damage mechanics in composite materials · hashin failure criteria • if any failure index ei t,c...
TRANSCRIPT
![Page 1: Damage Mechanics in Composite Materials · Hashin Failure Criteria • If any failure index ei t,c exceeds unity, then failure initiation has occurred for that strain component at](https://reader030.vdocuments.us/reader030/viewer/2022040303/5e92b2018502d028b41acc23/html5/thumbnails/1.jpg)
Damage Mechanics in Composite Materials
Dr. Bijan MohammadiSchool of Mechanical Engineering
Iran University of Science and Technology
![Page 2: Damage Mechanics in Composite Materials · Hashin Failure Criteria • If any failure index ei t,c exceeds unity, then failure initiation has occurred for that strain component at](https://reader030.vdocuments.us/reader030/viewer/2022040303/5e92b2018502d028b41acc23/html5/thumbnails/2.jpg)
Chapter 3Progressive Damage Analysis
Dr. Bijan Mohammadi
![Page 3: Damage Mechanics in Composite Materials · Hashin Failure Criteria • If any failure index ei t,c exceeds unity, then failure initiation has occurred for that strain component at](https://reader030.vdocuments.us/reader030/viewer/2022040303/5e92b2018502d028b41acc23/html5/thumbnails/3.jpg)
Maximum Stress Criteria
Dr. Bijan Mohammadi
![Page 4: Damage Mechanics in Composite Materials · Hashin Failure Criteria • If any failure index ei t,c exceeds unity, then failure initiation has occurred for that strain component at](https://reader030.vdocuments.us/reader030/viewer/2022040303/5e92b2018502d028b41acc23/html5/thumbnails/4.jpg)
Maximum Strain Criteria
Dr. Bijan Mohammadi
![Page 5: Damage Mechanics in Composite Materials · Hashin Failure Criteria • If any failure index ei t,c exceeds unity, then failure initiation has occurred for that strain component at](https://reader030.vdocuments.us/reader030/viewer/2022040303/5e92b2018502d028b41acc23/html5/thumbnails/5.jpg)
Tsai-Wu Failure Polynomial
Dr. Bijan Mohammadi
![Page 6: Damage Mechanics in Composite Materials · Hashin Failure Criteria • If any failure index ei t,c exceeds unity, then failure initiation has occurred for that strain component at](https://reader030.vdocuments.us/reader030/viewer/2022040303/5e92b2018502d028b41acc23/html5/thumbnails/6.jpg)
• Since the Tsai-Wu failure model is an interacting failure model that provides only a single condition for local material failure (i.e., where φ>1 denotes failure initiation), identifying the mode of failure requires a different approach for the material degradation step in the progressive failure model from that used with the maximum stress criteria.
Dr. Bijan Mohammadi
![Page 7: Damage Mechanics in Composite Materials · Hashin Failure Criteria • If any failure index ei t,c exceeds unity, then failure initiation has occurred for that strain component at](https://reader030.vdocuments.us/reader030/viewer/2022040303/5e92b2018502d028b41acc23/html5/thumbnails/7.jpg)
Dr. Bijan Mohammadi
![Page 8: Damage Mechanics in Composite Materials · Hashin Failure Criteria • If any failure index ei t,c exceeds unity, then failure initiation has occurred for that strain component at](https://reader030.vdocuments.us/reader030/viewer/2022040303/5e92b2018502d028b41acc23/html5/thumbnails/8.jpg)
• The largest value of the failure indices ei defines the failure mode as imax.
• No distinction is made between tension and compression values for the normal stress components in evaluating the Tsai-Wu failure polynomial terms.
Dr. Bijan Mohammadi
![Page 9: Damage Mechanics in Composite Materials · Hashin Failure Criteria • If any failure index ei t,c exceeds unity, then failure initiation has occurred for that strain component at](https://reader030.vdocuments.us/reader030/viewer/2022040303/5e92b2018502d028b41acc23/html5/thumbnails/9.jpg)
Hashin Failure Criteria
Dr. Bijan Mohammadi
![Page 10: Damage Mechanics in Composite Materials · Hashin Failure Criteria • If any failure index ei t,c exceeds unity, then failure initiation has occurred for that strain component at](https://reader030.vdocuments.us/reader030/viewer/2022040303/5e92b2018502d028b41acc23/html5/thumbnails/10.jpg)
Hashin Failure Criteria
Dr. Bijan Mohammadi
![Page 11: Damage Mechanics in Composite Materials · Hashin Failure Criteria • If any failure index ei t,c exceeds unity, then failure initiation has occurred for that strain component at](https://reader030.vdocuments.us/reader030/viewer/2022040303/5e92b2018502d028b41acc23/html5/thumbnails/11.jpg)
Hashin Failure Criteria
Dr. Bijan Mohammadi
![Page 12: Damage Mechanics in Composite Materials · Hashin Failure Criteria • If any failure index ei t,c exceeds unity, then failure initiation has occurred for that strain component at](https://reader030.vdocuments.us/reader030/viewer/2022040303/5e92b2018502d028b41acc23/html5/thumbnails/12.jpg)
Hashin Failure Criteria
• If any failure index eit,c exceeds unity, then failure initiation has occurred for that strain component at that material point and material degradation will be performed. That is, each failure mode may fail independently at different load levels
Dr. Bijan Mohammadi
![Page 13: Damage Mechanics in Composite Materials · Hashin Failure Criteria • If any failure index ei t,c exceeds unity, then failure initiation has occurred for that strain component at](https://reader030.vdocuments.us/reader030/viewer/2022040303/5e92b2018502d028b41acc23/html5/thumbnails/13.jpg)
Quadratic Polynomial Failure Criteria
* X, Y, and Z are either XC, YC, and ZC or XT, YT, and ZT depending upon the sign of S1, s2 and s3 respectively.† K12, K13, and K23 are the strength coefficients depending upon material.
Dr. Bijan Mohammadi
![Page 14: Damage Mechanics in Composite Materials · Hashin Failure Criteria • If any failure index ei t,c exceeds unity, then failure initiation has occurred for that strain component at](https://reader030.vdocuments.us/reader030/viewer/2022040303/5e92b2018502d028b41acc23/html5/thumbnails/14.jpg)
Post-failure degradation behavior in composite laminates
Dr. Bijan Mohammadi
![Page 15: Damage Mechanics in Composite Materials · Hashin Failure Criteria • If any failure index ei t,c exceeds unity, then failure initiation has occurred for that strain component at](https://reader030.vdocuments.us/reader030/viewer/2022040303/5e92b2018502d028b41acc23/html5/thumbnails/15.jpg)
Options for Material Degradation for Maximum Strain Criterion
Dr. Bijan Mohammadi
![Page 16: Damage Mechanics in Composite Materials · Hashin Failure Criteria • If any failure index ei t,c exceeds unity, then failure initiation has occurred for that strain component at](https://reader030.vdocuments.us/reader030/viewer/2022040303/5e92b2018502d028b41acc23/html5/thumbnails/16.jpg)
Material Degradation for Hashin’s and Christensen’s Failure Criteria
Dr. Bijan Mohammadi
![Page 17: Damage Mechanics in Composite Materials · Hashin Failure Criteria • If any failure index ei t,c exceeds unity, then failure initiation has occurred for that strain component at](https://reader030.vdocuments.us/reader030/viewer/2022040303/5e92b2018502d028b41acc23/html5/thumbnails/17.jpg)
Material degradation factors for 3D models and various failure modes based on the Max. Stress and max. Strain criteria
Dr. Bijan Mohammadi
![Page 18: Damage Mechanics in Composite Materials · Hashin Failure Criteria • If any failure index ei t,c exceeds unity, then failure initiation has occurred for that strain component at](https://reader030.vdocuments.us/reader030/viewer/2022040303/5e92b2018502d028b41acc23/html5/thumbnails/18.jpg)
Material degradation factors for three-dimensional models and various failure modes based on the Tsai-Wu criteria
Dr. Bijan Mohammadi
![Page 19: Damage Mechanics in Composite Materials · Hashin Failure Criteria • If any failure index ei t,c exceeds unity, then failure initiation has occurred for that strain component at](https://reader030.vdocuments.us/reader030/viewer/2022040303/5e92b2018502d028b41acc23/html5/thumbnails/19.jpg)
Material degradation factors for 3D models and various failure modes based on the Hashin criteria
Dr. Bijan Mohammadi
![Page 20: Damage Mechanics in Composite Materials · Hashin Failure Criteria • If any failure index ei t,c exceeds unity, then failure initiation has occurred for that strain component at](https://reader030.vdocuments.us/reader030/viewer/2022040303/5e92b2018502d028b41acc23/html5/thumbnails/20.jpg)
Dr. Bijan Mohammadi
![Page 21: Damage Mechanics in Composite Materials · Hashin Failure Criteria • If any failure index ei t,c exceeds unity, then failure initiation has occurred for that strain component at](https://reader030.vdocuments.us/reader030/viewer/2022040303/5e92b2018502d028b41acc23/html5/thumbnails/21.jpg)
Comparison of different progressive failure analysis models for the 16-ply cross-ply open-hole-tension coupon using recursive degradation with a degradation factor β of 0.5.
• Predictions obtained using a 0.02 value for the maximum solution increment size
Dr. Bijan Mohammadi
![Page 22: Damage Mechanics in Composite Materials · Hashin Failure Criteria • If any failure index ei t,c exceeds unity, then failure initiation has occurred for that strain component at](https://reader030.vdocuments.us/reader030/viewer/2022040303/5e92b2018502d028b41acc23/html5/thumbnails/22.jpg)
Comparison of different progressive failure analysis models for the 16-ply cross-ply open-hole-tension coupon using recursive degradation with a degradation factor β of 0.5.
• Predictions obtained using a 0.01 value for the maximum solution increment size
Dr. Bijan Mohammadi
![Page 23: Damage Mechanics in Composite Materials · Hashin Failure Criteria • If any failure index ei t,c exceeds unity, then failure initiation has occurred for that strain component at](https://reader030.vdocuments.us/reader030/viewer/2022040303/5e92b2018502d028b41acc23/html5/thumbnails/23.jpg)
Results using maximum strain criteria
Dr. Bijan Mohammadi
![Page 24: Damage Mechanics in Composite Materials · Hashin Failure Criteria • If any failure index ei t,c exceeds unity, then failure initiation has occurred for that strain component at](https://reader030.vdocuments.us/reader030/viewer/2022040303/5e92b2018502d028b41acc23/html5/thumbnails/24.jpg)
Results using Hashin criteria
Dr. Bijan Mohammadi
![Page 25: Damage Mechanics in Composite Materials · Hashin Failure Criteria • If any failure index ei t,c exceeds unity, then failure initiation has occurred for that strain component at](https://reader030.vdocuments.us/reader030/viewer/2022040303/5e92b2018502d028b41acc23/html5/thumbnails/25.jpg)
Results using maximum strain criteria
Dr. Bijan Mohammadi
![Page 26: Damage Mechanics in Composite Materials · Hashin Failure Criteria • If any failure index ei t,c exceeds unity, then failure initiation has occurred for that strain component at](https://reader030.vdocuments.us/reader030/viewer/2022040303/5e92b2018502d028b41acc23/html5/thumbnails/26.jpg)
Results using Hashin criteria
Dr. Bijan Mohammadi
![Page 27: Damage Mechanics in Composite Materials · Hashin Failure Criteria • If any failure index ei t,c exceeds unity, then failure initiation has occurred for that strain component at](https://reader030.vdocuments.us/reader030/viewer/2022040303/5e92b2018502d028b41acc23/html5/thumbnails/27.jpg)
Influence of maximum solution increment size on the progressive failure predictions for the 16-ply cross-ply open-hole-tension coupon using the
maximum strain criteria and instantaneous degradation with a degradation factor β of 10-6.
Dr. Bijan Mohammadi
![Page 28: Damage Mechanics in Composite Materials · Hashin Failure Criteria • If any failure index ei t,c exceeds unity, then failure initiation has occurred for that strain component at](https://reader030.vdocuments.us/reader030/viewer/2022040303/5e92b2018502d028b41acc23/html5/thumbnails/28.jpg)
Comparison of different progressive failure analysis models for the 16-ply quasi-isotropic open-hole-tension coupon using recursive degradation with a degradation factor β of 0.5 and a maximum solution increment size of 0.01.
Dr. Bijan Mohammadi