Triaxial Strain Research Articles

The Chinamora batholith, Zimbabwe: structure and emplacement-related magnetic rock fabric

The origin of dome-and-keel structural geometries in Archean granite–greenstone terrains appears to lack any modern analogues and is still poorly understood. The formation of these geometries is investigated using structural and anisotropy of magnetic susceptibility (AMS) data for the Chinamora batholith in Zimbabwe. The roughly circular-shaped batholith is surrounded by ca. 2.72–2.64 Ga greenstones. The batholith granitoid suites have been divided on the basis of their ages and fabric relationships into four distinct units: (i) banded basement gneisses; (ii) granodioritic gneisses; (iii) equigranular granites; and (iv) central porphyritic granites. In the gneissic granites a partial girdle (N–S) of poles to the magnetic foliation is developed that has been folded around a consistent, flat lying magnetic lineation plunging at shallow angles to the E or W. In the equigranular granites, the magnetic lineation generally plunges to the NW. The magnetic foliation has a variable strike, no clear trends can be distinguished. The AMS measurements of the porphyritic granite revealed a NW–SE striking foliation and showed subhorizontal magnetic lineations. The magnetic foliation is subparallel to the macroscopic foliation. Wall rocks are moderately inclined and show radial or concentric lineations, triaxial strain ellipsoids and kinematics that demonstrate off-the-dome sliding and coeval pluton expansion. The results of the observations do not point to a single emplacement process. Neither the observed structural data nor the magnetic fabric support a model envisaging spherically ‘ballooning’. It is argued that pluton diapirism played a major part in the formation of the fabrics in the gneisses, whereas the fabrics in the porphyritic granites reflect emplacement as laccolith-like sheets.

Influence of strain and quantum confinement on the optical properties of InGaAs/GaAs V-groove quantum wires

We report on the impact of quantum confinement and strain effects on the optical properties of state-of-the-art, densely stacked, In0.15Ga0.85As/GaAs V-groove quantum wires. High uniformity and efficient carrier capture lead to narrow (6 meV) and intense emission from the wires. Large optical polarization anisotropy is obtained thanks to the combined effects of lateral quantum confinement and triaxial strain. Band filling in the fundamental subband occurs at a modest carrier density (∼9×105 cm−1), and is accompanied by a small spectral blueshift of the emission. Several sharp excitonic resonances associated with two dimensionally confined subbands of dominant heavy-hole character are observed in photoluminescence excitation spectroscopy, together with a remarkably small Stokes shift (3 meV). The subband separations (∼24 meV) are nearly independent of the wire thickness, as the nonuniform Indium composition across the structure is found to dominate the lateral confinement for thick wires. Such strained quantum wires are promising for the realization of advanced nanostructure devices.

Failure analysis of R/C columns using a triaxial concrete model

Inelastic failure analysis of concrete structures has been one of the central issues in concrete mechanics. Especially, the effect of confinement has been of great importance to capture the transition from brittle to ductile fracture of concrete under triaxial loading scenarios. Moreover, it has been a challenge to implement numerically material descriptions, which are susceptible to loss of stability and localization. In this article, a novel triaxial concrete model is presented, which captures the full spectrum of triaxial stress and strain histories in reinforced concrete structures. Thereby, inelastic dilatation is controlled by a non-associated flow rule to attain realistic predictions of inelastic volume change at various confinement levels. Different features of distributed and localized failure of the concrete model are examined under confined compression, uniaxial tension, pure shear, and simple shear. The performance at the structural level is illustrated with the example of a reinforced concrete column subjected to combined axial and transverse loading.

Full Stress Tensor Determination in A textured Aerospace Aluminium Alloy Plate Using synchrotron X‐Ray Diffraction

Triaxial strain scanning has been performed on a 7mm thick 7150‐aluminium alloy Variable Polarity Plasma Arc (VPPA) weld using synchrotron X‐rays. It has been demonstrated that the use of specific advantageous (hkl) peaks that occur in this highly textured aerospace alloy plate permits fast deep measurements in reflection as well as in transmission. The sin⁡2ψ method was also utilised to monitor the variation in deviatoric stress component (σ11 − σ33) across the weld in both the test‐piece and a comb like reference specimen used to map the changes in stress‐free lattice spacings over the weld. The results suggest that microstresses have little effect on macrostress determination, particularly in the Heat Affected Zones (HAZ). Though small in magnitude, the macrostresses still present in the reference specimen can be allowed for to correct the stress tensor in the plate. Maximum tensile longitudinal stress values remain unchanged, whereas the stress condition in some parts of the HAZ is well described as biaxial after the proposed correction.

Critical state strength parameters of saturated clays from the modified Cam clay model

The evaluation of critical state strength parameters is important, especially with the introduction of limit state design. The modified Cam clay (MCC) model is often used, but it is suitable mainly for evaluating the critical state strength parameters from triaxial compression tests on isotropically consolidated soils. The initial stress condition of a natural soil is usually anisotropic, and the stress paths imposed by external loading could deviate from that of a simple triaxial compression. The use of MCC in practice deserves careful consideration. This paper describes a proposed extension of the MCC model for the evaluation of critical state strength parameters from undrained triaxial and plane strain tests on anisotropically consolidated clays. Using Lade's failure criterion and the plastic potential of MCC, a generalized yield surface is determined and the relationships between the critical state internal friction angles from various triaxial and plane strain tests are obtained. By relating the isotropic overconsolidation ratio to the conventional overconsolidation ratio (OCR), a procedure is suggested for the prediction of critical state undrained shear strength (su) for clays. The undrained strength normalized by the preconsolidation pressure is not a constant but a function of the angle of internal friction and the OCR. For overconsolidated clay, the predicted undrained strength ratio (su/σVO) for the triaxial compression condition is larger than that for the plane strain compression condition. Comparisons of predicted results with published data indicate that the procedure is applicable to various compression tests on normally and lightly to moderately overconsolidated clays. Key words: stress anisotropy, clay, constitutive model, critical state, laboratory test, shear strength parameters.

A general approach for predicting the drawing fracture load and limit drawing ratio of an axisymmetric drawing process

Based on Hill’s theory of plasticity and the Swift diffuse instability criterion, new theoretical models are proposed for predicting the drawing fracture load and limit drawing ratio (LDR) of an axisymmetric cup drawing. These models take into account the influence of triaxial stress state, anisotropy, strain hardening, bending, and tool geometry. By introducing both conventional and modified Hollomon’s equations, the influences of these variables on the constitutive relation of sheet steels are also analyzed. It is shown that the theoretical predictions of the drawing fracture load are in good agreement with experimental results for a wide range of sheet steels currently used in the automotive industry. Specific tool geometries are found to decrease the drawing fracture load and the LDR, because of increased triaxial stress states and bending effects at the critical section of the workpiece. The optimum punch-profile radius is found to be between 5.0 and 7.0 times the thickness of the sheet. Additionally, the role of both the anisotropy and strain-hardening properties of the sheet steels in determining the drawing fracture load and the LDR are, subsequently, discussed.

Anisotropy of Undrained Shear Strength of an Over-Consolidated Soil by Triaxial and Plane Strain Tests

In order to find out the real cause leading to the anisotropy of undrained shear strength of clayey soils, two types of undrained shear tests were carried out; 1) undrained plane strain tests on lightly over-consolidated kaolin clay, and 2) undrained triaxial tests on heavily over-consolidated kaolin clay. Analysis of the data has shown that the anisotropy of undrained shear strength of over-consolidated kaolin clay is primarily caused by the direction-dependent (anisotropic) shear strength parameters c' and ϕ' in terms of effective stresses. The anisotropy of pore water pressure parameter Ay is artificially generated as a result of the anisotropic change of the undrained shear strength itself, rather than of the anisotropic excess pore-pressure development during shearing, and is of secondary, if any, importance to interpret why the undrained shear strength is anisotropic. Intensity of the anisotropy in the undrained shear strength is not altered much by either changing the boundary conditions, such as triaxial and plane strain or increasing the over-consolidation ratio up to 32. The minimum values of cohesion c' and friction angle ϕ' appear when a specimen is compressed with the major principal stress inclined at about 30° to the consolidation plane. When a specimen is compressed either normal or parallel to the consolidation plane, values of cohesion c' and friction angle ϕ' are high with no significant difference between them. The difference between the maximum and the minimum friction angle ϕ' is almost the same as that observed in the triaxial tests of sands. In the case of sands, however, a specimen compressed normal to the bedding plane yields the maximum friction angle ϕ', while a specimen compressed parallel to the bedding plane yields the minimum value in the triaxial tests and a value close to the minimum in the plane strain tests. These observations suggest that the micro-deformation mechanism leading to the strength anisotropy is quite similar in both clay and sand, but not exactly the same.

Measurement of Local Strain in Thin Aluminium Interconnects Using Convergent Beam Electron Diffraction (CBED)

AbstractEnergy filtered convergent beam electron diffraction (CBED) was used to investigate localized strain in aluminium interconnects. An analysis of the higher order Laue zone (HOLZ) line positions in CBED patterns makes it possible to measure the lattice strain with high accuracy (∼10−4) and high spatial resolution (10 to 100 nm). The strain development in a single grain was measured during thermal cycling between −170°C and + 100°C. The grain showed reversible, elastic behaviour over the whole temperature range building up large strains at low temperatures. By comparing with finite element simulations, a detailed understanding of the tri-axial strain state could be achieved.

Measuring the Triaxial Load-Deformation Response of Orthotropic Materials Subjected to Large and Small Strain Regimes

Abstract A new method for obtaining triaxial stress versus strain data is presented. The method tests cubic specimens and can provide constitutive data along three mutually perpendicular axes. Issues of removing the effects of boundary conditions in the proposed device are discussed. Two devices were constructed and used to obtain triaxial stress versus strain data on paperboard and on redwood samples. Representative data are shown.

Polarization anisotropy and Zeeman splitting in strained quantum wires: Dimensional crossover effect on strain

Strain states in lattice-mismatched quantum wires have been studied by polarization analysis with a high magnetic field. Although biaxial strain should suppress quantum-confinement-induced in-plane linear polarization, large polarization is observed. This polarization remains even at a very high magnetic field, which shows that polarization is caused by non-biaxial ( anisotropic triaxial) strain states in which the symmetry of the strain is broken. Circular polarization experiments show that Zeeman splitting is highly nonlinear to the field, which is also explained by the non-biaxial nature. These results can be understood as dimensional crossover on strain.

Polarization and Broken Symmetry due to Anisotropic “Triaxial” Strain States in Lattice-Mismatched Quantum Wires

Strain states in buried lattice-mismatched quantum wires are studied by polarization analysis with high magnetic fields. Remarkably large in-plane polarization anisotropy is observed, which remains even in very high fields. These results cannot be explained by the isotropic biaxial strain picture, and theoretical calculations show that it is attributed to nonbiaxial (anisotropic triaxial) strain, the symmetry of which is broken. Circular polarization experiments show that Zeeman splitting is highly nonlinear to the field, which is also theoretically explained by the nonbiaxial nature of strain.

Effect of Self Stress on Flexural Strength of Gypsum-Polymer Composites

Self stress generated in polymer impregnated gypsum (referred as GPC) when it is composed is estimated, and its influence on flexural strength is discussed. The estimation of the self stress is based on measured values of shrinkage caused by polymerization of impregnated monomer and elastic modulus of dried gypsum base just before impregnation. The effect of this self stress on flexural strength of GPC is investigated. It was found that the following equation is valid to predict flexural strength of GPC (б b ) in terms of the self stress as a variable: б b = б gb + V p (б p − б sp ), where б gb = flexural strength of gypsum base, V p = specific volume of polymer, б p = tensile strength of polymer, and б sp = self stress generated in polymer phase. If extremely low water-gypsum ratio is adopted to prepare gypsum base, cracking is observed just after polymerization preceding any flexural loading. For somewhat higher water-gypsum ratio, specimens are not cracked, but their flexural strength is decreased after polymer impregnation. The self stress corresponding to this case turns out to be higher than the tensile strength of polymethyl methacryrate used for the impregnation. Since prediction of б sp in the equation is based on tri-axial compressive strain of gypsum base that is within its elastic region, б sp in polymer phase should positively exist. Even for this condition, the validity of the equation seems to be maintained, although the value in the parenthesis of the equation becomes negative. Based on this fact, an unstable physical state where one phase of a composite material is stressed beyond its macroscopic strength as an individual material owing to the crack arresting effect of the other phase (gypsum in this case) has been postulated. This state is designated as a “superstressed” state, taking its resemblance with supercooling or supersaturation into consideration.

Biaxial Yield for Nonlinearly Viscoelastic Materials with a Strain Clock

A constitutive equation with a dilatation dependent reduced time is used to model the mechanical response of solid amorphous polymers such as polycarbonate. Such constitutive equa- tions have the property that stress relaxation occurs faster with increasing dilatation. In previous work, it has been shown that this constitutive equation can account for yield in materials undergoing uniaxial strain or stress control histories. In the present work, yield is discussed when materials described by this constitutive equation undergo homogeneous biaxial and triaxial strain histories. Four sets of conditions are considered: in-plane biaxial constant strain rate histories and in-plane biaxial constant stress rate histories, for both plane stress and plane strain states. Yield is defined in a manner analogous to that in the corresponding strain and stress control conditions in the uniaxial case.

Interlamellar Residual Stresses in Single Grains of NiO–ZrO2(cubic) Directionally Solidified Eutectics

Phase‐to‐phase residual stresses due to thermal expansion mismatch were measured in lamellar NiO‐ZrO2(cubic) directionally solidified eutectics (DSEs). The triaxial strain tensors for both phases were measured using single‐crystal X‐ray diffractometry techniques on isolated grains of the DSE. From the strain tensors, the stress tensors were calculated, taking into account the full elastic anisotropy of the phases. The resulting stress tensors indicated that very large compressive stresses accumulated in ZrO2 whereas large tensile stresses were amassed in NiO parallel to the lamellae during the solidification process. The large magnitudes of the stresses indicated that the interfaces between the lamellae were very well bonded and did not facilitate slip or other stress‐relieving processes.

Constitutive Model for 3D Cyclic Analysis of Concrete Structures

A three-dimensional (3D) concrete material model for nonlinear finite-element analysis of concrete solids under short-term cyclic loading is presented. The proposed model is a hypoplastic orthotropic model based on a stress-equivalent uniaxial strain relation that is generalized to take into account triaxial stress conditions. The directions of orthotropy are assumed to coincide with the current principal stress directions according to the rotating smeared-crack approach. The model includes the effect of triaxial nonlinear stress-strain behavior, tensile cracking, compression crushing, and strain softening. The proposed model is compared in detail with selected test data of concrete behavior under 3D cyclic stress loading. These correlation studies demonstrate the ability of the model to represent the observed experimental behavior.

Angles of friction and dilatancy of sand : T. Schanz & P. A. Vermeer, Geotechnique, 46(1), 1996, pp 145–151

. It is generally realized that the peakfriction angel depends not only on density but alsoon the stress path, including differences betweenplane strain and triaxial testing conditions. Indeed,plane strain and triaxial strain angles can differ bymore than 58 for a dense sand. For a loose sand atthe critical density it is often suggested that similardifferences occur (e.g. Stroud, 1971; Lade, 1984).However, some authors have presented data thatsuggest a unique critical state angle (e.g. Rowe,1962, 1971; Bolton, 1986).This technical note presents data on a uniquecritical state angle. The implication is that thefailure criterion of a very loose sand is accuratelydescribed by the Mohr–Coulomb condition, whichgives the known six-sided pyramid in principalstress space.The test data on dense as well as loose Hostunsand are also used to study the rate of dilation.This topic was extensively treated by Bolton(1986), and it is now generally accepted that thetriaxial rate of dilation coincides with the rate ofdilation found in plane strain tests. FollowingRoscoe (1970), Bolton used an angle of dilatancyl

Strain effect on the critical temperatures of superconducting Nb 3Ge tapes

The resistively measured critical temperature, T c, was found to increase by 0.4–0.6 K due to an applied strain of about 0.5% for chemical-vapour-deposited Nb 3Ge tapes that had different Nb 3Ge layer thicknesses and different Nb Ge composition ratios. The T cs have also been measured using a magnetization method for these tapes and the Nb 3Ge films made by removing the 0.1-mm thick Hastelloy substrates from the Nb 3Ge tapes. The triaxial strain analysis that includes measurements of lattice spacing showed that both the hydrostatic and the non-hydrostatic strain components may considerably contribute to the T c strain effect in the present Nb 3Ge tapes.

Importance of anisotropy when estimating and measuring in situ stresses in rock

Foliated metamorphic rocks and laminated, stratified or bedded sedimentary rocks have properties (physical, dynamic, thermal, mechanical, hydraulic) that vary with direction and are said to be anisotropic. Rock mass anisotropy can be found in volcanic formations and sedimentary formations consisting of alternating layers or beds of different rock types. Rock masses cut by one or several regularly spaced joint sets are anisotropic in addition to being discontinuous. This paper deals with the subjects of rock anisotropy and rock stress. Both topics are important in rock engineering and are interrelated. Rock fabric controls the build-up in in situ stresses in the Earth's crust, their magnitude and orientation. On the other hand, stresses and in particular compressive stresses tend to close microcracks or discontinuities thus making rock behavior non-linear and rock anisotropy pressure dependent. This paper is divided into three parts. In the first part, existing models to describe the deformability properties of anisotropic rocks as well as the laboratory and field methods to determine those properties are reviewd. Then, it is shown how to account for both rock anisotropy (intact and joint induced) and the curvature of the Earth when estimating in situ stresses in rock masses. Finally, the effect of anisotropy on the analysis of overcoring measurements with cells similar to the CSIR Triaxial Strain Cell is discussed.

Angles of friction and dilatancy of sand

. It is generally realized that the peakfriction angel depends not only on density but alsoon the stress path, including differences betweenplane strain and triaxial testing conditions. Indeed,plane strain and triaxial strain angles can differ bymore than 58 for a dense sand. For a loose sand atthe critical density it is often suggested that similardifferences occur (e.g. Stroud, 1971; Lade, 1984).However, some authors have presented data thatsuggest a unique critical state angle (e.g. Rowe,1962, 1971; Bolton, 1986).This technical note presents data on a uniquecritical state angle. The implication is that thefailure criterion of a very loose sand is accuratelydescribed by the Mohr–Coulomb condition, whichgives the known six-sided pyramid in principalstress space.The test data on dense as well as loose Hostunsand are also used to study the rate of dilation.This topic was extensively treated by Bolton(1986), and it is now generally accepted that thetriaxial rate of dilation coincides with the rate ofdilation found in plane strain tests. FollowingRoscoe (1970), Bolton used an angle of dilatancyl

The determination of the profile of macrostress and thermal mismatch stress through an Al/SiC p composite plate from the average residual strains measured in each phase

Neutron diffraction has been used to measure uniquely the through-thickness profile of the average triaxial strain in each phase of an Al/SiC p metal-matrix composite plate which had been quenched after a solution treatment at 505°C. The data have been interpreted by modelling the measured strains in terms of three contributions: a long-range residual macrostrain field; an elastic mismatch strain; and a thermal mismatch strain. These strains and the associated stresses are described and discussed.