Stress-strain Dependence Research Articles

Thermoelastic behaviour of martensitic alloy in the vicinity of critical point in the stress–temperature phase diagram

The theoretical phase diagram of the shape memory alloy, which exhibits the first-order martensitic phase transition of the cubic–tetragonal type, has been considered. The thermoelastic behaviour of the ultra-soft Ni–Mn–Ga alloy in the vicinity of the endpoint of the phase transitions line has been modelled. To this end, the strain–temperature and stress–strain dependencies have been computed with the account of the temperature dependence of the elastic modulus of the alloy. Two important features of thermoelastic behaviour of the alloy have been disclosed: (1) even in the case of complete stress-induced martensitic transformation (MT), the MT strain determined from the length of the plateaus at the stress–strain curves is smaller than the ‘spontaneous’ tetragonal distortion of the crystal lattice, which arises on cooling of the alloy and (2) the stress–strain loops may include the plateau-like segment even at temperatures above the critical temperature, which corresponds to the endpoint of the stress–strain phase diagram. These features render the observation of the endpoint of phase transitions line impossible with the help of the stress–strain tests and make preferable the direct structural studies of MTs in the stressed single-crystalline specimens.

Suppressed molecular orientation in nylon 6/clay nanocomposite at large strain: Role of microvoiding

AbstractA micro‐FTIR measurement has been conducted to explore the molecular orientation of amorphous phase in the nylon 6/clay nanocomposite at large strain. Our results indicate that the molecular orientation in such a nanocomposite during stretching is lower than that observed for the pure nylon 6 counterpart, which is further evidenced by the true stress‐strain dependence. The relaxation of the molecular network, resulted from the destruction of γ‐crystals in part and mostly from microvoding (demonstrated by volume dilatation and 2D‐SAXS measurements), should be responsible for the suppressed molecular orientation in the nylon 6/clay nanocomposite. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 514–519, 2010

Prediction of Subgrade Resilient Modulus Using Genetic Algorithm and Curve-Shifting Methodology

This paper demonstrates the applicability of the genetic algorithm and curve-shifting methodology to the estimation of the resilient modulus at various stress states for subgrade soils by using the results of triaxial resilient modulus tests. This innovative methodology is proposed as an alternative to conventional nonlinear constitutive relationships. With the genetic algorithm, laboratory curves for different deviator stress levels at different confining pressures are horizontally shifted to form a final gamma distribution curve that can represent the stress–strain behavior of subgrade soils with the corresponding predicted shift factors. Resilient modulus values for a given stress state can be estimated on the basis of this curve and another gamma function that represents the variation of the shift values for different confining stresses. To compare the effectiveness of these two approaches, coefficients for the Uzan constitutive model were also determined for each laboratory test and compared with those determined by the approach described in this paper. Predicted resilient modulus values from each approach are separately compared with artificial neural network (ANN) model predictions to evaluate their efficiency and reliability for resilient response prediction. The results of the analysis indicated that the curve-shifting methodology gave superior estimates and a coefficient of determination 14% higher than the Uzan model predictions when the results were evaluated with the ANN model outputs. Thus, although it is not a constitutive model, use of the genetic algorithm and curve-shifting methodology is proposed as a promising technique for the evaluation of the stress–strain dependency of subgrade soils.

Plane nonaxisymmetric deformation of a viscoelastic cylinder with consideration of its physical and geometric nonlinearity

The nonaxisymmetric plane problem of the nonlinear theory of viscoelasticity is solved for a cylinder reinforced by an elastic circular shell. The cylinder has an internal cut resembling a Maltese cross in shape. The identification of the nonlinear endochronous theory of aging viscoelastic materials is conducted by a genetic algorithm method on the basis a nonmonotonic experimental stress-strain dependence. Some numerical results obtained for the stress-strain state of this cylinder under the action of internal pressure are discussed with consideration of the above physical nonlinearity and the finite logarithmic strains.

Bond Scrambling and Network Elasticity

Dynamic networks (DNs) recently reported in the literature are based on cross-linked supramolecular chains or on covalent chains with reversible bonds. As originally pointed out by Lehn, these networks should be regarded as dynamic materials exhibiting adaptive features due to continuous scrambling of their bonds and sequences. Results in the recent literature reveal that these networks undergo reversible long-range deformation resembling that of rubber networks. The present analysis of this process in terms of the theory of composite networks is based on the expectation that the scrambling process should allow rupture of bonds in the undeformed state and their reformation in the stretched state. Accordingly, a permanent set of the resting length of DNs should generally be expected and set materials should retain long-range elasticity relative to the set state. However, only a limited set is shown by DNs, implying that a strong memory of the initial network topology assists elastic recovery of the original dimensions. The analysis of reported experimental data further reveals that the stress-strain dependence of dynamic networks accurately follows the classical rubber elasticity theory. In this respect, DNs show better rubber behavior than typical covalent networks. Consistently with theoretical predictions, this surprising finding suggests that bond scrambling relieves local strain constraints on the fluctuations of networks junctions and favors the recovery of the initial network topology. Scrambling therefore allows compliance under stress and enhanced recovery when stress is released. Unprecedented applications of these advanced materials thus become foreseeable.

An experimental and numerical study of the effects of length scale and strain state on the necking and fracture behaviours in sheet metals

Within sheet metal forming, crashworthiness analysis in the automotive industry and ship research on collision and grounding, modelling of the material failure/fracture, including the behaviour at large plastic deformations, is critical for accurate failure predictions. In order to validate existing failure models used in finite element (FE) simulations in terms of dependence on length scale and strain state, tests recorded with the optical strain measuring system ARAMIS have been conducted. With this system, the stress–strain behaviour of uniaxial tensile tests was examined locally, and from this information true stress–strain relations were calculated on different length scales across the necking region. Forming limit tests were conducted to study the multiaxial failure behaviour of the material in terms of necking and fracture. The failure criteria that were verified against the tests were chosen among those available in the FE software Abaqus and the Bressan–Williams–Hill (BWH) criterion proposed by Alsos et al, 2008. The experimental and numerical results from the tensile tests confirmed that Barba's relation is valid for handling stress–strain dependence on the length scale used for strain evaluation after necking. Also, the evolution of damage in the FE simulations was related to the processes ultimately leading to initiation and propagation of a macroscopic crack in the final phase of the tensile tests. Furthermore, numerical simulations using the BWH criterion for prediction of instability at the necking point showed good agreement with the forming limit test results. The effect of pre-straining in the forming limit tests and the FE simulations of them is discussed.

The solid–fluid transition in a yield stress shear thinning physical gel

We present an experimental investigation of the solid–fluid transition in a yield stress shear thinning physical gel (Carbopol® 940) under shear. Upon a gradual increase of the external forcing, we observe three distinct deformation regimes: an elastic solid-like regime (characterized by a linear stress–strain dependence), a solid–fluid phase coexistence regime (characterized by a competition between destruction and reformation of the gel), and a purely viscous regime (characterized by a power law stress-rate of strain dependence). The competition between destruction and reformation of the gel is investigated via both systematic measurements of the dynamic elastic moduli (as a function of stress, the amplitude, and temperature) and unsteady flow ramps. The transition from solid behavior to fluid behavior displays a clear hysteresis upon increasing and decreasing values of the external forcing. We find that the deformation power corresponding to the hysteresis region scales linearly with the rate at which the material is being forced (the degree of flow unsteadiness). In the asymptotic limit of small forcing rates, our results agree well with previous steady state investigations of the yielding transition. Based on these experimental findings, we suggest an analogy between the solid–fluid transition and a first-order phase transition, e.g., the magnetization of a ferro-magnet where irreversibility and hysteresis emerge as a consequence of a phase coexistence regime. In order to get further insight into the solid–fluid transition, our experimental findings are complemented by a simple kinetic model that qualitatively describes the structural hysteresis observed in our rheological experiments. The model is fairly well validated against oscillatory flow data by a partial reconstruction of the Pipkin space of the material’s response and its nonlinear spectral behavior.

Hysteresis of the stress–strain dependences in Hooke’s region

A procedure is proposed for the construction [with high accuracy (∼ 0.02%)] of the stress–strain diagrams for specimens corresponding to a model of restrained circular plate. On the basis of these diagrams for 40Kh steel, it is shown that the phenomenon of hysteresis, the nonlinearity of the dependence of the amplitude of hysteresis on the mechanical stresses σ, and the initial residual strains appear for low σ (10–20 times lower than the yield strength). These results can serve as a basis for the subsequent development of the procedure of prediction of the strength of structural materials for low strains, much lower than the maximum strains corresponding to the ordinary Hooke’s region.

Stress–strain analysis of porous scaffolds made from titanium alloys synthesized via SLS method

A layer-by-layer selective laser sintering (SLS) technology seems to be greatly promising for solving the plastic surgery problems, particularly those pertaining to the facial reconstruction. Made from titanium-based alloys (titanium or nitinol, i.e. NiTi-intermetallic phase), the porous scaffolds for cranioplasty are an efficient tool for rectifying the face defects and for the dental orthopedic surgery. The progress in the oral surgery and teeth implantation is caused by the problem of an osteointegration on the one hand, and by achievements of the implant synthesis techniques, on the other hand. An important problem thereby is a profound study of the stress–strain behavior of porous implants under the masticatory load or pressure. In the present study the ways for the optimization of the porous implant structural and strength properties as the function of the laser synthesis parameters are described. The finite element approach (ANSYS) was used here for a complex dowel description and numerical simulations. In order to evaluate the processes in the porous implant under the external loading, a CAD 3D model was built for different internal and external configurations of the implant and/or initial shape of powdered particles. The stress–strain dependences were calculated that displayed the irregularity of the stress distribution by the implant volume in the bone tissue. Most of the values are concentrated in places of object contact.

Development of Time Dependent Stress-Strain Simulation of Clay

AbstractThe objective of this study is to derive a time dependent effective based constitutive law on the basis of framework of the Modified Cam-Clay model. This model takes into account the anisotropic characteristics and creep behavior, based on the theory of viscoplasticity. The model sets the initial yield surface symmetric to theKoline for modeling the initialKocondition. A method is then developed to compute the gyration and expansion of the loading surface to simulate the anisotropic behavior due to the principal stress gyration after shear. The creep or time dependent behavior is considered in the model by adopting Kutter and Sathialingam's model, which was derived from Taylor's secondary consolidation theory and Bjerrum's delayed compression model. Compared with the Modified Cam-Clay model, the model requires five additional parameters to describe the soil behavior. All of the additional parameters can be obtained through conventional soil tests or parametric studies. The model is evaluated through a series of simulation of undrained shear tests and undrained creep tests.

AC loss characteristics of copper-stabilized YBCO coated conductor

Influence of copper layer and mechanical stress–strain on AC losses in copper-stabilized YBCO coated conductor (CC) was investigated. The uni-axial tensile stress–strain was applied to the sample CC in liquid nitrogen at atmospheric pressure, and the AC losses (transport, magnetization and total AC losses) were measured by an electric method. Experimental results showed that the stress–strain dependence of the AC losses can be estimated by knowing stress dependent critical current and magnetization losses in the non-stressed CC. Influence of the copper layer was investigated by measuring frequency dependence of the AC losses. The experimental results showed that there are some influences of the copper layer. However, the influence of the copper layer was not significant from the stand point of practice applications.

Electrical, Mechanical and Thermal Characterization of Bi-2223/AgAu Material for Use in HTS Current Leads for W7-X

The superconducting magnet system of the W7-X stellarator presently under construction at the Max-Planck-Institute for Plasmaphysics in Greifswald, Germany, requires 7 pairs of current leads for a maximum current of 18.2 kA. The Forschungszentrum Karlsruhe is responsible for construction, manufacturing and performance testing of the current leads prior to installation in the W7-X machine. To reduce the overall cooling power for the refrigerator as well as the free convection problem due to the upside-down orientation of the leads, it was decided to use HTS material in the temperature range between approx. 5 K and 60 K. The optimization of the HTS part requires to know exactly the electrical, mechanical and thermal parameters of the HTS material. Actually two suppliers, EHTS and Sumitomo offer such Bi-2223/AgAu material. Single tapes as well as stacks were used to measure the critical current as a function of applied magnetic field for various temperatures. The thermal conductivity, the stress-strain dependence and the thermal contraction were also measured. In the paper the electrical, mechanical and thermal performance of different tapes and stacks will be described and discussed.

Modelling reinforced concrete structures subjected to impulsive loading using concrete lattice model

A two dimensional behavioral rate dependent lattice model (RDLM) capable of analyzing reinforced concrete members subjected to impulsive loading is presented. As a result of the impulsive loads reaching their peak intensity in extremely short durations of time, material nonlinearities and strain rate effects play an important role in the analysis. A numerical approach based on an explicit finite element formulation is introduced to solve two dimensional planar structural problems under impulsive loads. The procedure incorporates equilibrium and compatibility conditions and utilizes realistic rate dependent stressstrain relationships for cracked concrete. The model inherently takes into account some major influencing factors, progressive cracking of concrete in tension, the inelastic response in compression, the yielding of reinforcing steel, and strain rate sensitivity of concrete and steel. Correlation studies between analytical and experimental results on reinforced concrete beams subject to impulsive loading are conducted and are shown to be in good agreement.

Network Topology–Mechanical Properties Relationships of Model Elastomers

We review our recent studies on the mechanical properties of model elastomers with well-characterized network structures. Model elastomers were prepared by end-linking precursor poly(dimethylsiloxane) (PDMS) of known molecular weight with multifunctional crosslinkers. We then strictly assessed the modern entanglement models for rubber elasticity on the basis of the stress–strain data under general biaxial strains covering almost the entire range of accessible deformations for the model PDMS networks. We also demonstrated marked extensibility of more than 3000% for the deswollen networks prepared by removing the solvent from the end-linked gels prepared in the diluted state. The highly deswollen networks comprising the considerably compact conformation (supercoil) exhibited unusually weak strain dependence of stress. We also studied the viscoelastic properties of PDMS networks containing either unattached free chains or pendant chains. The former systems provided a model system to investigate the dynamics of the guest chains in invariant networks. The dynamics of the guest chains, as functions of their own sizes as well as the mesh sizes of host networks, were compared with the predictions of reptation theories. With the model networks with pendant chains, we elucidated the correlation between the damping properties and the amount of pendant chains. The elastomers with highly irregular structures exhibited high damping almost independent of both temperature and frequency.

A thermoviscoelastic model for amorphous shape memory polymers: Incorporating structural and stress relaxation

A thermoviscoelastic constitutive model is developed for amorphous shape memory polymers (SMP) based on the hypothesis that structural and stress relaxation are the primary molecular mechanisms of the shape memory effect and its time-dependence. This work represents a new and fundamentally different approach to modeling amorphous SMPs. A principal feature of the constitutive model is the incorporation of the nonlinear Adam–Gibbs model of structural relaxation and a modified Eyring model of viscous flow into a continuum finite–deformation thermoviscoelastic framework. Comparisons with experiments show that the model can reproduce the strain–temperature response, the temperature and strain-rate dependent stress–strain response, and important features of the temperature dependence of the shape memory response. Because the model includes structural relaxation, the shape memory response also exhibits a dependence on the cooling and heating rates.

Constitutive equation describing the biaxial stress–strain behavior of poly(dimethylsiloxane) networks reinforced with silica generated in situ

The structure-based constitutive equation (its Langevin statistics-based connectivity term predicting the high-strain hardening, the tube-theory-based constraint term predicting the low-strain softening) proposed and tested by us for homogenous elastomeric networks has recently been extended for filler-reinforced networks by incorporating the concept of a strain-dependent strain-amplification factor (Polymer 1976). The equation was found to offer a very good description of stress–strain dependences in different deformation modes of pre-strain-softened filler-reinforced networks of natural and butadiene-styrene rubbers up to high-strains; the more complex high-strain behavior of virgin networks has also been described. The same equation is now shown to give a very good description and reasonable interpretation of published experimental data measured in different deformation modes (uniaxial extension, pure shear, equibiaxial extension) on poly(dimethylsiloxane) networks reinforced with silica precipitated in situ using the sol–gel process. The concentration dependence of the obtained parameter values is discussed.

Nano-Underfills for High-Reliability Applications in Extreme Environments

Silica particles are used as a filler material in electronic underfills to reduce coefficient of thermal expansion of the underfill-epoxy matrix. In traditional underfills, the size of silica particles is in the micrometer range. Reduction in particle sizes into the nanometer range has the potential of attaining higher volume fraction particle loading in the underfills and greater control over underfill properties for higher reliability applications. Presently, no-flow underfills have very low or no filler content because micron-size filler particles hinder solder joint formation. Nano-silica underfills have the potential of attaining higher filler loading in no-flow underfills without hindering solder interconnect formation. In this paper, property prediction models based on representative volume element (RVE) and modified random spatial adsortion have been developed. The models can be used for development of nano-silica underfills with desirable thermo-mechanical properties. Temperature dependent thermo-mechanical properties of nano-underfills have been evaluated and correlated with models in a temperature range of -175degC to 150degC. Properties investigated include, temperature dependent stress-strain, creep and stress relaxation behavior. Nano-underfills on 63Sn37Pb eutectic and 95.5Sn3.5Ag1.0Cu leadfree flip-chip devices have been subjected to thermal shock tests in the range of -55degC to 125degC and -55degC to 150degC, respectively. The trade-offs between using nano-fillers instead of micron-fillers on thermo-mechanical properties and reliability has been benchmarked.

Application of modified superposition model to viscoelastic behavior of periodontal ligament

The periodontal ligament (PDL) is a soft bio-logical tissue which shows a strongly nonlinear and time dependent mechanical behavior. Re-cent experiments on rabbit PDL revealed that the rate of stress relaxation is strain dependent. This nonlinear behavior of PDL cannot be de-scribed well by the separable quasi linear vis-coelasticity theory which is usually used in tis-sue biomechanics. Therefore, PDL requires a more general description which considers this nonlinearity and time dependency. The purpose of this study was to model strain dependent stress relaxation behavior of PDL using modi-fied superposition method. It is shown herein that modified superposition method describes viscoelastic nonlinearties well and shows a good compatibility with available experimental PDL data. Hence, the modified superposition model is suggested to describe periodontal ligament data, because it can suitably demon-strate both elastic nonlinearity and strain-dependent stress relaxation behavior of PDL.

Biological peculiarities of someYersinia species: strain-dependent virulence and strain-dependent stress proteins

A pair ofYersinia enterocolitica serotype O∶3 strains — incubated in growth medium with 10% NaCl and 2 mM glycin betaine at 4 °C, were used to study the plasmid role in the infection of BALB/c mice. The isogenic plasmid-bearing strain, but not its plasmidless derivative, caused enteric infection and histological changes in intestines, stomach and liver of the mice. Two strainsY. enterocolitica andYersinia pseudotuberculosis were incubated at different temperatures (4 and 25 °C) in media, supplemented with different concentrations of NaCl. Two concentrations of betaine as osmoprotector were tested. The initial strains and their substrains were characterised by protein profiles using sodium dodecyl sulphate-polyacrylamide gel electrophoresis. Results show that in salinity conditions, the presence of osmoprotectant (betaine) as well as the temperature of cultivation plays a great role in the expression of some bacterial proteins. The manner in which the different strains answer to the stress situations is specific for each of them.

Modeling of stress-strain dependences for Berea sandstone under quasistatic loading

In this work, a phenomenological model to describe the complex stress-strain properties of a sandstone sample under slow loading is presented. We consider a combination of three methods to treat the elastic and nonlinear behavior observed in stress cycling experiments. The mechanisms to treat interior equilibration processes in sandstone are termed the standard solid relaxation mechanism, the sticky-spring mechanism, and the permanent plastic deformation mechanism. With a small number of parameters, the overall model displays both qualitatively and quantitatively the principal experimental observations of the stress-strain trajectories for Berea sandstone, in particular, the details of end-point memory under quasistatic loading.