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http://hdl.handle.net/10985/6830
Micromechanical modeling of the linear viscoelasticity of carbon-black filled styrene butadiene rubbers: the role of the rubber-filler interphase
DIANI, Julie; GILORMINI, Pierre; MERCKEL, Yannick; VION-LOISEL, Fabien
Micromechanics modeling of the linear viscoelasticity of carbon-black filled styrene butadiene rubbers (SBR) shows that a simple representation of a spherical rigid-phase surrounded by rubber gum and embedded in an homogeneous equivalent medium provides access to the effective volume fraction of fillers. This simple representation is successful for a significant range of filler amount, and for materials in the glassy state. For materials in the rubbery state, experimental results support the existence of a filler-rubber interphase with reduced mobility due to confinement. The 4-phase micromechanics model, which accounts for a bounded rubber layer coating the fillers, provides satisfactory estimates of the linear viscoelasticity of filled rubbers from the rubbery state to the glassy state. It also provides access to the filler rubber interphase behavior that appears viscoelastic, and to an estimate of the interphase thickness.
Version éditeur : http://www.sciencedirect.com/science/article/pii/S0167663612002190
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10985/68302013-01-01T00:00:00ZDIANI, JulieGILORMINI, PierreMERCKEL, YannickVION-LOISEL, FabienMicromechanics modeling of the linear viscoelasticity of carbon-black filled styrene butadiene rubbers (SBR) shows that a simple representation of a spherical rigid-phase surrounded by rubber gum and embedded in an homogeneous equivalent medium provides access to the effective volume fraction of fillers. This simple representation is successful for a significant range of filler amount, and for materials in the glassy state. For materials in the rubbery state, experimental results support the existence of a filler-rubber interphase with reduced mobility due to confinement. The 4-phase micromechanics model, which accounts for a bounded rubber layer coating the fillers, provides satisfactory estimates of the linear viscoelasticity of filled rubbers from the rubbery state to the glassy state. It also provides access to the filler rubber interphase behavior that appears viscoelastic, and to an estimate of the interphase thickness.A review on the Mullins effect
http://hdl.handle.net/10985/6683
A review on the Mullins effect
GILORMINI, Pierre; DIANI, Julie; FAYOLLE, Bruno
The Mullins’ effect remains a major challenge in order to provide good mechanical modeling of the complex behavior of industrial rubber materials. It’s been forty years since Mullins [1] wrote his review on the phenomenon and still no general agreement has been found either on the physical source or on the mechanical modeling of this effect. Therefore, we reviewed the literature dedicated to this topic over the past six decades. We present the experimental evidences, which characterize the Mullins’ softening. The phenomenon is observed in filled and crystallizing rubbers. Then, the phenomenological models dedicated to fit the mechanical behavior of rubbers undergoing some Mullins’ softening are studied. To overcome the limit of a descriptive phenomenological modeling, several authors looked for a physical understanding of the phenomenon. Various theories have been exposed, but none of them has been supported unanimously. Nonetheless, these theories favor the emergence of physically based mechanical behavior laws. We tested some of these laws, which show little predictive abilities since the values of their parameters do not compare well with the physical quantities they are linked to.
Thu, 01 Jan 2009 00:00:00 GMThttp://hdl.handle.net/10985/66832009-01-01T00:00:00ZGILORMINI, PierreDIANI, JulieFAYOLLE, BrunoThe Mullins’ effect remains a major challenge in order to provide good mechanical modeling of the complex behavior of industrial rubber materials. It’s been forty years since Mullins [1] wrote his review on the phenomenon and still no general agreement has been found either on the physical source or on the mechanical modeling of this effect. Therefore, we reviewed the literature dedicated to this topic over the past six decades. We present the experimental evidences, which characterize the Mullins’ softening. The phenomenon is observed in filled and crystallizing rubbers. Then, the phenomenological models dedicated to fit the mechanical behavior of rubbers undergoing some Mullins’ softening are studied. To overcome the limit of a descriptive phenomenological modeling, several authors looked for a physical understanding of the phenomenon. Various theories have been exposed, but none of them has been supported unanimously. Nonetheless, these theories favor the emergence of physically based mechanical behavior laws. We tested some of these laws, which show little predictive abilities since the values of their parameters do not compare well with the physical quantities they are linked to.The effect of moisture-induced swelling on the absorption capacity of transversely isotropic elastic polymer-matrix composites
http://hdl.handle.net/10985/6685
The effect of moisture-induced swelling on the absorption capacity of transversely isotropic elastic polymer-matrix composites
DERRIEN, Katell; GILORMINI, Pierre
The interaction between humid air and transversely isotropic fiber-reinforced composites with swelling polymeric matrix is considered. A model is proposed for the water saturation level in a polymer when stresses are applied, that uses directly obtainable material parameters only. In a composite, the reinforcements modify the water uptake of the polymer matrix because of the internal stresses that are induced by its restricted swelling, and this effect is evaluated. As a consequence of the coupling between stresses and absorption capacity, the sorption isotherm of a composite is ruled by the (nonlinear) Langmuir equation when the unreinforced matrix obeys the (linear) Henry’s law.
Thu, 01 Jan 2009 00:00:00 GMThttp://hdl.handle.net/10985/66852009-01-01T00:00:00ZDERRIEN, KatellGILORMINI, PierreThe interaction between humid air and transversely isotropic fiber-reinforced composites with swelling polymeric matrix is considered. A model is proposed for the water saturation level in a polymer when stresses are applied, that uses directly obtainable material parameters only. In a composite, the reinforcements modify the water uptake of the polymer matrix because of the internal stresses that are induced by its restricted swelling, and this effect is evaluated. As a consequence of the coupling between stresses and absorption capacity, the sorption isotherm of a composite is ruled by the (nonlinear) Langmuir equation when the unreinforced matrix obeys the (linear) Henry’s law.The effect of applied stresses on the equilibrium moisture content in polymers
http://hdl.handle.net/10985/6561
The effect of applied stresses on the equilibrium moisture content in polymers
DERRIEN, Katell; GILORMINI, Pierre
The relation between saturation moisture content in a polymer and applied stresses is derived as a function of the coefficient of moisture expansion. The model predictions are compared favourably with experimental data taken from the literature.
Mon, 01 Jan 2007 00:00:00 GMThttp://hdl.handle.net/10985/65612007-01-01T00:00:00ZDERRIEN, KatellGILORMINI, PierreThe relation between saturation moisture content in a polymer and applied stresses is derived as a function of the coefficient of moisture expansion. The model predictions are compared favourably with experimental data taken from the literature.An introduction to the statistical theory of polymer network formation
http://hdl.handle.net/10985/6886
An introduction to the statistical theory of polymer network formation
GILORMINI, Pierre
A short but detailed introduction to the statistical theory of polymer network formation is given, including gel formation, gel structure, and sol fraction. Focus is put on the use of probability generating functions, and results that are of interest for polymer network elasticity are emphasized. Detailed derivations are supplied, and a simple 6-step procedure is provided, so that the reader is able to adapt and apply the theory to his own chemical systems, even if examples are given on polyurethanes essentially.
Sat, 01 Jan 2011 00:00:00 GMThttp://hdl.handle.net/10985/68862011-01-01T00:00:00ZGILORMINI, PierreA short but detailed introduction to the statistical theory of polymer network formation is given, including gel formation, gel structure, and sol fraction. Focus is put on the use of probability generating functions, and results that are of interest for polymer network elasticity are emphasized. Detailed derivations are supplied, and a simple 6-step procedure is provided, so that the reader is able to adapt and apply the theory to his own chemical systems, even if examples are given on polyurethanes essentially.An experimental and analytical study of the elasticity of model polyurethane networks crosslinked by tri- and quadriisocyanate
http://hdl.handle.net/10985/6814
An experimental and analytical study of the elasticity of model polyurethane networks crosslinked by tri- and quadriisocyanate
FAYOLLE, Bruno; GILORMINI, Pierre; DIANI, Julie
Polyurethane networks have been prepared from a mix of tri- and quadriisocyanate and from two types of diols, polyether-based (with molar masses of 1,000, 2,000, and 4,000 g/mol) and polyester-based (1,035 g/mol). The weight fraction of sol has been measured, as well as the elastic shear modulus of the gels. It has been found that the statistical theory of network formation predicts a weight fraction of sol in agreement with the experimental results, but its standard combination with the theory of rubber elasticity disagrees significantly with the elastic modulus measured. This suggests a discrepancy between theory and experiment in terms of elastically active chains. In contrast, the assumption that all nodes in the gel, or even in the system, are elastically active gives much better predictions for the system considered.
The original publication is available at www.springerlink.com : http://link.springer.com/article/10.1007%2Fs00396-009-2145-6?LI=true
Fri, 01 Jan 2010 00:00:00 GMThttp://hdl.handle.net/10985/68142010-01-01T00:00:00ZFAYOLLE, BrunoGILORMINI, PierreDIANI, JuliePolyurethane networks have been prepared from a mix of tri- and quadriisocyanate and from two types of diols, polyether-based (with molar masses of 1,000, 2,000, and 4,000 g/mol) and polyester-based (1,035 g/mol). The weight fraction of sol has been measured, as well as the elastic shear modulus of the gels. It has been found that the statistical theory of network formation predicts a weight fraction of sol in agreement with the experimental results, but its standard combination with the theory of rubber elasticity disagrees significantly with the elastic modulus measured. This suggests a discrepancy between theory and experiment in terms of elastically active chains. In contrast, the assumption that all nodes in the gel, or even in the system, are elastically active gives much better predictions for the system considered.Charcaterization of the Mullins effect of carbon-black filled rubbers
http://hdl.handle.net/10985/6804
Charcaterization of the Mullins effect of carbon-black filled rubbers
MERCKEL, Yannick; DIANI, Julie; BRIEU, Mathias; GILORMINI, Pierre; CAILLARD, Julien
Several carbon-black filled styrene-butadiene rubbers showed different sensibilities to the Mullins softening when submitted to cyclic uniaxial tension. In order to quantify this softening, a damage parameter was introduced. It is defined by using a classic damage approach and can be estimated by using either the strain amplification factor method or the tangent modulus at zero stress. The proposed parameter is used to study the effects of crosslink density and filler amount on the Mullins softening. The latter is shown to remain unaffected by a change of crosslink density and to increase with an increase of filler amount. The damage parameter exhibits mere linear dependences on the maximum Hencky strain applied and on the filler volume fraction. A simple linear expression is given finally to predict the Mullins softening of filled rubbers. The parameter also provides an objective analysis for the Mullins softening that supports comments on a better understanding of this effect.
Publisher version : http://rubberchemtechnol.org/doi/abs/10.5254/1.3592294?journalCode=rcat
Sat, 01 Jan 2011 00:00:00 GMThttp://hdl.handle.net/10985/68042011-01-01T00:00:00ZMERCKEL, YannickDIANI, JulieBRIEU, MathiasGILORMINI, PierreCAILLARD, JulienSeveral carbon-black filled styrene-butadiene rubbers showed different sensibilities to the Mullins softening when submitted to cyclic uniaxial tension. In order to quantify this softening, a damage parameter was introduced. It is defined by using a classic damage approach and can be estimated by using either the strain amplification factor method or the tangent modulus at zero stress. The proposed parameter is used to study the effects of crosslink density and filler amount on the Mullins softening. The latter is shown to remain unaffected by a change of crosslink density and to increase with an increase of filler amount. The damage parameter exhibits mere linear dependences on the maximum Hencky strain applied and on the filler volume fraction. A simple linear expression is given finally to predict the Mullins softening of filled rubbers. The parameter also provides an objective analysis for the Mullins softening that supports comments on a better understanding of this effect.A torsion test for the study of the large deformation recovery of shape memory polymers
http://hdl.handle.net/10985/6560
A torsion test for the study of the large deformation recovery of shape memory polymers
DIANI, Julie; FREDY, Carole; GILORMINI, Pierre; MERCKEL, Yannick; REGNIER, Gilles; ROUSSEAU, Ingrid
A torsion device was designed and built for testing the shape fixity and shape recovery of shape memory polymers at large deformation. A simple thermal chamber was used to regulate the thermal environment during testing and a CCD camera was used for recording the deformation. Such a torsion testing system provided a quantitative estimate of the kinematics and kinetics of shape recovery for samples submitted to large deformations at moderate strains that are more likely expected in actual shape memory applications. In addition, such measurements are complementary to those obtained from large strain uniaxial tension tests usually run for during traditional shape memory effect characterization. As a result, the torsional shape memory testing device and testing method described is expected to contribute building complementary data for the thermomechanical modeling of shape memory polymers.
Sat, 01 Jan 2011 00:00:00 GMThttp://hdl.handle.net/10985/65602011-01-01T00:00:00ZDIANI, JulieFREDY, CaroleGILORMINI, PierreMERCKEL, YannickREGNIER, GillesROUSSEAU, IngridA torsion device was designed and built for testing the shape fixity and shape recovery of shape memory polymers at large deformation. A simple thermal chamber was used to regulate the thermal environment during testing and a CCD camera was used for recording the deformation. Such a torsion testing system provided a quantitative estimate of the kinematics and kinetics of shape recovery for samples submitted to large deformations at moderate strains that are more likely expected in actual shape memory applications. In addition, such measurements are complementary to those obtained from large strain uniaxial tension tests usually run for during traditional shape memory effect characterization. As a result, the torsional shape memory testing device and testing method described is expected to contribute building complementary data for the thermomechanical modeling of shape memory polymers.On the account of a cohesive interface for modeling the behavior until break of highly filled elastomers
http://hdl.handle.net/10985/10434
On the account of a cohesive interface for modeling the behavior until break of highly filled elastomers
TOULEMONDE, Paul-Aymé; DIANI, Julie; GILORMINI, Pierre; DESGARDIN, Nancy
The nonlinear behavior and failure of highly filled elastomers are significantly impacted by the volume fraction, the size and nature of fillers and the matrix stiffness. Original experimental data obtained on glass beads reinforced acrylates and on propellants allow illustrating and discussing the main effects generally observed. In order to better understand the effects of the microstructure and constitutive parameters on the behavior and failure of highly filled elastomers, a composite model, represented by a 2D periodic cell with randomly dispersed particles, with an account of a cohesive zone at the filler/matrix interface is used. Finite element simulations with finite strain provide insight on the stress-strain responses dependence to the model parameters and allow defining a failure criterion perceived by the appearance of a critical fibrillar microstructure.
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10985/104342016-01-01T00:00:00ZTOULEMONDE, Paul-AyméDIANI, JulieGILORMINI, PierreDESGARDIN, NancyThe nonlinear behavior and failure of highly filled elastomers are significantly impacted by the volume fraction, the size and nature of fillers and the matrix stiffness. Original experimental data obtained on glass beads reinforced acrylates and on propellants allow illustrating and discussing the main effects generally observed. In order to better understand the effects of the microstructure and constitutive parameters on the behavior and failure of highly filled elastomers, a composite model, represented by a 2D periodic cell with randomly dispersed particles, with an account of a cohesive zone at the filler/matrix interface is used. Finite element simulations with finite strain provide insight on the stress-strain responses dependence to the model parameters and allow defining a failure criterion perceived by the appearance of a critical fibrillar microstructure.On using the leveling of the free surface of a Newtonian fluid to measure viscosity and Navier slip length
http://hdl.handle.net/10985/7394
On using the leveling of the free surface of a Newtonian fluid to measure viscosity and Navier slip length
GILORMINI, Pierre; TEYSSEDRE, Hubert
Measuring the relaxation time involved in the leveling of the free surface of a Newtonian fluid laid on a substrate can give access to material parameters. It is shown here how most favorable pattern geometries of the free surface and film thicknesses can be defined for the measures of viscosity and Navier slip length at the fluid-solid interface, respectively. Moreover, special emphasis is put on the conditions required to avoid shear-thinning by controling the maximum shear rate. For initially sinusoidal patterns with infinitesimal amplitudes, an analytical solution including slip at the fluid-solid interface is used, and numerical simulations based on the natural element method allow to discuss the effect of finite amplitudes. This leads to the definition of a relevance domain for the analytical solution that avoids the need for numerical simulations in practical applications. It is also shown how these results can be applied to crenelated profiles, where Fourier series expansion can be used, but with caution.
Version éditeur : http://rspa.royalsocietypublishing.org/content/469/2160/20130457.short
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10985/73942013-01-01T00:00:00ZGILORMINI, PierreTEYSSEDRE, HubertMeasuring the relaxation time involved in the leveling of the free surface of a Newtonian fluid laid on a substrate can give access to material parameters. It is shown here how most favorable pattern geometries of the free surface and film thicknesses can be defined for the measures of viscosity and Navier slip length at the fluid-solid interface, respectively. Moreover, special emphasis is put on the conditions required to avoid shear-thinning by controling the maximum shear rate. For initially sinusoidal patterns with infinitesimal amplitudes, an analytical solution including slip at the fluid-solid interface is used, and numerical simulations based on the natural element method allow to discuss the effect of finite amplitudes. This leads to the definition of a relevance domain for the analytical solution that avoids the need for numerical simulations in practical applications. It is also shown how these results can be applied to crenelated profiles, where Fourier series expansion can be used, but with caution.