MicromechanicsBased Life Prediction of GlassReinforced Composites

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Micromechanics-Based Life Prediction of
Glass-Reinforced Composites

• T. Bandorawalla, S. Case, and J. Lesko
• Materials Response Group
• Virginia Tech
• EM2000
• May 23, 2000

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Problem
P

• Uni-directional Polymer Matrix Composite
• Loaded in fiber direction
• ? ?ult , failure, ?ult ?
• ? const lt ?ult, tr ?

P
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Literature Review

• Tensile Strength
• Bundle Strength
• Batdorf (1982)
• Gao and Reifsnider (1993)
• Lifetime
• Christensen (1981)
• Curtin (1996)

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Why Again?

• Try to improve on current techniques
• Micro-mechanics based
• Fiber
• Matrix
• No interphase so far
• Experiments have indicated how failure occurs
• Mechanics of each constituent is fairly well
  understood
• Combine the response of constituents to get
  composite response

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Simulations

• Combine constituent response
• Try to duplicate what we believe is happening
• Give us statistics for strength and lifetime
• Same framework for strength and lifetime
• Phoenix, Curtin, Halverson

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Tools for Simulation

• Strength and Lifetime
• Weibull Statistics for fiber strengths (1951)
• Shear-lag analysis for stress concentrations due
  to broken fibers
• Hedgepeth and Van Dyke (HVD) (1967)
• Lifetime
• Paris law type equation for crack growth
  velocity in fibers

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I. Weibull Statistics

• Applied to fibers in composite
• Weakest link theory
• Lo, ?o, m are determined from single fiber tests

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II. HVD Shear-Lag Analysis

• Yields load sharing with fibers breaks in one
  plane
• Square or Hex. packing
• Key assumptions
• Fibers carry all tensile load
• Matrix under shear only

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II. HVD Shear-Lag Analysis

• Original HVD analysis
• Infinitely many fibers
• Infinite fiber length
• All breaks in one plane
• Changes
• Finite array of fibers
• Periodicity of stresses
• Out of plane breaks

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III. Crack Growth in Fibers

• Paris Law type equation

• Mode I stress intensity factor

• Fiber remaining strength (assuming Y const.)

• C and N are material parameters

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III. Crack Growth in Fibers

• Thumb-nail crack
• Geometry factor, Y, is no longer constant
• Nisitani and Chen (1984)
• Assume aspect ratio (b/a) of crack is constant
  during propagation.

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III. Thumb-nail Crack Vs Yconst. Crack
N18
Remaining strength of fibers
Decreasing Stress
Time
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III. Thumb-nail Crack Vs Yconst. Crack
N4
Thumb-nail crack
Yconst
Remaining strength of fibers
Decreasing Stress
Time
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Periodic Volume for Simulation
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Flow-Chart for Strength Simulation
Divide fibers into elements
Assign strengths to fiber elements with Weibull
statistics
Ramp up far-field stress to break one more element
Re-distribute local stresses with HVD
Check for fiber breaks
YES
NO
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Flow-Chart for Lifetime Simulation
Divide fibers into elements
Assign strengths to fiber elements with Weibull
statistics
Ramp up far-field stress to desired level
Increase time to break one more element
Re-distribute local stresses with HVD
Check for fiber breaks
YES
NO
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Length Effect on Composite Strength
l00.42 mm
l02.64 mm
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Length Effect on Composite Strength
l0 5.27 mm
l0 10.54 mm
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Length Effect on Composite Strength
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Strength Comparison for S-2 Glass Epoxy Composite
All strengths, except for experimental strength,
reported for 15.2 cm i.e. 6.0 inches
1Hartman D. R., Greenwood M. E., Miller D. M.,
High Strength Glass Fibers, Owens Corning
Technical Paper, 1994.
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Lifetime Prediction for E-Glass Epoxy Composite
1Experimental Simulation
1Hartman D. R., Greenwood M. E., Miller D. M.,
High Strength Glass Fibers, Owens Corning
Technical Paper, 1994.
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Future Work

• Effect of interphase (de-bonding) on strength and
  life-time.
• Stress concentration due to matrix crack adjacent
  to broken fiber
• Matrix visco-elasticity for life-time modeling

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Summary

• Simulations provide us with a consistent
  framework for strength and lifetime predictions
• Strength prediction agrees well with experimental
  strength for S-2 Glass epoxy composite
• Effect of out of plane breaks accounted for in
  strength simulation
• Lifetime simulation clearly under-predicts time
  to rupture for E Glass epoxy composite
• inputs to simulation, particularly fiber rupture
  data
• thumb nail crack

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Questions ?