Showing papers on "Stress–strain curve published in 2001"

A split Hopkinson pressure bar technique to determine compressive stress-strain data for rock materials

Abstract: This paper presents a split Hopkinson pressure bar technique to obtain compressive stress-strain data for rock materials. This technique modifies the conventional split Hopkinson bar apparatus by placing a thin copper disk on the impact surface of the incident bar. When the striker bar impacts the copper disk, a nondispersive ramp pulse propagates in the incident bar and produces a nearly constant strain rate in a rock sample. Data from experiments with limestone show that the samples are in dynamic stress equilibrium and have constant strain rates over most of the test durations. In addition, the ramp pulse durations can be controlled such that samples are unloaded just prior to failure. Thus, intact samples that experience strains beyond the elastic region and postpeak stresses can be retrieved for microstructural evaluations. The paper also presents analytical models that predict the time durations for sample equilibrium and constant strain rate. Model predictions are in good agreement with measurements.

Complete Triaxial Stress-Strain Curves of High-Strength Concrete

Abstract: The axial-stress–axial-strain and axial-stress–lateral-strain behavior of concrete under active lateral confinement is presented. The uniaxial strengths investigated are 41.9 MPa, 60.6 MPa, 73.1 MPa, and 103.3 MPa. The confining pressures (σ3) used are 4 MPa, 8 MPa, and 12 MPa. Details of an economical lateral-strain-measuring device used in this investigation to produce accurate and repeatable measurements are presented. For low levels of confinement, the constant in the Mohr-Coulomb failure criterion (k) is shown to be closer to five than the traditional value of four. The axial strain at peak stress is shown to have a strong linear relationship with the level of confinement. Parameter values are suggested for Ottosen's constitutive model based on nonlinear elasticity. It was discovered that descending portion of the nonlinearity index (β) versus the secant value of Poisson's ratio (νa) was independent of the uniaxial strength and the level of confinement. A simple model is proposed for the descending p...

Derivation of plastic stress–strain relationship from ball indentations: Examination of strain definition and pileup effect

Abstract: The ball indentation technique has the potential to be an excellent substitute for a standard tensile test, especially in the case of small specimens or property-gradient materials such as welds. In our study, the true stress–true strain relationships of steels with different work-hardening exponents (0.1–0.3) were derived from ball indentations. Four kinds of strain definitions in indentation were attempted: 0.2sinγ, 0.4hc/a, ln[2/(1 + cosγ)], and 0.1tanγ. Here, γ is the contact angle between the indenter and the specimen, hc is the contact depth, and a is the contact radius. Through comparison with the standard data measured by uniaxial tensile testing, the best strain definition was determined to be 0.1tanγ. This new definition of strain, in which tanγ means the shear strain at contact edge, reflected effectively the work-hardening characteristics. In addition, the effects of pileup or sink-in were considered in determining the real contact between the indenter and the specimen from the indentation load–depth curve. The work-hardening exponent was found to be a main factor affecting the pileup/sink-in phenomena of various steels. These phenomena influenced markedly the absolute values of strain and stress in indentation by making the simple traditional relationship Pm/σR ≈ ≈ 3 valid for the fully plastic regime.

Stress-Strain Behavior of High-Strength Concrete Confined by Ultra-High-and Normal-Strength Transverse Reinforcements

Abstract: In situations where high-strength concrete (HSC) is used for reinforced concrete members subjected to seismic loading, it is more difficult to achieve ductile behavior of such members than when normal-strength concrete is used. This paper presents an experimental study of a number of quasi-static axial loading tests on HSC specimens confined by various amounts of transverse reinforcement. A stress-strain relationship for confined HSC is proposed that is found to give reasonably good prediction of the experimental behavior of circular and square specimens with HSC confined by either normal- or ultra-high-yield-strength with various configurations. An empirical formula for the ultimate longitudinal strain of confined HSC corresponding to the first hoop or spiral fracture is also proposed.

The ‘size effect’ on the stress–strain, fatigue and fracture properties of thin metallic foils

Abstract: In this investigation a microtensile machine in combination with a non-contacting laser-optical speckle correlation sensor to determine strain with high resolution was used to study the stress-strain behavior of thin metallic foils of Cu and Al with varying thickness ranging between 10 and up to 250 μm. The grain sizes varied between 2 and up to 250 μm. A size effect was detected resulting in an influence mainly on the fracture strain. This effect will be explained on the basis of texture differences, the number of activated gliding systems as a dependence on the ratio of grain size to foil thickness. To support these experimental findings the fracture topography has also been investigated. In addition, the fatigue crack propagation properties of the above mentioned Cu foils were studied as function of thickness. Using a specially designed fatigue testing set-up it was feasible to determine crack growth curves from free-standing foils. Depending on thickness, an unexpected crack growth behavior was detected. Using the ECCI technique it was feasible to study the interaction of the global dislocation arrangement with the crack tip.

Embedded optical fiber Bragg grating sensor in a nonuniform strain field: Measurements and simulations

Abstract: This paper investigates the use of embedded optical fiber Bragg gratings to measure strain near a stress concentration within a solid structure. Due to the nature of a stress concentration (i.e., the strong nonuniformity of the strain field), the assumption that the grating spectrum in reflection remains a single peak with a constant bandwidth is not valid. Compact tension specimens including a controlled notch shape are fabricated, and optical fiber Bragg gratings with different gage lengths are embedded near the notch tip. The form of the spectra in transmission varies between gages that are at different distances from the notch tip under given loading conditions. This variation is shown to be due to the difference in the distribution of strain along the gage length. By using the strain field measured using electronic speckle pattern interferometry on the specimen surface and a discretized model of the grating, the spectra in transmission are then calculated analytically. For a known strain distribution, it is then shown that one can determine the magnitude of the applied force on the specimen. Thus, by considering the nonuniformity of the strain field, the optical fiber Bragg gage functions well as an embedded strain gage near the stress concentration.

Stress-Strain Relations for Cracked Tensile Concrete from RC Beam Tests

Abstract: A method for determining the stress-strain relations for concrete form short-term flexural tests of reinforced concrete members is proposed. The method is based on the smeared crack approach. Average stress-strain relations for concrete in tension (including the descending branch) and in compression are computed from experimental moment-average strain and/or moment-curvature curves. Computation of stress-strain relations is performed incrementally for the extreme surface fibers, and is based on a novel idea of using the previously computed portions of the stress-strain relations at each load increment to compute the current increments of the stress-strain relations. The proposed method has been applied to some experimental data reported in the literature. Average stress-strain curves for concrete in tension, where cracking, bond, and shrinkage effects were taken into account in an integrated manner, have been computed for beams with various depths, reinforcement ratios, and rebar diameters. These and othe...

Thin hard coatings stress–strain curve determination through a FEM supported evaluation of nanoindentation test results

Abstract: The widespread use of thin hard physical vapor deposited (PVD) coatings in various technical applications necessitates the precise knowledge of their mechanical properties. Up to now the coating elasticity and plasticity properties were approached with the aid of simplified considerations of the nanoindentation procedure and a consequent evaluation of the obtained nanohardness measurement results, depending, however, on the indentation load. In the present paper a continuous finite elements method (FEM) simulation of the nanoindentation hardness test is introduced in order to describe the coating elastic and plastic deformation during this test and herewith to extract precisely and independent of the indentation load the coating stress–strain curve. Characteristic applications of the developed procedure demonstrate the adequacy of this method to determine the coatings constitutive laws of various coating materials deposited under different conditions.

Disturbed stress field model for reinforced concrete: implementation

Abstract: The Disturbed Stress Field Model (DSFM) is a smeared delayed-rotating-crack model, proposed recently as an alternative to fully fixed or fully rotating crack models, for representing the behavior of cracked reinforced concrete. It is an extension of the modified compression field theory; advancements relate to the inclusion of crack shear slip in the element compatibility relations, the decoupling of principal stress and principal strain directions, and a revised look at compression softening and tension stiffening mechanisms. This paper describes a procedure for implementing the formulations of the DSFM into a nonlinear finite-element algorithm. The procedure is based on a total-load secant-stiffness approach, wherein the crack slip displacements are treated as offset strains. Computational aspects of the formulation are shown to be simple and numerically robust. The hybrid crack slip formulation used is found to accurately model the divergence of stress and strain directions, providing an improved representation of behavior. Predictions of shear strength and failure mode are significantly influenced in some cases.

Tensile properties of Argiope trifasciata drag line silk obtained from the spider's web

Abstract: The tensile properties of Argiope trifasciata (Argiopidae) drag line silk retrieved from mooring threads in the web were characterized. Scanning electron microscope images were used to determine the cross-sectional area of the samples, allowing force-displacement plots to be rescaled as stress–strain curves and to characterize fracture surfaces. Twenty-eight samples were tested to obtain statistically significant values of the mechanical parameters (elastic modulus, stress and strain at the proportional limit, and tensile strength). The tensile strength of the material was subjected to a Weibull analysis—the first time that this has been attempted with a spider silk. A low value of the Weibull modulus, m = 3.4, was obtained, demonstrating that drag line monofilament does not have a sufficiently reliable tensile strength to function as an engineering material on its own. © 2001 John Wiley & Sons, Inc. J Appl Polym Sci 82: 2245–2251, 2001

Flip chip on board solder joint reliability analysis using 2-D and 3-D FEA models

Abstract: This study investigates the effects of employing different two-dimensional (2-D) and three-dimensional (3-D) finite element analysis (FEA) models for analyzing the solder joint reliability performance of a flip chip on board assembly. The FEA models investigated were the 2-D-plane strain, 2-D-plane stress, 3-D-1/8th symmetry and 3-D-strip models. The different stress and strain responses generated by the four different FEA models were applied to various solder joint low cycle fatigue life prediction relationships. The investigation shows that the 2-D-plane strain and 2-D-plane stress models gave the highest and lowest solder joint strains, respectively. The 3-D-strip and 3-D-1/8th symmetry model results fall in between the 2-D-plane strain and 2-D-plane stress model results. The 3-D-1/8th symmetry model agrees better with the 2-D-plane strain model, while the 3-D-strip model agrees better with the 2-D-plane stress model results. The results for the fatigue life prediction analyses also show similar trends.

Elasto-plastic stress and strain behaviour at notch roots under monotonic and cyclic loadings:

Abstract: Notch deformation behaviour under monotonic and cyclic loading conditions was investigated using circumferentially notched round bar and double-notched flat plate geometries, each with two different notch concentration factors. Notch strains for the double-notched plate geometry were measured with the use of miniature strain gauges bonded to specimens made of a vanadium-based microalloyed steel. Elastic as well as elasto-plastic finite element analyses of the two geometries were performed. Notch root strains and stresses were predicted by employing the linear rule, Neuber's rule and Glinka's rule relationships under both monotonic and cyclic loading conditions. The predicted results are compared with those from elastic-plastic finite element analyses and strain gauge measurements. Effects of notch constraint and the material stress-strain curve on the notch root stress and strain predictions are also discussed.

FE investigation of the effect of particle distribution on the uniaxial stress–strain behaviour of particulate reinforced metal-matrix composites

Abstract: A multi-particle 2D finite element model of a 20% particulate reinforced metal-matrix composite was developed on a statistical basis taking into account the correlations between the position, size and orientation of the ceramic particles in the matrix. The stress–strain curves in tension and compression given by the clustered multi-particle model are compared with the curves obtained from one-particle unit cell simulations. It is shown that clustering of particles increases the plastic strain accumulated in the matrix leading to a higher strain hardening and thus to a higher flow stress. The size of the representative volume element (RVE) should be at least equal to the correlation length of the geometrically relevant correlation functions, which was ∼2.4 times larger than the average interparticle distance for the experimentally studied case. Reasonable agreement is obtained between computed residual strains and data available in the literature.

Tensile mechanical behavior of T300 and M40J fiber bundles at different strain rate

Abstract: Tensile mechanical behavior of T300 fiber bundles and M40J fiber bundles have been studied in the strain rate range from 0.001 1/s to 1300 1/s and complete stress strain curves were obtained. Results show that both ultimate strength and failure strain of two materials are strain rate insensitive, and T300 fiber and M40J fiber can be regarded as strain rate insensitive materials. On basis of the fiber bundles model and the statistic theory of fiber strength, single Weibull distribution model and bimodal Weibull distribution model have been developed to describe mechanical behavior of fiber bundles. And a method for determine the statistic parameters of fibers by tensile tests of fiber bundles is established, too. The simulated stress strain curves from the model are in good agreement with the test data. Simulated results show that the strength of T300 fiber can be described by single Weibull distribution function, and the strength of M40J fiber should be described by bimodal Weibull distribution function.