Shear Stress-strain Relationship Research Articles

Experimental and numerical evaluations of Kirkuk field soil treated with waste shredded tire

In this study, an experimental and numerical investigation of Kirkuk real field soil treated with waste tire has been examined. Field soil samples from Kirkuk city have been collected and tested experimentally to evaluate the basic soil properties. The field soil has been treated with waste shredded tires and up to 10%. A series of direct shear tests under different normal stresses and unconfined compression tests with two different rates have been performed on both untreated and waste tire treated soils. For the untreated soil, the maximum shear stress measured by the direct shear test increased by 150% when the normal shear stress increased from 50 kPa to 150 kPa. For the 5% and 10% waste tire treated soils, the maximum shear stresses measured by the direct shear test increased by 110% and 105% when the normal stress increased from 50 kPa to 150 kPa respectively. The peak uniaxial stress measured by the unconfined compression test increased by 83% and 98% as the waste tire treatment increased from 0% to 10% for both testing rates of 0.125 mm/min and 0.25 mm/min respectively. Finally, finite element method using three different models represented by elastic, hyperbolic and Mohr-Coulomb elastic-plastic models have been used to model unconfined compression tests for both untreated and 10% waste tire treated soils. For both untreated and waste tire treated soils, the elastic model over predicted the shear stress versus shear strain relationship whereas the elastic-plastic model had a very good agreement with the experimental data. However, the hyperbolic model had a good prediction for the initial part of the shear stress versus shear strain relationship for both untreated and waste tire treated soils with an overestimation for the second part of the experimental data.

Dynamic Response and Failure Mechanism of Brittle Rocks Under Combined Compression-Shear Loading Experiments

A novel method is developed for characterizing the mechanical response and failure mechanism of brittle rocks under dynamic compression-shear loading: an inclined cylinder specimen using a modified split Hopkinson pressure bar (SHPB) system. With the specimen axis inclining to the loading direction of SHPB, a shear component can be introduced into the specimen. Both static and dynamic experiments are conducted on sandstone specimens. Given carefully pulse shaping, the dynamic equilibrium of the inclined specimens can be satisfied, and thus the quasi-static data reduction is employed. The normal and shear stress–strain relationships of specimens are subsequently established. The progressive failure process of the specimen illustrated via high-speed photographs manifests a mixed failure mode accommodating both the shear-dominated failure and the localized tensile damage. The elastic and shear moduli exhibit certain loading-path dependence under quasi-static loading but loading-path insensitivity under high loading rates. Loading rate dependence is evidently demonstrated through the failure characteristics involving fragmentation, compression and shear strength and failure surfaces based on Drucker–Prager criterion. Our proposed method is convenient and reliable to study the dynamic response and failure mechanism of rocks under combined compression-shear loading.

Entire solutions of nonlocal elasticity models for composite materials

Many structural materials, which are preferred for the developing of advanced constructions, are inhomogeneous ones. Composite materials have complex internal structure and properties, which make them to be more effectual in the solution of special problems required for civil and environmental engineering. As a consequence of this internal heterogeneity, they exhibit complex mechanical properties. In this work, the analysis of some features of the behavior of composite materials under different loading conditions is carried out. The dependence of nonlinear elastic response of composite materials on loading conditions is studied. Several approaches to model elastic nonlinearity such as different stiffness for particular type of loadings and nonlinear shear stress–strain relations are considered. Instead of a set of constant anisotropy coefficients, the anisotropy functions are introduced. Eventually, the combined constitutive relations are proposed to describe simultaneously two types of physical nonlinearities. The first characterizes the nonlinearity of shear stress–strain dependency and the latter determines the stress state susceptibility of material properties. Quite satisfactory correlation between the theoretical dependencies and the results of experimental studies is demonstrated, as described in [ 2 , 3 ] as well as in the references therein.

Experimental assessment and numerical modelling of exterior non-conforming beam-column joints with plain bars

The seismic performance of existing Reinforced Concrete (RC) frames is significantly influenced by the behaviour of beam-column intersections, especially in non-conforming buildings with poor structural details and completely unreinforced joints. In literature, a very limited number of studies deals with specimens reinforced with plain hook-ended longitudinal bars, widespread in Italian and Mediterranean building stock, or with the analysis of local aspects, such as the experimental evaluation of joint shear strains. The almost totality of the models proposed in literature for simulating the cyclic behaviour of RC joints was developed and calibrated by means of tests performed on elements with deformed bars, and, thus, these models may be not adequate for elements with hook-ended plain bars, especially due to the peculiarities in terms of failure mode and interaction mechanisms between concrete and steel.This study analyses the experimental cyclic behaviour of four full-scale exterior unreinforced RC beam-column joints with plain reinforcing bars in beams and columns, which differ for joint aspect ratio and beam longitudinal reinforcement ratio. First, experimental global and local responses of such tests – including energy dissipation capacity and observed damage evolution – are analysed. The main deformation mechanisms ascribable to the joint – namely rotation at the interface between beam/columns and joint, and shear deformation of the joint panel – are experimentally evaluated to provide a realistic support for the numerical modelling of this typology of beam-column joints. Then main joint shear strength models existing in codes and literature are compared with the experimental results. Finally, the numerical modelling of the specimens is carried out under monotonic loading to reproduce the envelope of the experimental responses. The joint panel constitutive parameters are defined to reproduce the experimental joint shear stress-strain relationships. Additionally, modelling of bond-slip is particularly taken into account due to the poor quality of steel-concrete interaction in the specific case of plain reinforcing bars.

Multi-laminate non-coaxial modelling of anisotropic sand behavior through damage formulation

A modified multi-laminate model, to predict non-coaxiality in anisotropic sand, is proposed in this paper. The model can easily be extended to other geo-materials only with implementing some minor provisions. To consider anisotropy of sand, two ellipsoids are utilized to summarize shear and compressive stiffness of material in different directions. Damage concept is used to take into account degradation of material through loading procedure. Ellipsoid of rigidity factors is being changed in both size and dimension, under applied strain path. Variation of ellipsoids results in change of stiffness distribution over different planes. In other words, fabric evolution in material is considered through variation of ellipsoids of rigidity factors. A simple rule is proposed for shear stress-strain relationship in loading-unloading and reloading, which captures most of the natural characteristics of sand behavior. In multi-laminate models, depending on stiffness distribution over sampling planes, stress and strain are not coaxial essentially. To achieve better results, non-coaxiality of shear stress and strain on sampling planes is considered by applying vector field concept. Shear stress in different directions of a sampling plane is considered as a vector field. This field is obtained from strain field, considering shear stiffness in various orientations. The model parameters are calibrated using uniaxial compressive test data in different directions, with respect to bedding plane on an anisotropic sand sample. To investigate capability of the model to predict non-coaxiality, results of the model are compared to experimental results obtained from pure principal stress rotation. Ultimately, good accuracy is observed in results.

Micromechanics-based multimechanism bounding surface model for sands

Within the multimechanism framework, a micromechanics-based sand model is presented based upon the bounding surface and critical state theories. This model follows the assumption that the macroscopic responses of sands can be determined by summing the contributions from a macroscopic volumetric mechanism and an infinite number of virtual microscopic shear mechanisms in various orientations. Each virtual shear mechanism characterizes the microscopic shear deformations and the dilatancy-induced volumetric deformations in three mutually perpendicular directions. The deformations in each direction are described by using a microscopic shear stress–strain relationship founded upon the bounding surface theory and a microscopic stress–dilatancy relationship, respectively. The shear strength with the SMP yield criterion and the stress–dilatancy relationship introduce a state variable for compatibility with the critical state theory. The correlations between the microscopic and macroscopic model parameters are established, and most of them are defined by soil parameters with a clear physical meaning. With a spatial distribution of microscopic shear mechanisms, the model can intrinsically consider the stress-induced anisotropy, the non-coaxial behaviour of stress and strain increment in their principal directions, and the effect induced by principal stress rotations without requiring additional model parameters. The comparison of the simulated and experimental results indicates its excellent capability in predicting sand responses in stress–strain curve as well as stress path under different drainage and loading conditions.

Influence of interference-fit percentage on stress and damage mechanism in hi-lock pin installation process of CFRP

The interference-fit technology is an effective way to enhance fatigue life of mechanical structures. However, for composites, oversized interference-fit percentage causes damages and then decreases the joint performance directly. Influence of percentages on stress and damage around Carbon Fiber Reinforced Plastics interference-fit hole is analyzed in this paper. The progressive damage theory is introduced into a three-dimensional finite-element model, which consists of the mixed failure criteria combining Hashin criteria and maximum stress criteria and the corresponding property degradation rules. A nonlinear shear stress–strain relationship is also built to solve the nonlinear material behavior. Three groups of 0.4%, 0.8%, and 1.2% interference-fit percentages are analyzed. Corresponding pin installation experiments are conducted to validate the accuracy of the model. The inserting force, stress distribution, and damage initialization around the hole are investigated and discussed in this model.

ELASTIC-PLASTIC BEAM-COLUMN FEM MODEL WITH FIBER ELEMENTS EVALUATING SHEAR DEFORMATION

This paper proposes a new beam-column FEM which consists of several fiber elements considering shear deformation. The distribution of normal strain obeys Bernouli-Euler hypothesis. The distribution of shear strain is suggested here to be Equation (17). The proposed distribution is expressed by the product of distribution of shear strain and shear deformation angle at the elastic state. The formulation is accomplished based on the incremental perturbation method. Normal stress-strain relation and shear stress-strain relation in the fiber element are supposed here to obey each different consistent law independently. The new generalized displacement vectors with a shear deformation angle and the corresponding force vectors are defined here as shown in Eqs. (2) and (3). In order to analyze combined non-linear problem, the moving coordinate system in the previous beam-column FEM known as FERT is adopted here. The matrix of coordinates transformation is conducted here. Also, the formularization described in chapter 2 is developed by the incremental perturbation theory. The verification of the proposed numerical method named FERTs-P is carried out for the problem of elastic beam and elastic-plastic beam. Also the simulation of the steel beam experiment and the frame experiment with a shear panel are done by the FERTs-P. The section quantities consisted by fiber elements are set up to be equivalent to area, moment of inertia and plastic section modules. The tri-linear models are adopted here as the relation of shear stress-strain and that of normal stress-strain. The main observations are as follows: (1) The ratios of shear deformation to bending deformation in elastic beams are almost coincident with theoretical values due to Timoshenko beam. (2) The numerical results by FERTs-P are relatively good predictions for the experimental load-deflection curves of beams and frame yielding at shear. (3) The FERTs-P is effective to predict elastic-plastic bending behavior. In spite of bold modeling, this numerical method may be expected considerably. Moreover the consistent law in shear stress-strain relation will be considered.

The shear behaviour of pine wood in the Arcan test with the digital image correlation

The Arcan shear test is used together with the digital image correlation to study the shear stress-strain relationship for pine wood in the symmetry plane LR . The relationship of shearing perpendicular to the grain direction is shown by the straight line below the proportional limit and the nonlinear curve beyond it describing hardening up to the ultimate limit. Subsequent failure modes are shown during the load increase. Additionally, some results of the off-axis tension tests, as well as the uniaxial tension tests, with the mechanical and electric resistance strain gauges are presented to determine and compare the shear modulus from both methods of testing.

Bearing strength and failure analysis on the interference-fit double shear-lap pin-loaded composite

Interference-fit technology has a wide effect on the strength and fatigue life of composite structures. The damage around the hole may accelerate the structure failure. In this paper, a progressive damage model is developed to predict the response of interference-fit pin-loaded composite laminates during the installation and loading process with the ABAQUS subroutine user-define-field (USDFLD). The model takes contact at the pin–hole interface, the nonlinear shear stress–strain relationship and the property progressive damage into consideration. The loading procedure is separated into two parts: (a) installing the Hi-Lok pin. (b) Applying the tensile load. To predict progressive failure, the mixed failure criteria combining Hashin criteria and the maximum stress failure criteria, and the Camanho and Matthews degradation rules are conducted. The insertion load, stress and damage around the hole, load–displacement curve, and the bearing strength are predicted. A series of experiments have also been performed and the rationality of the model is testified. The parametric study is also made to analyze the effect of fit conditions on insertion load, damage, and load–displacement curve.

A New Approach for Numerical Analysis of the RC Shear Walls Based on Timoshenko Beam Theory Combined with Bar-Concrete Interaction

In this paper, a new approach for nonlinear numerical modelling of the reinforced concrete shear walls with consideration of bar-concrete interaction and shear deformation is proposed. Bar and concrete stress-strain relations, the bar-concrete interaction, the shear stress-strain relation and, also, their cyclic behavior including the strength degradation and stiffness degradation are adopted as known specifications. In the modeling, shear wall is divided into two types of joint and reinforced concrete (RC) elements. In the RC element, the effect of shear deformation is considered based on Timoshenko beam theory. Separate degrees of freedom are used for the steel bars and concrete part. The effect of bar-concrete interaction has been considered in the formulation of the RC element. The reliability of the method has been assessed through the comparison of numerical and experimental results for a variety of tested specimens under cyclic and pushover loading. A good agreement between experimental and analytical results is obtained for both cases of strength and stiffness during the analysis.

炭素繊維のねじり-引張特性の評価

Torsional-tensile, dynamic torsional pendulum oscillation and static rotary tests of carbon mono-filament were carried out. Two high performance carbon fibers，a PAN-based and a pitch-based, were chosen for these tests. From static rotational behavior of carbon and glass series connected filament, shear stress-strain diagram of carbon fiber is determined. On the diagram, the PAN-based carbon fiber exhibits a very linear shear stress-shear strain relationship up to the torsional fracture. On the other hand, the pitch-based carbon fiber shows the linear relationship up to a point. Beyond the point, increasing shear strain, slope of the τ/γ (torsional stiffness) is decreased. However, for each carbon fiber, it does not show any plastic torsional deformation, that is, it is perfectly elastic until fracture. In other words, the torsional deformation is completely recovered when the torque is reduced at every torsional deformation stage. The mono-filament of carbon fiber is tensioned until fracture with fixing torsional strain. The torsional-tensile strength of the PAN-based carbon fiber shows that increasing torsional strain, the tensile strength decrease by insensible degrees with the small torsional strain and rapidly decrease coming up to the torsional fracture strain. The torsional-tensile strength of the pitch-based carbon fiber does not change until a torsional strain, and after then decreased rapidly. Tensile rigidity is gradually decreased, increasing torsional strain, and decreased sharply at closing torsional fracture strain. The ratios of anisotropic measure of strength by the tensile strength to the torsional strength are smaller than the ratios of elasticity by the tensile modulus to the torsional modulus. This torsional-tensile test method is useful in order to evaluate strength and structural anisotropy of fiber materials.

Influence of textured surface on the performance of non-recessed hybrid journal bearing operating with non-Newtonian lubricant

In the present work, a comparative study between textured surface and non-textured surface non-recessed hybrid journal bearing configurations is presented. To obtain the performance characteristics parameters of non-recessed hybrid journal bearing, the Reynolds equation, which governs the flow of lubricant in the clearance space, is solved using FEM and the performance parameters are computed. The shear stress–strain relation of lubricant is modeled with the help of a power-law fluid model. The numerically simulated results show that the textured non-recessed hybrid journal bearing provides improved stability parameter than that of journal bearing with non-texturing.

An experimental study of the mechanical characteristics of fractured loess in western China

Microstructural changes in the loess deposits due to the presence of joint planes is one of the primary causes of the geohazards (ground fissures, ground subsidence, landslides, collapses, and soil and water losses) that occur in the loess regions of western China. By means of uniaxial tensile tests and triaxial shear tests conducted under different confining pressures, we tested fractured loess Q2 samples with five fracture plane inclination angles (0°, 30°, 45°, 60°, and 90°) taken from Sanyuan County, Shaanxi Province in western China, where geohazards are prevalent. Analysis of the tensile stress–strain and shear stress–strain relationships of the fractured loess specimens revealed the characteristics of the fractures that induce instability in this area. These results provide important baseline data for future research on the mechanism of geohazards in the loess regions of western China.

Assessing 3D shear stress–strain properties of composites using Digital Image Correlation and finite element analysis based optimization

Abstract This work presents a method which uses the full-field measurement capability of Digital Image Correlation (DIC) for a simultaneous assessment of non-linear shear stress-–strain relations for composites in all three principal material planes. The method, which employs a small rectangular plate torsion specimen, advances our ability to measure 3D material properties compared to the previous methodology that was able to use only small regions of the specimen surfaces in the material characterization. The new methodology takes full advantage of the full-field measurement. Material stress–strain constitutive modeling is relying on the DIC data including the in-plane as well as out-of-plane strain components; and on iterative finite element model (FEM) updating based on the Levenberg–Marquardt algorithm for minimization of weighted least squares error between the DIC-measured and the FEM-predicted strains. Results include the in-plane and two interlaminar stress–strain curves simultaneously captured for a practical carbon/epoxy tape material system.

Closure to “Experimental Investigation of Pullout Behavior of Fiber-Reinforced Polymer Reinforcements in Sand” by Cheng-Cheng Zhang, Hong-Hu Zhu, Bin Shi, Fang-Dong Wu, and Jian-Hua Yin

Closure to “Experimental Investigation of Pullout Behavior of Fiber-Reinforced Polymer Reinforcements in Sand” by Cheng-Cheng Zhang, Hong-Hu Zhu, Bin Shi, Fang-Dong Wu, and Jian-Hua Yin

Improved strut-and-tie method for 2D RC beam-column joints under monotonic loading

In the previous analytical studies on 2D reinforced concrete (RC) beam-column joints, the modified compression field theory (MCFT) and the strut-and-tie method (STM) are usually employed. In this paper, the limitations of these analytical models for RC joint applications are reviewed. Essentially for predictions of RC joint shear behaviour, the MCFT is not applicable, while the STM can only predict the ultimate shear strength. To eliminate these limitations, an improved STM is derived and applied to some commonly encountered 2D joints, viz., interior and exterior joints, subjected to monotonic loading. Compared with the other STMs, the most attracting novelty of the proposed improved STM is that all critical stages of the shear stress-strain relationships for RC joints can be predicted, which cover the stages characterized by concrete cracking, transverse reinforcement yielding and concrete strut crushing. For validation and demonstration of superiority, the shear stress-strain relationships of interior and exterior RC beam-column joints from published experimental studies are employed and compared with the predictions by the proposed improved STM and other widely-used analytical models, such as the MCFT and STM.

Interface damage behaviour during interference‐fit bolt installation process for CFRP/Ti alloy joining structure

AbstractA numerical and experimental investigation was conducted to determine the effect of interference‐fit size on damage behaviour of bolted single‐lap carbon fibre‐reinforced plastic/Ti alloy composite structure. Three‐dimensional finite element analysis (FEA) was conducted for interference‐fit bolt installation process considering the friction coefficient and nonlinear shear stress–strain relationship, and damage sub‐routine was used to predict composite progressive failure region and failure type in single‐lap bolted‐joints. Experiments involving three interference‐fit sizes of 0.4%, 2.1% and 3.0% were designed to verify the FEA. In addition, micro‐analysis results show that damage type during interference‐fit bolt inserting process predicted by FEA was consistent with experimental results. Various types of micro‐scale damage around the hole after interference bolt installation were analysed and characterised, and the effects of interference‐fit size on structure strength were analysed in view of micro‐scale damage. An appropriate interference‐fit size can prompt the carbon fibre‐reinforced plastic hole to become ‘brush‐like’ and exhibit ‘soften’ and ‘buffering’ effect that improves the bearing capacity. In this paper, interference fit of 2.1% exhibits the maximum bearing damage strength.

Extreme softness of brain matter in simple shear

We show that porcine brain matter can be modelled accurately as a very soft rubber-like material using the Mooney–Rivlin strain energy function, up to strains as high as 60%. This result followed from simple shear experiments performed on small rectangular fresh samples (2.5cm3 and 1.1cm3) at quasi-static strain rates. They revealed a linear shear stress–shear strain relationship (R2>0.97), characteristic of Mooney–Rivlin materials at large strains. We found that porcine brain matter is about 30 times less resistant to shear forces than a silicone gel. We also verified experimentally that brain matter exhibits the positive Poynting effect of non-linear elasticity, and numerically that the stress and strain fields remain mostly homogeneous throughout the thickness of the samples in simple shear.

Interfacial stresses in strengthened beam with shear cohesive zone model

The failure of strengthened beams with fibre-reinforced polymer (FRP) materials is due to high stress concentration of FRP–concrete interface. Understanding the cause and mechanism of the debonding of the FRP plate and the prediction of the stress distribution at the concrete–FRP interface are important for more effective strengthening technique. This paper presents an analytical solution, based on Smith and Teng’s equations, for interfacial shear and normal stresses in reinforced concrete (RC) beams strengthened with a fibre reinforced polymer (FRP) plate. However, the shear stress–strain relationship is considered to be bilinear curve. The effects of the shear deformations are calculated in an RC beam, an adhesive layer, and an FRP plate. The results of parametric study are compared with those of Smith and Teng. They confirm the accuracy of the proposed approach in predicting both interfacial shear and normal stresses.