Stress Relaxation Model Research Articles

Stress Relaxation in a Cellular Model of Elements with Nonlinear Interaction

A model of stress relaxation in a system of discrete elements is analyzed. The model suggests analyzing a small-time scale of the process when external supply of additional stresses in the system are negligibly small. The nonlinear interaction of elements is similar to the interaction of elements in the open dissipative OFC model. Toppling conditions are determined by the static fatigue effect. It is shown that at a high level of element coupling, the model is characterized by a power-law decay of the drop frequency in time, similar to that observed in aftershock sequences of earthquakes. This regularity slightly depends on the initial distribution of stresses in the system, its exponent is p = 0.85–10 for the element coupling parameter α = 0–0.25. The analysis of the value of the time delay c for the formation of a power-law drop frequency decay shows that this parameter correlates with the duration of large-amplitude drops at the initial step of the relaxation process. The value c is defined in this case by the parameter α. Calculations also shows that relaxation of the mean stress σ(t) in the system of elements follows the relation \(t \propto {{e}^{{ - \gamma \sigma }}}\) with a time delay corresponding to the value for the drop frequency dependence. At the same time, there is no delay in the time series of the mean stress decrease during the drop of an individual element \(d\sigma \). The dependence \(d\sigma \left( t \right)\) is defined by the relation \(t \propto {{e}^{{ - \beta \Delta \sigma }}}\) in the entire temporal interval of the relaxation process. The value β linearly decreases with the increase of element coupling α in the model.

Kinetic model for prediction of subcritical crack growth, crack tip relaxation, and static fatigue threshold in silicate glass

Prediction of brittle fracture of amorphous oxide glasses continues to be a challenge due to the existence of multiple fracture mechanisms that vary with loading conditions. To address this challenge, we present a model for all three regimes of crack growth in glasses. Regimes I and III are controlled by Arrhenius processes while regime II is transport controlled along with a simple Arrhenius model for viscoelastic stress relaxation. Through dimensional arguments and physical reasoning, we propose a single mechanism which underlies both regime III subcritical crack growth and near-crack-tip viscoelastic relaxation. By combining the subcritical crack growth and viscoelastic models we obtain a prediction for a threshold stress intensity, Kth, below which stresses around the crack relax faster than it propagates. For stress intensity KI<Kth, no subcritical crack growth is predicted to occur, allowing for the design of stable glass systems. The prediction is compared to measured subcritical fracture threshold data for soda-lime silica glasses.

Stress relaxation characteristics of crushed cane tail straw

To gain insight into the mechanical properties of crushed sugarcane tail leaves during stress relaxation, a self-made compression equipment was used in this study. The variation law of different factors on the stress relaxation process of crushed cane tail was explored and a stress relaxation model was established. The three-element and five-element generalized Maxwell models were selected to fit the regression analysis of the stress relaxation curve of the crushed cane tail. The comparison showed that the determination coefficient R2 of the five-element stress relaxation model was higher, and a three-factor and three-level response surface test was designed. Following the quadratic regression polynomial of the stress rapid decay time and the equilibrium elastic modulus, the final optimization results obtained are as follows: The moisture content was 60.8%, the crushing particle size was 45 mm, the feeding amount was 150 g, and the stress rapid decay time was 14.0 s. The equilibrium elastic modulus was 129 kPa.

Study on stress relaxation characteristics of FGH95 powder superalloy treated by laser shock peening

Aiming at the phenomenon that the residual stress induced by Laser Shock Peening (LSP) will relax and redistribute under various loads, temperature, cyclic load, and the dual treatment of temperature and cyclic load on the residual stress relaxation of FGH95 powder superalloy after LSP treatment were studied, and the analysis model of relevant residual stress relaxation was constructed. The purpose is to understand the strengthening effect and stability of the alloy under temperature and cyclic load after LSP treatment. With the increase of treatment temperature, the relaxation of residual stress became more and more obvious. Most of the residual stress relaxation occurred in the first 30 min of temperature treatment, then slowed down and stabilized after 1 h. The residual stress was initially relaxed in the first 50 cycles, remained roughly unchanged between 50 and 5000 cycles. The intensify of the cyclic load increasing, adding material yield level, further plastic deformation and residual stress relaxation rate increases. With the increase of load intensify and load ratio, residual stress relaxation was also increased. The residual stress relaxation rate after 600 °C and cyclic load treatment was 56.2%, both greater than that after 600 °C or cyclic treatment of 25 °C, but less than the sum of the two conditions. The results of this paper provide a reference for the LSP of the FGH95 powder superalloy turbine disk and other aero engine parts.

Description of the instantaneous stress drop behavior of a cornstraw-potato residue mixture based on stress relaxation models

Studying the stress relaxation characteristics can provide important process parameters for the granulation and briquetting of biomass materials. In this study, a generalized Maxwell model and fractional model were established to describe and analyze the stress instantaneous drop behavior of a cornstraw-potato residue mixture during the stress relaxation process. Stress relaxation characteristic parameters, e.g., the stress instantaneous drop time, were obtained. Using this information, the influence of the compression speed on the stress instantaneous drop time, stress relaxation time ratio, and other parameters were analyzed. In addition, the regression model of the compression frequency and compression speed was established, which provided a method for determining the appropriate compression frequency of the molding equipment according to the compression speed.

In-situ monitoring of reinforcement compaction response via MXene-coated glass fabric sensors

In this study, MXene-coated glass fabric sensors were used to obtain reinforcement compaction and stress relaxation data within a closed mold. A layer of MXene-coated sensor was embedded within a multilayer glass fiber preform to monitor compaction forces under both dry and wet conditions i.e., when the stack was fully impregnated with resin or a test fluid. The effect of the test fluid type on compressibility and sensor piezo-resistivity was also determined. The sensors showed excellent sensitivity in both dry and impregnated states and were able to successfully monitor different loading conditions such as peak stresses carried by the reinforcement, long-term stress relaxation and cyclic loads. Polynomial data fitting and machine learning models were used to calibrate the sensors to predict the compaction response. An electro-mechanical based model, on the lines of traditional viscoelastic stress relaxation model, was used to represent piezo-resistivity for long term relaxation. The proposed technique has great potential of in-situ monitoring of mold clamping forces and part thickness by measuring piezo-resistive changes taking place throughout a molding cycle using MXene based embedded smart sensors.

Analytical Modeling of Stress Relaxation and Evaluation of the Activation Volume Variation: Effect of Temperature and Plasticizer Content for Poly(3-hydroxybutyrate-3-hydroxyvalerate).

In this study, stress-relaxation tests that have been carried out at different temperatures (quite below the heat deflection temperature) on a poly(3-hydroxybutyrate-3hydroxyvalerate) (PHB-HV) matrix containing different amounts of the acetyl tributyl citrate plasticizer (added at 5 and 10 wt %) are investigated. The analytical modeling of the stress relaxation behavior by the coupling of Eyring’s approach and the Guiu and Pratt model is successful. The activation volume results achieved are very interesting; in fact, not only the dependence of the activation volume from temperature is confirmed (and it resulted in dependence from the α′ relaxation temperature) but also, for the first time, the dependence of the activation volume from the plasticizer content is shown. In particular, the presence of a linear relationship between the activation volume and the plasticizer volume content is observed.

Formation of a pore as stress relaxation mechanism in decahedral small particles

A theoretical model of mechanical stress relaxation in decahedral particles by the formation of a central spherical pore is suggested and analyzed within an energy approach. The strain energy of a hollow decahedral particle is found in a closed analytical form. It is shown that there is a critical radius of a decahedral particle below which the formation of a central pore is not energetically favorable, while above which it is. The optimal radius of the pore increases with growth of the particle. Theoretical results are verified with available experimental data on observation of hollow decahedral particles.

A Unified Constitutive Model of Stress Relaxation of Ti-6Al-4V Alloy with Different Temperatures from Elastic to Plastic Loading

The effects of temperature and pre-strain levels on the stress relaxation behavior and corresponding microstructural evolutions of Ti-6Al-4V alloys have been investigated experimentally and numerically in this study. A series of tests (stress relaxation (SR) and repeated stress relaxation (RSR)) and microstructural observations (scanning electron microscope) have been performed, based on which the deformation-related variables, i.e., stress component and activation energy, as a function of the testing time are calculated according to the classical thermal activation theories. The experimental SR behavior and the obtained thermal related variables show that at lower temperatures (700 °C and 750 °C), a large number of dislocations introduced by plastic loading enhance dislocation slip/climb creep, giving rise to rapid relaxation compared with those with elastic loading conditions at the same temperature. At higher temperatures (800 °C and 850 °C), a similar SR phenomenon has been observed at both elastic and plastic loading conditions, which is due to the severe interaction between diffusion creep and dislocation creep after the loading stage. Based on these results, a unified constitutive equation has been proposed to successfully predict the behavior of the whole stress relaxation process composed of the loading stage and subsequent SR stage. The model considering the continuous evolution of internal variables, e.g., dislocation density and lamellar width, in two stages can predict the stress response and microstructure variation with different temperatures from elastic to plastic loading and provide a foundation to effectively optimize the hot forming process combining pre-deformation and stress relaxation.

Prismatic dislocation loops in crystalline materials with empty and coated channels

This paper presents for the first time an analytical solution to the boundary-value problem in the theory of elasticity for a circular prismatic dislocation loop (PDL) coaxial to a hollow cylindrical channel in an elastically isotropic infinite matrix. The stress fields and energy of the PDL are calculated and analyzed in detail. Based on the solution, a theoretical model for the misfit stress relaxation through the formation of a misfit PDL around a misfitting nanotube embedded in an infinite matrix is suggested. The critical radii of the embedded nanotube are found and discussed. It is shown that, for thin nanotubes prepared by nanolayer growth on the initial channel surface, there are two critical inner radii of the nanotube, between which the formation of a misfit PDL is energetically favorable.

Prediction model of residual stress during precision glass molding of optical lenses.

Precision glass molding (PGM) is an important processing technology for aspheric lenses that has the advantages of low complexity, high precision, and short processing time. The key problem in the PGM process is to accurately predict the residual stress of aspheric lenses. In this paper, we examine the residual stress relaxation model for aspheric lenses, including a creep experiment of D-K9 glass, calculating shear relaxation function, and predicting residual stress of aspheric lenses with the finite element method. Validations of the proposed model are conducted for three different process parameters, including molding temperature, molding pressure, and molding rate. The experimental and simulation results show that the errors of the residual stresses of the three process parameters are within 0.358 Mpa, which proves the validity of the model. The model can be used to predict the residual stress of the optical glass lens fabricated by PGM and analyze the processing parameters.

An Engineering Prediction Model for Stress Relaxation of Polymer Composites at Multiple Temperatures.

This study develops an engineering prediction model for stress relaxation of polymer composites, allowing the prediction of stress relaxation behaviour under a constant strain, over a range of temperatures. The model is based on the basic assumption that in the stress relaxation process the reversible strain is transformed to irreversible strain continuously. A strain-hardening model is proposed to incorporate nonlinear elastic behaviour, and a creep rate model is used to describe the irreversible deformation in the process. By using stress relaxation data at different temperatures, under different strains, the dependence on temperature and initial strain of the model parameters can be established. The effectiveness of the proposed model is verified and validated using three polymer composite materials. The performance of the model is compared with three commonly used stress relaxation models such as the parallel Maxwell and Prony series models. To ease the use of the proposed model in realistic structural problems, a user subroutine is developed, and the stress relaxation of a plate structure example is demonstrated.

Predicting variations of the least principal stress with depth: Application to unconventional oil and gas reservoirs using a log-based viscoelastic stress relaxation model

Knowledge of layer-to-layer variations of the least principal stress, S hmin, with depth is essential for optimization of multi-stage hydraulic fracturing in unconventional reservoirs. Utilizing a geomechanical model based on viscoelastic stress relaxation in relatively clay rich rocks, we present a new method for predicting continuous S hmin variations with depth. The method utilizes geophysical log data and S hmin measurements from routine diagnostic fracture injection tests (DFITs) at several depths for calibration. We consider a case study in the Wolfcamp formation in the Midland Basin, where both geophysical logs and values of S hmin from DFITs are available. We compute a continuous stress profile as a function of the well logs that fits all of the DFITs well. We utilized several machine learning technologies, such as bootstrap aggregation (or bagging), to improve the generalization of the model and demonstrate that the excellent fit between predicted and observed stress values is not the result of over-fitting the calibration points. The model is then validated by accurately predicting hold-out stress measurements from four wells within the study area and, without recalibration, accurately predicting stress as a function of depth in an offset pad about 6 miles away.

A New Model to Calculate Stress Relaxation of Viscoelastic Material for Polyester-Wool-Spandex Yarn with Analytical Mechanics Approach

Many researchers have studied the mechanical properties of yarn in textile science because mechanical properties are the essential parameter in determining yarn quality. This research aims to make a new model and prediction of the material properties of textile yarns, especially for stress relaxation of viscoelastic textile yarn for polyester-wool-spandex yarn cases. In this research, a new approximation of the analytical mechanics model of stress relaxation using a system of four springs and a dashpot to determine viscoelastic yarn properties as polyester-wool-spandex has been studied. A yarn movement equation for viscoelastic yarn as polyester-wool-spandex having 36 yarn count number (in unit tex or g/km) has been formulated using analytical mechanics, and the model has been validated experimentally. The coefficient of determination R2 ranges from 0.82, which shows the closeness between the experimental results and the theoretical predictions. In this research, it is found that this model can be implemented to determine the viscoelastic material of yarn based on the properties of yarn as stress relaxation using the analytical mechanics approach.

A nonlinear fractional-order damage model of stress relaxation of net-like red soil

It is essential to precisely describe the nonlinear characteristics of the stress relaxation behavior to ensure the long-term stability of geotechnical structures in the net-like red soil. A novel damage model of variable fractional-order was discussed here to accurately analyze the progress of stress relaxation for the net-like red soil. Moreover, unsaturated triaxial experiments on stress relaxation under a step-loading mode were performed to identify model parameters and investigate the nonlinear relaxation characteristics of the net-like red soil. The feasibility and validity of the proposed model were furthermore verified by comparisons with the experimental results and fitting curves obtained from the Nishihara model and the generalized Kelvin model. Results show that the analytical result by the proposed model is consistent with the measured data, and the proposed model can better depict the nonlinear characteristics of stress relaxation relative to other analytical models. It can better exhibit the relaxation evolution of soil compared with the conventional models.

Role of stress relaxation in stress-induced polymer crystallization

Stress relaxation is a common process that reduces the deformation of polymer coils against the strain-induced crystallization during the processing of polymeric materials for fibers, thinfilms and molding plastics. By introducing Maxwell model of stress relaxation into each polymer in dynamic Monte Carlo simulations, we compared stress-induced to strain-induced polymer crystallization under parallel conditions of various strain rates and temperatures. The results demonstrated the scenario of competitions among the factors of stress relaxation, strain rates and temperatures in the crystallization process. We found that, owing to fast stretching, the limited extent of stress relaxation plays the dominantly kinetic role rather than the expected thermodynamic role in the retardation of crystallization, similar to the factor of high strain rate. In addition, we observed the enhanced stress relaxation during the post-growth process of polymer crystallization, which influences the finally achieved crystallinity and crystal morphology. Our results facilitate a better understanding of polymer crystallization during the fast stretching processing.

Experimental Study and Simulation of the Stress Relaxation Characteristics of Machine-Harvested Seed Cotton

Seed cotton compression molding solves the inconvenience of seed cotton transportation and storage after mechanical harvesting. Stress relaxation is closely related to the performance of the compressed seed cotton. In this study, an electronic universal testing machine with a homemade compression device was used to study the stress relaxation characteristics of machine-harvested seed cotton. The stress relaxation model of machine-harvested seed cotton was established, the influence of test factors on the response indexes was analyzed and, finally, stress relaxation characteristics of machine-harvested seed cotton were simulated. Results show that machine-harvested seed cotton stress relaxation characteristics can be described by the five-element Maxwell model. The equilibrium elastic modulus is negatively correlated with moisture content and cross-section dimensions, and the equilibrium elastic modulus is positively correlated with trash content and compression density. The rapid decay time and the residual stress ratio are negatively correlated with moisture content and compression density, but the influence of trash content and cross-section dimensions are limited. The stress relaxation process of machine-harvested seed cotton was simulated using virtual prototype technology, and the maximum error between the experimental and simulated values was obtained as 4.96%. The feasibility of the virtual prototype technique for the viscoelastic simulation of biomaterials was demonstrated.

Development of a rheological model of stress relaxation in the structure of an oil film on the friction surface with fullerene additives

A rheological model of stress relaxation in a thin lubricant film, which is formed on the friction surface under the influence of the force field of the friction surface in the presence of fullerene compositions in lubricants, was developed. Analysis of the model made it possible to establish that the existence of elastic or viscous properties in surface structures depends on the ratio of two parameters. This is the time of stress relaxation in the structure on spots of actual contact and the duration of stress action on these spots, which is termed the lifetime of an actual contact spot. It was shown that an increase in the sliding rate reduces the time of relaxation of stresses in the surface structure. This is due to the destruction of aggregates in the structure of gel and the appearance of rotational movements of separate units ‒ flocs. An increase in the load on the tribosystem significantly increases the value of relaxation time. This is due to squeezing the viscous component out of the structure of a surface film. It was established that if the relaxation time exceeds the duration of actions of stresses on actual contact spots, the structure of a surface film behaves like an elastic solid. Conversely, if relaxation time becomes shorter than the duration of stress action, the film behaves like a viscous medium. Theoretically, it was shown that in the range of sliding and loading rates, when a film behaves like an elastic solid, a decrease in stresses on actual contact spots does not exceed the values of 1.1‒22.8 %. This property provides the bearing capacity of a film. The development of the model will make it possible to simulate elastic and viscous properties of "stitched" structures and substantiate the rational concentrations of additives to lubricants, as well as the ranges of their use.

Grain boundary sliding and non-constancy strain during stress relaxation of pure Mg.

Stress relaxation during plastic deformation has been reported to improve ductility of metallic materials. In this study, the stress relaxation behaviour in pure magnesium is investigated during interrupted uniaxial tensile tests. During intermittent stopping of the machine for relaxation studies, the total strain is expected to remain constant. However, an anomalous non-constancy in total strain is observed in the present work. The total strain increases with relaxation time. Additional in-situ tensile tests indicate that the non-constant total strain is restricted only in the gauge area of the specimen, indicating a likely shear dominated deformation such as grain boundary sliding (GBS) responsible for the anomalous behaviour. The role of GBS during relaxation is studied using the deformation induced evolution of surface inhomogeneity. Determinations of surface profiling step heights at grain boundaries and inclination of grains were used to quantify the effect of GBS. The estimated activation volume of 4.35 b 3 further confirms the role of slip induced GBS on the deformation. A new stress relaxation model accommodating GBS is proposed and is found to fit the experimental data accurately.

A Systematic Approach for the Reliability Evaluation of Electric Connector

Under the trend of high density and miniaturization, the current that the connector transmits per unit volume is getting higher and higher, which makes the reliability design of the connector more challenging. Under the pressure of high performance and low cost requirements, the design has to be more accurate and more efficient. Thus, in the design process, a systematic approach for reliability evaluation is required. However, there is no valid enough approach that is integrated, well-organized, and quantitative. In this article, a systematic approach for the reliability evaluation of connector was proposed, and by applying it on a typical object named a blade-spring connector, the validity of this approach was verified. After the framework of this approach has been established, the methods and models needed were provided, including the method to build up material selection criterion and the assessment models of stress relaxation, thermal diffusion, and sliding wear, respectively. Then, the feasibility of a newly developed copper alloy on the connector and the reliability behaviors of this connector were determined through this approach. The unsatisfactory aspects of reliability were pointed out and some possible redesign choices were provided. Results and discussion revealed that the proposed approach is a helpful tool for designing electric connectors, especially on the reliability design.