Prediction Of Stress Relaxation Research Articles

Dynamic Compressive Stress Relaxation Model of Tomato Fruit Based on Long Short-Term Memory Model.

Tomatoes are prone to mechanical damage due to improper gripping forces during automated harvest and postharvest processes. To reduce this damage, a dynamic viscoelastic model based on long short-term memory (LSTM) is proposed to fit the dynamic compression stress relaxation characteristics of the individual fruit. Furthermore, the classical stress relaxation models involved, the triple-element Maxwell and Caputo fractional derivative models, are compared with the LSTM model to validate its performance. Meanwhile, the LSTM and classical stress relaxation models are used to predict the stress relaxation characteristics of tomato fruit with different fruit sizes and compression positions. The results for the whole test dataset show that the LSTM model achieves a RMSE of 2.829×10-5 Mpa and a MAPE of 0.228%. It significantly outperforms the Caputo fractional derivative model by demonstrating a substantial enhancement with a 37% decrease in RMSE and a 36% reduction in MAPE. Further analysis of individual tomato fruit reveals the LSTM model's performance, with the minimum RMSE recorded at the septum position being 3.438×10-5 Mpa, 31% higher than the maximum RMSE at the locule position. Similarly, the lowest MAPE at the septum stands at 0.375%, outperforming the highest MAPE at the locule position by a significant margin of 90%. Moreover, the LSTM model consistently reports the smallest discrepancies between the predicted and observed values compared to classical stress relaxation models. This accuracy suggests that the LSTM model could effectively supplant classical stress relaxation models for predicting stress relaxation changes in individual tomato fruit.

Agarose as a Tissue Mimic for the Porcine Heart, Kidney, and Liver: Measurements and a Springpot Model.

Agarose gels are often used as a tissue mimic. The goal of this work was to determine the appropriate agarose concentrations that result in mechanical properties that match three different porcine organs. Strain tests were carried out with an amplitude varying from 0.01% to 10% at a frequency of 1 Hz on a range of agarose concentrations and porcine organs. Frequency sweep tests were performed from 0.1 Hz to a maximum of 9.5 Hz at a shear strain amplitude of 0.1% for agarose and porcine organs. In agarose samples, the effect of pre-compression of the samples up to 10% axial strain was considered during frequency sweep tests. The experimental measurements from agarose samples were fit to a fractional order viscoelastic (springpot) model. The model was then used to predict stress relaxation in response to a step strain of 0.1%. The prediction was compared to experimental relaxation data, and the results agreed within 12%. The agarose concentrations (by mass) that gave the best fit were 0.25% for the liver, 0.3% for the kidney, and 0.4% for the heart. At a frequency of 0.1 Hz and a shear strain of 0.1%, the agarose concentrations that best matched the shear storage modulus of the porcine organs were 0.4% agarose for the heart, 0.3% agarose for the kidney, and 0.25% agarose for the liver.

Numerical prediction for viscoelasticity of woven carbon fiber reinforced polymers (CFRPs) during curing accounting for variation of yarn angle caused by preforming

To model viscoelasticity of woven composites during curing, existing methods were mostly derived by directly mixing the material models for constituents and neglecting interaction among yarns, causing inaccuracy in numerical simulation. In addition, the preforming effects, which exist for production of parts with complex geometry, on curing of woven composites were rarely considered. In this paper, a novel geometric modeling method, involving finite element analysis (FEA) and element mapping, was first established to obtain voxel mesh for non-orthogonal representative volume element (RVE) structures. Through integration of the thermoviscoelastic constitutive models and voxel mesh, FEA was conducted to predict stress relaxation of woven CFRPs with varying yarn angles and degrees of curing (DOCs). Experimental validation indicates that the FEA can capture viscoelastic response of woven CFRPs with different yarn angles and DOCs with around 4.96% average weighed error, meaning the new approach can virtually characterize viscoelasticity of woven composites under complex processing conditions.

PyDSM: GPU-accelerated rheology predictions for entangled polymers in Python

Prior studies have extensively shown that the discrete slip-link model (DSM) accurately predicts the linear and nonlinear rheology of various entangled polymer systems. The only publicly available implementation of the DSM algorithm is written in the CUDA C++ programming language. In this work we discuss the implementation of the fixed slip-link model and the clustered fixed slip-link model in Python. Our work shows that Python can also utilize GPUs for fast quantitative rheological predictions. Our simulation code, named pyDSM, allows an easy-to-read and beginner-friendly approach for users wanting to utilize the efficiency of GPU computing while also enabling an open-source Python package that can easily couple or interact with other simulation or data analysis software. We demonstrate pyDSM's versatility by implementing MUnCH, a recently published algorithm that allows estimation of the statistical uncertainty in the autocorrelations for any time series data, properly accounting for the correlation in the data. An on-the-fly version of MUnCH is applied to calculate the uncertainty in the relaxation modulus and the chain center-of-mass mean squared displacement. Moreover, the uncertainty quantification in the relaxation modulus allows propagation of error through a multi-mode Maxwell fit to determine the uncertainty in the dynamic modulus. Lastly, as an example of a novel application of the pyDSM code we calculate the re-entanglement dynamics after cessation of flow which are fundamental to the weld quality in fused-filament 3D printing. Program summaryProgram Title: pyDSM – Discrete Slip-link Model (DSM) in Python for Fast Quantitative Rheology Predictions of Entangled PolymersCPC Library link to program files:https://doi.org/10.17632/v828b9cjp9.1Developer's repository link:https://github.com/jgethier/pyDSMLicensing provisions: GPLv3Programming language: PythonNature of problem: Predicting stress relaxation in entangled polymer systems is crucial for understanding the macroscopic properties of the material. Many existing models do not capture the physics of polymer entanglements in linear, star-branched, and other entangled polymeric systems. The discrete slip-link model has been shown to predict quantitatively the rheological behavior of polymers, but only one version of the model is publicly available using CUDA C++ programming.Solution method: We implement a less-detailed version of the discrete-slip link model to predict the linear and nonlinear rheology of entangled polymers in Python. Uncertainty in the predictions is implemented with the MUnCH algorithm. We implement GPU-based calculations for fast and accurate predictions of the linear and nonlinear rheology behavior, as well as re-entanglement dynamics after cessation of flow.

Constitutive modeling of stress relaxation for fabric reinforced rubber composites

Establishing an unsteady fractional order Zener model with degradation parameters has significant meaning for predicting stress relaxation of fabric reinforced rubber composites. Based on the experimental results, an integer order Zener model was deduced to demonstrate the stress relaxation behaviors of fabric reinforced rubber composites and pure rubber. Due to the limitations, however, the integer order Zener model could not explain the stress relaxation behavior of the fabric reinforced rubber composites (the FRR) very well. Therefore, a Zener model was developed based on the viscoelasticity theory and the fractional calculus theory to characterize the stress relaxation behavior, but errors still existed in the initial and final stages. With more reasonable physical interpretation, an unsteady fractional order Zener model degraded by parametric aging with 7 parameters is proposed in this paper to accurately capture the stress relaxation behavior of the FRR, whose correlation coefficient is over 99.99%. The parameter sensitivities of the seven-parameter model were analyzed. Present study may provide a critical step for designing and evaluating the fabric reinforced rubber composites.

A Rheological Model with Integer and Non-Integer Orders Nonlinearities for Predicting Stress Relaxation Behavior in Viscoelastic Materials

Viscoelastic materials are widely used as devices for vibration control in modern engineering applications. They exhibit both viscous and elastic characteristic when undergoing deformation. They are mainly characterized by three time-dependent mechanical properties such as creep, stress relaxation and hysteresis. Among them, stress relaxation is one of the most important features in the characterization of viscoelastic materials. This phenomenon is defined as a time-dependent decrease in stress under a constant strain. Due to the inherent nonlinearity shown by the material response over a certain range of strain when viscoelastic materials are subjected to external loads, nonlinear rheological models are needed to better describe the experimental data. In this study, a singlenonlinear differential constitutive equation is derived froma nonlinear rheological model composed of a generalized nonlinear Maxwell fluid model in parallel with a nonlinear spring obeying a power law for the prediction of the stress relaxation behavior in viscoelastic materials. Under a constant strain-history, the time-dependent stress is analytically derived in the cases where the positive power law exponent, α ˂ 1 and α ˃1. The Trust Region Method available in MATLAB Optimization Toolbox is used to identify the material parameters. Significant correlations are found between the experimental relaxation data taken from literature and exact analytical predictions. The obtained results show that the developed rheological model with integer and non-integer orders nonlinearities accurately describes the experimental relaxation data of some viscoelastic materials.

Developing a rheological model for predicting stress relaxation behavior of cotton-covered elastane core-spun yarns

Developing a rheological model for predicting stress relaxation behavior of cotton-covered elastane core-spun yarns

Linear viscoelastic shear and bulk relaxation moduli in poly(tetramethylene oxide) (PTMO) using united-atom molecular dynamics

A quantitative understanding and prediction of the viscoelastic relaxation behavior of polymer melts is required to build up predictive multiscale models, which can be utilized for the practical design of viscoelastic materials. We report the application of the Green–Kubo method to compute the common shear relaxation modulus and the rarely reported bulk relaxation modulus for a realistic united atom model of poly(tetramethylene oxide) (PTMO), which is one key components of the segmented polyurethane (PU) elastomers. The temperature and molecular weight dependent viscoelastic behavior is investigated in detail by computing the bulk relaxation modulus K(t) along with shear relaxation modulus G(t). Our results provide new rheological data for PTMO melt based on the united atom model, which incorporates the chemical details of the polymer backbone. The predicted stress relaxation are mapped onto master curves using the time–temperature superposition principle with horizontal and vertical shift factors. The computed shift factors agree with the Williams–Landel–Ferry equation and appear to be similar for the shear and bulk relaxation modulus. The underlying dynamics for the shear and bulk relaxation modulus appear to stem from the same mechanistic origin as both processes seem to sample similar kinetic signature of the reference time scale of the underlying thermally activated processes in the liquid. Our results demonstrate furthermore, that MD simulations with the chemical details beyond coarse-grained models can sample the Rouse dynamics and the transitions towards entanglement, which is evident by the emergence of a plateau in shear relaxation modulus and scaling relations in the diffusion behavior of the monomer at larger molecular weights.

Kinetics of intrinsic stress in nanocrystalline films

Conventional polycrystalline materials acquire high levels of intrinsic mechanical stress (ranging from MPa to a few GPa) during preparation and use, but this stress decays quickly (~minutes) to small residual values (~kPa) under standard resting conditions. Nanocrystalline materials reach similar or even higher levels of intrinsic stress, but surprisingly retain a significant portion of this stress over much longer time scales (~hours). This behavior directly contradicts current theoretical models that predict stress relaxation through diffusive currents. Diffusive currents, which flow mainly on the surfaces of grains, are expected to produce faster relaxation kinetics when the stress to be released is higher. In this work, we study the kinetics of intrinsic stress relaxation in nanocrystalline films and identify the limitations of this process as a preliminary step towards designing a strategy for high-stress stabilization in nanostructured systems.

Determination of opening stresses for railway steel under low cycle fatigue using digital image correlation

Crack closure phenomenon is important to study as it provides an estimation to fatigue life of the components. It becomes even more complex under low cycle fatigue (LCF), since under LCF high amount of plasticity is induced within the material near notches or defects, as a result the assumptions used by linear elastic fracture mechanics (LEFM) approach become invalid. Evaluation of opening stresses for mechanical components undergoing LCF phenomenon requires a robust methodology to correctly predict the fatigue life. In this study, an experimental campaign was carried out for determination of opening stresses of railway steels (25CrMo4 and 30NiCrMoV12) subjected to LCF using digital image correlation (DIC) technique. The concept of crack opening displacement (COD) was used for the analysis. Two different methodologies were introduced to analyze experimental data for the identification of opening levels. Experimental results were then compared with crack closure prediction model, Newman model. Results from Newman model agreed well with the experimental analysis. Newman model provided very good prediction for strain ratio Rε = −1, however, for the materials undergoing strain ratio Rε = 0, stress ratio must be considered rather than strain ratio, because Newman model can’t predict stress relaxation behaviour.

Time-Dependent Mechanical Properties in Polyetherimide 3D-Printed Parts Are Dictated by Isotropic Performance Being Accurately Predicted by the Generalized Time Hardening Model.

The Fused-Deposition Modelling (FDM) technique has transformed the manufacturing discipline by simplifying operational processes and costs associated with conventional technologies, with polymeric materials being indispensable for the development of this technology. A lack of quantification of viscoelastic/plastic behavior has been noted when addressing FDM parts with Polyetherimide (PEI), which is currently being investigated as a potential material to produce functional end-products for the aerospace and health industry. Primary and secondary creep along with stress relaxation tests have been conducted on FDM PEI specimens by applying stresses from 10 to 40 MPa for 100 to 1000 min. Specimens were 3D printed by varying the part build orientation, namely XY, YZ, and XZ. Creep results were fitted to the Generalized Time Hardening equation (GTH), and then this model was used to predict stress relaxation behavior. FDM PEI parts presented an isotropic creep and stress relaxation performance. The GTH model was proven to have a significant capacity to fit viscoelastic/plastic performances for each single build orientation (r > 0.907, p < 0.001), as well as a tight prediction of the stress relaxation behavior (r > 0.998, p < 0.001). Averaged-orientation coefficients for GTH were also closely correlated with experimental creep data (r > 0.958, p < 0.001) and relaxation results data (r > 0.999, p < 0.001). FDM PEI parts showed an isotropic time-dependent behavior, which contrasts with previous publications arguing the significant effect of part build orientation on the mechanical properties of FDM parts. These findings are strengthened by the high correlation obtained between the experimental data and the averaged-coefficient GTH model, which has been proven to be a reliable tool to predict time-dependent performance in FDM parts.

Hybridization effect on the bending properties of flax composites

Eco-friendly and biodegradable composites are desirable due to the enormous pressure on industry as a result of the air pollution, global warming and the scarcity of fossil fuels. On the other hand, due to inherent viscoelasticity of the matrix phase, polymer composites are prone to creep and stress relaxation. Therefore, the main goal of this work is to study the hybridization effect on the viscoelastic properties of composites reinforced natural fibres. For this purpose, composites with the same lay-up, but with different fibres (flax and glass fibres), were manufactured with a green epoxy resin. These viscoelastic properties were evaluated in bending mode. It was concluded that, contrary to creep deformation, stress decreases with time, but this tendency is strongly attenuated with the addition of glass fibres. Therefore, the hybridization is an efficient way to decrease the viscoelastic behaviour of natural fibre reinforced composites. Finally, due to the good accuracy obtained between the experimental and theoretical results, the Kohlrausch-Williams-Watts (KWW) equation and the Findley model can be used to predict stress relaxation time and creep displacement.

Effect of Fibre Orientation and Hostile Solutions on Stress Relaxation of Glass/Polyamide Composites.

Polyamide creates high-performance composite materials, which are replacing the traditional epoxy composites in several applications. In this context, exposure to hostile environments is expected. On the other hand, due to the viscoelastic nature of the matrix, these composite materials are prone to stress relaxation. Therefore, the stress relaxation behaviour of glass/polyamide 6 composites was studied considering different fibre directions, as well as exposure to NaOH and HCl solutions. Stress relaxation tests on the bending mode were carried out, and the stress recorded during the loading time (7200 s). All tests were characterized by a stress decrease over time, but laminates with higher fibre angles were more prone to stress relaxation. However, exposure to hostile solutions promoted more significant decreases, where the highest stress relaxation was achieved for alkaline environments with values that were three times higher for laminates with fibres at 0° and around one and half times higher for 45° fibre alignments when compared with the control samples. Finally, the Kohlrausch–Williams–Watts (KWW) model showed that it can be used to predict stress relaxation time, due to the accuracy that was obtained between the experimental and theoretical results.

Examining Stress Relaxation in a Dissimilar Metal Weld Subjected to Postweld Heat Treatment

Abstract Dissimilar metal welds are often required in nuclear power plants to join components made from austenitic steels to those from ferritic steels, particularly in fast breeder reactor plants, in order to join the intermediate heat exchanger to the steam generator. The process of welding alters the microstructure of the base materials and causes residual stresses to form, both because of the change in the microstructure and the differing thermal histories in various regions. Postweld heat treatment (PWHT) is required to relieve the residual stresses and achieve preferable microstructural gradients across the weld joint. Therefore, in order to arrive at the optimal PWHT process, it is necessary to investigate the effects of heat treatment on the joint integrity, microstructure, and residual stress relaxation in the welds. To investigate the effect of PWHT on the residual stress relaxation and corresponding alteration of microstructure across a welded joint, a dissimilar weld between modified 9Cr-1Mo steel and austenitic stainless steel AISI 316LN was made using autogenous electron beam welding. To achieve this, the welding process was first modeled numerically using finite element analysis, and the residual stress predictions were validated by experimental investigation using neutron diffraction. The validated model was then used to study the residual stress relaxation through the simulation of PWHT. The predicted stress relaxation was compared with contour method measurement of residual stresses in the actual welded plate subjected to PWHT. The results indicate that, although some relaxation of residual stresses occurred during PWHT, there is still a significant portion of highly localized residual stresses left in the specimen.

Rheological behavior of wood in stress relaxation under compression

Rheological behavior of wood under uniaxial compression along and perpendicular to the grain in constant environment was examined. Tests with constant deformation rate until failure and stress relaxation tests with constant deformation applied stepwise were carried out. The experimental results of stress relaxation showed nonlinear material behavior over time that got more prominent under high deformation levels. Considerable amount of stress relaxed during applying the deformation. Wood experienced greater stress relaxation along the grain than perpendicular to it. Three rheological models for orthotropic material were calibrated to the experimentally determined stress–time curves in longitudinal and transverse directions simultaneously. Small deformation levels assuming linear strains were accounted for in the models. Required elastic material parameters were determined from the tests with constant deformation rate. A model including the highest number of viscoelastic material parameters was the most successful in predicting stress relaxation of wood under stepwise deformation. Modeling indicated that wood behavior was very close to linear viscoelastic in relaxation under small deformation. The obtained material parameters made the model suitable for predicting rheological behavior of wood comprehensively, under sustained deformation or load in constant conditions.

Effect of elastic follow-up and ageing on the creep of an austenitic stainless steel

Elastic follow-up is a mechanical boundary condition lying between constant load and constant strain control. It exists in many engineering components operating at high temperature and can result in dramatically different creep stress relaxation and strain accumulation rates in a localized region of a component. We have performed creep tests under constant load, constant strain and elastic follow-up control on an aged (additional 22,000 h) 316H austenitic stainless steel after service in a nuclear power station for 65,000 h. Primary and secondary forward creep models with parameters derived from the constant-load data were able to describe constant-load creep adequately, but not able to predict stress relaxation and elastic follow-up. We show that this is because ageing has increased the constant-load creep strain rate significantly but has no effect on stress relaxation creep strain rate. Ageing promotes the formation of ferrite/chi phase at grain boundaries which are preferential sites for creep cavitation under load control. However, creep cavitation is less likely under constant strain and elastic follow-up control because a high creep strain rate, large creep strain and stress cannot coexist under these boundary conditions.

Creep deformation and stress relaxation of a martensitic P92 steel at 650 °C

This paper develops methods to predict creep stress relaxation in the presence of combined boundary conditions and explores the influence of primary-secondary stress dependent creep properties on predictions for a martensitic P92 steel at temperature of 650°C. A series of forward creep and elastic follow-up experiments have been conducted. A summary is provided of empirical creep equations for forward creep and creep stress relaxation (elastic follow-up) tests, including the link to the experimental procedure. The creep stress relaxation tests have been performed with two rigs to give elastic follow-up factors of 1.17 and 1.7. Both time hardening and strain hardening approaches have been considered where the strain hardening model provided more accurate predictions compared to time hardening; except at relatively low stress levels. The difference between stress relaxations predicted using strain hardening and time hardening approaches are considerable. The model predicts the creep stress relaxation accurately in the early stage of relaxation, indicating that the majority of stress relaxation occurs where primary creep needs to be taken into account. This study highlights the importance of stress dependent creep model to predict stress relaxation, especially with high level of initial residual stresses.

Prediction of viscoelastic properties with coarse‐grained molecular dynamics and experimental validation for a benchmark polyurea system

ABSTRACTTo explore the relationship between microscopic structure and viscoelastic properties of polyurea, a coarse‐grained (CG) model is developed by a structure matching method and validated against experiments conducted on a controlled, benchmark material. Using the Green‐Kubo method, the relaxation function is computed from the autocorrelation of the stress tensor, sampled over equilibrium MD simulations, and mapped to a real time scale established by matching self‐diffusion rates of atomistic and CG models. Master curves computed from the predicted stress relaxation function are then compared with dynamic mechanical analysis experiments mapped to a wide frequency range by time–temperature superposition, as well as measurements of ultrasonic shear wave propagation. Computational simulations from monodisperse and polydisperse configurations, representative of the benchmark polyurea, show excellent agreement with the experimental measurements over a multidecade range of loading frequency. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016, 54, 797–810

Continuum modeling of deformation and aggregation of red blood cells

In order to gain better understanding for rheology of an isolated red blood cell (RBC) and a group of multiple RBCs, new continuum models for describing mechanical properties of cellular structures of an RBC and inter-cellular interactions among multiple RBCs are developed. The viscous property of an RBC membrane, which characterizes dynamic behaviors of an RBC under stress loading and unloading processes, is determined using a generalized Maxwell model. The present model is capable of predicting stress relaxation and stress–strain hysteresis, of which prediction is not possible using the commonly used Kelvin–Voigt model. Nonlinear elasticity of an RBC is determined using the Yeoh hyperelastic material model in a framework of continuum mechanics using finite-element approximation. A novel method to model inter-cellular interactions among multiple adjacent RBCs is also developed. Unlike the previous modeling approaches for aggregation of RBCs, where interaction energy for aggregation is curve-fitted using a Morse-type potential function, the interaction energy is analytically determined. The present aggregation model, therefore, allows us to predict various effects of physical parameters such as the osmotic pressure, the thickness of a glycocalyx layer, the penetration depth, and the permittivity, on the depletion and electrostatic energy among RBCs. Simulations for elongation and recovery deformation of an RBC and for aggregation of multiple RBCs are conducted to evaluate the efficacy of the present continuum modeling methods.

Incorporating Density and Temperature in the Stretched Exponential Model for Predicting Stress Relaxation Behavior of Polymer Foams

This paper discusses an approach to incorporate density and temperature terms in the well-known stretched exponential (SE) model for predicting the stress relaxation behavior of polymer foams. We have developed this approach for closed-cell polyurethane foams (PUFs) and verified using experimental data for accuracy. The SE model was first examined using short-term experimental data to predict long-term stress relaxation behavior of PU solid (PUS). The corresponding model parameters were then extracted for PUS and two PUFs with different densities (PU404 and PU415) at three different test temperatures. Finally, an expression was developed in conjunction with the modified Gibson–Ashby relationship and the Arrhenius equation and validated for other foam density (PU420) and test temperatures. The predictions were found to be reasonably good with more than 90% accuracy.