Indentation Creep and Relaxation Measurements of Polymers

2004 ◽  
Vol 841 ◽  
Author(s):  
Mark R. VanLandingham ◽  
Peter L. Drzal ◽  
Christopher C. White
Keyword(s):  
Stress Relaxation ◽  
Mechanical Response ◽  
Creep Compliance ◽  
Relaxation Modulus ◽  
Polymeric Materials ◽  
Indentation Creep ◽  
Dimethyl Siloxane ◽  
Linear Viscoelastic Material ◽  
Linear Viscoelastic ◽  
Creep And Stress Relaxation

ABSTRACTInstrumented indentation was used to characterize the mechanical response of polymeric materials. A model based on contact between a rigid probe and a linear viscoelastic material was used to calculate values for creep compliance and stress relaxation modulus for epoxy, poly(methyl methacrylate) (PMMA), and two poly(dimethyl siloxane) (PDMS) elastomers. Results from bulk rheometry studies were used for comparison to the indentation creep and stress relaxation results. For the two glassy polymers, the use of sharp pyramidal tips produced responses that were considerably more compliant (less stiff) than rheometry values. Additional study of the deformation remaining in epoxy after creep testing revealed that a large portion of the creep displacement measured was due to post-yield flow. Indentation creep measurements of the epoxy using a rounded conical tip also produced nonlinear responses, but the creep compliance values appeared to approach linear viscoelastic values with decreasing creep force. Responses measured for the PDMS were mainly linear elastic, but the filled PDMS exhibited some time-dependence and nonlinearity in both rheometry and indentation measurements.

Solution of Viscoelastic Stress Analysis Problems Using Measured Creep or Relaxation Functions

1963 ◽  
Vol 30 (1) ◽  
pp. 127-133 ◽  
Author(s):  
E. H. Lee ◽  
T. G. Rogers
Keyword(s):  
Stress Analysis ◽  
Integral Equations ◽  
Creep Compliance ◽  
Relaxation Modulus ◽  
Material Behavior ◽  
Relaxation Functions ◽  
Analysis Theory ◽  
Linear Viscoelastic Material ◽  
Linear Viscoelastic ◽  
Improved Technique

Stress analysis problems for linear viscoelastic material behavior are solved on the basis of integral operator stress-strain relations. These characterize the material by relaxation modulus functions or creep compliances which are directly measurable over finite time ranges, and completely describe material behavior for stress determinations for the same duration. The stress analysis theory can lead to integral equations which are shown to be soluble with high accuracy by simple finite-difference numerical integration procedures. Examples are presented and compared with solutions obtained by other methods. A possible improved technique for relaxation modulus and creep compliance measurements is suggested, based on the method presented for numerical solution of the integral equations.

scholarly journals A Combined Exponential-Power-Law Method for Interconversion between Viscoelastic Functions of Polymers and Polymer-Based Materials

Polymers ◽  
2020 ◽  
Vol 12 (12) ◽  
pp. 3001
Author(s):  
Vitor Dacol ◽  
Elsa Caetano ◽  
João R. Correia
Keyword(s):  
Mechanical Response ◽  
Creep Compliance ◽  
Viscoelastic Behavior ◽  
Relaxation Modulus ◽  
Creep Tests ◽  
General Applicability ◽  
Wide Range ◽  
Long Time ◽  
Linear Viscoelastic ◽  
The Time Domain

Understanding and modeling the viscoelastic behavior of polymers and polymer-based materials for a wide range of quasistatic and high strain rates is of great interest for applications in which they are subjected to mechanical loads over a long time of operation, such as the self-weight or other static loads. The creep compliance and relaxation functions used in the characterization of the mechanical response of linear viscoelastic solids are traditionally determined by conducting two separate experiments—creep tests and relaxation tests. This paper first reviews the steps involved in conducting the interconversion between creep compliance and relaxation modulus in the time domain, illustrating that the relaxation modulus can be obtained from the creep compliance. This enables the determination of the relaxation modulus from the results of creep tests, which can be easily performed in pneumatic equipment or simple compression devices and are less costly than direct relaxation tests. Some existing methods of interconversion between the creep compliance and the relaxation modulus for linear viscoelastic materials are also presented. Then, a new approximate interconversion scheme is introduced using a convenient Laplace transform and an approximated Gamma function to convert the measured creep compliance to the relaxation modulus. To demonstrate the accuracy of the fittings obtained with the method proposed, as well as its ease of implementation and general applicability, different experimental data from the literature are used.

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.

STRESS RELAXATION OF MAGNETORHEOLOGICAL FLUIDS

2002 ◽  
Vol 16 (17n18) ◽  
pp. 2655-2661
Author(s):  
W. H. LI ◽  
G. CHEN ◽  
S. H. YEO ◽  
H. DU
Keyword(s):  
Stress Relaxation ◽  
Viscoelastic Model ◽  
Relaxation Modulus ◽  
Damping Function ◽  
Mr Fluids ◽  
Large Step ◽  
Linear Viscoelastic ◽  
Predicted Values ◽  
Two Parameters ◽  
Step Strain

In this paper, the experimental and modeling study and analysis of the stress relaxation characteristics of magnetorheological (MR) fluids under step shear are presented. The experiments are carried out using a rheometer with parallel-plate geometry. The applied strain varies from 0.01% to 100%, covering both the pre-yield and post-yield regimes. The effects of step strain, field strength, and temperature on the stress modulus are addressed. For small step strain ranges, the stress relaxation modulus G(t,γ) is independent of step strain, where MR fluids behave as linear viscoelastic solids. For large step strain ranges, the stress relaxation modulus decreases gradually with increasing step strain. Morever, the stress relaxation modulus G(t,γ) was found to obey time-strain factorability. That is, G(t,γ) can be represented as the product of a linear stress relaxation G(t) and a strain-dependent damping function h(γ). The linear stress relaxation modulus is represented as a three-parameter solid viscoelastic model, and the damping function h(γ) has a sigmoidal form with two parameters. The comparison between the experimental results and the model-predicted values indicates that this model can accurately describe the relaxation behavior of MR fluids under step strains.

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.

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.

Spherical Indentation Creep Following Ramp Loading

2004 ◽  
Vol 841 ◽  
Author(s):  
Michelle L. Oyen
Keyword(s):  
Contact Stiffness ◽  
Peak Load ◽  
Polymeric Materials ◽  
Spherical Indenter ◽  
Material Behavior ◽  
Spherical Indentation ◽  
Indentation Creep ◽  
Indentation Testing ◽  
Depth Sensing ◽  
Linear Viscoelastic Material

ABSTRACTDepth-sensing indentation testing is a common way to characterize the mechanical behavior of stiff, time-independent materials but presents both experimental and analytical challenges for compliant, time-dependent materials. Many of these experimental challenges can be overcome by using a spherical indenter tip with a radius substantially larger than the indentation depth, thus restricting deformation to viscoelastic (and not plastic) modes in glassy polymers and permitting large loads and contact stiffness to be generated in compliant elastomers. Elastic-viscoelastic correspondence was used to generate spherical indenter solutions for a number of indentation testing protocols including creep following loading at a constant rate and a multiple ramp-and-hold protocol to measure creep response at several loads (and depths) within the same test. The ramp-creep solution was recast as a modification to a step-load creep solution with a finite loading rate correction factor that is a dimensionless function of the ratio of experimental ramp time to the material time constant. Creep tests were performed with different loading rates and different peak load levels on glassy and rubbery polymeric materials. Experimental data are fit to the spherical indentation solutions to obtain elastic modulus and time-constants, and good agreement is found between the results and known modulus values. Emphasis is given to the use of multiple experiments (or multiple levels within a single experiment) to test the a priori assumption of linear viscoelastic material behavior used in the modeling.

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