Long-term Stress Relaxation Research Articles

Mechanical and biological properties of current materials of clear aligner

With the development of new materials related to clear aligners, the physical properties are improving, and the clinical performance of the devices is expected to improve. Clear aligners require constant, controlled force on the teeth to achieve the desired tooth movement. However, unlike superelastic wires for orthodontic treatment, clear aligner materials are characterized by significant short-term or long-term stress relaxation after installation of the device. In addition, clear aligners are a complex manufacturing process that requires creating a tooth model and trimming the aligners, and various degrees of shrinkage and expansion may occur during the thermoforming process or direct printing of device. These changes can affect the thickness or fit of each tooth area and make it difficult to achieve the clinical treatment goals of clear aligner.Recently, multi-layered clear orthodontic products with improved physical properties have been introduced to increase the predictability of aligner treatment, and with the recent introduction of direct printing materials, innovative manufacturing methods for clear orthodontic devices have become possible. As shape memory properties have been reported among direct printing materials, interest in related materials is increasing. In this issue, we will introduce the latest materials related to clear aligners and explain the physical and biological properties that clinicians need to know for proper use.

Time-varying compressive properties and constitutive model of EPDM rubber materials for tunnel gasketed joint

The stress relaxation of ethylene propylene diene monomer (EPDM) rubber material in a compressed state significantly increases the risk of water leakage at tunnel precast segmental joints. Additionally, EPDM rubber gaskets typically experience a complex precompression strain state, further complicating the prediction of long-term stress relaxation. Therefore, it is imperative to propose a novel constitutive model that realistically reflects the stress relaxation of rubber with arbitrary precompression strain, providing a reference for the long-term waterproof design of shield tunnels. In this study, the time-varying properties of EPDM rubber at material level were studied in detail. At first, a comprehensive set of accelerated aging tests were conducted on EPDM rubber samples with varying precompression strains. The hardening effect of rubber without precompression and the stress relaxation effect of rubber with precompression were explored. The time-varying law and mechanism governing rubber properties under these two effects were analyzed. Subsequently, a conversion relationship between the EPDM rubber test conditions and the actual service time was established. The predicted hardening coefficient for uncompressed EPDM after 100 years is 1.468, whereas the relaxation coefficient for compressed EPDM is 0.359. Comparative analysis revealed that the compression set index do not consider the beneficial effects of hardening, resulting in a 54.1% overestimation of the design water pressure. Finally, the analytical study on the constitutive model of EPDM rubber material was carried out. The error in compression curve for unaged sample obtained from empirical formulas exceeded three times that of the analytical model, underscoring the need to study time-varying constitutive models. An interpolation method was employed to extend the test curve, leading to the development of a new constitutive model that represents the stress relaxation characteristics of EPDM materials under arbitrary precompression strain states. By combining the proposed constitutive model with the timetemperature conversion relationship, the time-varying expressions of the constitutive parameters for relaxation and hardening effects during the service life were derived. In comparison with existing models, the proposed model demonstrates wider applicability, effectively captures the time-varying characteristics of EPDM materials under arbitrary precompression strains, offering an efficient approach for studying the long-term stress relaxation prediction of rubber gaskets in shield tunnels under complex precompression strain states.

Quantification of long-term nonlinear stress relaxation of bovine trabecular bone

The reliability of computational models in orthopedic biomechanics depends often on the accuracy of the bone material properties. It is widely recognized that the mechanical response of trabecular bone is time-dependent, yet it is often ignored for the sake of simplicity. Previous investigations into the viscoelastic properties of trabecular bone have not explored the relationship between nonlinear stress relaxation and bone mineral density. The inclusion of this behavior could enhance the accuracy of simulations of orthopedic interventions, such as of primary fixation of implants. Although methods to quantify the viscoelastic behavior are known, the time period during which the viscoelastic properties should be investigated to obtain reliable predictions is currently unclear. Therefore, this study aimed to: 1) Investigate the duration of stress relaxation in bovine trabecular bone; 2) construct a material model that describes the nonlinear viscoelastic behavior of uniaxial stress relaxation experiments on trabecular bone; and 3) implement bone density into this model. Uniaxial compressive stress relaxation experiments were performed with cylindrical bovine femoral trabecular bone samples (n = 16) with constant strain held for 24 h. Additionally, multiple stress relaxation experiments with four ascending strain levels with a holding time of 30 min, based on the results of the 24-h experiment, were executed on 18 bovine bone cores. The bone specimens used in this study had a mean diameter of 12.80 mm and a mean height of 28.70 mm. A Schapery and a Superposition model were used to capture the nonlinear stress relaxation behavior in terms of applied strain level and bone mineral density. While most stress relaxation happened in the first 10 min (up to 53 %) after initial compression, the stress relaxation continued even after 24 h. Up to 69 % of stress relaxation was observed at 24 h. Extrapolating the results of 30 min of experimental data to 24 h provided a good fit for accuracy with much improved experimental efficiency. The Schapery and Superposition model were both capable of fitting the repeated stress relaxation in a sample-by-sample approach. However, since bone mineral density did not influence the time-dependent behavior, only the Superposition model could be used for a group-based model fit. Although the sample-by-sample approach was more accurate for an individual specimen, the group based approach is considered a useful model for general application.

Material properties in regenerating axolotl limbs using inverse finite element analysis

BackgroundThe extracellular mechanical environment plays an important role in the skeletal development process. Characterization of the material properties of regenerating tissues that recapitulate development, provides insights into the mechanical environment experienced by the cells and the maturation of the matrix. In this study, we estimated the viscoelastic material properties of regenerating forelimbs in the axolotl (Ambystoma mexicanum) at three different regeneration stages: 27 days post-amputation (mid-late bud) and 41 days post-amputation (palette stage), and fully-grown time points. A stress-relaxation indentation test followed by two-term Prony series viscoelastic inverse finite element analysis was used to obtain material parameters. Glycosaminoglycan (GAG) content was estimated using a 1,9- dimethyl methylene blue assay. ResultsThe instantaneous and equilibrium shear moduli significantly increased with regeneration while the short-term stress relaxation time significantly decreased with limb regeneration. The long-term stress relaxation time in the fully-grown time point was significantly lower than 27 and 41 DPA groups. The GAG content was not significantly different between 27 and 41 DPA but the GAG content of cartilage in the fully-grown group was significantly greater than in 27 and 41 DPA. ConclusionsThe mechanical environment of the proliferating cells changes drastically during limb regeneration. Understanding how the tissue's mechanical properties change during limb regeneration is critical for linking molecular-level matrix production of the cells to tissue-level behavior and mechanical signals.

Investigation into the long-term stress relaxation behaviors of white oak (Quercus alba L.) based on the time–temperature–moisture superposition principle

ABSTRACT Curving woodworks exhibit wide applications in wooden furniture manufacturing due to the conformable visual and tactile experience, are welcome among consumers. However, the corresponding long-term shape stability facing the stress relaxation is an attention-worthy issue with the fundamental insights about the mesoscopic behaviors of vessels have not been provided. Here, we proposed the investigation into the effect of vessels on stress relaxation behavior of white oak (Quercus alba L.). Results demonstrated that stress relaxation modulus of specimen decreased with the elevation in MC and temperature, and vessel-containing specimens displayed more evident stress relaxation. Providing more physical connotation, Zener model is more suitable for the numerically investigation into the stress relaxation than logarithmic model. The time-temperature-moisture superposition principle (TTMSP) allows us to predict the~10 d and ~1 d stress relaxation behavior of white oak facing different temperatures and MCs. Additionally, stress relaxation of white oak with vessels is more evident, which can be attributed to the stress concentration and resultant deformation around the vessel. We believe that this work is beneficial for obtaining a mesoscopic understanding of vessels on stress relaxation behaviors of wood. It thus paves a way to exploit the methodologies to improve the shape-stability of curving woodworks.

Long-term stress relaxation behaviors and mechanisms of 2219 Al–Cu alloy under various temperatures and initial stresses

Large 2219 Al–Cu alloy aerospace integral components suffer from long-term stress relaxation aging (SRA) due to complex temperature and stress loads during aging treatment/forming and service process, which makes it difficult to ensure their appropriate residual stress and excellent mechanical and service properties. However, the research is limited to a thorough understanding of macroscopic and microscopic features and underlying mechanisms of the long-term SRA under multivariable aging conditions. Therefore, this study investigated macroscopic and microscopic features of long-term SRA under different temperatures (120 °C to 190 °C), initial stress levels (100 MPa to 250 MPa) and durations (0 h to 50 h) through stress relaxation curves, metallographic traits, Vickers hardness, tensile performance, dislocations and phases of precipitation. On the basis of experimental outcomes, the comprehensive mechanisms beneath SRA were unraveled through dislocation theory, multiphase strengthening mechanisms and thermodynamics, where the interplays of stress relaxation behavior with age-hardening response were taken into consideration. The results showed elevations in the rate of stress reduction as the temperature and initial stress rose. At an initial stress greater than the yield stress of alloy, a marked increase in stress relaxation was found, and the mechanisms transform from the intragranular motion of dislocations and diffusion of grain boundaries to the intragranular and intergranular motion of dislocations and migration of grain boundaries. The stress reduction rate rose sharply when the temperature exceeded 175 °C, and the dislocation movement mechanisms transform from gliding to climbing of dislocations. Stress relaxation is in nature progressive transformation of strain from elastic into a permanently inelastic state via the motion of dislocations, leading to the decrease of movable dislocations and the increase of immovable dislocations with more stable configurations. The age hardening is mainly determined by precipitation strengthening, supplementarily by dislocation strengthening, and obvious stress orientation effect (SOE) of G.P. zones and θ" phases degenerates strengthening effect. The interplay between stress relaxation behavior and age-hardening response influences the thermal–mechanical coupling SRA of 2219 Al–Cu alloy, which depends fundamentally on the motion of dislocations and their interplay with precipitated phases. This is a thermal activation process concerning the interplay between internal (age-hardening resistance) stress and external (initial) stress. The initial energy of elastic strain offers Gibbs free energy as the SRA driver, and a steady state of stress relaxation is attained with the lowest energy of elastic strain. These findings provide valuable insights into exploring innovative aging treatment/forming for optimizing residual stress, mechanical performance and service property in a synergistic manner.

Time-dependent extracellular matrix alterations of young tendons in response to stress relaxation: a model for the Ponseti method.

The Ponseti method corrects a clubfoot by manipulation and casting which causes stress relaxation on the tendons. Here, we examined the effect of long-term stress relaxation on tendon extracellular matrix (ECM) by (1) an ex vivo stress relaxation test, (2) an in vitro tenocyte culture with stress relaxation and (3) an in vivo rabbit study. Time-dependent tendon lengthening and ECM alterations including crimp angle reduction and cleaved elastin were observed, which illustrated the mechanism of tissue lengthening behind the treatment-a material-based crimp angle reduction resulted from elastin cleavage. Additionally, in vitro and in vivo results observed restoration of these ECM alterations along with increased elastin level after 7 days of treatment, and the existence of neovascularization and inflammation, indicating the recovery and adaptation from the tendon in reaction to the treatment. Overall, this study provides the scientific background and information that helps explain the Ponseti method.

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.

Experimental and simulative characterization for material and lifetime modelling of a silicone adhesive

Material and lifetime modelling of silicone adhesives has become more and more important due to their wide application in building and automotive industry. To find the most crucial material parameters for lifetime prediction, an elastomeric silicone adhesive is characterized with different thermomechanical methods. Above the first-order phase transition from crystalline to amorphous state at about -40 °C the frequency and temperature dependence for small and large strains is negligible and the time-temperature superposition principle cannot be used for extrapolation to other temperatures or frequencies. The first stretch invariant at break is independent of strain rate and shows a reciprocal temperature dependency, i.e. fracture energy can be provided by thermal and strain energy. Maximum principal strain is identified as a suitable failure criterion for different load cases and strain rates for static loading as well as for fatigue. Long-term stress relaxation behavior follows a power-law with stretch-dependent pre-exponential factor and exponent. Using compressibility from a hydrostatic pressure experiment, a hyperelastic material model is used to describe the quasistatic stress-stretch curves for different load cases at 23 °C with strain rates of 0.01 s−1. Validation experiments show good agreement for two joint geometries with multiaxial load cases.

Specific surface area: A reliable predictor of creep and stress relaxation in gas shales

In recent years, short-term creep parameters determined in the laboratory from cylindrical gas shale samples subjected to triaxial (in-situ) stress conditions have been used successfully to infer long-term deformation and stress relaxation at the reservoir scale across geologic time scales. Due to the viscoelastic formalism, both the laboratory creep response and field-scale stress relaxation can be modeled with power law functions of time involving the elastic compliance of the shale B, the time-dependence exponent n, and the amount of total strain ∊. Gas shales often exhibit a high specific surface area associated with their high content in clay minerals and/or total organic carbon (TOC). The low-pressure nitrogen adsorption technique can be used advantageously to estimate specific surface area (SN2); i.e., it is a relatively fast and cost-effective measurement conducted on powdered samples of shale material. A robust global empirical correlation between gas shale creep parameters and SN2 emerges from the analysis of laboratory data collected from multiple gas shale formations in Australia (the prospective Goldwyer Formation) and the United States (Barnett, Haynesville, and Eagle Ford formations), and spanning a broad range of clay content, organic matter, maturity, and porosity values. This data set also shows that the summed fractions of clay minerals, TOC, and porosity, the so-called weak phase fraction, correlates nearly as well with primary creep parameters. The weak phase fraction can also be estimated from faster and more cost-effective measurements or from well logs. To evaluate its predictive capacity, the key correlation between SN2 and creep parameters is used in a case study to predict the magnitude of present-day least principal stress Shmin across six depth intervals/lithologic layers in a prolific unconventional shale formation in the northeastern United States. Several Shmin measurements are available for verification, and our approach successfully captures the observed layered variation of stress with depth.

In-vitro stress relaxation response of neonatal peripheral nerves

Characterizing the viscoelastic behavior of neonatal peripheral nerves is critical in understanding stretch-related peripheral nerve injuries (PNIs) in neonates. This study investigated the in-vitro viscoelastic stress relaxation response of neonatal piglet brachial plexus (BP) and tibial nerves at two different strain levels (10% and 20%) and stress relaxation testing durations (90- and 300-seconds). BP and tibial nerves from 20 neonatal piglets were harvested and pre-stretched to either 10% or 20% strain at a dynamic rate of 100 mm/min to simulate conditions, such as shoulder dystocia, that may lead to stretch-related PNIs in neonates. At constant strain, the reduction in stress was recorded for 90- or 300-seconds. The biomechanical data were then fit to a viscoelastic model to acquire the short- and long-term stress relaxation time-constants. Though no significant differences in the degree of stress relaxation were found between the two tested strain levels after 90 seconds in both nerve types, reduction in stress was moderately greater (p = 0.056) at 10% strain than at 20% for BP after 300 seconds. The reduction in stress was significantly higher in nerves subjected to a 300 second testing duration than 90 second for both strain levels and nerve types. When comparing BP and tibial nerve stress relaxation response, BP nerve relaxed significantly more than tibial at both strain levels after 90 seconds, but no significant differences were observed after 300 seconds. Our results confirm that neonatal peripheral nerve tissue is highly viscoelastic. These novel biomechanical data can be incorporated into finite element and computational models studying neonatal PNIs.

Effect of Hydrothermal Aging on Mechanical Properties and Long-Term Durability of Recycled Polysulfone

The present experimental investigation aims to discover the effect of hydrothermal aging on the mechanical properties of virgin and recycled PSU, as well as the effect of hydrothermal aging on the long-term durability including stress relaxation and creep properties of virgin and recycled PSU. Virgin and recycled PSU specimens were exposed to pure hot water at temperatures of 98 °C for 1, 1.5, 3, 4.5, 6, 9, and 12 months, respectively. Mechanical test of tensile, three-point bending, impact, and fracture toughness was carried out on those aged specimens. To obtain the long-term stress relaxation and creep property, a series of short-time stress relaxation and creep tests were performed by using dynamic mechanical analysis (DMA), and the master curve of long-term stress relaxation modulus and creep compliance was drawn by shifting those short relaxation and creep curve based on the time–temperature superposition principle (TTSP). It was finally concluded that the virgin PSU exhibits excellent hydrothermal aging resistance in tensile, flexural, impact and fracture toughness, stress relaxation, and creep properties, even if it was aged in 98 °C hot water for 1 year. Although the tensile and flexural properties of the unaged recycle PSU are similar to those of virgin PSU, the hydrothermal aging resistance in tensile, flexural, stress relaxation, and creep properties of recycled PSU is worse than that of virgin PSU. In addition, the activation energy required for stress relaxation of PSU is same with that for creep.

Experimental mechanics and numerical prediction on stress relaxation and unrecoverable damage characteristics of rubber materials

Stress relaxation and unrecoverable damage deformation are common phenomenon in rubber materials, which greatly induces instability of geometrical dimension and deteriorates the mechanical performances. The present work proposes experimental mechanics and numerical prediction for studying stress relaxation and unrecoverable damage characteristics. A time-dependent strain energy principle is established to describe the relaxation decay over time, and a quasi-plastic function is combined by considering the plastic flow criteria in order to depict the unrecoverable deformation after stress relaxation. Experimental study is conducted on multi-modes hyper-elastic mechanics and stress relaxation performances, and key parameters of the proposed constitutive model are identified by multi-island genetic algorithm (MIGA). The established constitutive equation is integrated in finite element simulation, and the numerical prediction is conducted. Combined experimental results clearly present nonlinear elastic properties, time-decay relaxation, and unrecoverable damage deformation of rubber materials. The numerical results are in good agreement with experiment ones, and the mechanism of relaxation and damage characteristics are explored. Additionally, based on the time-temperature superposition principle (TTSP) method, long-term stress relaxation behavior at low temperature is estimated by the short-term high-temperature test. This work provides efficient methods of experimental mechanics and numerical prediction for predicting the stress relaxation and damage characteristics of rubber materials, which could be also beneficial for characterizing rubber-base devices in engineering applications.

Effects of loading rate, applied shear strain, and magnetic field on stress relaxation behavior of anisotropic magnetorheological elastomer

Experimental research and numerical computation of stress relaxation behavior of an anisotropic magnetorheological elastomer (MRE) have been conducted in this paper. The anisotropic MRE has been formed from silicone matrix and micro-sized carbonyl iron particles under a magnetic field. Stress relaxation response of the anisotropic MRE was examined by single- and multi-step relaxation tests in shear mode using double-lap shear specimens. The effects of loading rate, applied constant strain, and external magnetic field on the stress relaxation behavior of the anisotropic MRE were studied. Experimental results showed that the stress relaxation of the anisotropic MRE was slightly dependent on the loading rate, but strongly depended on the constant strain level and the magnitude of external magnetic field. When increasing the constant strain level the shear stress of the anisotropic MRE in the single-step relaxation enhanced, while the relaxation modulus declined. The shear stress and modulus of the anisotropic MRE in the relaxation periods increased with increasing the magnetic field intensity. The four-parameter fractional derivative Zener model was used to describe the stress relaxation behavior of the anisotropic MRE. The presented model was fitted well to experimental data of the anisotropic MRE in both single- and multi-step relaxation tests. The fittings of relaxation modulus and shear stress with long-term predictions for the anisotropic MRE are in a very good agreement with the experimental ones. The maximal relative error of the fitted curves compared with measured data for both relaxation modulus and shear stress is less than 5.0%. As a result, the presented model is applicable to predict the long-term stress relaxation behavior of the anisotropic MRE.

Erroneous or Arrhenius: A Degradation Rate-Based Model for EPDM during Homogeneous Ageing.

To improve the predictive capability of long-term stress relaxation of elastomers during thermo-oxidative ageing, a method to separate reversible and irreversible processes was adopted. The separation is performed through the analysis of compression set after tempering. On the basis of this separation, a numerical model for long-term stress relaxation during homogeneous ageing is proposed. The model consists of an additive contribution of physical and chemical relaxation. Computer simulations of compression stress relaxation were performed for long ageing times and the results were validated with the Arrhenius treatment, the kinetic study and the time-temperature superposition technique based on experimental data. For chemical relaxation, two decay functions are introduced each with an activation energy and a degradative process. The first process with the lower activation energy dominates at lower ageing times, while the second one with the higher activation energy at longer ageing times. A degradation-rate based model for the evolution of each process and its contribution to the total system during homogeneous ageing is proposed. The main advantage of the model is the possibility to quickly validate the interpolation at lower temperatures within the range of slower chemical processes without forcing a straight-line extrapolation.

Modified Pre-stretching Assembly Method for Cable-Driven Systems

Soft cable-driven systems have been employed in many assembled mechanisms, such as industrial robots, parallel kinematic mechanism machines, medical devices, and humaniform hands. A pre-stretching process is necessary to guarantee the quality of cable-driven systems during the assembly process. However, the stress relaxation of cables becomes a critical concern during long-term operation. This study investigates the effects of non-uniform deformation and long-term stress relaxation of the driven cables owing to moving parts in the system. A simple closed-loop cable-driven system is built and an alternating load is applied to it to replicate the operation of transmission cables. Under different experimental conditions, the cable tension is recorded and the boundary data are selected to be curve-fitted. Based on the fitted results, a formula is presented to estimate the stress relaxation of cables to evaluate the assembly performance. Further experimental results show that the stress relaxation is mainly caused by cable creep and the assembly procedure. To remove the influence of the assembly procedure, a modified pre-stretching assembly method based on the stress relaxation theory is proposed and verification experiments are performed. Finally, the assembly performance is optimized using a cable-driven surgical robot as an example. This paper proposes a dual stretching method instead of the pre-stretching method to assemble the cable-driven system to improve its performance and prolong its service life.

Study on compressive stress relaxation behavior of beech based on the finite element method

The compressive stress relaxation behaviors in three directions of beech (Fagus orientalis) were studied by experiments, and predicted by mechanical model and finite element method. Firstly, short-term (3 hours) compressive stress relaxation experiments were carried out in longitudinal (L), radical (R) and tangential (T) directions of beech, and then the experimental data was fitted by mechanical model with two single Maxwell bodies in parallel connection. Secondly, the method of predicting the long-term (12 hours) stress relaxation behaviors of beech based on the finite element method was studied using the experimental data of short-term stress relaxation. Finally, the long-term stress relaxation behaviors in three directions of beech were investigated by experiments, mechanical model and finite element method respectively, and the results of them were compared. The results showed that stress relaxation behaviors of beech were different in three directions, and the short-term stress relaxation in L was much smaller than those in R and T directions under the same load. Besides, the mechanical model with two single Maxwell bodies in parallel connection was able to be predict the short-term relaxation behaviors of beech in three directions with correlation coefficients beyond 0.99, but it did not work in long-term relaxation. In addition, the errors of FEM were smaller than those of the mechanical model compared with the results of experiments in the long-term stress relaxation, and the errors of the FEM were approximately 8% in L and 20% in R and T directions, which were all accepted in the field of wood engineer. This study will contributes to predict the long-term relaxation behaviors of wood products and wooden structures based on the FEM. Keywords: Fagus orientalis, Maxwell model, mechanical properties, modulus of elasticity, wood structures

Long-term stress relaxation behavior of Polyaniline-EPDM blends using the time-temperature-strain superposition method

Long-term nonlinear viscoelastic stress response of polyaniline filled EPDM blends at various temperatures and strain levels were measured in short-term tests to check the applicability of time-temperature-strain superposition principle. A unified relaxation modulus master curve was constructed from the short-term tests. The unified master curve establishes the relaxation modulus over 18 months, which is 4.6 decades longer than the test duration. It was demonstrated that the time-temperature-strain superposition principle offers an accelerated testing methodology for determining the material’s long-term stress relaxation response at a reference strain and temperature.

Effect of annealing on the viscoelastic behavior of poly(ether-ether-ketone)

Annealing is widely utilized in industry to manipulate the mechanical properties of semi-crystalline polymers. In this work, poly(ether-ether-ketone) (PEEK) was annealed at different temperatures above its glass transition temperature (Tg) to investigate its influences on the viscoelastic behavior of PEEK. A set of master curves on long-term creep and stress relaxation behaviors of PEEK were obtained via time-temperature superposition and showed that a higher annealing temperature leads to more retardation. The underlying molecular mechanism is related to a higher activation energy of β-relaxation (Eβ) associated with the molecular motions below Tg. A physics-based Ngai's Coupling model was chosen for the analysis, suggesting a higher degree of restriction on molecular mobility due to annealing, which is mainly attributed to the increases in the density of the amorphous phase and the crystallinity. Usefulness of the Ngai's Coupling model for the prediction of long-term viscoelastic behavior of semi-crystalline polymers is discussed.

Long-term bending stress relaxation in timber laths for the structural design of lattice shells

Timber lattice shells are multi-layered structures of great interest for medium and long span lightweight solutions in structural and aesthetic terms. They are constructed by bending initially straight laths. This curving process can lead to high initial stresses in the laths and the possibility of overstressing under service loads. However, these initial stresses may decrease over time to acceptable levels due to the stress relaxation phenomenon. The quantification of stress relaxation over the long-term is therefore a key aspect in the structural analysis of lattice shells. Unfortunately, no information is given in the standards and the available experimental data comes from short-term research, so that engineers have to make assumptions which are not properly verified. This work provides experimental results on long-term bending stress relaxation curves of dry Eucalyptus globulus L. laths bent with three different curvature radii (different stress levels) over two years. For this purpose an original test device was developed and used, overcoming the drawbacks of the other devices used to date in most experimental research. Initial bending stresses decreased very quickly during the first weeks of measurements. After two years, the bending stresses fell by from 45% to 66% of their initial values depending on their curvature radii, which implies an important structural reserve recovery.