finite element analysis of composites by dan milligan

2012 FALL WORKSHOP –

FINITE ELEMENT ANALYSIS OF COMPOSITES

DAN MILLIGAN, FIREHOLE COMPOSITES

MILLIGAND@FIREHOLE.COM

Why Do This Talk? The Composites EXPLOSION

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• 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

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• 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

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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

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businesspundit.com

Boundary Condition Stress Concentrations

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“Fixed” or “Encastre” BCs on plate ends…

Boundary Condition Stress Concentrations

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“Fixed” or “Encastre” BCs on plate ends…

BETTER APPROACH

Applying Pressure To Composite Cross-Sections

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Applying “Pressure” to a composite cross-section meshed with 1 element per ply…

P

Applying Pressure To Composite Cross-Sections

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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

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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

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Letting a mesh be generated “automatically”…

BETTER APPROACH: Use partitions to improve element quality

Poor Mesh Creation

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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

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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

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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

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halftimegames.com

What Is A Full 3D Analysis?

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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?

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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

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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

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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

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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

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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

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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

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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

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• 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

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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

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flyingblades.blogspot.com

Composite Failure Theories

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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

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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

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Max Stress

Max Strain

Tsai Hill

Tsai Wu

Christensen

Hashin

Puck

MCT

Require experimental correlation

Composite Failure Theories

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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

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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

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What Is Progressive Failure

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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

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Ultimate Failure Predictions – Load Displacement Curves

Uses For Progressive Failure

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Ultimate Failure Predictions – Carpet Plots

Uses For Progressive Failure

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Failure Mode Determination

Wrap - Up

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• 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