Showing papers on "Stress–strain curve published in 2005"

A numerical approach to spherical indentation techniques for material property evaluation

Abstract: In this work, some inaccuracies and limitations of prior indentation theories, which are based on experimental observations and the deformation theory of plasticity, are investigated. Effects of major material properties on the indentation load-deflection curve are examined via finite element (FE) analyses based on incremental plasticity theory. It is confirmed that subindenter deformation and stress–strain distribution from deformation plasticity theory are quite dissimilar to those obtained from incremental plasticity theory. We suggest an optimal data acquisition location, where the strain gradient is the least and the effect of friction is negligible. A new numerical approach to indentation techniques is then proposed by examining the FE solutions at the optimal point. Numerical regressions of obtained data exhibit that the strain-hardening exponent and yield strain are the two key parameters which govern the subindenter deformation characteristics. The new indentation theory successfully provides a stress–strain curve and material properties with an average error of less than 3%.

Plane-strain Bulge Test for Thin Films

Abstract: The plane-strain bulge test is a powerful new technique for measuring the mechanical properties of thin films. In this technique, the stress–strain curve of a thin film is determined from the pressure-deflection behavior of a long rectangular membrane made of the film of interest. For a thin membrane in a state of plane strain, film stress and stain are distributed uniformly across the membrane width, and simple analytical formulae for stress and strain can be established. This makes the plane-strain bulge test ideal for studying the mechanical behavior of thin films in both the elastic and plastic regimes. Finite element analysis confirms that the plane-strain condition holds for rectangular membranes with aspect ratios greater than 4 and that the simple formulae are highly accurate for materials with strain-hardening exponents ranging from 0 to 0.5. The residual stress in the film mainly affects the elastic deflection of the membrane and changes the initial point of yield in the plane-strain stress–strain curve, but has little or no effect on further plastic deformation. The effect of the residual stress can be eliminated by converting the plane-strain curve into the equivalent uniaxial stress–strain relationship using effective stress and strain. As an example, the technique was applied to an electroplated Cu film. Si micromachining was used to fabricate freestanding Cu membranes. Typical experimental results for the Cu film are presented. The data analysis is in good agreement with finite element calculations.

Nonsingular stress and strain fields of dislocations and disclinations in first strain gradient elasticity

Abstract: The aim of this paper is to study the elastic stress and strain fields of dislocations and disclinations in the framework of Mindlin's gradient elasticity. We consider simple but rigorous versions of Mindlin's first gradient elasticity with one material length (gradient coefficient). Using the stress function method, we find modified stress functions for all six types of Volterra defects (dislocations and disclinations) situated in an isotropic and infinitely extended medium. By means of these stress functions, we obtain exact analytical solutions for the stress and strain fields of dislocations and disclinations. An advantage of these solutions for the elastic strain and stress is that they have no singularities at the defect line. They are finite and have maxima or minima in the defect core region. The stresses and strains are either zero or have a finite maximum value at the defect line. The maximum value of stresses may serve as a measure of the critical stress level when fracture and failure may occur. Thus, both the stress and elastic strain singularities are removed in such a simple gradient theory. In addition, we give the relation to the nonlocal stresses in Eringen's nonlocal elasticity for the nonsingular stresses.

Silicone dielectric elastomer actuators: Finite-elasticity model of actuation

Abstract: A theory for the actuation strain of a silicone dielectric elastomer actuator with a simple geometry is developed. The stress is a function of two variables, the strain and the applied voltage. A lamination type stress–strain function was employed, due to the nature of the electrodes. All parameters are obtained from physical measurements. Then, measurements of the blocking force are shown to correspond to what is expected from the Maxwell stress. Actuation strain measurements are performed and compared with the developed theory. The developed model has no free parameters, yet it exhibits the features of the actuation strain: the optimum load is reproduced correctly (within the chosen experiment resolution of 5 g). The discrepancy on the actuation strain between the measurement results and the model vary between 15% and 37% at the optimum, which are ascribed to inaccuracies in dimension measurements of the actuator and the inherent crudeness in the assumption that the stress and strain fields are constant throughout the actuator. We conclude that even for high strains, the actuation of dielectric elastomer actuators is well described by only considering the elasticity of the material and the Maxwell stress due to the applied electric field.

Compressive behaviour of steel fibre reinforced concrete

Abstract: An experimental study to investigate the influence of matrix strength, fibre content and diameter on the compressive behaviour of steel fibre reinforced concrete is presented. Two types of matrix and fibres were tested. Concrete compressive strengths of 35 and 60 MPa, 0·38 and 0·55 mm fibre diameter, and 30 mm fibre length, were considered. The volume of fibre in the concrete was varied up to 1·5%. Test results indicated that the addition of fibres to concrete enhances its toughness and strain at peak stress, but can slightly reduce the Young's modulus. Simple expressions are proposed to estimate the Young's modulus and the strain at peak stress, from the compressive strength results, knowing fibre volume, length and diameter. An analytical model to predict the stress–strain relationship for steel fibre concrete in compression is also proposed. The model results are compared with experimental stress–strain curves.

A microbeam bending method for studying stress–strain relations for metal thin films on silicon substrates

Abstract: We have developed a microbeam bending technique for determining elastic–plastic, stress–strain relations for thin metal films on silicon substrates. The method is similar to previous microbeam bending techniques, except that triangular silicon microbeams are used in place of rectangular beams. The triangular beam has the advantage that the entire film on the top surface of the beam is subjected to a uniform state of plane strain as the beam is deflected, unlike the standard rectangular geometry where the bending is concentrated at the support. To extract the average stress–strain relations for the film, we present a method of analysis that requires computation of the neutral plane for bending, which changes as the film deforms plastically. This method can be used to determine the elastic–plastic properties of thin metal films on silicon substrates up to strains of about 1%. Utilizing this technique, both yielding and strain hardening of Cu thin films on silicon substrates have been investigated. Copper films with dual crystallographic textures and different grain sizes, as well as others with strong 〈1 1 1〉 textures have been studied. Three strongly textured 〈1 1 1〉 films were studied to examine the effect of film thickness on the deformation properties of the film. These films show very high rates of work hardening, and an increase in the yield stress and work hardening rate with decreasing film thickness, consistent with current dislocation models.

Stress-strain model for laterally confined concrete

Abstract: High strength concrete (HSC) with highly desirable structural properties can lead to significant cost savings in heavily loaded lower story columns of concrete structures. Its use has however, been limited by a concern regarding an increased brittleness compared to normal strength concrete. It is well established that the ductility of HSC columns can be increased by confinement of the core of concrete columns by lateral steel reinforcement. Confining pressure applied by the reinforcement is a function of the lateral strain of concrete. Therefore establishing axial stress, axial strain, and lateral strain relationships is a timely concern. Based on shear failure of concrete, a simple strain-based model is proposed in this paper. It is developed using prevailing test results for HSC with active confinement.

Factors Affecting the Initial Stiffness of Cohesive Soils

Abstract: The paper presents the results of an extensive laboratory program conducted to establish the factors affecting the initial stiffness (Young’s modulus) of cohesive soils in undrained triaxial compression. The testing program, conducted on resedimented Boston blue clay (RBBC) comprised more than 100 phases of undrained shear and isolated the role of: overconsolidation ratio (OCR), consolidation stress level, void ratio, lateral stress ratio, preshear consolidation path, strain rate and duration of laboratory aging. On-specimen measurement of the axial strain was performed employing a novel LVDT-based device capable of resolving displacements of less than 0.1 μm , corresponding to approximately 0.0001% axial strain for a 80 mm height triaxial specimen. Results indicate that for all testing conditions, at small strains the stress strain behavior of RBBC (OCR=1–8) is linear. Provided that the strain rate is sufficiently (by 25–30 times) greater than the preshear creep rate, the Young’s modulus is rate independ...

Stress-strain characteristic of SFRC using recycled fibres

Abstract: This paper presents work from a comprehensive study on the development of a flexural design framework for concrete reinforced with steel fibres that are recovered from used tyres. The experimental flexural behaviour of notched concrete prisms reinforced with these fibres is initially presented. For comparison purposes, prisms reinforced with industrially produced fibres are also considered. An attempt to adopt an existing RILEM design framework to derive appropriate tensile stress-strain blocks is made, but problems are identified with key parameters of the framework. The influence of crack propagation and location of neutral axis depth on the tensile stress distribution is examined. Following an analytical study, it is concluded that the uniaxial stress-strain model, proposed by RILEM overestimates the load-carrying capacity and should be modified by utilising more advanced analytical techniques.

Material Properties of the Human Lumbar Facet Joint Capsule

Abstract: The human facet joint capsule is one of the structures in the lumbar spine that constrains motions of vertebrae during global spine loading (e.g., physiological flexion). Computational models of the spine have not been able to include accurate nonlinear and viscoelastic material properties, as they have not previously been measured. Capsules were tested using a uniaxial ramp-hold protocol or a haversine displacement protocol using a commercially available materials testing device. Plane strain was measured optically. Capsules were tested both parallel and perpendicular to the dominant orientation of the collagen fibers in the capsules. Viscoelastic material properties were determined. Parallel to the dominant orientation of the collagen fibers, the complex modulus of elasticity was E* = 1.63MPa, with a storage modulus of E′ = 1.25MPa and a loss modulus of: E″ = 0.39MPa. The mean stress relaxation rates for static and dynamic loading were best fit with first-order polynomials: B (ɛ) = 0.1110 ɛ − 0.0733 and B (ɛ) = −0.1249ɛ 11794-8181 +0.0190, respectively. Perpendicular to the collagen fiber orientation, the viscous and elastic secant moduli were 1.81 and 1.00 MPa, respectively. The mean stress relaxation rate for static loading was best fit with a first-order polynomial: B (ɛ) = − 0.04ɛ − 0.06. Capsule strength parallel and perpendicular to collagen fiber orientation was 1.90 and 0.95 MPa, respectively, and extensibility was 0.65 and 0.60, respectively. Poisson’s ratio parallel and perpendicular to fiber orientation was 0.299 and 0.488, respectively. The elasticity moduli were nonlinear and anisotropic, and capsule strength was larger aligned parallel to the collagen fibers. The phase lag between stress and strain increased with haversine frequency, but the storage modulus remained large relative to the complex modulus. The stress relaxation rate was strain dependent parallel to the collagen fibers, but was strain independent perpendicularly.

Cyclic deformation and fatigue properties of Al-0.7 wt.% Cu alloy produced by equal channel angular pressing

Abstract: Fatigue damage behavior of an Al–0.7 wt.% Cu alloy, produced by equal channel angular pressing (ECAP) technique, was investigated under constant plastic strain control. It showed that the Al–0.7 wt.% Cu alloy displayed obvious cyclic softening at all the strain amplitudes. The cyclic softening can be attributed to a combination of higher yield strength and hysteresis energy density than the original material. The plastic deformation was carried out by shear bands at low or medium strain ranges, or by both shear bands and coarse deformation bands at high strain ranges. Consequently, fatigue cracks nucleated either along shear bands or along the coarse deformation bands, depending on the applied strain amplitude.

Quantification of temperature, stress, and strain fields during the start-up phase of direct chill casting process by using a 3D fully coupled thermal and stress model for AA5182 ingots

Abstract: A comprehensive coupled thermal-stress mathematical model, based on the commercial finite element (FE) package ABAQUS™, 1 has been formulated to describe thermal and stress–strain fields during the start-up phase of the direct chill (DC) casting process for AA5182 aluminum ingots. The computational domain includes industry-scale ingot and bottom block geometries. The heat transfer analysis incorporates the thermal boundary conditions that describe primary cooling via the mold, secondary cooling via the chill water, and ingot base cooling. To quantify the extent of secondary cooling, boiling curves that are a function of ingot surface temperature, water flow rate, impingement point temperature, and position relative to the point of water impingement have been used. Other complex heat transfer phenomena including water ejection on the vertical faces of the ingot, and water incursion into the gap at the base of the ingot have also been accounted for. The stress analysis employs a temperature dependent elastic rate-dependent plastic material constitutive behavior to quantify the stress and strain fields inside the ingot. The model has been validated against temperature and displacement measurements obtained from two 711 mm × 1680 mm AA5182 ingots, cast under different start-up conditions (non-typical “cold” practice and non-typical “hot” practice). The stress analysis was further validated by residual stress data obtained from the cold cast ingot. Comparison of the model predictions with the industrial and laboratory data indicates that the model is capable of satisfactorily simulating aspects of the thermomechancial behavior of the ingot during the start-up phase. The model has been applied in a preliminary way to analyze the problem of hot tearing in ingots during the startup phase. The need for further refinement of the mesh has been identified.

Numerical Validation of the Shear Compression Specimen. Part I: Quasi-static Large Strain Testing

Abstract: The shear compression specimen (SCS), which is used for large strain testing, is thoroughly investigated numerically using three-dimensional elastoplastic finite element simulations. In this first part of the study we address quasi-static loading. A bi-linear material model is assumed. We investigate the effect of geometrical parameters, such as gage height and root radius, on the stress and strain distribution and concentration. The analyses show that the stresses and strains are reasonably uniform on a typical gage mid-section, and their average values reflect accurately the prescribed material model. We derive accurate correlations between the averaged von Mises stress and strain and the applied experimental load and displacement. These relations depend on the specimen geometry and the material properties. Numerical results are compared to experimental data, and an excellent agreement is observed. This study confirms the potential of the SCS for large strain testing of material.