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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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2012 FALL WORKSHOP –
FINITE ELEMENT ANALYSIS OF COMPOSITES
DAN MILLIGAN, FIREHOLE COMPOSITES
Why Do This Talk? The Composites EXPLOSION
2
• 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
A Little About My Composites Experience
3
• 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.
What I Want To Talk About
4
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
BETTER FEA MODEL DESIGN
5
businesspundit.com
Boundary Condition Stress Concentrations
6
“Fixed” or “Encastre” BCs on plate ends…
Boundary Condition Stress Concentrations
7
“Fixed” or “Encastre” BCs on plate ends…
BETTER APPROACH
Applying Pressure To Composite Cross-Sections
8
Applying “Pressure” to a composite cross-section meshed with 1 element per ply…
P
Applying Pressure To Composite Cross-Sections
9
Applying “Pressure” to a composite cross-section meshed with 1 element per ply…
BETTER APPROACH
Use displacement equations or
coupling constraints to enforce
uniform displacement of end and
apply a concentrated force to
“control point”.
F
Poor Mesh Creation
10
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.
Poor Mesh Creation
11
Letting a mesh be generated “automatically”…
BETTER APPROACH: Use partitions to improve element quality
Poor Mesh Creation
12
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.
Improper Symmetry Constraint Use
13
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.
Improper Symmetry Constraint Use
14
Using symmetry boundary conditions to reduce element count in symmetric composite
structures…
BETTER APPROACH: Bite the bullet and model the full structure.
MOVE BEYOND 2D
15
halftimegames.com
What Is A Full 3D Analysis?
16
x y
z
σz
σy
σx
τxy
τyz τxz
Use FEA modeling techniques that
capture 3D stresses in a
composite part
A 2D analysis ignores or estimates 3 of the 6 stress components
Why Do We Need A Full 3D Analysis?
17
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.
When To Use 3D Analysis
18
Skin-Stringer Thick Wall Pressure
Vessel
cstcomposites.com sciencedirect.com
Joints
- bolt pretension
- lap shear
- scarf joints
structuralmechanics.com
How To Set Up A 3D Analysis
19
Starting with 3D geometry…
…Mesh the part using 3D elements
Accuracy Cost
3D solid elements with 1 (or more) element(s) per
composite ply.
3D layered solid elements with a minimum of 4
elements through-the-thickness.
3D layered continuum shell elements with 1 element
through-the-thickness
How To Set Up A 3D Analysis
20
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.
How To Set Up A 3D Analysis
21
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.
How To Set Up A 3D Analysis
22
3D layered continuum shell elements with 1 element
through-the-thickness
• Shell theory assumes σz is zero. • 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.
plies
How To Set Up A “2.5D” Analysis
23
Starting with 2D geometry…
…Mesh the part using 2D elements
Accuracy Cost
2D layered conventional shell elements
How To Set Up A “2.5D” Analysis
24
• Shell theory assumes σz is zero. • 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.
2D layered conventional shell elements
plies
How To Set Up A 3D Analysis – Material Properties
25
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-)|
COMPOSITE FAILURE THEORIES
26
flyingblades.blogspot.com
Composite Failure Theories
27
Max Stress
Max Strain
Tsai Hill
Tsai Wu
Christensen
Hashin
Puck
MCT
Simplest to use but not good for multi-
axial loads
Better correlation for multi-axial loads but do
not provide failure modes
Provide composite failure modes (matrix
or fiber) but are most complex to use
Composite Failure Theories
28
Max Stress
Max Strain
Tsai Hill
Tsai Wu
Christensen
Hashin
Puck
MCT
Require only in-plane stresses (strains)
and strengths (strains-to-failure)
Require 3D stresses and strengths
Composite Failure Theories
29
Max Stress
Max Strain
Tsai Hill
Tsai Wu
Christensen
Hashin
Puck
MCT
Require experimental correlation
Composite Failure Theories
30
Max Stress
Max Strain
Tsai Hill
Tsai Wu
Christensen
Hashin
Puck
MCT Predicts failure based on fiber and matrix
stresses (not composite ply stresses)
Composite Failure Theories
31
Max Stress
Max Strain
Tsai Hill
Tsai Wu
Christensen
Hashin
Puck
MCT
WHICH ONE SHOULD I USE ???
Cop Out Answer:
Use multiple failure criteria until you get a
feel for which one provides you the most
useful information for your purposes…
…But if you’re making a blind prediction
tomorrow, this presenter uses and would
recommend MCT
PROGRESSIVE FAILURE
32
flyingblades.blogspot.com
What Is Progressive Failure
33
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.
Uses For Progressive Failure
34
Ultimate Failure Predictions – Load Displacement Curves
Uses For Progressive Failure
35
Ultimate Failure Predictions – Carpet Plots
Uses For Progressive Failure
36
Failure Mode Determination
Wrap - Up
37
• I am happy to email a copy of this presentation, email me at:
• 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
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