Stage Of Stress Relaxation Research Articles

The three stages of stress relaxation - Observations for the time-dependent behaviour of brittle rocks based on laboratory testing

Underground openings can experience time-dependent deformations and stress changes. Studying time-dependent rock behaviour is commonly done with static load (creep) tests in the laboratory which typically exhibit three distinct stages of behaviour. In this study relaxation tests were conducted to examine if three stages also exist under constant strain boundary conditions and to understand how the relaxation behaviour changes as the driving stress to strength ratio is increased. Tests were conducted on two types of limestone. At different load levels similar stress-time responses were measured indicating three distinct stages of stress relaxation. The first stage of stress relaxation (RI) where the stress relaxes with a decreasing rate is followed by the second stage (RII) in which the stress decrease approaches a constant rate and in the third stage (RIII) no further stress relaxation takes place. In the first stage 55% to 95% of the total stress relaxation takes place. The test results are compared with literature data to understand the influence of the stiffness on the magnitude and time to reach the maximum stress relaxation. Relaxation tests could be used to derive numerical model inputs to describe the time-dependent behaviour in a manner similar to static load tests.

Calculation-experimental technique for predicting the relaxation properties of thin polymer fibers during long-term loading

A technique is developed to predict the strain and the stress in a fiber under combined relaxation and creep conditions during long-term loading. Stepwise exponential approximations of the characteristic segments in a relaxation curve are suggested for the initial stage of stress relaxation, and they are generalized by an adaptive exponential approximation containing at most two approximation parameters.

Initial stages of misfit stress relaxation through the formation of prismatic dislocation loops in GaN–Ga2O3 composite nanostructures

The initial stages of misfit stress relaxation through the formation of rectangular prismatic dislocation loops in model composite nanostructures have been considered. The nanostructures are either spherical or cylindrical GaN shells grown on solid or hollow β-Ga2O3 cores or planar thin GaN films on β-Ga2O3 substrates. Three characteristic configurations of prismatic dislocation loops, namely, square loops, loops elongated along the GaN/Ga2O3 interface, and loops elongated along the normal to the GaN/Ga2O3 interface, have been analyzed. The generation of prismatic dislocation loops from the interface into the bulk of the GaN shell (film), from the free surface into the GaN shell (film), and from the interface into the β-Ga2O3 core (substrate) has been investigated. It has been shown that, for the minimum known estimate of the lattice misfit (2.6%) in some of the considered nanostructures, no any prismatic dislocation loops can be generated. If the generation of prismatic dislocation loops is possible, then in all the considered nanostructures, the energetically more favorable case corresponds to prismatic dislocation loops elongated along the GaN/Ga2O3 interfaces, and the more preferred generation of prismatic dislocation loops occurs from the GaN free surface. The GaN/Ga2O3 nanostructures that are the most and least resistant to the formation of prismatic dislocation loops have been determined. It has been found that, among the considered nanostructures, the planar two-layer GaN/Ga2O3 plate is the most resistant to the generation of prismatic dislocation loops, which is explained by the action of an alternative mechanism for the relaxation of misfit stresses due to the bending of the plate. The least resistant nanostructure is the planar three-layer GaN/Ga2O3/GaN plate, in which GaN films have an identical thickness and which itself as a whole does not undergo bending. The critical thicknesses of the GaN shells (films), which must be exceeded to ensure the growth of these shells (films) so as to avoid the formation of prismatic dislocation loops, have been calculated for all the studied nanostructures and three known estimates of the lattice misfits (2.6, 4.7, and 10.1%).

Evaluation of Force-Time Changes During Impact of Hybrid Laminates Made of Titanium and Fibrous Composite

AbstractFibre metal laminates (FML) are the modern hybrid materials with potential wide range of applications in aerospace technology due to their excellent mechanical properties (particularly fatigue strength, resistance to impacts) and also excellent corrosion resistance. The study describes the resistance to low velocity impacts in Ti/CFRP laminates. Tested laminates were produced in autoclave process. The laminates were characterized in terms of their response to impacts in specified energy range (5J, 10J, 20J). The tests were performed in accordance with ASTM D7137 standard. The laminates were subjected to impacts by means of hemispherical impactor with diameter of 12,7 mm. The following values have been determined: impact force vs. time, maximum force and the force at which the material destruction process commences (Pi). It has been found that fibre titanium laminates are characterized by high resistance to impacts. This feature is associated with elasto-plastic properties of metal and high rigidity of epoxy - fibre composite. It has been observed that Ti/CFRP laminates are characterized by more instable force during impact in stage of stabilization of impactor-laminate system and stage of force growth that glass fibre laminates. It has been observed more stable force decrease in stage of stress relaxation and withdrawal of the impactor. In energy range under test, the laminates based on titanium with glass and carbon fibres reinforcement demonstrate similar and high resistance to low-velocity impact, measured by means of failure initiation force and impact maximum force.

Integrated experimental measurement and computational analysis of relaxation behavior of cement and asphalt mortar

The stress relaxation behavior of cement and asphalt mortar (CA mortar) under different initial strain levels was investigated. Results show that the stress relaxation of CA mortar can be divided into two parts: the attenuation stress relaxation stage and stable stress relaxation stage. With the increasing strain levels, the relaxed stress, stress relaxation rate, stress relaxation modulus and specific stress relaxation of CA mortar increase gradually. Under the same initial strain level, the relaxed stress of type I CA mortar and type II CA mortar are little different, whereas the specific stress relaxation of type I CA mortar is much greater than that of type II CA mortar. In the strain range of 0.32–0.80%, the isochronous stress-strain relation of type I CA mortar is linear. When the strain is greater than 0.80%, the isochronous stress-strain relationship concaves to the strain axis gradually. The isochronous stress-strain relationship of type II CA mortar show linear increase in the strain range of 0.47–1.42%. A stress relaxation model based on thermodynamic theory was established, which agrees very well with the experimental results.

Initial stage of stress relaxation in oriented polymers

The initial stage of stress relaxation, i.e., a decrease of the stress with time in an extended solid at a fixed length of the specimen, has been studied in oriented fibers of a linear polymer, polypropylene, chosen as the object of investigation. Experimental data have been obtained, and the stress in the object from the beginning of tensile loading of the specimen has been analyzed. It has been found that the stress relaxation caused by thermal fluctuation conformational transitions in stretched chain polymer molecules occurs from the beginning of the stretching of the polymer fiber. The time dependence of the stress relaxation of polypropylene fibers in all initial stages of deformation of the fibers has been elucidated.

Finite cohesion due to chain entanglement in polymer melts.

Three different types of experiments, quiescent stress relaxation, delayed rate-switching during stress relaxation, and elastic recovery after step strain, are carried out in this work to elucidate the existence of a finite cohesion barrier against free chain retraction in entangled polymers. Our experiments show that there is little hastened stress relaxation from step-wise shear up to γ = 0.7 and step-wise extension up to the stretching ratio λ = 1.5 at any time before or after the Rouse time. In contrast, a noticeable stress drop stemming from the built-in barrier-free chain retraction is predicted using the GLaMM model. In other words, the experiment reveals a threshold magnitude of step-wise deformation below which the stress relaxation follows identical dynamics whereas the GLaMM or Doi-Edwards model indicates a monotonic acceleration of the stress relaxation dynamics as a function of the magnitude of the step-wise deformation. Furthermore, a sudden application of startup extension during different stages of stress relaxation after a step-wise extension, i.e. the delayed rate-switching experiment, shows that the geometric condensation of entanglement strands in the cross-sectional area survives beyond the reptation time τd that is over 100 times the Rouse time τR. Our results point to the existence of a cohesion barrier that can prevent free chain retraction upon moderate deformation in well-entangled polymer melts.

Temperature sensitivity and model of stress relaxation properties of cement and asphalt mortar

The stress relaxation properties of two types of cement and asphalt mortar (CA mortar) in the temperature range of −40 to 60°C and at the initial strain of 0.1% was studied by dynamic mechanical thermal spectrometer. The results show that the stress relaxation process of CA mortar can be divided into attenuation stress relaxation stage and steady stress relaxation stage. The lower the temperature is, the higher the initial stress and residual stress are. At the same temperature, the stress relaxation rate and specific stress relaxation of type I CA mortar are larger than that of type II CA mortar, while the initial stress, residual stress and stress relaxation modulus are relatively smaller. The glass transition region of type I CA mortar characterized by the isochronous stress–temperature curves is −20 to 0°C. The established model agrees well with experimental results, and φ, δ are dominated parameters affecting the stress relaxation of CA mortar. This indicates that the established model can effectively predict the time dependence and temperature sensitivity of stress relaxation of CA mortar. The results can provide reference for the calculation of temperature stress of CA mortar filling layer of ballastless slab track.

Initial stages of misfit stress relaxation in composite nanostructures through generation of rectangular prismatic dislocation loops

Critical (necessary) conditions of misfit stress relaxation in bulk and hollow core–shell nanoparticles, bulk and hollow core–shell nanowires, and flat bi- and tri-nanolayers (composing of a substrate and one or two thin films, respectively) through generation of rectangular prismatic dislocation loops (PDLs) at the inner and outer interfaces of the composite nanostructures with subsequent extension of the PDLs into cores (substrates) or shells (films) are analyzed theoretically and discussed in detail. The critical conditions are considered for different shapes and places of generation of the PDLs. It is shown that the misfit parameter is the principal factor, which determines the energetic preference of PDL generation: the latter is energetically favorable when the misfit parameter reaches its critical value, which depends on the geometry parameters of a composite nanostructure and the PDL type. Regardless of the place of PDL generation, the most energetically favorable case is when the PDL is elongated along the interface. The generation of PDLs from the free surface is the most preferable for small thicknesses of the shells (films). Growth of the shell (film) leads to a change of places of PDL generation while maintains their preferential shape – elongated along the interface. Among the six composite nanostructures under consideration, the tri-nanolayers are the least stable to the PDL generation. The hollow nanoparticles and nanowires are more stable to the PDL generation than the bulk ones. The bi-nanolayers are the most stable to the PDL generation.

Initial stages of misfit stress relaxation by rectangular prismatic dislocation loops in composite nanostructures

Theoretical models are proposed for describing the initial stages of misfit stress relaxation in bulk and hollow core-shell nanoparticles and nanowires, and in planar bi- and trinanolayers through generation of rectangular prismatic dislocation loops at the inner and outer interfaces. We obtain the changes in the total energy of the system due to the appearance of dislocation loops and calculate the critical conditions of their formation. We also determine the most profitable shape of the loops and the preferred places of their generation. Finally, we choose the nanostructures which are the most stable against dislocation loop generation.

Hot Stretch Bending and Creep Forming of Titanium Alloy Profile

Titanium alloy is frequently used in aerospace applications such as load carrying airframe due to their excellent mechanical and corrosion properties in combination with being comparatively light weight. However, it is well-known that titanium alloy is difficult to form at room temperature. So hot stretch bending and creep forming process is used to improve formability and reduce springback in forming titanium alloy profile. The principle of hot stretch bending and creep forming is leading a stress relaxation stage by maintaining the workpiece against the die for a selected dwell time after hot stretch bending stage. This allows the benefits of low residual stress and minimum springback including inexpensive tooling and good repeatability. In the present work, a set of uniaxial tension tests was performed on OT4 titanium alloy at the temperature ranging from 773K to 973K and strain rate from 0.0025 s-1 to 0.01 s-1. Stress relaxation tests were carried out at the temperature range from 773K to 973K. Arrhenius model was employed to characterize the creep behaviour. Finite element model of hot stretch bending and creep forming process was created in ABAQUS. The results of FE simulation indicate that residual stress decreases greatly in stress relaxation stage and low residual stress lead smaller springback. The predicted springback show promising agreement with the corresponding experimental observations.

Stress relaxation behavior of an Al–Zn–Mg–Cu alloy in simulated age-forming process

The stress relaxation behavior of age-forming for an Al–Zn–Mg–Cu alloy was studied using a designed device that can simulate the age forming process. The mechanism of stress relaxation was also revealed through calculating thermal activation parameters and analyzing the microstructures. The results suggested that the stress relaxation behavior of the Al–Zn–Mg–Cu alloy in the simulated age-forming process can be divided into three stages according to the stress level. The three stages of stress relaxation are: (i) the initial high stress stage, (ii) the subsequent middle stress transition stage and (iii) the last low stress equilibrium stage, respectively. The deformation activation energies are 132kJ/mol in the initial high stress stage, 119kJ/mol in the subsequent middle stress transition stage and 91kJ/mol in the last low stress equilibrium stage, respectively. The analysis of the thermal activation parameters and microstructures revealed that dislocation creep was the dominant deformation mechanism in the initial and subsequent stages of the stress relaxation; whereas diffusion creep is the mechanism in the last stage of the stress relaxation. Additionally, a special threshold stress phenomena was present in the stress relaxation of the age-forming process, which was scribed to the interaction between precipitation and dislocation in the Al–Zn–Mg–Cu alloy

Study on Thermal Cycling of Sn0.7Cu Solder

Thermal cycling of a unit Sn0.7Cu solder was studied based on the steady-state creep constitutive equation and Matlab software. The results show that there is a steady-state cycle for the thermal cycling of unit Sn0.7Cu eutectic solder. In steady-state thermal cycling, the shear stress is increased with the increase of temperature. There is a stage of stress relaxation during high temperature. A liner relationship between maximum shear stress and maximum shear strain is observed during thermal cycling. The metastable cycle number is declined greatly with the increase of maximum shear strain.

The Effect of Material Models on Elastic Follow-Up

The phenomenon of elastic follow-up in high temperature piping has a long history and rules to limit its significance in design are well established. However, most design rules, and numerous associated supporting studies, have been limited to a simple power-law of creep, with variations to account for time- or strain-hardening in primary creep. A common feature of the most studies of elastic follow-up in structures subject to power-law creep is that a plot of (maximum) stress against strain—a so-called isochronous stress– strain trajectory—is almost insensitive to the creep law (in particular, the stress exponent in the power-law) and is almost linear (until perhaps the later stages of stress relaxation). A limitation of the power-law is that it assumes to be valid across all stress ranges, from low through moderate to high, yet it is well known that this is not generally the case. This paper aims to investigate the effect of stress-range dependent material models on the nature of elastic follow-up: both a simple two-bar structure (common in studies of elastic follow-up) and a detailed finite element analysis of a piping elbow are examined. It is found that stress-range dependent material models can have a significant effect on the accepted characteristics of elastic follow-up.

Creep Based Prediction Model of Stress Relaxation Behavior for High Temperature Materials

An average creep rate conversion model based on Schlottner-Seeley creep assessment procedure and creep damage equation has been developed by considering the relationship that two stages of stress relaxation are corresponding to the first and the second creep stage respectively and the effect of these two kinds of creep rate on relaxation, and stress relaxation is creep at various stresses. And an incremental calculation prediction methodology of stress relaxation performance was established. The predicted results are compared with the data of stress relaxation tests conducted on bolting steel 1Cr10NiMoW2VNbN used in ultra-supercritical turbines. Validation results indicate that the developed model has led to better consistent results with the measured data and thus can be recommended in stress relaxation behavior prediction of high temperature materials.

FEM simulation of viscous properties for granular materials considering the loading rate effect

The deformation and strength characteristics of sandy soils as a kind of granular materials are very complex. The experimental results show that when the strain rate suddenly changes in monotonic loading (ML) case, the stress–strain curve of sandy soils changes sharply and then gradually converges into the original inferred one that would be obtained by continuous ML at constant strain rate after having exhibited clear yielding. Similar behaviors are also observed when ML is restarted at a constant strain rate following a creep loading or stress relaxation stage. An elasto-viscoplastic constitutive model for granular materials is developed, which consists of three components. One of the most important features of the model is that it can take into account the effects of loading rate due to viscous properties on the stress–strain behavior. The stress ratio-axial strain–time relations from four drained plain strain compression (PSC) tests on the saturated Toyoura sand are successfully simulated by the finite element method (FEM) code incorporating the proposed constitutive model. It is shown that the FEM code can simulate the viscous behaviors of sand accurately under arbitrary loading history.

Deformation behavior of solid polymer during hot embossing process

Though hot embossing is a well known technique for the fabrication of polymer based micro-device, the deformation behavior of solid polymer during hot embossing process is not investigated clearly. In this paper, the deformation behavior of solid polymer was observed by two methods, synchronous observation and asynchronous analysis. A finite element simulation and a phenomenological model were used to evaluate the deformation behavior of solid polymer during hot embossing. Results showed that the deformation of solid polymer during embossing process included two stages. One was a stress concentration and strain hardening stage, which occurred during the heating and applying pressure process. The “swallowtails” induced by incomplete filling generate at this stage. The other was a stress relaxation and deformation recovery stage, which occurred during the remaining temperature and pressure process. The “swallowtails” were eliminated at this stage. The second stage was significant for improving replication precision, but it had not been reported before.

Stability of dislocation structures in copper towards stress relaxation investigated by high angular resolution 3D X‐ray diffraction

AbstractA 300 µm thick tensile specimen of OFHC copper is subjected to a tensile loading sequence and deformed to a maximal strain of 3.11%. Using the novel three‐dimensional X‐ray diffraction method ‘High angular resolution 3DXRD', the evolution of the microstructure within a deeply embedded grain is characterised in‐situ by the behaviour of individual subgrains. The loading sequence consists of three continuous deformation stages with strain rates of 1.1 × 10–6 s–1 and 3 × 10–2 s–1, in each case followed by a period of extended stress relaxation at fixed motor positions, as well as an unloading step. In contrast to the deformation stages, during each stress relaxation stage, number, size and orientation of subgrains are found to be constant, while a minor amount of clean‐up of the microstructure is observed as narrowing of the radial X‐ray diffraction line profile. The associated decrease in the width of the strain distribution indicates homogenization of the elastic strains present in the deformation structure. During reloading, the subgrain structure seemingly starts to develop further when the entire dislocation structure is deforming plastically. Upon unloading of the sample, the average backward strain of the subgrains increases. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

A biphasic theory for the viscoelastic behaviors of vocal fold lamina propria in stress relaxation

In this study, a biphasic theory is applied to investigate the viscoelastic behaviors of vocal fold lamina propria during stress relaxation. The vocal fold lamina propria tissue is described as a biphasic material composed of a solid phase and an interstitial fluid phase. The biphasic theory reveals the interaction between the solid and the fluid. For the one-dimensional case, the analytical solutions of solid displacement, fluid velocity, and stress are derived. The biphasic theory predicts the stress relaxation of the vocal fold lamina propria. The quasilinear viscoelastic model as well as its higher-order elastic parameters can be derived from this biphasic theory. Furthermore, the fluid is found to support the majority of the stress at the early stage of stress relaxation; however, when the time becomes sufficiently large, the solid eventually bears all the stress. The early fluid stress support is much higher than the eventual solid support and may be important for understanding the effects of dehydration on tissue damage. By considering the solid-fluid structure of the vocal fold lamina propria, the biphasic theory allows for a more physical theory of tissue viscoelasticity than a single phase solid description and may provide a valuable physical mechanism for the observed vocal fold rheologic behaviors.

Room temperature viscosity and delayed elasticity in infrared glass fiber

Infrared transparent optical fibers from the Te–As–Se system (TAS) exhibit a viscoelastic behavior at room temperature. The study of the change of the radius of curvature of fibers, once the fibers are unrolled from the mandrel onto which they were rolled just after fiber-drawing, allows the determination of constitutive laws both for the stress relaxation kinetics and for the delayed elasticity process. Whereas, a linear Burger's model provides a good modelling of the stress relaxation stage, a stretched exponential function gives a better description for the delayed elasticity behavior. The room temperature viscosity of the fibers ranges from 3 × 10 16 to 2 × 10 17 Pa s and the time constant of the anelastic strain recovery process is from 4 to 15 days.