An Overview of Multicontinuum Theory with Application to Progressive Failure of Large Scale Composite Structures

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An Overview of Multicontinuum Theory with
Application to Progressive Failure ofLarge Scale
Composite Structures

• Don Robbins
• Chief Engineer
• Firehole Technologies, Inc.
• Laramie, Wyoming

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TM
HeliusMCT is a software module that integrates
seamlessly with commercial F.E. codes, providing
accurate multiscale material response for
progress failure analysis of composite
structures.
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• Requirements for Effective Finite Element
  Analysis
• of Progressive Failure of Composite Structures

a) Deformation must be represented at the
appropriate scale (dictated entirely by
mesh density and element type) b) Material
Response must be predicted accurately c) Loading
and Constraints must be realistic d) Must use
an Effective Nonlinear Solution Strategy
(e.g., incrementation scheme, regularization,
etc.)
Common Difficulties

• Mesh discretization typically can not reach the
  
• material ply level ? must use ply grouping
  (sublaminates)
• Lack of practical constitutive relations that
  accurately
• represent material degradation
  (damage/failure)
• Convergence is very difficult to achieve

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OUTLINE

• Idealization of Failure in Composite Materials
• Independent Variables for Predicting Failure
• Failure Criteria, and the Consequences of
  Failure
• MCT Characterization of Composite Materials
• Selected Demonstration Problems

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Idealization of Failure in Composite Materials

In a heterogeneous composite material, failure is
assumed to occur at the constituent material
level.
Matrix damage/failure occurs due to stresses in
the Matrix
Matrix
The homogenized composite stress state does
not provide this info.
Fiber
Fiber damage/failure occurs due to stresses in
the Fibers
Matrix damage/failure degraded
Matrix properties
Fiber damage/failure degraded
Fiber properties
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Idealization of Failure in Composite Materials

A micromechanical finite element model is used to
establish consistency between the homogenized
composite properties and the damaged or failed
constituent properties.
Degraded Matrix Properties Degraded Fiber
Properties
Micromechanical Finite Element Model
Degraded Composite Properties
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• Idealization of Failure in Composite Materials

How should constituent material stiffness be
reduced in the event of a constituent
damage/failure event?
Matrix Failure
Fiber Failure
Should matrix stiffness be degraded
Isotropically or Orthotropically?
Should fiber stiffness be degraded Isotropically
or Orthotropically?
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Idealization of Failure in Composite Materials
1. Isotropic degradation requires less
experimental data, and there is usually a
lack of available experimental data 2.
Isotropic degradation does degrade the stiffness
of the primary load path. ? causes
redistribution of the primary load path. 3.
Isotropic degradation also degrades the stiffness
of non-primary load paths. ? largely
inconsequential for monotonic loading.
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Idealization of Failure in Composite Materials
Consequences of Fiber Damage/Failure
Orthotropic Stiffness Degradation
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• Idealization of Failure in Composite Materials

In Situ Matrix Properties In Situ Fiber
Properties
Measured Composite Properties
Micromechanical F.E. Model
Hypothesize the modes and consequences of
constituent damage or failure
1. Measured Composite Properties 2. In Situ
Constituent Properties 3. Constituent Damage or
Failure Model 4. Degraded In Situ Constituent
Properties 5. Degraded Composite Properties
Degraded Matrix Properties Degraded
Fiber Properties
Degraded Composite Properties
Micromechanical F.E. Model
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• Independent Variables for Predicting
• Damage/Failure in Composites

Constituent Failure f ( ? )
Logical Candidates Stress, Strain, or Both
But exactly which measures of stress or strain?
i.e., at what scale should strain stress be
represented?
Homogenized Laminate-Level Stress (Laminate
Average Stress) Homogenized Composite Stress
(Composite Average Stress) . . Constituent
Average Stress . Actual stress field within the
constituents of the microstructure
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Independent Variables for Predicting
Damage/Failure in Composites
Desired attributes for the independent variables
used to predict composite material response
The variables chosen for predicting material
response must be physically relevant to the
material considered. Calculation of the
variables should be efficient, adding minimal
computational burden to the structural level
finite element analysis. Calculation of the
variables should be consistent the calculated
variables should not be overly sensitive to
a) idealization of the microstructural
architectural, or b) micromechanical
mesh-related issues. Method used to calculate
the variables should be scalable as the
microstructural architecture becomes more complex
(e.g. unidirectional ? woven ? braided, etc.).
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Independent Variables for Predicting
Damage/Failure in Composites
Constituent Average Strain Stress States
?
?
?
(?j ? ?j ?T)
?i

?1,2, of constituents
i,j 1,2,,6
Retains a significant level of physical relevance

Efficient Calculation via MCT decomposition

Consistent (stability w/r to idealization and
meshing of microstructure)


Scalable (same basic calculation method for
unidirectional, woven, braided composites, etc.)
MCT decomposition requires linearized
constitutive relations
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• Filtering Characteristics of Volume Average
  Stress States

Constituent Average Stress States
Composite Average Stress States
Filters out all stress components that
are self-equilibrating over the entire RVE
Filters out all stress components that are
self-equilibrating over each individual
constituent material.
Retains Poisson interactions between
constituents.
Filters out Poisson interactions between
constituents.

Retains thermal interactions between
constituents caused by differences in thermal
expansion coefficients.
Filters out thermal interactions
between constituents caused by differences in
thermal expansion coefficients.

Filters out self-equilibrating shear stresses
that arise solely to satisfy local equilibrium.
Filters out self-equilibrating shear stresses
that arise solely to satisfy local equilibrium.
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• Computation of Constituent Average Stress States

matrix average stress state
Composite RVE
?m 1 ? ? dv
ij
Vm
ij
Dm
fiber average stress state
?f 1 ? ? dv
Dc Dm ? Df
ij
Vf
ij
Df
It is NOT necessary to integrate stresses and
strains over the micromechanical F.E. model.
MCT Decomposition Instead, we use
transfer functions Hill (1963), Garnich Hansen
(1990s) to accurately efficiently decompose
the composite average strain state into the
constituent average strain states.
composite average stress state
?c 1 ? ? dv
ij
Vc
ij
Dc
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• MCT Decomposition

matrix average strain state
composite average strain state
transfer function Hill (1963), Garnich Hansen
(1990s)
?m
?c
cTm
(C, C, C, ?, ?, ?, ? )
c m f c m f m
linearized about as many different discrete
damaged states as desired
?c ?m?m ?f?f
fiber average strain state
matrix average stress state
fiber average stress state
?f Cf (?f ? ? ?f )
?m Cm (?m ? ? ?m )
This process adds less than 3 to the overall
cost of an equilibrium iteration In a typical
F.E. analysis of a composite structure!
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Idealization of Failure in Composite Materials
A Simple Case Three Discrete Damaged States
matrix failure event
fiber failure event
Damaged State 1 Undamaged matrix, Undamaged fibers
Damaged State 2 Failed matrix, Undamaged fibers
Damaged State 3 Failed matrix, Failed fibers
matrix failure event
?c
Response of the composite to imposed deformation
1
fiber failure event
2
3
?c
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• Constituent Failure Criteria

Matrix Failure Criterion
Fiber Failure Criterion
If ?m (?m) ? 1,
If ?f (?f) ? 1,
Then Matrix properties are isotropically
degraded by a user-specified amount.
Then Fiber properties are orthotropically
degraded by a user-specified amount.
Micromechanical F.E. Model
Degraded Composite Properties
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• MCT Material Characterization

Step 1.
Optimize the in situ constituent properties so
that the micromechanical finite element model
matches the measured properties of the composite
material
in situ constituent properties
homogenized composite properties
Cm, ?m Cf , ?f
Micromechanical Finite Element Model of RVE
Cc, ?c
measured composite properties
c c c c c
c
?12, ?13, ?23, ?11, ?22, ?33
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• MCT Material Characterization

Step 2.
Determine the coefficients of the constituent
failure criteria so that the micromechanical
finite element model matches the measured
strengths of the composite material
constituent failure criteria
measured composite strengths
?m ?1 ?f ?1
Decomposition
measured composite strengths
c c? c c? c c
S11, S11, S22, S22, S12, S23
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• Summary

• Micromechanical F.E. models are only used during
  the material characterization process, not during
  the actual structural-level finite element
  analysis.
• During the material characterization process, the
  micromechanical F.E. model is used to establish
  in situ constituent properties and homogenized
  composite properties for a finite set of discrete
  damage states (?3).
• These properties are stored in a database and can
  be quickly accessed by the structural-level
  finite element model as dictated by the outcome
  of the constituent failure criteria.
• The coefficients of the constituent failure
  criteria are determined using only industry
  standard strength tests.
• The entire process of computing the constituent
  average stress states, evaluating the constituent
  failure criteria, and identifying the damaged
  properties of the composite material adds less
  than 3 to the total cost of an equilibrium
  Iteration in a structural-level finite element
  analysis.

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Example Atlas V CCB Conical ISA (Used on all
Atlas V 400 series launches)
Diameter 12.5 to 10 Height 65
inches Graphite/epoxy and honeycomb core
Loading Combined vertical compression
horizontal shear, designed to drive failure in
the top corner of the access door.
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Structural Response Predicted with HeliusMCTTM
of flight load
vertical displacement of load head (in)
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structural response softening becomes detectable
impending global failure
185 Flight Load
170 Flight Load
190 Flight Load
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• The modified ISA was tested to failure at AFRL
  Kirtland (Oct. 2008).
• Ultimate failure measured at 183 of Flight
  Load
• The ISA exhibited a nearly linear response up to
  ultimate failure
• Final failure process was very rapid (almost
  instantaneous)
• Failure initiated at door corners and progressed
  circumferentially

Failure initiated at door corners
Rapidly propagated around circumference
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measured global failure load
structural response predicted with MCT
of flight load
vertical displacement of load head (in)
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Excellent agreement was achieved for 1)
Location of Failure Initiation 2) Failure
Evolution Behavior 3) Ultimate Load
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Example Unlined Cryogenic Composite Pressure
Vessel
Loading 1. Submerge tank in liquid nitrogen
(?T -216?C) 2. Pressurize tank until a
constant leakage rate was detected
Six tanks were tested with an average leak
pressure of 1233 psi.
No Damage
Matrix Damage
Fiber Damage
?c
?c
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Good correlation between predicted region of
permeation and observed region of permeation
crack saturation
observed permeation
Matrix Damage
Fiber Damage
No Damage
?c
?c
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Sponsorship The work presented herein has been
sponsored by numerous DoD agencies as well as
internal RD at Firehole Technologies.
Current government sponsorship includes
AFRL AFOSR via contract number
FA9550-09-C-0074. Directors Dr. David Stargel
Dr. Victor Giurgiutiu. AFRL(Space Vehicles
Directorate) via contract number
FA9453-07-C-0191. Directors Dr. Tom Murphey
Dr. Jeff Welsh. NASAs Exploration Systems
Mission Directorate Director Wyoming NASA
Space Grant Consortium
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The End
The Firehole River (Yellowstone National Park,
Wyoming)
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The remaining slides are extras to be used as
needed
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Idealization of Failure in Composite Materials
Issues to Consider

• Failure of the Homogenized Composite Material
  vs.
• Failure of the Heterogeneous Composite
  Material
• Modes of Damage/Failure Addressed
• Consequences of Damage/Failure (i.e. stiffness
  degradation)
• ? Isotropic Degradation vs. Orthotropic
  Degradation
• ? Continuous Degradation vs. Discrete
  Degradation
• Local vs. non-local damage/failure

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Use of Micromechanical Finite Element Models
Why do we need In Situ Constituent
Properties? Arent Bulk Constituent Properties
good enough?
The Micromechanical F.E. Model represents an
idealized microstructure that is unlikely to
accurately represent a) the actual fiber
distribution statistics b) the actual
distribution of micro-defects caused by
manufacturing curing
The Micromechanical F.E. Model does not
accurately represent the fiber/matrix
interphase a) the model often does not
explicitly include the interphase b) knowledge
of interphase properties is typically absent or
incomplete
The properties of the Matrix constituent material
are sensitive to curing conditions (e.g.,
temperature, pressure, deformation, chemical
environment). It is unlikely that a sample of
bulk matrix material has been subjected to the
same curing conditions as the matrix material in
a fiber reinforced composite.
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• Imposed Uniform Temperature Reduction in an
  Unconstrained Composite

Composite Average Stress
Constituent Average Stress
Micromechanical Stress Field
tension
2
3
zero
2
2
3
3
compression
Thermal interactions between constituents are
self-equilibrating over the entire RVE, but not
self-equilibrating within each individual
constituent. Constituent averaging process
retains thermal interactions. Composite averaging
process filters out thermal interactions.
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• Imposed Uniform Temperature Reduction in an
  Unconstrained Composite

Micromechanical Stress Field
Composite Average Stress
Constituent Average Stress
tension
2
3
zero
2
2
3
3
compression
Thermal interactions between constituents are
self-equilibrating over the entire RVE, but not
self-equilibrating within each individual
constituent. Constituent averaging process
retains thermal interactions. Composite averaging
process filters out thermal interactions.
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• Imposed Uniform Temperature Reduction in an
  Unconstrained Composite

Constituent Average Stress
Composite Average Stress
Micromechanical Stress Field
tension
2
3
2
2
zero
3
3
compression
Thermal interactions between constituents are
self-equilibrating over the entire RVE, but not
self-equilibrating within each individual
constituent. Constituent averaging process
retains thermal interactions. Composite averaging
process filters out thermal interactions.
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• Imposed Uniform Temperature Reduction in an
  Unconstrained Composite

Composite Average Stress
Constituent Average Stress
Micromechanical Stress Field
2
2
2
2
zero
zero
3
3
3
3
Both the constituent averaging process and the
composite averaging process filter out the
transverse shear stress since it is
self-equilibrating within each individual
constituent as well as self-equilibrating over
the entire RVE.
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• Example Cryogenic cooling of a composite

?T ?217?C
fiber average stress state
?f ?f ?25.87 MPa
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?f ?66.75 MPa
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The constituent average stress states are
inherently triaxial due to the thermal
interactions between constituents!
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• Example Composite under biaxial compression

?c ?10 MPa
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?c ?10 MPa
22
all other ?c 0
ij
The constituent average stress states are
inherently triaxial due to the Poisson
interactions between constituents!
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Example Composite Adapter for Shared PAyload
Rides Two identical laminated composite
monocoque shells IM7/8552 unidirectional tape (up
to 64 plies thick) 60 inches tall, 74 inches in
diameter
CASPAR
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HeliusMCT Progressive Failure Simulation
Predicted
Observed
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1st Signif. Slope Change 980
Initiation of Fiber Failure 740
Test Stopped 847
Initiation of Matrix Failure 260
Hashin Ultimate 1950 ???
Hashin Fiber 1300
Hashin Matrix 1100