Shear Stress-strain Relationship Research Articles

Measurement of meso-scale shear deformations for modelling textile composites

Textile preforms undergo complex in-plane and out-of-plane deformations during forming processes. In-plane shear is the most significant mode of deformation during draping or forming around double-curvature surfaces. This paper reports an improved method for measuring the constitutive shear properties of textile preforms—a wide strip bias extension test has been found to give significantly better results in comparison to conventional narrow strip bias test. Shear angles, computed directly from global strains, were in close agreement to those measured using an optical method. Constitutive shear stress–strain relation, computed from the bias extension test data, was in good agreement with KES (Kawabata Evaluation System) test results. Meso-scale tow deformations have been measured using two techniques: an inexpensive flatbed scanner-based full-field strain measurement technique for measuring in-plane tow deformations and a strain-freezing technique for measuring through-thickness tow deformations. With this data, a 3D Representative Volume Element (RVE) can be constructed for each stage of shear deformation. Beyond the geometric shear limit, tow deformations during bias extension appear to be somewhat different from those normally expected from pure shear—a reduction in tow thickness and tow cross-sectional area and a corresponding increase in packing factor.

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.

A state-dependent multi-mechanism model for sands

A state-dependent multi-mechanism model for sands in three-dimensional space is proposed within the framework of critical-state soil mechanics. The mechanical deformation behaviour of sands is characterised with a macroscopic volumetric mechanism and a number of one-dimensional equivalent microscopic shear mechanisms (EMSMs) in various orientations. Each one-dimensional EMSM includes a shear deformation and a volumetric deformation due to dilatancy, which are described by a microscopic shear stress–strain relationship and a microscopic stress–dilatancy relationship respectively. The detailed relationships between the macroscopic and microscopic model parameters are established, and all microscopic model parameters can be defined explicitly or implicitly by soil parameters with a clear and easily understandable physical meaning. Moreover, a state parameter, ψ, defined by the difference between the current and critical void ratios at the same confining stress is used, relating the dilatancy and peak stress ratios to the critical stress ratio. Successful simulations of the responses of sands under drained, undrained, monotonic and cyclic loading conditions and during rotation of principal stress direction are obtained.

Modelling the effective elasto-plastic properties of unidirectional composites reinforced by fibre bundles under transverse tension and shear loading

The effect of fibre bundling on the effective transverse properties of unidirectional fibre composites has been investigated by way of finite element method and micromechanics models of fibre bundles. Based on the micromechanical model of single-fibre composites, plane strain models for composites reinforced by fibre bundles are presented. The effective elasto-plastic stress–strain behaviour was obtained numerically by analysing a boron/aluminium composite reinforced by three-fibre and four-fibre bundles. The results are compared with the modelled behaviour for the composites reinforced by single fibres. The study shows that there is a remarkable influence of fibre bundling on plastic deformation, transverse tension and shear tangent stiffness of composites, while the influence on effective elastic properties can be ignored, fibre bundling enhances the transverse tangent stiffness of plastic deformation of composite materials, and the transverse normal stress–strain relations are more sensitive to fibre bundling than the transverse shear stress–strain relations.

Dynamic shear stress of tough-pitch copper at high strain and high strain-rate

Dynamic shear tests for the tough-pitch copper at high strain and high strain rate was performed. The Split Hopkinson Pressure Bar (SHPB) compression test system was modified to yield a shear deformation in the specimen. Hat-shaped specimens for the tough-pitch copper were adopted to generate high strain of γ=3–4 and high strain-rate of γ=104/s. The dynamic analysis by ABAQUS 5.5/EXPLICIT code verified that shear zone can be localized in hat-shaped specimens. A proper impact velocity and the axial length of the shear localization region were determined through the elastic wave analysis. The displacement in a hat-shaped specimen is limited by a spacer ring which was installed between the specimen and the incident bar. The shear bands were obtained by measuring the direction of shear deformation and the width of deformed grain in the shear zone. The decrease of specimen length has been measured on the optical displacement transducer. Dynamic shear stress-strain relations in the tough-pitch copper were obtained at two strain-rates.

Characterization of Aluminum Honeycomb Material Failure in Large Deformation Compression, Shear, and Tearing

Large deformation failures of aluminum honeycomb materials in dynamic compression, static shear and static tearing are characterized in this comprehensive experimental study. Two low density honeycomb materials that make up the Offset Deformable Barrier (ODB) used in vehicle crash test were tested. Material characterization methods, including one for studying material tearing, have been developed. The honeycomb material data under large deformation, including complete curves of compression and shear stress-strain relations in the three principal directions, are presented and analyzed. Honeycomb material tearing strength, defined as tearing force per unit tearing length, is introduced. Strain-rate dependence of honeycomb materials under dynamic loading is investigated. Local failure mechanisms of honeycombs in compression, shear, and indentation punch tests and their relations with the bulk properties of the materials are studied in detail. The results of this research may be used to improve the material fidelity of finite element simulations of the ODB.

반복하중을 받는 철근콘크리트 막요소의 비선형거동에 대한 예측

지진하중을 받는 철근콘크리트 패널의 이력거동을 힘의 평형조건, 변형의 적합조건 및 재료의 구성법칙을 이용한 재료메카니즘을 이용하여 예측하였다. 해석에서는 7단계의 압축응력-변형률곡선과 6단계의 인장응력-변형률곡선으로 구성된 콘크리트의 응력-변형률 모델을 이용하였다. 콘크리트의 응력-변형률 모델에는 균열이 발생한 콘크리트의 연화효과에 의한 압축강도 저감효과가 고려되었다. 해석에 적용된 반복하중을 받는 철근의 평균 응력-변형률관계에는 바우싱거효과 및 철근과 콘크리트의 부착작용을 고려한 인장경화효과가 고려되었다. 해석에 의하여 예측된 패널의 이력거동은 철근비가 다른 3개의 철근콘크리트 패널시험에 의하여 검증되었다. 해석법은 패널의 이력곡선을 추적하여 철근비가 점차 증가하는 시험체의 최대전단응력을 매우 정확히 예측하였다. 또한, 해석에 의하여 예측된 수직 및 수평변형률은 실험에서 관찰된 변형률과 잘 일치하였다. The behaviors of the reinforced concrete membrane elements are expected by Navier's three principles of the mechanics of materials. The adopted cyclic stress-strain curves of concrete consist of seven different unloading and loading stages in the compressive zone and six other stages in the tensile zone. The curves took into account the softening of concrete that was influenced by the tensile strain in the perpendicular direction of cracks. The stress-strain relationships for steel bar embedded in concrete subjected to reversed cyclic forces considered the tension stiffening effect and Baushinger effect. The predicted results of the analysis based on Navier's principles were in good agreement with the observed shear stress-strain relationships as well as transverse and longitudinal strains.

Cyclically thermomechanical plasticity analysis for a broken fiber in ductile matrix composites using shear lag model

The local cyclic plasticity of the interface around a broken fiber in ductile matrix composites under the in-phase and out-of-phase thermomechanical fatigue (TMF) loads is analyzed by using the single-fiber shear-lag model. The elastic, perfectly-plastic shear stress–strain relation is used to model the thermomechanical behavior of the fiber/matrix interface. It is shown that the alternating plastic shearing of the interface takes place under an appropriate combination of mechanical stress and thermal load. In the stress versus temperature diagram the so-called cyclic plasticity zone is identified. A new parameter, i.e. the cyclic plasticity length, L −s, is found which is smaller than the yield length, L s, caused by monotonic loading. The closed-form solutions for L −s, L s, the fiber stress profiles and the cyclic plastic shear strain range, Δ γ p, are obtained. L −s and Δ γ p increase for both the in-phase and out-of-phase TMF conditions as the mechanical load and/or thermal load increase. The in-phase condition produces a higher plastic shear strain range than the out-of-phase condition does. The solutions obtained may be used for modeling fiber/matrix debonding caused by the fiber breakage under TMF fatigue loading.

Response and failure of a double-shear beam subjected to mass impact

Abstract Experimental results are reported for the response and failure of a notched double-shear (DS) beam made from BS970/En24 medium carbon steel alloy when subjected to a mass impact loading. Mechanical properties and constitutive equations were obtained from quasi-static, dynamic and temperature tests on the beam material. Response and failure features were recorded for impact velocities between 30 and 110 m s −1 . A failure mode transition was observed between a ductile tensile rupture failure and an adiabatic shear banding failure. This test method could be used for studying shear stress–strain relations over a broad range of strain rates and for investigating different failure modes and their transitions. Finite-element numerical simulations were conducted for the response and failure in the notch section of the DS beam. Calibration factors were obtained, which may be used to calculate the actual stress and strain at the mid-point of a notch section in terms of the nominal values. Isothermal and adiabatic conditions obtained from a dimensional analysis were examined with the aid of FE simulations. An analytical model is used to predict the central block motions of DS beams and gives good agreement with experimental results. Various ductile fracture failure criteria were examined, among which the generalised plastic work density failure criterion leads to successful predictions for the ductile tensile failure within the notch section.

453 鉛材料の数値モデル化 : 大ひずみ域の繰り返しせん断応力-ひずみ関係

This paper shows shear stress-strain relation of lead material to develop a numerical model. The specimens were composed of circumferential lead and two steel flanges. Vertical displacement and rotation of the upper and bottom flanges were constrained and horizontal displacements were applied to the upper flange of the specimens by a dynamic biaxial test device. The loading test results show the shear stress-strain relation in small and large strain and effect of the height-diameter ratio f specimens on stress-strain curve.

Shear fracture of C/C composites with variable stacking sequence

Cross-ply laminated carbon–carbon composites with changing ply ratio of 0° and 90° were fractured under shear using several test methods. In these tests, special attention was placed on the understanding of the damage mechanisms. The ±45° off-axis shear test yielded the most precise shear stress–strain relation and was recommended to measure the shear modulus G 12. On the other hand, for shear strength measurement, the Iosipescu test was superior. The non-linearity in the shear stress–strain curve was found to be solely due to matrix cracking, while the peak shear stress was determined by fibre failure. In order to measure the shear strength by the Iosipescu test, two fracture planes normal and parallel to the loading axes have to be considered. The shear strength increased linearly with fibre volume fraction normal to the corresponding plane. The overall highest shear strength was obtained for the (0/90) n laminate.

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.

Stress and failure analysis of mechanically fastened joints in composite laminates

The literature published on single mechanically fastened joints in fiber-reinforced plastics is reviewed. A finite-element model is developed to predict the response of pin-loaded composite plates. The model takes into account contact at the pin–hole interface, progressive damage, large deformation theory, and a non-linear shear stress–strain relationship. To predict the progressive ply failure, the analysis combines Hashin and the maximum stress failure criteria. The objectives of the study are to determine the influence of the failure criteria, the inclusion of a non-linear shear behavior on the strength prediction and the load–pin displacement curve. The proposed model is used to predict the bearing response of composite plates with different stacking sequences. Good agreement between experimental results and numerical predictions is observed.

Microstructure and flow stress of polycrystals and single crystals

The relation between polycrystal deformation and single crystal deformation has been studied in this work. A pure aluminium polycrystal having an average grain size of 300 μm has been strained in tension at room temperature. The flow stress has been determined at four different strains (0.05, 0.14, 0.22 and 0.34) and deformation microstructures have been characterized qualitatively and quantitatively by transmission electron microscopy. Improved experimental techniques have allowed large foil areas to be characterized and in total 89 grains have been examined. At the four strains examined a classification of the deformation microstructures into three different types has shown a correlation between the grain orientation and the type of deformation microstructure which develops during straining. The dislocation density has been calculated at each strain and by assuming that the shear stress is proportional to the square root of the dislocation density the shear stress–strain relationship has been derived for each of the three groups of grains showing different deformation microstructures. The stress–strain curves show a strain hardening behaviour which depends on the orientation of the grain. The behaviour of the grains embedded in the polycrystal is compared with the behaviour of single crystals and the stress–strain curve of the polycrystal is estimated with good accuracy from single crystal data, which are weighted based on a quantitative texture analysis of the polycrystal.

Seismic Behavior of an Underlying Alluvial Clay on Man-Made Islands During the 1995 Hyogoken-Nambu Earthquake

ABSTRACT The authors have studied the seismic behavior of the alluvial clay layer on Kobe Port Island during the 1995 Hyogoken-Nambu earthquake. First the shear stress-strain relationship of the clay was estimated from the main shock of seismic array data. Next using the stress wave inferred from array records we conducted a cyclic simple shear test. The samples used in this study were the clay sampled from Port Island and Rokko Island. The clay sampled from the two man-made islands are from the same clay layer, but the clay from Rokko Island was not as consolidated as the clay at Port Island. After consolidation with the confining pressure at the array site, we applied a dynamic shear stress at the same stress rate as the actual earthquake. The shear strain time histories inferred from array records were compared with those from the simple shear test. The strain time history obtained from the simple shear test gave good comparison to that obtained from array records. Finally the settlement due to dynamic shearing was studied through the simple shear test. It was found that the difference of the degree of consolidation affects the seismic behavior of soft clay.

差分方程式に基づく単杭の鉛直荷重-沈下量関係の理論解析法およびその砂地盤への適用

An analytical method on vertical load-settlement relations of single pile is proposed based on the difference equations in consideration of nonlinear characteristics on vertical stress-strain of pile, frictional stress-settlement and point load-point settlement. A method of formulation on the relation between frictional stress and settlement is also proposed made up from shear stressstrain relation of soil. Then the procedure of analysis is mentioned on the model of bored steel pipe pile in sand ground. The results of the analysis express the behavior of pile rationally and accurately.

Contact analysis of mechanically fastened joints in composite laminates by linear complementarity problem formulation

The contact phenomena and stress distributions in the vicinity of the hole on mechanically fastened joints are investigated in composite laminates exhibiting nonlinear elastic behavior. The effects of fastener stiffness, friction force between the fastener and the composite laminates, geometrical nonlinearities due to concentrated fastener load around the hole edge for the snug and clearance-fit in the [0 °] S, [± 45 °] S, [0°/± 45 °] S and laminates are also considered. An efficient numerical procedure is developed for the solution of the contact problems with Coulomb friction between the fastener and the hole based on a linear complementarity problem (LCP) formulation in an incremental form. A nonlinear finite element code for stress analysis of laminated composites using Lemke's complementary pivoting algorithm is developed for solving the LCP. The nonlinear analysis is composed of the combination of updated Lagrangian formulation of the frictional contact problem and the nonlinear shear stress-strain relation in each ply. The accuracy, applicability and computational efficiency of the proposed method are confirmed by comparison with previous researches.

The KES Shear Test for Fabrics

Many fabric mechanics researchers have reported that specimens being tested on the KES shear tester are not subjected to pure shear deformation; therefore, test results cannot lead directly to a determination of the fabric shear modulus and stress/strain relationship, particularly in the nonlinear range of stress-strain. Combined with finite element analysis, this paper presents an analytical solution for the distribution of shear stresses and strains in fabric specimens tested on the kes tester. A fabric is treated as an orthotropic sheet during the analysis, which leads to a closed-form solution for the shear modulus as a function of fabric tensile and shear moduli from the kes shear test. A modified shear stress-strain relationship can also be derived. From calculations for fabrics used here, the difference between modified and tested shear modulus values is about 25–30%. The study also suggests that although the shear modulus and curves obtained on the kes shear tester are significantly different from those under the pure shear state, the kes results can still reflect the nature of a fabric under shear deformation and are valid for general objective evaluations. The exact shear stress-strain relationship and actual shear modulus may be modified only when they are required for fabric complex deformation analysis.

Dynamic Constitutive and Failure Behavior of a Two-Phase Tungsten Composite

The constitutive response and failure behavior of a W-Ni-Fe alloy over the strain rate range of 10-4 to 5 X 105 s-1 is experimentally investigated. Experiments conducted are pressure-shear plate impact, torsional Kolsky bar, and quasi-static torsion. The material has a microstructure of hard tungsten grains embedded in a soft alloy matrix. Nominal shear stress-strain relations are obtained for deformations throughout the experiments and until after the initiation of localization. Shear bands form when the plastic strain becomes sufficiently large, involving both the grains and the matrix. The critical shear strain for shear band development under the high rate, high pressure conditions of pressure-shear is approximately 1–1.5 or 6–8 times that obtained in torsional Kolsky bar experiments which involve lower strain rates and zero pressure. Shear bands observed in the impact experiments show significantly more intensely localized deformation. Eventual failure through the shear band is a combination of grain-matrix separation, ductile matrix rupture, and grain fracture. In order to understand the effect of the composite microstructure and material inhomogeneity on deformation, two other materials are also used in the study. One is a pure tungsten and the other is an alloy of W, Ni, and Fe with the same composition as that of the matrix phase in the overall composite. The results show that the overall two-phase composite is more susceptible to the formation of shear bands than either of its constituents.

Effect of Degradation on Seismic Response of Israeli Continental Slope

Seismic site response analyses are often carried out using constitutive models for soil behavior under cyclic loading that incorporate Masing rules. In such analyses the effect of cyclic degradation of stiffness and strength on the seismic response of horizontal, soft clay strata is often ignored. In a recent publication, the authors have proposed a normalized form of the shear stress-strain relationship for undrained, cyclic simple shear of soft clay. Cyclic degradation is accounted for through a single fatigue parameter—the mean effective stress, utilized in normalization of stresses and strains. Cyclic degradation of the small strain shear modulus is neglected, i.e. the stiffness degrades only due to strength degradation. This normalized model has been combined with an effective stress model for simple shear loading and boundary conditions, developed within the framework of bounding surface kinematic and isotropic hardening plasticity, to provide an overall model that may be used in site response analysis. In the present paper, this model is utilized in one-dimensional propagation analysis to compare the expected response in a soft clay profile (comprising the Israeli continental slope) to that that would be predicted without accounting for cyclic degradation. Neglect of cyclic degradation is shown to be nonconservative, resulting in underestimation of velocities and accelerations developed in the profile.