- Email: [email protected]
Effect of Mean Stress on Small Fatigue Crack Growth Rate on Low Carbon Steel with Several Simulated HAZ Heat Treatment
Available Available online online at at www.sciencedirect.com www.sciencedirect.com
ScienceDirect
Available online www.sciencedirect.com Available online at at www.sciencedirect.com Structural Structural Integrity Integrity Procedia Procedia 00 00 (2016) (2016) 000–000 000–000
ScienceDirect ScienceDirect
Procedia Structural 2 (2016) 3002–3009 Structural IntegrityIntegrity Procedia 00 (2016) 000–000
www.elsevier.com/locate/procedia www.elsevier.com/locate/procedia
www.elsevier.com/locate/procedia
21st European Conference on Fracture, ECF21, 20-24 June 2016, Catania, Italy
Effect of Mean Stress on Small Fatigue Crack Growth Rate on Low Carbon Steel with Several Simulated HAZ Heat Treatment Thermo-mechanical modeling ofaa*,aYoshiyuki high pressure Hide-aki Nishikawa Furuyaaa turbine blade of an airplane gas turbine engine National National Institute Institute for for Materials Materials Science, Science, 1-2-1 1-2-1 Sengen, Sengen, Tsukuba-shi, Tsukuba-shi, Ibaraki, Ibaraki, 305-0047 305-0047 Japan Japan
XV Portuguese Conference on Fracture, PCF 2016, 10-12 February 2016, Paço de Arcos, Portugal
aa
P. Brandãoa, V. Infanteb, A.M. Deusc* a Abstract AbstractDepartment of Mechanical Engineering, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1, 1049-001 Lisboa, b
Portugal
IDMEC, Department of Mechanical Engineering, Instituto Superior Técnico, Universidaderesidual de Lisboa, Av. of Rovisco Pais, 1, 1049-001 Lisboa, In Zone In this this study, study, to to clarify clarify the the effect effect of of microstructure microstructure of of Heat Heat Affected Affected Zone (HAZ) (HAZ) and and residual stress stress of weld weld on on small small fatigue fatigue crack crack Portugal c growth behavior, uniaxial fatigue testing with surface small fatigue crack growth observation were carried out for low carbon steel growth behavior, uniaxialoffatigue testing with surface smallSuperior fatigueTécnico, crack growth observation wereAv. carried outPais, for 1, low carbonLisboa, steel CeFEMA, Department Mechanical Engineering, Instituto Universidade de Lisboa, Rovisco 1049-001 n with conditions. Portugal type small small crack crack growth growth law law was was with three three simulated simulated HAZ HAZ heat heat treatment treatment under under several several mean mean stress stress conditions. As As aa results, results, εεnaa type also also effective effective to to HAZ HAZ microstructure microstructure under under zero zero mean mean stress. stress. Under Under tensile tensile mean mean stress stress condition, condition, fatigue fatigue fracture fracture life life and and small small fatigue fatigue crack crack growth growth life life were were decreased. decreased. In In addition, addition, it it is is clarified clarified that that small small fatigue fatigue crack crack growth growth rate rate acceleration acceleration under under tensile tensile Abstract which is obtained from mean stress was able to be evaluated by using Smith-Watson-Topper equivalent strain ε eq mean stress stress mean stress was able to be evaluated by using Smith-Watson-Topper equivalent strain εeq which is obtained from mean nn dependency a type type modified modified small small crack crack growth growth law law was was proposed. proposed. dependency of of fatigue fatigue fracture fracture life life for for smooth smooth specimen specimen and and εεeq eq a During their modern engineto subjected to increasingly demanding conditions, proportional εεeff evaluated by opening measured with Image Furthermore, it clarified εεeq wasaircraft proportional to components which was wasare evaluated by crack crack opening point point measuredoperating with Digital Digital Image Furthermore, it is isoperation, clarified that that eq was eff which especially the high pressure turbine (HPT) blades. Such conditions cause these parts to undergo different types of time-dependent Correlation technique. It is considered that equivalent strain ε implicitly includes small crack growth life and effect eq Correlation technique. It is considered that equivalent strain εeq implicitly includes small crack growth life and effect of of crack crack degradation, one of which is creep. A model using the finite element method (FEM) was developed, in order to be able to predict closure. closure. the creep behaviour of HPTbyblades. Flight data records (FDR) for a specific aircraft, provided by a commercial aviation © 2016 The Published Elsevier B.V. © The Authors. Authors. Published byIntegrity) ElsevierHosting B.V. by Elsevier Ltd. All rights reserved. © 2016 2016, PROSTR (Procedia Structural company, were used to obtain thermal and mechanical data for three different flight cycles. In order to create the 3D model Peer-review under responsibility of the Scientific Committee of Peer-review under responsibility Scientific Committee of ECF21. ECF21.and its chemical composition and material properties were Peer-review under responsibility of theofScientific Committee of ECF21. needed for the FEM analysis, athe HPT blade scrap was scanned,
obtained. The data that was gathered was fed into the FEM model and different simulations were run, first with a simplified 3D
Keywords: Fatigue; Heat affected zone; crack growth Mean Digital image correlation Keywords: Fatigue; Heat affected zone; Small Small crack growth rate; rate; Mean stress; stress; Digital image rectangular block shape, in order to better establish the model, and then with thecorrelation real 3D mesh obtained from the blade scrap. The
overall expected behaviour in terms of displacement was observed, in particular at the trailing edge of the blade. Therefore such a model can be useful in the goal of predicting turbine blade life, given a set of FDR data.
1. 1. Introduction Introduction
© 2016 The Authors. Published by Elsevier B.V. Since fracture of components are in Peer-review under responsibility of the Scientific Committee of PCFoccurred 2016. Since fatigue fatigue fracture of mechanical mechanical components are mainly mainly occurred in welding, welding, aa lot lot of of fatigue fatigue data data for for welding welding
were were accumulated accumulated before before now. now. However, However, since since these these fatigue fatigue data data were were widely widely scattered, scattered, too too much much conservative conservative fatigue fatigue Keywords: High Pressure Turbine Blade; Creep; Finite Element Method; 3D Model; Simulation. design is frequently required. One of the reason why such problem occurred is that a lots of effective design is frequently required. One of the reason why such problem occurred is that a lots of effective fatigue fatigue parameter parameter
* * Corresponding Corresponding author: author: E-mail E-mail address: address: [email protected] [email protected] 2452-3216 2452-3216 © © 2016 2016 The The Authors. Authors. Published Published by by Elsevier Elsevier B.V. B.V. * Corresponding Tel.: +351of Peer-review under responsibility the Peer-review underauthor. responsibility of218419991. the Scientific Scientific Committee Committee of of ECF21. ECF21. E-mail address: [email protected]
2452-3216 © 2016 The Authors. Published by Elsevier B.V.
Peer-review under responsibility of the Scientific Committee of PCF 2016. 2452-3216 © 2016, PROSTR (Procedia Structural Integrity) Hosting by Elsevier Ltd. All rights reserved. Peer-review under responsibility of the Scientific Committee of ECF21. 10.1016/j.prostr.2016.06.376
2
Hide-aki Nishikawa et al. / Procedia Structural Integrity 2 (2016) 3002–3009 Author name / Structural Integrity Procedia 00 (2016) 000–000
3003
in welding affects its performance and it is difficult to evaluate each factor quantitatively. For example, since fatigue crack is initiated from weld toe, not only stress concentration but also effect of variable microstructure in the heat affected zone (HAZ) is necessary to be considered. Furthermore residual stress formed around HAZ which affect fatigue crack growth behavior is also have to be considered. By the way, it is well known that fatigue life is mainly occupied by small fatigue crack growth life. However, small fatigue crack growth behavior in the welding is not enough investigated. To clarify the small fatigue crack growth behavior in the welding is possibly helpful to considering complex effective parameter such as residual stress and stress concentration quantitatively. This study focusing on the effect of HAZ microstructure and residual stress (mean stress) on small fatigue crack growth behavior. By the way, measurement of crack closure effect which is important to mean stress dependency of fatigue crack growth rate is difficult especially for small crack. Since fatigue life is mainly occupied by crack growth life, conventional fatigue parameter for fatigue fracture life of smooth specimen is possibly useful also for small crack growth evaluation. For example, Smith et al. (1970) proposed stress-strain function which is able to fix mean stress effect on fatigue life of smooth specimen. In this study, to clarify the effect of these factor on the small fatigue crack growth behavior, fatigue testing with successive small fatigue crack growth observation were carried out for low carbon steel with several simulated HAZ heat treatment under some tensile mean stress conditions. Furthermore, crack opening-closing behavior which is important for mean stress dependency was investigated with Digital Image Correlation (DIC) technique. Nomenclature
σa σmax σop εa εmax εop εeq l a
∆K
√area c C n
stress amplitude maximum stress during fatigue cycle Crack opening stress during fatigue cycle strain amplitude maximum strain during fatigue cycle crack opening strain during fatigue cycle equivalent strain calculated from Smith-Watson-Topper (SWT) equation surface fatigue crack length fatigue crack depth stress intensity factor range projected area of the fatigue crack materials constant for SWT equation materials constant for small fatigue crack growth law materials constant for small fatigue crack growth law
2. Material and testing procedure Materials used in this study were three types of low carbon steel. Table 1 shows chemical compositions. Three types of simulated HAZ heat treatments were conducted with controlling cooling rate after holding 5 second at 1400℃ for each materials. Table 2 shows heat treatment conditions for each materials. Finally, three different simulated HAZ microstructures were obtained. Fig. 1 shows microstructure morphologies. Microstructures were acicular ferrite, perlite and grain boundary ferrite for material A, ferrite and bainite for material B and martensite for material C respectively. Vickers hardness were HV148, HV182 and HV350 respectively. Fatigue tests were conducted with load controlled uniaxial loading by servo hydraulic type fatigue testing equipment. Fig. 2 shows specimen configurations. Specimen surface were etched by 3 % nital after mirror polished to crack observation. Small fatigue crack growth behavior is observed using digital microscope. In addition, strain amplitude was measured by strain gage on the back surface of fatigue specimen.
Hide-aki Nishikawa et al. / Procedia Structural Integrity 2 (2016) 3002–3009 Author name / Structural Integrity Procedia 00 (2016) 000–000
3004
3
Table 1. Chemical compositions. Material
C
Si
Cr
Mn
P
S
Mo
Al
N
A
0.07
<0.01
0.51
1.51
0.006
0.003
<0.01
0.025
0.003
B
0.07
<0.01
0.01
1.50
0.006
0.003
0.21
0.026
0.003
C
0.15
0.02
0.54
1.51
0.007
0.001
-
0.019
0.002
Table 2. Heat treatment conditions for each materials. Cooling rate (℃ /s) A
B
C
1400~1000 ℃
10
60
50
1000~800 ℃
4
40
800~500 ℃
1
20
500~350 ℃
0.5
12
30
Fig. 1. Simulated HAZ Microstructures.
φ10
2
2
16.8
(32.5)
R31
16.8
Fig. 2. Specimen configurations.
3. Experimental results and discussions 3.1. Mean stress effects on S-N diagrams Figure 2 shows S-N diagram. Fig. 2 (a) is represented with stress amplitude. Solid mark shows results under fully reversed tension-compression condition and open mark shows under tensile mean stress condition. Fatigue lives under tensile mean stress conditions were shorter than that of fully reversed tension-compression results. It is known that mean stress dependency is able to be fixed using Smith-Watson-Topper (SWT) equivalent strain proposed by Smith et al. (1970). SWT equivalent strain εeq is expressed as:
ε eq = ε ac (σ max E )1−c
(1)
where εa is strain amplitude, σmax is maximum stress, E is Young’s modules and c is materials constant which is related to mean stress sensitivity. Fig. 2 (b) shows S-N diagrams represented with SWT equivalent strain. Although mean
4
Hide-aki Nishikawa et al. / Procedia Structural Integrity 2 (2016) 3002–3009 Author name / Structural Integrity Procedia 00 (2016) 000–000
3005
stress sensitivities were deferent depends on microstructure, mean stress dependency of simulated HAZ microstructure was able to be fixed by SWT equivalent strain as shown in Fig. 2 (b). In addition, material constant value c for Eq (1) were 0.6, 0.7 and 0.35 for material A, B and C respectively. Such a conventional mean stress dependency of fatigue life is possibly related to fatigue crack growth behavior. Therefore mean stress effect for fatigue crack growth rate will be discussed below. Equivalent Strain amplitude εeq (-)
1000
Stress amplitude σa (MPa)
a *
*
*
TP σm=0 σmax≂σ y-c A B
100
* Round bar specimen
C
103
104
105
106
Number of cycles to failure (cycles)
107
0.01
εeq = εac (σmax/E)(1-c)
b
TP A
0.00
*
.1
*
c value σ =0 σmax≂σ y-c for eq. 1 m 0.6
B
0.7
C
0.35
103
*
…eq
* Round bar specimen
104
105
106 Number of cycles to failure (cycles)
107
Fig. 2. S-N diagrams represented with (a) stress amplitude and (b) SWT equivalent strain calculated by eq. 1.
3.2. Mean stress effects on small fatigue crack growth rate Figure 3 shows small fatigue crack growth rate versus stress intensity factor. Stress Intensity factor range was calculated by Eq. (2). Stress intensity factor range was able to be approximately calculated with √area, projected area of the crack, as shown in Eq (2) which proposed by Murakami (2002).
∆K = 0.65∆σ π area
σ max (σ min ≤ 0 ) ∆σ = σ max − σ min (σ min > 0 )
(2)
Long fatigue crack growth property of welding reported by NRIM (1980) also represented in the figure. Fatigue crack growth rates were not uniformly evaluated by stress intensity factor range. In addition, fatigue crack growth rate was partly higher than that of long crack property. It is well known that evaluating crack closure effect is necessary to estimate fatigue crack growth rate as mentioned by Elber (1971). To evaluate small fatigue crack growth rate and its mean stress dependency, considering crack closure effect seems necessary also for small fatigue crack growth rate of simulated HAZ microstructure. Since quantitative estimation for crack closure effect is difficult, simple modeling is one of the useful approach for small fatigue crack growth problem. Nishitani (1981) proposed small fatigue crack growth law expressed as:
da / dN = Cσ nl
(3) where C and n are materials constant and l is surface crack length. In this study, applicability of similar εan a type parameter where a is crack depth was considered. Since uniaxial loading, it is assumed that l=2a. Figure 4 shows small fatigue crack growth rate versus εan a parameter. Fatigue crack growth rate under σm = 0 conditions were uniformly evaluated by εan a parameter in spite of simulated HAZ microstructure. On the other hands, this model can’t estimate fatigue crack growth rate acceleration under tensile mean stress conditions. As described above, SWT equivalent strain εeq is effective to fix the mean stress dependency for fatigue fracture life. Since large part of fatigue life is occupied by small fatigue crack growth life, εeq may be also related to mean stress dependency of small fatigue crack growth rate. Therefore, modified crack growth equation using εeqn a parameter expressed as Eq. 4 is considered below. n
da / dN = Cε eq a
(4)
Hide-aki Nishikawa et al. / Procedia Structural Integrity 2 (2016) 3002–3009 Author name / Structural Integrity Procedia 00 (2016) 000–000
3006
5
Figure 5 shows small fatigue crack growth rate versus εeqn a parameter calculated from SWT equation. Used materials constants c for εeq described in Eq. (1) was same as Fig. 2 (b). As described in Fig. 5, all fatigue data including tensile mean stress condition were uniformly evaluated by modified small fatigue crack growth law which using εeqn a parameter. It is clarified that εeqn a parameter is effective to estimate the mean stress dependency of small fatigue crack growth rate as a simple parameter. As mentioned in Fig. 3, considering crack opening behavior is important to evaluate fatigue crack growth rate. It is possible that SWT εeq is indirectly including the effect of crack opening behavior. To clarify the relationship between crack opening behavior and SWT equivalent strain, direct measurement for the crack opening point were carried out by DIC technique. 3.3. Direct measurement for crack opening-closing behavior with DIC technique DIC analysis were conducted for microscope images which successively obtained during loading-unloading process and vertical direction strain were analyzed. Figure 6 shows small fatigue crack opening behavior observed with DIC technique. Fig. 6 (a) is reference image obtained at minimum load. Fig. 6 (b)~(f) are contour image of successively analyzed vertical strain for loading process. Strain distribution related to fatigue crack is not detected in Fig. 6 (b). In Fig. 6 (c), higher strain distribution is observed around the fatigue crack. After that this strain distribution becomes bigger as applied load becomes bigger. 1.E-06 10-6
Material A (0.07C, 1℃/s)
Typical long crack data (SM50B welding, NRIM (1980))
1.E-07 10-7
l
σa
[MPa]
280
0
240
0
210
0
240
100
210
130
1.E-09 10-9
1.E-10 10-10
1
σm
[MPa]
l
10
a=0.5l σa
1.E-09 10-9
100
1.E-10 10-10
1
Material C (0.15C, 30℃/s)
Typical long crack data (SM50B welding, NRIM (1980))
Crack coalescence 0.2 ≲ l ≲ 1 mm
1.E-08 10-8
a σm
[MPa]
[MPa]
340
0
320
0
280
0
280
120
280
120
10
∆ K (MPa √m)
c
1.E-07 10-7
0.2 ≲ l ≲ 1 mm
1.E-08 10-8
a
a=0.5l
1.E-06 10-6
Material B (0.07C, 20℃/s)
Typical long crack data (SM50B welding, NRIM (1980))
1.E-07 10-7
0.2 ≲ l ≲ 1 mm
1.E-08 10-8
b
Fatigue crack growth rate da/dN (m/cycle)
Fatigue crack growth rate da/dN (m/cycle)
a
Fatigue crack growth rate da/dN (m/cycle)
1.E-06 10-6
l
a=0.5l
1.E-09 10-9
100
σa
[MPa]
a σm
[MPa]
480
1.E-10 10-10
1
0
420
0
400
300
10
100
∆ K (MPa √m)
∆ K (MPa √m)
a
Material A (0.07C, 1℃/s)
10-7 10-8 0.2 ≲ l ≲ 1 mm
10-9
σa
10-10
l a=0.5l
10-11 10-25
10-24
a
10-23
εa6.62 ･ a (mm)
σm
[MPa]
[MPa]
280
0
240
0
210
0
240
100
210
130
10-22
10-21
10-6
b
Fatigue crack growth rate da/dN (mm/cycle)
10-6
Fatigue crack growth rate da/dN (mm/cycle)
Fatigue crack growth rate da/dN (mm/cycle)
Fig. 3. Small fatigue crack growth rate versus stress intensity factor.
Material B (0.07C, 20℃/s)
10-7 10-8 0.2 ≲ l ≲ 1 mm
10-9
σa
l
10-10 a=0.5l
10-11 10-28
10-27
a
10-26
σm
[MPa]
[MPa]
340
0
320
0
280
0
280
120
280
120
10-25
10-24
10-6
c
Material C (0.15C, 30℃/s)
10-7 Crack coalescence
10-8 10-9 10-10
εa7.91 ･ a (mm)
Fig. 4. Small fatigue crack growth rate versus εan a parameter.
σa
l a=0.5l
10-11 10-10
0.2 ≲ l ≲ 1 mm
10-9
a
10-8
εa1.49 ･ a (mm)
σm
[MPa]
[MPa]
480
0
420
0
400
300
10-7
10-6
1.E-07 10-7
1.E-08 10-8
1.E-06 10-6
a
Material A (0.07C, 1℃/s)
1.E-07 10-7
εeq = εac (σmax/E)(1-c) c = 0.6
1.E-08 10-8
0.2 ≲ l ≲ 1 mm
1.E-09 10-9
σa
1.E-10 10-10
1.E-11 10-11 1E-28 10-28
Fatigue crack growth rate da/dN (m/cycle)
Fatigue crack growth rate da/dN (m/cycle)
1.E-06 10-6
Hide-aki Nishikawa et al. / Procedia Structural Integrity 2 (2016) 3002–3009 Author name / Structural Integrity Procedia 00 (2016) 000–000
l a=0.5l
1E-27 10-27
a
1E-26 10-26
εeq7.48 ･ a (mm)
[MPa]
[MPa]
280
0 0
210
0
240
100
210
130
1E-25 10-25
Material B (0.07C, 20℃/s)
c = 0.7
1.E-08 10-8
0.2 ≲ l ≲ 1 mm σa
1.E-10 10-10
1E-24 10-24
1.E-07 10-7
εeq = εac (σmax/E)(1-c)
1.E-09 10-9
σm
240
1.E-06 10-6
b
1.E-11 10-11 1E-31 10-31
Fatigue crack growth rate da/dN (m/cycle)
6
l a=0.5l
1E-30 10-30
a
1E-29 10-29
εeq8.95 ･ a (mm)
1.E-09 10-9
σm
[MPa]
[MPa]
340
0
320
0
280
0
280
120
280
120
1E-28 10-28
Material C (0.15C, 30℃/s)
c
εeq = εac (σmax/E)(1-c) c = 0.35
Crack coalescence
1.E-10 10-10
1E-27 10-27
3007
1.E-11 10-11 10-19 1E-19
0.2 ≲ l ≲ 1 mm σa
l a=0.5l
10-18 1E-18
a
10-17 1E-17
σm
[MPa]
[MPa]
480
0
420
0
400
300
10-16 1E-16
10-15 1E-15
εeq4.81 ･ a (mm)
Fig. 5. Small fatigue crack growth rate versus εeqn a parameter calculated from SWT equation.
Such a strain distribution around the fatigue crack is mainly related to Crack Opening Displacement (COD) during loading cycle. Conventionally, macroscopic COD is effective for measuring crack opening point for long crack such as CT specimen. Therefore, strain analyzed by DIC which related to microscopic COD is possibly effective to detect the crack opening point even for small fatigue crack. Figure 7 shows the example of the relationship between stress and crack opening strain measured with DIC technique for crack length of (a) 0.3 mm and (b) 0.8 mm. Crack opening strain is measured on the fatigue crack where a few tens of µm behind from the crack tip as described in the figures. Figures also includes the strain measured by strain gage. Although, for long crack, crack opening point is able to be detected by strain gage conventionally, strain gage data of Fig. 7 is approximately linier and crack opening point is not able to be detected. On the other hand, crack opening point is clearly appeared in the strain measured by DIC as shown in Fig. 7 even for 0.3 mm length fatigue crack. Rabblini et al. (2015) reported DIC technique applicability for crack closure measurement for relatively larger crack of length more than 1 mm. It is clarified that DIC technique is effective to detect the crack opening point even for early stage small fatigue crack of length less than 0.3 mm which naturally initiated on the material surface. Then, relationship between effective strain range and SWT equivalent strain is confirmed below. Effective strain εeff calculated from εop which is correspond to σop obtained by DIC is expressed as Eq. (5). (5) ε eff = ε max − ε op Figure 8 shows relationship between εeq and εeff measured with DIC technique. As shown in the figure, εeq is approximately proportional to εeff. This results indicates that since SWT εeq is indirectly including the effect of crack opening behavior, it is also effective to evaluate the mean stress effect on small fatigue crack growth rate. As described above, SWT equivalent strain is able to be obtained without crack growth test. Therefore, modified small fatigue crack growth law described in Eq. (4) is effective to evaluate the mean stress effect for small crack as a simple approach. Figure 9 shows relationship between small fatigue crack growth rate and ∆Keff evaluated with DIC technique. Micro structure dependency of fatigue crack growth rate is not clear. This results indicates fatigue life difference related to microstructure seems subjected to crack closure effect. Since quantitative crack closure evaluation is difficult, modified small crack growth law proposed above which implicitly includes crack closure effect is seems effective to evaluate small fatigue crack growth rate. To estimate the fatigue life of welding, it is also necessary to considering stress concentration. Small fatigue crack growth behavior under the stress concentration and fatigue life estimation method based on small fatigue crack growth property for actual weld joint will be investigated in future.
Hide-aki Nishikawa et al. / Procedia Structural Integrity 2 (2016) 3002–3009 Author name / Structural Integrity Procedia 00 (2016) 000–000
3008
c
b
a
σ = σmin (reference image)
σ = σmin + 0.4∆σ
σ = σmin + 0.3∆σ
f
e
d
σ = σmin + 0.5∆σ
7
σ = σmin + 0.6∆σ -0.002
100 μm
σ = σmin + ∆σ = σmax 0.012
Strain in vertical direction (-)
Loading direction
Fig. 6. Small fatigue crack opening behavior observed with DIC technique.
400 300
Strain gage
-100
σop
Strain measurement area
-200
Material B, σa = 280 MPa, l=0.8mm
b
Strain gage
200
DIC strain
100 0
300
Stress (MPa)
Stress (MPa)
200
400
Material B, σa = 280 MPa, l=0.3mm
a
DIC strain
100 0 -100
σop
Strain measurement area
-200
-300
-300
100 μm
-400 -0.005
0
0.005 0.01 Strain (-)
0.015
0.02
-400 -0.005
100 μm
0
0.005 0.01 Strain (-)
0.015
0.02
Fig. 7. Relationship between stress and crack opening strain measured with DIC technique for crack length of (a) 0.3 mm and (b) 0.8 mm.
0.30%
TP
0.25% A
εeq (-)
0.20% 0.15%
B
0.10% 0.05%
C
0.00% 0.00%
0.10%
0.20%
εeff (-)
0.30%
σa
[MPa] 280 240 210 240 210 340 320 280 280 280 480 420 400
0.40%
Fig. 8. Relationship between εeq and εeff measured with DIC technique.
σm
[MPa] 0 0 0 100 130 0 0 0 120 120 0 0 300
8
Hide-aki Nishikawa et al. / Procedia Structural Integrity 2 (2016) 3002–3009 Author name / Structural Integrity Procedia 00 (2016) 000–000 1.E-06 10-6
Material A (0.07C, 1℃/s)
Typical long crack data (SM50B welding, NRIM (1980))
1.E-07 10-7
a=0.5l
a
σa
1
10
σm
[MPa]
[MPa]
280
0
240
0
210
0
240
100
210
130
1.E-10 10-10
l a=0.5l
a
σa
10
σm
[MPa]
[MPa]
340
0
320
0
280
0
280
120
280
120
Material C (0.15C, 30℃/s)
Typical long crack data (SM50B welding, NRIM (1980))
Crack coalescence
l
10-8 1.E-08
0.2 ≲ l ≲ 1 mm
1
c
10-7 1.E-07
1.E-09 10-9
100
∆ Keff (MPa √m)
Material B (0.07C, 20℃/s)
Typical long crack data (SM50B welding, NRIM (1980))
1.E-08 10-8
0.2 ≲ l ≲ 1 mm
1.E-09 10-9
1.E-10 10-10
b
1.E-07 10-7
l
1.E-08 10-8
1.E-06 10-6
Fatigue crack growth rate da/dN (m/cycle)
a
Fatigue crack growth rate da/dN (m/cycle)
Fatigue crack growth rate da/dN (m/cycle)
1.E-06 10-6
3009
a=0.5l
0.2 ≲ l ≲ 1 mm
10-9 1.E-09
100
10-10 1.E-10
a
σa
1
∆ Keff (MPa √m)
10
σm
[MPa]
[MPa]
480
0
420
0
400
300
100
∆ Keff (MPa √m)
Fig. 9. Small fatigue crack growth rate versus ∆Keff evaluated with DIC technique.
4. Summary In this study, to clarify the effect of tensile mean stress and HAZ micro structure on the small fatigue crack growth behavior, uniaxial fatigue testing with small fatigue crack growth observation were carried out for low carbon steel with several simulated HAZ heat treatment under some tensile mean stress conditions. As a results, it is clarified that εna type small crack growth law is effective even for HAZ microstructure under zero mean stress. Furthermore it is clarified that small fatigue crack growth rate acceleration under tensile mean stress is able to be evaluated by proposed εeqna type modified small crack growth law which includes conventional SmithWatson-Topper (SWT) equivalent strain εeq. In addition, it is clarified that DIC technique is effective to detect the crack opening point even for early stage small fatigue crack and εeq is proportional to εeff which is evaluated by crack opening point measured with DIC. It is considered that since SWT equivalent strain εeq is implicitly includes small crack growth property and crack closure effect, εeq is effective to evaluate small crack growth rate as a simple parameter. Acknowledgements This work was supported by Council for Science, Technology and Innovation (CSTI), Cross-ministerial Strategic Innovation Promotion Program (SIP), “Structural Materials for Innovation” (Funding agency: JST). References Smith K.N., Watson P., Topper T.H., 1970. A Stress-Strain Function for the Fatigue of Metals, Journal of Materials 5, 767–778. Murakami Y., 2002, Metal fatigue: effects of small defects and nonmetallic inclusions. Elsevier, UK. NRIM Fatigue Data Sheet No. 21, 1980. Data sheet on fatigue crack propagation for butt welded joints of sm50b rolled steel for welded structure. NRIM, Japan. Elber W., 1971. The Significance of Fatigue Crack Closure, Damage Tolerance in Aircraft Structures. ASTM STP 486, 230-242. Nishitani H., 1981. Unifying treatment of fatigue crack growth laws in small, large and non-propagating cracks. Mechanics of Fatigue-AMD 47, 151–166. Rabbolini S., Beretta S., Foletti S., Cristea M.E., 2015. Crack closure effects during low cycle fatigue propagation in line pipe steel: An analysis with digital image correlation. Engineering Fracture Mechanics 148, 441-456.
ScienceDirect
Available online www.sciencedirect.com Available online at at www.sciencedirect.com Structural Structural Integrity Integrity Procedia Procedia 00 00 (2016) (2016) 000–000 000–000
ScienceDirect ScienceDirect
Procedia Structural 2 (2016) 3002–3009 Structural IntegrityIntegrity Procedia 00 (2016) 000–000
www.elsevier.com/locate/procedia www.elsevier.com/locate/procedia
www.elsevier.com/locate/procedia
21st European Conference on Fracture, ECF21, 20-24 June 2016, Catania, Italy
Effect of Mean Stress on Small Fatigue Crack Growth Rate on Low Carbon Steel with Several Simulated HAZ Heat Treatment Thermo-mechanical modeling ofaa*,aYoshiyuki high pressure Hide-aki Nishikawa Furuyaaa turbine blade of an airplane gas turbine engine National National Institute Institute for for Materials Materials Science, Science, 1-2-1 1-2-1 Sengen, Sengen, Tsukuba-shi, Tsukuba-shi, Ibaraki, Ibaraki, 305-0047 305-0047 Japan Japan
XV Portuguese Conference on Fracture, PCF 2016, 10-12 February 2016, Paço de Arcos, Portugal
aa
P. Brandãoa, V. Infanteb, A.M. Deusc* a Abstract AbstractDepartment of Mechanical Engineering, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1, 1049-001 Lisboa, b
Portugal
IDMEC, Department of Mechanical Engineering, Instituto Superior Técnico, Universidaderesidual de Lisboa, Av. of Rovisco Pais, 1, 1049-001 Lisboa, In Zone In this this study, study, to to clarify clarify the the effect effect of of microstructure microstructure of of Heat Heat Affected Affected Zone (HAZ) (HAZ) and and residual stress stress of weld weld on on small small fatigue fatigue crack crack Portugal c growth behavior, uniaxial fatigue testing with surface small fatigue crack growth observation were carried out for low carbon steel growth behavior, uniaxialoffatigue testing with surface smallSuperior fatigueTécnico, crack growth observation wereAv. carried outPais, for 1, low carbonLisboa, steel CeFEMA, Department Mechanical Engineering, Instituto Universidade de Lisboa, Rovisco 1049-001 n with conditions. Portugal type small small crack crack growth growth law law was was with three three simulated simulated HAZ HAZ heat heat treatment treatment under under several several mean mean stress stress conditions. As As aa results, results, εεnaa type also also effective effective to to HAZ HAZ microstructure microstructure under under zero zero mean mean stress. stress. Under Under tensile tensile mean mean stress stress condition, condition, fatigue fatigue fracture fracture life life and and small small fatigue fatigue crack crack growth growth life life were were decreased. decreased. In In addition, addition, it it is is clarified clarified that that small small fatigue fatigue crack crack growth growth rate rate acceleration acceleration under under tensile tensile Abstract which is obtained from mean stress was able to be evaluated by using Smith-Watson-Topper equivalent strain ε eq mean stress stress mean stress was able to be evaluated by using Smith-Watson-Topper equivalent strain εeq which is obtained from mean nn dependency a type type modified modified small small crack crack growth growth law law was was proposed. proposed. dependency of of fatigue fatigue fracture fracture life life for for smooth smooth specimen specimen and and εεeq eq a During their modern engineto subjected to increasingly demanding conditions, proportional εεeff evaluated by opening measured with Image Furthermore, it clarified εεeq wasaircraft proportional to components which was wasare evaluated by crack crack opening point point measuredoperating with Digital Digital Image Furthermore, it is isoperation, clarified that that eq was eff which especially the high pressure turbine (HPT) blades. Such conditions cause these parts to undergo different types of time-dependent Correlation technique. It is considered that equivalent strain ε implicitly includes small crack growth life and effect eq Correlation technique. It is considered that equivalent strain εeq implicitly includes small crack growth life and effect of of crack crack degradation, one of which is creep. A model using the finite element method (FEM) was developed, in order to be able to predict closure. closure. the creep behaviour of HPTbyblades. Flight data records (FDR) for a specific aircraft, provided by a commercial aviation © 2016 The Published Elsevier B.V. © The Authors. Authors. Published byIntegrity) ElsevierHosting B.V. by Elsevier Ltd. All rights reserved. © 2016 2016, PROSTR (Procedia Structural company, were used to obtain thermal and mechanical data for three different flight cycles. In order to create the 3D model Peer-review under responsibility of the Scientific Committee of Peer-review under responsibility Scientific Committee of ECF21. ECF21.and its chemical composition and material properties were Peer-review under responsibility of theofScientific Committee of ECF21. needed for the FEM analysis, athe HPT blade scrap was scanned,
obtained. The data that was gathered was fed into the FEM model and different simulations were run, first with a simplified 3D
Keywords: Fatigue; Heat affected zone; crack growth Mean Digital image correlation Keywords: Fatigue; Heat affected zone; Small Small crack growth rate; rate; Mean stress; stress; Digital image rectangular block shape, in order to better establish the model, and then with thecorrelation real 3D mesh obtained from the blade scrap. The
overall expected behaviour in terms of displacement was observed, in particular at the trailing edge of the blade. Therefore such a model can be useful in the goal of predicting turbine blade life, given a set of FDR data.
1. 1. Introduction Introduction
© 2016 The Authors. Published by Elsevier B.V. Since fracture of components are in Peer-review under responsibility of the Scientific Committee of PCFoccurred 2016. Since fatigue fatigue fracture of mechanical mechanical components are mainly mainly occurred in welding, welding, aa lot lot of of fatigue fatigue data data for for welding welding
were were accumulated accumulated before before now. now. However, However, since since these these fatigue fatigue data data were were widely widely scattered, scattered, too too much much conservative conservative fatigue fatigue Keywords: High Pressure Turbine Blade; Creep; Finite Element Method; 3D Model; Simulation. design is frequently required. One of the reason why such problem occurred is that a lots of effective design is frequently required. One of the reason why such problem occurred is that a lots of effective fatigue fatigue parameter parameter
* * Corresponding Corresponding author: author: E-mail E-mail address: address: [email protected] [email protected] 2452-3216 2452-3216 © © 2016 2016 The The Authors. Authors. Published Published by by Elsevier Elsevier B.V. B.V. * Corresponding Tel.: +351of Peer-review under responsibility the Peer-review underauthor. responsibility of218419991. the Scientific Scientific Committee Committee of of ECF21. ECF21. E-mail address: [email protected]
2452-3216 © 2016 The Authors. Published by Elsevier B.V.
Peer-review under responsibility of the Scientific Committee of PCF 2016. 2452-3216 © 2016, PROSTR (Procedia Structural Integrity) Hosting by Elsevier Ltd. All rights reserved. Peer-review under responsibility of the Scientific Committee of ECF21. 10.1016/j.prostr.2016.06.376
2
Hide-aki Nishikawa et al. / Procedia Structural Integrity 2 (2016) 3002–3009 Author name / Structural Integrity Procedia 00 (2016) 000–000
3003
in welding affects its performance and it is difficult to evaluate each factor quantitatively. For example, since fatigue crack is initiated from weld toe, not only stress concentration but also effect of variable microstructure in the heat affected zone (HAZ) is necessary to be considered. Furthermore residual stress formed around HAZ which affect fatigue crack growth behavior is also have to be considered. By the way, it is well known that fatigue life is mainly occupied by small fatigue crack growth life. However, small fatigue crack growth behavior in the welding is not enough investigated. To clarify the small fatigue crack growth behavior in the welding is possibly helpful to considering complex effective parameter such as residual stress and stress concentration quantitatively. This study focusing on the effect of HAZ microstructure and residual stress (mean stress) on small fatigue crack growth behavior. By the way, measurement of crack closure effect which is important to mean stress dependency of fatigue crack growth rate is difficult especially for small crack. Since fatigue life is mainly occupied by crack growth life, conventional fatigue parameter for fatigue fracture life of smooth specimen is possibly useful also for small crack growth evaluation. For example, Smith et al. (1970) proposed stress-strain function which is able to fix mean stress effect on fatigue life of smooth specimen. In this study, to clarify the effect of these factor on the small fatigue crack growth behavior, fatigue testing with successive small fatigue crack growth observation were carried out for low carbon steel with several simulated HAZ heat treatment under some tensile mean stress conditions. Furthermore, crack opening-closing behavior which is important for mean stress dependency was investigated with Digital Image Correlation (DIC) technique. Nomenclature
σa σmax σop εa εmax εop εeq l a
∆K
√area c C n
stress amplitude maximum stress during fatigue cycle Crack opening stress during fatigue cycle strain amplitude maximum strain during fatigue cycle crack opening strain during fatigue cycle equivalent strain calculated from Smith-Watson-Topper (SWT) equation surface fatigue crack length fatigue crack depth stress intensity factor range projected area of the fatigue crack materials constant for SWT equation materials constant for small fatigue crack growth law materials constant for small fatigue crack growth law
2. Material and testing procedure Materials used in this study were three types of low carbon steel. Table 1 shows chemical compositions. Three types of simulated HAZ heat treatments were conducted with controlling cooling rate after holding 5 second at 1400℃ for each materials. Table 2 shows heat treatment conditions for each materials. Finally, three different simulated HAZ microstructures were obtained. Fig. 1 shows microstructure morphologies. Microstructures were acicular ferrite, perlite and grain boundary ferrite for material A, ferrite and bainite for material B and martensite for material C respectively. Vickers hardness were HV148, HV182 and HV350 respectively. Fatigue tests were conducted with load controlled uniaxial loading by servo hydraulic type fatigue testing equipment. Fig. 2 shows specimen configurations. Specimen surface were etched by 3 % nital after mirror polished to crack observation. Small fatigue crack growth behavior is observed using digital microscope. In addition, strain amplitude was measured by strain gage on the back surface of fatigue specimen.
Hide-aki Nishikawa et al. / Procedia Structural Integrity 2 (2016) 3002–3009 Author name / Structural Integrity Procedia 00 (2016) 000–000
3004
3
Table 1. Chemical compositions. Material
C
Si
Cr
Mn
P
S
Mo
Al
N
A
0.07
<0.01
0.51
1.51
0.006
0.003
<0.01
0.025
0.003
B
0.07
<0.01
0.01
1.50
0.006
0.003
0.21
0.026
0.003
C
0.15
0.02
0.54
1.51
0.007
0.001
-
0.019
0.002
Table 2. Heat treatment conditions for each materials. Cooling rate (℃ /s) A
B
C
1400~1000 ℃
10
60
50
1000~800 ℃
4
40
800~500 ℃
1
20
500~350 ℃
0.5
12
30
Fig. 1. Simulated HAZ Microstructures.
φ10
2
2
16.8
(32.5)
R31
16.8
Fig. 2. Specimen configurations.
3. Experimental results and discussions 3.1. Mean stress effects on S-N diagrams Figure 2 shows S-N diagram. Fig. 2 (a) is represented with stress amplitude. Solid mark shows results under fully reversed tension-compression condition and open mark shows under tensile mean stress condition. Fatigue lives under tensile mean stress conditions were shorter than that of fully reversed tension-compression results. It is known that mean stress dependency is able to be fixed using Smith-Watson-Topper (SWT) equivalent strain proposed by Smith et al. (1970). SWT equivalent strain εeq is expressed as:
ε eq = ε ac (σ max E )1−c
(1)
where εa is strain amplitude, σmax is maximum stress, E is Young’s modules and c is materials constant which is related to mean stress sensitivity. Fig. 2 (b) shows S-N diagrams represented with SWT equivalent strain. Although mean
4
Hide-aki Nishikawa et al. / Procedia Structural Integrity 2 (2016) 3002–3009 Author name / Structural Integrity Procedia 00 (2016) 000–000
3005
stress sensitivities were deferent depends on microstructure, mean stress dependency of simulated HAZ microstructure was able to be fixed by SWT equivalent strain as shown in Fig. 2 (b). In addition, material constant value c for Eq (1) were 0.6, 0.7 and 0.35 for material A, B and C respectively. Such a conventional mean stress dependency of fatigue life is possibly related to fatigue crack growth behavior. Therefore mean stress effect for fatigue crack growth rate will be discussed below. Equivalent Strain amplitude εeq (-)
1000
Stress amplitude σa (MPa)
a *
*
*
TP σm=0 σmax≂σ y-c A B
100
* Round bar specimen
C
103
104
105
106
Number of cycles to failure (cycles)
107
0.01
εeq = εac (σmax/E)(1-c)
b
TP A
0.00
*
.1
*
c value σ =0 σmax≂σ y-c for eq. 1 m 0.6
B
0.7
C
0.35
103
*
…eq
* Round bar specimen
104
105
106 Number of cycles to failure (cycles)
107
Fig. 2. S-N diagrams represented with (a) stress amplitude and (b) SWT equivalent strain calculated by eq. 1.
3.2. Mean stress effects on small fatigue crack growth rate Figure 3 shows small fatigue crack growth rate versus stress intensity factor. Stress Intensity factor range was calculated by Eq. (2). Stress intensity factor range was able to be approximately calculated with √area, projected area of the crack, as shown in Eq (2) which proposed by Murakami (2002).
∆K = 0.65∆σ π area
σ max (σ min ≤ 0 ) ∆σ = σ max − σ min (σ min > 0 )
(2)
Long fatigue crack growth property of welding reported by NRIM (1980) also represented in the figure. Fatigue crack growth rates were not uniformly evaluated by stress intensity factor range. In addition, fatigue crack growth rate was partly higher than that of long crack property. It is well known that evaluating crack closure effect is necessary to estimate fatigue crack growth rate as mentioned by Elber (1971). To evaluate small fatigue crack growth rate and its mean stress dependency, considering crack closure effect seems necessary also for small fatigue crack growth rate of simulated HAZ microstructure. Since quantitative estimation for crack closure effect is difficult, simple modeling is one of the useful approach for small fatigue crack growth problem. Nishitani (1981) proposed small fatigue crack growth law expressed as:
da / dN = Cσ nl
(3) where C and n are materials constant and l is surface crack length. In this study, applicability of similar εan a type parameter where a is crack depth was considered. Since uniaxial loading, it is assumed that l=2a. Figure 4 shows small fatigue crack growth rate versus εan a parameter. Fatigue crack growth rate under σm = 0 conditions were uniformly evaluated by εan a parameter in spite of simulated HAZ microstructure. On the other hands, this model can’t estimate fatigue crack growth rate acceleration under tensile mean stress conditions. As described above, SWT equivalent strain εeq is effective to fix the mean stress dependency for fatigue fracture life. Since large part of fatigue life is occupied by small fatigue crack growth life, εeq may be also related to mean stress dependency of small fatigue crack growth rate. Therefore, modified crack growth equation using εeqn a parameter expressed as Eq. 4 is considered below. n
da / dN = Cε eq a
(4)
Hide-aki Nishikawa et al. / Procedia Structural Integrity 2 (2016) 3002–3009 Author name / Structural Integrity Procedia 00 (2016) 000–000
3006
5
Figure 5 shows small fatigue crack growth rate versus εeqn a parameter calculated from SWT equation. Used materials constants c for εeq described in Eq. (1) was same as Fig. 2 (b). As described in Fig. 5, all fatigue data including tensile mean stress condition were uniformly evaluated by modified small fatigue crack growth law which using εeqn a parameter. It is clarified that εeqn a parameter is effective to estimate the mean stress dependency of small fatigue crack growth rate as a simple parameter. As mentioned in Fig. 3, considering crack opening behavior is important to evaluate fatigue crack growth rate. It is possible that SWT εeq is indirectly including the effect of crack opening behavior. To clarify the relationship between crack opening behavior and SWT equivalent strain, direct measurement for the crack opening point were carried out by DIC technique. 3.3. Direct measurement for crack opening-closing behavior with DIC technique DIC analysis were conducted for microscope images which successively obtained during loading-unloading process and vertical direction strain were analyzed. Figure 6 shows small fatigue crack opening behavior observed with DIC technique. Fig. 6 (a) is reference image obtained at minimum load. Fig. 6 (b)~(f) are contour image of successively analyzed vertical strain for loading process. Strain distribution related to fatigue crack is not detected in Fig. 6 (b). In Fig. 6 (c), higher strain distribution is observed around the fatigue crack. After that this strain distribution becomes bigger as applied load becomes bigger. 1.E-06 10-6
Material A (0.07C, 1℃/s)
Typical long crack data (SM50B welding, NRIM (1980))
1.E-07 10-7
l
σa
[MPa]
280
0
240
0
210
0
240
100
210
130
1.E-09 10-9
1.E-10 10-10
1
σm
[MPa]
l
10
a=0.5l σa
1.E-09 10-9
100
1.E-10 10-10
1
Material C (0.15C, 30℃/s)
Typical long crack data (SM50B welding, NRIM (1980))
Crack coalescence 0.2 ≲ l ≲ 1 mm
1.E-08 10-8
a σm
[MPa]
[MPa]
340
0
320
0
280
0
280
120
280
120
10
∆ K (MPa √m)
c
1.E-07 10-7
0.2 ≲ l ≲ 1 mm
1.E-08 10-8
a
a=0.5l
1.E-06 10-6
Material B (0.07C, 20℃/s)
Typical long crack data (SM50B welding, NRIM (1980))
1.E-07 10-7
0.2 ≲ l ≲ 1 mm
1.E-08 10-8
b
Fatigue crack growth rate da/dN (m/cycle)
Fatigue crack growth rate da/dN (m/cycle)
a
Fatigue crack growth rate da/dN (m/cycle)
1.E-06 10-6
l
a=0.5l
1.E-09 10-9
100
σa
[MPa]
a σm
[MPa]
480
1.E-10 10-10
1
0
420
0
400
300
10
100
∆ K (MPa √m)
∆ K (MPa √m)
a
Material A (0.07C, 1℃/s)
10-7 10-8 0.2 ≲ l ≲ 1 mm
10-9
σa
10-10
l a=0.5l
10-11 10-25
10-24
a
10-23
εa6.62 ･ a (mm)
σm
[MPa]
[MPa]
280
0
240
0
210
0
240
100
210
130
10-22
10-21
10-6
b
Fatigue crack growth rate da/dN (mm/cycle)
10-6
Fatigue crack growth rate da/dN (mm/cycle)
Fatigue crack growth rate da/dN (mm/cycle)
Fig. 3. Small fatigue crack growth rate versus stress intensity factor.
Material B (0.07C, 20℃/s)
10-7 10-8 0.2 ≲ l ≲ 1 mm
10-9
σa
l
10-10 a=0.5l
10-11 10-28
10-27
a
10-26
σm
[MPa]
[MPa]
340
0
320
0
280
0
280
120
280
120
10-25
10-24
10-6
c
Material C (0.15C, 30℃/s)
10-7 Crack coalescence
10-8 10-9 10-10
εa7.91 ･ a (mm)
Fig. 4. Small fatigue crack growth rate versus εan a parameter.
σa
l a=0.5l
10-11 10-10
0.2 ≲ l ≲ 1 mm
10-9
a
10-8
εa1.49 ･ a (mm)
σm
[MPa]
[MPa]
480
0
420
0
400
300
10-7
10-6
1.E-07 10-7
1.E-08 10-8
1.E-06 10-6
a
Material A (0.07C, 1℃/s)
1.E-07 10-7
εeq = εac (σmax/E)(1-c) c = 0.6
1.E-08 10-8
0.2 ≲ l ≲ 1 mm
1.E-09 10-9
σa
1.E-10 10-10
1.E-11 10-11 1E-28 10-28
Fatigue crack growth rate da/dN (m/cycle)
Fatigue crack growth rate da/dN (m/cycle)
1.E-06 10-6
Hide-aki Nishikawa et al. / Procedia Structural Integrity 2 (2016) 3002–3009 Author name / Structural Integrity Procedia 00 (2016) 000–000
l a=0.5l
1E-27 10-27
a
1E-26 10-26
εeq7.48 ･ a (mm)
[MPa]
[MPa]
280
0 0
210
0
240
100
210
130
1E-25 10-25
Material B (0.07C, 20℃/s)
c = 0.7
1.E-08 10-8
0.2 ≲ l ≲ 1 mm σa
1.E-10 10-10
1E-24 10-24
1.E-07 10-7
εeq = εac (σmax/E)(1-c)
1.E-09 10-9
σm
240
1.E-06 10-6
b
1.E-11 10-11 1E-31 10-31
Fatigue crack growth rate da/dN (m/cycle)
6
l a=0.5l
1E-30 10-30
a
1E-29 10-29
εeq8.95 ･ a (mm)
1.E-09 10-9
σm
[MPa]
[MPa]
340
0
320
0
280
0
280
120
280
120
1E-28 10-28
Material C (0.15C, 30℃/s)
c
εeq = εac (σmax/E)(1-c) c = 0.35
Crack coalescence
1.E-10 10-10
1E-27 10-27
3007
1.E-11 10-11 10-19 1E-19
0.2 ≲ l ≲ 1 mm σa
l a=0.5l
10-18 1E-18
a
10-17 1E-17
σm
[MPa]
[MPa]
480
0
420
0
400
300
10-16 1E-16
10-15 1E-15
εeq4.81 ･ a (mm)
Fig. 5. Small fatigue crack growth rate versus εeqn a parameter calculated from SWT equation.
Such a strain distribution around the fatigue crack is mainly related to Crack Opening Displacement (COD) during loading cycle. Conventionally, macroscopic COD is effective for measuring crack opening point for long crack such as CT specimen. Therefore, strain analyzed by DIC which related to microscopic COD is possibly effective to detect the crack opening point even for small fatigue crack. Figure 7 shows the example of the relationship between stress and crack opening strain measured with DIC technique for crack length of (a) 0.3 mm and (b) 0.8 mm. Crack opening strain is measured on the fatigue crack where a few tens of µm behind from the crack tip as described in the figures. Figures also includes the strain measured by strain gage. Although, for long crack, crack opening point is able to be detected by strain gage conventionally, strain gage data of Fig. 7 is approximately linier and crack opening point is not able to be detected. On the other hand, crack opening point is clearly appeared in the strain measured by DIC as shown in Fig. 7 even for 0.3 mm length fatigue crack. Rabblini et al. (2015) reported DIC technique applicability for crack closure measurement for relatively larger crack of length more than 1 mm. It is clarified that DIC technique is effective to detect the crack opening point even for early stage small fatigue crack of length less than 0.3 mm which naturally initiated on the material surface. Then, relationship between effective strain range and SWT equivalent strain is confirmed below. Effective strain εeff calculated from εop which is correspond to σop obtained by DIC is expressed as Eq. (5). (5) ε eff = ε max − ε op Figure 8 shows relationship between εeq and εeff measured with DIC technique. As shown in the figure, εeq is approximately proportional to εeff. This results indicates that since SWT εeq is indirectly including the effect of crack opening behavior, it is also effective to evaluate the mean stress effect on small fatigue crack growth rate. As described above, SWT equivalent strain is able to be obtained without crack growth test. Therefore, modified small fatigue crack growth law described in Eq. (4) is effective to evaluate the mean stress effect for small crack as a simple approach. Figure 9 shows relationship between small fatigue crack growth rate and ∆Keff evaluated with DIC technique. Micro structure dependency of fatigue crack growth rate is not clear. This results indicates fatigue life difference related to microstructure seems subjected to crack closure effect. Since quantitative crack closure evaluation is difficult, modified small crack growth law proposed above which implicitly includes crack closure effect is seems effective to evaluate small fatigue crack growth rate. To estimate the fatigue life of welding, it is also necessary to considering stress concentration. Small fatigue crack growth behavior under the stress concentration and fatigue life estimation method based on small fatigue crack growth property for actual weld joint will be investigated in future.
Hide-aki Nishikawa et al. / Procedia Structural Integrity 2 (2016) 3002–3009 Author name / Structural Integrity Procedia 00 (2016) 000–000
3008
c
b
a
σ = σmin (reference image)
σ = σmin + 0.4∆σ
σ = σmin + 0.3∆σ
f
e
d
σ = σmin + 0.5∆σ
7
σ = σmin + 0.6∆σ -0.002
100 μm
σ = σmin + ∆σ = σmax 0.012
Strain in vertical direction (-)
Loading direction
Fig. 6. Small fatigue crack opening behavior observed with DIC technique.
400 300
Strain gage
-100
σop
Strain measurement area
-200
Material B, σa = 280 MPa, l=0.8mm
b
Strain gage
200
DIC strain
100 0
300
Stress (MPa)
Stress (MPa)
200
400
Material B, σa = 280 MPa, l=0.3mm
a
DIC strain
100 0 -100
σop
Strain measurement area
-200
-300
-300
100 μm
-400 -0.005
0
0.005 0.01 Strain (-)
0.015
0.02
-400 -0.005
100 μm
0
0.005 0.01 Strain (-)
0.015
0.02
Fig. 7. Relationship between stress and crack opening strain measured with DIC technique for crack length of (a) 0.3 mm and (b) 0.8 mm.
0.30%
TP
0.25% A
εeq (-)
0.20% 0.15%
B
0.10% 0.05%
C
0.00% 0.00%
0.10%
0.20%
εeff (-)
0.30%
σa
[MPa] 280 240 210 240 210 340 320 280 280 280 480 420 400
0.40%
Fig. 8. Relationship between εeq and εeff measured with DIC technique.
σm
[MPa] 0 0 0 100 130 0 0 0 120 120 0 0 300
8
Hide-aki Nishikawa et al. / Procedia Structural Integrity 2 (2016) 3002–3009 Author name / Structural Integrity Procedia 00 (2016) 000–000 1.E-06 10-6
Material A (0.07C, 1℃/s)
Typical long crack data (SM50B welding, NRIM (1980))
1.E-07 10-7
a=0.5l
a
σa
1
10
σm
[MPa]
[MPa]
280
0
240
0
210
0
240
100
210
130
1.E-10 10-10
l a=0.5l
a
σa
10
σm
[MPa]
[MPa]
340
0
320
0
280
0
280
120
280
120
Material C (0.15C, 30℃/s)
Typical long crack data (SM50B welding, NRIM (1980))
Crack coalescence
l
10-8 1.E-08
0.2 ≲ l ≲ 1 mm
1
c
10-7 1.E-07
1.E-09 10-9
100
∆ Keff (MPa √m)
Material B (0.07C, 20℃/s)
Typical long crack data (SM50B welding, NRIM (1980))
1.E-08 10-8
0.2 ≲ l ≲ 1 mm
1.E-09 10-9
1.E-10 10-10
b
1.E-07 10-7
l
1.E-08 10-8
1.E-06 10-6
Fatigue crack growth rate da/dN (m/cycle)
a
Fatigue crack growth rate da/dN (m/cycle)
Fatigue crack growth rate da/dN (m/cycle)
1.E-06 10-6
3009
a=0.5l
0.2 ≲ l ≲ 1 mm
10-9 1.E-09
100
10-10 1.E-10
a
σa
1
∆ Keff (MPa √m)
10
σm
[MPa]
[MPa]
480
0
420
0
400
300
100
∆ Keff (MPa √m)
Fig. 9. Small fatigue crack growth rate versus ∆Keff evaluated with DIC technique.
4. Summary In this study, to clarify the effect of tensile mean stress and HAZ micro structure on the small fatigue crack growth behavior, uniaxial fatigue testing with small fatigue crack growth observation were carried out for low carbon steel with several simulated HAZ heat treatment under some tensile mean stress conditions. As a results, it is clarified that εna type small crack growth law is effective even for HAZ microstructure under zero mean stress. Furthermore it is clarified that small fatigue crack growth rate acceleration under tensile mean stress is able to be evaluated by proposed εeqna type modified small crack growth law which includes conventional SmithWatson-Topper (SWT) equivalent strain εeq. In addition, it is clarified that DIC technique is effective to detect the crack opening point even for early stage small fatigue crack and εeq is proportional to εeff which is evaluated by crack opening point measured with DIC. It is considered that since SWT equivalent strain εeq is implicitly includes small crack growth property and crack closure effect, εeq is effective to evaluate small crack growth rate as a simple parameter. Acknowledgements This work was supported by Council for Science, Technology and Innovation (CSTI), Cross-ministerial Strategic Innovation Promotion Program (SIP), “Structural Materials for Innovation” (Funding agency: JST). References Smith K.N., Watson P., Topper T.H., 1970. A Stress-Strain Function for the Fatigue of Metals, Journal of Materials 5, 767–778. Murakami Y., 2002, Metal fatigue: effects of small defects and nonmetallic inclusions. Elsevier, UK. NRIM Fatigue Data Sheet No. 21, 1980. Data sheet on fatigue crack propagation for butt welded joints of sm50b rolled steel for welded structure. NRIM, Japan. Elber W., 1971. The Significance of Fatigue Crack Closure, Damage Tolerance in Aircraft Structures. ASTM STP 486, 230-242. Nishitani H., 1981. Unifying treatment of fatigue crack growth laws in small, large and non-propagating cracks. Mechanics of Fatigue-AMD 47, 151–166. Rabbolini S., Beretta S., Foletti S., Cristea M.E., 2015. Crack closure effects during low cycle fatigue propagation in line pipe steel: An analysis with digital image correlation. Engineering Fracture Mechanics 148, 441-456.