Life prediction based on material state changes in ceramic materials

Ken Reifsnider

Mechanical Engineering

University of Connecticut

Storrs, CT 06269

Scott Case

Engineering Science and Mechanics

Virginia Tech

Blacksburg, VA 24061-0219

Outline:

• Residual Strength Modeling philosophy• Model implementation (CCLife code)• Development of Micromechanical Models• Incorporation in Finite Element Analysis (ANSYS)• Summary

Objectives in Lifetime Prediction Effort:

• To develop a life-prediction method for composites based on an understanding of the relevant damage processes

• To validate the method by comparing with existing experimental evidence

Sult

Cycles

Str

ess

or

Str

eng

th Residual Strength

Life Curve

1

Sa1

Sa2

2

Remaining Strength Predictions:

• Track remaining strength during the time-dependent 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 Miner’s rule

Sa1

Sr1

Sult

Cycles

Str

ess

or

Str

eng

th Residual Strength

Life Curve

n1

1

Sa2

2

n20

Implication: n1 cycles at Sa1 is

equivalent to n20 cycles at Sa

2

Remaining Strength Predictions:

• Track remaining strength during the time-dependent 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 Miner’s rule

Sa1

Sa2

Sr1

Sult

Cycles

Str

ess

or

Str

eng

th Residual Strength

• Track remaining strength during the time-dependent 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 Miner’s rule

Miner’s rule

Failure

Failure occurs when residual strength equals applied load

Remaining Strength Predictions:

nFr

FaN

Fr Fan

N

n

N

j

j j

20 1

2

1

2

22

0

2

20

2

1

1

11 2

=−−FHG

IKJ

=− −+L

NMOQP−LNMOQP

RS|T|

UV|W|

Δ b g /

σij t Ttafaf,

Dt

sijT,

t Tij111, ,σd i

t Tij000, ,σd i t Tij3

33, ,σd i

t Tij444, ,σd i

t Tij555, ,σd i

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

• Begin with matrix stiffness reduction as a function of time and stress level

• Use a simple stress model (2-D, laminate level) to calculate failure function as a function of time, stress, and temperature

• Fit stress rupture data as a function of stress level and temperature

• Use incremental approach previously presented to sum influence of changing stresses (rupture influence)

• Adaptively refine increments until residual strength converges to some prescribed tolerance

• Account for cyclical loading by counting reversals and reducing remaining strength

• Originated under EPM program

Implementation for Ceramic Matrix Composites: CCLife Program

Stiffness Reduction Data for Nicalon/E-SiC 2-D Woven Composite [0/90]2s:

1 10 100 1000 10000 100000

Fatigue Cycles

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

E/E

0

83 MPa

103 MPa

134 MPa

173 MPa

207 MPa

100

101

102

103

104

105

106

107

Time to rupture (s)

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Normalized Applied Stress

1100 CExperimental, 1100 C982 CExperimental, 982 C

Stress Rupture Data for Nicalon/E-SiC 2-D Woven Composite [0/90]2s:

500 600 700 800 900 1000 1100 1200

Temperature ( oC)

0.0x100

2.0x105

4.0x105

6.0x105

8.0x105

1.0x106

1.2x106

1.4x106

1.6x106

1.8x106

Time to rupture (s)

Stress Rupture Data for Nicalon/E-SiC 2-D Woven Composite [0/90]2s:

1 100 10,000 10,000,0000.0

0.2

0.4

0.6

0.8

1.0

Cycles

Normalized Stress

CCLife 2.0

Data

Fatigue Data for Nicalon/E-SiC 2-D Woven Composite [0/90]2s:

Interrupted Fatigue Test ResultsR=-1

σmax = 13 ksi

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1 10 100 1000 10000 100000

Fatigue Cycles

,Normalized Remaining Strength Normalized Failure Function

Normalized Remaining Strength

Normalized Failure Function

Normalized Experimental RemainingStrength

Residual Strength Data for Nicalon/E-SiC 2-D Woven Composite [0/90]2s:

Time

s ij t T taf af,

sij

T,

Dt

t Tij11

1, ,sd i

t Tij00

0, ,σd i t Tij33

3, ,sd i

t Tij22

2, ,sd i

Validation: Mission loading profile

1 3 10 30 100 300 1,000 3,0000.0

0.2

0.4

0.6

0.8

1.0

Cycles

Normalized Stress

CCLife 2.0

Data

Validation: Mission loading profile

103

104

105

Cycles

0

20

40

60

80

100

120

140

Maximum Applied Stress (MPa)

Trapezoidal 1:1:1:1Trapezoidal 1:1:1:1 Prediction

Validation results: Trapezoidal loading profile

10-1

100

101

102

103

104

105

106

107

Experimental Repetitions to Failure[Experimental time to Rupture (s)]

10-1

100

101

102

103

104

105

106

107

Predicted Repetitions to Failure[Predicted time to Rupture (s)]

1100C Rupture982 C Rupture700 C Rupture982 C Rupture982 C Mission Loading1100C 0.5 Hz Fatigue1100C Trapezoidal1100C Trapezoidal950C Rupture950 C Spike & Hold

All results for Nicalon/E-SiC 2-D Woven Composite [0/90]2s:

Validation with Oxide/Oxide System:

• Begin with fatigue tests at room temperature and stress-rupture tests at 1093°C on a Nextel 610 reinforced alumina-yttria composite

• Represent the changes in remaining strength due to these mechanisms with a residual-strength based model

• Create predictions based on the summation of damage due to the action of both mechanisms

• Verify predictions with fatigue tests at 1093°C

Basic Inputs:

0

20

40

60

80

100

120

140

160

180

200

1 10 100 1000 10000 100000

Cycles/Seconds

Stress (MPa) Ambient Fatigue

1093°C Stress-Rupture

-5 MPa / decade

-35 MPa / decade

Fatigue Testing:

0

2000

4000

6000

8000

10000

12000

1 10 100 1000 10000 100000

Cycle

Loop Area (Pa)

• An increase in hysteresis loop area - consistent with degradation of interface frictional stress• A decrease in composite stiffness - associated with composite delamination

0

20

40

60

80

100

120

1 10 100 1000 10000 100000 1E+06Cycles

Stiffness (MPa)

172 MPa

190 MPa

Rupture Testing:

0

20

40

60

80

100

120

140

160

0 1 2 3 4

Strain (%)

Stress (MPa)

• In stress-rupture tests there is little evidence of modulus decrease• Strength reduction is accomplished by the degradation of the Nextel fibers

Elevated Temperature Fatigue:

Sum the changes in remaining strength due to each mechanism acting independently

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1 10 100 1000 10000 100000

Cycles

Fa, Fr Predicted Lifetime Curve

Predicted Residual Strength Curves

Analysis of Hi-Nicalon/SiC Composite:

Attempt to relate center-hole notched composite behavior to coupon behavior

ANSYS user-programmable functions and macros used to generate stress profile, track element strength, and determine failed elements

Quasi-Static Tensile Behavior:

0

20

40

60

80

100

120

140

160

180

200

0 0.05 0.1 0.15 0.2 0.25 0.3

Strain (%)

Stress (MPa)

Unnotched Behavior

Notched Experiment

ANSYS Result

ANSYS Life Prediction Result:

102

103

104

105

106

Cycles to Failure

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Normalized Stress

Predicted LifetimeExperimental Lifetime

Failureinitiation

Integration with FEA: SiC/SiC Recession Analysis

Summary and Conclusions:

• Life prediction analysis based on residual strength has been developed an applied to ceramic matrix composite systems

• Validation studies include– SiC/SiC composites of various geometries and loading

conditions

– Nextel 610 reinforced alumina-yttria

• Successful integration into commercial finite element packages

In Memoriam:

We will continue to invent the future through our blood and tears and through all our sadness.... We will prevail....

Prof. Liviu LibrescuProf. Kevin Granata