Finite Element Analysis of Composites by Dan Milligan
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Firehole Composites was recently invited to present at the 2012 Rocky Mountain SAMPE Fall Workshop. Dan Milligan from Firehole gave a presentation entitled "Finite Element Analysis of Composites". Below is the abstract of the presentation: Overview of topics that should be considered when using the finite element method to simulate the response of a laminated composite at the structural, component, or coupon level. Consequences of various choices will be discussed, and recommendations for best practices will be presented. Topics covered in the presentation include: Setting up the Best FEA Model Moving from 2D to 3D Modeling Composite Failure Theories Progressive Failure
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Finite Element Analysis of Composites by Dan Milligan
- 1. 2012 FALL WORKSHOP – FINITE ELEMENT ANALYSIS OF COMPOSITES DAN MILLIGAN, FIREHOLE COMPOSITES MILLIGAND@FIREHOLE.COM
- 2. Why Do This Talk? The Composites EXPLOSION • Composites are expanding into new markets - UPS has just put in an order for 150 composite body vehicles. • Composites are becoming more used everyday – Exelis predicts that the market for composite structures will grow from $4 Trillion USD to $12 Trillion in 10 years. • Now The Challenge…How Do We Design and Analyze These New Composite Applications • Limited Budgets, Limited Materials and Limited Time all lead to Finite Element Analysis 2
- 3. A Little About My Composites Experience • I have worked as a Composites Engineering Consultant for Firehole Composites for 7+ years. I have seen some “interesting” FEA analysis techniques and I would like to highlight some of those today… • I also got to work at NASA Jet Propulsion Laboratory when the Mars Curiosity Rover was being designed and composite part studies and trade-offs were being investigated. 3
- 4. What I Want To Talk About 1. Finite Element Modeling of Composite Part Recommendations A. Setting up the Best FEA Model B. Moving from 2D to 3D Modeling 2. Determining Composite Failure A. Composite Failure Theories B. Progressive Failure 4
- 5. businesspundit.com BETTER FEA MODEL DESIGN 5
- 6. Boundary Condition Stress Concentrations “Fixed” or “Encastre” BCs on plate ends… 6
- 7. Boundary Condition Stress Concentrations “Fixed” or “Encastre” BCs on plate ends… BETTER APPROACH 7
- 8. Applying Pressure To Composite Cross-Sections Applying “Pressure” to a composite cross-section meshed with 1 element per ply… P 8
- 9. Applying Pressure To Composite Cross-Sections Applying “Pressure” to a composite cross-section meshed with 1 element per ply… BETTER APPROACH F Use displacement equations or coupling constraints to enforce uniform displacement of end and apply a concentrated force to “control point”. 9
- 10. Poor Mesh Creation Letting a mesh be generated “automatically”… Geometric complexities in an FEA model often times will result in poor mesh quality. • Elements with high aspect ratios >7:1 • Elements with large (or small) interior angles >135° or <45 ° Both of these conditions reduce the accuracy of the element calculations. 10
- 11. Poor Mesh Creation Letting a mesh be generated “automatically”… BETTER APPROACH: Use partitions to improve element quality 11
- 12. Poor Mesh Creation Letting a mesh be generated “automatically”… BETTER APPROACH: Try different automatic meshing algorithms to get best quality In Abaqus™, used “medial axis” algorithm instead of “advancing front” algorithm. 12
- 13. Improper Symmetry Constraint Use Using symmetry boundary conditions to reduce element count in symmetric composite structures… Example: Use symmetry boundary conditions to model ¼ of an axially loaded [30/-30/90]3 tube meshed with 1 element per ply. The 30° plies want to shear as they are axially pulled. By constraining these plies with symmetric boundary conditions, artificial stress concentrations are generated. 13
- 14. Improper Symmetry Constraint Use Using symmetry boundary conditions to reduce element count in symmetric composite structures… BETTER APPROACH: Bite the bullet and model the full structure. 14
- 16. What Is A Full 3D Analysis? z Use FEA modeling techniques that y capture 3D stresses in a x composite part σz τyz τxz σy τxy σx A 2D analysis ignores or estimates 3 of the 6 stress components 16
- 17. Why Do We Need A Full 3D Analysis? Failure of a composite part cannot be accurately predicted without using 3D stresses (or strains) in a composites appropriate failure criterion. Example: DELAMINATION Delamination is caused by interlaminar shear stresses and through-thickness normal stresses. This can only be captured with access to 3D stresses. 17
- 18. When To Use 3D Analysis Thick Wall Pressure Skin-Stringer Joints Vessel - bolt pretension - lap shear - scarf joints cstcomposites.com sciencedirect.com structuralmechanics.com 18
- 19. How To Set Up A 3D Analysis Starting with 3D geometry… …Mesh the part using 3D elements 3D solid elements with 1 (or more) element(s) per composite ply. 3D layered solid elements with a minimum of 4 Accuracy Cost elements through-the-thickness. 3D layered continuum shell elements with 1 element through-the-thickness 19
- 20. How To Set Up A 3D Analysis 3D solid elements with 1 (or more) element(s) per composite ply. • All 6 stress components can be directly extracted from elements • This will cause the size of your model to be large. Restricted to use for coupons and sub- components. 20
- 21. How To Set Up A 3D Analysis 3D layered solid elements with a minimum of 4 elements through-the-thickness. • All 6 stress components can be directly extracted from elements, HOWEVER, interlaminar shear stress calculations are less accurate. • 4 elements through-the- thickness are required to capture proper bending stiffness. Restricted to use for coupons and sub-components. 21
- 22. How To Set Up A 3D Analysis 3D layered continuum shell elements with 1 element through-the-thickness • Shell theory assumes σz is zero. plies • With shell theory, out-of-plane shear stresses are not directly output (can be calculated indirectly – depend on input transverse shear stiffness values). • Typically used for full component. NOT RECOMMENDED for detailed analysis. 22
- 23. How To Set Up A “2.5D” Analysis Starting with 2D geometry… …Mesh the part using 2D elements Accuracy Cost 2D layered conventional shell elements 23
- 24. How To Set Up A “2.5D” Analysis 2D layered conventional shell elements • Shell theory assumes σz is zero. plies • With shell theory, out-of-plane shear stresses are not directly output (can be calculated indirectly – depend on input transverse shear stiffness values). • Typically used for full component. NOT RECOMMENDED for detailed analysis. 24
- 25. How To Set Up A 3D Analysis – Material Properties 3D analyses require 2 additional material properties that are sometimes difficult to find for the composite material(s) being analyzed: • ν23 – interlaminar Poisson ratio Typical values for UD materials: carbon fiber/epoxy = 0.5 glass/epoxy = 0.41 • S23 – transverse shear strength Typical value for UD materials: S23 = |0.33(S22-)| 25
- 27. Composite Failure Theories Max Stress Simplest to use but not good for multi- Max Strain axial loads Tsai Hill Better correlation for multi-axial loads but do Tsai Wu not provide failure modes Christensen Hashin Provide composite failure modes (matrix Puck or fiber) but are most complex to use MCT 27
- 28. Composite Failure Theories Max Stress Max Strain Require only in-plane stresses (strains) Tsai Hill and strengths (strains-to-failure) Tsai Wu Christensen Hashin Require 3D stresses and strengths Puck MCT 28
- 29. Composite Failure Theories Max Stress Max Strain Tsai Hill Tsai Wu Christensen Hashin Require experimental correlation Puck MCT 29
- 30. Composite Failure Theories Max Stress Max Strain Tsai Hill Tsai Wu Christensen Hashin Puck Predicts failure based on fiber and matrix MCT stresses (not composite ply stresses) 30
- 31. Composite Failure Theories Max Stress Max Strain WHICH ONE SHOULD I USE ??? Tsai Hill Cop Out Answer: Tsai Wu Use multiple failure criteria until you get a Christensen feel for which one provides you the most Hashin useful information for your purposes… Puck …But if you’re making a blind prediction tomorrow, this presenter uses and would MCT recommend MCT 31
- 33. What Is Progressive Failure Progressive failure predicts both composite failure: • initiation – Use a composite failure criterion to predict when a ply (element) has failed. • progression – When an element fails, the stiffness of the element is reduced so that stress is redistributed around the failed element and increases the stress level of adjacent elements. 33
- 34. Uses For Progressive Failure Ultimate Failure Predictions – Load Displacement Curves 34
- 35. Uses For Progressive Failure Ultimate Failure Predictions – Carpet Plots 35
- 36. Uses For Progressive Failure Failure Mode Determination 36
- 37. Wrap - Up • I am happy to email a copy of this presentation, email me at: milligand@firehole.com • I write a composites analysis blog that I invite you to follow: info.firehole.com/blog • I also invite you to connect with me on LinkedIn 37