Some Good Practices to BuildRobust DIGIMAT Constitutive Models on Polyamide Matrixes Gilles ROBERT/Olivier MOULINJEUNE Gilles ROBERT Rhodia : Who are we ? Rhodia Polyamide Engineering plastics Rhodia group Gilles ROBERT Organics & Services 2007 net sales : €5 billion Performance Materials Functional Chemicals Novecare Polyamide Eco Services Organics Energy Services Silcea Acetow Rhodia in 2009: an undisputed leader in its core businesses 80 percent of sales generated in markets where the Group is number 1, 2 or 3 worldwide 36 percent of sales generated in fast-growing regions: Asia Pacific and Latin America Gilles ROBERT 18 PRODUCTION sites 1 566 EMPLOYEES 17% OF SALES Rhodia in 2009: a global presence 20 PRODUCTION sites 3 210 EMPLOYEES 20% OF SALES 7 PRODUCTION sites 3 063 EMPLOYEES 16% OF SALES 24 PRODUCTION sites 8 085 EMPLOYEES 47% OF SALES Gilles ROBERT Rhodia Polyamide Engineering plastics Rhodia group Rhodia Gilles ROBERT Rhodia Polyamide Performance Materials Intermediates & Polymers N°2 worldwide in Polyamide 6.6 Engineering Plastics N°3 worldwide Gilles ROBERT Industrial sites 14 plants worldwide N°2 in Polyamide 6.6 N°3 in Engineering Plastics Polyamide: A sustainable pillar of Rhodia 40%Group Net Sales 41%Group Recurring EBITDA Net Sales € 1,975 million Employees 4,000 2007 data Gilles ROBERT Rhodia Polyamide Engineering plastics Rhodia group Rhodia Gilles ROBERT Leveraging our mastery of the PA 6.6 chain: from intermediates to polymers and compounds • Polymers and compounds with improved ageing and high temperature performances • Cost effective polymers and compounds with improved "Flowability" and surface aspects • Compounds with higher dimensional stability • Application development • Design support Gilles ROBERT Summary Data used for matrix behaviour identification Impact of data quality on modeling : some examples Building an elastoplastic model : impact of input data What should be taken into account in the constitutive model Gilles ROBERT Summary Data used for matrix behaviour identification Impact of data quality on modeling : some examples Building an elastoplastic model : impact of input data What should be taken into account in the constitutive model Gilles ROBERT Matrix identification with Digimat : input data • The material : Polyamide 6.6 filled with glass fibres • The target : identify PA66 matrix mechanical properties • Glass properties necessary : • Modulus, density, Poisson’s ratio • No specific difficulty • Glass fibres properties : • Weight fraction • Measured after burning away the polymer • Simple and accurate, weak fluctuations • Aspect ratio • Measured by image processing • Accuracy can be sometimes be questioned • Orientation • Modelled • Or measured • Accuracy must be questioned Gilles ROBERT Quantification of orientation • Injection molding of short glass fibres reinforced polymer generates orientation • Orientation of a fiber is described with • θ,φ Euler angles • Many ways to represent orientation of a population : • Ψ (θ, φ) distribution function • No information loss • Orientation tensors • Hand (’62) • Tensors and orientation functions represent only a part of total information available in Ψ (θ, φ) x y z | u | | | | . | \ | = | | | | . | \ | u | u | u cos sin sin cos sin 3 2 1 p p p Gilles ROBERT Orientation tensor a 2 • a 2 is the most common representation of fiber orientation • Used by Folgar and Tucker model • Essential in injection Molding • Used by Moldflow, Moldex, REM3D… • a 2 must be used simultaneously with a 4 • a 4 expressed as a function of a 2 thanks to closure approximations ( ( ( ( ( ¸ ( ¸ · · · · · · · · · · · · · u | u u | u u | u u | u | | u | u u | | u | u 2 2 2 2 2 2 2 cos sin cos sin cos cos sin sin cos sin sin sin cos sin sin cos cos sin cos sin sin cos sin ( ( ¸ ( ¸ 0 0 0 1 ( ( ¸ ( ¸ 1 0 0 0 ( ( ¸ ( ¸ 5 , 0 0 0 5 , 0 Gilles ROBERT Summary Data used for matrix behaviour identification Impact of data quality on modeling : some examples Building an elastoplastic model : impact of input data What should be taken into account in the constitutive model Gilles ROBERT Summary Data used for matrix behaviour identification Impact of data quality on modeling : some examples Building an elastoplastic model : impact of input data What should be taken into account in the constitutive model Gilles ROBERT Approach followed • How to identify the impact of input data on matrix elastic modulus identification ? • Input mechanical data : modulus of a dumbbell • Study of changes • In orientation tensor used • … on the matrix modulus identified • Then comparison with modulus measured for several orientations and those modelled. Gilles ROBERT Impact of orientation tensors on identifications • Three tensors : • Measured • Modelled with Moldflow Mid Plane • Automatic choice of parameters • Modelled with Moldflow MidPlane, • Optimised parameters • Constant aspect ratio • Same composite modulus for identification • Mistake quite important 360 100 50 100 2 Thickness=2,1mm 100 1 gate 0 0,2 0,4 0,6 0,8 1 1,2 0 500 1000 1500 2000 Position in thickness (µm) o r i e n t a t i o n a 1 1 Expérimental Auto Optimum a 2 Moldflow auto E matrix =2715 MPa a 2 Moldflow opt. E matrix =3460 MPa a 2 µtomo E matrix =3250 MPa Gilles ROBERT Impact of mistakes : general case • Use of Moldflow mid plane requires precautions • With optimised parameters : good predictions • Though not perfect • Auto modelling : 25% max. mistake • Best choice for identification : measured tensors 4000 5000 6000 7000 8000 9000 10000 11000 0 20 40 60 80 100 Angle between fibres and strain applied (°) M o d u l u s ( M P a ) Experimental values Modelled values_a2_Moldflow_auto Modelled values_a2_Moldflow_optim Modelled values_a2_µtomo Gilles ROBERT First conclusions • First good practises : • Be careful with Moldflow mid plane • Optimised parameters are compulsory for good data fitting • And experimental measurements of orientation are even better • Sensitivity to aspect ratio is lower, but only in the linear range! Gilles ROBERT Summary Data used for matrix behaviour identification Impact of data quality on modeling : some examples Building an elastoplastic model : impact of input data What should be taken into account in the constitutive model Gilles ROBERT Summary Data used for matrix behaviour identification Impact of data quality on modeling : some examples Building an elastoplastic model : impact of input data What should be taken into account in the constitutive model Gilles ROBERT 0 50 100 150 200 250 0,0 0,5 1,0 1,5 2,0 2,5 3,0 3,5 Engineering Strain (%) E n g i n e e r i n g S t r e s s ( M P a ) 0 50 100 150 200 250 0,0 0,5 1,0 1,5 2,0 2,5 3,0 3,5 Engineering Strain (%) E n g i n e e r i n g S t r e s s ( M P a ) Bottom line • Minimal values necessary for matrix identification : • Tensile curve “ISO 527” as found in Campus • Moldflow modelling of the dumbbell • Aspect ratio (nicely given in Moldflow) • Identification of elastoplastic behaviour of the matrix • Modulus • Re • R ∞ • m • Use of spectral method for homogenisation E matrix 3020 MPa R E 14,1 MPa R ∞ 34,8 MPa m 258,8 ∑( R E + R ∞ ) 48,9 MPa Gilles ROBERT Bottom line : comparison with tensile trials at several angles • Constitutive model applied to tensile specimens cut in plaques • Same aspect ratio • Structure modelled with MF • 23°C, dry, 10 -3 s -1 • Results are rather good • However • Between 5% and 25% mistake on elastic modulus • Between 5% and 20% mistake on stresses Lines : experiments Dots : Digimat 0 50 100 150 200 0,00 0,02 0,04 0,06 0,08 0,10 True strain T r u e s t r e s s ( M P a ) fibres 0° 15° 30° 45° 60° 90° Gilles ROBERT How to go further ? (1) • Always with a single tensile curve • Use optimised parameters in Moldflow • Use measured aspect ratios • Re quite sensitive to aspect ratio • Or use direct measured orientation tensors • Laws quite dissimilar. Which one is best ? AR literature a 2 MF auto Measured AR a 2 MF auto Measured AR a 2 MF optim Measured AR Measured a 2 E matrix 3017 3080 2715 3406 R E 14,1 15,2 20,3 20,7 R ∞ 34,8 36,2 27,5 36,7 m 258,8 270,9 234,6 248,3 ∑( R E + R ∞ ) 48,9 51,4 47,8 57,4 Gilles ROBERT How to go further ? (2) • The only way to discriminate the models : • Use at least 2 tensile curves. • With measured input data, transverse behaviour is better predicted • Which improvement to expect ? 0 50 100 0,00 0,02 0,04 0,06 0,08 0,10 True strain T r u e s t r e s s ( M P a ) fibres 90° exp 90° "bottom line" 90° one curve, measured structure Gilles ROBERT Matrix behaviour identification with two tensile curves • Choice of an identification based on two tension curves with varying angles • 0 and 30° • 0 and 45° • 0 and 90° • Experimental conditions • Room temperature • Strain rate 10-3s-1 • Material : dry polyamide 66 filled with 30w% glass fibers Gilles ROBERT Results • Identifications quite OK • 0-45°fits slightly better 0°-30° 0°-45° 0°-90° 0 20 40 60 80 100 120 140 160 180 200 0,00 0,02 0,04 0,06 0,08 Strain S t r e s s ( M P a ) Trac_Digi_0 (0°-45°) Trac_Digi_45 (0°-45°) Trac_exp_0 Trac_exp_45 0 20 40 60 80 100 120 140 160 180 200 0,00 0,01 0,02 0,03 0,04 0,05 0,06 Strain S t r e s s ( M P a ) Trac_Digi_0 (0°-90°) Trac_Digi_90 (0°-90°) Trac_exp_0 Trac_exp_90 0 20 40 60 80 100 120 140 160 180 200 0,00 0,01 0,02 0,03 0,04 0,05 0,06 Strain S t r e s s ( M P a ) Trac_Digi_0 (0°-30°) Trac_Digi_30 (0°-30°) Trac_exp_0 Trac_exp_30 Gilles ROBERT Conclusions • Accuracy only slightly improved • 0°-90°is not the best choice to build a matrix constitutive model • Main change : R E is much higher when two tensile curves are used • Matrix plasticization changes much, while tensile behaviour is quite constant • Optimal method to identify a constitutive model still not found Identification 0°-30° Identification 0°-45° Identification 0°-90° E matrix 3050 3050 3050 R E (MPa) 36,8 39,5 39,8 R ∞ (MPa) 12 14,8 22,9 m 241,2 96,8 54,6 ∑(R E+ R ∞ ) (MPa) 48,8 54,3 62,7 Gilles ROBERT Matrix identification with six tensile curves • For some specific conditions • W% fibres • Temperature • Water content • Strain rate • Six different orientations have been tested. • Optimal fit is performing • Except at 30° • And 90° • If two curves only are used : best choice 0°and 45° • Constitutive models for 6 curves or 2 curves, 0°and 45°are close Gilles ROBERT • Use of modified spectral • Modulus and Poisson’ ratio fixed • R E • R ∞ • m • 3/4 possible parameters • free variables • Residual mistake on stresses reduced from 8% to 4,5% • Situation worse at 0° • But much better on all other angles Change of isotropisation method 0 20 40 60 80 100 120 140 160 180 200 0 0,01 0,02 0,03 0,04 0,05 0,06 0,07 0,08 True strain T r u e s t r e s s ( M P a ) 0°_exp 15°_exp 30°_exp 45°_exp 60°_exp 90°_exp 0° Digi 15°_Digi 30°_Digi 45°_Digi 60°_Digi 90°_Digi 0 20 40 60 80 100 120 140 160 180 200 0 0,02 0,04 0,06 0,08 True strain T r u e s t r e s s ( M P a ) 0°_exp 15°_exp 30°_exp 45°_exp 60°_exp 90°_exp 0° Digi 15°_Digi 30°_Digi 45°_Digi 60°_Digi 90°_Digi Gilles ROBERT Extension of constitutive models • Constitutive model of the matrix determined for • Several w% fibres • Several w% water • Several temperatures and strain rates • For many sets of parameters : three tensile curves measured • Main conclusions : • Parameters of modified spectral isotropisation methods are constant • 18 sets of three tensile curves • Each time identification converges towards similar values • Aspect ratio and orientation have a big impact • Especially on R E 87,5 72,6 62,3 51,9 ∑(R E +R ∞ ) (MPa) 120,6 174,7 118,8 96,2 m (MPa) 52,1 37,1 26,4 14,1 R ∞ (MPa) 36,4 35,5 35,9 37,8 R E (MPa) 3240 3050 3240 3050 E matrix (MPa) 6 curves several w% fibres optimal modified spectral 6 curves 1w% fibres optimal modified spectral 6 curves several w% fibres spectral 6 curves 1w% fibres spectral 87,5 72,6 62,3 51,9 ∑(R E +R ∞ ) (MPa) 120,6 174,7 118,8 96,2 m (MPa) 52,1 37,1 26,4 14,1 R ∞ (MPa) 36,4 35,5 35,9 37,8 R E (MPa) 3240 3050 3240 3050 E matrix (MPa) 6 curves several w% fibres optimal modified spectral 6 curves 1w% fibres optimal modified spectral 6 curves several w% fibres spectral 6 curves 1w% fibres spectral Gilles ROBERT Extension of constitutive models (2) • Comparison between experimental matrix and real matrix • With spectral modified method, both curves are very close • But of course, you have to choose the right values for the four parameters…. 0 10 20 30 40 50 60 70 80 90 100 0,00 0,05 0,10 0,15 0,20 Déformation C o n t r a i n t e ( M P a ) 10-4s-1 10-3s-1 10-2s-1 10-3s-1 exp 10-4s-1 exp Strain S t r e s s ( M P a ) Gilles ROBERT Conclusions • To develop good constitutive models : • Be careful about orientation modelling • Except if optimised parameters are available • Use at least two tensile curves • Or the yield won’t be determined accurately • Choose the right angles • Avoid transverse tensile tests • Be very careful about the microstructure • Preferred measured characteristics • If you really want accuracy : • Work on isotropisation method • And take carefully into account the polymer behaviour! Gilles ROBERT Summary Data used for matrix behaviour identification Impact of data quality on modeling : some examples Building an elastoplastic model : impact of input data What should be taken into account in the constitutive model Gilles ROBERT Summary Data used for matrix behaviour identification Impact of data quality on modeling : some examples Building an elastoplastic model : impact of input data What should be taken into account in the constitutive model ? Gilles ROBERT Extension of constitutive models : what’s next ? • Polyamide behaviour is not equal in tension and compression. • Difference between both solicitations depends on : • Temperature • W% of fibres • Constitutive models used should be pressure sensitive. • Drücker-Präger ? 0 50 100 150 200 250 0,00 0,02 0,04 0,06 0,08 0,10 0,12 0,14 0,16 True strain T r u e s t r e s s ( M P a ) 0°_tensile 15°_tensile 45°_tensile 60°_tensile 0°_compression 15°_compression 45°_compression 60°_compression Gilles ROBERT • Polymers close to glass transition are not elastoviscoplastic • They are also viscoelastic • Models developed on purpose are a necessity Extension of constitutive models : what’s next ? Frequency(Hz) M o d u l u s ( M P a ) 23°C 0 20 40 60 80 100 120 140 160 0 0,02 0,04 0,06 0,08 0,1 0,12 0,14 Strain S t r e s s ( M P a ) 100s -1 10 -4 s -1 Gilles ROBERT DIGIMAT-MX release : Rhodia offer • Based on the identification work presented here … • Accurate aspect ratio distribution measurement • µTomography for experimental fiber orientation tensors • Large experimental database in tension, compression and high speed • At various speed, temperature and humidity content • Accurate retro fitting of matrix properties • Global model identified : F ( T , W% , c , Moisture ) to generate a coherent database • RHODIA Polyamide offers two levels of availability for all TECHNYL PA66 grades from 15% to 50% : • Direct access to : • all elastic models, in temperature and humidity • elasto-plastic models, at 23°and 60°C dry and conditioned • On demand access to : • all temperature elasto-plastic models • all temperature elasto-visco plastic models • Thermo-elastic and dilatation models • All data are directly usable in Digimat as .mat file ! . Gilles ROBERT Thank you for your attention Rhodia : Who are we ? Rhodia group Rhodia Polyamide Engineering plastics Gilles ROBERT Rhodia in 2009: an undisputed leader in its core businesses Performance Materials Functional Chemicals Organics & Services Polyamide Novecare Eco Services Organics Acetow Silcea Energy Services 2007 net sales : €5 billion 80 percent of sales generated in markets where the Group is number 1, 2 or 3 worldwide 36 percent of sales generated in fast-growing regions: Asia Pacific and Latin America Gilles ROBERT Rhodia in 2009: a global presence 18 PRODUCTION sites 24 PRODUCTION sites 1 566 EMPLOYEES 8 085 EMPLOYEES 17% OF SALES 47% OF SALES 7 PRODUCTION sites 20 PRODUCTION sites 3 063 EMPLOYEES 3 210 EMPLOYEES 16% OF SALES 20% OF SALES Gilles ROBERT Rhodia Rhodia group Rhodia Polyamide Engineering plastics Gilles ROBERT . Rhodia Polyamide Performance Materials Engineering Plastics N°3 worldwide Intermediates & Polymers N°2 worldwide in Polyamide 6.6 Gilles ROBERT . 6 N°3 in Engineering Plastics 40% Group Net Sales 41% Group Recurring EBITDA Gilles ROBERT .Polyamide: A sustainable pillar of Rhodia 2007 data Net Sales € 1.000 N°2 in Polyamide 6.975 million Industrial sites 14 plants worldwide Employees 4. Rhodia Rhodia group Rhodia Polyamide Engineering plastics Gilles ROBERT . Leveraging our mastery of the PA 6.6 chain: from intermediates to polymers and compounds • Polymers and compounds with improved ageing and high temperature performances Cost effective polymers and compounds with improved "Flowability" and surface aspects Compounds with higher dimensional stability Application development Design support • • • • Gilles ROBERT . Summary Data used for matrix behaviour identification Impact of data quality on modeling : some examples Building an elastoplastic model : impact of input data What should be taken into account in the constitutive model Gilles ROBERT . Summary Data used for matrix behaviour identification Impact of data quality on modeling : some examples Building an elastoplastic model : impact of input data What should be taken into account in the constitutive model Gilles ROBERT . weak fluctuations • Aspect ratio • Measured by image processing • Accuracy can be sometimes be questioned • Orientation • Modelled • Or measured • Accuracy must be questioned Gilles ROBERT .Matrix identification with Digimat : input data • The material : Polyamide 6.6 filled with glass fibres • The target : identify PA66 matrix mechanical properties • Glass properties necessary : • Modulus. density. Poisson’s ratio • No specific difficulty • Glass fibres properties : • Weight fraction • Measured after burning away the polymer • Simple and accurate. Quantification of orientation z • • y Injection molding of short glass fibres reinforced polymer generates orientation Orientation of a fiber is described with • θ. φ) q • x f p1 sin q cos f p 2 sin q sin f p cos q 3 Gilles ROBERT .φ Euler angles Many ways to represent orientation of a population : • Ψ (θ. φ) distribution function • • • No information loss Orientation tensors • Hand (’62) Tensors and orientation functions represent only a part of total information available in Ψ (θ. 5 • a2 is the most common representation of fiber orientation • Used by Folgar and Tucker model • Essential in injection Molding • Used by Moldflow. Moldex. REM3D… • a2 must be used simultaneously with a4 • a4 expressed as a function of a2 thanks to closure approximations Gilles ROBERT .Orientation tensor a2 sin 2 q cos 2 f sin 2 q sin f cos f sin q cos q cos f sin 2 q sin f cos f sin 2 q sin 2 f sin q cos q sin f sin q cos q cos f sin q cos q sin f 2 cos q 1 0 0 0 0 0 0 1 0.5 0 0 0. Summary Data used for matrix behaviour identification Impact of data quality on modeling : some examples Building an elastoplastic model : impact of input data What should be taken into account in the constitutive model Gilles ROBERT . Summary Data used for matrix behaviour identification Impact of data quality on modeling : some examples Building an elastoplastic model : impact of input data What should be taken into account in the constitutive model Gilles ROBERT . Gilles ROBERT .Approach followed • How to identify the impact of input data on matrix elastic modulus identification ? • Input mechanical data : modulus of a dumbbell • Study of changes • In orientation tensor used • … on the matrix modulus identified • Then comparison with modulus measured for several orientations and those modelled. • Optimised parameters orientation a11 1 • Measured • Modelled with Moldflow Mid Plane 0.2 • Three tensors : • Automatic choice of parameters • Modelled with Moldflow MidPlane.1mm .4 • Constant aspect ratio • Same composite modulus for identification 0. a2 µtomo Gilles ROBERT Ematrix=3460 MPa Ematrix=3250 MPa gate 1 2 100 Thickness=2.2 Expérimental Auto Optimum 0 0 500 1000 1500 2000 • Mistake quite important 100 Position in thickness (µm) 360 100 50 a2 Moldflow auto Ematrix=2715 MPa a2 Moldflow opt.Impact of orientation tensors on identifications 1.8 0.6 0. mistake • Best choice for identification : measured tensors 0 20 40 60 80 100 Angle between fibres and strain applied (°) Gilles ROBERT .Impact of mistakes : general case 11000 • Use of Moldflow mid plane requires precautions 10000 9000 Experimental values Modelled values_a2_Moldflow_auto Modelled values_a2_Moldflow_optim Modelled values_a2_µtomo • With optimised parameters : good predictions • Though not perfect Modulus (MPa) 8000 7000 6000 5000 4000 • Auto modelling : 25% max. but only in the linear range! Gilles ROBERT .First conclusions • First good practises : • Be careful with Moldflow mid plane • Optimised parameters are compulsory for good data fitting • And experimental measurements of orientation are even better • Sensitivity to aspect ratio is lower. Summary Data used for matrix behaviour identification Impact of data quality on modeling : some examples Building an elastoplastic model : impact of input data What should be taken into account in the constitutive model Gilles ROBERT . Summary Data used for matrix behaviour identification Impact of data quality on modeling : some examples Building an elastoplastic model : impact of input data What should be taken into account in the constitutive model Gilles ROBERT . 0 3.5 Engineering Strain (%) Ematrix RE R∞ 3020 MPa 14.0 2.8 MPa • m ∑( RE+ R∞) 258.9 MPa Gilles ROBERT .5 3.0 0.5 1.Bottom line Engineering Stress (MPa) 250 • Minimal values necessary for matrix identification : • Tensile curve “ISO 527” as found in Campus • Moldflow modelling of the dumbbell • Aspect ratio (nicely given in Moldflow) 200 150 100 50 • Identification of elastoplastic behaviour of the matrix • Modulus • Re • R∞ • m Use of spectral method for homogenisation 0 0.5 2.1 MPa 34.0 1.8 48. 00 0.08 0.04 0.06 0.10 True strain Gilles ROBERT .Bottom line : comparison with tensile trials at several angles Lines : experiments Dots : Digimat • Constitutive model applied to tensile True stress (MPa) specimens cut in plaques • Same aspect ratio • Structure modelled with MF • 23°C. dry. 10-3s-1 200 0° 15° fibres 150 30° 100 • Results are rather good • However • Between 5% and 25% mistake on elastic modulus • Between 5% and 20% mistake on stresses 45° 90° 60° 50 0 0.02 0. 6 47.2 36.5 234.3 57.8 20.9 51.How to go further ? • Always with a single tensile curve • Use optimised parameters in Moldflow • Use measured aspect ratios • Re quite sensitive to aspect ratio • Or use direct measured orientation tensors (1) • Laws quite dissimilar.3 27.7 248.8 48.1 34.4 .7 36. Which one is best ? AR literature a2 MF auto Measured AR a2 MF auto 3080 Measured AR a2 MF optim 2715 Measured AR Measured a2 3406 Ematrix 3017 RE R∞ m ∑( RE+ R∞) Gilles ROBERT 14.9 15.4 20.2 270.8 258. • With measured input data.02 0.00 0.08 0.04 0.06 0.10 True strain Gilles ROBERT . True stress (MPa) 90° exp 90° one curve. measured structure 90° "bottom line" transverse behaviour is better predicted 50 • Which improvement to expect ? fibres 0 0.How to go further ? • The only way to discriminate the models : 100 (2) • Use at least 2 tensile curves. Matrix behaviour identification with two tensile curves • Choice of an identification based on two tension curves with varying angles • 0 and 30° • 0 and 45° • 0 and 90° Experimental conditions • Room temperature • Strain rate 10-3s-1 • Material : dry polyamide 66 filled with 30w% glass fibers • Gilles ROBERT . 06 0.00 0.00 0.01 0.05 0.03 0°-90° Stress (MPa) 140 120 100 80 60 40 20 0 0.04 0.02 Trac_Digi_0 (0°-30°) Trac_Digi_30 (0°-30°) Trac_exp_0 Trac_exp_30 0.04 0.01 0.02 0.04 0°-45° • • Identifications quite OK 0-45° fits slightly better Trac_Digi_0 (0°-45°) Trac_Digi_45 (0°-45°) Trac_exp_0 Trac_exp_45 0.06 Trac_Digi_0 (0°-90°) Trac_Digi_90 (0°-90°) Trac_exp_0 Trac_exp_90 0.02 0.03 0.05 0.00 200 0.200 Results Stress (MPa) 180 160 140 120 100 80 60 40 20 0 0.06 Strain Gilles ROBERT Strain .08 Strain 200 180 160 0°-30° Stress (MPa) 180 160 140 120 100 80 60 40 20 0 0. 8 12 241.2 3050 39.8 3050 39.6 ∑(RE+R∞) (MPa) Gilles ROBERT 48. while tensile behaviour is quite constant • Optimal method to identify a constitutive model still not found Identification 0°-30° Identification 0°-45° Identification 0°-90° Ematrix RE (MPa) R∞ (MPa) m 3050 36.9 54.Conclusions • Accuracy only slightly improved • 0°-90° is not the best choice to build a matrix constitutive model • Main change : RE is much higher when two tensile curves are used • Matrix plasticization changes much.5 14.8 54.8 96.7 .3 62.8 22. • Optimal fit is performing • Except at 30° • And 90° • If two curves only are used : best choice 0° and 45° • Constitutive models for 6 curves or 2 curves. 0° and 45° are close Gilles ROBERT .Matrix identification with six tensile curves • For some specific conditions • • • • W% fibres Temperature Water content Strain rate • Six different orientations have been tested. Change of isotropisation method • Use of modified spectral • • • • • • Modulus and Poisson’ ratio fixed RE R∞ m 3/4 possible parameters free variables 200 180 2 1 True stress (MPa) True stress (MPa) 160 140 120 100 80 60 40 20 • Residual mistake on stresses reduced from 8% to 4.02 0.08 True strain Gilles ROBERT .04 0.5% 0°_exp 15°_exp 30°_exp 45°_exp 60°_exp 90°_exp 0° Digi 15°_Digi 30°_Digi 45°_Digi 60°_Digi 90°_Digi 1 1 1 1 • Situation worse at 0° • But much better on all other angles 0 0 0.06 0. 2 51.5 37.3 3050 35.1 174.6 87.Extension of constitutive models • Constitutive model of the matrix determined for • Several w% fibres • Several w% water • Several temperatures and strain rates For many sets of parameters : three tensile curves measured Main conclusions : • Parameters of modified spectral isotropisation methods are constant • 18 sets of three tensile curves • Each time identification converges towards similar values • • • Aspect ratio and orientation have a big impact • Especially on RE 6 curves 1w% fibres spectral Ematrix (MPa) RE (MPa) R∞ (MPa) m (MPa) ∑(RE+R∞) (MPa) Gilles ROBERT 6 curves several w% fibres spectral 6 curves 1w% fibres optimal modified spectral 6 curves several w% fibres optimal modified spectral 3050 37.7 72.5 .4 118.1 120.8 62.1 96.9 3240 35.9 26.6 3240 36.8 14.4 52. both curves are very close • But of course.00 0. you have to choose the right values for the four parameters….Extension of constitutive models (2) 100 • Comparison between experimental matrix and real matrix 90 80 • With spectral modified method.10 0.05 0. Contrainte (MPa) Stress (MPa) 70 60 50 40 30 20 10 0 0.15 0.20 10-4s-1 10-3s-1 10-2s-1 10-3s-1 exp 10-4s-1 exp Déformation Strain Gilles ROBERT . Conclusions • To develop good constitutive models : • Be careful about orientation modelling • Except if optimised parameters are available • Use at least two tensile curves • Or the yield won’t be determined accurately • Choose the right angles • Avoid transverse tensile tests • Be very careful about the microstructure • Preferred measured characteristics • If you really want accuracy : • Work on isotropisation method • And take carefully into account the polymer behaviour! Gilles ROBERT . Summary Data used for matrix behaviour identification Impact of data quality on modeling : some examples Building an elastoplastic model : impact of input data What should be taken into account in the constitutive model Gilles ROBERT . Summary Data used for matrix behaviour identification Impact of data quality on modeling : some examples Building an elastoplastic model : impact of input data What should be taken into account in the constitutive model ? Gilles ROBERT . Extension of constitutive models : what’s next ? • Polyamide behaviour is not equal in tension and compression. • Drücker-Präger ? 50 0°_tensile 15°_tensile 45°_tensile 60°_tensile 0°_compression 15°_compression 45°_compression 60°_compression 0.12 0.02 0.06 0.08 0.00 True strain Gilles ROBERT .14 0. 250 • Difference between both True stress (MPa) 200 solicitations depends on : • Temperature • W% of fibres 150 100 • Constitutive models used should be pressure sensitive.16 0 0.04 0.10 0. 12 0.Extension of constitutive models : what’s next ? • Polymers close to glass transition are • • not elastoviscoplastic They are also viscoelastic Models developed on purpose are a necessity Stress (MPa) 160 140 120 100 80 60 40 20 0 23°C 100s-1 10-4s-1 Modulus (MPa) 0 0.06 0.1 0.02 0.04 0.08 0.14 Strain Frequency(Hz) Gilles ROBERT . . compression and high speed • At various speed.DIGIMAT-MX release : Rhodia offer • Based on the identification work presented here … • Accurate aspect ratio distribution measurement • µTomography for experimental fiber orientation tensors • Large experimental database in tension.mat file ! Gilles ROBERT . Moisture ) to generate a coherent database F ( T . in temperature and humidity • elasto-plastic models. W% . RHODIA Polyamide offers two levels of availability for all TECHNYL PA66 grades from 15% to 50% : • Direct access to : • all elastic models. at 23° and 60°C dry and conditioned • On demand access to : • all temperature elasto-plastic models • all temperature elasto-visco plastic models • Thermo-elastic and dilatation models • All data are directly usable in Digimat as . temperature and humidity content • Accurate retro fitting of matrix properties Global model identified : • • . Thank you for your attention Gilles ROBERT .
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