Characterization of Isotropic Viscoelastic Moduli and Compliances from 1-D Tension Experiments

Michaeli, Michael; Shtark, Abraham; Grosbein, Hagay; Hilton, Harry H.

doi:10.2514/6.2012-1547

Cited by 5 publications

(3 citation statements)

References 18 publications

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“…Attempts at determining the time time 1 t when steady-state loadings are reached based on examination of strains as seen in Figure 9 have been disappointing and misleading [103]. This protocol produced physically indefensible results with erroneous trends [104].…”

Section: Discussionmentioning

confidence: 99%

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Elastic and Viscoelastic Poisson’s Ratios: The Theoretical Mechanics Perspective

Hilton¹

2017

MSA

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A recent review publication presented an extensive and comprehensive assessment of the phenomenological relations of Poisson's ratios (PRs) to the behavior and responses of contemporary materials under specific loading conditions. The present review and analysis paper is intended as a theoretical mechanics complement covering mathematical and physical modeling of a single original elastic and of six time and process (i.e. path and stress) dependent viscoelastic PR definitions as well as a seventh special path independent one. The implications and consequences of such models on material characterization are analyzed and summarized. Indeed, PRs based on experimentally obtained 2-D strains under distinct creep and/or relaxation processes exhibit radically different time responses for identical material specimen. These results confirm the PR's implicit path dependence in addition to their separate intrinsic time reliance. Such non-uniqueness of viscoelastic PRs renders them unsuitable as universal material descriptors. Analytical formulations and experimental measurements also examine the physical impossibility of instantaneously achieving time independent loads or strains or their rates thus making certain PR definitions based on constant state variables, while mathematically valid, physically unrealistic and unachievable. A newly developed theoretical/experimental protocol for the determination of the time when loading patterns reach stead-state conditions based on strain accelerations demonstrates the capability to measure this time from experimental data. Due to the process dependent PRs, i.e. stress and stress history paths, the non-existence of a unique viscoelastic PR and of a universal elastic-viscoelastic correspondence principle or analogy (EVCP) in terms of PRs is demonstrated. Additionally and independently, the required double convolution integral construction of linear viscoelastic constitutive relations with the inclusion of PRs is cumbersome analytically and computationally needlessly highly CPU intensive. Furthermore, there is no theoretical fundamental hint as to what loading path is required to produce a unique universal viscoelastic PR definition necessary for formulating a PR based constitutive relation or an EVCP protocol. The analysis associated with an additional Class VII viscoelastic PR establishes it as a universal representation which is loading path and strain independent while still remaining time dependent. This Class PR can be the one used if it is desired to express constitutive relations in terms of PRs, subject to the caveat applying to all PR Classes regarding the CPU intensiveness in the time space due to triple product and double convolution integral constitutive relations. However, the use PRs is unnecessary since any set of material behavior can be uniquely and completely defined in terms of only moduli and/or compliances. The mathematical model of instantaneous initial loading paths, based on Heaviside functions, is examined in detail and shown to lead to infinite vel...

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Section: Discussionmentioning

confidence: 99%

“…In addition, testing machine crossheads have inertia and require finite times to develop displacements and loads as demonstrated in [103]. In Section 4 data is displayed for experimental loading cycle results of high polymer tension cou- …”

Section: ( )mentioning

confidence: 99%

Elastic and Viscoelastic Poisson’s Ratios: The Theoretical Mechanics Perspective

Hilton¹

2017

MSA

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“…The experimental values of σ 11 and 11 , 22 were measured by a tensile machine load-cell and a photogrammetric system respectively [100], which were synchronized. Thus, Eqs.…”

Section: Analytical Considerationsmentioning

confidence: 99%

Uncertainty in Characterizations of Isotropic Linear Viscoelastic Shear and Bulk Moduli from 1 - D Tensile Experiments

Michaeli¹,

Shtark²,

Grosbein³

et al. 2014

55th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference

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Previous experiments at constant strain rates, while valuable in their own right, indicated that relaxation experiments at nominally constant strains are more conducive to obtaining data over numerous time decades in order to establish proper moduli/compliances, which cover the entire time range from instantaneous to fully relaxed moduli. The purpose of this paper, then, is to report on a series of relaxation experiments in order to produce high fidelity characterization of the statistical properties of viscoelastic materials, such as relaxation moduli, creep compliances, times to achieve constant strains, etc. Photometric, load cell, extensometers and accelerometer equipment was employed for data harvesting. Beta probability density functions with time dependent parameters were used to best describe the statistics as they answer the need to represent the data in a finite interval. A new analytical protocol for material determination, called the direct numerical calculation of viscoelastic moduli (DVM), has been developed and tested. Various protocols to determine the actual time to complete experimental loading phases are formulated as well as simple dynamic experiments for evaluating instantaneous moduli. Parallel to the above development the instantaneous modulus is determined from separate dynamic experiments and its statistical results are combined with 1 Copyright© the quasi-static experimental statistical data, thus providing time dependent probability density functions covering the entire positive time domain t ≥ 0. The time when the loading cycle ends is calculated from extensometers and its non-trivial influence on the characterization process is evaluated.It is shown that a stochastic elastic/viscoelastic correspondence principle can only be formulated based on integral transforms, since the constitutive relations are no longer of the convolution type. However, its utility for purposes of analysis of stress and strains is severely limited compared deterministic EVCPs because of the complicated non-convolution type constitutive relations.

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Analytical and Experimental Protocols for Unified Characterizations in Real Time Space for Isotropic Linear Viscoelastic Moduli from 1–D Tensile Experiments

Michaeli

Shtark²,

Grosbein³

et al. 2013

Challenges in Mechanics of Time-Dependent Materials and Processes in Conventional and Multifunctional Materials, Volume 2

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Characterization of Isotropic Viscoelastic Moduli and Compliances from 1-D Tension Experiments

Cited by 5 publications

References 18 publications

Elastic and Viscoelastic Poisson’s Ratios: The Theoretical Mechanics Perspective

Elastic and Viscoelastic Poisson’s Ratios: The Theoretical Mechanics Perspective

Uncertainty in Characterizations of Isotropic Linear Viscoelastic Shear and Bulk Moduli from 1 - D Tensile Experiments

Analytical and Experimental Protocols for Unified Characterizations in Real Time Space for Isotropic Linear Viscoelastic Moduli from 1–D Tensile Experiments

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