True Stress-strain Relationship Research Articles

Two-step procedure for identification of metal behavior from dynamic compression tests

Simulation of forming processes requires accurate constitutive models describing material behavior at large strains up to 150% and intermediate strain rates up to 10 3 s −1, and taking into account adiabatic heating. The choice of a rheological model and the determination of its parameters should be made from tests generating such conditions. The major difficulty encountered is that few experimental tests satisfy these criteria. The uniaxial compressive test seems well adapted and is frequently used to characterize the rheological behavior at operating conditions corresponding to forming applications. However, for high strain rate tests, the load measurement is disturbed by the elastic response of the experimental set-up. Therefore, the difficulty is to identify the behavior of the material studied independently of the experimental set-up. This paper proposes to improve the analysis of the dynamic compression test and presents a method to convert experimental data into true stress–strain relationships. A specific experimental set-up is used to realize compression tests at high velocities and at elevated temperatures. The dynamic response of the experimental set-up is analyzed and a finite-element (FE) model taking into account the elastic and inertia effects of the whole experimental structure is defined. A two-step sequential identification method of the material behavior based on inverse analysis is presented. Finally, behavior of a 27MnCr5 steel, submitted to different compression velocities and heated to different temperatures is identified.

Correlation of structure and flow behaviour of Cu–Ti–Cd alloys

The work hardening behaviour of Cu–3Ti–1Cd and Cu–4Ti–1Cd alloys has been studied by conducting tensile tests at room temperature in solution treated, peak aged and overaged conditions. The flow behaviour has been analyzed using various true stress–true strain relationships. The Ludwigson relationship provides the best fit for the true stress–strain data of the two alloys at 298 K in all the conditions studied. The Hollomon equation as well as Ludwik equation fits the experimental σ– ɛ data for both the alloys reasonably well in highly overaged condition. While both the alloys exhibit transient flow behaviour at lower strains in solution treated condition, Cu–3Ti–1Cd alloy only exhibits this behaviour in peak aged condition. No such transition was observed in overaged condition of both the alloys. Further, these alloys display higher flow stress and strain hardening rates in peak aged condition than that in solution treated condition. Cu–3Ti–1Cd alloy shows higher flow stress and lower strain hardening rates in overaged condition than in the solution treated condition. On the other hand, Cu–4Ti–1Cd alloy exhibits lower flow stress as well as lower strain hardening rates in overaged condition when compared to that in solution treated condition. The observed behaviour in Cu–4Ti–1Cd alloy is related to the modulated structure with fine precipitates of Cu 4Ti present in solution treated condition as compared to coarse and diffuse lamellar structure in overaged condition.

Deformation behavior of reduced activation ferritic steel during tensile test

Deformation behavior of reduced activation martensitic steel F82H during tensile tests were studied. True stress–true strain diagrams were calculated with minimum diameter determined from the specimen profile obtained by laser micro-gauge scanning the diameter along the longitudinal direction during tensile test. Cylindrical specimens of F82H were used for the measurement and test temperatures were room temperature (RT), 300, 400, 500 and 600 °C. Tensile tests were carried out with 1 × 10 −4 s −1 of strain rate. Other strain rates (1 × 10 −3 and 1 × 10 −5 s −1) were applied for the tests at RT. Although uniform elongation of F82H is relatively small at elevated temperature, true stress increases to fracture after necking starts. True stress decreases temporarily after yielding at 600 °C, but it increases again to fracture like the specimens tested at lower temperatures. Influence of strain rate to true stress–true strain relationship at room temperature was small, but unstable deformation occurred in narrower area at higher strain rate.

Application of an interpenetrating network model to the necking in the microcrystalline region in four annealed isotactic polypropylene films subjected to uniaxial stretching at room temperature

The microscopic infrared dichroism, mesoscale deformation and macroscopic stress measurements are made on the microcrystalline region in four annealed isotactic polypropylene (iPP) thin films subjected to uniaxial stretching at room temperature. Results reveal that volume dilatation might occur during stretching and the necking causes the anisotropic shrinkage in the thickness and the width directions. The average orientation function f av and the true stress as a function of local draw ratio in the samples showing volume dilatation can be respectively overlapped onto those of the sample undergoing constant volume deformation. The pseudo-affine deformation is applicable for molecular orientation at f av<0.50 and the true stress–strain relationship on the mesoscale can be well described in the same region by the interpenetrating network model previously proposed for necking in the quenched iPP film. This model becomes invalid for deformations above f av=0.50 due to that plastic deformations in the crystalline phase, depending on the annealing time, start to play a major role.

Segmental orientations and deformation mechanism of a poly(ether‐block‐amide) film

AbstractSimultaneous measurements of microscopic infrared dichroism, mesoscale deformation, and macroscopic stress have been made for a microphase‐separated film of poly(ether‐block‐amide) 4033 during uniaxial stretching at temperatures between 30 and 91 °C, well below the melting point of the hard polyamide‐12 (PA) domains. Before the onset of dramatic microstructural alterations, the true stress–strain relationship on the mesoscale can be described with an interpenetrating network model, and poly(tetramethylene oxide) (PTMO) soft segments undergo affine deformation. Beyond a threshold strain at which stress from the soft network becomes larger than that from the hard network, plastic deformation occurs in the hard PA domains, and this is accompanied by the downward derivations of the true stress and molecular orientation of PTMO blocks from the model predictions. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 1161–1167, 2005

Room Temperature Deformation Behavior of Inconel718

The deformation behavior of Inconel718 at room temperature was studied by tensile tests. Three kinds of specimens were tested, including cold rolled, heat treated with grain size ASTM5 and heat treated with grain size ASTM7. The true stress-strain curves were obtained based on the tensile test records. The true stress-strain relation can express the room temperature deformation behavior, which can be described by equations similar to the Voce equation. The limit value of the work-hardening rate θ0 is very sensitive to the microstructure of the alloy.

断続引張試験による局所くびれ以降の真応力-真ひずみ線図の評価

断続引張試験による局所くびれ以降の真応力-真ひずみ線図の評価

Assessment of the constitutive properties from small ball punch test: experiment and modeling

An assessment of the true stress–true strain relationship has been done by means of tensile and small ball punch tests on austenitic and tempered martensitic steel at room temperature. A finite element model was developed and validated to calculate the force–deflection curve obtained from the ball punch experiment. The effects of the specimen thickness and material properties on the overall shape of the ball punch test curve are discussed. The constitutive behavior assigned to the specimen for the calculations was determined from the tensile test but we showed that assumptions have to be done to extend it to large strains as those arising during the punch tests. Using an inverse methodology, it was possible to show that a linear strain-hardening stage takes place at large strains. The potential for evaluating the evolution of the strain-hardening capacity after irradiation is outlined.

Modelling of overall plastic deformation in rubber-toughened polymers

In this paper, we provide a constitutive model for overall (macroscopic) plastic deformation behavior in a rubber-toughened polymer blend. A porous plasticity theory is employed as a basis for the constitutive modeling. In our investigation, the polycarbonate (PC) is chosen as a matrix material of polymer blend. First, the true uniaxial stress-strain relation for PC, which is an important part of the constitutive model, is carefully measured. Secondly, finite element analyses of neck propagation in a tensile specimen of PC are performed to test the efficiency of the introduction of the accurately measured true stress-strain relation into the model. Then, in order to investigate local and average deformation behavior of the matrix material (PC) around cavitated rubber particles in polymer blend, an axisymmetric unit cell analysis is carried out. Finally, finite element analyses of the neck propagation in a tensile specimen of a rubber-toughened PC are performed, and the numerical results are compared to experimental results. It is revealed that the present constitutive model has the ability to well reproduce the behavior of a rubber-toughened polymer blend with rather small volume fraction of rubber particles, which is up to about 10%. However, for blends with larger volume fraction of the rubber particles, the discrepancy between the computational and the experimental results increases. Several possibilities of enhancing the model are discussed.

Constitutive equation for Ti–6Al–4V at high temperatures measured using the SHPB technique

A high temperature split Hopkinson pressure bar (SHPB) test system is used to investigate the effects of temperature as well as those of strain and strain-rate. Effects of temperature for the titanium alloy (Ti–6Al–4V) are investigated by developing a high temperature SHPB test system. In this work, high temperatures greater than 1000°C are attained in the SHPB test specimens by using two ellipsoidal radiant heating reflectors with two halogen lamps. The thermal gradients in the specimens are observed as they are heated. Methods for solving problems related to conduction between the specimens and elastic bars and techniques for measuring the temperature of the specimens are suggested. When testing with the high-temperature SHPB apparatus, care is required to prevent oxidation of the surface of the specimen, and to prevent an inhomogeneous temperature distribution from developing in the specimen. To determine the true flow stress–true strain relationship, specimens are tested from room temperature to 1000°C at intervals of 200°C and at a strain-rate of 1400 s −1 . The parameters for a Johnson–Cook constitutive equation and a modified Johnson–Cook constitutive equation are determined from the test results. The modified Johnson–Cook constitutive equation is more suitable for expressing the dynamic behavior of the Ti–6Al–4V titanium alloy in the vicinity of the recrystallization temperature.

Predicting the Permeability and Tensile Properties of Multilayer Films from the Properties of the Individual Component Layers

We have fabricated typical three-layer films (A/B/C multilayer structures), comprising polyamide-6 (PA-6), low-density polyethylene (LDPE), and adhesive (low-density ethylene grafted with maleic anhydride, LDPE-g-MAH), by a coextrusion blown-film process using various compositions of the three layers. With the goal of predicting the permeability and tensile properties of the three-layer films, we examined model predictions and the properties of the individual component layers to provide an economical and efficient pathway to designing desired multilayer structures. We used the series model for predicting permeability; a good agreement exists between experimental data and this model for predicting both gas and water vapor permeabilities of three-layer films having various contents of PA-6. By using the additive rule model, we can also predict the tensile properties, including the true yield stress, strain hardening parameter, and tensile modulus of the three-layer film from those of the individual component layers, with particularly high accuracy in the true stress–strain relationship.

Plastic deformation of a binary Cd–Yb icosahedral quasicrystal

Polycrystalline icosahedral quasicrystals in a binary Cd–Yb alloy have been compressed at high temperatures for the first time. As-grown specimens were plastically deformable only above 698 K with the yield stress rapidly decreasing with increasing temperature. The true stress vs. true strain relation revealed continuous work softening to a large strain; the decrease of the true stress reaches 85% of the yield stress at 698 K and it is 20–50% at 773 K. Temperature change tests showed that the flow stress is sensitive to the deformation history; once a specimen has been initially deformed to a large strain at 773 K, it is plastically deformable even at 600 K. The activation analysis showed that the activation enthalpy decreases to two-third of that at the yielding stage as the strain increases, which is the cause of the work softening.

SOME PRELIMINARY RESULTS ON ANALYSIS OF CONCRETE FLEXURAL MEMBERS WITH HYBRID REINFORCEMENTS

It is generally accepted that conventional steel reinforced concrete (RC) flexural members usually fails in a ductile mode with low load-carrying capacity. In contrast, recent introduction of fibre-reinforced-polymer (FRP) rods into RC beams gives rise to a higher ultimate load but it lacks ductility. It is anticipated that a hybrid combination of conventional steel rebars and novel FRP rods as reinforcing materials in concrete beam can provide a strong and ductile beam characteristics. Prior to the experimental verifications, a preliminary analytical study is carried out. The analytical model describes some features of the flexural behaviour of concrete members reinforced with hybrid reinforcing materials. The model implementation is based on the use of the true stress-strain relationships for plain concrete, steel rebar and FRP rod. The main variable considered in present study is the arrangement of steel rebars and FRP rods. This paper presents some particular findings from the model. Most results are also compared with that of concrete beam reinforced only with steel rebars.

Determining the stress–strain behaviour of small devices by nanoindentation in combination with inverse methods

The ongoing miniaturisation of thin films, coatings, micro-electromechanical systems (MEMS) components and devices demands for new characterising tools and methods. Conventional mechanical tests cannot be readily applied to small scales, first because one can expect new mechanical properties of such small-scale materials and second because minuscule samples are difficult to handle in conventional mechanical experiments such as tensile tests. Here we present a new method for determining the mechanical properties of LIGA (German acronym for ‘Lithographie, Galvanoformung und Abformung’) processed MEMS, mechanical watch parts and devices. The method is based on a reverse analysis of load-displacement data obtained from nanoindentation experiments that can be performed on micrometer sized volumes. To validate the method for typical applications in microengineering, a comparison of microtensile and nanoindentation tests is presented in this paper. The comparison of microtensile and nanoindentation tests showed that the elastic modulus obtained in nanoindentation for all tested materials was systematically about 15% higher than the values obtained in tensile testing, which can be attributed to the different size and microstructural levels that are probed. The numerical simulation of the nanoindentation tests allowed to estimate the true stress–true strain relationship up to strain levels of 30%, whereas in microtensile experiments the rheology of the tested materials can be determined to 5% only.

A complete three-dimensional finite element analysis of the bar-bar tensile impact apparatus

A complete three-dimensional FEM model of the Bar-Bar Tensile Impact Apparatus (BTIA) is constructed, in which the slots in the bars and the glue layers between the bars and the flat-shaped specimen are included. For elastic-plastic specimen material, Ly12cz aluminum alloy, the process of tensile impact experiments is simulated and the matching relation between the specimen geometry and the bars is investigated. Based on the FEM analysis, an iterative method is proposed to design a reasonable specimen geometry for obtaining the true dynamic stress-strain relation for a certain specimen material.

SOME PRELIMINARY RESULTS ON ANALYSIS OF CONCRETE FLEXURAL MEMBERS WITH HYBRID REINFORCEMENTS

Abstract It is generally accepted that conventional steel reinforced concrete (RC) flexural members usually fails in a ductile mode with low load-carrying capacity. In contrast, recent introduction of fibre-reinforced-polymer (FRP) rods into RC beams gives rise to a higher ultimate load but it lacks ductility. It is anticipated that a hybrid combination of conventional steel rebars and novel FRP rods as reinforcing materials in concrete beam can provide a strong and ductile beam characteristics. Prior to the experimental verifications, a preliminary analytical study is carried out. The analytical model describes some features of the flexural behaviour of concrete members reinforced with hybrid reinforcing materials. The model implementation is based on the use of the true stress-strain relationships for plain concrete, steel rebar and FRP rod. The main variable considered in present study is the arrangement of steel rebars and FRP rods. This paper presents some particular findings from the model. Most res...

The Effect of Prior Cold Work on Tensile Residual Stress Development in Nuclear Weldments

Austenitic alloy weldments in nuclear reactor systems are susceptible to stress corrosion cracking (SCC) failures. SCC has been observed for decades and continues to be a primary maintenance concern for both pressurized water and boiling water reactors. SCC can occur if the sum of residual stress and applied stress exceeds a critical threshold tensile stress. Residual stresses developed by prior machining and welding can accelerate or retard SCC depending on their sign and magnitude. The residual stress, cold work and yield strength distributions on the inside diameter of an Alloy 600 tube J-welded into a pressure vessel were determined by a combination of X-ray diffraction (XRD) and mechanical techniques. A new method was used to relate the XRD line broadening to the percent cold work or true plastic strain in the Alloy 600 tube. The accumulated cold work in the layers deformed by prior machining, in combination with the true stress-strain relationship for Alloy 600, was used to determine the increase in yield strength as a result of deformation due to machining and weld shrinkage. The yield strength of the deformed layer was found to be well in excess of the bulk yield for the alloy, and is therefore capable of supporting residual stresses correspondingly higher. Tension as high as +700 MPa, exceeding the SCC threshold stress, was observed in both the hoop and axial directions on the inside diameter of the Alloy 600 tubing adjacent to the weld heat affected zone (HAZ). The cold worked high tensile zones correlated with the locations of field SCC failures. The tensile residual stresses are shown to result from a combination of the high cold working from initial machining followed by weld shrinkage. The development of surface tension during weld shrinkage has been modeled using finite element methods, and the benefits of minimizing or removing the cold worked layer prior to welding are demonstrated. Further laboratory studies showing the influence of prior cold working on the formation of residual stresses following bulk plastic deformation are presented.

Plastic deformation of EVA, EVOH and their multilayers

The high strain rate, plastic deformation of multilayer films is analyzed in relation to the tensile properties of the components. The multilayers combine ethylene-vinyl acetate (EVA) blend surface-layers with an ethylene-vinyl alcohol (EVOH) core-layer; the volume of the EVOH layer is varied from 1% to 20%. Individually, the components exhibit markedly different tensile behavior in terms of yielding and ductility in the temperature range from 55°C to 95°C. The EVA blend deforms homogeneously whereas EVOH forms a neck at an extension rate of 10,000%/min. It is shown that the true stress-strain relationship of the components in the plastic region can be described with two parameters, the true yield stress and the strain hardening parameter. Multilayers deform homogeneously, as does the EVA blend. A simple rule of mixtures approach is used to describe the plastic behavior of the multilayers as a function of temperature, composition and moisture, and to predict whether or not deformation will be uniform.

Effect of Polarization on Deformation and Fracture of Tetragonal PZT

Four-point bending tests were conducted with smooth specimens of poled and non-poled lead zirconate titanate (PZT) ceramics with a tetragonal structure. The specimens poled in the longitudinal, transverse and short-transverse directions were called PL, PT and PS specimens, respectively. The non-poled specimens were called NP specimens. The true stress-strain relation showed nonlinearity and was different between tension and compression. The nonlinearity of the stress and strain relation resulted from domain switching induced by external loading, and the degree of nonlinearity increased with easiness of domain switching under bending. The fracture strength expressed in terms of the nominal and true stresses followed the Weibull distribution. The shape parameter took a large value around 18 to 22 for PT and PS specimens, while it was the smallest around 7 to 8 for PL specimens. NP specimens took values in between. The mean strength was the largest for NP specimen and was the lowest for PL specimen. Domain switching during loading will relieve local stress concentrations of defects within the material, thus increases the strength and the shape parameter. The change in intensity ratio of the 002 to 200 diffractions can be used to assess the degree of domain switching caused by external straining.

Deformation mechanism of quasicrystals

Characteristics of the high-temperature compressive deformation behavior of icosahedral and decagonal quasicrystals are reviewed. In icosahedral quasicrystals, the true stress versus true strain relation shows a pronounced yield drop, followed by gradual softening towards a minimum at a large true strain of about 0.5 and then changes to hardening at higher strain; the yield and flow stresses are quite sensitive to temperature and strain rate. In decagonal quasicrystals, the yield stress depends weekly on orientation in spite of its anisotropic structure. In both types of quasicrystals, the yield stress is higher in higher quality samples. The deformation mechanism of the quasicrystals is discussed in terms of dislocations glide in the quasicrystalline lattice governed by the Peierls mechanism. The Peierls mechanism in quasicrystals differs from that in crystals in that the dislocation glide is accompanied by a phason atrain relaxation and the Peierls potential is not periodic but quasiperiodic.