Showing papers on "Stress–strain curve published in 2002"

Constitutive analysis in hot working

Abstract: Constitutive equations including an Arrhenius term have been commonly applied to steels with the objective of calculating hot rolling and forging forces. The function relating stress and strain rate is generally the hyperbolic-sine since the power and exponential laws lose linearity at high and low stresses, respectively. In austenitic steels, the equations have been used primarily for the peak stress (strain) associated with dynamic recrystallization (DRX) but also for the critical and steady state stresses (strains) for nucleation and first wave completion of DRX. Since the peak strain is raised by the presence of solutes and fine particles, the stress is raised more than by simple strain hardening increase, thus causing a marked rise in activation energy in alloy steels. In contrast, large carbides, inclusions or segregates, if hard, may lower the peak strain as a result of particle stimulated nucleation. Due to the linear relation between stress and strain at the peak, flow curves can be calculated from the constitutive data with only one additional constant. Maximum pass stresses can also be calculated from a sinh constitutive equation determined in multistage torsion simulations of rolling schedules. Comparison is made between carbon, micro-alloyed, tool and stainless steels and to ferritic steels which usually do not exhibit DRX. Parallels to the effects of impurities and dispersoids on the constitutive equations for Al alloys are briefly discussed.

Correlations between Mechanical Properties of High-Strength Concrete

Abstract: This paper discusses some important engineering properties of plain concrete for a wide range of compressive strength. A large volume of selected experimental data has been collected from existing literature and then analyzed. Particular emphasis has been given to studying the effects of concrete strength on the modulus of elasticity, tensile strength (flexural and splitting tensile), and Poisson’s ratio of concrete. Study on the effect of the size of specimens on the compressive strength and modulus of elasticity of concrete has also been included. The adequacy of some of the familiar relationships for predicting the modulus of elasticity and tensile strengths of concrete has been critically examined, and suitable expressions are suggested to cover concrete strength up to 120 MPa.

Mechanical properties of individual southern pine fibers. Part I. Determination and variability of stress-strain curves with respect to tree height and juvenility

Abstract: This paper is the first in a three-part series investigating the mechanical properties of loblolly pine fibers. This paper outlines the experimental method and subsequent variation of latewood fiber mechanical properties in relation to tree position. Subsequent papers will deal with differences between earlywood and latewood fibers and effect of juvenility and tree height on global fiber properties. In this paper, the mechanical properties were determined on individual wood fiber with a user-built tensile testing apparatus. Cross-sectional areas of post-tested fibers were determined with a confocal scanning laser microscope and used to convert acquired load-elongation curves into stress-strain curves. The modulus of elasticity and ultimate tensile stress of loblolly pine latewood fibers tested in this study ranged from 6.55 to 27.5 GPa and 410 to 1,422 MPa, respectively. Fibers from the juvenile core of the main stem were on the low end of the mechanical property scale, whereas fibers beyond the twentieth growth ring were near the high end of the scale. Coefficient of variation for fiber stiffness and strength averaged around 20 to 25%. The shape of the fiber stress-strain curves is dependent on their growth ring origins: Mature fibers were linear from initial loading until failure, whereas juvenile fibers demonstrated curvilinearity until about 60% of maximum load followed by linear behavior to failure.

A critical-strain criterion for hydrogen embrittlement of cold-drawn, ultrafine pearlitic steel

Abstract: A stress-modified, critical-strain model of fracture-initiation toughness has been adapted to the case of hydrogen-affected pearlite shear cracking, which is a critical event in transverse fracture of cold-drawn, pearlitic steel wire. This shear cracking occurs via a process of cementite lamellae failure, followed by microvoid nucleation, growth, and linkage to create shear bands that form across pearlite colonies. The key model feature is that the intrinsic resistance to shear-band cracking at a transverse notch or crack is related to the effective fracture strain at the notch root. This fracture strain decreases with the logarithm of the diffusible hydrogen concentration (C H). Good agreement with experimental transverse fracture-initiation-toughness values was obtained when the sole adjustable parameter of the model, the critical microstructural dimension (l*), was set to the mean dimension of shearable pearlite colonies within this steel. The effect of hydrogen was incorporated through the relationship between local effective plastic strain (ɛ eff f ) and C H, obtained from sharply and bluntly notched tensile specimens analyzed by finite-element analysis (FEA) to define stress and strain fields. No transition in the transverse fracture-initiation morphology was observed with increasing constraint or hydrogen concentration. Instead, shear cracking from transverse notches and precracks was enabled at lower global applied stresses when C H increased. This shear-cracking process is assisted by absorbed and trapped hydrogen, which is rationalized to either reduce the cohesive strength of the Fe/Fe3C interface, localize slip in ferrite lamellae so as to more readily enable shearing of Fe3C by dislocation pileups, or assist subsequent void growth and link-up. The role of hydrogen at these sites is consistent with the detected hydrogen trapping. Large hydrogen-trap coverages at carbides can be demonstrated using trap-binding-energy analysis when hydrogen-assisted shear cracking is observed at low applied strains.

The Equivalent Strain Energy Density approach re-formulated and applied to sharp V-shaped notches under localized and generalized plasticity

Abstract: In the case of a rounded notch, the stress and strain at the notch tip can be determined by the traditional Neuber rule or by the Equivalent Strain Energy Density (ESED) approach, as formulated by Glinka and Molski. In the latter case the elastoplastic strain energy density at the notch tip is thought of as coincident with that determined under purely elastic conditions. For sharply V-shaped notches this approach is not directly applicable, since the strain energy density at the notch tip tends toward infinity both for a material obeying an elastic law and a material obeying a power hardening law. By using the notch stress intensity factors, the present paper suggests a re-formulation of the ESED approach which is applied no longer at the notch tip but to a finite size circular sector surrounding the notch tip. In particular we have adopted the hypothesis that, under plane strain conditions, the value of the energy concentration due to the notch is constant and independent of the two constitutive laws. When small scale yielding conditions are present, such a hypothesis immediately results in the constancy of the strain energy averaged over the process volume. As a consequence, plastic notch stress intensity factors valid for sharp V-shaped notches can be predicted on the basis of the linear elastic stress distributions alone.

A generalized model for the uniaxial isothermal deformation of a viscoelastic body

Abstract: Using the notion of a fractional derivative we formulate a new model for a uniaxial deformation of a visco-elastic body. The basic assumption is that all derivatives σ(γ) with respect to time of the stress depend (with specified weighting factor) on all derivatives e(γ) with respect to time of the strain (multiplied with another weighting factor), for 0≤γ≤1. In this respect our model is a generalization of the Zener model, i.e., it is a Zener fractional model with infinitely many terms. The relation between stress and strain is given in explicit form. For two specific choices of parameters the behavior of the model under suddenly applied stress (creep) and suddenly applied strain (stress relaxation) are examined.

Mechanical Properties and Fracture Characterization of Cross-Linked PVC Foams:

Abstract: The tensile stress-strain response and fracture behavior of cross-linked PVC foams have been characterized over a range of foam densities from 36 to 400 kg/m3. The foams were found to be nearly isotropic. Young’s modulus, yield strength and fracture toughness data were compared to micro-structural relations derived for open and closed-cell foams. The failure process and stress strain response were indicative of brittle material behavior. Short gage length tension specimens bonded to aluminum loading blocks showed a tensile strength that increased with decreasing gage length as a result of improved support of the cell-walls of the foam under constrained lateral deformation. The plastic zone size for each of the fracture specimens, estimated from the von Mises yield criterion, was small indicating quasi-brittle failure. Testing of scaled single edged notch bend (SENB) fracture specimens revealed a toughness that decreases with decreasing specimen size.

Simple Performance Test for Fatigue Cracking and Validation with WesTrack Mixtures

Abstract: Viscoelastic characterization of asphalt concrete in indirect tensile (IDT) testing and development of a simple performance test for fatigue cracking are described A 50-mm gauge length was adopted to measure the horizontal and vertical deformations with surface-mounted linear variable differential transducers on an IDT specimen with a 100- or 150-mm diameter and 38-mm thickness The effect of a concentrated load under loading strips on vertical displacement within the 50-mm gauge length was evaluated by the digital image correlation method, a noncontact, full-field displacement and strain measurement technique The theory of viscoelasticity was used to develop analytical solutions for creep compliance and center strain from displacements measured on the specimen surface These solutions were verified by three-dimensional finite element viscoelastic analysis IDT creep and strength tests were performed on fine and coarse mixtures from WesTrack with various asphalt contents and air void contents, and vario

Stress-strain model for fiber-reinforced polymer-confined concrete

Abstract: The design of fiber-reinforced polymer (FRP)-confined concrete members requires accurate evaluation of the performance enhancement due to the confinement provided by FRP composite jackets. A strain ductility-based model is developed for predicting the compressive behavior of normal strength concrete confined with FRP composite jackets. The model is applicable to both bonded and nonbonded FRP-confined concrete and can be separated into two components: a strain-softening component, which accounts for unrestrained internal crack propagation in the concrete core, and a strain-hardening component, which accounts for strength increase due to confinement provided by the FRP composite jacket. A variable strain ductility ratio described in a companion paper is used to develop the proposed stress-strain model. Equilibrium and strain compatibility are used to obtain the ultimate compressive strength and strain of FRP-confined concrete as a function of the confining stiffness and ultimate strain of the FRP jacket.

Behavior of damaged and undamaged concrete strengthened by carbon fiber composite sheets

Abstract: Many existing concrete structures suffer from low quality of concrete and inadequate confinement reinforcement. These deficiencies cause low strength and ductility. Wrapping concrete by carbon fiber reinforced polymer (CFRP) composite sheets enhances compressive strength and deformability. In this study, the effects of the thickness of the CFRP composite wraps on the behavior of concrete are investigated experimentally. Both monotonic and repeated compressive loads are considered during the tests, which are carried out on strengthened undamaged specimens, as well as the specimens, which were tested and damaged priorly and strengthened after repairing. The experimental data shows that, external confinement of concrete by CFRP composite sheets improves both compressive strength and deformability of concrete significantly as a function of the thickness of the CFRP composite wraps around concrete. Empirical equations are also proposed for compressive strength and ultimate axial deformation of FRP composite wrapped concrete. Test results available in the literature, as well as the experimental results presented in this paper, are compared with the analytical results predicted by the proposed equations.

A finite element study of the stress and strain fields of InAs quantum dots embedded in GaAs

Abstract: We report on a stress and strain analysis, using the finite element method, of the heterosystem of InAs quantum dots embedded in GaAs. The methodology of using the finite element method to simulate the lattice mismatch is discussed and a three-dimensional (3D) model of the heterostructure shows the 3D stress distribution in the InAs islands embedded in a matrix of GaAs substrate and cap layer. The initial shape of the InAs islands is pyramidal. The stress and strain distribution calculated corresponds well with the strain induced by the lattice mismatch. Factors such as the height of the spacer layer and the height of the island are found to play an important role in the stress and strain distribution. With the island having the shape of a truncated pyramid, the stress and strain distribution deviates from that of a full pyramidal island showing the effects that a change of shape in the islands has on the stress field. The stress distribution contributes to the driving force for the mechanism of surface diffusion in molecular beam epitaxy. The effects of anisotropy on the strain distribution are also studied.

Effects of temperature and strain rate on the tensile behavior of short fiber reinforced polyamide-6

Abstract: Tensile behavior of extruded short E-glass fiber reinforced polyamide-6 composite sheet has been determined at different temperatures (21.5°C, 50°C, 75°C, 100°C) and different strain rates (0.05/min, 0.5/min, 5/min). Experimental results show that this composite is a strain rate and temperature dependent material. Both elastic modulus and tensile strength of the composite increased with strain rate and decreased with temperature. Experimental results also show that strain rate sensitivity and temperature sensitivity of this composite change at a temperature between 25°C and 50°C as a result of the glass transition of the polyamide-6 matrix. Based on the experimental stress-strain curves, a two-parameter strain rate and temperature dependent constitutive model has been established to describe the tensile behavior of short fiber reinforced polyamide-6 composite. The parameters in this model are a stress exponent n and a stress coefficient σ*. It is shown that the stress exponent n, which controls the strain rate strengthening effect and the strain hardening effect of the composite, is not only strain rate independent but also temperature independent. The stress exponent σ*, on the other hand, varies with both strain rate and temperature.

3D finite element analysis of particle-reinforced aluminum

Abstract: Deformation in particle-reinforced aluminum has been simulated using three distinct types of finite element model: a three-dimensional repeating unit cell, a three-dimensional multi-particle model, and two-dimensional multi-particle models. The repeating unit cell model represents a fictitious periodic cubic array of particles. The 3D multi-particle (3D-MP) model represents randomly placed and oriented particles. The 2D generalized plane strain multi-particle models were obtained from planar sections through the 3D-MP model. These models were used to study the tensile macroscopic stress-strain response and the associated stress and strain distributions in an elastoplastic matrix. The results indicate that the 2D model having a particle area fraction equal to the particle representative volume fraction of the 3D models predicted the same macroscopic stress-strain response as the 3D models. However, there are fluctuations in the particle area fraction in a representative volume element. As expected, predictions from 2D models having different particle area fractions do not agree with predictions from 3D models. More importantly, it was found that the microscopic stress and strain distributions from the 2D models do not agree with those from the 3D-MP model. Specifically, the plastic strain distribution predicted by the 2D model is banded along lines inclined at 45 deg from the loading axis while the 3D model prediction is not. Additionally, the triaxial stress and maximum principal stress distributions predicted by 2D and 3D models do not agree. Thus, it appears necessary to use a multi-particle 3D model to accurately predict material responses that depend on local effects, such as strain-to-failure, fracture toughness, and fatigue life.

Strength and durability performance of concrete axially loaded members confined with AFRP composite sheets

Abstract: The performance of concrete columns externally wrapped with aramid fiber reinforced polymer composite sheets is presented in this paper. The confined and unconfined (control) specimens were loaded in uniaxial compression. Axial load and axial and hoop strains were measured in order to evaluate stress–strain behavior, ultimate strength, stiffness, and ductility of the wrapped specimens. Results show that external confinement of concrete by fiber reinforced polymer (FRP) composite sheets can significantly enhance strength, ductility and energy absorption capacity. An analytical model developed earlier by the author to predict the entire stress–strain response of concrete specimens wrapped with FRP composite sheets was applied. Comparison between the experimental and analytical results indicates that the model provides satisfactory predictions of the stress–strain response. The paper also presents the performance of the wrapped concrete specimens subjected to severe environmental conditions such as wet–dry and freeze–thaw cycles. The specimens were exposed to 300 cycles of wetting and drying using salt water. Results show that specimens wrapped with aramid fibers experienced no reduction in strength due to wet/dry exposure, but some reduction was observed due to freeze/thaw exposure.

Calculation of the incremental stress-strain relation of a polygonal packing.

Abstract: The constitutive relation of the quasistatic deformation on two-dimensional packed samples of polygons is calculated using molecular dynamics simulations. The stress values at which the system remains stable are bounded by a failure surface, which shows a power law dependence on the pressure. Below the failure surface, nonlinear elasticity and plastic deformation are obtained, which are evaluated in the framework of the incremental linear theory. The results show that the stiffness tensor can be directly related to the microcontact rearrangements. The plasticity obeys a nonassociated flow rule with a plastic limit surface that does not agree with the failure surface.