Creep Relaxation Research Articles

Proteoglycans play a role in the viscoelastic behaviour of the canine cranial cruciate ligament.

Proteoglycans (PGs) are minor extracellular matrix proteins, and their contributions to the mechanobiology of complex ligaments such as the cranial cruciate ligament (CCL) have not been determined to date. The CCLs are highly susceptible to injuries, and their extracellular matrix comprises higher PGs content than the other major knee ligaments. Hence these characteristics make CCLs an ideal specimen to use as a model in this study. This study addressed the hypothesis that PGs play a vital role in CCL mechanobiology by determining the biomechanical behaviour at low strain rates before and after altering PGs content. For the first time, this study qualitatively investigated the contribution of PGs to key viscoelastic characteristics, including strain rate dependency, hysteresis, creep and stress relaxation, in canine CCLs. Femur-CCL-tibia specimens (n = 6 pairs) were harvested from canine knee joints and categorised into a control group, where PGs were not depleted, and a treated group, where PGs were depleted. Specimens were preconditioned and cyclically loaded to 9.9N at 0.1, 1 and 10%/min strain rates, followed by creep and stress relaxation tests. Low tensile loads were applied to focus on the toe-region of the stress-strain curves where the non-collagenous extracellular matrix components take significant effect. Biochemical assays were performed on the CCLs to determine PGs and water content. The PG content was ∼19% less in the treated group than in the control group. The qualitative study showed that the stress-strain curves in the treated group were strain rate dependent, similar to the control group. The CCLs in the treated group showed stiffer characteristics than the control group. Hysteresis, creep characteristics (creep strain, creep rate and creep compliance), and stress relaxation values were reduced in the treated group compared to the control group. This study suggests that altering PGs content changes the microstructural organisation of the CCLs, including water molecule contents which can lead to changes in CCL viscoelasticity. The change in mechanical properties of the CCLs may predispose to injury and lead to knee joint osteoarthritis. Future studies should focus on quantitatively identifying the effect of PG on the mechanics of intact knee ligaments across broader demography.

Failure Mechanisms of Ba0.5Sr0.5Co0.8Fe0.2O3-δ Membranes after Pilot Module Operation.

The step from the testing of oxygen transport membranes on a lab scale to long-term operation on a large scale is a challenge. In a previous study, membrane failure was observed at defined positions of one end of the cooled tubular Ba0.5Sr0.5Co0.8Fe0.2O3-δ membranes after an emergency shutdown. To understand the failure mechanisms, strength degradation and transient stress distribution were investigated by brittle-ring tests and finite element simulations, respectively. A 15% decrease in the characteristic strength of 162 MPa was proven after aging at 850 °C and was attributed to grain coarsening. The reduction in characteristic strength after thermal shock ranged from 5 to 90% depending on the cooling rates, and from 5 to 40% after the first and 20th soft thermal cycling. Simulations indicated the chemical strains induced by a 10-bar feed air and 50 mbar permeate pressure, which caused tensile stresses of up to 70 MPa at the outer surface. These stresses relaxed to 43 MPa by creep within a 1000 h operation. A remaining local stress maximum seemed to be responsible for the fracture. It evolved near the experimentally observed fracture position during a 1000 h permeation and exceeded the temperature and time-dependent strength. The maximum stress was formed by a chemical strain at temperatures above 500 °C but effective creep relaxation needed temperatures above 750 °C.

Effect of cure temperature on the mechanical properties of epoxy-aluminium single lap joints

ABSTRACT Mixed adhesive joints combining different stiffnesses and strengths in the same overlap is a good strategy to increase the mechanical properties. For this purpose, different adhesives with distinct curing temperatures are used, whose optimization is crucial to maximize the mechanical performance. In this context, this study considers Araldite® AV 4076–1/HY 4076 and Araldite® AW 106/HV 953 U adhesives to evaluate the effect of curing temperature on tensile strength, creep and stress relaxation response and fatigue strength of single lap joints. It was possible to conclude that both adhesives exhibited higher static strength, lower stress relaxation and lower creep displacements with increasing curing temperature, but while for the brittle adhesive this trend occurred up to 150°C for the ductile one it was only up to 70°C. After this value, all properties regressed due to the degradation of the ductile adhesive with temperature. Considering values corresponding to 25% of the tensile strength, for example, it was noted that the ductile adhesive relaxes 54.7% more than the fragile one and presents a creep displacement around 95.1% higher. On the other hand, while the fatigue life was shown to be insensitive to the curing temperature for the brittle adhesive, in the case of the ductile one it decreases after 70°C. Therefore, when these adhesives are combined into a mixed adhesive joint, the curing temperature must never exceed 70°C.

Reverse-traction skin-stretching device for primary closure of large skin defects.

The tension in the skin margin of a wound is the major determinant for wound healing. The difficulty of primary closure for large skin defects due to excessive wound tension has long been a clinical challenge. In this study, we designed and fabricated a reverse-traction skin-stretching device (RT-SSD) to relieve the skin tension of a large skin defect and thereby allow primary wound closure. The novel RT-SSD designed in this study drives the fixing device fixed on the skin edge of the wound by rotating the pulling device, thus exerting a reverse tensile force on both sides of the wound, causing creep and stress relaxation, thus reducing the skin tension. Through the tension analyses; microcirculation detection; clinical scores; and a series of histological staining in vivo, it is verified that intraoperative application of RT-SSD can stretch and straighten collagen and fragment elastin, thus effectively reducing skin tension of large skin defect of miniature pigs. In addition, its special linear and planar traction protects the subcutaneous microcirculation of the wound site. The evaluation of wound healing confirmed that RT-SSD had negligible negative impact on wounds, reduced the incidence of complications, and promoted the healing of large skin defects. Therefore, this study provides a new safe and effective device for the primary closure of large skin defects.

Laboratory Investigation of the Low-Temperature Crack Resistance of Wood Tar-Based Rejuvenated Asphalt Mixture Based on the Semi-Circular Bend and Trabecular Bending Test.

Low-temperature crack resistance is the core issue affecting the promotion of rejuvenated asphalt, but most current studies do not consider the creep relaxation characteristics of rejuvenated asphalt mixture at low temperatures, which is inconsistent with the actual situation. To explore the low-temperature crack resistance of a wood tar-based rejuvenated asphalt mixture, we observed the low-temperature crack resistance of styrene butadiene styrene (SBS) modified asphalt, wood tar-based rejuvenated asphalt, and RA-102 rejuvenated asphalt and their mixtures using laboratory tests. Our results showed that the low temperature crack resistance of the wood tar-based rejuvenated asphalt mixture was better than that of the RA-102 rejuvenated asphalt mixture, but slightly worse than that of the original SBS asphalt mixture. After the synergistic action of wood tar and biomass fiber, wood tar can be fully mixed into the new asphalt, effectively alleviating the bonding failure between asphalt and aggregate and improving the stiffness of the mixture, so that the toughness and crack resistance of rejuvenated asphalt mixture at low temperatures are evidently improved. Wood tar-based rejuvenated asphalt mixture has a good creep deformation ability at low temperatures. The established creep damage model can better describe the flexural creep performance of rejuvenated asphalt mixtures at low temperatures, and can be used to infer the deformation characteristics at other low temperatures.

Optimizing Regenerant Content of Aged SBS Modified Asphalt Binder Based on High- and Low-Temperature Performance

The performance of the recycled asphalt pavement is directly influenced by the content of the used regenerant (i.e., rejuvenator and/or unaged asphalt binder). The goal of this study is to optimize regenerant content of aged styrene-butadiene-styrene (SBS) modified asphalt binder based on high-temperature creep and low-temperature relaxation performance tests. Initially, penetration, ductility, softening point, multiple stress creep recovery (MSCR), and bending beam rheometer (BBR) tests were carried out to investigate the rheological behavior of the aged SBS modified binder (AMB) regenerated with different contents of the rejuvenator and unaged SBS modified binder (UMB). A method is proposed, based on the rheological behavior of the regenerated AMB, to determine the optimum contents of the regenerants (i.e., rejuvenator and UMB). To reach a successful trade-off between low- and high-temperature properties of the regenerated AMB, the relaxation rate VR and nonrecoverable creep compliance J3.2 (at 3.2 kPa) were selected as the evaluation indices to settle the optimum contents of the rejuvenator and UMB. The results showed that the ductility of regenerated AMB is on par with the UMB when the contents of rejuvenator and UMB are 4% and 70%, respectively. The nonrecoverable creep compliance and relaxation rate of the regenerated AMB tended to increase with the increase in the content of the rejuvenator and UMB, whereas the recovery rate and relaxation modulus decreased. It indicated that the low-temperature performance increased while the high-temperature performance was adversely affected by the increase in the content of the regenerants. The VR and J3.2 of the regenerated AMB were comparable to those of unaged state, when the contents of the rejuvenator and UMB in the aged binder were 5% and 70%, respectively. It indicated that the high-temperature creep and low-temperature relaxation performance of the AMB reach a balance.

Application of viscoelastic-plastic model in blended yarn

This paper investigates the mechanical properties of a blended yarn and its correlation with the characteristics of constituent yarns of different materials. Each yarn’s creep and stress relaxation tests are curves fitted to a six-element constitutive model. The results show that the higher the chemical fiber content in the yarn, the better the plastic properties. The experimental data fit the six-element model with 99% confidence. Compared with the commonly used viscoelastic Burgers and Ering models, the six-element model has a much more precise forecasting ability. Within the scope of this study, the ratio of yield stress to initial stress under different stress conditions calculated from the same yarn test is similar, and the ratio is only related to the blending ratio of polyester-cotton blended yarn. In yarns with strong plasticity, this ratio can reflect the proportional relationship between plastic deformation and elastic deformation in relaxation experiments.

Viscoelastic Influence on the Board Level Assessment of Wafer Level Packages Under Drop Impact and Under Thermal Cycling

Abstract Structural components such as printed circuit boards (PCBs) are critical in the thermomechanical reliability assessment of electronic packages. Previous studies have shown that geometric parameters such as thickness and mechanical properties like elastic modulus of PCBs have a direct influence on the reliability of electronic packages. Elastic material properties of PCBs are commonly characterized using equipment such as tensile testers and used in computational studies. However, in certain applications viscoelastic material properties are important. Viscoelastic influence on materials is evident when one exceeds the glass transition temperature of materials. Operating conditions or manufacturing conditions such as lamination and soldering may expose components to temperatures that exceed the glass transition temperatures. Knowing the viscoelastic behavior of the different components of electronic packages is important in order to perform accurate reliability assessment and design components such as PCBs that will remain dimensionally stable after the manufacturing process. Previous researchers have used creep and stress relaxation test data to obtain the Prony series terms that represent the viscoelastic behavior and perform analysis. Others have used dynamic mechanical analysis in order to obtain frequency-domain master curves that were converted to time domain before obtaining the Prony series terms. In this paper, nonlinear solvers were used on frequency domain master curve results from dynamic mechanical analysis to obtain Prony series terms and perform finite element analysis on the impact of adding viscoelastic properties when performing reliability assessment. The computational study results were used to perform a comparative assessment to understand the impact of including viscoelastic behavior in reliability analysis under thermal cycling and drop testing for Wafer Level Chip Scale Packages.

A Numerical Model for Investigating the Effect of Viscoelasticity on the Partial Slip Solution.

To investigate the effects of viscoelasticity on the stick-slip behaviour, a new model reproducing the partial slip of viscoelastic materials under fully coupled conditions is developed in this paper. The ratio of retardation time to relaxation time is employed to characterize the rheological property of a viscoelastic material. It is found that materials with higher ratios exhibit more fluid-like behaviours while those with lower ratios perform more like solid. As long as the contact input (load or displacement) is constant, the stick ratio (ratio of stick area to contacting area) is found to be insensitive to the viscoelasticity of materials. However, the separation pattern of the stick and slip regions varies with time when different contact phenomena (creep or stress relaxation) are encountered in the lateral and normal directions. The transition process from partial slip to gross sliding of viscoelastic materials, unlike the elastic response, tends to be abrupt when fully coupled conditions between shear tractions and pressure are introduced. When identical contact parameters are specified for different viscoelastic materials, the more fluid-like material always experiences a quicker transition from partial slip to gross sliding.

Force-Displacement Analysis in Diaphragm-Embedded Fiber Bragg Grating Sensors.

This paper presented the force and displacement analyses of a diaphragm-embedded fiber Bragg grating (FBG) sensor. In the first step, a numerical analysis (via finite element method) was performed considering linear elastic materials, where there is a linear variation on the strain in the optical fiber for both displacement and force (or pressure). In the second step, the experimental analysis was performed using two approaches: (i) controlling the displacement applied in the diaphragm-embedded FBG (while the force is also measured). (ii) Controlling the force applied in the sensor (also with the measurement of the displacement). Results showed reflected optical power variations and wavelength shift following the application of displacement and force. The sensitivities of both wavelength shift and optical power were different (and non-proportional) when displacement and force were compared. However, a higher correlation, determination coefficient (R2) of 0.998, was obtained in the analysis of the wavelength shift as a function of the displacement, which indicated that the strain transmission in the optical fiber is directly related to the strain in the diaphragm, whereas the force has an indirect relation with the strain and depends on the material features. Then, the possibility of simultaneous estimation of force and displacement was investigated, where the linear relation of both parameters (displacement and force) with the wavelength shift and the optical power were obtained in a limited range of displacement and force. In this range, root mean squared errors of 0.37 N and 0.05 mm were obtained for force and displacement, respectively. In addition, the force variation with a step displacement input also shows the possibility of using the proposed FBG device for the characterization of the materials’ viscoelastic features such as phase delay, creep, and stress relaxation, which can be employed for in situ characterization of different viscoelastic materials.

Creep relaxation in nonlinear viscoelastic twisted rods

AbstractThe solution to the problem of stress relaxation in a twisted nonlinear viscoelastic isotropic incompressible rod is presented. We address the multiplicative decomposition of the deformation gradient into reversible (elastic) and irreversible (creep) parts. The elastic potential and the creep potential can be chosen arbitrarily. In particular, the creep law can take into account both the nonlinearity of the relationship between the strain rate and the effective stress, and time‐hardening or softening. We consider two variants of creep constitutive relations. One is based on the Tresca equivalent stress, the other is based on the von Mises equivalent stress. The first of them leads to a significant simplification of the governing equations because in this case a radial elastic strain vanishes. In this framework, we obtain a closed‐form solution in elementary functions for the coupling of Mooney–Rivlin elastic model and linear creep law. For the von Mises material, numerical‐analytical results are obtained. The results are compared with the known small‐strain solutions.

Uncertain Quasi-static and Nonlinear Dynamic Analysis of Viscoelastic Dielectric Elastomer with Interval Parameters

Dielectric elastomers as a soft active material have been widely used in the field of artificial muscle actuator, acoustic actuator, loudspeaker, active control of vibration, soft robots and membrane resonators. Compared with traditional materials, there are many unknown uncertainties in the properties of the DE actuators. In this work, a viscoelastic dynamic model of dielectric elastomer is proposed with considering the uncertainties in material parameters, external mechanical load and voltage. By introducing the interval perturbation method and first-order Taylor series expansion method, the creep analysis, relaxation analysis and dynamic analysis of the dielectric elastomer with interval uncertain parameters are implemented. The effectivity of the proposed interval method is verified by the Monte Carlo simulation. This uncertain prediction method could be used in the design of active control systems with dielectric elastomers as actuators or sensors in the future.

A Core Damage Constitutive Model for the Time-Dependent Creep and Relaxation Behavior of Coal

The creep and stress relaxation behaviors of coal are common in coal mining. The unified constitutive model is suitable to describe and predict both the creep and relaxation evolution characteristics of rocks. The generalized Kelvin model is the core element for traditional and improved component models to reflect both the nonlinear creep and relaxation. In this paper, an improved core damage model, which could both reflect the creep and stress relaxation in relation to the damage evolution, was established based on a comparison of the traditional and improved component models, and the responding constitutive equations (creep and stress relaxation equation) at constant stress/strain were deduced. Then, the core damage model was validated to the uniaxial compressive multistage creep and stress relaxation test results of coal, showing that the model curves had great accordance with the experimental data. Moreover, the model comparisons on accuracy, parameter meaning, and popularization among the core damage model, hardening-damage model, and the fractional derivative model were further discussed. The results showed that the parameters in the core damage model had clear and brief physical significances. The core damage model was also popularized to depict the time-dependent behaviors of other rocks, showing great accuracy.

Laboratory Study and Simulation Analysis on Anticrack Properties of Open-Graded Friction Course Based on Creep Tests

Cracking is a common early disease of asphalt pavements. To evaluate the temperature shrinkage cracking resistance of an open-graded friction course (OGFC), the viscoelastic parameters of an OGFC mixture at different temperatures were obtained by uniaxial compression creep tests. According to the viscoelastic parameters, numerical models of the creep, relaxation, and temperature shrinkage cracking of an OGFC were established. Subsequently, the reliability of the numerical model was verified based on the creep test results and the extensive Maxwell model. The crack initiation temperature of the OGFC mixture at different cooling rates was analyzed by combining indirect tensile strength and temperature shrinkage stress. The results showed that the simulation results were close to the model results, and the average errors of the simulation results for creep compliance and relaxation modulus did not exceed 7.18% and 1.83%, respectively. The faster the cooling was, the greater the temperature shrinkage stress and the higher the crack initiation temperature were. The crack initiation temperature of the OGFC at a cooling rate of 20°C/h was about −3.5°C. This research provides a reference for quickly obtaining the crack initiation temperature of asphalt mixtures at different cooling rates.

A recursive-cluster based reduced order method for numerical prediction of effective properties of heterogeneous viscoelastic materials

A novel recursive-cluster based reduced order method is presented to predict the effective properties of heterogeneous viscoelastic materials. By virtue of a piecewise series expansion based variable separation, a temporally and spatially homogenization process is decoupled into a series of recursive elastic homogenization ones, which require only one-time clustering decomposition with one-time elastic heterogeneous analysis. Such that, the heavy computational burden caused by the direct numerical simulation over the whole domain of viscoelastic heterogeneous RUC can significantly be alleviated. The effective creep compliance or relaxation modulus is presented via a time varying average strain or average stress, and a piecewise adaptive technique is proposed to secure the temporal accuracy when step size varies. Numerical examples are provided to demonstrate the effectiveness and efficiency of proposed approach, and the predicted results agree well with those given by FEM/SBFEM based viscoelastic DNS. • Propose a recursive-cluster based reduced order method to evaluate effective properties of heterogeneous viscoelastic materials. • Decouple a temporally and spatially homogenization process into a series of recursive elastic homogenization ones. • Take only one-time clustering decomposition with one-time elastic heterogeneous analysis. • Execute a piecewise adaptive computing to gain the effective strains of clusters on RUC. • Circumvent the heavy computational burden caused by the high-fidelity viscoelastic DNS on RUC significantly.

Internal stress development within wood during drying: regime and kinetics

Internal stress (IS) development in juvenile and mature rubberwood during drying has been studied using an online measurement of a restoring force (RF) required to restrain a half-split rectangular wood specimen. According to an abrupt change in the restoring force rate, the evolution of IS can be divided into four distinct regimes, i.e., (i) zero IS, (ii) accelerating IS, (iii) reversing IS and (iv) decelerating IS. In stage I, the wood moisture content (MC) is still above fiber saturation point (FSP) with no drying shrinkage. In stage II, the negative RF constantly accelerates. IS mainly develops due to drying shrinkage with the activation energy of 19 kJ/mol. In stage III, the negative RF sharply decelerates and later reverses to the positive value. This regime takes place as the dried zone moves inwards and ends when there is no wet zone left. The stress reversal phenomenon having the activation energy of 36 kJ/mol contains two negative maxima, which occur faster in mature wood than in juvenile wood. Possible creep relaxation due to shear deformation of hemicellulose/lignin matrix between the cellulose fibrils is discussed. Finally, the positive RF decelerates in stage IV with the RF rate gradually declining and remaining at zero up until the end of drying. The corresponding activation energy of stage IV is 52 kJ/mol for both juvenile and mature rubberwood.

A multi-bolt tightening method based on elastic interaction coefficient and gasket creep relaxation

Flange connections are widely used in various mechanical components. The most important purpose of tightening for flanged bolts is to achieve designed clamping force for the maintenance of overall performance. In this work, a multi-bolt tightening algorithm is proposed based on elastic interaction coefficient and gasket creep relaxation. Firstly, dispersion of the individual bolt clamping forces for torque control method is considered in the algorithm. Relationship between the nut factors of the flange bolts in multi-pass tightening is established through experiment. Subsequently, the elastic interaction coefficient matrix was updated during the multi-pass tightening process to reduce the error. Two cases, without gasket and silicone gasket, are considered in the multi-bolt tightening experiment. Without gasket, the elastoplastic deformation at the initial stage after tightening will also cause a loss of clamping force. When using gasket, the clamping force loss due to gasket creep relaxation is more pronounced. Through experimental verification, the proposed multi-bolt tightening algorithm are able to achieve the target range of designed clamping forces and reduce its dispersion. Finally, the main influencing factors of the multi-bolt tightening are analyzed to provide a reference for the design of flange connections.

Nonlinear rheological models and their application to describe the mechanical behavior of highly oriented polymer materials

The nonlinear viscoelasticity of uniaxial oriented polymer materials is considered. To explain the deformation mechanisms of oriented polymers and the possibility of predicting their mechanical behavior in various operating modes, new nonlinear rheological models have been proposed. The application of the simplest rheological model of a real viscoelastic solid to the description and explanation of the recovery process in polymer materials is studied. From the standpoint of rheology, a model of an ideal viscoelastic solid is introduced. Using the balance equation for the number of transitions through energy barriers, a method for calculating the new nonlinear rheological model has been proposed. To eliminate the shortcomings of the ideal viscoelastic solid model associated with the impossibility of predicting creep and stress relaxation modes for long times, a generalized rheological model of a real viscoelastic solid was obtained. In the corrected model, the simplest elements are connected in parallel, which means the presence of not one, but several energy barriers in the materials, the transmission through which have their own relaxation times. To describe the recovery processes in polymer materials, the model of an ideal viscoelastic solid is supplemented by a parallel connected elastic spring. An additional Hooke spring replaces the interfibrillar interaction between the individual elements of the structure and is responsible for possible obstacles during jump-like transitions through the energy barrier. Using the method of rheological models and describing interfibrillar bonds within the framework of the theory of elasticity, a constitutive equation was obtained for the case of recovery processes. Based on the constitutive equation of viscoelasticity for uniaxial oriented polymer materials, a new nonlinear highly elastic element is introduced, which replaces the Maxwell’s element in the theory of linear viscoelasticity. A new rheological model of parallel connection of elastic elements is shown. An explanation of the retardation of the recovery process in polymers is given. The simplest rheological model of a real viscoelastic solid is proposed, in which an elastic spring is responsible for interfibrillar bonds. A constitutive equation is obtained that describes the recovery process in polymers. This equation can be integrated by quadratures and gives a solution that is an analogue of the Newton-Leibniz formula for the proposed model. It is shown that the deformation recovery process in polymer does not depend on the level of initial deformation and the loading method. The obtained result is confirmed by experimental data for polyamide and polyethylene film yarns. When specifying a certain initial level of deformation, generalized recovery curves of these materials are obtained. The proposed simplest rheological model of a real viscoelastic solid makes it possible to predict the reducing properties of polymer materials. And also makes it possible to determine the height of the energy barrier and the magnitude of the elastic modulus in the model. Based on the new rheological models, it is planned in the future to consider the issues of modeling and forecasting different modes of deformation.

Comparison of Prestressing Methods with CFRP and SMA Materials in Flexurally Strengthened RC Members.

Over the years, prestressing concrete has become a well-known technique to improve the ultimate and serviceability state of RC members. Besides steel reinforcement, relatively new materials such as carbon fiber reinforced polymers (CFRP) or especially shape memory alloys (SMA) can be used to active strengthening. The main scope of this paper is to compare various prestressing methods using carbon composites and memory steel alloys. A description of SMA, shape memory effect, its utilization for prestressing, and CFRP materials are presented in the paper. Moreover, current state-of-the-art developments in the field of both materials, considering prestressing systems and available anchorage, material behavior, creep and stress relaxation, durability issues, thermal compatibility with concrete, and fire behavior, are described. A general revision of previous studies based on flexural strengthening using both materials is conducted and the selected results of these studies are briefly presented. The behavior of RC beams after strengthening with mentioned techniques is compared and discussed. Selected on-site applications are described to confirm the feasibility and practicality of the strengthening systems. Finally, the main advantages and disadvantages of CFRP and SMA materials for prestressing concrete structures are summarized and further recommendations for the future research are listed.

Viscoelastic-plastic constitutive model for the creep and stress relaxation characteristics of a geogrid

Viscoelastic-plastic constitutive model for the creep and stress relaxation characteristics of a geogrid