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http://hdl.handle.net/10985/18692
Constitutive modeling of the anisotropic behavior of Mullins softened filled rubbers
MERCKEL, Yannick; DIANI, Julie; BRIEU, Mathias; CAILLARD, Julien
Original constitutive modeling is proposed for filled rubber materials in order to capture the anisotropic softened behavior induced by general non-proportional pre-loading histories. The hyperelastic framework is grounded on a thorough analysis of cyclic experimental data. The strain energy density is based on a directional approach. The model leans on the strain amplification factor concept applied over material directions according to the Mullins softening evolution. In order to provide a model versatile that applies for a wide range of materials, the proposed framework does not require to postulate the mathematical forms of the elementary directional strain energy density and of the Mullins softening evolution rule. A computational procedure is defined to build both functions incrementally from experimental data obtained during cyclic uniaxial tensile tests. Successful comparisons between the model and the experiments demonstrate the model abilities. Moreover, the model is shown to accurately predict the non-proportional uniaxial stress-stretch responses for uniaxially and biaxially pre-stretched samples. Finally, the model is efficiently tested on several materials and proves to provide a quantitative estimate of the anisotropy induced by the Mullins softening for a wide range of filled rubbers.
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10985/186922013-01-01T00:00:00ZMERCKEL, YannickDIANI, JulieBRIEU, MathiasCAILLARD, JulienOriginal constitutive modeling is proposed for filled rubber materials in order to capture the anisotropic softened behavior induced by general non-proportional pre-loading histories. The hyperelastic framework is grounded on a thorough analysis of cyclic experimental data. The strain energy density is based on a directional approach. The model leans on the strain amplification factor concept applied over material directions according to the Mullins softening evolution. In order to provide a model versatile that applies for a wide range of materials, the proposed framework does not require to postulate the mathematical forms of the elementary directional strain energy density and of the Mullins softening evolution rule. A computational procedure is defined to build both functions incrementally from experimental data obtained during cyclic uniaxial tensile tests. Successful comparisons between the model and the experiments demonstrate the model abilities. Moreover, the model is shown to accurately predict the non-proportional uniaxial stress-stretch responses for uniaxially and biaxially pre-stretched samples. Finally, the model is efficiently tested on several materials and proves to provide a quantitative estimate of the anisotropy induced by the Mullins softening for a wide range of filled rubbers.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.Effect of the microstructure parameters on the Mullins softening in carbon-black filled SBRs
http://hdl.handle.net/10985/6805
Effect of the microstructure parameters on the Mullins softening in carbon-black filled SBRs
MERCKEL, Yannick; DIANI, Julie; BRIEU, Mathias; GILORMINI, Pierre; CAILLARD, Julien
A quantitative estimate of the Mullins softening is proposed and tested on various carbon-black filled styrene-butadiene rubbers. In order to model the behaviour of elastomeric materials, some constitutive equations reported in the literature are based on the account of a strain amplification factor, which evolves with the maximum strain history. The amplification factor is grounded on the representation of filled rubbers as heterogeneous materials made of hard rigid domains and soft deformable domains. In the present work, this factor is splitted into two parts with opposite effects that account for the Mullins softening and for the filler reinforcement, respectively. Evolutions of both parts are obtained through a direct analysis of cyclic uniaxial tensile tests performed on a series of materials. The Mullins softening part is shown to linearly depend on the filler volume fraction and on the maximum strain applied, when defined as the first invariant of the Hencky tensor. Its changes with the gum crosslink density parameter are insignificant. The reinforcement part of the amplification factor shows quadratic dependence on the filler volume fraction.
[The definitive version is available at www3.interscience.wiley.com]
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/10985/68052012-01-01T00:00:00ZMERCKEL, YannickDIANI, JulieBRIEU, MathiasGILORMINI, PierreCAILLARD, JulienA quantitative estimate of the Mullins softening is proposed and tested on various carbon-black filled styrene-butadiene rubbers. In order to model the behaviour of elastomeric materials, some constitutive equations reported in the literature are based on the account of a strain amplification factor, which evolves with the maximum strain history. The amplification factor is grounded on the representation of filled rubbers as heterogeneous materials made of hard rigid domains and soft deformable domains. In the present work, this factor is splitted into two parts with opposite effects that account for the Mullins softening and for the filler reinforcement, respectively. Evolutions of both parts are obtained through a direct analysis of cyclic uniaxial tensile tests performed on a series of materials. The Mullins softening part is shown to linearly depend on the filler volume fraction and on the maximum strain applied, when defined as the first invariant of the Hencky tensor. Its changes with the gum crosslink density parameter are insignificant. The reinforcement part of the amplification factor shows quadratic dependence on the filler volume fraction.A Mullins softening criterion for general loading conditions
http://hdl.handle.net/10985/17617
A Mullins softening criterion for general loading conditions
MERCKEL, Yannick; BRIEU, Mathias; DIANI, Julie; CAILLARD, Julien
Samples of carbon-black filled styrene butadiene rubbers (SBRs) were submitted to successive nonproportional loadings in order to define a general criterion for the Mullins softening. For this purpose, each sample was initially submitted to uniaxial or biaxial preloadings followed by a cyclic uniaxial tension test. An original experimental analysis aimed at defining the activation threshold for the Mullins softening during cyclic uniaxial loadings. The experimental data provide substantial evidences establishing the surface of the maximum directional stretch undergone by the material as a relevant Mullins softening criterion. The latter was used to successfully predict the Mullins softening surfaces for additional loading cases.
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/10985/176172012-01-01T00:00:00ZMERCKEL, YannickBRIEU, MathiasDIANI, JulieCAILLARD, JulienSamples of carbon-black filled styrene butadiene rubbers (SBRs) were submitted to successive nonproportional loadings in order to define a general criterion for the Mullins softening. For this purpose, each sample was initially submitted to uniaxial or biaxial preloadings followed by a cyclic uniaxial tension test. An original experimental analysis aimed at defining the activation threshold for the Mullins softening during cyclic uniaxial loadings. The experimental data provide substantial evidences establishing the surface of the maximum directional stretch undergone by the material as a relevant Mullins softening criterion. The latter was used to successfully predict the Mullins softening surfaces for additional loading cases.Constitutive modeling of the anisotropic behavior of Mullins softened ﬁlled rubbers
http://hdl.handle.net/10985/8156
Constitutive modeling of the anisotropic behavior of Mullins softened ﬁlled rubbers
MERCKEL, Yannick; DIANI, Julie; BRIEU, Mathias; CAILLARD, Julien
Original constitutive modeling is proposed for ﬁlled rubber materials in order to capture the anisotropic softened behavior induced by general non-proportional pre-loading histo-ries. The hyperelastic framework is grounded on a thorough analysis of cyclic experimental data. The strain energy density is based on a directional approach. The model leans on the strain ampliﬁcation factor concept applied over material directions according to the Mul-lins softening evolution. In order to provide a model versatile that applies for a wide range of materials, the proposed framework does not require to postulate the mathematical forms of the elementary directional strain energy density and of the Mullins softening evo-lution rule. A computational procedure is deﬁned to build both functions incrementally from experimental data obtained during cyclic uniaxial tensile tests. Successful compari-sons between the model and the experiments demonstrate the model abilities. Moreover, the model is shown to accurately predict the non-proportional uniaxial stress-stretch responses for uniaxially and biaxially pre-stretched samples. Finally, the model is efﬁ-ciently tested on several materials and proves to provide a quantitative estimate of the anisotropy induced by the Mullins softening for a wide range of ﬁlled rubbers.
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/10985/81562012-01-01T00:00:00ZMERCKEL, YannickDIANI, JulieBRIEU, MathiasCAILLARD, JulienOriginal constitutive modeling is proposed for ﬁlled rubber materials in order to capture the anisotropic softened behavior induced by general non-proportional pre-loading histo-ries. The hyperelastic framework is grounded on a thorough analysis of cyclic experimental data. The strain energy density is based on a directional approach. The model leans on the strain ampliﬁcation factor concept applied over material directions according to the Mul-lins softening evolution. In order to provide a model versatile that applies for a wide range of materials, the proposed framework does not require to postulate the mathematical forms of the elementary directional strain energy density and of the Mullins softening evo-lution rule. A computational procedure is deﬁned to build both functions incrementally from experimental data obtained during cyclic uniaxial tensile tests. Successful compari-sons between the model and the experiments demonstrate the model abilities. Moreover, the model is shown to accurately predict the non-proportional uniaxial stress-stretch responses for uniaxially and biaxially pre-stretched samples. Finally, the model is efﬁ-ciently tested on several materials and proves to provide a quantitative estimate of the anisotropy induced by the Mullins softening for a wide range of ﬁlled rubbers.Micromechanical modeling of the linear viscoelasticity of carbon-black filled styrene butadiene rubbers: the role of the rubber-filler interphase
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 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; ROUSSEAU, Ingrid; REGNIER, Gilles
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, YannickROUSSEAU, IngridREGNIER, GillesA 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.Effects of the Amount of Fillers and of the Crosslink Density on the Mechanical Behavior of Carbon-Black Filled Styrene Butadiene Rubbers
http://hdl.handle.net/10985/8196
Effects of the Amount of Fillers and of the Crosslink Density on the Mechanical Behavior of Carbon-Black Filled Styrene Butadiene Rubbers
MERCKEL, Yannick; DIANI, Julie; BRIEU, Mathias; CAILLARD, Julien
Several carbon-black filled styrene-butadiene rubbers are subjected to monotonic uniaxial tension tests in order to investi-gate the effects of the amount of fillers and of the crosslink density on their mechanical properties. The Young modulus, the volume changes associated with material damage and the stretch to failure are extracted and discussed. Results compare well to the literature results when exist and quantitative analysis are proposed when possible. Results show that filled rubbers are not incompressible when submitted to uniaxial tension tests and their volume changes are strongly dependent of the amount of fillers but are unaffected by the crosslink density. The latter shows strong impact on the filled rubbers stretch to failure but more interestingly this impact is com-parable to what is encountered in unfilled rubbers. The stretch to failure is improved by the addition of fillers with an optimum for material filled around 30 phr.
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10985/81962013-01-01T00:00:00ZMERCKEL, YannickDIANI, JulieBRIEU, MathiasCAILLARD, JulienSeveral carbon-black filled styrene-butadiene rubbers are subjected to monotonic uniaxial tension tests in order to investi-gate the effects of the amount of fillers and of the crosslink density on their mechanical properties. The Young modulus, the volume changes associated with material damage and the stretch to failure are extracted and discussed. Results compare well to the literature results when exist and quantitative analysis are proposed when possible. Results show that filled rubbers are not incompressible when submitted to uniaxial tension tests and their volume changes are strongly dependent of the amount of fillers but are unaffected by the crosslink density. The latter shows strong impact on the filled rubbers stretch to failure but more interestingly this impact is com-parable to what is encountered in unfilled rubbers. The stretch to failure is improved by the addition of fillers with an optimum for material filled around 30 phr.Volume changes in a filled elastomer studied via digital image correlation
http://hdl.handle.net/10985/6521
Volume changes in a filled elastomer studied via digital image correlation
DE CREVOISIER, Jordan; BESNARD, Gilles; MERCKEL, Yannick; ZHANG, Huan; CAILLARD, Julien; VION-LOISEL, Fabien; BERGHEZAN, Daniel; CRETON, Costantino; DIANI, Julie; BRIEU, Mathias; HILD, François; ROUX, Stéphane
Volumetric strains in a filled SBR specimen subjected to cyclic uniaxial tension with increasing extensions are studied. Digital image correlation is used to follow the kinematics of two orthogonal free faces. A volume expansion is observed past a critical elongation, which can be interpreted as the onset of cavitation. Under unloading, the volume returns to its original value and remains constant upon reloading. Increasing the elongation to higher values than the previous cycle leads again to a volumetric expansion.
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/10985/65212012-01-01T00:00:00ZDE CREVOISIER, JordanBESNARD, GillesMERCKEL, YannickZHANG, HuanCAILLARD, JulienVION-LOISEL, FabienBERGHEZAN, DanielCRETON, CostantinoDIANI, JulieBRIEU, MathiasHILD, FrançoisROUX, StéphaneVolumetric strains in a filled SBR specimen subjected to cyclic uniaxial tension with increasing extensions are studied. Digital image correlation is used to follow the kinematics of two orthogonal free faces. A volume expansion is observed past a critical elongation, which can be interpreted as the onset of cavitation. Under unloading, the volume returns to its original value and remains constant upon reloading. Increasing the elongation to higher values than the previous cycle leads again to a volumetric expansion.