Life Prediction of Composite Materials in Severe Service Environments

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Life Prediction of Composite Materials in Severe
Service Environments
Scott W. Case and Howard G. Halverson Materials
Response Group Virginia Tech June 12, 1999
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Objectives

• Develop methods for life prediction of composite
  materials that incorporate different modeling
  scales in the materials
• Apply the techniques to composite materials under
  differing loading conditions and environments

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Outline

• Micromechanics of tensile strength (ceramic
  fiber/ceramic matrix composite)
• Single damage mechanism (slow crack growth)
• Combined damage mechanisms (slow crack growth and
  interfacial asperity creep)
• Residual strength approach to lifetime prediction
• Integration with finite element code

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Tensile Strength Modeling
An accurate relationship between applied stress
and the stress on the intact fibers under global
load sharing with randomly distributed fiber
breaks is
where sc is the characteristic strength
Curtin Zhou (1995)
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Stress-Rupture Lifetime Prediction
Slow Crack Growth Modeling
Assume that crack growth is the mechanism for
fiber failure at elevated temperatures.
Crack growth is dictated by the Paris Law
So with time the strength of an individual fiber
is
Iyengar Curtin (1997)
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Slow Crack Growth Modeling
When combined with a Weibull distribution of
individual fiber strengths, we can track the
number of fibers which have failed under a
stress, T, after a time, t, in a gage length, L.
Where si satisfies the fiber strength degradation
equation
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Slow Crack Growth Modeling
Combine this with the tensile strength model and
we have a system of two equations which relate
damage (r), stress on intact fibers (T), and time
(t).
where
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Fiber Rupture Behavior
Obtain the fiber stress rupture parameters from
single fiber testing
Yun DiCarlo, 1993
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Predict Composite Lifetimes (1093C)
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Micromechanics of Combined Degradation Mechanisms

• Two particular damage mechanisms
• Slow crack growth
• Interfacial creep
• Analytic solution has not been develop ? use
  simulation approach

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Micromechanics of Combined Degradation
Mechanisms Slow-crack growth
Slow crack growth residual strength
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Micromechanics of Combined Degradation
Mechanisms Interfacial Creep
Interfacial creep residual strength
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Micromechanics of Combined Degradation
Mechanisms Both Mechanisms
Interfacial creep residual strength
Slow crack growth residual strength
Combined residual strength
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The Use of Remaining Strength as a State Variable

• Track remaining strength during the fatigue
  process
• Define a scalar failure function based upon
  tensor strength and stresses use this failure
  function for calculations
• May include the effects of changing loading
  conditions
• May be directly validated experimentally, unlike
  Miners rule

Residual Strength
Sult
Stress or Strength
Life Curve
t1
t2
Cycles
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Mathematical Representation

• Define a failure criterion, Fa, and a remaining
  strength in terms of that failure criterion, Fr
• Define a generalized time (for example
  t/trupture)
• From kinetics we have the change in remaining
  strength over the interval
• Fa is constant over
  
• For the special case in which is equal to zero

• Some possible choices for failure criteria
• Maximum stress/strain
• Tsai-Hill/Tsai-Wu

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Test Case Results from Micromechanical
Simulation
Residual strength prediction for combined case
Residual strength fits to simulation results
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Approach for Variable Loading with Rupture and
Fatigue Acting

• Divide each step of loading into time increments
• Treat each increment as a stress rupture problem
  (constant applied stress and temperature)
• Reduce residual strength due to time dependent
  damage accumulation
• Refine number of intervals until residual
  strength converges
• Input next load level
• Check for load reversal. If load reversal,
  increment by 1/2 cycle and reduce residual
  strength due to fatigue damage accumulation

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Stress Rupture Data for Nicalon/E-SiC 2-D Woven
Composite 0/902s
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Stress Rupture Data for Nicalon/E-SiC 2-D Woven
Composite 0/902s
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Fatigue Data for Nicalon/E-SiC 2-D Woven
Composite 0/902s
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Residual Strength Data for Nicalon/E-SiC 2-D
Woven Composite 0/902s
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Validation Mission Loading Profile
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Validation Mission Loading Profile
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Integration with Finite Element Analysis
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Summary

• Successfully demonstrated connections between
  analytical models and computation simulations.
  This may serve as a basis for structural codes.
• Models (particularly micromechanics) still need
  much work before they may be used with confidence