Transcript Workshop on 3-D Woven Composite Structures

Principles of Modeling Textile
Composites
Issues
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Textile composites are not monolithic
Mechanical characterization is not complete
High degree of heterogeneity
More variation in modulus than strength
Modelling Approach
 Must have understanding of ultimate objective
 Stiffness or strength?
 Ideal or real geometry?
 Computational cost…
Application of Models
Component Design
Process Design
Material Characterization
Component Testing
Structural Analysis
Unit Cell Modelling
Material Variations
Reliability
Modelling Needs
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Correct kinematics
Reasonable assumptions
Correct properties
Correlation between experiment and predictions
Kinematics
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Satisfy External Boundary Conditions
Satisfy Internal Boundary Conditions
Continuity of displacements
Continuity of strains or stresses as appropriate
Assumptions
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Fiber-resin interface - bonding
Isostrain, Isostress, ???
Small deformation
Plastic deformation in matrix?
Properties
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Fiber or yarn properties?
Twisted yarns?
Crimp
Interaction of yarns at cross-overs
Effect of yarn size
Coarse Characterization
 Homogeneous
 Heterogeneous
 Mosaic
Homogeneous
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"Smearing Method"
Don't identify individual phases
Only concerned with point correlations of phases
Model typically insensitive to geometric parameters
Heterogeneous
 Finite Element Methods
 Strictly distinguish yarns from matrix
 Sensitive to geometry
Mosaic
 Separate structure into blocks
 Each block contains homogeneous material
 Between blocks is heterogeneous
Homogeneous History
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Rules of mixtures
Modified Matrix Method (XYZ)
Stiffness Averaging (FGM)
Compliance Averaging
Property Blending
Homogeneous Philosophy
Fiber Properties
Micromechanics
Matrix Properties
Ply/yarn orientation Transformation
Unidirectional
Properties
Combine layers
Unidirectional
Properties
Layer properties
Composite stiffness matrix
Modified Matrix Method
 Developed by Tarnopolskii to model XYZ type
structures.
 The Z yarns are accounted by developing a “modified
matrix” which consists of resin and Z yarns.
 The X and Y yarns are then treated as laminates
where the unidirectional properties are calculated
using the orthotropic modified matrix
FGM
 The FGM Method is a variation on the stiffness
averaging method developed by Kregers and Teters.
 Unidirectional stiffness matrices are developed based
on the overall part fiber volume fraction
 The fabric is subdivided into piecewise linear
elements
 Transformation matrices are developed for each
element and corresponding stiffness matrices
calculated (similar to laminate theory)
 Element stiffness matrices are combined iso-stress
Comparison test
 Two types of XYZ weaves were fabricated and tested
 Glass/epoxy
 Different amounts of Z yarns in the two systems
Homogeneous Results
Type I
Type II
30
30
25
25
Exper 20
MM-1
MM-2 15
20
15
FGM
10
10
5
5
0
0
E11
E22
E33
E11
E22
E33
Variations on Homogeneity
3.8
FGM
3.6
Kregers
MMM
3.4
3.2
3
2.8
q
2.6
2.4
2.2
2
0
15
30
45
E11as a function of Weave Angle
Homogeneous Advantages
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Calculations are quick
Model insensitive to geometry
Good predictions of elastic properties
Simple failure criteria can be applied
Output is constitutive law
Homogeneous Disadvantages
 No way to account for interface/interphase
 Cannot track damage progression
 Cannot account for size, edges, local defects, etc.
Homogenization for Reliability
 Evaluate the distribution of elastic properties based
on the material variations in a unit cell
 Apply stiffness averaging method in a Monte Carlo simulation
 Applicable to stochastic structural analysis
Heterogeneous History
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Stick models (frames and trusses)
"Mosaic" model (semi-heterogeneous)
Full 3-D Modelling
2-D "Modal" analysis
Heterogeneous Types
 Finite Element Models
 Stick Models
FEA Example
 Whitcombe - Plain weave
1.3
Z
Y
Normalized Modulus
1.2
Ex
1.1
Ez
Gxy
1.0
Gyz
0.9
0.8
0.7
0.1
X
0.2
0.3
0.4
Waviness Ratio
0.5
Stick Example
Y
Matrix Member
Fiber Member
X
Z
Stick Comparison
FGM
Exp
FGM
100
80
75
60
Stress (ksi)
Stress (ksi)
FCM
50
FCM
EXP
40
20
25
0
0
0
0.25
0.5
0.75
Strain
Carbon/Epoxy 3-D Braids, 50% Axial
1
0
0.5
1
1.5
2
2.5
Strain
Carbon/Epoxy 3-D Braid, No Axial
3
Heterogeneous Advantages
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Output is structural analysis
Can be used to track damage progression
Complex failure criteria can be incorporated
Pedagogical
Heterogeneous Disadvantages
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Highly geometry sensitive
Large number of degrees of freedom
Hard to mesh
Output is structural analysis
Mosaic History
 "Sugar cube" method (Foye)
 GINA (Gowayed)
 SEDAF-sugar cube (Bogdanovich)
Mosaic Types
By
Sub-volume
"Sugar
Cube"
Mosaic Advantages
 Can provide partial heterogeneity
 Not very geometry sensitive
 Can be used for material property or structural
analysis purposes
 Partial damage tracking
Mosaic Disadvantages
 Does not fully represent geometry
 Partial damage tracking
 More degrees of freedom than homogenization
Sensitivity to Material Modelling
 SEDAF Mosaic approach
 3-D Weave, transverse bending
 Plain weave, axial tension
 Use material smart solution algorithm
 Solution is sensitive to material description
Mechanical Property Predictions
 to model the structural response it is necessary to describe the
mechanical properties of the material.
 The simplest form is to treat as homogenous medium with
anisotropic properties.
 This is termed homogenization of the material.
 If the volume of material to be homogenized is small compared to the
structural component, this approach seems reasonable.
 In the case of textile reinforced materials, the RVE is typically quite large,
on the order of cm in some cases. It may not be reasonable to consider the
RVE as representing the response of the material
 Special analytical tools need to be developed to understand the local
response within the RVE.
Homogenization of Properties
 Analytical techniques have been developed to predict the elastic
properties of textile composite RVE's.
 averaging mechanical properties of the constituent materials,
 Bolotin (1966), Nosarev (1967), Tarnopol'skii et al. (1967), and Sendeckyj (1970), Roze and
Zhigun (1970), Kregers and Melbardis (1978), Kregers and Teters (1979), Chou et al. (1986),
Ishikawa and Chou (1982), Jortner (1984), Whyte (1986), Ko et al. (1987), Ko and Pastore
(1989) , Howarth (1991) , Jaranson et al. (1993), Singletary (1994), Pochiraju et al. (1993)
 property predictions based upon detailed geometric descriptions of the
reinforcement, and
 Foye (1991), Gowayed (1992), Bogdanovich et al. (1993), Carter et al. (1995).
 finite element methods treating matrix and fiber as discrete components.
 Kabelka (1984), Woo and Whitcomb (1993), Sankar and Marrey (1993), Yoshino and Ohtsuka
(1982), Whitcomb (1989), Dasgupta et al. (1992), Naik and Ganesh (1992), Lene and Paumelle
(1992), Blacketter et al. (1993) and Glaesgen et al. (1996), Hill et al. (1994), Naik (1994)
Non-RVE Considerations
 The size of the RVE is relatively large compared to
test specimens and some actual structures.
 The application of RVE based analysis may not be
appropriate
 Even experimental data can be effected by this
assumption
 The strain gage used in tensile testing usually covers
only a few RVEs of the textile, and sometimes even
less than 1.
Moiré Interferometry Field on Axially
Loaded Braided Composite
Measurements of Elastic Properties
 If the measurement system does not contain a large
number of RVEs, then the measurements do not
reflect a true average value.
 The location of the gage will affect the measured
values.
 Some of the perceived high variation in tensile
modulus may be due to the relationship between
strain gage and RVE size.
Elastic Modulus vs. Gage Area for
Braided and 3D Woven Composites
1.3
1.2
1.1
Normalized
Tensile
1
Modulus
0.9
0.8
0.7
0
2
4
6
Gage Area/ Unit Cell Area
8
Location of Test Cell
with Respect to Unit Cells in a Triaxial Braid
Predicted Tensile Moduli for 60° Triaxial Braid AS-4/
Epoxy Test Cell with y1 = b and x1 = 4.1a
Predicted and Experimental Tensile Modulus of a Triaxially Braided AS-4/
Epoxy Composite with 45° Braid Angle and 12% Longitudinal Yarns
Predicted and Experimental Tensile Modulus of a Triaxially Braided AS4/Epoxy Composite with 45° Braid Angle and 46% Longitudinal Yarns
Predicted and Experimental Tensile Modulus of a Triaxially Braided AS-4/
Epoxy Composite with 70° Braid Angle and 46% Longitudinal Yarns
Physical Limitations
 Current cost of production.
 modifications to machines are needed for shaping capabilities,
 capital cost is applied to a few prototypes, the unit cost is
tremendous (no economy of scale)
 Processing difficulties.
 infiltration at high pressure, and thermal effects during curing.
 frequently results in internal yarn geometry distortions.
 elastic and strength properties have high variation.
 thermal effects can result in local disbonds from yarns.
 One approach that seems promising is the use of cold cure systems such as ebeam curing to reduce the temperature of cure and thus reduce the effect of
different coefficients of thermal expansion between the fiber and resin.
Analytical Shortcomings
 Analytical techniques are still not adequate to satisfy
structural analysts planning to apply these materials
to load bearing structures.
 Some “variation” in elastic performance is expected
due to a non-integer number of RVE's.
 the design allowables for the materials are greatly reduced,
frequently making them appear unsuitable for structural application
due to the perception of high weight penalty.
 It is possible to account for this behavior even with simple tools
such as stiffness averaging if the non-RVE element is modeled.
Failure Analysis
 Understanding of failure initiation and growth is still
required.
 Greater resolution of the internal stress state is needed than that for
establishing homogenized elastic constants.
 Failure modes are poorly understood.
 These modes are associated with local curvature and distortion of the
yarns at crossover points, and cracking between yarn bundles (interbundle cracking).
 Transverse cracking and fiber failure within the yarns (intra-bundle
cracking) are also a function of the complex stress state inherent in a
textile.
 An important issue is how curvature and inter-bundle cracking affect
compression by reducing the stability of the yarn.