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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.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.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.Some features of the PPR cohesive-zone model combined with a linear unloading/reloading relationship
http://hdl.handle.net/10985/11537
Some features of the PPR cohesive-zone model combined with a linear unloading/reloading relationship
GILORMINI, Pierre; DIANI, Julie
A loading/unloading/reloading process is applied to a cohesive zone where the model proposed by Park, Paulino and Roesler in 2009 is combined with a linear unloading/reloading relationship. The applied loading and unloading use the same mixed mode and reloading is in mode I. When the amplitude of preloading is varied, several features are evidenced: jumps of the dissipated energy, reversibility maintained after a traction peak, nonlinear traction variations during unloading, increasing traction during unloading, finite traction after a fracture criterion has been fulfilled, different traction values at the beginning of unloading and when dissipative reloading begins. Moreover, the results depend strongly on the path followed during unloading. Simple modifications of the model allow none of these questionable features to appear.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10985/115372017-01-01T00:00:00ZGILORMINI, PierreDIANI, JulieA loading/unloading/reloading process is applied to a cohesive zone where the model proposed by Park, Paulino and Roesler in 2009 is combined with a linear unloading/reloading relationship. The applied loading and unloading use the same mixed mode and reloading is in mode I. When the amplitude of preloading is varied, several features are evidenced: jumps of the dissipated energy, reversibility maintained after a traction peak, nonlinear traction variations during unloading, increasing traction during unloading, finite traction after a fracture criterion has been fulfilled, different traction values at the beginning of unloading and when dissipative reloading begins. Moreover, the results depend strongly on the path followed during unloading. Simple modifications of the model allow none of these questionable features to appear.Molecular mobility with respect to accessible volume in Monte Carlo lattice model for polymers
http://hdl.handle.net/10985/11439
Molecular mobility with respect to accessible volume in Monte Carlo lattice model for polymers
DIANI, Julie; GILORMINI, Pierre
A three-dimensional cubic Monte Carlo lattice model is considered to test the impact of volume on the molecularmobility of amorphous polymers. Assuming classic polymer chain dynamics, the concept of locked volume limiting the accessible volume around the polymer chains is introduced. The polymer mobility is assessed by its ability to explore the entire lattice thanks to reptation motions. When recording the polymer mobility with respect to the lattice accessible volume, a sharp mobility transition is observed as witnessed during glass transition. The model ability to reproduce known actual trends in terms of glass transition with respect to material parameters, is also tested.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10985/114392017-01-01T00:00:00ZDIANI, JulieGILORMINI, PierreA three-dimensional cubic Monte Carlo lattice model is considered to test the impact of volume on the molecularmobility of amorphous polymers. Assuming classic polymer chain dynamics, the concept of locked volume limiting the accessible volume around the polymer chains is introduced. The polymer mobility is assessed by its ability to explore the entire lattice thanks to reptation motions. When recording the polymer mobility with respect to the lattice accessible volume, a sharp mobility transition is observed as witnessed during glass transition. The model ability to reproduce known actual trends in terms of glass transition with respect to material parameters, is also tested.Study on the temperature dependence of the bulk modulus of polyisoprene by molecular dynamics simulations
http://hdl.handle.net/10985/6677
Study on the temperature dependence of the bulk modulus of polyisoprene by molecular dynamics simulations
DIANI, Julie; FAYOLLE, Bruno; GILORMINI, Pierre
The temperature dependence of the bulk modulus of polyisoprene has been studied using molecular dynamics simulations. Virtual polyisoprenes have been submitted to volume contractions above and below the glass transition. Bulk modulus has been observed to be linearly dependent on temperature both above and below the glass transition respectively, and it dropped by a factor of about 2 while temperatures was risen above the glass transition. By monitoring the energy changes during volume contractions, it was observed that the bulk modulus arises mainly from the Van de Waals interactions. Nevertheless, the entropy contribution to the bulk modulus becomes significant above the glass transition. At a first order, the entropy part of the bulk modulus can be considered as independent on the temperature.
Tue, 01 Jan 2008 00:00:00 GMThttp://hdl.handle.net/10985/66772008-01-01T00:00:00ZDIANI, JulieFAYOLLE, BrunoGILORMINI, PierreThe temperature dependence of the bulk modulus of polyisoprene has been studied using molecular dynamics simulations. Virtual polyisoprenes have been submitted to volume contractions above and below the glass transition. Bulk modulus has been observed to be linearly dependent on temperature both above and below the glass transition respectively, and it dropped by a factor of about 2 while temperatures was risen above the glass transition. By monitoring the energy changes during volume contractions, it was observed that the bulk modulus arises mainly from the Van de Waals interactions. Nevertheless, the entropy contribution to the bulk modulus becomes significant above the glass transition. At a first order, the entropy part of the bulk modulus can be considered as independent on the temperature.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.Effect of the Mullins softening on mode I fracture of carbon-black filled rubbers
http://hdl.handle.net/10985/9887
Effect of the Mullins softening on mode I fracture of carbon-black filled rubbers
DIANI, Julie; BRIEU, Mathias; BATZLER, Katharina; ZERLAUTH, Pierre
The effect of the Mullins softening on mode I fracture of carbon-black filled rubbers was investigated experimentally. Large specimen of NR and SBR filled with the same amount and nature of carbon-black were submitted to uniaxial tension. Then, single edge notch tension samples were cut along various directions with respect to the direction of preconditioning, and submitted to tension until break. The fracture energy was estimated and compared according to the intensity of Mullins softening already undergone in the direction of crack opening and according to the softening undergone in other directions. The NR shows significantly improved resistance to crack propagation compared to the SBR due to its crystallization ability. For both materials, it was observed that a moderate prestrain has a positive impact increasing the material fracture toughness and that material softening and anisotropy induced by Mullins effect does not show on resistance to mode I crack propagation.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10985/98872015-01-01T00:00:00ZDIANI, JulieBRIEU, MathiasBATZLER, KatharinaZERLAUTH, PierreThe effect of the Mullins softening on mode I fracture of carbon-black filled rubbers was investigated experimentally. Large specimen of NR and SBR filled with the same amount and nature of carbon-black were submitted to uniaxial tension. Then, single edge notch tension samples were cut along various directions with respect to the direction of preconditioning, and submitted to tension until break. The fracture energy was estimated and compared according to the intensity of Mullins softening already undergone in the direction of crack opening and according to the softening undergone in other directions. The NR shows significantly improved resistance to crack propagation compared to the SBR due to its crystallization ability. For both materials, it was observed that a moderate prestrain has a positive impact increasing the material fracture toughness and that material softening and anisotropy induced by Mullins effect does not show on resistance to mode I crack propagation.Stress-strain response and volume change of a highly filled rubbery composite: experimental measurements and numerical simulations
http://hdl.handle.net/10985/11804
Stress-strain response and volume change of a highly filled rubbery composite: experimental measurements and numerical simulations
GILORMINI, Pierre; TOULEMONDE, Paul-Aymé; DIANI, Julie; GARDERE, Antoine
The stress-strain response of a rubbery polymer network highly filled with micrometric glass beads was measured at low strain rate in uniaxial tension. The volume change of the glass bead filled material upon stretching was recorded by video extensometry and X-ray tomography scans were used to identify the type of damage within the composite material. The modeling used a cohesive-zone model from the literature depending on the polymer/glass adhesion energy that was measured by peeling polymer strips from a glass plate. Nonlinear finite element simulations were performed on representative three-dimensional microstructures defined by periodic cubic unit cells containing randomly dispersed spherical particles}. Good reproductions of both the composite response and the volume change were obtained prior to the appearance of inner cracks.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10985/118042017-01-01T00:00:00ZGILORMINI, PierreTOULEMONDE, Paul-AyméDIANI, JulieGARDERE, AntoineThe stress-strain response of a rubbery polymer network highly filled with micrometric glass beads was measured at low strain rate in uniaxial tension. The volume change of the glass bead filled material upon stretching was recorded by video extensometry and X-ray tomography scans were used to identify the type of damage within the composite material. The modeling used a cohesive-zone model from the literature depending on the polymer/glass adhesion energy that was measured by peeling polymer strips from a glass plate. Nonlinear finite element simulations were performed on representative three-dimensional microstructures defined by periodic cubic unit cells containing randomly dispersed spherical particles}. Good reproductions of both the composite response and the volume change were obtained prior to the appearance of inner cracks.