Stress Relaxation Curves Research Articles

Influence of stoichiometry on the glass transition and bond exchange reactions in epoxy thermoset polymers

Thermally malleable polymers which undergo covalent bond exchange reactions (BERs) have been shown to be able to rearrange their network topology at high temperatures without impairing the network integrity. At low temperatures, the BERs are so sluggish that the materials behave like traditional thermosetting polymers. In this paper, we demonstrated that the temperature dependent BER rate could be tuned by adjusting the stoichiometry of monomers. As the ratio of hard segments in the epoxy thermoset network is increased, the material's glass transition temperature (Tg) is increased, with a corresponding increase in the temperature required to achieve a given stress relaxation rate. The material stress relaxation behavior was studied from both a theoretical and experimental point of view. Based on the kinetics of BERs, we derived the detailed expression of stress relaxation time, which reveals an Arrhenius type dependency of material relaxation behavior on the applied temperature. Subsequently, from the experimental stress relaxation curves, we determined the energy barrier for the BERs in different networks. With the Tg being elevated from 30.3 °C to 63.0 °C, the BER energy barrier is linearly increased from 68.2 kJ mol−1 to 97.3 kJ mol−1. Such a correlation between these two thermomechanical behaviors provides an additional design parameter (beyond catalyst choice) which can aid in achieving highly tunable service conditions for practical engineering applications of thermally malleable thermosets.

بررسی رفتار لزج -کشسان میوه خرمالو در طی نگه‌داری با استفاده از مدل‌های آسایش تنش

Introduction: Persimmon fruits are subjected to different environmental conditions from harvest to consumption. Foods, those are exhibiting characteristics of both liquid and solid, are described as viscoelastic where stress relaxation and strength properties are time dependant. Knowledge of viscoelastic properties of foods and agricultural materials are important when considering harvesting, handling, transportation, processing, and storage. Also the data on viscoelastic properties are required as an input for mathematical models, which describe and predict internal stress and cracking during different handling and processing procedures. The mechanical properties are considered one of the most important four parameters, which reflect the quality of food material. Those parameters include texture, firmness and chewability. Viscoelastic material exhibit stress relaxation phenomena, which is one of the most important factors in characterizing agricultural materials. The objectives of the current study were: (1) to obtain data to describe the stress relaxation characteristic of Persimmon fruits during Storage, (2) to investigate the effect of storage time on stress relaxation properties, and (3) to find the best model to describe the obtained stress relaxation data. Materials and Methods: The persimmon fruits were manually picked up at maturity stage from persimmon trees in a garden, in Fars province, Iran. They were handled to Biophysics laboratory in Agricultural Engineering department, at Shiraz University, on the foam sheets in one layer array for minimizing any likely compaction. Initial moisture content was determined by gravimetric method in an oven at 70C till obtaining constant successive weight loss of 0.001 g. The initial moisture content was 44.26% (d.b). Since the rheological characteristics of fruits are important for any processing operation, viscoelastic behavior of persimmon fruits during storage in environmental conditions was investigated using estimating its relaxation parameters from experimental stress relaxation data. The rheological behavior of persimmon fruits was evaluated to uniaxial compression test for relaxing the stress during 480 s. Texture Profile Analyser (TPA) (TA.XT2 plus model, Stable Microsystems, England) with Exponent Lite (Version 4,0,8,0, UK) software was used to compress whole date samples and export data into Excel worksheets. TPA was equipped with a 30 kgf load cell. The cross head speed was adjusted on 1 mm/s, and samples compressed with 30% strain. The cross head then kept at 30% of strain for relaxing the stress in 480 s duration. A chamber with temperature control circuit was fabricated around the TPA cross head to prepare constant temperature identical to sample temperature with an accuracy of ±0.1C during the stress relaxation tests. All tests were performed with ten replications. Three popular stress relaxation models, namely the generalized Maxwell with three elements, Nussinovitch, and Peleg were fitted to experimental data and was used from R-square, standard error of estimation (SEE) and percent of average relative error (ARE%) indexes for evalution of models. Results and Discussion:The force–time curves were converted to stress–time curves by dividing the true compression force values to the corresponding true values of contact surface area. Analysis of variance showed that storage time had significant effect on initial stress relaxation. The results showed that the magnitude of initial stress (stress at time zero) required to create a fixed strain on whole fruit was significantly decreased up to 80% during storage in environmental conditions, but the relaxation time was increased at the range of 312.10 to 353.90 s. Based on the results, elastic behavior of persimmon fruit was enhanced and its firmness decreased during fruit storage. Persimmon is sugar rich fruit that its behavior is principally partly controlled by physico-chemical properties of sugar. Changes in sugar type as a result of enzymatic action are taken place during the storage process. However, in the present study all samples were in the time of maturation, and therefore the physical state of sugar was influenced by free water which is resulted in increasing in fruit moisture content. Stress relaxation curves were plotted at different storage time. Some variations were apparently observed among the curves. Sucrose decreased initial stress decay rate and increased proportion of un-relaxed force. Variations in stress decay rate might refer to the amount of initial stress which was affected by physic-chemical properties of the sugar. Recall that nonlinear regression method with non-negative constraint was used to derive the models constant. Conclusion: All three models were valid for quantifying the viscoelastic behavior of persimmons; however the generalized Maxwell with three elements (with R2=0.999, SEE=0.017 and ARE=0.19%) and Nussinovitch (with R2=0.996, SEE=0.057, ARE=0.36%) were the best models in predicting experimental data.

FEM analysis of vacuum hot bulge forming of Hastelloy C-276 thin-walled cylindrical workpiece

A stress relaxation test has been carried out for Hastelloy C-276 at temperature of 800 °C and initial stress level of 250 MPa. Based on the experimental stress relaxation curve, the relationship between creep strain rate and stress has been derived. Then, a set of creep constitutive equations has been built and the values of constants arising in the constitutive equations have been determined by fitting the creep strain rate-stress curve. Close agreement between computed results and experimental ones is obtained for stress relaxation data. The creep constitutive equation set has been integrated with the commercial FE (finite element) solver MSC. Marc via the user defined subroutine, CRPLAW, for the vacuum hot bulge forming process modelling of Hastelloy C-276 thin-walled cylindrical workpiece. The temperature field, the radius-direction displacement field and the stress-strain field are calculated and analyzed. Furthermore, the bulging dimension and the final internal diameter of workpiece are predicted and the test results verify the reliability of the finite element method.

Fatigue Life Estimation of Lead-Free Solder Joints Using Viscoplastic-Creep Separate Constitutive Model

When we estimate the fatigue life of lead-free solder joints under cyclic temperature load, we have to get equivalent inelastic strain range accurately. In this study, in order to show the example of using our previously proposed constitutive model, which can describe stress strain curves, stress strain hysteresis loops and stress relaxation curves, with these temperature dependencies and these rate dependencies, we conducted FE analysis of the chip component under thermal cycle using the constitutive model. We also conducted fatigue tests of Sn3.5Ag0.5Cu0.07Ni0.01Ge lead-free solder using micro test pieces and estimated the fatigue life.

Eyring-Halsey 모델의 유동파라메타로부터 열역학 성질과 자체 확산

Poly(methyl acrylate)-poly(acrylonitrile) 공중합체의 응력완화 실험은 용매기를 부착한 인장 시험기를 사용하여 여러 온도의 공기 중, 증류수 용액에서 실행하였다. Eyring-Halsey 모델의 이론적인 응력완화식에 응력완화 실험 결과를 적용하여 여러 가지 유동 파라메타를 계산하였다. 비결정성 영역에서의 유동단위의 고찰을 위하여 유동 파라메타와 결정크기로부터 섬유고분자 물질의 자체확산, 홀 부피, 점성, 열역학파라메타 등을 계산하였다. 이들 시료의 유동 파라메타는 유동 단위의 홀부피, 자체확산, 유동 열역학 파라메타와 직접적인 연관을 갖는 것으로 규명되었다. The stress relaxation of poly(methyl acrylate)-poly(acrylonitrile) copolymer samples were carried out in air and distilled water at various temperatures using the tensile tester with the solvent chamber. The rheological parameters were obtained by applying the experimental stress relaxation curves to the theoretical equation of the Eyring-Halsey non-Newtonian model. The self diffusion, hole volume, viscosities, and thermodynamic parameters of copolymer samples were calculated from rheological parameters and crystallite size in order to study of flow segments in amorphous region. It was observed that the rheological parameters of these copolymer samples are directly related to the self diffusion, hole volume, viscosities, and thermodynamic parameters of flow segments.

Modelling of loading, stress relaxation and stress recovery in a shape memory polymer

A multi-element constitutive model for a lactide-based shape memory polymer has been developed that represents loading to large tensile deformations, stress relaxation and stress recovery at 60, 65 and 70°C. The model consists of parallel Maxwell arms each comprising neo-Hookean and Eyring elements. Guiu–Pratt analysis of the stress relaxation curves yields Eyring parameters. When these parameters are used to define the Eyring process in a single Maxwell arm, the resulting model yields at too low a stress, but gives good predictions for longer times. Stress dip tests show a very stiff response on unloading by a small strain decrement. This would create an unrealistically high stress on loading to large strain if it were modelled by an elastic element. Instead it is modelled by an Eyring process operating via a flow rule that introduces strain hardening after yield. When this process is incorporated into a second parallel Maxwell arm, there results a model that fully represents both stress relaxation and stress dip tests at 60°C. At higher temperatures a third arm is required for valid predictions.

Observation of the relation between uniaxial creep and stress relaxation of filled rubber

This paper presents an experimental evaluation of the stress relaxation and creep of filled rubber. A detailed study of the influence of different test programs, where the main variable was the load sequence on the creep and relaxation processes, is discussed. The final goal of the research is to find a method to predict stress relaxation from known creep, or vice versa, in a simple way that would give sufficiently accurate results over both primary and secondary creep regions. Therefore suggestion for converting the creep test result into a stress relaxation curve and vice versa is presented. The idea is based on the assumption that both processes (creep and stress relaxation) are the result of the same viscoelastic mechanism and that the stress relaxation can be treated as creep under decreasing stress. Experimental data shows these assumptions to be correct. For the conversion of the creep parameters into stress relaxation parameters a reverse stress-strain curve is needed, therefore factors affecting the unloading stress-strain curve are also presented. Finally, the transition from the suggested conversion to the final method will be discussed.

Evolution in Dislocation Configuration of Deformed Fe-40Ni-Ti Alloy during Isothermal Relaxation

The thermo-simulation test and transmission electron microscopy (TEM) were applied to investigate the evolution of dislocation configuration and strain induced precipitation behavior during relaxation at 850°C in a deformed Fe-40Ni-Ti alloy. The stress relaxation curve can be divided into three stages, namely, the process of incubation, nucleation and growth, and the coarsening of strain-induced precipitates. The highly dense and twisted dislocations formed during the deformation develop into dislocation cells and finally, the sub-grains can be observed when relaxing to 1000s. The strain induced precipitates occur both onto the dispersed dislocations and dislocation cells. The precipitates pin the dislocations which results in retarding the progress of dislocation configuration evolution. As precipitates start to coarsen, the pinning effect weakens and the dislocations get rid of the pinning though bypassing mechanism. Adopting the same simulation test to bainitic steel, the optimum refinement could be obtained at 60-200s during relaxation processing, corresponding to the perfect dislocation cells formation of Fe-40Ni-Ti alloy.

Stress relaxation behaviors of articular cartilages in porcine temporomandibular joint

In this study, we tested the compressive stress relaxation behaviors of the mandibular condylar and temporal cartilages in the porcine temporomandibular joint (TMJ). The aim was to determine the quantitative and qualitative similarities and differences of compressive stress relaxation behaviors between the two cartilages. Ten porcine TMJs were used; the articular surface was divided into 5 regions: anterior, central, posterior, lateral and medial. Compressive relaxation test was carried out at a strain level of 5% in each region of the two cartilages. The stress relaxation was monitored over a period of 5min. In all the regions of the two cartilages, the time-dependent stress relaxation curves showed a marked drop in stress within the initial 10s, which can be fitted by a standard linear viscoelastic model. The instantaneous moduli in the temporal cartilage were dominantly larger than those in the condylar cartilage, while the condylar cartilage had slightly larger relaxation moduli than the temporal cartilage except for the medial region. The both cartilages showed the regional differences in the compressive stress relaxation behavior, and in the temporal cartilage the lateral and medial regions revealed the largest values for the instantaneous and relaxation moduli. The present results demonstrate that the viscoelastic properties of compressive stress relaxation in both cartilages are region-specific, which might have an important implication for stress distribution and transmission along with the TMJ disc.

Effect of silicon on recrystallisation of V–Ti microalloyed steel

The dynamic recrystallisation (DRX) and static recrystallisation (SRX) behaviours of three V–Ti microalloyed steels were studied by the analysis of the true stress–strain curves and the stress relaxation curves under different deformation conditions. The results of DRX showed that deformation activation energy Qdef, peak stress and peak strain increased, as a result of the solute strengthening and dragging effect due to Si. The results of SRX showed that Si increased the SRX activation energy QSRX. The solute retardation parameter for static recrystallisation of Si was calculated. Based on the SRX results, to quantify the drag effect of Si and V, a new model was proposed to describe the time for 50% recrystallisation (t0·5), which was tested and verified by previously published data on similar steels. Precipitation during recrystallisation could lead to a lower value of the Avrami exponent.

10109 微小せん断試験片を用いた鉛フリーはんだの引張・応力緩和試験

When we estimate the fatigue life of lead-free solder joints under cyclic temperature load, we have to get mechanical properties of them and conduct FE analysis using the FE technology which can exhibit these properties. We think stress strain curves and stress relaxation curves containing these temperature dependencies and these rate dependencies as examples of these mechanical properties of these solder joints under cyclic temperature load, hi addition, these solder joints under cyclic temperature load are stressed mainly in shear and the solder alloys have scale effect. Thus in this study, for FE analysis of solder joints under cyclic temperature load, we carried out tensile tests and the stress-relaxation tests of lead-free solder alloy using the micro-shear specimen.

Analysis of polymer viscoelastic properties based on compressive creep tests during hot embossing for two‐dimensional polyethylene terephthalate nanochannels

Hot embossing is an emerging technology, which enables cost‐effective and high‐productivity nanofabrication. It is important to optimize the processing parameters to achieve high replication accuracy nanostructure fabrication. In this article, to reveal the interrelationship between the hot embossing conditions and replication accuracy of two‐dimensional (2D) polyethylene terephthalate (PET) nanochannels, the numerical simulations were conducted by using the generalized Maxwell model. The constants of the generalized Maxwell model were calculated by a newly established fitting formula based on experimental compressive creep curves rather than tensile stress relaxation curves. Replication accuracy of 2D PET nanochannels was evaluated by a method based on weighted averages. Orthogonal method was employed during numerical simulations to optimize the hot embossing process. Under optimized hot embossing parameters, 2D PET nanochannels, ∼80 nm wide, 250 nm deep and 4 mm long, were precision‐imprinted into a PET sheet. POLYM. ENG. SCI., 54:2398–2406, 2014. © 2013 Society of Plastics Engineers

Comparison of viscoelasticity between normal human sciatic nerve and amniotic membrane.

Sciatic nerve tissue was obtained from the gluteus maximus muscle segment of normal human cadavers and amniotic membrane tissue was obtained from healthy human puerperant placentas. Both tissues were analyzed for their stress relaxation and creep properties to determine suitability for transplantation applications. Human amniotic membrane and sciatic nerve tissues had similar tendencies for stress relaxation and creep properties. The stress value of the amniotic membrane stress relaxation group decreased to a greater extent compared with the sciatic nerve stress relaxation group. Similarly, the stress value of the amniotic membrane creep group increased to a greater extent compared with the sciatic nerve creep group. The stress relaxation curve for human amniotic membrane and sciatic nerve showed a logarithm correlation, while the creep curve showed an exponential correlation. These data indicate that amniotic membrane tissue has better stress relaxation and creep properties compared with sciatic nerve tissue.

REM 모델에 의한 Poly(methyl acrylate)-Poly(acrylonitrile) 공중합체 완화스펙트럼의 pH 영향

Poly(methyl acrylate)-poly(acrylonitrile) 공중합체의 응력완화 실험은 용매기를 부착한 인장 시험기를 사용하여 여러 온도의 공기 중, 증류수, pH 3, 7, 11 용액에서 실행하였다. Ree-Eyring and Maxwell 모델로부터 얻은 완화스펙트럼 식에 실험적인 응력완화 곡선을 대입하여 poly(methyl acrylate)-poly(acrylonitrile) 공중합체의 완화스펙트럼을 얻었다. 완화스펙트럼의 계산은 Laplace 변환법을 사용한 컴퓨터 프로그램을 이용하였다. 이들 시료의 완화스펙트럼은 유동단위의 분자량과 자체확산 분포와 밀접한 관계가 있음을 알 수 있었다. The stress relaxation of poly(methyl acrylate)-poly(acrylonitrile) copolymer samples was carried out in air, distilled water, pH 3, 7 and 11 solutions at various temperatures using a tensile tester equipped with a solvent chamber. The relaxation spectra of poly(methyl acrylate)-poly(acrylonitrile) copolymers were obtained by applying the experimental stress relaxation curves to the equation of relaxation spectrum derived from the Ree-Eyring and Maxwell model. The determination of relaxation spectra was performed from computer calculation using a Laplace transform method. It was observed that the relaxation spectra of these samples are directly related to the distribution of molecular weights and self-diffusions of flow segments.

Computation and Comparison of Dynamic Viscosity Based on Quasi-Static and Dynamic FEM Analysis for AL7050-T7451

Coefficients of dynamic viscosity for AL7050-T7451 at room temperature is extracted by creep and stress relaxation simulations in Ansys. An analogy has been established for both creep and stress relaxation, with simple Maxwell Model. The stress relaxation curve thus obtained is then used to generate the Prony series coefficients which are then used to run some dynamic analysis in Ansys to see the effect of loading at different frequencies on the value of η (i.e dynamic viscosity). This will be verified with the simple analytical dynamic formulation based on the Maxwell Model. A good agreement has been found for both quasi-static and dynamic tests with Maxwell model.

Viscoelasticity and compaction behaviour of the foam-like pomelo (Citrus maxima) peel

The pomelo (Citrus maxima) is the largest and heaviest fruit of the genus Citrus and can acquire considerable potential energy as it ripens hanging up to 15 m height. Its thick foam-like structured peel presumably acts inter alia as a shock absorbing layer, protecting the fruit as it impacts on the ground upon being shed. Thereby the peel dissipates kinetic energy by being compacted. In order to elucidate the compaction mechanism of the highly heterogeneous pomelo peel, we conducted incremental stress relaxation tests. Two different models describing the stress relaxation curves, namely, the well-known Maxwell model and the Peleg model were compared and found to be suitable to describe the stress relaxation. As the Peleg model involves only two constants describing the relaxation curves it was the method of choice for interpreting the compaction of the peel samples. The inverse of k 1 reflects the initial decay rate of the relaxation process and k 2 is a measure of the samples’ solidity. The behaviour of these constants with increasing strain indicates the strong influence of the peel samples’ geometry and composition which is attributed to the fruit shape, a gradual changing density of the peel, which can be considered as a stacked array of foam layers differing in density, and the turgescence of the biological cells.

The Influence of the Specimen Shape and Loading Conditions on the Parameter Identification of a Viscoelastic Brain Model

The mechanical properties of brain under various loadings have been reported in the literature over the past 50 years. Step-and-hold tests have often been employed to characterize viscoelastic and nonlinear behavior of brain under high-rate shear deformation; however, the identification of brain material parameters is typically performed by neglecting the initial strain ramp and/or by assuming a uniform strain distribution in the brain samples. Using finite element (FE) simulations of shear tests, this study shows that these simplifications have a significant effect on the identified material properties in the case of cylindrical human brain specimens. Material models optimized using only the stress relaxation curve under predict the shear force during the strain ramp, mainly due to lower values of their instantaneous shear moduli. Similarly, material models optimized using an analytical approach, which assumes a uniform strain distribution, under predict peak shear forces in FE simulations. Reducing the specimen height showed to improve the model prediction, but no improvements were observed for cubic samples with heights similar to cylindrical samples. Models optimized using FE simulations show the closest response to the test data, so a FE-based optimization approach is recommended in future parameter identification studies of brain.

Dynamic stress relaxation of orthodontic thermoplastic materials in a simulated oral environment

Mechanical properties are crucial for screening orthodontic thermoplastic materials for invisible aligners. However, most of previous studies were carried out within laboratory conditions which limit our understanding of the mechanical behaviors of aligners within oral environment. In this study, we studied the dynamic stress relaxation of thermoplastic materials by combination of Bose ElectroForce and a homemade temperature-controlled water bath. The 3-h stress relaxation curves of five orthodontic thermoplastic materials were measured within 37°C water bath as well as comparatively in ambient atmospheric environment (~20°C). The percentage residual stress at 0, 30, 60, 90, 120, 150, and 180 min was selected for statistical analyses. As expected, the experimental results showed that the residual stress within all five materials decreased with time, and that this process was significantly accelerated in the 37°C water bath (p<0.05). Compared with other materials, Erkodur and Masel exhibited slower relaxing rates in the 37°C water bath (p<0.05).

Investigations on the viscoelastic behaviour of a human healthy heel pad: In vivo compression tests and numerical analysis

The aim of this study was to investigate the viscoelastic behaviour of the human heel pad by comparing the stress-relaxation curves obtained from a compression device used on an in vivo heel pad with those obtained from a three-dimensional computer-based subject-specific heel pad model subjected to external compression. The three-dimensional model was based on the anatomy revealed by magnetic resonance imaging of a 31-year-old healthy female. The calcaneal fat pad tissue was described with a viscohyperelastic model, while a fibre-reinforced hyperelastic model was formulated for the skin. All numerical analyses were performed to interpret the mechanical response of heel tissues, with loading conditions and displacement rate in agreement with experimental tests. The heel tissues showed a non-linear, viscoelastic behaviour described by characteristic hysteretic curves, stress-relaxation and viscous recovery phenomena. The reliability of the investigations was validated by the interpretation of the mechanical response of heel tissues under the application of three pistons with diameter of 15, 20 and 40 mm, at the same displacement rate of about 1.7 mm/s. The maximum and minimum relative errors were found to be less than 0.95 and 0.064, respectively.

A Mathematical Approach for Describing Time-Dependent Poisson’s Ratios of Periodontal Ligaments

Periodontal ligament is a thin layer of soft tissue that connects root of a tooth to the surrounding alveolar bone. These ligaments play an important role in initiating tooth movement when loads are applied to teeth with orthodontic appliances. The majority of such soft tissues exhibit as viscoelastic bodies or have a time-dependent behavior. Due to the viscoelastic behavior of the periodontal ligaments, the mechanical properties are strongly affected by the loading history. Poisson’s ratios for the viscoelastic materials are time-dependent (in time domain) or complex frequency-dependent (in frequency domain) quantities. Moreover, three-dimensional stress fields depend on these Poisson’s ratios. The main objective of this work was to develop a mathematical approach capable of determining the time-dependent Poisson’s ratios of the periodontal ligaments based on experimental data of stress relaxation and creep tests. The resulting stress relaxation and creep curves are described by a three-parameter viscoelastic models. The time-dependent Poisson’s ratios of the periodontal ligaments have been obtained as increasing functions of time, because shear modulus of these ligaments relaxes much more than their bulk modulus.