The Evolution of Internal Damage Identified by Means of X-ray Computed Tomography in Two Steels and the Ensuing Relation with Gurson’s Numerical Modelling
Abstract
:1. Introduction
2. Experimental Work
2.1. Materials
2.1.1. Material 1
2.1.2. Material 2
2.2. Specimens
2.3. Testing Procedure Used to Study the Damage Evolution
- X-ray tomographic analysis before the specimen is tested.
- The specimen is tested until the maximum load is reached, which is identified as Step 1; then, it is unloaded.
- X-ray tomographic analysis of the specimen.
- The specimen is tested until the second step is reached; then, it is unloaded.
- X-ray tomographic analysis of the specimen.
- The previous actions are repeated for subsequent steps until the point of failure.
2.4. Results
2.4.1. Fractographic Analysis of the Fracture Surfaces
2.4.2. Metallographic Analysis after the Test
2.4.3. Internal Damage Evolution Analysis
2.4.4. Longitudinal and Radial Distribution of Voids at Each Step
2.5. Discussion on the Experimental Data
3. Numerical Work
3.1. Description of the Finite Element Model
3.1.1. Geometry
3.1.2. Boundary Conditions and Load
3.1.3. Materials
3.2. Calibrated Models
- Material relative density, d. Please note that here we follow the Gurson model parameters used in the implementation of the model available in Abaqus®, therefore a value of implies a fully dense material with an initial VVF of .
- Hardening slope after the maximum load defined as a stress–strain ratio, r.
- Mean equivalent plastic strain for void nucleation, .
- Standard deviation of the distribution, .
- Volumetric fraction of nucleated voids, .
3.2.1. Comparison with the Experimental Data
3.2.2. Mesh-Size Effect on the Voids Volume Profiles
4. Conclusions and Final Remarks
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Appendix A. Voids Volume Evolution Profiles
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Material | C | Si | Mn | P | S | Cr | Mo |
1 | 0.83 | 0.25 | 0.72 | 0.012 | 0.004 | 0.24 | <0.01 |
2 | 0.22 | 0.18 | 1.00 | 0.024 | 0.042 | 0.08 | 0.03 |
Material | Ni | Cu | Al | Ti | Nb | V | N |
1 | 0.02 | 0.01 | <0.003 | <0.005 | <0.005 | <0.01 | 0.0097 |
2 | 0.14 | 0.46 | <0.003 | <0.005 | <0.005 | <0.01 | 0.0113 |
Step | 1 | 2 | 3 | 4 | 5 |
---|---|---|---|---|---|
Material 1 | 0.076 | 0.104 | 0.118 | 0.128 | — |
Material 2 | 0.193 | 0.267 | 0.288 | 0.306 | 0.319 |
Material | E [N/mm] | r | d | ||||
---|---|---|---|---|---|---|---|
1 | 160,385 | 0.30 | 782 | 0.999 | 0.4 | 0.1 | 0.02 |
2 | 191,536 | 0.30 | 762 | 0.99 | 0.3 | 0.1 | 0.06 |
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Suárez, F.; Sket, F.; Gálvez, J.C.; Cendón, D.A.; Atienza, J.M.; Molina-Aldareguia, J. The Evolution of Internal Damage Identified by Means of X-ray Computed Tomography in Two Steels and the Ensuing Relation with Gurson’s Numerical Modelling. Metals 2019, 9, 292. https://doi.org/10.3390/met9030292
Suárez F, Sket F, Gálvez JC, Cendón DA, Atienza JM, Molina-Aldareguia J. The Evolution of Internal Damage Identified by Means of X-ray Computed Tomography in Two Steels and the Ensuing Relation with Gurson’s Numerical Modelling. Metals. 2019; 9(3):292. https://doi.org/10.3390/met9030292
Chicago/Turabian StyleSuárez, Fernando, Federico Sket, Jaime C. Gálvez, David A. Cendón, José M. Atienza, and Jon Molina-Aldareguia. 2019. "The Evolution of Internal Damage Identified by Means of X-ray Computed Tomography in Two Steels and the Ensuing Relation with Gurson’s Numerical Modelling" Metals 9, no. 3: 292. https://doi.org/10.3390/met9030292