Advanced Plasticity Modeling for Ultra-Low-Cycle-Fatigue Simulation of Steel Pipe
Abstract
:1. Introduction
- (1)
- isotropic hardening model combined with von Mises, Hill and facet yield loci.
- (2)
- linear kinematic hardening model in combination with von Mises and Hill yield loci.
- (3)
- combined hardening model combined with von Mises and Hill yield loci.
2. ULCF Testing and FE Simulation Setup
2.1. Experimental Test Setup
2.2. Finite Element Simulation Setup
3. Material Model Description
3.1. Pipe Material
3.2. Plastic Strain Hardening
3.2.1. Mechanical Tests
3.2.2. Strain Hardening Models
- (1)
- For the isotropic hardening, the Voce hardening law is used:
- (2)
- For the linear kinematic hardening, the evolution law (3) describes the translation of the yield surface in stress space through the backstress with constant hardening modulus :
- (3)
- The evolution law of combined hardening model consists of two components: (i) a nonlinear kinematic hardening component as:
3.3. Plastic Anisotropy
3.3.1. Texture Measurements
3.3.2. Advanced Plasticity Modeling
- (1)
- von Mises: the isotropic von Mises yield function calibrated by giving the value of the uniaxial yield stress as a function of uniaxial equivalent plastic strain.
- (2)
- Hill-average: the anisotropic Hill yield function calibrated by r-values in three directions. The r-values are obtained from the ALAMEL multi-scale model on the basis of the overall average texture.
- (3)
- Hill-gradient: the Hill yield function with different r-value parameters for the different integration points across tube thickness. They are calibrated by the ALAMEL model from the corresponding texture gradient.
- (4)
- Facet: the anisotropic facet yield function with 360 parameters, calibrated to closely reproduce the behavior of ALAMEL under all conceivable deformation conditions.
3.3.3. The Hill-Average Yield Function
3.3.4. The Hill-Gradient Yield Function
3.3.5. The Facet Yield Function
4. Numerical Results of ULCF
4.1. Onset of Buckling
4.2. Strain Evolution
4.2.1. Influence of Anisotropic Yield Locus on Strain Evolution and Buckling Subjected to ULCF
4.2.2. Influence of Strain Hardening on Strain Evolution and Buckling Subjected to ULCF with Hill-Gradient Anisotropic Yield Locus
5. Summary and Conclusions
- 1
- In terms of simulations with different strain-hardening models, the combined hardening model enables predicting accurately the onset of buckling. Compared to isotropic and linear kinematic hardening assumptions, the prediction of buckling is delayed with two bending cycles, resulting in eight or 8.5 cycles in total for the ULCF test setup under consideration, whereas eight cycles are experimentally found.
- 2
- Regarding the yield function assumption, it is systematically found that strain evolution predictions during the ULCF process are closest in agreement with the experiment for the Hill anisotropic model that accounts for the gradient in properties over the tube wall thickness.
- 3
- A significant texture gradient across thickness is observed. The texture anisotropy gradient has an obvious effect on the strain evolution of ULCF simulation and to some degree also on the buckling failure process.
- 4
- Hardening modeling matters more than modeling assumptions regarding the (an-)isotropy (i.e., the choice and calibration of the yield locus) in the simulation of pipeline steel undergoing ULCF.
Acknowledgments
Author Contributions
Conflicts of Interest
References
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Hardening Law | Material Parameters | |||
---|---|---|---|---|
(MPa) | Tabular Data | |||
Isotropic hardening | --- | --- | = 760 MPa | |
B = 0.05 | ||||
Linear kinematic hardening | 594 | 0 | = 656 MPa | |
678 | 0.128 | |||
Combined hardening | Nonlinear kinematic hardening component | --- | --- | = 600 MPa |
= 49,376 MPa | ||||
= 234.351 | ||||
Isotropic hardening component | 600 | 0 | --- | |
444 | 0.044 | |||
512 | 1 |
r Value of Overall Merged Texture | |||
---|---|---|---|
ALAMEL | r0 | r45 | r90 |
0.858 | 1.250 | 1.070 |
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Li, R.; Eyckens, P.; E, D.; Gawad, J.; Poucke, M.V.; Cooreman, S.; Bael, A.V. Advanced Plasticity Modeling for Ultra-Low-Cycle-Fatigue Simulation of Steel Pipe. Metals 2017, 7, 140. https://doi.org/10.3390/met7040140
Li R, Eyckens P, E D, Gawad J, Poucke MV, Cooreman S, Bael AV. Advanced Plasticity Modeling for Ultra-Low-Cycle-Fatigue Simulation of Steel Pipe. Metals. 2017; 7(4):140. https://doi.org/10.3390/met7040140
Chicago/Turabian StyleLi, Rongting, Philip Eyckens, Daxin E, Jerzy Gawad, Maarten Van Poucke, Steven Cooreman, and Albert Van Bael. 2017. "Advanced Plasticity Modeling for Ultra-Low-Cycle-Fatigue Simulation of Steel Pipe" Metals 7, no. 4: 140. https://doi.org/10.3390/met7040140