Design of a Locomotive Engine for Dalian Locomotive

The Shutoff Overload Ratio and its
Sensitivity to Analytical Parameters
and Techniques
Luciano Smith
Southwest Research Institute
AFGROW Workshop
September 12, 2012
Summary
 The Generalized Willenborg Equation
 The Shutoff Overload Ratio (SOLR)
 SOLR Sensitivity to Material Properties and
AFGROW Parameters
 SOLR Sensitivity to Correlation Techniques
 Recommendations for Determining SOLR
The Generalized Willenborg
Equation
 Analytically accounts for spectrum effects with
the incorporation of an effective stress ratio:
Reff
K min  K r K min,eff


K max  K r K max,eff
K th
1

K max  OL 1  a
Kr 
 K max 
 K max
OL
( SOLR  1) 
r

 This effective stress ratio (Reff) is lower than the
actual R, which causes less crack growth during
each cycle
The Generalized Willenborg
Equation
K th

K max  OL 1  a
Kr 
 K max 
 K max
OL
( SOLR  1) 
r

1
 Parameter definitions:
 Defined by current cycle (Kmax, Δa)
 Defined by recent overload cycle (KOLmax , rOL)
 Material property (ΔKth)
 Dependent on material and loading (SOLR)
The Generalized Willenborg
Equation
K th

K max  OL 1  a
Kr 
 K max 
 K max
OL
( SOLR  1) 
r

1
 Shutoff Overload Ratio (SOLR)
 Definition: The maximum ratio of the overload
maximum SIF to the subsequent maximum SIF
 Effect: If SOLR is exceeded during a cycle, K max,eff is
equal to ΔKth /(1-R) and crack growth is arrested
 Practical Use: Tuning parameter
Determination of SOLR
 Coupon spectrum test
 Test coupon design
–
–
–
–
Material matching actual structure
Geometry similar to actual structure
Geometry simple to analyze
Boundary conditions known
 Spectrum test loads
–
–
Comparable to actual structure
Simple to determine and analyze
 Correlation analysis
 Simulate test as closely as possible
 Use different SOLR values until analysis matches test
Sensitivity of SOLR to
AFGROW Parameters
 Determine the effect on the correlated SOLR of
changes to
 Fracture toughness
 Tensile yield strength
 Crack growth rates
 Limits on R shift
 ΔK threshold
Sensitivity of SOLR to
AFGROW Parameters
 Fracture toughness: Used by AFGROW only for
determination of failure
 Only exception is Kc when using the Forman equation
 No impact on retardation
Sensitivity of SOLR to
AFGROW Parameters
 Tensile yield strength: Used in two ways by
AFGROW
 Determination of stress state for toughness
–
No impact on retardation
 Calculation of yield zone size
–
–
The higher the yield strength, the smaller the yield zone
Increasing the yield strength (and leaving all other parameters
constant) accelerates the analytical crack growth
Sensitivity of SOLR to
AFGROW Parameters
 Tensile yield strength: Impact on SOLR is small
Sensitivity of SOLR to
AFGROW Parameters
 Crack growth rates
 Increasing crack growth rates accelerates the
analytical crack growth
 SwRI compared eight materials for differences
between ground rules growth rates and tested rates
7075-T6511
1.E-03
GR 0.1
GR 0.5
Test 0.1
Test 0.5
1.E-04
da/dN
1.E-05
1.E-06
1.E-07
1.E-08
1
10
Delta K
100
Sensitivity of SOLR to
AFGROW Parameters
 Crack growth rates: Impact on SOLR can be large
depending on the conservatism or
unconservatism in data fits
 Small impact for materials reviewed
7075-T6511
1.E-03
GR 0.1
GR 0.5
Test 0.1
Test 0.5
1.E-04
da/dN
1.E-05
1.E-06
1.E-07
1.E-08
1
10
Delta K
100
Sensitivity of SOLR to
AFGROW Parameters
 Limits on R shift: Used by AFGROW as the cutoff
points for extrapolation of crack growth rates at
high or low stress ratios
 Higher limit on R shift (RHI): At stress ratios above this
value, crack growth rates (da/dN vs. ΔK) equal those at
this value
–
Because the Willenborg equation uses an Reff that is lower than
the actual, RHI has no impact on SOLR
 Lower limit on R shift (RLO): At stress ratios below this
value, crack growth rates (da/dN vs. Kmax) equal those
at this value
Sensitivity of SOLR to
AFGROW Parameters
 Lower limit on R shift: Impact is dependent on
two criteria
 Stress ratio of significant events in spectrum
–
–
Tension dominated spectra will show minimal impact
Compression dominated spectra will show significant impact
Sensitivity of SOLR to
AFGROW Parameters
 Lower limit on R shift: Impact is dependent on
two criteria
 Amount of spread in crack growth rates between
stress ratios
Wide spread will show significant impact
Narrow spread will show minimal impact
7075-T6511
1.E-03
GR 0.1
GR 0.5
Test 0.1
Test 0.5
1.E-04
1.E-05
da/dN
–
–
1.E-06
1.E-07
1.E-08
1
10
Delta K
100
Sensitivity of SOLR to
AFGROW Parameters
 Lower limit on R shift: Appropriate value?
 Study of 9 materials shows default of -0.30 appropriate
2024-T3
1.00E-02
0.00
-0.31
1.00E-03
-0.50
-1.00
-2.00
1.00E-04
AFGROW -0.30
2024-T351
AFGROW 0.00
1.00E-05
da/dN
1.00E-02
0.00
-0.30
1.00E-06
1.00E-03
-0.50
-1.00
1.00E-07
AFGROW -0.30
1.00E-04
7075-T7351
AFGROW 0.00
1.00E-08
1.00E-02
1.00E-05
0.02
da/dN
1.00E-09
10
-1.00
1.00E-03
100
1.00E-06
AFGROW -0.30
Kmax
AFGROW 0.00
1.00E-04
1.00E-07
1.00E-05
1.00E-08
da/dN
1
1.00E-06
1.00E-09
1
10
100
Kmax
1.00E-07
1.00E-08
1.00E-09
1
10
Kmax
100
Sensitivity of SOLR to
AFGROW Parameters
 ΔK threshold (ΔKth): The minimum ΔK that
causes crack growth at R = 0
 Typical values between 1 and 3 ksi√in for the materials
being reviewed
 When no retardation is assumed, an increase in ΔKth
slows crack growth
Sensitivity of SOLR to
AFGROW Parameters
 ΔK threshold (ΔKth): In general, an increase in
ΔKth slows analytical crack growth: Decreased
SOLR
5.00
4.50
4.00
SOLR
3.50
3.00
2.50
2.00
1.50
1.00
1
1.2
1.4
1.6
1.8
2
2.2
2.4
Delta K Threshold (ksi-in^1/2)
2.6
2.8
3
Sensitivity of SOLR to
Correlation Techniques
 Determine the effect on the correlated SOLR of
changes to
 Fracture mechanics model
0.500
7E6-47-A1
 Curve vs. endpoint
C1 SOLR = 3.88
0.450
C2 SOLR = 2.39
V SOLR = 4.10
0.400
M SOLR = 3.63
0.350
1.200
7F6-46-1
Crack Length (in)
Curve fit
Endpoint fit
1.000
0.300
0.250
0.200
Crack Length (in)
0.800
0.150
0.100
0.600
0.050
0.400
0.000
0
1000
2000
3000
4000
Flight Hours
0.200
0.000
0
2000
4000
6000
Flight Hours
8000
10000
12000
5000
6000
7000
8000
Sensitivity of SOLR to
Correlation Techniques
 Different methods for determining stress
intensities for SOLR correlation:
 Constant aspect ratio (a/c = 1) corner crack followed by
straight through crack
 Constant aspect ratio (a/c = initial from test) corner
crack followed by straight through crack
 Varying aspect ratio corner crack and through crack
(initial a/c = initial from test)
 Measured crack lengths and aspect ratios (input using
user-defined betas)
Sensitivity of SOLR to
Correlation Techniques
 Different methods for determining stress
intensities for SOLR correlation:
0.350
0.500
7P6-71-5
7E6-47-A1
C1 Unretarded
C2 SOLR = 4.60
0.300
C2 SOLR = 2.39
V SOLR = 10.00
V SOLR = 4.10
0.400
M SOLR = 4.50
0.250
M SOLR = 3.63
Crack Length (in)
0.350
0.200
0.150
0.500
0.300
0.250
0.200
0.900
2E6-44B-1
0.100
CP11-H-1
0.150
C1 SOLR = 1.72
0.450
C2 SOLR = 1.50
0.400
C SOLR = 2.18
0.800
V SOLR = 1.87
V SOLR = 1.52
0.100
M SOLR = 1.51
M SOLR = 1.88
0.700
0.050
0.050
0.350
0.600
0
0.000
0.300
20000
40000
60000
80000
100000
120000
140000
0
Flight Hours
0.250
0.200
Crack Length (in)
0.000
Crack Length (in)
Crack Length (in)
C1 SOLR = 3.88
0.450
1000
0.500
2000
3000
4000
5000
6000
7000
8000
Flight Hours
0.400
0.300
0.150
0.200
0.100
0.100
0.050
0.000
0.000
0
2000
4000
6000
8000
10000
Flight Hours
12000
14000
16000
18000
20000
0
2000
4000
6000
8000
Flight Hours
10000
12000
14000
16000
Sensitivity of SOLR to
Correlation Techniques
 Different methods for determining stress
intensities for SOLR correlation:
 Significant impact in SOLR for most test specimens
 Not much consistency to results
 Constant aspect ratio = 1 and straight through crack
method:
–
Higher on average than the other methods
–
Generally provided the worst fit
 Corner
crack growth slower than test
 Through
crack growth faster than test
Sensitivity of SOLR to
Correlation Techniques
 Curve vs. endpoint SOLR correlation:
 Depending on geometry, some SOLR values increased
and some decreased
 Curve correlation generally fits early growth better and
endpoint correlation generally fits late growth better
1.200
7F6-46-1
Curve fit
Endpoint fit
1.000
Crack Length (in)
0.800
0.600
0.400
0.200
0.000
0
2000
4000
6000
Flight Hours
8000
10000
12000
Summary and Recommendations
 Ideally, SOLR tunes crack growth to the
material/spectrum loading history combination
 Also dependent on specimen thickness, crack
location, etc.
 Also compensates for inaccuracies in the analytical
model
 Because SOLR compensates for inaccuracies,
making material properties conservative ends up
having no effect when accounting for retardation
Summary and Recommendations
 SOLR also compensates for inaccuracies caused
by correlation techniques
 Analytical stress intensities should therefore match
the test as closely as possible
 However, the analytical methods used in the final
analysis should also be considered