Showing papers on "Stress–strain curve published in 2011"

Effect of microstructure on retained austenite stability and work hardening of TRIP steels

Abstract: Retained austenite is a metastable phase in transformation induced plasticity (TRIP) steels that transforms into martensite under local stress and strain. This transformation improves sheet formability, allowing this class of higher strength steels to be used for applications such as automotive structural components. The current work studies two distinct TRIP steel microstructures, i.e. equiaxed versus lamellar, and how microstructure affects the austenite transformation during uniaxial tensile loading. Different heat treatments were employed to obtain the two microstructures, and the bainite hold times of the treatments were varied to change the volume fraction of retained austenite. Based on uniaxial tensile response and magnetic saturation measurements, the bainite hold time of 100 s was determined to produce the best results in terms of largest strain at the ultimate tensile strength and highest volume fraction of retained austenite. The work hardening of the samples with a 100 s bainite hold was evaluated by calculating the instantaneous n value as a function of strain. It was found that the lamellar microstructure has a lower maximum instantaneous n value than the equiaxed microstructure, but has higher work hardening values for strain levels greater than 0.05 and up to the ultimate tensile strength. This difference in work hardening behaviour corresponds directly to the transformation rate of retained austenite in the two microstructures. The slower rate of transformation in the lamellar microstructure allows for work hardening to persist at high strains where the transformation effect has already been exhausted in the equiaxed microstructure. The different rates of transformation can be attributed to the location, carbon content, and size of the retained austenite grains in the respective TRIP microstructures.

Deformation of Earth Materials : an Introduction to the Rheology of Solid Earth

Abstract: Part I. General Background: 1. Stress and strain 2. Thermodynamics 3. Phenomenological theory of deformation Part II. Materials Science of Deformation: 4. Elasticity 5. Crystalline defects 6. Experimental techniques in the study of plastic deformation 7. Brittle fracture, brittle-plastic transition 8. Diffusional creep 9. Dislocation creep 10. Effects of pressure and water 11. Physical mechanisms of seismic wave attenuation 12. Deformation of multi-phase materials 13. Grain size 14. Lattice preferred orientation 15. Effects of phase transformations 16. Stability and localization of deformation Part III. Geological and Geophysical Applications: 17. Composition and structure of Earth's interior 18. Time-dependent deformation of Earth and rheological structures 19. Inference of rheological structure of Earth from mineral physics 20. Heterogeneity of seismic wave velocities and its geodynamic significance 21. Seismic anisotropy and its geodynamic significance References Index.

Strain hardening behavior of a TRIP/TWIP steel with 18.8% Mn

Abstract: Tensile tests were carried out to study the strain hardening behavior of a TRIP/TWIP steel with 18.8% manganese. The results indicated that the true stress–strain curve can be divided into 4 stages in tension testing. Material is in an elastic region when the true strain is below 0.06. In the initial stage of the plastic deformation (ɛ = 0.06–0.14), ɛ-martensite was preliminarily formed, and that austenite transformed to α-martensite through the ɛ-martensite formation. When the true strain was between 0.14 and 0.35, the stacking fault energies were elevated by the increase of strain energy, deformation twinning occurred instead of the ɛ-martensite formation. The second derivative of the stress–strain curve satisfied the condition d2σ/dɛ2 > 0. Twinning induced plasticity dominated this stage. In the last plastic deformation stage (ɛ = 0.35–0.45), γ → α transformation occurred at the crossing of twins, and α-martensite grew along the thickness of the twinned regions.

Constitutive modeling for the dynamic recrystallization evolution of AZ80 magnesium alloy based on stress–strain data

Abstract: In order to improve the understanding of the dynamic recrystallization (DRX) behaviors of as-cast AZ80 magnesium alloy, a series of isothermal upsetting experiments with height reduction 60% were performed at the temperatures of 523 K, 573 K, 623 K and 673 K, and the strain rates of 001 s−1, 01 s−1, 1 s−1 and 10 s−1 on a Gleeble 1500 thermo-mechanical simulator Dependence of the flow stress on temperature and strain rate is described by means of the conventional hyperbolic sine equation By regression analysis, the activation energy of DRX in the whole range of deformation temperature was determined to be Q = 21582 kJ mol−1 Based on dσ/dɛ versus σ curves and their processing results, the flow stress curves for AZ80 magnesium alloy were evaluated that they have some characteristic points including the critical strain for DRX initiation (ɛc), the strain for peak stress (ɛp), and the strain for maximum softening rate (ɛ*), which means that the evolution of DRX can be expressed by the process variables In order to characterize the evolution of DRX volume fraction, the modified Avrami type equation including ɛc and ɛ* as a function of the dimensionless parameter controlling the stored energy, Z/A, was evaluated and the effect of deformation conditions was described in detail Finally, the theoretical prediction on the relationships between the DRX volume fractions and the deformation conditions were validated by the microstructure graphs

Effect of twinning, slip, and inclusions on the fatigue anisotropy of extrusion-textured AZ61 magnesium alloy

Abstract: In this study, experiments were conducted to quantify structure-property relations with respect to fatigue of an extruded AZ61 magnesium alloy using a MultiStage Fatigue (MSF) model. Experiments were conducted in the extruded and transverse directions under low and high cycle strain control fatigue conditions. The cyclic behavior of this alloy displayed varying degrees of twinning and slip depending on the strain amplitude as observed in the hysteresis loops of both directions. Under low cyclic conditions, asymmetrical stress strain response was observed for both orientations. However, systematic stabilization of the hysteresis occurred by half-life due to subsequent twinning and detwinning mechanisms. In addition, under high cycle fatigue, pseudo-elasticity was observed at the first and at half-life cycles. Structure-property relations were quantified by examining the fracture surfaces of the fatigued specimens using a scanning electron microscope. In terms of crack incubation, fatigue cracks were found to initiate from intermetallic particles (inclusions) that were typically larger than the mean size. Quantified sources of fatigue crack incubation, microstructurally small cracks, and cyclic stress–strain behavior were correlated to the MSF model. Based on the specific material parameters, the MSF model was able to predict the difference in the strain-life results of the AZ61 magnesium alloy in the extruded and extruded transverse directions including the scatter of the experimental results. Finally, the MSF model revealed that the inclusion size was more important in determining the fatigue life than the anisotropic effects from the texture, yield, and work hardening.

Determination of Mechanical Properties of Sand Grains by Nanoindentation

Abstract: Determination of the mechanical properties of individual sand grains by conventional material testing methods at the macroscale is somewhat difficult due to the sizes of the individual sand particles (a few μm to mm). In this paper, we used the nanoindentation technique with a Berkovich tip to measure the Young’s modulus, hardness, and fracture toughness. An inverse problem solving approach was adopted to determine the stress-strain relationship of sand at the granular level using the finite element method. A cube-corner indenter tip was used to generate radial cracks, the lengths of which were used to determine the fracture toughness. Scatter in the data was observed, as is common with most brittle materials. In order to consider the overall mechanical behavior of the sand grains, statistical analysis of the mechanical properties data (including the variability in the properties) was conducted using the Weibull distribution function. This data can be used in the mesoscale simulations.

Stress-Block Parameters for Unconfined and Confined Concrete Based on a Unified Stress-Strain Model

Abstract: Equations to obtain equivalent rectangular stress-block parameters for unconfined and confined concrete are derived for rapid (hand) analysis and design purposes. To overcome a shortcoming of existing commonly used stress-strain models that are not easy to integrate, a new stress-strain model is proposed and validated for a wide range of concrete strengths and confining stresses. The efficacy of the equivalent rectangular stress-block parameters is demonstrated for hand calculations in predicting key moment-curvature results for a confined concrete column. Results are compared with those obtained from a computational fiber-element analysis using the proposed stress-strain model and another widely used existing model; good agreement between the two is observed.

Modification of properties of structural lightweight concrete with steel fibres

Abstract: Structural lightweight aggregate concrete (SLWAC) is an alternative building material to normal-weight one, due to its ability to reach a relatively high compressive strength at still significantly lower density. Nevertheless, the application of lightweight aggregate instead of normal-weight one to concrete must result in deterioration of some characteristics of the composite. One of the methods of improving SLWAC properties is incorporation of fibers into concrete. This paper focuses on the influence of steel fibres on modification of properties of structural lightweight concrete with sintered fly ash aggregate. Two different concrete mixtures, producing various levels of matured composite density and compressive strength, were modified with three dosages of fibers: 30, 45 and 60 kg/m3. The applied amounts did not result in significant deterioration of the rheological parameters of concrete mixtures. Despite relatively low volume content of fibres, a considerable increase of flexural and tensile...

Strain rate effect on the tensile behaviour of textile-reinforced concrete under static and dynamic loading

Abstract: This paper presents the results of an experimental investigation into the strength, deformation, and fracture behaviour of textile-reinforced concrete (TRC) subjected both to low and high-rate tensile loading ranging from 0.0001 to 50 s −1 . High strain rates were achieved using a high-rate servo-hydraulic testing machine. The effect of the addition of short fibres on the static and dynamic response of TRC has been investigated, and the microstructure of both composite and fibre was observed after the tests using an ESEM. An increase in tensile strength, strain capacity, and work-to-fracture was observed for strain rates up to 0.1 s −1 with increasing strain rate. The addition of short glass fibres increased the tensile strength and first crack strength of the TRC. For high-speed tests (rates above 5 s−1) an increase in the tensile strength, first crack strength and work-to-fracture was also observed, but at the same time there was a decrease in the strain capacity. The tests at high loading rates showed a pronounced effect of the specimen length on the measured mechanical properties: with increasing gauge length the tensile strength and strain capacity decreased, while the work-to-fracture increased. © 2010 Elsevier B.V. All rights reserved.

Effect of freeze–thaw cycles on the stress–strain curves of unconfined and confined concrete

Abstract: An experimental research was performed on the complete compressive stress–strain relationship for unconfined and confined concrete after exposure to freeze–thaw cycles. For the unconfined concrete, tests were carried out on three series of prisms specimens (100 mm × 100 mm × 300 mm) with water/cement ratio of 0.60, 0.54 and 0.48 respectively. While for confined concrete, two series of tied columns (150 mm × 150 mm × 450 mm prisms) with confinement index of 0.317 and 0.145 were prepared. Analytical models for the stress–strain relationship of frozen-thawed unconfined and confined concrete were empirically developed respectively. Through the regression analysis, formulations for the main parameters were established, including the compressive strength, peak strain and elastic modulus. Compared with the available experimental data, the proposed models were shown to be applicable to concrete after different numbers of freeze–thaw cycles.

Unified calculation method and its application in determining the uniaxial mechanical properties of concrete

Abstract: This paper presents a unified calculation method and its application in determining the uniaxial mechanical properties of concrete with concrete strengths ranging from 10 to 140 MPa. By analyzing a large collection of test results of the uniaxial mechanical properties of normal-strength, high-strength and super high-strength concrete in China and performing a regression analysis, unified calculation formulas for the mechanical indexes of concrete are proposed that can be applied to various grades of concrete for determining the size coefficient, uniaxial compressive strength, uniaxial tensile strength, elastic modulus, and strain at peak uniaxial compression and tension. Optimized mathematical equations for the nonlinear stress-strain relationship of concrete, including the ascending and descending branches under uniaxial stress, are also established. The elastic modulus is almost constant throughout the elastic stage for the ascending branches of the stress-strain relationship for concrete. The proposed stress-strain relationship of concrete was applied to the nonlinear finite element analysis of both a steel-concrete composite beam and a concrete-filled steel tubular stub column. The analytical results are in good agreement with the experiment results, indicating that the proposed stress-strain relationship of concrete is applicable. The achievements presented in this paper can be used as references for the design and nonlinear finite element analysis of concrete structures.

Damage and rupture dynamics at the brittle-ductile transition: The case of gypsum

Abstract: [1] Triaxial tests on gypsum polycrystal samples are performed at confining pressure (Pc) ranging from 2 to 95 MPa and temperatures up to 70°C. During the tests, stress, strain, elastic wave velocities, and acoustic emissions are recorded. At Pc ≤ 10 MPa, the macroscopic behavior is brittle, and above 20 MPa the macroscopic behavior becomes ductile. Ductile deformation is cataclastic, as shown by the continuous decrease of elastic wave velocities interpreted in terms of microcrack accumulation. Surprisingly, ductile deformation and strain hardening are also accompanied by small stress drops from 0.5 to 6 MPa in amplitude. Microstructural observations of the deformed samples suggest that each stress drop corresponds to the generation of a single shear band, formed by microcracks and kinked grains. At room temperature, the stress drops are not correlated to acoustic emssions (AEs). At 70°C, the stress drops are larger and systematically associated with a low-frequency AE (LFAE). Rupture velocities can be inferred from the LFAE high-frequency content and range from 50 to 200 m s−1. The LFAE amplitude also increases with increasing rupture speed and is not correlated with the amplitude of the macroscopic stress drops. LFAEs are thus attributed to dynamic propagation of shear bands. In Volterra gypsum, the result of the competition between microcracking and plasticity is counterintuitive: Dynamic instalibilities at 70°C may arise from the thermal activation of mineral kinking.

Hot deformation behavior of austenite in HSLA-100 microalloyed steel

Abstract: Dynamic recrystallization of austenite in the Cu-bearing HSLA-100 steel was investigated by hot compression testing at a temperature range of 850–1150 °C and a strain rate of 0.001–1 s −1 . The obtained flow curves at temperatures higher than 950 °C were typical of DRX while at lower temperatures the flow curves were associated with work hardening without any indication of DRX. At high temperatures, flow stress exhibited a linear relation with temperature while at temperatures below 950 °C the behavior changed to non-linear. Hence, the temperature of 950 °C was introduced as the T nr of the alloy. All the flow curves showed a yield point elongation like phenomenon which was attributed to the interaction of solute atoms, notably carbon, and moving dislocations. The maximum elongation associated with the yield point phenomenon was observed at about 950 °C. Since the maximum yield point elongation was observed about the calculated T nr , it was concluded that carbon atoms were responsible for it. It was also concluded that the temperature at which the yield point elongation reaches the maximum value increases as strain rate rises. The stress and strain of the characteristic points of DRX flow curves were successfully correlated to the Zener–Hollomon parameter, Z , by power-law equations. The constitutive exponential equation was found more precise than the hyperbolic sine equation for modeling the dependence of flow stress on Z . The apparent activation energy for DRX was determined as 377 kJ mol −1 . The kinetics of DRX was modeled by an Avrami-type equation and the Avrami's exponent was determined around 1.1.

Effect of Strain Rate on the Stress-Strain Behavior of Sand

Abstract: Drained triaxial compression tests on crushed coral sand were performed from near-static strain rates to very high strain rates (up to approximately 1,800%/s). Experiments were performed on dry, vacuum-confined axisymmetric specimens at two different confining pressures (98 and 350 kPa) and two different densities (Dr approximately 36 and 60%). A gravity drop weight loading system was used to generate high strain rates. High-speed film photographs of the specimen were taken through the flat sides of a square triaxial cell. By using digital image analysis techniques, strains were locally measured near the center of the specimen to obtain the most uniform assessment. Stress-strain relationships are presented. The following effects were observed with increasing strain rates: the elastoplastic stiffness increased significantly; the failure shear strength increased moderately; the axial strain at peak stress decreased significantly; and volumetric strains became more dilatant. Unusual behavior was observed at ...

Effect of recycling on rheological and mechanical properties of poly(lactic acid)/polystyrene polymer blend

Abstract: A continued increase in the use of plastics has led to an increasing amount of plastics ending up in the waste stream; and the increasing cost of landfill disposal and public interest in support of recycling has meant that plastics recycling must increase. In this work, the effect of multiple extrusion and injection of poly(lactic acid)/polystyrene polymer blend (PLA/PS) on its rheological and mechanical properties is presented. Rheological properties were studied using a capillary rheometer, apparent shear rate (γ a), apparent shear stress (τ a), apparent viscosity (η a), and flow activation energy were determined. The mechanical properties of the blend were investigated on dog bone-shaped samples obtained by injection molding, tensile tests were performed, stress at break, strain at break, and Young’s modulus were determined. The results showed that the apparent viscosity of PLA/PS blend decreases monotonously with increasing the processing number. Also it was found that stress and strain at break of the blend decrease sharply after two processing cycles, whereas the processing number has a little effect on Young’s modulus.