A systematic methodology for creep master curve construction using the stepped isostress method (SSM): a numerical assessment

Long-term creep of viscoelastic materials is experimentally inferred through accelerating techniques based on the time–temperature superposition principle (TTSP) or on the time–stress superposition principle (TSSP). According to these principles, a given property measured for short times at a higher temperature or higher stress level remains the same as that obtained for longer times at a lower temperature or lower stress level, except that the curves are shifted parallel to the horizontal axis, matching a master curve. These procedures enable the construction of creep master curves with short-term experimental tests.The Stepped Isostress Method (SSM) is an evolution of the classical TSSP method. Higher reduction of the required number of test specimens to obtain the master curve is achieved by the SSM technique, since only one specimen is necessary. The classical approach, using creep tests, demands at least one specimen per each stress level to produce a set of creep curves upon which TSSP is applied to obtain the master curve.This work proposes an analytical method to process the SSM raw data. The method is validated using numerical simulations to reproduce the SSM tests based on two different viscoelastic models. One model represents the viscoelastic behavior of a graphite/epoxy laminate and the other represents an adhesive based on epoxy resin.     

Accelerated creep testing for aramid fibres using the stepped isothermal method

The article shows how the stepped isothermal method (SIM), which has hitherto been applied to polyester fibres, can be applied to the creep testing of aramids. The method is an improvement over the time temperature superposition method since a complete creep curve can be obtained from a single fibre. However, adjustments have to be made to account for the temperature changes and the past history of the fibre. Techniques are shown for performing these adjustments and the resulting master curves are compared from several different tests with different temperature sequences. Activation energies are calculated, which show that the same mechanism is acting at all stages, and creep rupture lifetime predictions are made which are longer than those hitherto made by extrapolations from short-term creep tests.     

Nonlinear creep behavior of viscoelastic polycarbonate

A study of the tension behavior of polycarbonate (PC) under room temperature and various sustained loads is presented. Time-dependent axial elongations and transverse contractions of the specimen were simultaneously measured at nine different stress levels, from 15.89 to 59.4 MPa, and modeled according to a time-stress superposition principle. The test duration was only one hour. It was shown that creep compliance vs. log time curves at different stresses can be horizontally shifted to form a smooth master curve for one year at a reference stress of 30.97 MPa. Moreover, the stress shift factors for axial extension creep curves and transverse contraction creep curves are found to be identical for the stress levels considered, and this is verified using the Poisson's ratio measurements.     

Prediction of long-term viscoelastic behavior of amorphous resin based on the time-temperature superposition principle

This paper deals with the prediction of long-term viscoelastic behavior of amorphous resin at a temperature below the glass transition temperature T _g from measuring the short-term viscoelastic behavior at elevated temperatures based on the time-temperature superposition principle (TTSP) with vertical shift as well as horizontal shift. The long-term creep compliance as well as short-term and medium-term creep compliances were measured at elevated temperatures. The master curves of creep compliance can be constructed from measured data by shifting vertically as well as horizontally. The master curves of creep compliance constructed from measured data by short-term and medium-term creep tests agree well with those measured by long-term creep tests. Furthermore, the horizontal and vertical shift factors obtained from constructing the master curve are independent of the time period of creep tests. Therefore, the long-term viscoelastic behavior at a temperature below T _g can be predicted accurately from measuring the short-term viscoelastic behavior at elevated temperatures based on the TTSP with vertical shift as well as horizontal shift.     

Fatigue behaviour of synthetic fibres,yarns, and ropes

S-N fatigue and creep-rupture data have been obtained for nylon 6,6 single fibres, interlaced yarns, and small ropes under a variety of loading conditions. The results show a similar degradation rate at each level of structure, with no apparent influence of inter-fibre effects. Cyclic lifetimes of single fibres of nylon 6,6 as well as polyester and aramid can be predicted from a creep rupture model. Consistent with this model, the time to failure is insensitive to frequency over a broad range. For each level of structure the strain at failure is the same whether tested in simple tension or under cyclic or creep loading. Failure modes were generally similar in creep rupture and cyclic fatigue tests; no effect of a slack load on each cycle was evident either in the failure mode or specimen lifetime.     

Z-parameter Method for Damage Evaluation in HK40 Steel

A Z-parameter method is used to evaluate the damage process of HK40 austenitic steel. By using Z-parameter based on the Larson-Miller method, the nonlinear master curve of the log stress vs Larson-Miller parameter P can be expressed as： P=27.74-3.41gσ-0.032σ, and a family of curves parallel to the master curve can be written as： P=（27.74-Z）-3.41gσ-0.032σ, where Z represents the magnitude of the deviation from the master curve. According to the creep rupture data both from different segments of a serviced tube and from the same segment locations with different service time, the value of parameter Z has close relationship with the deterioration of creep rupture properties. The damage state of the samples is evaluated by monitoring the changes in natural frequency f and Young＇s modulus E, and the relationships between Z and the damage parameters are discussed.     

Visco-elasticity of aramid fibres

Tests are described to measure the creep and relaxation response of aramid fibres with the specific aim of determining whether the visco-elastic response is linear or non-linear. Hitherto, creep and relaxation tests have been carried out in different circumstances and at different loads, which has led to disagreement about the type of response that aramid fibres exhibit. Tests are carried out at stresses between 10% and 80% of the short-term strength of the fibres under controlled temperature and humidity conditions, and it is shown that both creep and relaxation are non-linear at stresses below 40% of the breaking load, but both are linear at stresses above this level. This result explains the contradictions in earlier work and also indicates that there may be two different processes underway in the visco-elasticity of aramids.     

Continuous relaxation and retardation spectrum method for viscoelastic characterization of asphalt concrete

This paper presents a simple and practical approach to obtain the continuous relaxation and retardation spectra of asphalt concrete directly from the complex (dynamic) modulus test data. The spectra thus obtained are continuous functions of relaxation and retardation time. The major advantage of this method is that the continuous form is directly obtained from the master curves which are readily available from the standard characterization tests of linearly viscoelastic behavior of asphalt concrete. The continuous spectrum method offers efficient alternative to the numerical computation of discrete spectra and can be easily used for modeling viscoelastic behavior. In this research, asphalt concrete specimens have been tested for linearly viscoelastic characterization. The linearly viscoelastic test data have been used to develop storage modulus and storage compliance master curves. The continuous spectra are obtained from the fitted sigmoid function of the master curves via the inverse integral transform. The continuous spectra are shown to be the limiting case of the discrete distributions. The continuous spectra and the time-domain viscoelastic functions (relaxation modulus and creep compliance) computed from the spectra matched very well with the approximate solutions. It is observed that the shape of the spectra is dependent on the master curve parameters. The continuous spectra thus obtained can easily be implemented in material mix design process. Prony-series coefficients can be easily obtained from the continuous spectra and used in numerical analysis such as finite element analysis.     

Temperature effects on creep behavior of continuous fiber GMT composites

The effects of temperature on the tensile creep of continuous random fiber glass mat thermoplastic composite (GMT) have been studied following an accelerated characterization procedure. The objectives of this work are twofold. First, is to obtain a long-term creep model using time–temperature superposition (TTS) that can represent behavior within the linear viscoelastic regime (up to 20 MPa) at room temperature. The second is to develop a non-linear viscoelastic model that accounts for a wide range of stresses and temperatures. Creep and recovery tests were carried out for a stress range between 20 and 60 MPa over a temperature range of room temperature to 90 °C. TTS was applied to obtain a master curve which was curve fitted to a nine-term Prony series. It was found that material generally behaved non-linearly for all stresses and temperature. For stresses up to 50 MPa, the non-linear viscoelastic behavior due to temperature can be reasonably modeled by only the time–temperature shift factors from TTS. At 60 MPa, however, the non-linear parameters have to be modeled as a product of stress and temperature dependent functions. The model predictions are in good agreement with the experimental results at most stress and temperature levels. The creep curves predicted at higher temperatures especially at 60 MPa tend to underestimate at longer times.     

An experimental investigation of the stress-rupture behaviour of a parallel-lay aramid rope

The results from a series of short-term stress-rupture tests on a parallel-lay aramid rope are presented. General trends of behaviour are established from lifetime and strain data; the results provide a firm basis around which methods of predicting long-term stress-rupture response may be developed.     

The master curve and the constitutive equation for creep deformation and fracture for Cr-Mo-V steel throughout smooth,notched and precracked specimens

It has been shown experimentally that the master curve for creep deformation versus the ratio of time to fracture time, can be obtained for smooth, notched and precracked specimens of Cr-Mo-V steel, a high-temperature ductile material. A simple unified constitutive equation, i.e. a master curve equation, has been proposed. It is suggested that there is some correlation between the creep deformation fracture curve and the creep damage size master curve. Although the range of the applicability of methodology might be rather limited, the development of this concept is needed for improved long-term creep lives and for other creep ductile materials.     

湿度对玻璃微珠增强硬质聚氨酯复合泡沫塑料黏弹力学性能影响

实验研究了温度与湿度因素对玻璃微珠增强硬质聚氨酯复合泡沫塑料(玻璃微珠/RPUF)黏弹力学性能的影响。结果表明, 湿度对黏弹力学性能有显著的影响, 随着湿度的增加, 玻璃微珠/RPUF的储能模量减小, 刚度下降, 力学损耗因子值增加, 蠕变柔量增大, 柔韧性增强。湿度对玻璃微珠/RPUF弯曲蠕变性能的影响具有类似于时间-温度等效原理的等效关系, 并给出了60 ℃/50%RH参考温湿度下玻璃微珠/RPUF的蠕变主曲线和平移因子。     

Study of the Effect of Aging Progression on Creep Behavior of PPE Composites

In this study, creep behavior of stainless fiber-PPE composites was analyzed in an oil environment at elevated temperatures, and the effects of physical aging on creep behavior were intensively investigated. The results showed that the creep phenomena of metal fiber-PPE composite with pre-aging treatment correlated with the Arrhenius time-temperature reciprocation law and within the aging range; time-aging time superposition also held good. Thus, prediction of short-term creep behavior for any pre-aging time was possible, based on the grand master curve of the creep compliance master curves and the shift factor for aging progression. It was clarified that a pre-aged composite can withstand higher temperatures and longer times. It was also observed that the energy of activation during creep decreased with an increase in pre-aging treatment time. This revised version was published online in August 2006 with corrections to the Cover Date.     

沥青混合料黏弹性主曲线模拟及换算

基于时间-温度等效原理将不同温度下沥青混合料的储存模量和蠕变柔量进行平移形成主曲线,采用广义Maxwell和Kelvin模型分别模拟沥青混合料的松弛和蠕变特性,利用Prony级数表达式和Laplace变换实现黏弹性主曲线间的相互换算,并将换算结果与试验结果进行了比较。结果表明,广义Maxwell和Kelvin模型可以较好地模拟沥青混合料黏弹性主曲线,储存模量和蠕变柔量主曲线相互换算结果与试验结果规律基本一致,松弛模量实际结果应介于由储存模量和蠕变柔量换算的松弛模量主曲线之间,这可为沥青混合料黏弹性力学研究及黏弹性参数的获取提供有益参考。     

Long-term creep-rupture failure envelope of epoxy

An accelerated testing methodology based on the time-temperature superposition principle has been proposed in the literature for the long-term creep strength of polymer matrices and polymer composites. Also, it has been suggested that a standard master curve may be a feasible assumption to describe the creep behavior in both tension and compression modes. In the present research, strength master curves for an aerospace epoxy (8552) were generated for tension and compression, by shifting strength data measured at various temperatures. The shift function is obtained from superposition of creep-compliance curves obtained at different temperatures. A standard master curve was presented to describe the creep-rupture of the polymer under tension and compression. Moreover, long-term creep-rupture failure envelopes of the polymer were presented based on a two-part failure criterion for homogeneous and isotropic materials. Ultimately, the approach presented allows the prediction of creep-rupture failure envelopes for a time-dependent material based on tensile strengths measured at various temperatures, considering that the ratio between tensile and compressive strengths is known.     

Deformation micromechanics in high-modulus fibres and composites

It is demonstrated that Raman spectroscopy can be used to study the deformation micromechanics of aramid fibres and of the fibres in a model single-fibre composite with an epoxy resin matrix. It is shown that the peak position of the 1610cm⁻¹ aramid Raman band shifts to lower frequency under the action of stress or strain as a result of the macroscopic deformation leading to direct stretching of the aramid molecules. The strain-induced band shifts can be used to follow the deformation of the aramid fibres in a composite matrix. This allows the distribution of strain to be mapped along a fibre, and it is shown that the behaviour is consistent with that predicted by the classical shear-lag analysis. It is also demonstrated that the interfacial shear stress can be calculated from the distribution of strain along the fibre. Finally, the technique is extended to measure the strain in fibres in a single-fibre composite which are aligned at an angle to the tensile axis. In this case it is shown that the strain in the centre of the fibres is identical to that predicted by classical elasticity theory.     

Application of Nonlinear Superposition to Creep and Relaxation of Commercial Die-Casting Aluminum Alloys

Die-cast aluminum alloys are heavily used in small engines, where they are subjected to long-term stresses at elevated temperatures. The resulting time-dependent material responses can result in inefficient engine operation and failure. A method to analytically determine the stress relaxation response directly from creep tests and to accurately interpolate between experimental time-history curves would be of great value. Constant strain, stress relaxation tests and constant load, creep tests were conducted on aluminum die-casting alloys: B-390, eutectic Al–Si and a 17% Si–Al alloy. A nonlinear superposition integral was used to (i) interpolate between empirical primary inelastic creep-strain and stress-relaxation time histories and (ii) to determine the stress relaxation response from corresponding creep data. Using isochronal stress-strain curves, prediction of the creep response at an intermediate stress level from empirical creep curves at higher and lower stresses resulted in a correlation (R) of 0.98. Similarly for relaxation, correlations of 0.98 were obtained for the prediction of an intermediate strain level curve from higher and lower empirical relaxation curves. The theoretical prediction of stress relaxation from empirical creep curves fell within 10% of experimental data.This paper has not been submitted elsewhere in identical or similar form, nor will it be during the first three months after its submission to Mechanics of Time-Dependent Materials     

Unification of the most commonly used time-temperature creep parameters

The determination of the time to rupture at low stresses and temperatures despite existing methods still remains a challenge. A new unifying time-temperature parameter is proposed. It represents a modification of the efficient, but numerically unstable Manson-Brown parameter. It incorporates the most commonly used time-temperature parameters such as Larson-Miller, Manson-Haferd and Orr-Sherby-Dorn as special cases for the calculation of the master curves. The procedure chooses the most appropriate master curve for the test data and calculates the corresponding coefficients. The inputs for the determination of the master curves are minimised to the least possible amount of test data. The proposed time-temperature parameter is included in a fast creep damage calculation procedure which is a part of a method for evaluating the total damage of the thermomechanically loaded components.     

Modelling the Non-Linear Viscoelastic and Viscoplastic Behaviour of Aramid Fibre Yarns

A non-linear viscoelastic viscoplastic model is proposed for the tensilebehaviour of aramid fibres, based on an analysis of the deformationmechanisms of these materials. This model uses the macroscopicformulation developed by Schapery together with the plasticity conceptof Perzyna. A simple identification procedure for the model parametershas been developed using creep/recovery cycles at different load levels.The identification reveals that two of the four parameters of theviscoelastic model (g ₁ and a _σ) are independent of stresslevel. This may be due to the simple and regular nature of the fibrestructure. The model enables the parameters which characterise thenon-linear reversible viscoelasticity to be identified independentlyfrom those which characterise the viscoplasticity. The model predictionsare compared to experimental data for a more complex load sequence andreasonable correlation is obtained.     

预压对瓦楞纸板蠕变特性的影响

目的通过一系列的实验,研究预压对瓦楞纸板蠕变特性的影响,从而得到瓦楞纸板的蠕变曲线。方法通过对瓦楞纸板进行3种恒定载荷、4种不同预压处理条件下的蠕变特性研究实验,得出其蠕变曲线,并分别进行比较,分析预压对瓦楞纸板蠕变特性的影响。结果预压对瓦楞纸板的蠕变都有显著的影响,在不同的预压下,A瓦楞纸板和BC型双瓦楞纸板的蠕变量都是有所不同的。结论瓦楞纸板的蠕变会随着预压的增加而增大。