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The DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Wed, 21 Aug 2019 23:05:02 GMT2019-08-21T23:05:02ZPhysical interpretation of the Mullins softening in a carbon-black filled SBR
http://hdl.handle.net/10985/8457
Physical interpretation of the Mullins softening in a carbon-black filled SBR
DIAZ, Rodrigo; DIANI, Julie; GILORMINI, Pierre
A 40 phr carbon-black filled styrene butadiene rubber has been submitted to several experiments in order to identify the physical damage responsible for the mechanical softening recorded upon first stretch. Damage in the rubber matrix was determined by swelling. The filler structure alteration was monitored by electrical conductivity measurements. Both damages are shown to be of minor importance compared to the substantial mechanical softening undergone by the material. Degradation at the rubber-filler interface may be recovered by exposing the material at high temperatures in vacuo. The chain mobility in such storage conditions promotes free chain adsorption at the filler surface. The existence of a layer of polymer whose movements are hindered adds to the filler reinforcement and its desorption creates Mullins softening.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10985/84572014-01-01T00:00:00ZDIAZ, RodrigoDIANI, JulieGILORMINI, PierreA 40 phr carbon-black filled styrene butadiene rubber has been submitted to several experiments in order to identify the physical damage responsible for the mechanical softening recorded upon first stretch. Damage in the rubber matrix was determined by swelling. The filler structure alteration was monitored by electrical conductivity measurements. Both damages are shown to be of minor importance compared to the substantial mechanical softening undergone by the material. Degradation at the rubber-filler interface may be recovered by exposing the material at high temperatures in vacuo. The chain mobility in such storage conditions promotes free chain adsorption at the filler surface. The existence of a layer of polymer whose movements are hindered adds to the filler reinforcement and its desorption creates Mullins softening.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.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.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.Testing some implementations of a cohesive-zone model at finite strain
http://hdl.handle.net/10985/10171
Testing some implementations of a cohesive-zone model at finite strain
GILORMINI, Pierre; DIANI, Julie
This study shows how the results given by a cohesive-zone model at finite strain may depend strongly on its numerical implementation. A two-dimensional four-node cohesive element is considered, which includes several variants depending on a part of the strain-displacement matrix, on the quadrature rule applied, and on the configuration chosen to perform integration. Finite element simulations combine these variants with a very simple, bilinear, cohesive-zone model, in two tests. The first test involves a single element and illustrates some features of the various implementations. The other test simulates the peeling of an elastomer strip from a rigid substrate.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10985/101712015-01-01T00:00:00ZGILORMINI, PierreDIANI, JulieThis study shows how the results given by a cohesive-zone model at finite strain may depend strongly on its numerical implementation. A two-dimensional four-node cohesive element is considered, which includes several variants depending on a part of the strain-displacement matrix, on the quadrature rule applied, and on the configuration chosen to perform integration. Finite element simulations combine these variants with a very simple, bilinear, cohesive-zone model, in two tests. The first test involves a single element and illustrates some features of the various implementations. The other test simulates the peeling of an elastomer strip from a rigid substrate.Crosslink Density Changes during the Hydrolysis of Tridimensional Polyesters
http://hdl.handle.net/10985/8276
Crosslink Density Changes during the Hydrolysis of Tridimensional Polyesters
RICHAUD, Emmanuel; GILORMINI, Pierre; COQUILLAT, Marie; VERDU, Jacques
The hydrolysis of almost ideal networks based on macrodiols of average molar mass about 2 kg mol 1, with L¼18 ester groups per chain is studied. Tensile testing is used to evaluate the crosslink density through the statistical theory of rubber elasticity at two temperatures and three values of relative humidity. A kinetic model for ester consumption including an autocatalysis term is proposed and combined with two original approaches for modeling the crosslink density changes. This allows kinetic parameters of hydrolysis to be determined, and very good predictions are obtained for the variations of crosslink density (or elastic modulus) in the three aging conditions considered. The initial curvature of elastic modulus versus time is predicted positive for weak autocatalysis and negative for strong autocatalysis. The obtained conversion ratio at degelation is found to decrease sharply with the number of esters per elastically active chain
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10985/82762014-01-01T00:00:00ZRICHAUD, EmmanuelGILORMINI, PierreCOQUILLAT, MarieVERDU, JacquesThe hydrolysis of almost ideal networks based on macrodiols of average molar mass about 2 kg mol 1, with L¼18 ester groups per chain is studied. Tensile testing is used to evaluate the crosslink density through the statistical theory of rubber elasticity at two temperatures and three values of relative humidity. A kinetic model for ester consumption including an autocatalysis term is proposed and combined with two original approaches for modeling the crosslink density changes. This allows kinetic parameters of hydrolysis to be determined, and very good predictions are obtained for the variations of crosslink density (or elastic modulus) in the three aging conditions considered. The initial curvature of elastic modulus versus time is predicted positive for weak autocatalysis and negative for strong autocatalysis. The obtained conversion ratio at degelation is found to decrease sharply with the number of esters per elastically active chainOn 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.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.