Innovation Intelligence®

CAE Simulation Catalyzes Composites Growth:

Material Characterization

Modeling

Optimization

Giuseppe Resta

September 11-13, 2013

2013 SPE Automotive Composites

Conference & Exhibition (ACCE)

Intro: CAE Catalyzes Composites Growth in Automotive

• FEA established part of vehicle design process

• OEMs have developed simulation processes to meet Crash, NVH,

Durability, Vehicle Dynamic and Aerodynamic requirements

• CAE brings confidence to engineers and management comfortable with

CAE deliverables for traditional designs

Composite integration in existing automotive infostructure

also means integration in CAE processes

Agenda:

1. CAE for Material Characterization and Composite Failure

2. Stiffness and Strength Requirements

3. Composite CAE Process Overview

4. Laminate Composite Optimization

Innovation Intelligence®

Material Characterization and

Composite Failure

Material Knowledge as Composite Design Foundation

• Material performance and repeatability influenced by supplier and final

manufacturing process

• Role of complex shapes in composite variability

• Higher safety factor is not the answer:

• Predictability during crash may be compromised

• Overdesigned parts defies the initial selection of CF

• More expensive testing than metals > change material less frequently

Classic crash for axisymmetric tube as example

of limited shapes analyzed Dallara: Nose box Crash Simulation with modified

Tsai-Wu model for composites in RADIOSS

Material Characterization & Simulation: Building Block

• Tests and simulations at coupon, element and subcomponent levels

• Properties of materials derived from robust testing strategies and CAE

• Limit number of laminate configurations for coupon tests at the end of envelope

• Perform CAE calibration to cover additional condition and\or shapes for increased

confidence in composites material characterization

• Address the issues of variability, environment conditions, structural discontinuity,

damage, manufacturing defects, design or process-specific details

Building block approach: from coupon to full vehicle models

Material Characterization & Simulation: Micromechanics

• Calculate the homogenized engineering constants of a ply given the

engineering constants for each individual constituent making up the ply

• Calculate the constituent mechanical stress and strain tensors given the

homogenized mechanical strain tensor of the ply and the engineering

constants for each constituent of the ply

• Material and failure modeling

),,,,,,,,( 12231221mmmffffff

ijij VEVGEESS

),,,,,,( 211mmmffff

ii VEVE

Altair Partner Alliance offering in Micromechanics

Material Characterization & Simulation: Optimization

• Material calibration performed using optimization techniques:

• Select as design variables key material parameters

• Run design of experiments (DoE) :

1. understand the relations between responses and design variables.

2. screen the design variables that do not have significant effect on the responses

• Mathematical techniques used to minimize difference between sets of data for

efficient solution finding:

1. minimize the sum of normalized-difference-squared

2. calculating the area between two curves

• System identification to set target values to a number of responses and

automatically creates the difference equation and uses it as the objective function

Material Characterization & Simulation: Failure Modeling

• Composite failure models at the macroscopic level traditionally have

been empirically curve-fit models

• Seeking to curve-fit an assumed interaction equation given empirical

single state failure values

• Composite Failure Modes

• Excessive linear elastic deflection

• Instability or buckling

• Creep

• Fatigue

• Matrix crazing and/or shear yielding (onset of failure in the matrix)

• Fiber fracture (onset of failure in the fiber)

• Transverse ply fracture (creation of new surfaces within a ply)

• Ply delamination (creation of new surfaces between plies)

Material Characterization & Simulation: Failure Criteria

1,,max 1221

SYX

Maximum Stress Criteria

Maximum Strain Criteria

1,,max 1221

SYX

12

212

2

21

2

22

2

21

SXYX

Tsai-Hill First Ply Failure Criteria

Tsai-Wu First Ply Failure Criteria

2112

2 2 PiPiiiiPi WFWFWFF

11111

2 212

2

12

2

22112

2

1

CTCTCTCT YYXXSYYF

XX

Mat

rix

2-D

irec

tio

n S

tres

s

Fiber 1-Direction Stress

First Ply Failure Envelopes

Maximum Stress Tsai-Hill Tsai-Wu

XT

YT

XC

YC

Crasurv

Example: Fitting for Crasurv Failure Criteria by Simulation

• Composites often show a close-to-elastic behavior in fiber direction (0

deg and 90 deg) and brittle failure

• Shear tests (traction/compression in the direction of 45 degrees to the

fibers) show more non linear behavior In the present case we have

damage and rest stress in compression

One-shell model is used to verify material card data

0 degree

90 degree

45 degree

Tension

Compression

0-90 degree

45 degree

RADIOSS LAW25 with Crasur Criteria

• The parameters b and n in Crasurv criteria determined by curve fitting

Example: Fitting for Crasurv Criteria Through Simulation

Innovation Intelligence®

Stiffness and Strength

Requirements

Balancing Stiffness and Crash Requirements

• Stiffness mainly related to ride and handling performance

• Most body structure requirements are stiffness and fatigue dominated

• Strength dominant regions benefit from high specific strength

(side\roof impact)

• Energy management also require high level of elongation (front\rear

crash)

Typical weight involved for crash and stiffness

BIW

322 Kg

CRASH

191 Kg

STIFFNESS

199 Kg

96

95

104

27

Vehicle regions have different requirements

Crash Performance and Energy Absorption in Composites

• CFRP performance highly dependent on fiber orientation

• May show brittle and unstable deformation

• May show poor energy absorption

Brittle and unstable deformation

Stiff but low energy absorption Better energy absorption

Crash absorbers in helicopter crash

Thinner elements as crush initiator

Innovation Intelligence®

Composite CAE Process Overview

Pre Processing Zone or Ply Based Composites Modeling

Visualizations Visually Verify the Math Model

Optimization Composites

Design Optimization & Analysis

Post Processing Composites

Post-Processing & Failure Analysis

Typical CAE Process for Laminate Composites

Solution Export Ply Based Models to

Solver Zone Based Models

Detailed Composite Material

Modeling & Structural Modeling

CAD Manufacturing Interoperability

Typical CAE Modeling Process for Laminate Composites

• Import ply shape (geometric shape, lines) and ply data

(name, thickness, material, relative angles) Import CAD model

• Import existing mesh or create mesh Import/Create mesh

• Realize geometric shapes to FE ply shapes Geometric ply shape

realization

• Contains additional FE required for design/analysis but not required for manufacturing/documentation Template properties

• Defines the stacking sequence direction and the reference material orientation

Stack & Material orientation

• Visually verify math model via 3D visualizations (Ply shapes/orientation/thickness, Stacking sequence) Review & Modify

• Conversion of ply to zone based modeling Ply based model

realization

• Export to any supported solver Export & Solve

Pre-Processing: Composite Modeling Visualization

3D Representation of Traditional 1D & 2D Representations

Visually Verify Engineering Data Associated with a Math Model

3D Representation

Traditional 1D & 2D

Representation

3D Representation with

Composite Layers

Pre-Processing: Plies and Laminate

• Generic modeling approach

• Continuum Shells

• Visualization of elemental thickness against ply thickness as reference

• Review and adjust stacking direction

• 3D ply and ply angle visualization

• By thickness difference’ visualization mode

• Ply to zone based model realization

• Automatic property creation

• Conversion of ply based into zone based model

Normal/Stack direction

review 3D representation of plies

Review of ply angles

Ply based model

Creation of equivalent zone properties

Realize

Laminate

Pre-Processing: Composite Zone-Based Modeling

P1 45

P2 90

P3 -45

P4 0

Zone 1 Zone 2 Zone 3 Zone 2 Zone 1

P5 -45

P6 90

P7 45

Zone 1 – Property Table

Ply Mat Thk Theta

P7 M1 0.01 45

P4 M1 0.01 0

P1 M1 0.01 45

Zone 2 – Property Table

Ply Mat Thk Theta

P7 M1 0.01 45

P5 M1 0.01 -45

P4 M1 0.01 0

P3 M1 0.01 -45

P1 M1 0.01 45

Zone 3 – Property Table

Ply Mat Thk Theta

P7 M1 0.01 45

P6 M1 0.01 90

P5 M1 0.01 -45

P4 M1 0.01 0

P3 M1 0.01 -45

P2 M1 0.01 90

P1 M1 0.01 45

Zone 1

Zone 2

Zone 3

• One property is required for each laminate zone

• Plies are not linked across zones

• Data Duplication

• No Ply Shape

• No Relationship to the Mfg Process

• Design update requires 3 updates

• A composite part is made up of one laminate with multiple plies

• no data duplication

• direct relationship to the manufacturing process

• Ply based modeling process

• define ply shapes and related ply data

• define stacking sequence

• design update requires only 1 update

Pre-Processing: Composite Ply Based Modeling

P1 45

P2 90

P3 -45

P4 0

P6 90

P7 45

P5 -45

Stack Table

Ply Mat Thk Theta

P7 M1 0.01 45

P6 M1 0.01 90

P5 M1 0.01 -45

P4 M1 0.01 0

P3 M1 0.01 -45

P2 M1 0.01 90

P1 M1 0.01 45

Post-Processing: User Defined Failure Criteria

• User Defined Results Utilizing

• Existing Results

• Model Data

• External Tables

• Tcl/Tk or XML Scripts

• Example Onset Theory

Onset of failure occurs due to either dilatation

(change in volume - J1) or distortion (change in

shape - vm) exceeding critical material values

(J1cr, vm

cr)

J1 = 1+3 = x+y

J1/ J1cr < 1.0

vm = sqrt(12+3

2)/2.0

vm /vmcr < 1.0

Result Math applications in post processing

Innovation Intelligence®

Laminate Composite Optimization

Optimization in Composite Design

• Optimization as engineers’ best strategy to design laminate composite

structures and choose the right selection of laminate ply thickness,

orientation, and stacking

• Unless an optimized-based design is followed, the results will be a

composite part often overdesigned with redundant material, which adds

cost and weight

• Optimization injects innovation, urges thinking differently about design,

get the right answer faster, gives more insight into the design behavior

and manages conflicts

Laminate Composites Optimization in Optistruct

1. Free-Size Optimization (Concept) : used to generate design concepts,

while only considering global responses and optional manufacturing

constraints. “What ply shapes, for each ply layer, would build up the most

efficient composite part?”

2. Size Optimization (Dimension) : performed to control the thickness of each

ply bundle, while considering all design responses and optional

manufacturing constraints. “Exactly how many plies of each ply shape are

required to satisfy strength and manufacturing engineering requirements?”

3. Shuffling Optimization (Sequence) : optimization is applied to determine

the detailed stacking sequence, again while considering all behavior

responses and manufacturing constraints. “What are possible stacking

sequences that satisfy final part manufacturing requirements?”

Laminate Composite Optimization Process Overview

• (Free Size) What ply shapes, for each ply layer

• (Size) How many plies of each ply shape

• (Shuffling) Which stacking sequence

STACK

Sizing optimization

Number of Plies

Ply stacking optimization

Ply Sequence

OU

TP

UT

,FS

TO

SZ

OU

TP

UT

,SZ

TO

SH

Free size

Tailoring

Phase I: Composite Free-Size Optimization

• Typical setup

• Objective such as maximize stiffness (minimize compliance)

• Design constraint such as minimize volume fraction

• Design concept stage applied to super plies of nominal thickness

• At this stage of the process the shape of the part is already known

• The thickness for each element of each “super ply” with a particular fiber

orientation varies continuously to achieve the optimal composition of the

composite laminate at every point (element)

T = Ply3 (opti) 90

T = Ply2 (opti) -45 T = Ply4 (nom) 45

PCOMP

sym

T = Lower T = Upper

T = Ply3 (nom) 90

T = Ply2 (nom) -45

T = Ply1 (nom) 0

T = Ply4 (opti) 45

PCOMP

sym

T = Ply1 (opti) 0 T_0

T_Total

After Optimization

Phase I: Free-Size Optimization Interpretation

• Phase-I output contains the composite free-size optimization thickness results which

can be contour plotted to facilitate interpretations of the resulting optimized ply shapes.

Phase I: Free-Size Optimization Results Interpretation

• Automatic extraction of plies from free-sizing optimization

• User defined number of ply bundles per ply orientation

• Tune manufacturing complexity

• Automatic\Manual Ply Shape Interpretation

Phase II: Composite Ply Bundle Size Optimization

• Size optimization modifies a function of key input parameters controlling the

behavior of structural FE such as shell thickness, cross-sectional properties,

and stiffness:

• Free Size to Size automation generates plies for sizing and automatically

defines design variables and design variable property relationships for the

thickness of each ply shape resulting from the composite free-size

optimization. Manufacturing constraints are carried over from the Free Sizing

Phase automatically

• All behavior constraints (failure, displacement, buckling etc.) need to be

added

• Ensure manufacturing thickness is defined for each ply so that discrete ply

thicknesses is selected during the composite size optimization

Phase II: Bundle Sizing with Ply-Based FEA Modeling

• Composite Size Optimization determines number of plies of each ply

shape required to satisfy strength and manufacturing engineering

requirements

• Typical setup

• Design constrain like minimize displacement, strain less than.. no stress failure

• Objective such as minimize mass

Sizing optimization

Ply stacking optimization

OU

TP

UT

,FS

TO

SZ

OU

TP

UT

,SZ

TO

SH

Free size

ABD Matrix and Smear Technology

• Classic Lamination Theory:

• The [A] matrix relates plate resultant forces to middle surface strains defining the

extensional behavior of a laminate.

• The [B] matrix relates plate resultant forces to middle surface curvatures and plate

resultant moments to middle surface strains.

• The [D] matrix relates plate resultant moments to middle surface curvatures

defining the bending behavior of a laminate

• SMEAR technology is used to calculate a stacking sequence independent ABD

matrix for a laminated plate, by utilizing the homogeneous plate [B] and [D]

matrix equations with the laminated plate [A] matrix.

xt

t

x

o

xM

N

DB

BA

M

N

ABD Matrix with Symmetric and Balanced Laminates

• Classic Lamination Theory:

• The [B] Matrix is zero for symmetric laminates

• Balanced laminates have zero A14 and A24 components and exhibit no

extensional shear coupling behavior (A balanced laminate is defined as a laminate

for which every +q ply there exists a −q ply of the same thickness and material.

Txy

Ty

Tx

Txy

Ty

Tx

xy

y

x

xy

y

x

xy

y

x

xy

y

x

M

M

M

N

N

N

DDDBBB

DDDBBB

DDDBBB

BBBAAA

BBBAAA

BBBAAA

M

M

M

N

N

N

o

o

o

442414442414

242212242212

141211141211

442414442414

242212242212

141211141211

Extension-Shear

Extension-Bending Extension-Twist Shear-Twist

Bending-Twist Shear-Bending

Phase III: Composite Stacking Optimization

• Stacking optimization determines optimal stacking sequence for given

design optimization problem while also satisfying additional

manufacturing constraint

• Meet ply book rules, all behavior constraints, stacking manufacturing constraints

Sizing optimization

Ply stacking optimization

OU

TP

UT

,FS

TO

SZ

OU

TP

UT

,SZ

TO

SH

Free size

Conclusions:

• Prediction and validation of composites with CAE brings confidence to

the automotive industry comfortable with its deliverables for traditional

designs

• Material knowledge is at the foundation of composite design. Simulation

enables a more robust material characterization

• Extensive software offering now support the complete composite

design process

• Optimization as engineers’ best strategy to design laminate composite

efficiently