Shear Strain Relationship Research Articles

A modified split Hopkinson torsional bar system for correlated study of τ – γ relations, shear localization and microstructural evolution

The conventional split Hopkinson torsional bar (SHTB) system consists of two bars, which can successfully produce the data for the construction of dynamic torsional shear stress and strain relationships. However, the system cannot provide reliable information on the progression of the deformed micro-structure during the test. The reverberation of waves in the bars and the tested specimen can spoil the microstructural pattern formed during the effective loading. This paper briefly reviews a modified version of the SHTB system consisting of four bars that has been developed. This modified system can eliminate the reverberation of waves in the specimen and provide only a single rectangular torsional stress pulse, thus it can properly freeze the microstructure formed during the effective period of loading in the specimen. By using the advantage of the modified SHTB system, together with a new design of specimen, it is possible to perform a correlated study of the dynamic stress-strain response, shear localization and the evolution of the microstructure at a fixed view-field (position) on a given specimen during the sequence of the loading time. The principles, experimental set-up and procedure, calibration and some preliminary results of the correlated study are reported in this paper.

Non-linear response of the rockfill in a concrete-faced rockfill dam under seismic excitation

This study investigates the non-linear response of the rockfill in a concrete-faced rockfill dam under seismic excitation for various concrete slab thicknesses from 30 to 100 cm thick. The effect of the friction in the concrete slab rockfill interface on the non-linear response of the rockfill is also considered in the numerical solutions. The friction contact in the concrete slab joints is provided with contact elements based on the Coulomb’s friction law. The hydrodynamic pressure of the reservoir water is considered by the fluid finite elements based on the Lagrangian approach. Geometrical and material non-linear behaviours of the dam-foundation-reservoir interaction system are considered together in the finite element analyses. The Drucker–Prager model is used to obtain materially non-linear behaviour of the concrete slab. The multi linear kinematic hardening model is used for rockfill and foundation rock in the material non-linear analyses. Therefore, the uniaxial stress–strain relations of the rockfill and foundation rock are determined from the shear stress–shear strain relations of the gravel and rock, respectively. The principle compressive and tensile stresses of the rockfill are investigated along the horizontal section of the rockfill. According to numerical analyses, the most critical stresses occur in the upstream and downstream faces of the dam for the concrete slab thickness of 30 cm, while the optimum thickness for seismic performance is 58 cm.

Non-linear earthquake response of CFR DAM–reservoir–foundation systems

The aim of this article is to clearly show linear and non-linear earthquake behaviour of a concrete-faced rockfill (CFR) dam. For this purpose, a typical CFR dam model is considered with its reservoir water. Reservoir water is modelled by using fluid finite elements based on the Lagrangian approach. Free-field surface motions recorded during earthquakes are deconvolved to the base of the foundation from the soil layers for earthquake analysis. Geometrically and materially non-linear behaviours of the dam are considered in the finite element analysis. The Drucker–Prager model is used for concrete slab, and the multi-linear kinematic hardening model is used for rockfill and foundation rock in the materially non-linear analysis. Non-linear behaviour of the rockfill is obtained by the uniaxial stress–strain relation. Stress–strain curve of the rockfill is obtained using the shear modulus–shear strain relation produced for the gravels. Various joints in the CFR dam are modelled considering welded and friction contacts. In this study, one-dimensional surface-to-surface contact–target element pair based on the Coulomb's friction law provides friction. According to this study, maximum displacements appear when the friction is considered in the joints. In addition, hydrodynamic pressure increases the horizontal displacements of the dam. The horizontal displacements also increase by the effect of the non-linear behaviour of the rockfill and concrete slab.

Polycrystalline Model Predictions of Flow Stress and Textural Hardening during Monotonic Deformation

A series of mechanical tests in different specimen orientations was performed to study the anisotropic behavior of an IF steel (DC06). State-of-the-art polycrystalline models Alamel [1], VPSC [2], as well as the classical FC Taylor model were employed to predict flow stress curves. A two-stage Voce law was used to describe the single crystal shear stress-accumulated shear strain relationship. In this approach, the textural hardening and the dislocation hardening are effectively modeled separately. Results demonstrate that both the Alamel and VPSC models could reproduce the flow stress curves adequately. Also, the quantitative agreement of texture prediction is used to validate the model predictions. It is concluded that the better performance of grain interaction models compared to the FC Taylor model is mainly due to an improved prediction of the slip inside the constituting grains, and not in particular due to an improved prediction of texture evolution.

Development and analytical verification of an inelastic reinforced concrete joint model

Previous experimental research indicated that beam-to-column connections of reinforced concrete (RC) moment resisting frame structures experience considerable deformations under earthquake loading and these deformations have a major contribution to the story drift of the building. In current analysis and design applications, however, the connection regions are generally modeled as rigid zones and the inelastic behavior of the joint is not considered. This assumption gives rise to an underestimation of the story drifts and hence to an improper assessment of the seismic performance of the structure. In order to implement the effect of shear distortions observed in these regions into the seismic design and analysis of buildings, a model that represents their inelastic behavior needs to be developed. In this study, a parametric model that predicts the joint shear strength versus strain relationship is developed by investigating several previous experimental studies on RC beam-to-column connection subassemblies subjected to cyclic loading and establishing an extensive database. Based on this experimental database, parameters that significantly influence the joint behavior are determined by employing statistical correlation method and these key parameters are assembled to form a joint model. This model is then verified by comparing the results obtained from the dynamic earthquake analysis carried out by using Perform 3D with the experimental ones. Based on the verification results, it is observed that the analysis including the developed joint model improves the prediction of the seismic behavior.

Post-cyclic settlement and tilting potential of mat foundations

A simplified procedure for the estimation of cyclic shear stresses on foundation soil layers due to interactions of seismic excitation, foundation mat and overlying structural system, incorporating both kinematic and inertial aspects was described earlier in Cetin et al. [1,2]. This simplified procedure is now used, along with laboratory-based cyclic shear and volumetric strain relationships for the assessment of cyclically induced settlement and tilting potential of mat foundations. The proposed methodology is calibrated by well-documented seismic foundation performance case histories of 3–6 story, relatively rigid residential structures with no basements. Immediately after 1999 Kocaeli and Duzce, Turkey earthquakes, foundation settlements of these case history buildings were carefully mapped relative to available elevation benchmarks, such as relatively rigid concrete pavements, drainage pipes and ditches, and entrance stairs, located in the immediate vicinity of the buildings. Tilt angles of these buildings were also mapped in orthogonal multi-directions. Relative settlement and tilt angle values vary in the range of 0–60cm and 0–5.5rad, respectively. As part of subsurface characterization studies, SPT and seismic CPTU were performed. For the retrieved disturbed and undisturbed samples, an intensive laboratory testing program including sieve analysis, Atterberg Limit, hydrometer, oedometer, static and cyclic triaxial and cyclic simple shear tests was executed. The foundation soil profiles generally consist of silty soils, sand–silt mixtures and silt–clay mixtures of SPT-N values varying in the range of 2–5 blows/30cm in the upper 5m and gradually increases up to a maximum value of 25 blows/30cm beyond depths of 5–8m. As part of the proposed framework, displacement potential indices, defined as the product of induced-cyclic strains and the thickness of soil sub-layers, were estimated, the sum of which produce settlement and tilting potentials. Then, these settlement and tilting potentials were calibrated against recorded settlement and tilt values through a statistically based calibration scheme. The proposed simplified procedure is shown to reliably and precisely capture both deviatoric and volumetric components of post-cyclic settlements, as well as tilting responses of mat foundations.

Effects of initial deviatoric stress ratios on dynamic shear modulus and damping ratio of undisturbed loess in China

The foundation soil masses are always in complex initial stress states. However, the traditional study did not take account of the effects of complex initial stress state parameters on the dynamic characteristic parameters of structural loess. This study investigated the influences of initial deviatoric stress ratios, one of the complex initial stress state parameters, on dynamic shear modulus and damping ratio of undisturbed loess in China through laboratory testing. The results show that the effects of initial deviatoric stress ratios on the dynamic shear stress and strain relations are significant. In addition, the dynamic shear modulus and damping ratio are also influenced by the initial deviatoric stress ratios. The capacities of resisting shear deformations of undisturbed loess under high initial deviatoric stress ratios are weak, while the capacities of consuming dynamic energies are strong. The anti-seismic design and dynamic response analysis of practical engineering projects should take into consideration the effects of initial deviatoric stress ratios.

SHEAR BEHAVIOR OF REDUCED-WEIGHT REINFORCED CONCRETE BEAMS

This paper presents an investigation to improve the understanding of the shear behavior of reinforced reduced-weight concrete beams made of light-weight expanded clay aggregate (LECA) as a partial replacement (by volume) to the normal-weight aggregates. Eleven reinforced concrete beams divided into two groups were fabricated and tested using the symmetrical two-point loads test. The tested beams consisted of seven reinforced reduced-weight concrete beams and four reinforced normal-weight control beams. The effects of several variables such as type of concrete according to its weight, shear span to depth ratio (a/d), concrete grade and the amount of stirrups were experimentally investigated. The behavior of the tested beams was analyzed in terms of mode of failure, load-deflection response, load-strains response, shear stress- shear strain relationships, first shear cracking loads, ultimate carrying capacity, stiffness and ductility. Furthermore, the test results were compared with the predictions using the Egyptian Code for Concrete Structures, (ECP 203). Despite the experimental results illustrated that the reduced-concrete beams were shown less load carrying capacity, stiffness and ductility than those of the comparative normal-weight concrete beams, the theoretical predictions using the Egyptian Code were quite conservative. This could be attributed to that the effect of arch action is still underestimated in the Egyptian Code.

Mechanical properties of stapedial annular ligament

Stapedial annular ligament (SAL) provides a sealed but mobile boundary between the stapes footplate and oval window bony wall. Mechanical properties of the SAL affect the transmission of ossicular movement into the cochlea in sound conduction. However, the mechanical properties of this tissue have never been investigated due to its complexity. In this paper, we report measurement of the viscoelastic properties of SAL on human cadaver temporal bones using a micro-material testing system with digital image correlation analysis. The measured load–deformation relations of SAL samples were converted into shear stress–shear strain relationship, stress relaxation function, and ultimate shear stress and shear strain of the SAL. The hyperelastic Ogden model was used to describe constitutive behavior of the SAL and a 3D finite element model of the experimental setup with SAL was created for assessing the effects of loading variation and measurement errors on results. The study demonstrates that the human SAL is a typical viscoelastic material with hysteresis, nonlinear stress–strain relationship and stress relaxation function. The shear modulus changes from 3.6 to 220 kPa when the shear stress increases from 2 to 140 kPa. These results provide useful information on quasi-static behavior of the SAL.

A stabilized mixed finite element method for the incompressible shear-rate dependent non-Newtonian fluids: Variational Multiscale framework and consistent linearization

This paper presents a stabilized mixed finite element method for shear-rate dependent incompressible fluids. The viscosity of the fluid is considered a function of the second invariant of the rate-of-deformation tensor, thus making the shear-stress shear-strain relation nonlinear. The weak form of the generalized Navier–Stokes equations is cast in the Variational Multiscale (VMS) framework that leads to a two-level description of the problem. Consistent linearization of the fine-scale problem with respect to the fine-scale velocity field and the use of bubble functions to expand the fine-scale trial and test functions lead to an analytical expression for the fine-scale velocity along with a definition of the stabilization tensor τ . The ensuing nonlinear stabilized form is presented and the consistent tangent tensor is derived. Numerical convergence of the proposed method on structured and unstructured meshes that are composed of linear triangles and bilinear quadrilaterals are presented. Shear-thinning and shear-thickening effects are investigated via the backward facing step problem and the effects of geometric parameters on the flow characteristics are highlighted. Time dependent features are investigated via the transient vortex-shedding problem and the accuracy and stability properties of the new method are shown.

Modeling and analysis of reclamation process

The process of reclamation consists of laying a geotextile and spreading granular fill over it in several lifts, each lift being densified before the next one is spread. Self-weight of the granular fill increases with increasing height of each lift causing the ground to settle, with the fill placed during the previous lifts acting as a shear layer. The clay, granular fill and the reinforcement layers are modeled by non-linear Winkler springs, Pasternak shear layer of increasing stiffness and rough membrane respectively incorporating hyperbolic (Kondner, 1963) responses for stress - displacement relation of soft clay and shear stress - shear strain relation for the granular fill. As the reclamation process entails large settlements, finite deformation theory is used in the present work. The steps involved in modeling of the reclamation process are described herein.

Development of nano-composite lead-free electronic solders

Inert, hybrid inorganic/organic, nano-structured chemicals can be incorporated into low melting metallic materials, such as lead-free electronic solders, to achieve desired levels of service performance. The nano-structured materials technology of polyhedral oligomeric silsesquioxanes (POSS), with appropriate organic groups, can produce suitable means to promote bonding between nano-reinforcements and the metallic matrix. The microstructures of lead-free solder reinforced with surface-active POSS tri-silanols were evaluated using scanning electron microscopy (SEM). Wettability of POSS-containing lead-free solders to copper substrate was also examined. Steady-state deformation of solder joints made of eutectic Sn-Ag solder containing varying weight fractions of POSS of different chemical moieties were evaluated at different temperatures (25°C, 100°C, and 150°C) using a rheometric solids analyzer (RSA-III). Mechanical properties such as shear stress versus simple shear-strain relationships, peak shear stress as a function of rate of simple shear strain, and testing temperature for such nano-composite solders are reported. The service reliability of joints made with these newly formulated nano-composite solders was evaluated using a realistic thermomechanical fatigue (TMF) test profile. Evolution of microstructures and residual mechanical property after different extents of TMF cycles were evaluated and compared with joints made of standard, unreinforced eutectic Sn-Ag solder.

Effects of stress paths on the small-strain stiffness of completely decomposed granite

Research on the small-strain (0.001%–1%) characteristics of sedimentary soils and sands has advanced to the stage where it has been utilized in engineering analysis and design for some time. Despite the progress, the stiffness characteristics of weathered materials such as completely decomposed granite (CDG) at small strains have still attracted relatively little research attention. This paper describes a systematic laboratory investigation of the small-strain characteristics of intact CDG subjected to various triaxial stress paths, including drained compression and extension tests. The small-strain stiffness was measured using bender elements and internal local transducers. Measurements from bender elements illustrate that the elastic shear modulus of CDG increases as the mean effective stress increases and the void ratio decreases. Significant nonlinear shear stiffness – shear strain and bulk modulus – volumetric strain relationships were observed. At 0.01% shear strain, the measured average shear stiffness obtained from the extension tests was about 60% higher than that from the compression tests. The average shear stiffness for the tests with a 90° rotation of the stress path was about 50%–70% higher than that of tests without a change in the direction of the stress path after saturation.Key words: completely decomposed granite, nonlinearity, small strains, extension, compression, recent stress history.

A Modelling Procedure for Shear Yielding Characteristics Affected by Viscous Properties of Sand in Triaxial Compression

A series of triaxial compression (TC) tests were performed on Toyoura sand to evaluate the viscous effects on the stress-strain behaviour following the shear yielding mechanism. It is shown that very different shear stress and shear strain relations obtained from TC tests performed along different stress paths become rather unique when converted into relationships between the stress parameter Xst = (q/pa)/(p ' /pa)βsf, which is deemed to control the shear yield mechanism, and the normalized irreversible shear strain energy κs , which is the stress path-independent strain hardening parameter for shear yielding. Along each inviscid yield locus quantified based on the test results, with an increase in the effective mean principal stress p', the deviator stress q increases at a relatively large rate while the stress ratio q/p' decreases at a relatively small rate. According to the non-linear three-component model described in the paper, the stress parameter Xst is decomposed into the inviscid and viscous components, Xsf and Xsv. The inviscid shear yield loci are described in terms of Xsf and develop with an increase in Ks. The viscosity function gvκ̇s is introduced to relate Xsv to Xsf in the form of Xsv=Xsf⋅gvκ̇s based on the test results. It is shown that the viscous effects on the Xst − κs-Ks relations obtained from the TC tests performed along a wide variety of stress path could be simulated rather well by the model taking into account the decay of the viscous component Xsv with an increase in κs.

Study on ASTM Shear-loaded Adhesive Lap Joints

Finite element analyses and experiments are conducted to analyze the mechanical behavior of ASTM shear-loaded adhesive lap joints. Adhesive is characterized for the stress-strain relation by comparing the apparent shear-strain relations obtained from finite element analysis and experiments following ASTM D 5656 Standard. With the established stress-strain relation, two failure criteria using equivalent plastic strain and J-integral are adopted to predict the failure loads for joint specimens following ASTM D 5656 and ASTM D 3165 Standard, respectively. Good correlation is found between the finite element results and the experimental results. The strength of ASTM D 3165 specimens with debonding defects is also studied. Calculation results shows that experiment data following the standards provide only relative material constants, such as apparent shear modulus and strengths. Further investigation is required to find out the engineering properties needed for actual joint design. For the specimens with debonding defects, the locations of defects have great effects on their load bearing ability.

Creep instability of the weak layer and natural slab avalanche triggerings

The weak layer connecting the snow slab with the older snow substrate is modelled as an open cell ice foam made of an array of ice bonds. The bond rupture and rewelding rates under load are derived using simple analytical equations. We show that the weak layer experiences stable flow for a wide range of loads, bond brittleness and bond rewelding rates. However, a critical point may be reached, corresponding to a finite shear rate of the weak layer, beyond which the shear rate increases catastrophically, leading to a natural avalanche release. This critical situation is equivalent to a ductile to britte transition, whose activation energy is one-half of that of diffusion in ice. A measurement of the exponent in the shear strain vs. stress relation may give a hint on the imminence of the avalanche release. A similar calculation performed at the tip of a pre-existing basal crack gives a simple criterion for crack stability and an analytical expression for snow fracture toughness.

Shear induced collapse settlement of arid soils

This paper presents the results of studies of deformation, strength and collapsibility of loess soils. Samples were taken from Al Dalam in central Saudi Arabia, which resembles an arid region. These samples were subjected to various laboratory tests to determine their physical and engineering properties. Sets of oedometer and direct shear tests were carried out in which the initial dry density and the normal pressure at wetting and shearing were each varied in turn. Oedometer results indicate that collapse potential decreases with density and increases logarithmically with normal pressure. Shear induces further collapse potential which increase with density due to further destruction of soil fabric. A unique shear stress–shear strain relationship was obtained for specimens prepared at different initial fabrics. Dry and soaked failure envelopes were both non-linear in the low-pressure range. Wetting induced a reduction in the shear strength parameters. The results of the tests are reported, and the significance of each variable is assessed.

Shear modulus and damping ratio characteristics of gravelly deposits

In this paper, the results of an experimental investigation of dynamic characteristics of gravelly cobble deposits, such as shear modulus (G) and damping ratio (D), are presented. The gravelly cobble deposits are very common in the Taichung metropolitan area of Taiwan where there is an urgent need to determine G and D for dynamic analysis and design of structures. The test program includes measurements of shear wave velocity by the downhole method and large-scale dynamic triaxial tests and resonant-column tests. Special consideration is given to preparing samples of gravelly cobble deposits for laboratory tests. The "equal-weight replacement method" to scale down the real gravelly deposits to cell diameters is used for the preparation of samples. This method is found to be satisfactory, as consistent and reasonable results are obtained. The results of the present study show that the shear modulus - shear strain (G-γ) relationship for this gravelly deposit does not follow exactly those reported in the literature. The deviation of this G-γ relationship from those reported in the literature is investigated and explained.Key words: shear modulus, damping ratio, downhole, shear wave velocity, gravel.

Free vibration of a laminated composite shell of revolution: Effects of shear non-linearity

Effects of shear non-linearity on free vibration of a laminated composite shell of revolution are investigated using a semi-analytical method based on the Reissner–Mindlin shell theory. The coupling between symmetric and anti-symmetric vibration modes of the shell is considered in the shear deformable shell element employed in this study. The Hahn–Tsai non-linearly elastic shear stress–shear strain relation is adopted. Numerical examples are given for laminated composite circular cylindrical and conical shells with various boundary conditions. The numerical results indicate that shear non-linearity may reduce significantly the fundamental frequencies of cross-ply composite shells of revolution.

ON THE CHARACTERISTICS OF NON-LINEAR SOIL RESPONSE AND DYNAMIC SOIL PROPERTIES USING VERTICAL ARRAY DATA IN JAPAN

Non-linear response of the soil is investigated by comparing the spectral ratios (uphole/downhole) using weak and strong motions. Data from seven vertical arrays in Japan are analysed in this study. The frequency-dependent transfer function of soil is calculated as a ratio of the spectrum at uphole to the spectrum at downhole, considering the horizontal component of shear wave. In spectral ratio analysis auto- and cross-spectra are employed. The reduction in the predominant frequency of the transfer function with increases in excitation level reflects the non-linear response of the soil. Results of analysis demonstrate a significant non-linear ground response at six sites with surface PGA exceeding 90 gal. However, the results of one site show the linear response up to 130 gal surface PGA. Furthermore, the in situ strain-dependent soil behaviour is examined through the shear modulus - shear strain relationship. When compared, the actual and laboratory results of the shear strain - shear modulus relationship are in agreement. Additionally, a good consistency between the tendency of reduction in shear modulus ratio with shear strain increases, and reduction of predominant frequency with ground motion increases, confirms the significance of non-linearity in site effects study.