Transcript Life Prediction of (Ceramic Matrix) Composite Materials

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
• 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
Stress or Strength
Remaining Strength Predictions:
Residual Strength
Sult
S1
a
S2
a
Life Curve
N1 Cycles
N2
• 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
Stress or Strength
Remaining Strength Predictions:
Residual Strength
Sult
S1
r
S1
a
S2
a
n1
n20
Life Curve
N1 Cycles
Implication: n1 cycles at Sa1 is
equivalent to n20 cycles at Sa2
N2
• 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
Stress or Strength
Remaining Strength Predictions:
Residual Strength
Sult
S1
r
S1
a
S2
a
Failure
Miner’s rule
Cycles
Failure occurs when residual strength
equals applied load
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
1
j
F1  Fr IJ N
n G
H1  Fa K
R
U
n 1/ 2 O L
n O
|SL
|
Fr  b
1  Fa g
 M PV
M
P
|TN N Q NN Q|W
2
0
1
2
2
2
2
j
0
2
2
0
2
j
t
,,

T
t
,,

T
d
id
i

t
,
T
t
a
a
f
f
1
4
1
i
j1 4
i
j4
i
j

,
T
i
j


d
id

id
i
0
t ,,
3
5
t
,,
T
T
t
,,
T
0
i
j
0 t
3
i
j3 5
i
j
5
Implementation for Ceramic Matrix
Composites: CCLife Program
• 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
Stiffness Reduction Data for Nicalon/
E-SiC 2-D Woven Composite [0/90]2s:
1.0
0.9
83 MPa
0.8
0.7
E/E 0
103 MPa
0.6
134 MPa
0.5
0.4
173 MPa
0.3
207 MPa
0.2
1
10
100
1000
Fatigue Cycles
10000
100000
Stress Rupture Data for Nicalon/
E-SiC 2-D Woven Composite [0/90]2s:
1.0
1100 C
Experimental, 1100 C
982 C
Experimental, 982 C
Normalized Applied Stress
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1 0
10
10
1
10
2
10
3
10
4
Time to rupture (s)
10
5
10
6
10
7
Stress Rupture Data for Nicalon/
E-SiC 2-D Woven Composite [0/90]2s:
6
1.8x10
6
1.6x10
6
Time to rupture (s)
1.4x10
6
1.2x10
6
1.0x10
5
8.0x10
5
6.0x10
5
4.0x10
5
2.0x10
0
0.0x10
500
600
700
800
900
Temperature ( oC)
1000
1100
1200
Fatigue Data for Nicalon/
E-SiC 2-D Woven Composite [0/90]2s:
1
.
0
C
C
L
i
f
e
2
.
0
0
.
8
D
a
t
a
0
.
6
NormalizedStrs
0
.
4
0
.
2
0
.
0
1
1
0
0
1
0
,
0
0
0
C
y
c
l
e
s
1
0
,
0
0
0
,
0
0
0
Residual Strength Data for Nicalon/
E-SiC 2-D Woven Composite [0/90]2s:
Interrupted Fatigue Test Results
R=-1
max = 13 ksi
1.2
Normalized Remaining Strength,
Normalized Failure Function
1.0
0.8
0.6
0.4
Normalized Remaining Strength
0.2
Normalized Failure Function
Normalized Experimental Remaining
Strength
0.0
1
10
100
1000
Fatigue Cycles
10000
100000
Validation: Mission loading profile
t
,

,
T
d
i
1
1
i
j1

t
,
T
t
a
a
f
f
i
j
t
,

,
T
d
i
2
2
i
j2

,
T
i
j
i
d

t
0
t
,
,
T
0
i
j0
T
i
m
e
t
,

,
T
d
i
3
3
i
j3
Validation: Mission loading profile
1
.
0
C
C
L
i
f
e
2
.
0
0
.
8
D
a
t
a
0
.
6
NormalizedStrs
0
.
4
0
.
2
0
.
0
1 3 1
03
01
0
0
3
0
0
1
,
0
0
0
3
,
0
0
0
C
y
c
l
e
s
Validation results:
Trapezoidal loading profile
Maximum Applied Stress (MPa)
140
120
100
80
60
40
Trapezoidal 1:1:1:1
Trapezoidal 1:1:1:1 Prediction
20
0 3
10
10
4
Cycles
10
5
All results for Nicalon/
E-SiC 2-D Woven Composite [0/90]2s:
10
Predicted Repetitions to Failure
[Predicted time to Rupture (s)]
10
10
10
10
10
10
10
10
7
1100C Rupture
982 C Rupture
700 C Rupture
982 C Rupture
982 C Mission Loading
1100C 0.5 Hz Fatigue
1100C Trapezoidal
1100C Trapezoidal
950C Rupture
950 C Spike & Hold
6
5
4
3
2
1
0
-1
10
-1
10
0
10
1
10
2
10
3
10
4
10
5
Experimental Repetitions to Failure
[Experimental time to Rupture (s)]
10
6
10
7
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:
200
-5 MPa / decade
180
Stress (MPa)
160
140
120
100
80
-35 MPa / decade
Ambient Fatigue
60
1093°C Stress-Rupture
40
20
0
1
10
100
1000
Cycles/Seconds
10000
100000
Fatigue Testing:
12000
120
10000
100
Stiffness (MPa)
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
8000
6000
4000
2000
190 MPa
80
60
172 MPa
40
20
0
0
1
10
100
1000
Cycle
10000
100000
1
10
100
1000 10000 100000 1E+06
Cycles
Rupture Testing:
• In stress-rupture tests there is little evidence of modulus decrease
• Strength reduction is accomplished by the degradation of the
Nextel fibers
160
Stress (MPa)
140
120
100
80
60
40
20
0
0
1
2
Strain (%)
3
4
Elevated Temperature Fatigue:
Sum the changes in remaining strength due to each mechanism
acting independently
1.2
Predicted Residual Strength Curves
1.0
Fa, Fr
0.8
0.6
Predicted Lifetime Curve
0.4
0.2
0.0
1
10
100
1000
Cycles
10000
100000
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:
200
180
Unnotched Behavior
Stress (MPa)
160
140
120
Notched Experiment
100
80
ANSYS Result
60
40
20
0
0
0.05
0.1
0.15
Strain (%)
0.2
0.25
0.3
ANSYS Life Prediction Result:
1.0
0.9
Predicted Lifetime
Experimental Lifetime
N ormalized Stress
0.8
0.7
0.6
Failure
initiation
0.5
0.4
0.3
0.2
0.1
0.0 2
10
3
10
4
10
C ycles to Failur e
5
10
6
10
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:
Prof. Liviu Librescu
Prof. Kevin Granata
We will continue to invent the future through our blood and
tears and through all our sadness.... We will prevail....