Micro-mechanics based fatigue modeling and validation of the damage behavior of short wavy fiber composites Yasmine Abdin*, Atul Jain, Ignaas Verpoest, Stepan V. Lomov, Department of Metallurgy and Materials Engineering, KULeuven, Belgium 09/04/2015 Yasmine Abdin COMPTEST 2015, Madrid 1 Short wavy steel fiber composites • Short steel fiber composites are novel material combining outstanding properties of stiffness and ductility. • Typically used for improved shielding properties of polymers. • Processing of injection molded short steel fiber composites leads to significant fiber waviness. VF 0.5% VF 2% Very dense and wavy structures at low volume fractions 09/04/2015 Yasmine Abdin COMPTEST 2015, Madrid 2 Micro-Mechanics based fatigue model: solution overview Interfacing •Ψ(L) •Ψ(θ,φ) •waviness (MOSCO.Translate) •For each segment i •Xc(i), Yc(i), Zc(i) •l(i) •Θ(i), φ(i) Geometrical Model (MOSCO.GEO) Geometrical model • Modeling of an RVE of wavy fiber with described fiber waviness, random orientation, length distribution • Validation with microCT scans of real samples 09/04/2015 Damage •Ceff •<σ(i)>, <ε(i)> •Plasticity of matrix •Plasticity of fibers •Debonding •Breakage Micro-Mechanical Model (MOSCO.MICRO) •Cyclic failure criteria •Final output: cyclic damage of composite •Stiffness degradation of composite Fatigue MicroAnalyzer (MOSCO.FAT) Micro-mechanical elastic model Damage model Fatigue model •Extension of Mori-Tanaka solution to wavy fibers •Validation needed for MicroMechanical model for: -prediction of overall composite effective response -- prediction of the local stress and strain states in inclusions <σ(i)>, <ε(i)> • Modeling and validation of nonlinear plasticity behavior of matrix • Modeling and validation of damage of the wavy fiber composite • Modeling and validation of fatigue lifetime of short fiber composites based on input of fatigue life of constituents Yasmine Abdin COMPTEST 2015, Madrid 3 Characterization and modeling of geometry of short steel fiber composites Geometrical characterization of short steel fiber composites Micro-CT characterization for determination of geometrical parameters 09/04/2015 Yasmine Abdin COMPTEST 2015, Madrid 5 Micro-structural modeling of wavy fibers 09/04/2015 Yasmine Abdin COMPTEST 2015, Madrid 6 Micro-mechanical modeling for static properties of RFRC Poly-Inclusion model Aim: • Model for extending mean field based algorithms to wavy fibers. • Validation of homogenized elastic properties predicted by model. • Validation of stress state in inclusions as a significant parameter for modeling damage analysis. Transformation of a wavy fiber into an equivalent ellipsoidal inclusion system 09/04/2015 Yasmine Abdin COMPTEST 2015, Madrid 8 Poly-Inclusion model: Validation - 1 • Good agreement of model predictions compared to full FEA simulations 09/04/2015 Yasmine Abdin COMPTEST 2015, Madrid 9 Poly-Inclusion model: Validation - 2 09/04/2015 Yasmine Abdin COMPTEST 2015, Madrid 10 Non-linear quasi-static modeling Matrix plasticity model Debonding model J2 plasticity model: secant approach by Tandon and Weng [1988] 09/04/2015 Yasmine Abdin COMPTEST 2015, Madrid d = percentage of debonded points γ = percentage of debonded points in tension δ = percentage of frictional sliding interface 11 Validation of micromechanical and damage model for short steel fiber composites • Using the same value of interface strength of GF-PA for the SF-PA samples lead to overestimation of the stress-strain curves. • It can then be concluded that the steel fibers exhibit weak interface strength with the matrix. 60 2 VF% 50 40 Experimental VF2% 30 Model with strong interface 20 Model with weaker interface 10 0 0 09/04/2015 0,02 0,04 0,06 0,08 0,1 0,12 Yasmine Abdin COMPTEST 2015, Madrid 0,14 12 SEM quasi-static failed samples SF-PA High percentage of debonding in all volume fractions due to weak interface 0.5VF% 4VF% 09/04/2015 2VF% 5VF% Yasmine Abdin COMPTEST 2015, Madrid 13 Validation of micromechanical and damage model for short glass fiber composites -1 Stress-strain curves of SG-PP 200 180 • 0 degees coupon • 30 wt% GF • High orientation a11 = 0.823 • Long fibers • Length distribution Lognormal (6.9, 0.5) 160 140 Plasticity Stress/MPa 120 Elastic 100 80 Platicity+damage 60 40 20 0 0 0,005 0,01 0,015 0,02 0,025 0,03 Strain 09/04/2015 Yasmine Abdin COMPTEST 2015, Madrid 14 Validation of micromechanical and damage model for short glass fiber composites -3 Stress-strain curves GF-PBT 200 180 160 Stress, MPa 140 120 Experimental Plasticity + damage 100 Plasticity Elastic 80 60 • 0 degees coupon • 50 wt% GF • High orientation a11 = 0.801 • Very short fibers • Contant fiber length 40 20 0 0 09/04/2015 0,002 0,004 0,006 Strain 0,008 0,01 Yasmine Abdin COMPTEST 2015, Madrid 0,012 0,014 15 Fatigue Modelling of short fiber composites Micro-mechanics based Fatigue Model (FATIGUE MICRO-ANALYZER) S matrix interface N S Fiber • Geometrical model (generator) • Micro-mechanical model • Damage model • Fatigue failure criteria S Short fiber composite N σmax stress N Micro-mechanics based fatigue model σmin time 09/04/2015 Yasmine Abdin COMPTEST 2015, Madrid 17 17 The Fatigue Model 09/04/2015 Yasmine Abdin COMPTEST 2015, Madrid 18 The Fatigue Model – Validation -1 GF-PP 80 S-N curve of SG-PP Max Stress, MPa 70 60 50 Experimental 40 Model Slope = 0.05 Model Slope Int = 0.1 30 Model Slope int = 0 20 10 0 100 1000 10000 100000 Cycles to failure 35 1000000 Max Stress, MPA 30 25 20 Interface Slope = 0 15 Interface Slope = 0.506 10 Interface Slope =1.012 5 0 1 10 100 1000 10000 10000000 • 0 degees coupon • 30 wt% GF • High orientation a11 = 0.823 • Long fibers • Length distribution Lognormal (6.9, 0.5) • Parametric study shows the increased effect of the fatigue of interface on the accurate prediction of short fibers S-N curves Model results generated with using the slope of critical interface strength vs. cycles curve the same as that of S-N curve of matrix 100000 1000000 10000000 Cycles to failure 09/04/2015 Yasmine Abdin COMPTEST 2015, Madrid 19 The Fatigue Model – Validation -2 GF-PBT 115 • 0 degees coupon • 50 wt% GF • High orientation a11 = 0.801 • Very short fibers • Constant fiber length Stress, MPa Tσ = 0-deg Model Model Slope =0 Model Slope = 0.138 20 10 100 1000 60 10000 Number of cycles 100000 1000000 Max Stress, MPa 50 Interface Slope = 0.069 Interface Slope = 0 Interface Slope =0.138 40 30 Model results generated with using the slope of critical interface strength vs. cycles curve the same as that of S-N curve of matrix 20 10 0 100 1000 10000 Cycles to failure 09/04/2015 100000 1000000 Yasmine Abdin COMPTEST 2015, Madrid 20 Summary • A geometrical model is developed for generation of RVE of • • • • short wavy fibers. A micro-mechanical modelling approach is validated for extension of the mean-field model for short wavy fiber composite systems. Non-linear models developed for damage of short fiber composites: straight and wavy. A micro-mechanics based fatigue model is proposed based on fatigue of constituents. Validation of overall modelling approaches against experimental findings. 09/04/2015 Yasmine Abdin COMPTEST 2015, Madrid 21 Acknowledgment The work has been funded by SIM-IWT“ ModelSteelComp” project 09/04/2015 Yasmine Abdin COMPTEST 2015, Madrid 22 Thank you! 23
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