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Simulation of crack propagation in ductile materials under non-proportional loading conditions. Part II: Phase field modelling of crack propagation

The aim of this research is to simulate fatigue crack propagation in ductile materials subjected to cyclic non-proportional and mixed-mode loading by means of the phase field method. For the investigated materials, it is to be expected that non-proportional hardening has a major influence on the crack initiation and further evolution.
In the first part of this work a constitutive model for the description of the material behavior in such cases was proposed. This model is now extended by a phase field variable to describe the complex crack phenomena, cf. Tsakmakis and Vormwald [1,2]. The underlying crack growth mechanism is assumed to be driven by plastic deformation. Thermodynamic consistency of the model is ensured in the present work within the framework of so-called…

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The aim of this research is to simulate fatigue crack propagation in ductile materials subjected to cyclic non-proportional and mixed-mode loading by means of the phase field method. For the investigated materials, it is to be expected that non-proportional hardening has a major influence on the crack initiation and further evolution.
In the first part of this work a constitutive model for the description of the material behavior in such cases was proposed. This model is now extended by a phase field variable to describe the complex crack phenomena, cf. Tsakmakis and Vormwald [1,2]. The underlying crack growth mechanism is assumed to be driven by plastic deformation. Thermodynamic consistency of the model is ensured in the present work within the framework of so-called non-conventional thermodynamics proposed in Dunn and Serrin [3].
Finally, the capabilities of the proposed model are analyzed with the help of experimental results. For this purpose, predicted crack paths are compared with experimentally determined crack paths in thin-walled tubes under combined tension/compression and torsional loading. In particular, both proportional and non-proportional cyclic loads are analyzed. Fig. 1 shows exemplarily results of the comparison.

Reference
ICMFF14-2025-59

Title
Simulation of crack propagation in ductile materials under non-proportional loading conditions. Part II: Phase field modelling of crack propagation
Author(s)
A. Gibb, A. Tsakmakis, M. Vormwald
DOI
10.48447/ICMFF14-2025-59
Event
14. International Conference on Multiaxial Fatigue and Fracture 2025
Year of publication
2025
Publication type
conference paper (PDF)
Language
English
Keywords
Plasticity,Phase Field,Multi-axial,Fatigue,Damage

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On the life estimation of wires using non-local machine learning methodology
On the life estimation of wires using non-local machine learning methodology
G. A. Brito Oliveira, I. M. Matos, R. A. Cardoso, J. A. Araújo
10.48447/ICMFF14-2025-51
14. International Conference on Multiaxial Fatigue and Fracture 2025
2025
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English
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10.48447/ICMFF14-2025-51
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Notch sensitivity and short cracks tolerance in environmentally assisted cracking under multiaxial tension-torsion loadings
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H. Wu, M. A. Meggiolaro, A. C. Miranda, J. T.P. Castro
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10.48447/ICMFF14-2025-29
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The Use of Polar Damage Sum Concept for Calculating Mean Stress Effect in Multiaxial Fatigue Loading Conditions
The Use of Polar Damage Sum Concept for Calculating Mean Stress Effect in Multiaxial Fatigue Loading Conditions
J. Albinmousa, A. Alhammali, M. Ismail
10.48447/ICMFF14-2025-29
14. International Conference on Multiaxial Fatigue and Fracture 2025
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The Use of Polar Damage Sum Concept for Calculating Mean Stress Effect in Multiaxial Fatigue Loading Conditions
J. Albinmousa, A. Alhammali, M. Ismail
10.48447/ICMFF14-2025-29
14. International Conference on Multiaxial Fatigue and Fracture 2025
2025
conference paper (PDF)
English
Fatigue damage,multiaxial,Mean stress,Polar damage sum concept,critical plane concept
Price €25.00
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10.48447/ICMFF14-2025-15
14. International Conference on Multiaxial Fatigue and Fracture 2025
2025
conference paper (PDF)
English
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Crack growth behavior of steel S235 under proportional and non-proportional fatigue loading
Crack growth behavior of steel S235 under proportional and non-proportional fatigue loading
P. Zerres, M. Vormwald
10.48447/ICMFF14-2025-15
14. International Conference on Multiaxial Fatigue and Fracture 2025
2025
Publication type: conference paper (PDF)
English
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Crack growth behavior of steel S235 under proportional and non-proportional fatigue loading
P. Zerres, M. Vormwald
10.48447/ICMFF14-2025-15
14. International Conference on Multiaxial Fatigue and Fracture 2025
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conference paper (PDF)
English
fracture mechanics,fatigue crack growth,non-proportional loading
Price €25.00
Online only New
Simulation of crack propagation in ductile materials under non-proportional loading conditions. Part I: Modelling of deformation-induced plastic anisotropy
Author(s): A. Gibb, A. Tsakmakis, M. Vormwald
10.48447/ICMFF14-2025-58
14. International Conference on Multiaxial Fatigue and Fracture 2025
2025
conference paper (PDF)
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Simulation of crack propagation in ductile materials under non-proportional loading conditions. Part I: Modelling of deformation-induced plastic anisotropy
Simulation of crack propagation in ductile materials under non-proportional loading conditions. Part I: Modelling of deformation-induced plastic anisotropy
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10.48447/ICMFF14-2025-58
14. International Conference on Multiaxial Fatigue and Fracture 2025
2025
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Simulation of crack propagation in ductile materials under non-proportional loading conditions. Part I: Modelling of deformation-induced plastic anisotropy
A. Gibb, A. Tsakmakis, M. Vormwald
10.48447/ICMFF14-2025-58
14. International Conference on Multiaxial Fatigue and Fracture 2025
2025
conference paper (PDF)
English
Plasticity,Phase Field,Multi-axial,Damage,Fatigue
Price €25.00
Online only New
Unifying multiaxial fatigue life prediction of welded joints by considering support effects
Author(s): N. M. Bauer, A. Wöhle, J. Baumgartner
10.48447/ICMFF14-2025-33
14. International Conference on Multiaxial Fatigue and Fracture 2025
2025
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Unifying multiaxial fatigue life prediction of welded joints by considering support effects
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10.48447/ICMFF14-2025-33
14. International Conference on Multiaxial Fatigue and Fracture 2025
2025
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Unifying multiaxial fatigue life prediction of welded joints by considering support effects
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14. International Conference on Multiaxial Fatigue and Fracture 2025
2025
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Online only New
Fatigue strength assessment of different materials under variable amplitude loadings with the Findley damage parameter
Author(s): C. Fällgren, M. Vormwald
10.48447/ICMFF14-2025-01
14. International Conference on Multiaxial Fatigue and Fracture 2025
2025
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Fatigue strength assessment of different materials under variable amplitude loadings with the Findley damage parameter
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10.48447/ICMFF14-2025-01
14. International Conference on Multiaxial Fatigue and Fracture 2025
2025
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Fatigue strength assessment of different materials under variable amplitude loadings with the Findley damage parameter
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14. International Conference on Multiaxial Fatigue and Fracture 2025
2025
conference paper (PDF)
English
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Price €25.00
Online only New
Systematic investigation of the influence of T-stress and LCF overloads in biaxially loaded cruciform specimen on plasticity-induced crack closure using digital image correlation
Author(s): A. Zaiat, A. Blug, G. Laskin, A. Bertz, F. Conrad, C. Kontermann, M. Oechsner
10.48447/ICMFF14-2025-27
14. International Conference on Multiaxial Fatigue and Fracture 2025
2025
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Systematic investigation of the influence of T-stress and LCF overloads in biaxially loaded cruciform specimen on plasticity-induced crack closure using digital image correlation
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A. Zaiat, A. Blug, G. Laskin, A. Bertz, F. Conrad, C. Kontermann, M. Oechsner
10.48447/ICMFF14-2025-27
14. International Conference on Multiaxial Fatigue and Fracture 2025
2025
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Systematic investigation of the influence of T-stress and LCF overloads in biaxially loaded cruciform specimen on plasticity-induced crack closure using digital image correlation
A. Zaiat, A. Blug, G. Laskin, A. Bertz, F. Conrad, C. Kontermann, M. Oechsner
10.48447/ICMFF14-2025-27
14. International Conference on Multiaxial Fatigue and Fracture 2025
2025
conference paper (PDF)
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PICC,Biaxial-Testing,Cruciform Specimens,T-Stress
Price €25.00
Online only New
Evaluation of multi-axial stresses using the FKM guideline - status quo and how it can be improved
Author(s): M. Wächter, R. Wuthenow, C. Fällgren, H.-T. Beier, M. Obermayr, R. Rennert, M. Vormwald, A. Esderts
10.48447/ICMFF14-2025-62
14. International Conference on Multiaxial Fatigue and Fracture 2025
2025
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10.48447/ICMFF14-2025-62
14. International Conference on Multiaxial Fatigue and Fracture 2025
2025
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Evaluation of multi-axial stresses using the FKM guideline - status quo and how it can be improved
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10.48447/ICMFF14-2025-62
14. International Conference on Multiaxial Fatigue and Fracture 2025
2025
conference paper (PDF)
English
multiaxial stresses,guideline,FKM,scaled normal stresses
Price €25.00
Online only New
Interior fatigue of gears under special consideration of multiaxial stresses and local material properties
Author(s): J.-A. Meis
10.48447/ICMFF14-2025-23
14. International Conference on Multiaxial Fatigue and Fracture 2025
2025
conference paper (PDF)
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Interior fatigue of gears under special consideration of multiaxial stresses and local material properties
Interior fatigue of gears under special consideration of multiaxial stresses and local material properties
J.-A. Meis
10.48447/ICMFF14-2025-23
14. International Conference on Multiaxial Fatigue and Fracture 2025
2025
Publication type: conference paper (PDF)
English
Flank Fracture,Interior Fatigue,Critical Plane,Nonmetallic Inclusions,Probabilistic Design 
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Interior fatigue of gears under special consideration of multiaxial stresses and local material properties
J.-A. Meis
10.48447/ICMFF14-2025-23
14. International Conference on Multiaxial Fatigue and Fracture 2025
2025
conference paper (PDF)
English
Flank Fracture,Interior Fatigue,Critical Plane,Nonmetallic Inclusions,Probabilistic Design
Price €25.00
Online only New
Numerical Analysis of Defect Population Influence on the Multiaxial High-cycle Fatigue Strength Anisotropy of Ti64 Manufactured by Laser Powder Bed Fusion (L-PBF)
Author(s): S.S. Penkulinti, N. Saintier, M. Bonneric, B. Verquin, T. Palin-Luc, F. Lefebvre
10.48447/ICMFF14-2025-61
14. International Conference on Multiaxial Fatigue and Fracture 2025
2025
conference paper (PDF)
English
Laser Powder Bed Fusion (L-PBF),Defects,High-cycle Fatigue,Finite Element Analysis 
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Numerical Analysis of Defect Population Influence on the Multiaxial High-cycle Fatigue Strength Anisotropy of Ti64 Manufactured by Laser Powder Bed Fusion (L-PBF)
Numerical Analysis of Defect Population Influence on the Multiaxial High-cycle Fatigue Strength Anisotropy of Ti64 Manufactured by Laser Powder Bed Fusion (L-PBF)
S.S. Penkulinti, N. Saintier, M. Bonneric, B. Verquin, T. Palin-Luc, F. Lefebvre
10.48447/ICMFF14-2025-61
14. International Conference on Multiaxial Fatigue and Fracture 2025
2025
Publication type: conference paper (PDF)
English
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Numerical Analysis of Defect Population Influence on the Multiaxial High-cycle Fatigue Strength Anisotropy of Ti64 Manufactured by Laser Powder Bed Fusion (L-PBF)
S.S. Penkulinti, N. Saintier, M. Bonneric, B. Verquin, T. Palin-Luc, F. Lefebvre
10.48447/ICMFF14-2025-61
14. International Conference on Multiaxial Fatigue and Fracture 2025
2025
conference paper (PDF)
English
Laser Powder Bed Fusion (L-PBF),Defects,High-cycle Fatigue,Finite Element Analysis
Price €25.00
Online only New
New tests and multiaxial fatigue modeling of steels with different small defects
Author(s): L. C. Araujo, J. A. Araújo
10.48447/ICMFF14-2025-10
14. International Conference on Multiaxial Fatigue and Fracture 2025
2025
conference paper (PDF)
English
Multiaxial fatigue,Small defects,√area Parameter,Principal stresses amplitude 
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New tests and multiaxial fatigue modeling of steels with different small defects
New tests and multiaxial fatigue modeling of steels with different small defects
L. C. Araujo, J. A. Araújo
10.48447/ICMFF14-2025-10
14. International Conference on Multiaxial Fatigue and Fracture 2025
2025
Publication type: conference paper (PDF)
English
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1
New tests and multiaxial fatigue modeling of steels with different small defects
L. C. Araujo, J. A. Araújo
10.48447/ICMFF14-2025-10
14. International Conference on Multiaxial Fatigue and Fracture 2025
2025
conference paper (PDF)
English
Multiaxial fatigue,Small defects,√area Parameter,Principal stresses amplitude
Price €25.00
Online only New
Crack Orientation and Multiaxial Fatigue Analysis in Steel and Cast Iron
Author(s): J. Kraft, M. Vormwald
10.48447/ICMFF14-2025-02
14. International Conference on Multiaxial Fatigue and Fracture 2025
2025
conference paper (PDF)
English
multiaxial fatigue,critical plane modells,Non-proportional loading,Crack initiation orientation 
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1
Crack Orientation and Multiaxial Fatigue Analysis in Steel and Cast Iron
Crack Orientation and Multiaxial Fatigue Analysis in Steel and Cast Iron
J. Kraft, M. Vormwald
10.48447/ICMFF14-2025-02
14. International Conference on Multiaxial Fatigue and Fracture 2025
2025
Publication type: conference paper (PDF)
English
multiaxial fatigue,critical plane modells,Non-proportional loading,Crack initiation orientation 
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1
Crack Orientation and Multiaxial Fatigue Analysis in Steel and Cast Iron
J. Kraft, M. Vormwald
10.48447/ICMFF14-2025-02
14. International Conference on Multiaxial Fatigue and Fracture 2025
2025
conference paper (PDF)
English
multiaxial fatigue,critical plane modells,Non-proportional loading,Crack initiation orientation
Price €25.00
Online only New
Multiaxial Fatigue of Weldments: Experiments and Modeling
Author(s): A. Razi, A. Fatemi
10.48447/ICMFF14-2025-21
14. International Conference on Multiaxial Fatigue and Fracture 2025
2025
conference paper (PDF)
English
Fatigue life prediction, Welded joint, Multiaxial loading, Variable amplitude loading, Fracture mechanics, Weld fatigue design codes 
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Multiaxial Fatigue of Weldments: Experiments and Modeling
Multiaxial Fatigue of Weldments: Experiments and Modeling
A. Razi, A. Fatemi
10.48447/ICMFF14-2025-21
14. International Conference on Multiaxial Fatigue and Fracture 2025
2025
Publication type: conference paper (PDF)
English
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Multiaxial Fatigue of Weldments: Experiments and Modeling
A. Razi, A. Fatemi
10.48447/ICMFF14-2025-21
14. International Conference on Multiaxial Fatigue and Fracture 2025
2025
conference paper (PDF)
English
Fatigue life prediction, Welded joint, Multiaxial loading, Variable amplitude loading, Fracture mechanics, Weld fatigue design codes
Price €25.00
Online only New
Crack Initiation Life Estimate for Notched Specimens of SUS304 and Mod.9Cr-1Mo Steels under Nonproportional Cyclic Loading
Author(s): M. Sakane
10.48447/ICMFF14-2025-43
14. International Conference on Multiaxial Fatigue and Fracture 2025
2025
conference paper (PDF)
English
Low cycle fatigue,notch,nonproportional loading,crack initiation life,life estimate 
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Crack Initiation Life Estimate for Notched Specimens of SUS304 and Mod.9Cr-1Mo Steels under Nonproportional Cyclic Loading
Crack Initiation Life Estimate for Notched Specimens of SUS304 and Mod.9Cr-1Mo Steels under Nonproportional Cyclic Loading
M. Sakane
10.48447/ICMFF14-2025-43
14. International Conference on Multiaxial Fatigue and Fracture 2025
2025
Publication type: conference paper (PDF)
English
Low cycle fatigue,notch,nonproportional loading,crack initiation life,life estimate 
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1
Crack Initiation Life Estimate for Notched Specimens of SUS304 and Mod.9Cr-1Mo Steels under Nonproportional Cyclic Loading
M. Sakane
10.48447/ICMFF14-2025-43
14. International Conference on Multiaxial Fatigue and Fracture 2025
2025
conference paper (PDF)
English
Low cycle fatigue,notch,nonproportional loading,crack initiation life,life estimate
Price €25.00
Online only New
Assessing Phase Relationships Between Stress Components in Statistical Fatigue Evaluations
Author(s): A. Trapp, K. Rother
10.48447/ICMFF14-2025-46
14. International Conference on Multiaxial Fatigue and Fracture 2025
2025
conference paper (PDF)
English
Variable Amplitude Loading,Random Vibration Loading,Critical Plane Approach,Statistical Fatigue Assessment 
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Assessing Phase Relationships Between Stress Components in Statistical Fatigue Evaluations
Assessing Phase Relationships Between Stress Components in Statistical Fatigue Evaluations
A. Trapp, K. Rother
10.48447/ICMFF14-2025-46
14. International Conference on Multiaxial Fatigue and Fracture 2025
2025
Publication type: conference paper (PDF)
English
Variable Amplitude Loading,Random Vibration Loading,Critical Plane Approach,Statistical Fatigue Assessment 
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1
Assessing Phase Relationships Between Stress Components in Statistical Fatigue Evaluations
A. Trapp, K. Rother
10.48447/ICMFF14-2025-46
14. International Conference on Multiaxial Fatigue and Fracture 2025
2025
conference paper (PDF)
English
Variable Amplitude Loading,Random Vibration Loading,Critical Plane Approach,Statistical Fatigue Assessment
Price €25.00
Online only New