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.

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.

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.

The Creep of Natural and Snythetic Rubber Compounds in Shear

1941 ◽  
Vol 14 (2) ◽  
pp. 433-443 ◽  
Author(s):  
Stuart H. Hahn ◽  
Ivan Gazdik
Keyword(s):  
Processing Technique ◽  
Creep Tests ◽  
Time Service ◽  
Wide Range ◽  
Recent Developments ◽  
Long Time ◽  
The Many ◽  
Short Time ◽  
Relative Creep ◽  
Rubberlike Materials

Abstract Creep tests, extending in some cases as long as 900 days, indicate that both natural and synthetic rubbers such as Neoprene and butadiene copolymer can be compounded to give satisfactory service in shear mountings. At 140° F, creep is from two to nine times greater than at 80° F, depending on the compound. Tests at room temperature do not indicate either the amount of creep or the life to be expected at higher temperatures. Actual creep (measured in inches) increases with stress, but when expressed at percentage of initial deflection, it may be independent of stress. Creep curves are linear over a considerable range of time when plotted on log-log scales. However, extrapolation of such curves to predict results after very long times is not justified, because the curves may not continue to be linear, or failure of the mountings may occur, particularly at high temperatures. Short time tests of any sort are not necessarily indicative of the relative creep or life of compounds in long-time service. The tests reported here are a small portion of a large number which is being continued and augmented. It is hoped that these and other investigations now under way may contribute to clearing the picture of the complex interrelations between the many physical properties of compounds of rubberlike materials. The rubber technologist uses his specialized knowledge to develop a wide variety of compounds, making use of several types of basic rubberlike materials. He chooses whichever fits service requirements best from performance and economic viewpoints. Modern materials and recent developments in processing technique have made possible compounds suitable for a wide range of service conditions.

A viscoelastic Timoshenko shaft finite element for dynamic analysis of rotors

2016 ◽  
Vol 24 (11) ◽  
pp. 2180-2200 ◽  
Author(s):  
Smitadhi Ganguly ◽  
A Nandi ◽  
S Neogy
Keyword(s):  
Finite Element ◽  
Elastic Strain ◽  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Viscoelastic Behavior ◽  
Beam Shape ◽  
Unit Step ◽  
Linear Viscoelastic Behavior ◽  
Linear Viscoelastic ◽  
The Time Domain

A new shaft element is proposed for viscoelastic rotors in a spinning frame considering the shear deformation in addition to bending deformation. The Maxwell–Wiechert model is considered here to replicate linear viscoelastic behavior. This model considers additional internal damping displacement variables between elastic and viscous elements and the stress depends not only on the elastic strain and elastic strain rate, but also on additional strains and their rates corresponding to the damping variables. The present work assumes that these additional strains can be derived from continuous fictitious displacement variables, which in turn are interpolated from their nodal values using the Timoshenko beam shape functions. Therefore, in addition to the standard degrees of freedom for a three-dimensional shaft, extra degrees of freedom are defined at the nodes. The finite element matrices are assembled in state space. The time domain equations are then used for stability analysis and computation of response to a unit step load and an unbalance.

scholarly journals Keratins determine network stress responsiveness in reconstituted actin-keratin filament systems

2020 ◽  
Author(s):  
Iman Elbalasy ◽  
Paul Mollenkopf ◽  
Cary Tutmarc ◽  
Harald Herrmann ◽  
Jörg Schnauß
Keyword(s):  
Mechanical Response ◽  
Epithelial Mesenchymal Transition ◽  
Viscoelastic Behavior ◽  
Mesenchymal Transition ◽  
Linear Viscoelastic Behavior ◽  
Linear Viscoelastic ◽  
Network Partner ◽  
Keratin Filament ◽  
The Stability

The cytoskeleton is a major determinant of cell mechanics, a property that is altered during many pathological situations. To understand these alterations, it is essential to investigate the interplay between the main filament systems of the cytoskeleton in the form of composite networks. Here, we investigate the role of keratin intermediate filaments (IFs) in network strength by studying in vitro reconstituted actin and keratin 8/18 composite networks via bulk shear rheology. We co-polymerized these structural proteins in varying ratios and recorded how their relative content affects the overall mechanical response of the various composites. For relatively small deformations, we found that all composites exhibited an intermediate linear viscoelastic behavior compared to that of the pure networks. In stark contrast, the composites displayed increasing strain stiffening behavior as a result of increased keratin content when larger deformations were imposed. This strain stiffening behavior is fundamentally different from behavior encountered with vimentin IF as a composite network partner for actin. Our results provide new insights into the mechanical interplay between actin and keratin in which keratin provides reinforcement to actin. This interplay may contribute to the overall integrity of cells, providing an explanation for the stability of stressed epithelial tissues due to their high keratin contents. Additionally, this helps us to understand the physiological necessity to exchange IF systems during epithelial-mesenchymal transition (EMT) in order to suppress strain stiffening of the network, making cells more elastic and, thus, facilitating their migration through dense tissues.

Linear Viscoelastic Behavior of Bentonite-Water Suspensions

2002 ◽  
Vol 12 (5) ◽  
pp. 234-240 ◽  
Author(s):  
Karim Bekkour ◽  
Nadia Kherfellah
Keyword(s):  
Low Frequency ◽  
Viscoelastic Behavior ◽  
Colloidal Dispersions ◽  
Frequency Scale ◽  
Water Suspensions ◽  
Wide Range ◽  
Linear Viscoelastic Behavior ◽  
Linear Viscoelastic ◽  
Exhaustive Study ◽  
Using Data

Abstract Bentonite are extensively used materials in a wide range of applications. Creep and oscillatory shear experiments in the linear viscoelastic domain were carried out on bentonite-water suspensions at different solid fractions. It was found that bentonite dispersions exhibit important viscoelastic behavior which could be represented by the generalized Kelvin-Voigt mechanical model. It is well known that an exhaustive study of colloidal dispersions may require the determination of its viscoelastic properties over a wide frequency scale. Unfortunately, due to microstructure changes, the experiments are limited in time. In order to avoid such limitation, oscillatory data were deduced from creep curves - without actually vibrating the clay dispersions - because a periodic experiment at frequency ω is qualitatively equivalent to a creep test at time 1/ω. That is, it was possible to complete the dynamic response in the low-frequency range using data obtained from the transient response in creep.

scholarly journals On the frequency dependence of viscoelastic material characterization with intermittent-contact dynamic atomic force microscopy: avoiding mischaracterization across large frequency ranges

2020 ◽  
Vol 11 ◽  
pp. 1409-1418
Author(s):  
Enrique A López-Guerra ◽  
Santiago D Solares
Keyword(s):  
Atomic Force Microscopy ◽  
Mechanical Response ◽  
Viscoelastic Behavior ◽  
Partial Solution ◽  
Electromagnetic Properties ◽  
Multiple Characteristic ◽  
Force Microscopy ◽  
Atomic Force ◽  
Linear Viscoelastic ◽  
Intermittent Contact

Atomic force microscopy (AFM) is a widely use technique to acquire topographical, mechanical, or electromagnetic properties of surfaces, as well as to induce surface modifications at the micrometer and nanometer scale. Viscoelastic materials, examples of which include many polymers and biological materials, are an important class of systems, the mechanical response of which depends on the rate of application of the stresses imparted by the AFM tip. The mechanical response of these materials thus depends strongly on the frequency at which the characterization is performed, so much so that important aspects of behavior may be missed if one chooses an arbitrary characterization frequency regardless of the materials properties. In this paper we present a linear viscoelastic analysis of intermittent-contact, nearly resonant dynamic AFM characterization of such materials, considering the possibility of multiple characteristic times. We describe some of the intricacies observed in their mechanical response and alert the reader about situations where mischaracterization may occur as a result of probing the material at frequency ranges or with probes that preclude observation of its viscoelastic behavior. While we do not offer a solution to the formidable problem of inverting the frequency-dependent viscoelastic behavior of a material from dynamic AFM observables, we suggest that a partial solution is offered by recently developed quasi-static force–distance characterization techniques, which incorporate viscoelastic models with multiple characteristic times and can help inform dynamic AFM characterization.

Characterization of Viscoelastic Behavior of Stereoregular Poly(Isoprenes) by Relaxation Experiments

1974 ◽  
Vol 47 (1) ◽  
pp. 1-18
Author(s):  
L. Szilagyi ◽  
T. Riccò ◽  
F. Danusso
Keyword(s):  
Viscoelastic Behavior ◽  
Supermolecular Structure ◽  
Relaxation Modulus ◽  
Mechanical Relaxation ◽  
Recent Theory ◽  
Mean Values ◽  
Linear Viscoelastic ◽  
Viscoelastic Theory ◽  
Linear Viscoelastic Theory ◽  
Relationship Of

Abstract The mechanical relaxation of twelve samples of unvulcanized cis poly-(isoprene)s, including both natural and synthetic polymers, was studied over a range of temperatures. Master curves of relaxation modulus obtained from these data were used to derive relaxation spectra according to linear viscoelastic theory. A recent theory was used to calculate mean values of quantities related to the supermolecular structure which occurs spontaneously in these materials and is responsible for their viscoelastic properties. This structure is schematized in a model consisting of a system of macromolecules which interact with each other by elastic forces and frictions corresponding to points of entanglement between chains. The analysis leads to the determination, for each sample, of the number of entanglements per molecule, the physical network density, the value of relaxation parameters, and the relationship of each of these quantities to molecular weight.

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