A Synergistic Multiscale Modeling Approach

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A Synergistic Multiscale Modeling Approach to
Damage in Composites
Ramesh Talreja Aerospace Engineering Texas AM
University, College Station, Texas
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Contents

• The Engineering Motivation
• Damage Scenarios
• Multiple Scales
• ? of heterogeneities
• ? of damage entities
• Hierarchical approach (up-the-scales)
• Motivated (need-based) treatment of scales
• Conclusion

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Question What is the best sequence of modeling
Right to Left, Or Left to Right, Or Combined
(Synergistic)?
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Damage classification Damage in
composites Multiple cracking where shear-lag
(at interfaces) is involved

• Pre-damage regime
• Damage regime
• Post-damage regime
• (Localization and fracture)

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Pre-Damage Regime Example Unidirectional
Composite in Transverse Tension
s
Debonding induces matrix cracking
Matrix cracking causes debonding
s
Length scales of microstructure Fiber diameter,
Inter-fiber spacing
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Local Stress State resulting from transverse
loading of fiber composites
s
Dilatational

• Depends on
• Fiber and matrix properties
• Fiber distribution

s
Distortional
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Effect of Dilatational (hydrostatic tension)
stress
Cavitation, presumably from free volume
in polymers
Unstable growth of cavitation at critical
dilatational energy
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Effect of Dilatational (hydrostatic tension)
stress
s
When dilatational energy reaches a critical
value, cavities burst open causing debonding
Length scales of damage Cavity diameter (before
debonding) Fiber diameter (after debonding)
s
Asp, Berglund, Talreja (1996)
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Effect of Distortional stress
s
Distortional
Matrix cracks form by Yielding, Void growth
and Coalescence, crazing
Length scales of damage Cavity diameter (before
cracking) Inter-fiber spacing (after cracking)
Models Rice, Tracey (1969) Boyce, Parks, Argon
(1988) Gearing, Anand (2004)
s
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Polymer Fracture Through Crazing
A
B
C
E
D
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Damage Regime Example 1 Unidirectional Ceramic
Matrix Composite in Tension
Fiber-bridged matrix crack
Fibers
Increasing load
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Damage Regime Example 2 Cross-Ply Polymer
Matrix Composite in Fatigue
Transverse cracks
Delaminations
Axial splits
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Cross Ply Composites and Woven Fabric Composites
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Damage Regime Example 3 General laminate with
off-axis ply cracking
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Damage in Composites

• Multiple matrix cracks, interfacial disbonds,
  delaminations, fiber breaks, microbuckled fibers,
  and more
• Multiple orientations
• Multiple scales of damage entities
• Multiple rates of evolution
• Multiple effects on material response

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The Multi-Scale Nature ofDamage in Composites

• What is the Lowest Damage Scale?
• A Purist (Scientific) View
• The first (basic) scale at which dissipative
  mechanism(s) occur.
• A Pragmatist (Engineering) View
• The first significant scale (manifesting behavior
  of lower scales, if any) that governs the
  property of interest. Preferably, scale of
  observable entities.

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The Choice of Scales in an Engineering Approach

• Should be guided by the purpose (Model)
• -- To predict properties and performance, or
• -- To design properties for selected
  performance
• Should account for the scale of inhomogeneities
• (fibers, particles, plies, etc.)
• -- Damage entities are often initiated by
• inhomogeneities, and evolve under their
  influence

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Damage Mechanisms Unidirectional Ceramic Matrix
Composite in Tension
Increasing Load Increasing Crack Density
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Stress-Strain Response Unidirectional Ceramic
Matrix Composite in Tension
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Stage II Damage Mechanism
sliding
debonding
Fiber-bridged Matrix Cracking
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Length Scales of Stage II Damage Mechanism
Damage Entity Length Scale Crack length RVE
Length Scale Crack spacing Microstructural
Length Scale Fiber diameter
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Damage Mechanisms Cross-Ply Polymer Matrix
Composite in Fatigue
Delaminations
Multiple Damage Modes Transverse Ply
Cracks Axial Splits
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Length Scales - Ply Cracking in Laminates

Damage Entity Length Scale Ply thickness,
tc RVE Length Scale Crack spacing,
s Microstructural Length Scale Ply thickness, t0
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Ply Cracking with Delamination

Damage Entity Length Scale Ply thickness,
tc RVE Length Scale Crack spacing,
s Microstructural Length Scale Ply thickness, t0
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A Continuum Characterization of Damage
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A Tensorial Representation of Damage
RVE
ni Unit normal to damage entity surface ai
Represents pre-specified influence of damage
entity on the surrounding medium
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• The damage tensor for intralaminar-cracking is
  given as follows

tc Thickness of the cracked ply tT Total
laminate thickness s1 Spacing between cracks ?
Effect of constraint on the crack opening
displacement imposed by the uncracked laminae
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The Internal Variable of Damage

• All terms are measurable, except ?
• ? depends on microstructure and its
• length scales, and can be experimentally
• identified or calculated by analytical
• or computational micromechanics

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?
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Examples of SDM

• Multiple cracking in UD CMC (Sørensen,Talreja,
  1993)
• Multiple ply cracking in cross ply laminates
  (Varna, Akshantala, Talreja , 1999)
• Multiple transverse cracking with varying
  constraints (Varna, Akshantala, Talreja, 1999
  Varna, Joffe, Talreja, 2001)
• Linear viscoelastic cross ply laminates with
  transverse cracks (Kumar, Talreja, 2003 Varna,
  Krasnikovs, Kumar, Talreja, 2004)
• Off-axis multiple cracking one mode (Varna,
  Joffe, Akshantala, Talreja, 1999 Singh, Talreja,
  2008)
• Off-axis multiple cracking two modes (Singh,
  Talreja, 2009)

• Review papers
• Talreja, R., Journal of Materials Science, 2006
• Talreja, R. and Singh, C.V., In Multiscale
  Modeling
• and Simulation of Composite Materials and
  Structures,
• Y. Kwon, D.H. Allen and R. Talreja, Eds., Chapter
  12, Springer, 2007.

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Conclusion

• Damage in composite materials is complex
  (multitude of size, shape, orientation) and not
  suited for up-the scale multi-scale approach
• For application to complex shaped structures in
  service loading (time-varying multiaxial stress,
  temperature) continuum damage mechanics is the
  most suitable approach
• Synergistic approach (CDM with access to
  judiciously selected micromechanics results) has
  been demonstrated for elastic and linear
  viscoelastic composites.
• Damage evolution, not discussed here, is treated
  by micromechanics