Showing papers on "Stress–strain curve published in 2003"

Coupling of hydraulic hysteresis and stress–strain behaviour in unsaturated soils

Abstract: Consideration of the different roles of pore air pressure, pore water pressure within bulk water and pore water pressure within meniscus water suggests that the degree of saturation will have a significant influence on the stress–strain behaviour of an unsaturated soil, in addition to any influence of suction. This suggestion is supported by experimental evidence. In the light of this, a new elasto-plastic framework for unsaturated soils is proposed, involving coupling of hydraulic hysteresis and mechanical behaviour. Within the proposed framework, plastic changes of degree of saturation influence the stress–strain behaviour, and plastic volumetric strains influence the water retention behaviour. A specific constitutive model for isotropic stress states is proposed, and model predictions are compared with experimental results, in order to demonstrate some of the capabilities of the new framework. Forms of behaviour that can be represented include proper transitions between saturated and unsaturated types ...

Initiation of Dynamic Recrystallization in Constant Strain Rate Hot Deformation

Abstract: In constant strain rate tests, the occurrence of dynamic recrystallization (DRX) is traditionally identified from the presence of stress peaks in flow curves. However, not all materials display well-defined peaks when tested under these conditions. Using plain carbon, Nb-bearing and 321 austenitic stainless steels, it is shown that the onset of DRX can also be detected from inflections in plots of the strain hardening rate θ against stress a or, equivalently, from inflections in In θ-In a and In θ-e plots regardless the presence of stress peaks in the flow curves. These observations are verified by means of metallography. A unified description of the flow curve is introduced based on normalization of the stress and strain by the respective peak or steady state values. This approach reveals that, in a given material, the ratio of DRX critical stress to the peak or steady state stress is constant, as is that of the critical strain to the corresponding strain values. Furthermore, it is shown that the present technique can be used to establish the occurrence of DRX when this cannot be determined unambiguously from the shape of the flow curve.

Some characteristics of high strength fiber reinforced lightweight aggregate concrete

Abstract: The effect of polypropylene and steel fibers on high strength lightweight aggregate concrete is investigated. Sintered fly ash aggregates were used in the lightweight concrete; the fines were partially replaced by fly ash. The effects on compressive strength, indirect tensile strength, modulus of rupture, modulus of elasticity, stress–strain relationship and compression toughness are reported. Compared to plain sintered fly ash lightweight aggregate concrete, polypropylene fiber addition at 0.56% by volume of the concrete, caused a 90% increase in the indirect tensile strength and a 20% increase in the modulus of rupture. Polypropylene fiber addition did not significantly affect the other mechanical properties that were investigated. Steel fibers at 1.7% by volume of the concrete caused an increase in the indirect tensile strength by about 118% and an increase in the modulus of rupture by about 80%. Steel fiber reinforcement also caused a small decrease in the modulus of elasticity and changed the shape of the stress–strain relationship to become more curvilinear. A large increase in the compression toughness was recorded. This indicated a significant gain in ductility when steel fiber reinforcement is used.

Stress- and strain-controlled measurements of interfacial shear viscosity and viscoelasticity at liquid/liquid and gas/liquid interfaces

Abstract: An interfacial rheometer for both stress- and strain-controlled measurements of shear rheological properties at liquid/liquid and gas/liquid interfaces is presented. The device is based on a rotating or oscillating biconical bob design in combination with a low friction electronically commutated motor system. The interfacial shear stress, viscosity, and dynamic moduli are obtained by solving the Stokes equations (low Reynolds number) along with the Boussinesq–Scriven interfacial stress tensor, which is used for the boundary conditions at the interface. An improved and simple numerical method for the calculation of the velocity distribution in the measuring cell is presented. The scope and limitations of the rheometer are discussed. Results from steady shear and oscillatory experiments as well as creep recovery and stress relaxation tests at both oil/water and air/water interfaces with adsorbed films of a globular protein (ovalbumin) and spread films of a surfactant (sorbitan tristearate) are presented.

Role of collagen and other organics in the mechanical properties of bone

Abstract: Relevant mechanical properties of bone The mechanical properties of bone material are determined by the relative amounts of its 3 major constituents: mineral, water, and organics (mainly type I collagen); by the quality of these components; and by how the resulting material is arranged in space. For our purposes, the mechanical properties of bone can be summed up as follows: modulus of elasticity, yield stress and yield strain, post-yield stress and post-yield strain, and the total area under the stress-strain curve. Also important are some fracture mechanics properties, but these are not discussed here. A typical tensile stress-strain curve for a bone specimen is shown in Fig. 1. The modulus of elasticity shows how stiff the bone material is. Indeed, stiffness is the prime property of bone, distinguishing it from tendon, which has much less tensile stiffness, almost no shear stiffness, but which is nearly as strong and is much tougher. Yield stress and strain determine how much energy can be absorbed before irreversible changes take place. Post-yield stress and strain determine mainly how much energy can be absorbed after yield but before fracture. Irreversible changes take place at yield, caused by microdamage. The total area under the stress-strain curve is equivalent to the work that must be done per unit volume on the specimen before it breaks. Fracture mechanics properties show the extent to which bone is resistant to crack initiation and to crack travel (which are different things and governed by somewhat different features). In fact, crack travel resistance is given rather well by post-yield stress and strain.

Thermomechanical recovery couplings of shape memory polymers in flexure

Abstract: Shape memory polymers (SMPs) have the capacity to recover large strains when pre-deformed at an elevated temperature, cooled to a lower temperature and reheated. The thermomechanical recovery behavior of an SMP is examined in three-point flexure for various pre-deformation and recovery conditions. Results indicate that when pre-deformed well above the glass transition temperature, Tg, the stress–strain response at the pre-deformation temperature governs the relationship between the recovery stress/strain and the corresponding pre-deformation strain/stress. When pre-deformed at a temperature below Tg, the relationship between recoverable stress and strain level in the SMP is not governed by the stress–strain response of the material at the pre-deformation temperature. Rather, a peak recovery stress, which is less than the applied pre-deformation stress, appears near Tg. Higher cooling rates during constraint lower the temperature necessary for complete shape fixity, but increase the recoverable stress level. Higher heating rates during recovery raise the recovery onset temperature and decrease the peak recoverable stress. Ramifications of the results on future research efforts and emerging applications of SMPs are discussed.

Development and finite element implementation of stress-dependent elastoviscoplastic constitutive model with damage for asphalt

Abstract: The development and finite element (FE) implementation of a stress-dependent elastoviscoplastic constitutive model with damage for asphalt is described. The model includes elastic, delayed elastic, and viscoplastic components. The strains (and strain rates) for each component are additive, whereas they share the same stress (i.e., a series model). This formulation was used so that a stress-based nonlinearity and sensitivity to confinement could be introduced into the viscoplastic component without affecting the behavior of the elastic and delayed elastic components. A simple continuum damage mechanics formulation is introduced into the viscoplastic component to account for the effects of cumulative damage on the viscoplastic response of the material. The model is implemented in an incremental formulation into the CAPA-3D FE program developed at Delft University of Technology in the Netherlands. A local strain compatibility condition is utilized such that the incremental stresses are determined explicitly from the incremental strains at each integration point. The model is demonstrated by investigating the response of a semirigid industrial pavement structure subjected to container loading. Results show that the permanent vertical strains in the non-stress-dependent case are significantly lower than the permanent vertical strains in the stress-dependent case. Results also show that in the stress-dependent case, there is a more localized area of high permanent vertical compressive strain directly under the load at approximately half-depth in the asphalt compared with the non-stress-dependent case, in which the distribution is more even.

On the Sensitivity of Wall Stresses in Diseased Arteries to Variable Material Properties

Abstract: Accurate estimates of stress in an atherosclerotic lesion require knowledge of the material properties of its components (e.g., normal wall, fibrous plaque, calcified regions, lipid pools) that can only be approximated. This leads to considerable uncertainty in these computational predictions. A study was conducted to test the sensitivity of predicted levels of stress and strain to the parameter values of plaque used in finite element analysis. Results show that the stresses within the arterial wall, fibrous plaque, calcified plaque, and lipid pool have low sensitivities for variation in the elastic modulus. Even a +/- 50% variation in elastic modulus leads to less than a 10% change in stress at the site of rupture. Sensitivity to variations in elastic modulus is comparable between isotropic nonlinear, isotropic nonlinear with residual strains, and transversely isotropic linear models. Therefore, stress analysis may be used with confidence that uncertainty in the material properties generates relatively small errors in the prediction of wall stresses. Either isotropic nonlinear or anisotropic linear models provide useful estimates, however the predictions in regions of stress concentration (e.g., the site of rupture) are somewhat more sensitive to the specific model used, increasing by up to 30% from the isotropic nonlinear to orthotropic model in the present example. Changes resulting from the introduction of residual stresses are much smaller.

Fracture and Fatigue Emanating from Stress Concentrators

Abstract: Preface. * 1: Notch effects in fracture and fatigue. 1.1. Notch effects in fracture. 1.2. Notch effects in fatigue. 1.3. Conclusion. * 2: Stress distribution at notch tip. 2.1. Introduction. 2.2. Elastic stress distribution at notch tip. 2.3. Stress distribution at notch tip for perfectly plastic material. 2.4. Stress distribution for an elastic perfectly plastic material. 2.5. Elastoplastic stress distribution for a strain hardening material. 2.6. Conclusion. * 3: Stress concentration factor. 3.1. Definition of the stress concentration factor. 3.2. Elastoplastic stress and strain concentration factor. 3.3. Relationship between the elastic and elasto-plastic concentration stress and strain concentration factors and the elastic one. 3.4. Evolution of elastic and elasto-plastic stress (or strain) concentration factor with net stress. 3.5. Comparison of evolution with net stress. 3.6. Conclusion. * 4: Concept of notch stress intensity factor and stress criteria for fracture emanating from notches. 4.1. Introduction. 4.2. Concept of stress intensity factor. 4.3. Concept of notch stress intensity factor. 4.4. Global stress criterion for fracture emanating from notches. 4.5. Local stress criterion for fracture emanating from notches. 4.6. Notch sensitivity in mixed mode fracture. 4.7. Conclusion. * 5: Energy criteria for fracture emanating from notches. 5.1. Introduction. 5.2. Influence of notch radius on the J integral. 5.3. Influence of notch radius on the z coefficients. 5.4. Local energy criterion for fracture emanating from notches. 5.5. Conclusion. * 6: Strain criteria for fracture emanating from notches. 6.1. Introduction. 6.2. Critical strain criterion for fracture emanating from notch. 6.3. Strain distribution at the notch tip. 6.4. Notch plastic zone. 6.5. Conclusion. * 7: The use of notch specimens to evaluate the ductile to brittle transition temperature the Charpy impact test. 7.1. History of the Charpy impact test. 7.2. Stress distribution at notch tip of a Charpy specimen. 7.3. Local stress fracture criterion for Charpy V notch specimens. 7.4. Influence of notch geometry on brittle-ductile transition in Charpy tests. 7.5. Instrumented Charpy impact test. 7.6. Equivalence fracture toughness KIc and impact resistance KCV. 7.7. Conclusion. * 8: Notch effects in fatigue. 8.1. Notch effects in fatigue and fatigue strength reduction factor. 8.2. Relation between fatigue strength reduction factor and stress concentration factor. 8.3. Volumetric approach. 8.4. Influence of loading mode. 8.5. Notch effects in low cycle fatigue. 8.6. Conclusion. * 9: Role of stress concentration on fatigue of welded joints. 9.1. Introduction. 9.2. Stress concentration factor in welding cords. 9.3. Fatigue strength reduction factor. 9.4. Standard methods for the design against fatigue of welded components. 9.5. Innovative methods for the design against fatigue of welded joints. 9.6.

The Stress–Strain Behavior of Coronary Stent Struts is Size Dependent

Abstract: Coronary stents are used to re-establish the vascular lumen and flow conditions within the coronary arteries; the typical thickness of a stent strut is 100 μm, and average grain sizes of approximately 25 μm exist in stainless steel stents. The purpose of this study is to investigate the effect of strut size on the stress strain behavior of 316 L stainless steel. Other materials have shown a size dependence at the micron size scale; however, at present there are no studies that show a material property size dependence in coronary stents. Electropolished stainless steel stent struts within the size range of 60–500 μm were tensile tested. The results showed that within the size range of coronary stent struts a size dependent stress–strain relationship is required to describe the material. Finite element models of the final phase of fracture, i.e., void growth models, explained partially the reason for this size effect. This study demonstrated that a size based stress–strain relationship must be used to describe the tensile behavior material of 316 L stainless steel at the size scale of coronary stent struts. © 2003 Biomedical Engineering Society. PAC2003: 8719Rr, 8780Rb, 8719Uv

Nanoindentation stress–strain curves as a method for thin-film complete mechanical characterization: application to nanometric CrN/Cr multilayer coatings

Abstract: The mechanical behavior of CrN/Cr multilayer coatings deposited by rf magnetron sputtering has been investigated by nanoindentation measurements performed with indenters of different geometries. Nanoindentation stress–strain curves generated from these measurements allow us to characterize the complete mechanical behavior of these coatings in the elastic, elastoplastic, plastic and fracture deformation regimes. In particular, indentation measurements carried out with a 100-μm-radius spherical indenter allowed us to study the elastic deformation regime and estimate the yield stress parameter through the initial indentation yielding point. The elastoplastic deformation regime has been studied using a 5-μm-radius spherical indenter and the stationary yielding regime (fully plastic regime) has been investigated with a pyramidal indenter of Berkovich geometry. The use of a pyramidal cube-corner indenter allowed us to study coating fracture characteristics. Nanometric CrN/Cr multilayer structures as well as single CrN and Cr coatings have been characterized. The study has shown that multilayered coatings with period thicknesses less than 46 nm present values of yield stress, Young’s modulus, hardness and toughness higher than those for single-layer CrN and Cr coatings.

One-Dimensional Dynamic Compressive Behavior of EPDM Rubber

Abstract: Dynamic compressive stress-strain curves at various strain rates of an Ethylene-Propylene-Diene Monomer Copolymer (EPDM) rubber have been determined with a modified split Hopkinson pressure bar (SHPB). The use of a pulse-shaping technique ensures that the specimen deforms at a nearly constant strain rate under dynamically equilibrated stress. The validity of the experiments was monitored by a high-speed digital camera for specimen edge deformation, and by piezoelectric force transducers for dynamic stress equilibrium. The resulting dynamic stress-strain curves for the EPDM indicate that the material is sensitive to strain rates and that the strain-rate sensitivity depends on the value of strain. Based on a strain energy function theory, a one-dimensional dynamic constitutive equation for this rubber was modified to describe the high strain-rate experimental results within the ranges of strain and strain rates presented in this paper.

Time-dependent stress–strain behaviour due to viscous properties of geogrid reinforcement

Abstract: A series of conventional and unconventional tensile tests were performed on six types of geosynthetic reinforcement to evaluate their viscous properties. It is shown that the isochronous model, according to which the load (or the stress) is a unique function of instantaneous strain and elapsed time, is unable to explain the major viscous aspects of the test results. In particular the model is unable to predict the stress–strain behaviour and rupture strength observed after loading is restarted at a constant strain rate following a creep loading or stress relaxation stage. It is argued that the widely prevailing concept that creep is a degrading phenomenon requiring the design strength to be reduced with an increase in the design lifetime is not realistic under typical field conditions where the stress–strain property does not deteriorate noticeably with time. It is also argued that this concept stems from the isochronous model. A non-linear three-component model is proposed to simulate the viscous aspects...

Glyph and hyperstreamline representation of stress and strain tensors and material constitutive response

Abstract: Results of numerical analyses of boundary value problems in geomechanics include output of three-dimensional stress and strain states. Two-dimensional plots of stress–stress or stress–strain quantities, often used to represent such output, do not fully communicate the evolution of stress and strain states. This paper describes the use of glyphs and hyperstreamlines for the visual representation of three dimensional stress and strain tensors in geomechanics applications. Glyphs can be used to represent principal stress states as well as normal stresses at a point. The application of these glyphs is extended in this paper to represent strain states. The paper introduces a new glyph, called HWY glyph for the representation of shear tensor components. A load step-based hyperstreamline is developed to show the evolution of a stress or strain tensor under a general state of loading. The evolution of stress–strain states from simulated laboratory tests and a general boundary value problem of a deep braced excavation are represented using these advanced visual techniques. These visual representations facilitate the understanding of complex multidimensional stress–strain soil constitutive relationships. The visual objects introduced in this paper can be applied to stress and strain tensors from general boundary value problems. Copyright © 2003 John Wiley & Sons, Ltd.

A multiscale analysis of fixed-end simple shear using molecular dynamics, crystal plasticity, and a macroscopic internal state variable theory

Abstract: We examine FCC nickel undergoing simple shear by using three different numerical frameworks formulated at three different size scales. The three frameworks included embedded atom method potentials used in molecular dynamics simulations, crystal plasticity used in finite element simulations, and a macroscale internal state variable formulation used in finite element simulations. Simple shear simulations were performed in which the specimen aspect ratio was varied to give insight into the homogeneous and inhomogeneous aspects of large deformation. This study revealed that the `apparent' yield stress was sensitive to the specimen aspect ratio except when the length-to-height ratio reached about 8 : 1, the yield stress remained constant. The three numerical frameworks gave similar qualitative responses related to inhomogeneous stress and strain distributions in the corner regions of the specimens and also similar responses in the centralized homogeneous deformation region. However, when comparing the shear stress distribution for the finite element analyses to the atomistic simulations, a much narrower distribution arose for the finite element analyses due to the lack of thermal vibrations experienced in the atomistic simulations at 300 K. A 10 K an atomistic simulation which dampened out the high frequency thermal vibrations verified this reasoning. Three different sizes of blocks of atoms were also used in the atomistic simulations and the results showed very similar stress and strain distributions with respect to each other indicating that no size scale effect is evidenced when normalized by the global shear stress. However, a size scale effect exists related to the global (volume average) shear stress in the specimen. As the specimen size increased, the yield stress decreased. Finally, when comparing the three different numerical frameworks, the location of maximum dislocation nucleation occurred at the location of the maximum plastic spin, stress gradients, and strain gradients.

Postnecking elastoplastic characterization: Degree of approximation in the Bridgman method and properties of the flow-stress/true-stress ratio

Abstract: The stress and strain radial distributions within the minimum cross section of a tensile specimen undergoing necking, calculated with the Bridgman method, differ, in some cases substantially, from finite-element method (FEM) results. Analyses of the possible reasons for these differences show that an important role is played by the uniformity of the strain distribution assumed by Bridgman. In this study, three types of steels were subjected to tensile testing, and FEM analyses were performed to simulate the experimental trails. The comparison of the experimental and numerical results indicates the magnitude of the approximations intrinsic to the Bridgman method. Through further FEM analyses, it was possible to isolate, in qualitative terms, the influence of the Bridgman approximation from that of the void growth. This has been made by applying the Bridgman formulation to the proper FEM output data and comparing the resulting curves to the curves used as material input for the same analyses. Finally, it was found that, over a certain range of hardening materials, the correction of the true curve depends only on the necking strain, within the same error level given by the Bridgman method. This means that, once the corrective law common to many materials is found, then the correction procedure is substantially improved in terms of effort and time consumption, because it does not need the necking-curvature measurements required by the Bridgman method.