Improved viscoelastic model for laminate composite under static and dynamic loadings

Berthe, Julien; Brieu, Mathias; Deletombe, E.

doi:10.1177/0021998312451294

Cited by 9 publications

(17 citation statements)

References 21 publications

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“…In this section, the previous experimental results are used in order to identify a non‐linear viscoelastic model , developed to describe the behaviour of organic matrix composite materials over a large range of strain rate. This identification procedure will highlight the need of performing dynamic tests that give consistent results with static and creep tests.…”

Section: Model Identificationmentioning

confidence: 99%

“…It has been recently extended to account for a large range of strain rates by Berthe et al . . In this model, the non‐linear extension of the classical laminate theory is used to link the macroscopic load to the non‐linear mesoscopic ply behaviour.…”

Section: Model Identificationmentioning

confidence: 99%

“…The temporal spectrum of the model, defined by all the relaxation times and weights, is the sum of two Gaussian spectrum (one for a family of quick mechanisms and one for a family of slow mechanisms) in order to be more representative than the single spectrum in the initial ONERA model for a large range of strain rates (more details can be found in Berthe et al

\begin{matrix} center \\ center τ_{i} = exp ((), i) & center normaland & center μ_{i} = \frac{{\overset{μ_{i}}{true}}^{italicquick}}{\sum_{i} {\overset{μ_{i}}{true}}^{italicquick}} + \frac{{\overset{μ_{i}}{true}}^{italicslow}}{\sum_{i} {\overset{μ_{i}}{true}}^{italicslow}} \end{matrix}

with

{\overset{μ_{i}}{true}}^{k} = \frac{1}{n_{0}^{k} \sqrt{π}} exp (- {((), \frac{i - n_{c}^{k}}{n_{0}^{k}})}^{2})

…”

Section: Model Identificationmentioning

confidence: 99%

“…In such a case, the identification of a viscoelastic model like the one proposed by Berthe et al . , which requires dynamic, quasi‐static and creep tests (necessarily realised on various testing machines) to model the behaviour of CFRPs from low to high strain rates, cannot be performed without inconsistency appearing on the shear modulus values, due to variation of the geometry of the samples from a testing machine to another. It can be noticed that in this example of geometrical effect, only in‐plane dimensions are modified.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Consistent Identification of CFRP Viscoelastic Models from Creep to Dynamic Loadings

Berthe¹,

Brieu²,

Deletombe

et al. 2013

Strain

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Rate‐dependent models require creep or mechanical tests at various strain rates in order to be identified and validated. Different geometries coexist for creep and static tests (normative geometry) and for dynamic tests. Therefore, due to geometrical sample considerations, experimental results could be inconsistent for identification or validation procedures, inducing, for example, differences on the shear modulus only due to the change of geometry. The objective of this work is to present an improved sample geometry that allows to obtain consistent mechanical tests results at various strain rates highlighting the rate dependencies of laminates. In particular, a complete mechanical validation of the sample geometry for dynamic tests is successfully performed in order to avoid inconsistency. Results of static and dynamic tests on the validated geometry are analysed, and the rate dependency of the elastic properties of the UD T700GC/M21 mesoscopic ply is highlighted on a wide strain rate range (10−3 to 102 s−1). Finally, the identification of a non‐linear viscoelastic model is performed on dynamic and creep tests results in order to obtain a representative model for dynamic, static and creep loadings, and to demonstrate the importance of introducing the improved geometry for the dynamic tests.

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Section: Model Identificationmentioning

confidence: 99%

Section: Model Identificationmentioning

confidence: 99%

\begin{matrix} center \\ center τ_{i} = exp ((), i) & center normaland & center μ_{i} = \frac{{\overset{μ_{i}}{true}}^{italicquick}}{\sum_{i} {\overset{μ_{i}}{true}}^{italicquick}} + \frac{{\overset{μ_{i}}{true}}^{italicslow}}{\sum_{i} {\overset{μ_{i}}{true}}^{italicslow}} \end{matrix}

with

{\overset{μ_{i}}{true}}^{k} = \frac{1}{n_{0}^{k} \sqrt{π}} exp (- {((), \frac{i - n_{c}^{k}}{n_{0}^{k}})}^{2})

…”

Section: Model Identificationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Consistent Identification of CFRP Viscoelastic Models from Creep to Dynamic Loadings

Berthe¹,

Brieu²,

Deletombe

et al. 2013

Strain

View full text Add to dashboard Cite

show abstract

“…In order to describe the mechanical response of CFRPs, some authors typically proposed models that include three main components: a first elastic reversible behaviour then a non‐linear behaviour of the material, which can be phenomenologically associated to viscosity again, plasticity, or damage following by the final rupture of the material. The elastic reversible behaviour of the material can be strain rate and temperature dependent, see for instance the viscoelastic linear model proposed by Berthe et al to model the linear response of the T700GC/M21 material . Concerning the failure behaviour of the material, different criteria for composite materials can be found which can also be strain rate dependent .…”

Section: Introductionmentioning

confidence: 99%

Experimental evaluation of the elastic limit of carbon‐fibre reinforced epoxy composites under a large range of strain rate and temperature conditions

Castres

Berthe

Deletombe

et al. 2017

Strain

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The mechanical behaviour of organic matrix composite materials such as T700GC/M21 carbon fibre reinforced polymer (CFRP) is generally considered by the industry as being orthotropic elastic for the sizing of aeronautical structures under normal isothermal "static" flight loads. During the aircraft lifetime, it may be exposed to severe loading conditions at various temperatures. However, the mechanical behaviour of CFRP is known to exhibit a linear behaviour or a non-linear behaviour according to the types of loads that are considered creep or extreme conditions. The observed non-linearity can be commonly attributed to several physical phenomena such as non-linear viscosity, plasticity, or damage.In the literature, different models can be found that are based on three components: a first elastic reversible behaviour, a second non-linear behaviour, and a failure criterion. An important issue is to understand and characterize the transition between the elastic reversible behaviour and the non-linear behaviour. To answer this question, the present paper describes an experimental methodology that permits to evaluate this transition thanks to raw experimental data, and its application to a range of constant but different strain rate and temperature tests performed on the T700GC/M21 CFRP material. KEYWORDS dynamic properties, mechanical properties, non-linear behaviour, polymer-matrix composite, temperature dependency Strain. 2017;53:e12248.wileyonlinelibrary.com/journal/str

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A Virtual Testing Approach for Laminated Composites Based on Micromechanics

Néron¹,

Bainier²

2016

The Structural Integrity of Carbon Fiber Composites

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Improved viscoelastic model for laminate composite under static and dynamic loadings

Cited by 9 publications

References 21 publications

Consistent Identification of CFRP Viscoelastic Models from Creep to Dynamic Loadings

Consistent Identification of CFRP Viscoelastic Models from Creep to Dynamic Loadings

Experimental evaluation of the elastic limit of carbon‐fibre reinforced epoxy composites under a large range of strain rate and temperature conditions

A Virtual Testing Approach for Laminated Composites Based on Micromechanics

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