ‘plastic hardening’. Spruce compression yield strength in different directions is sensitive to strain rate. The loading direction has effects on the spruce failure modes. For axial loading conditions, the middle part of the specimen bulges, folds, and finally fiber breaks. When the angle between loading and axial direction increases, grain delamination and tears occur when loading is near to radial or tangential direction. Hill strength theory is adopted to simplified describe spruce spatial yield behavior. The spatial yield surface is an elliptic cylindrical surface for all strain rate loading conditions. Yield surface radius increases with strain rate. Experimental and theoretical analysis results indicate spruce mechanical properties are spatially anisotropic. Yield strength is sensitive to strain rate and loading direction. Loading direction is the primary determining factor of failure mode under compression.

Stress, strain rate and anisotropy in Kyushu, Japan

Seismic anisotropy, the directional dependence of wave speeds, may be caused by stress-oriented cracks or by strain-oriented minerals, yet few studies have quantitatively compared anisotropy to stress and strain over large regions. Here we compare crustal stress and strain rates on the Island of Kyushu, Japan, as measured from inversions of focal mechanisms, GPS and shear wave splitting. Over 85,000 shear wave splitting measurements from local and regional earthquakes are obtained from the NIED network between 2004 and 2012, and on Aso, Sakurajima, Kirishima and Unzen volcano networks. Strain rate measurements are made from the Japanese Geonet stations. JMA-determined S arrival times processed with the MFAST shear wave splitting code measure fast polarisations (Φ), related to the orientation of the anisotropic medium and time delays (dt), related to the path length and the percent anisotropy. We apply the TESSA 2-D delay time tomography and spatial averaging code to the highest quality events, which have nearly vertical incidence angles, separating the 3455 shallow (depth < 40 km) from the 4957 deep (>=40 km) earthquakes. Using square grids with 30 km sides for all the inversions, the best correlations are observed between splitting from shallow earthquakes and stress. Axes of maximum horizontal stress (SHmax) and Φ correlate with a coefficient c of 0.56, significant at the 99% confidence level. Their mean difference is 31.9°. Axes of maximum compressional strain rate and SHmax are also well aligned, with an average difference of 28°, but they do not correlate with each other, meaning that where they differ, the difference is not systematic. Anisotropy strength is negatively correlated with the stress ratio parameter determined from focal mechanism inversion (c=−0.64; significant at the 99% confidence level). The anisotropy and stress results are consistent with stress-aligned microcracks in the crust in a dominantly strike-slip regime. Eigenvalues of maximum horizontal strain rate correlate positively with stress ratio (c=0.43, significant at 99% confidence). All three orientations are E–W in central Kyushu, where the compressional strain rate is highest. Both splitting and stress suggest plate-boundary-parallel maximum principal stress just off the coast of Kyushu, where strain rate measurements are sparse. South western Kyushu has the largest difference between directions of strain rate and stress. Φ from shallow and deep earthquakes are not well aligned, suggesting that the deep earthquake waveforms are not simply split in the crust. Causes for the anisotropy may be olivine crystals aligned by drag of the subducting Philippine Sea plate in the mantle and stress-aligned microcracks in the crust.

An experimental and numerical study of the dynamic response of composites under impact at low temperatures

ABSTRACTAn analytical method was applied to investigate the effects of strain rate, low temperature, and impact direction on the energy absorption of composite specimens. The performance of an analytical model was found to be adequate for modeling composites before failure initiation. Results indicated that impact performance of composites is affected over the range of temperatures. Failure mechanism was changed from matrix cracking at room temperature to delamination and fiber breakage at low temperatures. Moreover, it was shown that about 70% of total energy absorbed by a specimen was used to destroy the composite under different types of failure mechanisms.

Laboratory and micromechanical investigation of soil anisotropy

This paper presents an experimental investigation revisiting the anisotropic behavior of geomaterials in drained monotonic shear using Hollow Cylinder Apparatus. The test program has been designed to cover the effect of material anisotropy, pre-shearing and material density on the behavior of Leighton Buzzard sand. Experiments have also been performed on glass beads to understand the effect of particle shape. The test results demonstrate that the stress-strain-strength behavior of the specimen shows strong dependence on the principal stress direction. The pre-shearing history, material density and particle shape are found to be influential. The deformation non-coaxiality, i.e., non-coincidence between the principal stress direction and the principal strain rate direction is observed. In particular, it was found that non-coaxiality is more significant in presheared specimens. This paper also explains the phenomenological observations based on the recently acquired understanding in micromechanics, with attention focused on strength and deformation non-coaxiality.

A laboratory study of anisotropic geomaterials incorporating recent micromechanical understanding

This paper presents an experimental investigation revisiting the anisotropic stress–strain–strength behaviour of geomaterials in drained monotonic shear using hollow cylinder apparatus. The test programme has been designed to cover the effect of material anisotropy, preshearing, material density and intermediate principal stress on the behaviour of Leighton Buzzard sand. Experiments have also been performed on glass beads to understand the effect of particle shape. This paper explains phenomenological observations based on recently acquired understanding in micromechanics, with attention focused on strength anisotropy and deformation non-coaxiality, i.e. non-coincidence between the principal stress direction and the principal strain rate direction. The test results demonstrate that the effects of initial anisotropy produced during sample preparation are significant. The stress–strain–strength behaviour of the specimen shows strong dependence on the principal stress direction. Preloading history, material density and particle shape are also found to be influential. In particular, it was found that non-coaxiality is more significant in presheared specimens. The observations on the strength anisotropy and deformation non-coaxiality were explained based on the stress–force–fabric relationship. It was observed that intermediate principal stress parameter b(b = (σ2 − σ3)/(σ1 − σ3)) has a significant effect on the non-coaxiality of sand. The lower the b-value, the higher the degree of non-coaxiality is induced. Visual inspection of shear band formed at the end of HCA testing has also been presented. The inclinations of the shear bands at different loading directions can be predicted well by taking account of the relative direction of the mobilized planes to the bedding plane.

Molecular Dynamics Study of Uniaxial Deformation in Perfect and Defective Aluminum

In materials, strength is usually controlled by the occurrence of grain boundaries, dislocations, voids, and other microstructural defects. molecular dynamics (MD) simulations with the embedded atom method potential have been employed to investigate the uniaxial tension and compression of single crystal aluminum with and without defects. In this paper, defect refers to a void or grain boundary. For perfect crystal aluminum, the ideal strengths and stress-strain curves obtained from the MD simulations agree well with those obtained by first principles calculations. The strength and ductility of Al decrease with the occurrence of void and grain boundaries. The effect of void size on the uniaxial stress-strain relations is investigated. Also, dislocation nucleation and emission from the void free surface are observed. In order to study the effect of a grain boundary, we generate a symmetric tilt grain boundary Σ5(310) and strain is imposed perpendicular to the boundary interface. We can clearly see that fracture starts in the grain boundary. The observed defect pattern is expected to provide some helpful insights into the damage mechanism of ductile materials at the microscale. The effects of temperature, strain rate, and crystalline direction on the ideal strength are also discussed.

PRESENT DAY TECTONIC GRADIENT IN NINH THUAN AND SURROUNDING REGION

The estimation of the present day tectonic movement and tectonic gradient (strain rate) has an important practical signification in the assessment of active fault and seismic hazards for the selection of Ninh Thuan nuclear power plant. Based on the three campaigns of GPS measurement between 2012 - 2013, we used BERNESE 5.0 software to determine present day slip rates of 13 stations in ITRF08 frame. The GPS stations move eastwards at the slip rates of 22 - 25 mm/yr, southwards at the velocities of 5 - 10 mm/yr. The standard errors in latitudinal and longitudinal directions are 1.2 mm/yr and 0.9 mm/yr, respectively. Combined with GPS data from the project of the study on actual geodynamics in Tay Nguyen TN3/06, we determined the strain rate ranging from 50 to 100 nanostrains with the standard error of 50 nanostrains. The direction of maximum compressive strain rate is from northwest - southeast to east - west.

Influences of Strain Rate and Load Direction on the Thermo-mechanical Behavior of a Nano-Alumina-Containing Copper Alloy Bar

The effects of strain rate and load direction on the thermo-mechanical behavior of Cu-2.7vol.%Al2O3 alloy bar with high strength and electrical conductivity were investigated. The results show that the thermo-mechanical behavior of the alloy changes greatly with changing load direction or strain rate. For the same compression strain rate, the peak yield stress in the longitudinal compression is much higher than that of transverse compression. The homogeneous distribution of dynamic recrystallization grains or subgrains after longitudinal compression is much higher than that of transverse compression. For the longitudinal or transverse compression, the size of dynamical recrystallization grains decreases with increasing strain rate, the initial elongated bands can only be observed in the transverse compressions due to the effect of load direction. The flow stress oscillation phenomenon appears in both transverse and longitudinal compressions with a strain rate of 20 s−1. Accordingly, the relationship between flow stress and microstructure, and a model of dynamic recrystallization in the transverse and longitudinal compressions, were established and analyzed in this paper.

Multi-level modelling of mechanical anisotropy of commercial pure aluminium plate: Crystal plasticity models, advanced yield functions and parameter identification

The mechanical anisotropy of an AA1050 aluminium plate is studied by the use of five crystal plasticity models and two advanced yield functions. In-plane uniaxial tension properties of the plate were predicted by the full-constraint Taylor model, the advanced Lamel model (Van Houtte et al., 2005) and a modified version of this model (Mánik and Holmedal, 2013), the viscoplastic self-consistent model and a crystal plasticity finite element method (CPFEM). Results are compared with data from tensile tests at every 15° from the rolling direction (RD) to the transverse direction (TD) in the plate. Furthermore, all the models, except CPFEM, were used to provide stress points in the five-dimensional deviatoric stress space at yielding for 201 plastic strain-rate directions. The Facet yield surface was calibrated using these 201 stress points and compared to in-plane yield loci and the planar anisotropy which were calculated by the crystal plasticity models. The anisotropic yield function Yld2004-18p (Barlat et al., 2005) was calibrated by three methods: using uniaxial tension data, using the 201 virtual yield points in stress space, and using a combination of experimental data and virtual yield points (i.e. a hybrid method). Optimal yield-surface exponents were found for each of the crystal plasticity models, based on calibration to calculated stress points at yielding for a random texture, and used in the latter two calibration methods. It is found that the last hybrid calibration method can capture the experimental results and at the same time ensure a good fit to the anisotropy in the full stress space predicted by the crystal plasticity models.