scholarly journals A New Viscoelasticity Dynamic Fitting Method Applied for Polymeric and Polymer-Based Composite Materials

Materials ◽  
2020 ◽  
Vol 13 (22) ◽  
pp. 5213
Author(s):  
Vitor Dacol ◽  
Elsa Caetano ◽  
João Correia
Keyword(s):  
Composite Materials ◽  
Dynamic Behaviour ◽  
Creep Compliance ◽  
Complex Modulus ◽  
Relaxation Modulus ◽  
Viscoelastic Behaviour ◽  
Harmonic Load ◽  
Load Case ◽  
Accurate Analysis ◽  
Complex Moduli

The accurate analysis of the behaviour of a polymeric composite structure, including the determination of its deformation over time and also the evaluation of its dynamic behaviour under service conditions, demands the characterisation of the viscoelastic properties of the constituent materials. Linear viscoelastic materials should be experimentally characterised under (i) constant static load and/or (ii) harmonic load. In the first load case, the viscoelastic behaviour is characterised through the creep compliance or the relaxation modulus. In the second load case, the viscoelastic behaviour is characterised by the complex modulus, E*, and the loss factor, η. In the present paper, a powerful and simple implementing technique is proposed for the processing and analysis of dynamic mechanical data. The idea is to obtain the dynamic moduli expressions from the Exponential-Power Law Method (EPL) of the creep compliance and the relaxation modulus functions, by applying the Carson and Laplace transform functions and their relationship to the Fourier transform, and the Theorem of Moivre. Reciprocally, once the complex moduli have been obtained from a dynamic test, it becomes advantageous to use mathematical interconversion techniques to obtain the time-domain function of the relaxation modulus, E(t), and the creep compliance, D(t). This paper demonstrates the advantages of the EPL method, namely its simplicity and straightforwardness in performing the desirable interconversion between quasi-static and dynamic behaviour of polymeric and polymer-composite materials. The EPL approximate interconversion scheme to convert the measured creep compliance to relaxation modulus is derived to obtain the complex moduli. Finally, the EPL Method is successfully assessed using experimental data from the literature.

A Theory Relating Creep and Relaxation for Linear Materials With Memory

2010 ◽  
Vol 77 (3) ◽  
Author(s):  
R. C. Koeller
Keyword(s):  
Experimental Data ◽  
Fractional Calculus ◽  
Creep Compliance ◽  
Complex Modulus ◽  
Relaxation Times ◽  
Relaxation Modulus ◽  
Experimental Methods ◽  
Generalized Function ◽  
Materials With Memory ◽  
With Memory

The purpose of this paper is to suggest a linear theory of materials with memory, which gives a description for the similarities resulting when the various analytical and experimental methods used to reduce the creep and relaxation data are imposed on the observational changes in curvature that take place in both the creep compliance and relaxation modulus graphs. On a Log-Log graph both have one, two, or at most three pairs of changes in curvature depending on whether the material is a fluid or solid. These changes in curvature have been observed in many experiments and various regions have been discussed and classified. Section 1 gives a few of the many applications of fractional calculus to physical problems. In Sec. 2 an equation that contains both integration and differentiation is presented using geometrical observations about the relationship between the changes in curvature in the relaxation modulus and creep compliance based on published experiments. In Sec. 3 the generalized function approach to fractional calculus is given. In Sec. 4 a mechanical model is discussed. This model is able to share experimental data between the creep and relaxation functions, as well as the real and imaginary parts of the complex compliance or the complex modulus. This theory shares information among these three experimental methods into a unifying theory for solid materials when the loads are within the linear range. Under a limiting case, this theory can account for flow so that the material need not return to its original shape after the load is removed. The theory contains one physical parameter, which is related to the speed of sound and a group of phenomenological parameters that are functions of temperature and the composition of the material. These phenomenological parameters are relaxation times and creep times. This theory differs from the classical polynomial constitutive equations for linear viscoelasticity. It is a special case of Rabotnov’s equations and Torvik and Bagley’s fractional calculus polynomial equations, but it imposes symmetry conditions on the stress and strain when the material is a solid. Sections 56 are comments and conclusions, respectively. No experimental results are given at this time since this paper presents the foundations of materials with memory as related to experimental data. The introduction of experimental data to fit this theory will result in the breakdown of an important part of this research.

Interconversion of Frequency Domain Complex Modulus to Time Domain Modulus and Compliance of Asphalt Concrete: Numerical Modeling and Laboratory Validation

2016 ◽  
Author(s):  
A. S. M. Asifur Rahman ◽  
Rafiqul A. Tarefder
Keyword(s):  
Viscoelastic Material ◽  
Asphalt Concrete ◽  
Creep Compliance ◽  
Complex Modulus ◽  
Relaxation Modulus ◽  
Modulus Function ◽  
Approximate Methods ◽  
Material Functions ◽  
Linear Viscoelastic Material ◽  
Linear Viscoelastic

Viscoelastic material functions such as time domain functions, such as, relaxation modulus and creep compliance, or frequency domain function, such as, complex modulus can be used to characterize the linear viscoelastic behavior of asphalt concrete in modeling and analysis of pavement structure. Among these, the complex modulus has been adopted in the recent pavement Mechanistic-Empirical (M-E) design software AASHTOWare-ME. However, for advanced analysis of pavement, such as, use of finite element method requires that the complex modulus function to be converted into relaxation modulus or creep compliance functions. There are a number of exact or approximate methods available in the literature to convert complex modulus function to relaxation modulus or creep compliance functions. All these methods (i.e. exact or approximate methods) are applicable for any linear viscoelastic material up to a certain level of accuracy. However, the applicability and accuracy of these interconversion methods for asphalt concrete material were not studied very much in the past and thus question arises if these methods are even applicable in case of asphalt concrete, and if so, what is the precision level of the interconversion method being used. Therefore, to investigate these facts, this study undertaken an effort to validate a numerical interconversion technique by conducting representative laboratory tests. Cylindrical specimens of asphalt concrete were prepared in the laboratory for conducting complex modulus, relaxation modulus, and creep compliance tests at different test temperatures and loading rates. The time-temperature superposition principle was applied to develop broadband linear viscoelastic material functions. A numerical interconversion technique was used to convert complex modulus function to relaxation modulus and creep compliance functions, and hence, the converted relaxation modulus and creep compliance are compared to the laboratory tested relaxation modulus and creep compliance functions. The comparison showed good agreement with the laboratory test data. Toward the end, a statistical evaluation was conducted to determine if the interconverted material functions are similar to the laboratory tested material functions.

Relationships Among Rate-Dependent Stiffnesses of Asphalt Concrete Using Laboratory and Field Test Methods

1998 ◽  
Vol 1630 (1) ◽  
pp. 3-9 ◽  
Author(s):  
Jo Sias Daniel ◽  
Y. Richard Kim
Keyword(s):  
Asphalt Concrete ◽  
Creep Compliance ◽  
Complex Modulus ◽  
Relaxation Modulus ◽  
Test Methods ◽  
Rate Dependent ◽  
Creep Stiffness ◽  
Linear Viscoelastic ◽  
Linear Viscoelastic Theory ◽  
Falling Weight

As the application of nondestructive testing on pavements in service becomes more frequent, it is increasingly important to relate the resulting stiffnesses to those from laboratory test methods. The relationship among stiffnesses measured from five test methods currently used for asphalt concrete is addressed: creep compliance, complex modulus, impact resonance, falling weight deflectometer, and surface wave. Established relationships from linear viscoelastic theory are used to relate stiffnesses, including a comparison of creep stiffness, S( t), and relaxation modulus, E( t), calculated from creep compliance, D( t). Using laboratory and field measured stiffnesses, a linear relationship was discovered between stiffness and frequency on a log-log scale.

On the Consistency of Complex Moduli for Transversely-Isotropic Viscoelastic Materials

1994 ◽  
Vol 28 (5) ◽  
pp. 382-391 ◽  
Author(s):  
George A. Lesieutre
Keyword(s):  
Composite Materials ◽  
Complex Modulus ◽  
Transversely Isotropic ◽  
Elastic Behavior ◽  
Complex Moduli ◽  
Isotropic Materials ◽  
Advanced Composite ◽  
Advanced Composite Materials ◽  
Transversely Isotropic Materials ◽  
Definition Of

The ability of advanced composite materials and structures to damp vibration is important in many applications. Use of the complex modulus approach to represent the dissipative properties of transversely-isotropic materials, such as unidirectional fiber-reinforced composites, requires the definition of a set of 5 (imaginary) loss moduli in addition to the 5 (real) storage moduli needed to describe the elastic behavior. In practice, designers of composite materials rarely have experimental data for all 5 loss moduli, and must assume values for the remaining moduli in their analyses. If values for these unknown loss moduli are specified arbitrarily, physically unreasonable behavior can result. This paper develops the conditions necessary for physical consistency of the complex moduli of transversely isotropic materials.

Effect of Cure State on Stress Relaxation in 3501-6 Epoxy Resin

1997 ◽  
Vol 119 (3) ◽  
pp. 262-265 ◽  
Author(s):  
S. R. White ◽  
A. B. Hartman
Keyword(s):  
Stress Relaxation ◽  
Epoxy Resin ◽  
Creep Compliance ◽  
Numerical Technique ◽  
Matrix Material ◽  
Relaxation Modulus ◽  
Master Curves ◽  
Creep Tests ◽  
Three Point Bending ◽  
Direct Inversion

Little experimental work has been done to characterize how the viscoelastic properties of composite material matrix resins develop during cure. In this paper, the results of a series of creep tests carried out on 3501–6 epoxy resin, a common epoxy matrix material for graphite/epoxy composites, at several different cure states is reported. Beam specimens were isothermally cured at increasing cure temperatures to obtain a range of degrees of cure from 0.66 to 0.99. These specimens were then tested in three-point bending to obtain creep compliance over a wide temperature range. The master curves and shift functions for each degree of cure case were obtained by time-temperature superposition. A numerical technique and direct inversion were used to calculate the stress relaxation modulus master curves from the creep compliance master curves. Direct inversion was shown to be adequate for fully cured specimens, however it underpredicts the relaxation modulus and the transition for partially cured specimens. Correlations with experimental stress relaxation data from Kim and White (1996) showed that reasonably accurate results can be obtained by creep testing followed by numerical conversion using the Hopkins-Hamming method.

EXPERIMENTAL RESEARCH ON VISCOELASTICITY PROPERTY OF DIFFERENT LAYERS PERIODONTAL LIGAMENT UNDER COMPRESSION

2021 ◽  
pp. 2150050
Author(s):  
JINLAI ZHOU ◽  
YANG SONG ◽  
CHENGUANG XU ◽  
CHUNQIU ZHANG ◽  
XUE SHI
Keyword(s):  
Elastic Modulus ◽  
Periodontal Ligament ◽  
Creep Compliance ◽  
Relaxation Modulus ◽  
Maxwell Model ◽  
Kelvin Model ◽  
Generalized Maxwell Model ◽  
Relaxation Stress ◽  
Generalized Kelvin Model ◽  
Fitting Accuracy

The periodontal ligament (PDL) exhibits different material mechanical properties along the long axis of the teeth. To explore the creep and the relaxation effects of dissimilar layers of PDL, this paper took the central incisors of porcine mandibular as experimental subjects and divided them perpendicular to the teeth axis into five layers. Creep experiments and relaxation experiments on five layers were conducted to obtain the creep compliance and relaxation modulus at different layers. Linear elastic model, generalized Kelvin model, and generalized Maxwell model were used to describe the major characteristics of the PDL: Instantaneous elasticity, creep and relaxation. Fitting accuracy of three-parameter, five-parameter, and seven-parameter of the model was compared, and the constitutive equations of different layers were established by the least square method. The results presented that the creep strain and the relaxation stress of PDL were exponentially correlated with time under different loading conditions. Different layers showed a significant effect on the creep strain and relaxation stress of PDL. Along the long axis of the teeth, the changing rule of the creep compliance and relaxation modulus of each layer showed quite the contrary, and the instantaneous elastic modulus first decreased to the minimum, then increased to the maximum. Higher instantaneous elastic modulus led to lower creep compliance and higher relaxation modulus. The generalized Kelvin model and the generalized Maxwell model well characterized the creep and relaxation properties of PDL. Fitting accuracy increased with the number of model parameters. The relaxation time of PDL was about one order of magnitude shorter than the creep retardation time, which indicated that the relaxation effect lasted shorter than the creep effect.

Obtaining shear relaxation modulus and creep compliance of linear viscoelastic materials from instrumented indentation using axisymmetric indenters of power-law profiles

2009 ◽  
Vol 24 (10) ◽  
pp. 3013-3017 ◽  
Author(s):  
Yang-Tse Cheng ◽  
Fuqian Yang
Keyword(s):  
Inverse Problem ◽  
Laplace Transform ◽  
Power Law ◽  
Creep Compliance ◽  
Relaxation Modulus ◽  
Instrumented Indentation ◽  
Loading Paths ◽  
Linear Viscoelastic ◽  
Shear Relaxation ◽  
Analytical Expressions

Using Laplace transform, we solve the inverse problem of obtaining the shear relaxation modulus and creep compliance of linear viscoelastic solids from indentation by axisymmetric indenters of power-law profiles. We identify several simple, though nontrivial, loading paths for carrying out indentation measurements such that the inverse problem has analytical solutions. We show that the shear relaxation modulus and creep compliance may be readily obtained using the newly derived analytical expressions together with proposed indentation loading paths.

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