Cyclic Plasticity Modelling: Advanced Models for Ratcheting Simulation
Dr Kyriakos Kourousis Lecturer (Aerospace & Aviation Engineering)
School of Aerospace, Mechanical and Manufacturing Engineering
[email protected]
QUT - Brisbane, 9 Sep 13
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Cyclic Plasticity Modelling Stress space
Isotropic hardening Stress space
Final yield surface Initial yield surface
Final yield surface
Initial yield surface
Kinematic hardening
Distortional hardening
RMIT University©2013
Feigenbaum H, Dugdale J, Dafalias Y, Kourousis K, Plesek J (2012) Multiaxial ratcheting with advanced kinematic and directional distortional hardening rules, International Journal of Solids and Structures, 49, 30633076
School of Aerospace, Mechanical an Manufacturing Engineering
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Armstrong & Frederick (AF) model Basic Models used in commercial FE packages:
Multi-component Armstrong & Frederick (MAF) (Chaboche et al, 1979)
a ai i
ai
2 ci ais n ai 3
m 1
a ai i
Multi-component Armstrong & Frederick with Threshold Term (MAFT)
ai
2 ci ais n ai (i 1, 2,..., m 1) 3
am
am 2 s cm am n 1 am 3 f am
f am
3 am : am 2
(Chaboche, 1991)
RMIT University©2013
School of Aerospace, Mechanical an Manufacturing Engineering
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Multicomponent AF model with Multiplier (MAFM) Advanced models (ratcheting-specific) ai
MAFMδ (δ term)
2 2 s ci ai n ai 1 ai : n n 3 3
2 2 2 a4 c4 c4* a4*s a4*s : n a4s n a4 1 a4 : n n 3 3 3 a4* c4*
ai
MAFMr (r term)
2 2 *s * a4 n a4 3 3
2 2 s ci ai n ri ai 1 ri ai : n n 3 3
i 1, 2,3
2 2 *s 2 s * *s a4 c4 c4 a4 a4 : n a4 n r4a4 1 r4 a4 : n n 3 3 3 a4* c4*
ri RMIT University©2013
i 1, 2,3
2 2 *s * a n a 4 4 3 3
3 2 ai : ai ais
School of Aerospace, Mechanical an Manufacturing Engineering
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Mean Stress Relaxation AA7050
AA7050
Experiment
Aluminum Alloy 7050 - Cyclic hysteresis loops mean stress relaxation experimental data and computed results
Simulation
AA7050
Kourousis KI, Dafalias YF (2013), Constitutive Modeling of Aluminum Alloy 7050 Cyclic Mean Stress Relaxation and Ratcheting, Mechanics Research Communications – In press RMIT University©2013
School of Aerospace, Mechanical an Manufacturing Engineering
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Ratchetting: Uniaxial AA7050 TA16
Experimental data versus Computed results for Aluminum Alloy 7050 ratcheting rate (strain at peak of cycle versus number of loading cycles). Kourousis KI, Dafalias YF (2013), Constitutive Modeling of Aluminum Alloy 7050 Cyclic Mean Stress Relaxation and Ratcheting, Mechanics Research Communications – In press RMIT University©2013
Experimental data versus computed results for Titanium Alloy16 ratcheting rate (strain at peak of cycle versus number of loading cycles). Kourousis KI (2013) A Cyclic Plasticity Model for Advanced Light Metal Alloys, Applied Mechanics and Materials, 391, 3-8.
School of Aerospace, Mechanical an Manufacturing Engineering
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Ratchetting: Uniaxial TA16
Experiment
TA16
Simulation
Experimental data versus computed results for Titanium Alloy 16 ratcheting hysteresis loops (stress – strain curves).
Kourousis KI (2013) A Cyclic Plasticity Model for Advanced Light Metal Alloys, Applied Mechanics and Materials, 391, 3-8.
RMIT University©2013
School of Aerospace, Mechanical an Manufacturing Engineering
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Ratchetting: Multiaxial (Biaxial)
Strain controlled biaxial ratcheting data from complex load paths simulated with various kinematic hardening rule with and without directional distortional hardening (DDH) Feigenbaum H, Dugdale J, Dafalias Y, Kourousis K, Plesek J (2012) Multiaxial ratcheting with advanced kinematic and directional distortional hardening rules, International Journal of Solids and Structures, 49, 3063-3076 RMIT University©2013
School of Aerospace, Mechanical an Manufacturing Engineering
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Ratchetting: Multiaxial (Biaxial) εθp (%)
3.0
CS1018 Loading type VI σθa = 2,36 ksi εxc = 0,5% σθm = 9,65 ksi
2.5
2.0
Πειραματικά Δεδομένα Experimental data
1.5
MAFT MAFM
1.0
MAFTδ (δ=0,18)
ΜΑFMδ (δ=0,18)
0.5
MAFMr
Ν
0.0
0
5
10
15
20
Strain controlled biaxial ratcheting data from complex load paths simulated with various kinematic hardening rules
Kourousis K (2011) Plasticity of Metals Subjected to Cyclic Loadings: A Multiplicatively Decomposed Kinematic Hardening Rule, PhD Thesis, National Technical University of Athens, Greece. RMIT University©2013
School of Aerospace, Mechanical an Manufacturing Engineering
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MAFM model - References 1. Kourousis KI, Dafalias YF (2013), Constitutive Modeling of Aluminum Alloy 7050 Cyclic Mean Stress Relaxation and Ratcheting, Mechanics Research Communications – In press. 2. Kourousis KI (2013) A Cyclic Plasticity Model for Advanced Light Metal Alloys, Applied Mechanics and Materials, 391, 3-8. 3. Feigenbaum H, Dugdale J, Dafalias Y, Kourousis K, Plesek J (2012) Multiaxial ratcheting with advanced kinematic and directional distortional hardening rules, International Journal of Solids and Structures, 49, 3063-3076. 4. Dafalias YF, Feigenbaum H (2011) Biaxial ratcheting with novel variations of kinematic hardening, International Journal of Plasticity 27, 4, 479-491. 5. Dafalias YF, Kourousis KI, Saridis G. (2008) Multiplicative AF kinematic hardening in plasticity. International Journal of Solids and Structures 45, 2861-2880. 6. Kourousis KI, Saridis G, Dafalias YF. (2007) Cyclic Plasticity Model with Multiplicative Backstress Decomposition, (Chapter 12), Experimental and Computational Analysis of Damaged Materials, Transworld Research Network, ISBN 978-81-7895-308-3.
RMIT University©2013
School of Aerospace, Mechanical an Manufacturing Engineering
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