Wide Range Of Strain Amplitudes Research Articles

Effect of Gd on microstructure, mechanical properties and damping properties of Fe-Cr-Al alloys

Fe-21Cr-4Al-xGd (x = 0, 1, 2, 4 wt%) alloy was prepared by spark plasma sintering (SPS) in this study. The effect of Gd on the microstructure, mechanical properties and damping properties of Fe-21Cr-4Al alloy was investigated. The results show that the compressive strength and hardness of the alloy containing Gd are improved by fine grain strengthening and second phase strengthening, and the hardness and compressive strength of the Gd alloy increase with increasing Gd content. When Gd content is 4 wt%, the average grain size is 7.20 μm, which is much smaller than Fe-21Cr-4Al (9.15 μm). The hardness and compressive strength of the alloy are increased by 16.38% and 9.87%, respectively, compared with those of the alloy without Gd. The microstructure and phase composition show that the alloy is mainly composed of the body-centered cubic (BCC) structure α-Fe phase, Gd and Gd 2 O 3 . A large number of Gd and Gd 2 O 3 are scattered in the grain interior and grain boundary. The peak intensity of the α-Fe phase decreases with increasing Gd content. The Gd containing alloys maintain high damping properties in a wide range of strain amplitudes, and the maximum damping capacity of the Fe-21Cr-4Al-2Gd alloy is Q max −1 =0.072. In addition, after Gd is added to the Fe-21Cr-4Al alloy, ferromagnetic damping and dislocation damping exists in the appropriate strain amplitude region to jointly increase the internal friction, which may enhance the damping capacity of the alloy. • FeCrAl alloys with different compositions were sintered by spark plasma sintering (SPS). • Gd doped alloy has better mechanical properties and damping properties than FeCrAl alloy. • The damping properties of the alloy with Gd are composed of ferromagnetic damping and dislocation damping. • Gd-rich phase is located near grain boundary and dislocation to refine the alloy grain and hinder dislocation movement. • The Gd containing alloys maintain high damping properties in a wide range of strain amplitudes.

Constitutive rubber model suitable for rolling resistance simulations of truck tyres

Tyres are a vital vehicle component forming an interface between a vehicle and the road, enabling the generation of braking, steering and traction forces. However, they also generate rolling resistance which researchers have tried to minimise through the years for environmental and economic reasons. Despite numerous attempts to model rolling resistance of tyres there still does not seem to exist a simple, flexible and accepted way of modelling rolling resistance in the time domain as well as parametrising models in an easy and accessible way. This study explores a simple and intuitive way of parametrising a hyperviscoplastic parallel rheological framework. In the experimental part of this study, rubber samples with various amounts of carbon black filler are extracted from a truck tyre section and tested using dynamic mechanical analysis. The test data was used to parametrise the material model. The model consists of Mooney-Rivlin hyperelasticity, 40 Prony elements and 8 perfectly plastic elements with Ogden hyperelasticity. The paper introduces a method to obtain a large number of parameters using only six tuneable parameters, which simplifies the tuning of the model drastically. The parametrised model is suitable for tyre rolling resistance simulations with frequency and strain amplitude dependency of the storage and loss modulus. A wide range of strain amplitudes and frequencies can be covered with the proposed method and it is possible to achieve a good fit for the storage and loss modulus values with the benefit of only a few tuneable parameters. Additional Prony or plastic networks do not increase the amount of tuneable parameters. Moreover, the method can be used to parametrise the material using manual iterations which is generally not possible for a parallel rheological framework with such a large amount of parameters.

Surface-tension effects in oscillatory squeeze flow rheometry

Oscillatory squeeze flow rheometry (OSFR) is a technique for measuring fluid viscosity and linear viscoelasticity between oscillating parallel plates. While several corrections to the basic viscous flow model for OSFR have been considered (e.g., due to inertial effects), the role of surface tension remains largely unexplored. The present work revisits the classical liquid bridge problem subject to an oscillatory squeeze flow and considers the role of viscosity and surface tension on the dynamic force exerted by the liquid on the supporting plates. Using a combination of theory and experiment, we show that the (dimensionless) force collapses onto a master curve when plotted against a modified capillary number (measuring the relative importance of viscosity and surface tension) and that this prediction is robust over a wide range of strain amplitudes and aspect ratios. In doing so, we also demonstrate the ability of OSFR to measure surface-tension forces with reasonably high resolution. We test this capability for several low-viscosity fluids, demonstrating that, with current instrumentation and protocol, OSFR can measure surface tension to within 20% relative error. Finally, we provide an operating diagram that demarcates the regimes in which either viscosity or surface tension can be ignored in OSFR measurements. The results of this study may be used to further develop OSFR as a tool for measuring dynamical surface phenomena in addition to bulk viscoelasticity.

On Cohesive Soil Damping Estimation by Free Vibration Method in Resonant Column Test

Abstract Measurement of soil properties under cyclic and dynamic loading conditions is a critical task in the solution of most geotechnical earthquake engineering problems. The main dynamic properties of soils are usually expressed in terms of shear modulus and damping ratio that are generally obtained from laboratory tests. To date, the resonant column test is considered one of the most accurate ways to determine dynamic soil properties at low to medium-strain levels. Because it allows for investigation of a wide range of strain amplitudes, it is a valuable tool for characterizing the shear soil behavior for a large number of practical geotechnical problems. One of the approaches followed in estimating the damping ratio from the resonant column test is the free vibration method (also called logarithmic decrement or amplitude decay method). It consists of analyzing the time history of the damped free vibrations of the specimen once harmonic loading is cut off after reaching the resonant conditions. The soil damping ratio is determined measuring the logarithmic ratio of the amplitude of any two successive peaks of the system damped motion (logarithmic decrement). In this article, the influence on the damping ratio of the shear strain level, the plasticity index, the confining pressure, and the time interval between the peaks selected in calculating the logarithmic decrement is evaluated from the results of resonant column tests performed on 51 undisturbed isotropically consolidated fine-grained soil specimens.

Modeling shear stress response of bituminous materials under small and large strains

The paper at hand focuses on modeling the stress response of different mastics and asphalt binders exposed to small and large shear strains using Bergström-Boyce (BB) constitutive model as well as Finite Element (FE) approach. In this paper, a set of experiments based on Large Amplitude Oscillatory Shear (LAOS) test were designed and conducted to capture the state of strain dependence of bituminous mastics and binders over a broad spectrum of strain domain (0.5%, 10%, 20%, 30%, and 40%) pertaining linear and nonlinear regimes of such materials. Using the experimental data, the BB constitutive model was utilized to describe the attained behavior at two temperatures (30 °C and 40 °C) and varied strain amplitudes. The material properties derived from the BB model were further implemented into a Finite Element Model (FEM) using the ABAQUS platform to simulate the stress response of bituminous materials for a wide range of strain amplitudes. It has been shown that the bituminous mastics and binders have strong nonlinearity at high strain amplitudes, depicted graphically based on the progressive distortion from the elliptical form of Lissajous-Bowditch (LB) plot. Based on the observed goodness of fitting, the BB model well-described the experimental results for linear and nonlinear behaviors. Using the optimized parameters, it was confirmed that the BB model is well suited to build a numerical model that could reproduce stress responses derived from the LAOS results for a wide range of strain levels. The advantage of the methodology presented herein allows adaptable model constants of the BB model depending on the imposed level of strain and temperature and hence, the FEM can describe both linear and nonlinear behaviors of bituminous mastics and binders. From this paper, researchers can take advantage of capturing the stress response of binders and mastics under small and large strain amplitudes to stimulate the research on better representation of the complex behavior of asphalt mixes based on the role of mastic and asphalt binder.

Specific Features of the Rheological Behavior of a Protic Oligomeric Ionic Liquid of Cationic Type with Basic Sites of Two Types in the Region of the Solid–Liquid Transition

The structure and rheological behavior of a reactive oligomeric ionic liquid (OIL) have been studied. The OIL has a linear structure and contains ionic fragments of two types at both ends of oligo(ethylene oxide) chain. The ionic fragments are represented by secondary amino groups and nitrogen-containing heterocycles protonated with ethane sulfonic acid. The results obtained using rotational rheometry in different dynamic regimes indicate that, in the linear region of deformation at temperatures T G '). The boundary, which is located at nearly 30°C, is characterized by equality between G ' and G '' in a wide range of strain amplitudes. The structural transformations induced by thermal and mechanical energies have been explained using a hypothesis of the existence of micellar structures and a “normal micelle–reverse micelle” transition in the OIL, as well as changes in micelle shapes. The analysis of the temperature dependences for the viscoelastic characteristics and scattered light intensity, as well as the data of DSC and optical microscopy, has led to the hypothesis that at, T = 21–28°C, the OIL may occur in an ordered state similar to the liquid-crystalline one.

Elastic properties of Ti and its alloys nanostrctured due to severe plastic deformation

Studies of elastic properties of titanium and its alloys processed by severe plastic deformation are presented. The evolution of the modulus of elasticity resulting from the transformation from a coarse-grained state to an ultrafine-grained one due to severe plastic deformation (SPD) was investigated. The acoustic composite oscillator technique was used to measure the elastic modulus in a wide strain amplitude range. The microstructure was studied in detail by scanning electron microscopy and electron backscatter diffraction methods. Parameters of nanoscale porosity were measured by small-angle X-ray scattering before and after treatment with a high hydrostatic pressure (1.5 GPa). In addition, densities of titanium and its alloys in various structural states were determined by the precision method of hydrostatic weighing. As experiments showed, noticeable changes in the elastic properties resulting from the change in the grain state can be attributed to several factors, such as dislocations, nanoporosity, high internal stresses, and the structure of the materials before SPD processing.

Medium-strain dynamic behavior of fiber-reinforced sand subjected to stress anisotropy

A comprehensive database is established to investigate the behavior of polypropylene fiber reinforced sands under anisotropic stress state in a wide range of strain amplitudes from about 4 × 10−4% to 1.4 × 10−1%. A fixed-partly fixed Hardin-type resonant column which has a system that allows the specimen to be tested in resonance while maintaining an anisotropic loading path, is utilized. The results show important influence of the fiber content as well as the anisotropic stress state on the normalized modulus reduction and damping increase curves of the reinforced soils. Specifically, the increase of fiber content and stress ratio tend to increase the linearity in the normalized modulus reduction curves. On the other hand, the inclusion of fiber leads to the damping increase curves to shift to greater values, while the stress ratio has an opposite effect. An expression is proposed to predict the normalized shear modulus, as a function of mean effective confining pressure, stress ratio, coefficient of uniformity of the host sand and fiber content. The damping ratio, in a normalized form, is correlated with the normalized shear modulus reduction.

Fatigue of ZEK100-F magnesium alloy: Characterisation and modelling

Fatigue and cyclic behaviour of rolled ZEK100-F magnesium alloy in rolling direction are investigated by conducting fully-reversed strain-control uniaxial tension-compression cyclic experiments at a wide range of strain amplitudes. The experimental alloy possesses less asymmetric (less skewed) hysteresis loops, and higher ductility at the room temperature, relative to other conventional wrought magnesium alloys, e.g., AZ31B-H24 and AM30. Cyclic straining at amplitudes less than 0.6% results in material softening, while at higher amplitudes cyclic hardening occurs. Through stress-control cyclic tests at stress ratios of 0 and −1, mean stress is shown to have an adverse effect on the fatigue life of rolled ZEK100-F alloy. Finally, strain- and energy-based fatigue life prediction models are assessed against generated constant and variable amplitude experimental data, and Jahed-Varvani energy-based approach is observed to give statistically better life predictions.

An ISA-plasticity-based model for viscous and non-viscous clays

The ISA-plasticity is a mathematical platform which allows to propose constitutive models for soils under a wide range of strain amplitudes. This formulation is based on a state variable, called the intergranular strain, which is related to the strain recent history. The location of the intergranular strain can be related to the strain amplitude, information which is used to improve the model for the simulation of cyclic loading. The present work proposes an ISA-plasticity-based model for the simulation of saturated clays and features the incorporation of a viscous strain rate to enable the simulation of the strain rate dependency. The work explains some aspects of the ISA-plasticity and adapts its formulation for clays. At the beginning, the formulation of the model is explained. Subsequently, some comments about its numerical implementation and parameters determination are given. Finally, some simulations are performed to evaluate the model performance with two different clays, namely a Kaolin clay and the Lower Rhine clay. The simulations include monotonic and cyclic tests under oedometric and triaxial conditions. Some of these experiments include the variation of the strain rate to evaluate the viscous component of the proposed model.

Dynamic Strain Ageing Behaviour of Modified 9Cr-1Mo Steel Under Monotonic and Cyclic Loading

Dynamic strain ageing (DSA) behavior of modified 9Cr-1Mo steel under uniaxial tensile and constant strain cyclic loading is presented in this paper. Tensile tests are carried out at different strain rates from 10-3 to 10-5 s-1 in the temperature range from room temperature to 600°C. DSA has been established in the temperature range between 250 and 400°C in terms of peak in tensile strength, minima in ductility, serrated plastic flow and negative strain rate sensitivity. In the region of DSA dislocation substructure revealed high density of dislocations and features like kinks and bowing of dislocations are observed. Low cycle fatigue behavior was studied at 300°C, over a wide range of strain amplitudes at different strain rates. An inverse effect of strain rate was observed on cyclic stress response and fatigue life at 300°C due to DSA.

Mechanical formulations for bilinear and trilinear hysteretic models used in base isolators

The best known model for numerically simulating the hysteretic behavior of various structural components is the bilinear hysteretic system. There are two possible mechanical formulations that correspond to the same bilinear model from a mathematical viewpoint. The first one consists of a linear elastic spring connected in series with a parallel system comprising a plastic slider and a linear elastic spring, while the second one comprises a linear elastic spring connected in parallel with an elastic-perfectly plastic system. However, the bilinear hysteretic model is unable to describe either softening or hardening effects in these components. In order to account for this, the bilinear model is extended to a trilinear one. Thus, two trilinear hysteretic models are developed and numerically tested, and the analysis shows that both exhibit three plastic phases. More specifically, the first system exhibits one elastic phase, while the second one exhibits two elastic phases according to the level of strain amplitude. Next, the change of slope between the plastic phases in unloading does not occur at the same displacement level in the two models. Furthermore, the dissipated energy per cycle in the first trilinear model, as proven mathematically and explained physically, decreases in the case of hardening and increases in the case of softening, while in the second trilinear model the dissipated energy per cycle remains unchanged, as is the case with the bilinear model. Numerical examples are presented to quantify the aforementioned observations made in reference to the mechanical behavior of the two trilinear hysteretic models. Finally, a set of cyclic shear tests over a wide range of strain amplitudes on a high damping rubber bearing is used in the parameter identification of the two different systems, namely (a) trilinear hysteretic models of the first type connected in parallel, and (b) trilinear hysteretic models of the second type also connected in parallel. The results show that the complex nonlinear shear behavior of high damping rubber bearings can be correctly simulated by a parallel system which consists of only one component, namely the trilinear hysteretic system of the first type. The second parallel system was not able to describe the enlargement of the dissipated hysteresis area for large strain amplitudes.

A Novel Method for Strain Controlled Tests

The present paper aims at providing a contribution to the testing strategies in the field of mechanics of materials, with particular reference to low cycle fatigue in the strain control mode. After a detailed analysis of the state of the art on possible techniques for strain controlling, the paper points out the difficulties that could be encountered when a conventional longitudinal contact extensometer cannot be used. This methodology, based on controlling the strain at a particular specimen location, by controlling the relative displacement between its ends, was developed to provide an alternative solution in such occurrences. The paper introduces its analytical fundamentals for its most general application in the execution of fatigue or even static tests. Particular attention was devoted to the validation of the proposed methodology: this task was conducted by applying the suggested technique to both static and fatigue testing of hourglass specimens, by analyzing results also in comparison to other experimentations or numerical simulations, always observing a good agreement. The methodology proved to be efficient and reliable on a wide range of strain amplitudes.

Cyclic behaviour of wrought magnesium alloy under multiaxial load

This paper investigates the multiaxial cyclic behaviour of extruded AZ31B magnesium alloy. Tubular specimens were machined from large AZ31B extrusion sections. Two loading modes were considered for multiaxial testing: axial and torsional. All tests were performed at standard laboratory and in as-received conditions. In- and out-of-phase loading at a wide range of strain amplitudes were considered. Nonproportional loading tests were conducted at 45° and 90° phase angle shifts. Correlations between hysteresis shape and deformation mechanisms have been made. Twinning has a major role in deformation under multiaxial loading. Also, it was found that nonproportionality has no significant influence on the fatigue life. Axial and torsional modes were found to have different cyclic behaviour. Fatigue life of AZ31B was examined using different fatigue parameters. Two strain-based parameters based on the critical plane concept were examined. Furthermore, an energy approach was employed as a damage parameter. It was shown that the Fatemi–Socie critical plane model and the Jahed–Varvani energy model provided good estimates to the fatigue life of AZ31B under proportional and nonproportional loading.

Magnetomechanical damping in Ni–Fe–Ga poly and single crystals

Magnetomechanical damping has been studied in poly and single crystalline Ni–Fe–Ga ferromagnetic shape memory alloys in the austenitic state, with emphasis on the non-linear hysteretic component. The experiments were performed at an ultrasonic frequency, over a wide range of strain amplitudes, at room temperature with different transverse polarizing fields and from 255 to 365 K with different axial polarizing fields. We found that polycrystalline samples demonstrate higher damping level than single crystals. The contribution of the hysteretic magnetomechanical damping is low in polycrystals and damping properties in the austenite are predominantly controlled by existing defects, like dislocations, grain boundaries, and cracks. Single crystalline samples are characterized by substantially lower values of the total damping due to their higher degree of structural perfectness. In contrast to the polycrystals, the non-linear damping in the austenitic state is associated in single crystals with the hysteretic magnetomechanical damping.

Magneto-mechanical and Pseudoelastic Damping of Fe–Al Based Single Crystals

Damping behavior of Fe–16.0~28.0at%Al and Fe–23.0at%Al–2.0at%M (M=Cr, Mn, Co, Ni) in the wide strain amplitude range was examined and the damping mechanism was discussed. In Fe–Al binary single crystals, magneto-mechanical damping caused by irreversible motion of magnetic domain walls took place at low strain amplitudes. On the other hand, pseudoelasticity based on reversible motion of 1/4 ‹111› superpartial dislocations appeared in Fe–23.0at%Al single crystals which also contributed to the high damping capacity at high strain amplitudes. The effect of Cr, Mn, Co and Ni on the vibration attenuation of Fe–23.0at%Al crystals was also examined. As a result, Ni doping was found to be effective in the increase in both internal friction and yield strength of Fe–Al alloys.

Strain-amplitude dependent fatigue resistance of low-alloy pressure vessel steels in high-temperature water

Low cycle fatigue resistance of low-alloy pressure vessel steels was investigated in 561 K air and water over a wide strain amplitude range. It was found that fatigue resistance of the steels was enhanced in high-temperature water relative to high-temperature air under the low strain amplitude conditions ( 2 × 104 cycles), while it was remarkably degraded in high-temperature water under the higher strain amplitude conditions. Fatigue cracking and fractographic features suggested that effects of hydrogen be involved in the present corrosion fatigue process in high-temperature water. Possible environmentally assisted cracking mechanisms are discussed.

Phenomenological description of cyclic deformation using the overlay model

Abstract The overlay model of cyclic deformation is considered to be physically motivated and has definite advantages over the classical models. It can describe qualitatively a variety of effects that the classical models are not able to describe. This model successfully describes the deformation behavior of a material that obeys Masing’s hypothesis. However, there are many materials that do not satisfy Masing’s hypothesis, and show the cyclic hardening (or cyclic softening) and the strain range dependence. In this investigation, we modified the overlay model to consider the characteristics in the cyclic deformation behavior of non-Masing material, observed through low cycle fatigue (LCF) tests of 316L and 429EM stainless steel. The yield stress of the subelement in the model was divided into two parts: one part describes the master curve and another represents the change of the elastic limit. The memory surface of the plastic strain range was introduced to consider the strain range dependence. The prediction by the modified overlay model shows good agreement with the actual hysteresis loops at a wide range of strain amplitudes and temperatures.

Metallurgy and performance of electrodeposited copper for flexible circuits

In this paper, we consider intrinsic properties of copper electrodeposited as plateup on polyimide substrate, thermal response of electrodeposited copper and fatigue performance of copper and copper/polyimide construction. The critical material characteristics examined are grain morphology and structure, crystallographic texture, microhardness, uniaxial strength and ductility and isothermal cyclic fatigue life. Given optimum processing conditions, copper plateup in flexible circuits displays fine grain structure, high ductility, adequate thermal stability, freedom from thermal embrittlement and excellent fatigue endurance over a wide range of strain amplitudes.

Mechanical fatigue of thin copper foil

The electrodeposited and the rolled 12 to 35 µm thick copper foils are subjected to the bending/unbending strain-controlled flex fatigue over a wide range of strain amplitudes. The fatigue life is associated with an increase in electrical resistance of the specimen beyond a preassigned threshold. For each foil type, in the rolled or as-deposited as well as in the (recrystallization-like) annealed conditions, the inverse Coffin-Manson (C-M) relationship between strain amplitude (Δe/2) and fatigue life (Nf) is established in the high Δe/2 (low Nf) and the low Δe/2 (high Nf) regimes. The Nf, Δe/2, and C-M slopes (c,b) are utilized to calculate the cyclic strain hardening (n′) and fatigue ductility (Df) parameters. It is shown that for a given foil thickness, an universal relationship exists between Df and the strength (σ) normalized fatigue life (Nf/σ). The propagation of fatigue crack through the foil thickness and across the sample width is related to the unique fine grain structure for each foil type: pancaked grains for the rolled foil and equiaxed grains for the electrodeposited foil. The fatal failure corresponds to convergence of the through-thickness and the across-the-width fatigue cracks. The variations in (i) electrical resistance, (ii) mid-thickness microhardness and grain structure and (iii) dislocation configurations with fatigue are monitored. Except for a small but significant fatigue induced softening (or hardening), no convincing evidence of strain localization (and the associated dislocation configurations generally observed for the bulk samples) has been found.