Camanho2008.pdf

Faculdade de Engenharia da Universidade do Porto
Departamento de Engenharia Mecânica e Gestão Industrial
Numerical simulation of damage
in composites: current status and
future developments
Pedro P Camanho
University of Porto
Portugal
Carlos G Dávila
NASA Langley Research Center
Hampton, VA, USA
Contents
9 Introduction.
9 Finite Element models for damage and
fracture of composites
• Delamination.
• Intralaminar damage.
9 Applications.
9 Conclusions.
Introduction
Building Block
Integration.
Structural Levels of Analysis
Full Scale
Article
Analysis
Chronological Sequence
Specimen Complexity
Certification Methodology (Mil-Hbk.-17)
Static/
Fatigue
Verification of Design
Data and Methodology
Components
Sub-components
No
T
Structural Elements
es Development of Design
Data
tin
g
Design Allowables Coupons
Material Selection and Qualifications Coupons
Number of Specimens
• High-fidelity Progressive Damage Analysis
•reduced reliance on testing
reduced non-recurring costs
•faster design process
•more accurate design tools
reduced recurring costs
Introduction
• The failure of composites is a progressive event;
even fiber failure may not be catastrophic
• Emerging composite DT requirements – need for
life/residual strength prediction, including damage
onset and growth
• Scale effects
• Virtual testing:
• load incrementation without user’s intervention
• reduced testing
• Applications:
• detail design
• failure investigations
Introduction
+45°
Matrix
cracking
delamination
-45°
-45°
Matrix
cracking
0°
Fibre
fracture (kinck)
Introduction
Modeling
Modeling Complexities
Complexities
•• Failure
Failure of
of unidirectional
unidirectional plies
plies
•• Failure
Failure of
of laminated
laminated composites
composites (in-situ)
(in-situ)
•• Material
Material nonlinearity
nonlinearity
•• Material
Material degradation
degradation laws
laws
•• Thermal
Thermal residual
residual stresses
stresses
•• Finite
Finite Element
Element implem.
implem. (mesh
(mesh effects)
effects)
•• Effects
Effects of
of stress
stress gradients
gradients &
& notches
notches
•• Built-up
Built-up structures
structures
•• Stitched
Stitched composites
composites and
and textiles
textiles
•• Delamination
Delamination growth
growth
•• Damage
Damage mode
mode interaction
interaction
σR
ϕ
σR
Introduction
Through-the-thickness crack
• fracture mechanics and modifications
• strain softening
Ply Damage
• continuum damage modeling (CDM)
• strength-based methods
• micromechanics approach
Delamination/Debonding
• fracture mechanics approaches (FM)
• decohesion elements
Introduction
Finite Element representation of failure process
x
Strong discontinuity
Band of localized strain separated by
two weak discontinuities
Continuous profile of localised strain
Jirásek, ECCM-2001
Introduction
Main difficulties
Strain softening
constitutive models
Bifurcation of the
solution.
• Non-local constitutive models.
• Gradient methods.
• Rate-dependence.
• Inability of FEM to
represent energy dissipated.
• Localization.
• Mesh dependence.
• Include element
characteristic length in
constitutive model:
W Fracture = AeW Cont ( ε u , h )
σ
σ
U
σ
U
ε
Energia = U × A × L
Energia = U × A ×
L
n
ε
ε
Energia = U × A ×
L
2
n → ∞ ⇒ Energy → 0
Delamination
VCCT
+45°
-45°
GI = −
1 ⎡
⎤
'
F
v
−
v
(
)
∑ yi di d 'i ⎥⎦
2∆b j ⎢⎣ i
Delamination
Objective
Develop a methodology to predict progressive delamination
• non self-similar delamination growth
• capable of simultaneous delamination fronts
• no post-process analyses required
• no user intervention during analysis
• works in conjunction with intra-ply damage simulations
Approach: decohesion elements
• Zero-thickness nonlinear elements simulate
bond between layers.
• Mixed-mode failure criterion combines
stresses and energy release rates
Delamination
⎛ σz
⎜
⎝ T
2
+
2
⎞ ⎛ τ xz ⎞ ⎛ τ yz ⎞
⎟ +⎜ ⎟ +⎜ ⎟ =1
⎠ ⎝ S ⎠ ⎝ S ⎠
2
Mode I
Mode II
• Stress interaction law maps
damage initiation
• Mixed-mode critical Gcc
maps delamination growth
η
⎛ GII ⎞
Gc = GIc + (GIIc − GIc ) ⎜
⎟
⎝ GI + GII ⎠
Delamination
MMB Specimen
Force (N)
AS4/PEEK
Analysis (P. Camanho)
Experimental (J. Reeder)
Applied Displacement (mm)
Intralaminar damage
Matrix failure
2
σy
2
⎛ σ y ⎞ ⎛ τ xy ⎞
⎜
⎟ +⎜
⎟ =1
⎝ Yt / c ⎠ ⎝ S c ⎠
Xt /c
Xt / c , Yt / c , Sc
=1
Fiber-matrix shear
2
Ply Strengths:
σx
Fiber damage
σx
τxy
σx
2
⎛ σ x ⎞ ⎛ τ xy ⎞
⎜
⎟ +⎜
⎟ =1
⎝ X c ⎠ ⎝ Sc ⎠
τxy
Material Degradation Table
Material state
Elastic Properties
FV1
FV2
Elastic
E
property
0
0
FV3
No failure
Ex
Ey
υ xy
Gxy
Matrix failure
Ex
0
0
Gxy
1
0
0
Fiber/matrix shear
Ex
Ey
0
0
0
1
0
Fiber
damage
Fiber
buckling
0
0
0
0
0
0
1
0
Residual=E/1000
1
Failure criterion
Intralaminar damage
Ψ ( ε,d,T )
∂Ψ
σ=
= (1 − d )C:ε
∂ε
t
t
Fk := Φ k (σ ) − rk
Free Energy per unit volume:
Constitutive equation:
Damage activation functions:
Damage evolution:
t
t
d = G ( rk )
Intralaminar damage
Final biaxial failure stress envelope for
(90/±30/90) E-glass/LY556 laminate.
World Wide Failure Exercise
Puck
• International round robin to compare
the most advanced failure criteria
• Organized by Hinton & Soden
(QinetiQ, UK), published in ’98, ‘02
• Cases of simplest constructions,
e.g., no stress concentrations, or
structural issues
• Comparison indicates that strength
prediction methodologies still
immature.
• What is the consensus?
Intralaminar damage : σ22>0 and σ12
σ22
t
T
0
2a
σ22
0.3
Transverse Strength of 90 ° Ply, GPa
Main unresolved issue:
9 ‘In-situ’ effects.
T300/944
Dvorak, 1987
[±25/90n]s
[252/-252/902]s
[908]s
Onset of
delamination
0.2
[0/90n/0]
Thin ply model
Thin Thick
0.1
Thick ply model
Unidirectional
0
0
0.4
0.8
1.2
1.6
Inner 90° Ply Thickness 2a, mm
2.0
Intralaminar damage: σ22<0 and σ12
Main unresolved issue:
9 Increase of strength when moderate transverse compression
τ12 , MPa
is combined with in-plane shear.
Test (WWFE)
σ22
120
100
80
60
Max Stress
40
Hashin
20
σ22
0
-160
-140
-120
-100
-80
-60
σ 22 , MPa
-40
-20
0
Intralaminar damage
LaRC03 Failure Criteria
3 (T)
3 (T)
t
2a0
Matrix Crack
1(L)
2a0
σ22
Fibre kinck
2a0
2
L
-XC
ϕ
σ11
σ22m
σ11m
-XC
Intralaminar damage
LaRC03 Failure Criteria
Scotchply
E-glass-LY556
T800-3900-2
CFRP laminate
160,0
LaRC03
Compressive stress, MPa
140,0
120,0
Max. Stress
τ 12 [MPa]
100,0
80,0
Hashin
60,0
40,0
20,0
Hashin ‘73
[±θ]s
LaRC02
Test, Shuart ‘89
α=00
α=44
0,0
-250,0
-200,0
-150,0
-100,0
-50,0
0,0
50,0
100,0
σ 22 [MPa]
Lamination angle, degrees
0
α0=530
Applications
Detail of notch tip
Stitched/RFI Upper Wing Cover Panel
7-ply stack
Potting
Load
⎡ 45 / − 45 / 0 / 90 ⎤
⎣
⎦S
Knife edges
α
Notch
5
43 in.
z
Potting
y
x
7 in.
19 in.
Length of damage zone (in.)
simulation
4
F
3
experiment
E
2
D
stitches
C
1
B
A
0
0
0.05
0.1
Applied end shortening (in.)
0.15
notch tip
Conclusions
Predicting Strength of Composites is Difficult
9 Calculation of stresses, strains, natural frequencies, buckling loads, is routine
in aerospace industry.
9 Calculation of fracture and damage growth is not routine.
Role of Progressive Damage Analysis
9 Simulates damage accumulation, load redistribution, and failure of a
component.
9 Can reduce the cost of design certification.
9 Can lead to a better design.
The technologies developed have a clear impact on the industry and
services:
9 Abaqus Inc. selected the decohesion element developed to be implemented in
version 6.5 of Abaqus FE code.
9 LaRC03 failure criteria selected to be implemented in Hypersizer.
9 Failure investigation of aircraft accident based on the technologies developed.