Triaxial Strain Research Articles

Acoustic Measurements of the Anisotropy of Dynamic Elastic and Poromechanics Moduli under Three Stress/Strain Pathways

A series of triaxial compression experiments have been conducted to investigate the effects of induced stress on the anisotropy developed in dynamic elastic and poroelastic parameters in rocks. The measurements were accomplished by utilizing an array of piezoelectric compressional and shear wave sensors mounted around a cylindrical sample of porous Berea sandstone. Three different types of applied states of stress were investigated using hydrostatic, triaxial, and uniaxial strain experiments. During the hydrostatic experiment, where an isotropic state of stress was applied to an isotropic porous rock, the vertical and horizontal acoustic velocities and dynamic elastic moduli increased as pressure was applied and no evidence of stress induced anisotropy was visible. The poroelastic moduli (Biot’s effective stress parameter, α ) decreased during the test but also with no evidence of anisotropy. The triaxial compression test involved an axisymmetric application of stress with an axial stress greater than the...

Application of the White/Monochromatic X-Ray μ-Diffraction Technique to the Study of Texture and Triaxial Strain at the Submicron Level

A scanning X-ray microdiffraction beamline using white or monochromatic beam has been recently made available to the user’s community at the Advanced Light Source, Berkeley, USA. Samples are scanned under an X-ray beam with size ranging from 15 microns down to less than a micron, and 2D diffraction patterns are collected at each step. A specifically written software allows for the full treatments of these patterns to obtain as outputs high spatial resolution grain orientation, strain/stress or mineral species distribution maps. The range of applications of this technique goes from the study of the mechanical properties of thin films to the understanding of trace elements speciation in environmental sciences.

Mapping the 3D-surface strain field of patterned tensile stainless steels using atomic force microscopy

The quantification of microstructural strains at the surface of materials is of major importance for understanding the reactivity of solids. The present paper aims at demonstrating the potentialities of the atomic force microscopy (AFM) for mapping the three-dimensional surface strain field on patterned tensile specimens. Electron beam (e-beam) lithography has been used to deposit 16×16 arrays of gold-squared pads. Monitoring the evolution of such a pattern under applied strain allows to quantify the triaxial strains both at the micro-(plastic) domain and nanoscale (elastic) domain vs. applied strain. The proposed method was applied to stainless steels after 4.5% plastic strain.

Examination of the Response of Regularly Packed Specimens of Spherical Particles Using Physical Tests and Discrete Element Simulations

Significant insight into the response of granular materials can be gained by coupling accurately controlled physical tests with complementary discrete element simulations. This paper discusses a series of triaxial and plane strain laboratory compression tests on steel spheres with face-centered-cubic and rhombic packings, as well as discrete element simulations of these tests. The tests were performed on specimens of uniform-sized steel balls and on specimens of steel balls with specified distributions of ball diameters. The packing configurations are ideal and differ considerably from real sand specimens, however, studies of such idealized granular materials can yield considerable insight into the response of granular materials and the capability of discrete element simulations to capture the response. The differences in response for the two packing configurations considered illustrate the importance of fabric. The numerical simulations captured the observed laboratory response well if the particle configurations, particle sizes, and boundary conditions were accurately represented. However, the postpeak response is more difficult to capture, and it is shown to be sensitive to the coefficient of friction assumed along the specimen boundaries. The simulations of the tests on the nonuniform-sized specimens demonstrated a clear correlation between strength and coordination number.

Generalized strain probing of constitutive models

AbstractAdvanced material constitutive models are used to describe complex soil behaviour. These models are often used in the solution of boundary value problems under general loading conditions. Users and developers of constitutive models need to methodically investigate the represented soil response under a wide range of loading conditions. This paper presents a systematic procedure for probing constitutive models. A general incremental strain probe, 6D hyperspherical strain probe (HSP), is introduced to examine rate‐independent model response under all possible strain loading conditions. Two special cases of HSP, the true triaxial strain probe (TTSP) and the plane‐strain strain probe (PSSP), are used to generate 3‐D objects that represent model stress response to probing. The TTSP, PSSP and general HSP procedures are demonstrated using elasto‐plastic models. The objects resulting from the probing procedure readily highlight important model characteristics including anisotropy, yielding, hardening, softening and failure. The PSSP procedure is applied to a Neural Network (NN) based constitutive model. It shows that this probing is especially useful in understanding NN constitutive models, which do not contain explicit functions for yield surface, hardening, or anisotropy. Copyright © 2004 John Wiley & Sons, Ltd.

Effects of volumetric ice content and strain rate on shear strength under triaxial conditions for frozen soil samples

AbstractA set of triaxial constant strain rate and constant stress tests was performed on artificially frozen soil samples to study the effect of the volumetric ice fraction, strain rate and also confining stress on the mobilized shear strength. In general, the peak shear strength increased with decreasing volumetric ice content and increasing strain rate. Pure ice samples, however, showed a peak shear strength that was higher than that for those containing about 80% ice by volume for a similar strain rate, although the loss in strength after this maximum was usually much more pronounced, reaching a lower large strain strength than that for frozen sands. The influence of the ice in samples with low ice contents was primarily noticeable at low strains, whereas the large strain behaviour was very similar to that of the unfrozen material. The tests showed the dependency of the mechanical failure and deformation mode of frozen soils on the loading conditions. It could be demonstrated further that large strains have a significant influence on the strength of frozen geo‐materials and therefore efforts should be made to establish in situ strain states when analysing the stability of frozen slopes. Copyright © 2004 John Wiley & Sons, Ltd.

Discrete fracture in quasi-brittle materials under compressive and tensile stress states

A method for modelling discrete fracture in geomaterials under tensile and compressive stress fields has been developed based on a Mohr–Coulomb failure surface in compression and three independent anisotropic rotating crack models in tension. Extension fracturing is modelled by coupling the softening of the anisotropic rotating crack failure criterion to the compressive plastic strain evolution. Modifications were introduced into an explicit discrete element/finite element code with an explicit Lagrangian contact algorithm to enforce non-penetration of the surfaces created when the tensile strength is depleted. The model is applied to triaxial and plane strain tests, as well as punch tests and borehole breakouts to show that the model is able to quantitatively predict the appropriate load–displacement response of the system in addition to the observed evolution of discrete fracturing in situations comprising a variety of compressive and tensile stress states.

Discrete fracture in quasi-brittle materials under compressive and tensile stress states

A method for modelling discrete fracture in geomaterials under tensile and compressive stress fields has been developed based on a Mohr–Coulomb failure surface in compression and three independent anisotropic rotating crack models in tension. Extension fracturing is modelled by coupling the softening of the anisotropic rotating crack failure criterion to the compressive plastic strain evolution. Modifications were introduced into an explicit discrete element/finite element code with an explicit Lagrangian contact algorithm to enforce non-penetration of the surfaces created when the tensile strength is depleted. The model is applied to triaxial and plane strain tests, as well as punch tests and borehole breakouts to show that the model is able to quantitatively predict the appropriate load–displacement response of the system in addition to the observed evolution of discrete fracturing in situations comprising a variety of compressive and tensile stress states.

Notch Effects on Impact Tensile Properties in A6061-T6 Aluminum Alloy

The strain rate sensitivity of a A6061-T6 aluminum is examined as a function of triaxial stress. The triaxial stress state is changed by changing the notch acuity of notched specimens. Under the high strain rate conditions, increasing triaxiality increases flow stress. Plastic constraint factor decreases in notched specimens under high strain rate conditions. Reduction-of-area in notched specimen increases with increasing strain rate. The relaxation of plastic constraint takes place under high strain rate in the notched specimens. The effects of triaxial stress and strain rate on the fracture surfaces are discussed.

Carboniferous Orogenic Gold Deposits at Pataz, Eastern AndeanCordillera, Peru: Geological and Structural Framework, Paragenesis, Alteration,and 40Ar/39Ar Geochronology

The Pataz province forms the central part of a ≥160-km-long orogenic gold belt extending along the Eastern Andean Cordillera in northern Peru and has produced a total of 6 million ounces (Moz) gold from vein-type deposits during the last 100 yr. The deposits present several recurrent and typical field characteristics, including (1) at a regional scale, location of the mineralization in low-order structures within a 1- to 5-km-wide structural corridor east of a major north-northwest–striking lineament and in spatial association with the northnorthwest– striking margins of the 330 to 327 Ma Pataz batholith; (2) at the mine scale, strong lithological controls of the vein geometries and styles, the lodes occurring as fairly continuous ≤5-km-long quartz veins inside or along the margins of the batholith or as branching and bedding-concordant narrow ore shoots within adjacent folded Ordovician turbidite sequences; (3) consistent orientations of veins, in particular within the batholith, where more than 80 percent of the quartz veins are emplaced in north- to northwest-striking, eastdipping, brittle-ductile deformation zones; (4) a consistent Au, Ag, As, Fe, Pb, Zn, ±Cu, ±Sb, ±Bi-Te-W metal association and a sulfide-rich paragenetic sequence, with a first stage composed of milky quartz, pyrite, arsenopyrite, and ankerite and a second stage of blue-gray microgranular quartz, galena, sphalerite, chalcopyrite, Sb sulfosalts, electrum, and native gold, followed by barren calcite-dolomite-quartz veinlets; and (5) hydrothermal alteration of the vein wall rocks, consisting of pervasive muscovite alteration with minor chlorite, carbonate minerals, and pyrite associated with strong bleaching in plutonic rocks, and of weak muscovite and chlorite alteration in sedimentary rocks. Structural analysis of the deposits outlines four synchronous sets of mineralized fractures in the Pataz district. The predominant north- to northwest-striking, east- to northeast-dipping system, which is generally located in reactivated reverse faults, accounts for more than 80 percent of the gold resource of the district. Three subordinate systems include, in decreasing order of economic importance, (1) east-west–striking flat extensional veins, (2) bedding-concordant veinlets in east-west–striking and north-dipping to north-south–striking and east-dipping limbs of long wavelength folds in Ordovician sedimentary rocks, and (3) weakly mineralized roughly east-west–striking, sinistral vertical faults. The vein orientations of the four structural sets are compatible with a triaxial strain model, with the main shortening axis P oriented at 080°/15°, an intermediate axis oriented at 165°/00°, and a subvertical extensional T axis oriented at 255°/80°. Under these conditions, the richest ore shoots are preferentially sited in sinistral pull-aparts, which occur at the intersection of either north-south–striking lodes or extensional lodes with roughly east-west–striking vertical faults. 40Ar/39Ar dating of the granodiorite-monzogranite bodies of the Pataz batholith provides good plateau ages at 329.2 ±1.4 and 328.1 ± 1.2 Ma for biotite separates, which are similar to a published 329 Ma U/Pb age for the granodiorite. A muscovite and a biotite sample from an aplite dike yielded plateau ages at 322.1 ± 2.8 and 325.4 ± 1.4 Ma, respectively. Muscovite samples from alteration intimately associated with the gold mineralization yielded three 40Ar/39Ar spectra with low-temperature staircase-shaped patterns followed by plateau segments at 314 to 312 Ma. These ages, analytically indistinguishable at the 2σ level, are considered to be the most probable ages for the mineralization event. Three other plateaulike ages between 305 and 288 Ma have been obtained and are interpreted to reflect partial argon loss during late fluid circulation associated with the intrusion of Late Cretaceous monzonite porphyries. The age determinations are inconsistent with a genetic link between the 314 to 312 Ma Pataz gold deposits and the 330 to 327 Ma calc-alkaline Pataz batholith, or with the 327 to 319 Ma aplite dikes, or the Late Cretaceous porphyry magmatism. Instead, the overall homogeneity of the structural, mineralogical, and geochemical characteristics of the deposits over the ≥160-km-long mineralized belt and the geotectonic evolution suggest that gold mineralization is linked to a large-scale thermal event that occurred in a thickened collisional belt undergoing uplift tectonics.

A test of different stress measurement methods in two orthogonal bore holes in Äspö Hard Rock Laboratory (HRL), Sweden

Within the scope of works to provide the necessary rock mechanics support for site investigations for a radioactive waste repository, the Swedish Nuclear Fuel and Waste Management Co (SKB) has studied some of the available equipment for in situ stress measurements in deep boreholes. A project with the objective of comparing three different types of equipment for in situ stress measurement under similar conditions has been carried out. The tests were performed in orthogonal boreholes at the Aspo Hard Rock Laboratory (HRL), Oskarshamn, Sweden. The two most common methods to measure in situ stress are the overcoring and hydraulic fracturing methods. Among the three tests, two are carried out using the overcoring method, the third uses the hydraulic fracturing method. The overcoring equipment's are the AECL's Deep Doorstopper Gauge System (DDGS) and SwedPower's Triaxial Strain Cell (Borre Probe). The measured results could be verified against known conditions at the Aspo HRL. The results from the three in situ stress measurement methods illustrate the complexity of determining the in situ stresses in a rock mass. To understand the difference in results and answer the associated questions, it was necessary to undertake deeper investigations involving laboratory tests and theoretical calculations.

Measurement of in-situ stress in weak rocks at Mont Terri Rock Laboratory, Switzerland

In-situ stress measurements in weak rocks, such as clay shales, that respond strongly to environmental changes are particularly difficult. An extensive in-situ stress measurement program has been conducted at the Mont Terri Rock Laboratory in Northwestern Switzerland. Hydraulic fracturing, Undercoring around a 600-mm-diameter borehole using CSIRO triaxial strain cells and the Borehole Slotter were used to establish the state of stress for the Opalinus Clay at this location. Conflicting orientations and magnitudes resulted from the measurement programs. Three dimensional elastic modelling was used in conjunction with tunnel and borehole observations to establish the most likely stress tensor. A stress measurement program using a borehole deformation gauge is currently underway to check the stress tensor resulting from the observational modelling.

Direct measurement of triaxial strain fields around ferroelectric domains using X-ray microdiffraction

Ferroelectric materials, such as BaTiO(3), have piezoelectric properties that make them attractive for microelectronic and sensing applications. It is well known that the application of mechanical stress or electric field can alter the domain structure in ferroelectrics. Indeed, the constitutive behaviour of a ferroelectric is largely governed by the formation, movement and interaction of its domains. Therefore, it is crucial that the micromechanics of domains and their effect on internal stresses in ferroelectrics be understood. Here we show that the emerging technique of scanning X-ray microdiffraction can be used to measure directly, for the first time, the local triaxial strain fields around 90 degrees domains in single-crystal BaTiO(3). Specifically, residual strain maps in a region surrounding an isolated, approximately 40 microm wide, 90 degrees domain were obtained with 3 microm resolution, revealing significant residual strains. This information is critical for accurate micromechanical modelling of domain behaviour in ferroelectrics.

A multiaxial failure criterion for a brittle orthotropic composite

A multiaxial failure criterion is validated for a brittle orthotropic composite, namely a tridirectional carbon–carbon composite (3D CC). It is aimed at designers of 3D CC structures. The composite is subjected to a triaxial strain state along its reinforcement axes, which is representative of its in-service loading conditions. A multiaxial test rig is designed in order to reproduce this required strain state. Its mock-up dimensions are optimised by combining Taguchi experimental strategy with tridimensional finite element modelling. Comparison of experimental results with numerical modelling shows that failure occurs due to the required strain state; failure is brittle and corresponds to simultaneous breakage of carbon yarns along the three reinforcement axes. Subsequently, the experiment validates a failure criterion, which assumes linear coupling between the three principal strains.

A Laboratory Investigation on the Behaviour of Reinforced Sand Samples Under Plane Strain and Triaxial Conditions

An experimental study on the behaviour of reconstituted samples of sand reinforced with geotextile layers is presented using standard triaxial and plane strain tests. After describing the main features of the plane strain device and of the data acquisition system, details are provided on the procedure developed for preparing plane strain samples containing inclined reinforcements with respect to the principal stress directions. Comments are also made on the influence of the preparation procedure on the overall behaviour observed during loading. Finally, the results of the experimental investigation are described with reference to standard triaxial tests with horizontal reinforcements, and to plane strain tests with horizontal and inclined reinforcements. The study complements data already available in the literature, for the development of constitutive laws applicable to the numerical analysis of reinforced earth structures.

Evaluation of a constitutive model for clays and sands: Part I – sand behaviour

AbstractThis paper evaluates the performance of a generalized effective stress soil model for predicting the rate independent behaviour of freshly deposited sands, while a companion paper describes model capabilities for clays and silts. Most material parameters can be obtained from standard laboratory data, including hydrostatic or one‐dimensional compression, drained and undrained triaxial shear testing. A compilation of data on compression behaviour allows for estimation of compression parameters when this type of data is not available. Extensive comparisons of model predictions with measured data from undrained triaxial shear tests shows that the model gives excellent predictions of the transition from dilative to contractive shear response as the confining pressure and/or the initial formation void ratio increases. A parametric study of drained response shows that the model describes realistically the variation of peak friction angle and dilation rate as a function of confining pressure and density when compared with an empirical correlation valid for many sands. The proposed formulation predicts a unique critical state locus for both drained and undrained triaxial testing which is non‐linear over the entire range of stresses and is in excellent agreement with recent experimental data. Overall, the model provides excellent predictions of the stress–strain–strength relationships over a wide range of confining pressures and formation densities. Copyright © 2002 John Wiley & Sons, Ltd.

Evaluation of a constitutive model for clays and sands: Part II – clay behaviour

AbstractThe undrained response of cohesive soils is of paramount importance in geomechanics and it has been modelled extensively for the last 50 years. In comparison, drained behaviour of clays has received only modest attention. Drained and undrained behaviour is significantly affected by past consolidation stress history. This paper evaluates the capabilities of the MIT‐S1 effective stress model, described in a companion paper, for predicting the anisotropic stress–strain–strength behaviour of clays. The paper illustrates the selection of model parameters for Lower Cromer Till, using data from standard types of laboratory tests. Comparison of model simulations with measured response for Lower Cromer Till and Boston Blue Clay illustrate model capabilities. The work focuses initially on comparisons of model predictions with measurements from undrained triaxial and plane strain tests on initially K0‐consolidated specimens. Comparisons with measured data from undrained shear tests performed in different modes of shearing for LCT and BBC show that the model: (a) gives excellent predictions of maximum shear stress conditions and accurately describes the non‐linear shear stress–strain behaviour; (b) accurately describes the anisotropic shear stress–strain–strength conditions for different consolidation stress histories; and (c) gives realistic description of mobilized friction angles, especially at large OCR's. The paper then focuses on the effects of consolidation stress history for isotropically consolidated specimens of resedimented Lower Cromer Till and Boston Blue Clay. Finally, the paper compares model predictions for drained shear tests on K0 and isotropically consolidated specimens with overconsolidation ratios, OCR⩽10, used to evaluate particular aspects of the critical state framework of soil behaviour. Overall, the model gives excellent predictions of the effect of initial anisotropy and overconsolidation stress history on the shear stress–strain and volumetric behaviour of clays. Copyright © 2002 John Wiley & Sons, Ltd.

Fracture behavior of explosively loaded spherical molded steel shells

Experimental and numerical works are made to study the fracture of explosively loaded spherical molded steel shells. The first series of experiments included three sawdust recovery shots to save fragments for examination. In this series, detonation was initiated from the center of the sphere. Results of the experiments show that two types of fractures are observed in spherical shells: radial and shear as in cylindrical shells. Spall fracture is also observed in spherical shells. To assist understanding of the experimental results, a computer simulation of expanding shells is performed to provide information on the stress, strain, strain rate and position of each element of the shell wall as a function of time after detonation. For t=7.5 μs after detonation, triaxial non-uniform strain prevails in the middle of the thickness of the wall. The peak of the stress equals to 6.5 GPa and exceeds the spall strength of carbon steel. In the second series of experiments, spall fracture is suppressed by displacing the point of detonation initiation from the center to periphery of HE charge.

Contemporary in situ stress determinations at three sites in Scotland and northern England

During 1987, in situ stress measurements using two overcoring techniques (doorstopper and triaxial strain cell) were made in England and Scotland as part of the former SFB 108 Project ‘Stress and Stress Release in the Lithosphere’ at Karlsruhe University. The results for three of the test sites—Spittal in Caithness, Gartur in the Midland Valley of Scotland and at Burton in Cumbria—are reported. Complementary studies on cores from Gartur using portable ASR equipment are included. The maximum horizontal stress orientations agree closely with those seen in the general contemporary stress field in NW Europe. These results confirm that, in favourable circumstances, these shallow methods offer effective approaches to the acquisition of reliable contemporary stress information, whether derived from boreholes or rock cores.

Yielding Behaviour in Strain Controlled Compactions of Metal Powder Assembles.

Metal powder assembles show some volumetric change under irreversible deformation, and their yield function (yield curve) is represented in the space of equivalent deviatoric stress q and hydrostatic pressure p. In the mechanics of metal powder assembles yield curves are assumed to be contours of constant density. However, there is something questionable in this concept. We already examined the consistency of the concept referring to the experimental data of tri-axial compression tests carried out in the past by other investigators, who compressed cylindrical specimens subjected to constant lateral pressure. The results showed that the concept of constant density was inconsistent with the actual constitutive behaviour under the assumption that associated flow rule is applicable and yield curve expands in a similar shape with increasing of compressive deformation. Here, we newly referred to the data obtained from compaction tests by Brown and A-Chedid who collected them using uni- and tri-axial strain control systems. In these compaction tests the direction of stress vector (p, q) do not change largely, and so whole view of yield curve is not obtainable. But the correspondence between directions of stress and strain rate vectors can be determined in the compactions. The comparison of the results with those in compression tests does not show good agreement. That suggests the necessity of inspection on the suitability of constitutive model used in the mechanics of metal powder assembles. Hardening strain rate ey is defined here which is composed of volumetric strain rate ep and equivalent deviatoric one eq accompanying with constant parameter. Finally, it is found that this definition is valid from the view point of inherent characteristic of hardening.