Upload
morgan-gist
View
221
Download
0
Tags:
Embed Size (px)
Citation preview
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