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High-R low growth rate fatigue crack propagation at elevated temperatures
Accepted Manuscript High-R low growth rate fatigue crack propagation at elevated temperatures Zhen Chen, Stuart Holdsworth PII: DOI: Reference:
S0142-1123(17)30349-3 https://doi.org/10.1016/j.ijfatigue.2017.08.020 JIJF 4445
To appear in:
International Journal of Fatigue
Received Date: Accepted Date:
4 July 2017 21 August 2017
Please cite this article as: Chen, Z., Holdsworth, S., High-R low growth rate fatigue crack propagation at elevated temperatures, International Journal of Fatigue (2017), doi: https://doi.org/10.1016/j.ijfatigue.2017.08.020
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High-R low growth rate fatigue crack propagation at elevated temperatures Zhen Chen,Stuart Holdsworth ¨ EMPA:Swiss Federal Laboratories for Materials Science and Technology, Uberlandstrasse 129, 8600 D¨ubendorf, Z¨urich, Switzerland
Abstract While fatigue cracking is widely considered as the primary cracking mode under cyclic loading conditions, this is not the case for high-R (Kmin =Kmax ) low growth rate fatigue crack propagation at elevated temperatures. Creep cracks can sometimes be observed in such situations when the stress intensity factor range K is around the fatigue crack growth threshold stress intensity factor Kth . A Time Dependent Failure Assessment Diagram (TDFAD) has been adopted in this study for predicting creep cracking in high-R cyclic loading conditions at elevated temperatures. In addition, attention is also paid to oxide-induced crack closure which is greatly influential at high temperatures. Three power plant steels with di erent chromium contents, namely 1%Cr, 9%Cr and 18%Cr steels, have been investigated at temperatures between 550 C and 650 C. The experiments were performed by reducing K continuously to Kth . Good accordance has been found between fracture surface observations and the TDFAD approach predictions of creep crack initiation. Apart from creep cracking, high-R Kth values have also been found to be influenced by oxideinduced crack closure at elevated temperatures. The enhancement is studied through the relationship between the crack tip opening displacement and stress intensity factor. Keywords: Fatigue, High temperature, Creep cracking, High R, Oxide induced crack closure
1. Introduction High cycle fatigue crack growth may be described in terms of cyclic stress intensity factor K (Kmax Kmin ), as shown schematically in Figure 1. Conventionally, the diagram is considered in three regimes, namely a low-K regime in which K is close to the fatigue crack growth (FCG) threshold Kth , a mid-K regime in which crack growth rate da=dN and K obey a power law [1], and a high-K regime in which crack propagation approaches conditions for unstable fracture or plastic collapse. The standard ASTM E647 [2] defines the fatigue crack growth threshold Kth as the cyclic stress intensity factor K that corresponds to 1 10 10 m/cycle fatigue crack growth rate. The ISO standard [3] uses a similar definition but with a threshold crack growth rate criterion of 1 10 11 m/cycle. In the mid-K and high-K regimes, fatigue cracks propagate at rates greater than 10 nm/cycle and dominate the crack growth process. However, this is not the case in the low-K regime near Kth where fatigue crack growth is close to arrest. Other fracture modes can become more influential in this regime. For example, during high frequency high-R FCG at elevated temperatures, creep cracks were detected during post-test inspection in the current study on the fracture surfaces of the test pieces as K drops to near Kth . This is despite the generally perceived notion that high frequency fatigue crack growth is exempt from creep cracking. To the author’s knowledge, this has not been addressed before in the literatures. Therefore a method for predicting creep crack initiation in these circumstance has been devised. Methods have been developed for the assessment of creep crack initiation (CCI). A d approach [4] determines the crack initiation time by evaluating the stress state at a characteristic distance ’d’ from the crack tip. A Two Criteria Diagram (2CD) approach [5] has been developed in Germany. The 2CD approach requires two material properties, the creep rupture strength Rr and the creep crack initiation stress intensity factor KIi . By normalizing the operating stress and stress intensity factor respectively with the two material properties, the 2CD approach predicts if creep crack extension is likely to occur. Preprint submitted to International Journal of Fatigue
September 28, 2017
The Time Dependent Failure Assessment Diagram (TDFAD) concept [6], which is developed from the Failure Assessment Diagram (FAD) approach [7, 8], is incorporated into the R5 procedure [9] for the assessment of creep failure at high temperatures. The approach also requires few material properties, and it avoids calculation of the elastic-plastic stress state at the crack tip. It also has the advantage that the failure envelope is time dependent. The approach has been applied to predict the creep crack initiation in ferrtic and austenitic steels at elevated temperatures, where slightly non-conservative predictions may be found for the ferritic steels [10, 11]. For high-R low growth rate FCG at elevated temperatures, a more proper parameter is proposed in the TDFAD approach for a conservative prediction of creep cracking at the crack tip. The concept of crack closure was introduced by Elber [12] as an influential factor determining the magnitude of Kth . A large number of authors have proposed various mechanisms of crack closure [13–17] at ambient temperature, which are regarded mainly as a consequence of the plastic wake at the crack tip, but also with contributions from surface roughness and oxide wedging. Crack closure was noticed to have less impact on Kth at high-R. However, in recent years the evidence of crack closure at high-R has been observed and measured in the experiments, which may be attributed to surface roughness or oxide debris [18, 19]. At the crack tips of specimens tested to give high-R Kth at elevated temperatures, thicker oxide layers can be generated and significant enhancement of Kth due to oxide-induced crack closure may be observed. The enhancement of the crack tip opening displacement (CTOD) caused by the oxide layer is therefore used to study the oxide-induced crack closure at high-R.
Figure 1: High cycle fatigue crack growth behaviour from low to high K regions
2. Experiment and Methods 2.1. Test Details and Materials A dynamic resonance testing machine was used to carry out a series of FCG experiments. The test were performed at frequencies between 50 and 60Hz and at temperatures ranging from 25 to 650 C. The crack length was continuously monitored using the electrical direct current potential drop (DCPD) method [2]. To achieve low growth rate FCG, K was decreased continuously following Equation (1)
K = Kini e
ca
(1)
where Kini is the initial stress intensity factor, a is the length of crack extension and c is the load reduction rate. After the experiments, the specimens were broken open in order to visually measure the crack length and to verify the 2
Figure 2: Dimension of the compact tension specimen
(a) R constant K decrease mode
(b) Kmax constant K decrease mode
Figure 3: Two control mode for Kth determination test, both with K decreasing
DCPD crack length calibration. In addition, this step also allowed the fracture surface detail to be characterised, e.g. for any evidence of creep cracking. Three power plant steels with di erent chromium levels were investigated, namely a low alloy 1CrMoV steel, a martensitic 9CrMoCo steel and an austenitic 18Cr8Ni steel. With reference to typical power plant operating temperatures, the 1%Cr steel was tested only at 550 C, the 9%Cr steel was tested at 550 C and 600 C, and the 18%Cr steel was tested at 550 C and 650 C. In addition, the values of Kth at room temperature were also determined for the three steels. The tests were conducted using standard compact tension (CT) specimens with thickness B=12.5mm and width W=25mm. This is accord to the standard ASTM E647 [2], where the thickness of the compact tension specimen may be up to half of the width. Figure 2 shows the dimensions of the adopted CT specimen geometry. Experiments were performed with either a constant stress ratio R = 0:1, 0:3, 0:7 or 0:9, or a constant Kmax = p 35MPa m [2, 3]. According to Equation (1), K decreases as the crack extends, and this was achieved by adjusting Kmax and/or Kmin during the experiments. Figure 3 schematically shows how Kmax , Kmin , and K change with crack extension for (a) the constant-R and (b) the constant Kmax control modes.
3
Figure 4: Oxide layer observed in SEM with tilt angle 52 after polishing the vertical face of the FIB trench
2.2. Oxide layer thickness measurement An SEM-FIB drilling technique was adopted for the measurement of oxide layer thickness, with the thickness being measured adjacent to the final crack tip of each FCG specimen. This involved FIB drilling a small trench of 20m depth with one vertical face and one stepped face. Prior to drilling, a platinum coating of 0.1m thickness was locally electron sputter-deposited on the fracture surface to provide edge protection, and another platinum layer of 1m thickness was deposited on the former platinum layer by means of ion-sputtering to act as a marker. After rough drilling, the ion beam was used to polish the vertical face of the trench. By tilting the sample, the oxide layer thickness was measured directly in the SEM as shown in Figure 4. The observed oxide layer from FIB drilling is not always above the original metal surface [20]. In 1%Cr steel, the oxide composition is mostly Fe3 O4 with a thin outer layer of Fe2 O3 and 100% of the oxide scale forms above the original metal surface [20]. For 9% steel the oxide is composed of Fe3 O4 +Fe2 O3 above, and (Fe,Cr)3 O4 spinel below the original metal surface. Typically only 50% of the whole oxide scale forms above the original metal surface [20]. In the case of 18%Cr steel, the oxide is composed of (Fe,Cr)2 O3 where only 30% forms above the original metal surface [20]. Only the proportion of oxide scale above the original surface is later adopted to study the oxide induced crack closure. 2.3. TDFAD approach The TDFAD approach was adopted for the prediction of creep crack initiation during FCG experiments. The approach proposes the construction of a creep crack initiation assessment diagram in terms of two parameters, Kr and c Lr . While the approach suggests using creep toughness Kmat to calculate Kr and proved to be sucient for austenitic steels [10, 11], evidence has shown that this parameter can be non-conservative for high strength lower Chromium containing martensitic and bainitic steels [20]. In this study, the parameter KIi adopted in the 2CD approach [5] c appeared to be a more appropriate representation of the material creep toughness. Conventionally the Kmat and KIi parameters used in the TDFAD and 2CD approaches, respectively, are determined using 25mm thick CT specimens. However, it should be recognised that both parameters are section size dependent. It is acknowledged that thicker specimens exhibit lower fracture toughness at ambient temperatures. However, this is in contrast with our measurements of creep toughness as tabulated in Table 1, in which the CT specimen of 25mm thickness exhibits higher creep toughness than that from the 12.5mm thick CT specimen. The determined values using 25mm thick CT specimen were non-conservative relative to those obtained with the 12.5mm thick CT specimens which were adopted in the current study. The KIi values for 12.5mm thick specimens were therefore adopted in the TDFAD analysis conducted, where KIi was determined for a crack initiation criterion (d) of 0.5mm according to the experience reviewed in [21]. Two material properties, Rc0:2 and Rr , are required to perform the creep crack initiation assessment. Rc0:2 denotes the stress corresponding to 0.2% inelastic (plastic plus creep) strain taken from the isochronous stress-strain curve for
4
Figure 5: Schematic isochronous stress strain curve
the assessment time and temperature, as illustrated in Figure 5, and Rr denotes the creep rupture stress at the same time and temperature as for which Rc0:2 is evaluated. For the case of a single primary load, Kr and Lr are calculated as Kr where K denotes stress intensity factor, and Lr
= K=KIi
(2)
= re f =Rc0:2
(3)
where re f [10] denotes the reference stress. Apart from Kr and Lr , a cut-o point Lrmax
Lrmax
is required and is defined as
= Rr =Rc0:2
(4)
Rr should not be higher than the flow strength, i.e. the average of the yield strength R p;0:2 and the ultimate tensile strength Rm . In the case of lack of data, the flow strength may be taken as Rr . The TDFAD [6] is defined as 2 6 6 6 6 4
Kr
=
Kr
=0
E re f Lr Rc0:2
+
3 0:5
Lr3 Rc0:2 777 7 5 2E re f
Lr 6 Lrmax
(5)
Lr > Lrmax
(6)
where E is Young’s modulus, and re f is the total strain from the isochronous curve at the reference stress re f , as illustrated in Figure 5. The loading condition for the assessment with reference stress re f and stress intensity factor K are converted to Lr and Kr according to Equations (2) and (3). The assessment point (Lr ,Kr ) is plotted in the assessment diagram, as schematically shown in Figure 6. If it lies within the envelope formed by Equation (5) and (6), which is denoted by the square square data point in Figure 6, the assessed structure is predicted not to be vulnerable to creep cracking. In contrast, if (Lr ,Kr ) falls outside the envelope as denoted by the triangle data point in Figure 6, creep crack development is expected. The stress intensity factor K for calculating Kr took the value of the maximum threshold stress intensity factor Kmax;th , which was the maximum stress intensity factor when K equalled Kth . Similarly, re f was calculated from the maximum load Fmax;th at the fatigue threshold. As an essential parameter for creep crack initiation assessment, re f depends on the choice of deformation state, namely plane strain or plane stress, and the yield criterion, e.g. Tresca or Von Mises. The evidence from all the tests conducted in this study indicated that the 12.5mm thick CT specimens deformed in plane strain during the FCG tests at elevated temperatures. The assessment in this study adopted the plane strain Von Mises reference stress.
5
Figure 6: A schematic TDFAD
(a) SEM photo of the smooth transgranular fracture surface
(b) SEM photo of the dark and rough fracture surface at the crack tip, indicating a ductile intergranular cracking mechanism
Figure 7: Examples of fracture surface detail
3. Results and Discussion 3.1. da dN(K) response /
Figure 8 shows an example of the da/dN(K) p response of apK reducing FCG experiment and its corresponding fracture surface. As K decreases from 5MPa m to 2.9MPa m, the crack growth rate drops first to 0.3nm/cycle after which it turns to increase up to 0.5nm/cycle. The fracture surface is smooth for the first 5mm crack extension, but becomes dark and rough thereafter until the crack tip. The smooth surface, which is an indication of transgranular fracture, reflects a fatigue dominated cracking mechanism during the first 5mm before it changes to creep dominated fracture as indicated by the rough surface, i.e. intergranular fracture. The fracture modes were later confirmed by the SEM, which were shown in Figure 7. The fracture mechanism highly depends on the loading frequency, stress and temperature. At frequencies greater than 10Hz and high cyclic stress, the fracture mode at elevated temperatures is likely to be transgranular and fatigue dominated [22]. This is exactly the case when the crack growth rate is greater than 0.3nm/cycle, where high load reversals in a short time lead to planar slip inside grains resulting in transgranular fracture [23]. The crack tip is blunted and resharpened rapidly due to high frequency loading, leading to fatigue dominated crack propagation. In 6
(a) da/dN(K) response
(b) CT specimen fracture surface (B=12.5mm)
Figure 8: An example of an FCG test which involves creep cracking
contrast, the fracture mode at high temperature, high peak stress and low cyclic stress is more likely to be intergranular and creep dominated. When the fatigue crack growth rate drops to ∼ 0.3nm/cycle, cracking is assumed to be quasistationary and the low reversal load is no longer able to blunt and resharpen the crack tip. Creep damage has enough time to accumulate on the grain boundary in the form of ductile intergranular cracking. The cracking mode changes to creep dominated, leading to an increasing overall crack growth rate. It is acknowledged that the creep crack initiation during high temperature FCG tests cannot always be identified from the da/dN(K) response. Figure 9 shows the fracture surface of another test piece which involves creep cracking. In this case, evidence of creep cracking could hardly be discerned from its da/dN(K) response. This evidence indicated that a reliable method is essential for predicting creep crack initiation. For a non-destructive assessment, the TDFAD approach is then adopted. 3.2. Creep crack initiation assessment Construction of the TDFAD envelope requires the material’s isochronous stress-strain curve ( ) and KIi , which are both functions of time and temperature. The K reducing FCG test at high temperature takes around 30 hours until the crack growth rate meets the ASTM E647 criteria. During this period, the crack tip is at a low growth rate below 0.3nm/cycle for about 24 hours. The material properties for this period are summarized in Table 1 with the appropriate isochronous stress strain curves modelled by the Ramberg-Osgood relationship [24], Equation (7). Table 1 c also summarizes the Kmat and KIi measured using 25mm thick CT specimen, and KIi values measured using a 12.5mm c c thick CT specimen. The Kmat values are much higher than those for KIi in short term tests mainly because Kmat is a toughness parameter which incorporates the consequence of both instantaneous plastic and creep deformation. The section size sensitivity of KIi has also been observed. The KIi values for a 12.5mm thick CT specimen were adopted for the TDFAD approach. = + 0 (7) E k Figure 10 shows assessment envelopes for the 1%Cr, 9%Cr and 18%Cr steels held for 24 hours after fatigue cracks became quasi-stationary at various temperatures between 550 C and 650 C. The filled points represent the FCG tests involving creep cracking observed at the fatigue crack tip, while the unfilled points represent FCG tests without creep cracking detected on the fracture surface. The filled point falls outside the assessment envelope, while all unfilled points stay inside the envelope. The predictions fit well with the fracture surface observations.
7
(a) da/dN(K) response
(b) CT specimen fracture surface (B=12.5mm)
Figure 9: Unexpected da/dN(K) response from an FCG test where creep cracking is involved
Table 1: Summary of time dependent material properties of three steels
Material
T
k0
C
c Kmat (CT25)
KIi (CT25)
KIi (CT12.5)
Rc0:2
MPa m
MPa m
MPa m
MPa m
p
p
p
p
1%Cr
550
730
9
>100
48
< 40
366
9%Cr
550
1280
5
>110
65
< 40
345
9%Cr
600
400
10
>100
55
< 40
410
18%Cr
550
368
8.2
>130
55
< 40
123
18%Cr
650
373
5.94
>130
48
< 40
121
8
(a) 1%Cr steel at 550 C
(b) 9%Cr steel at 550 C
(d) 18%Cr steel at 550 C
(c) 9%Cr steel at 600 C
(e) 18%Cr steel at 650 C
Figure 10: TDFAD of 1%Cr, 9%Cr and 18%Cr steels loaded in quasi-stationary state for 24 hours at temperatures between 550 C and 600 C
3.3. Oxide induced crack closure The increase in thickness of the oxide layer in many steels at elevated temperatures in air may be predicted by assuming parabolic growth kinetics [20, 25] x2 = k p t (8) where k p is the parabolic oxidation constant, x is the oxide layer thickness and t is the time. At high R, the plasticity induced crack closure sets the crack opening load at the Kmin load level, and any small amount of oxide layer may cause earlier contact of fracture surfaces during the unloading portion of the loading cycle [18], i.e. the actual crack tip opening displacement (CTOD) at minimum load is higher than anticipated. A widely adopted CTOD formulation is proposed by Wells [26] K 2 (1 2 ) (9) CT OD = 2ER p;0:2 where R p;0:2 is the material yield strength, E is the material Young’s modulus, K is the stress intensity factor and is the material Poisson ratio. The early crack face contact due to oxidation, i.e. oxide-induced crack closure, causes an enhancement of Kth . This enhancement due to oxidation (dKth;ox ) equals the di erence between the e ective closure load Kcl and the nominal minimum load Kmin at the fatigue crack growth threshold. According to Equation (9), Kmin and Kcl correspond to two crack tip opening displacements, namely CT ODmin and CT ODcl . Their di erence at the fatigue crack growth threshold, i.e. dCT ODth;ox = CT ODcl CT ODmin , is twice the e ective oxide layer thickness. It should be noticed that only the proportion of oxide scale above the original metal surface is e ective for dCT ODth;ox , which for 1%Cr steel is 100%, for 9% Cr steel is 50% and for 18%Cr steel is 30% of the total observed [20]. The material properties of the three steels are summarized in Table 2, where k p;true denotes the parabolic constant associated with oxide layer development above the original metal surface, as determined by FIB drilling. Tests have shown that dKth;ox may be observed in high-R tests at elevated temperatures. Table 2 summarizes dKth;ox and dCT ODth;ox values for the three steels at temperatures between 550 C and 650 C. Unlike the Kth measured at high temperatures Kth;HT , the Kth measured at room temperature Kth;RT and high R is merely influenced by crack closure, it is therefore adopted as Kth;e f f at elevated temperatures for the calculation of dKth;ox , i.e. dKth;ox = Kth;HT Kth;RT , and the corresponding dCT ODth;ox by Equation p (9). The 1%Cr steel, which has the highest k p;true of the three steels, shows an enhancement of Kth;ox of 2.3MPa m at 550 C, while for the 9%Cr and 9
p
18%Cr steels the dKth;ox values are both below 1MPa m at the same temperature. For the 9%Cr steel the dKth;ox is higher at 600 C than at 550 C. Higher k p has been shown to result in higher dKth;ox . It has also been noticed that 18%Cr steel shows lower Kth at 650 C than at room temperature which results in negative dKth;ox . This is probably due to the drop in Young’s modulus that lowers Kth [27], while the thin oxide layer contributes little enhancement from oxide-induce crack closure. When performing a Kth test, K is slightly reduced to Kth , such that the crack propagates at threshold crack growth rates according to di erent standards [2, 3]. The oxide scale is formed on the newly exposed fracture surface, and the newly formed oxide scale thickens following Equation (8). Due to thicker oxide scale at elevated temperatures, the crack faces close at the early contact point before unloading to the minimum load at high R. The oxide layer thickness at the early contact point, which is several micrometers behind the crack tip [28], is then related to dCT ODth;ox according to Equation (8) dCT ODth;ox
=2
and
q q
q
k p;true t
k p;true 4dc =(da=dt)
(10)
k p;true = f 4dc =(da=dN)
log(dCT ODth;ox ) = 1=2 log(k p;true = f ) + 1=2 log 4dc =(da=dN)
(11)
where dc is the distance between the early contact point and the crack tip, and f is loading frequency. Depending on the standard, da=dN is either 1 10 10 m/cycle [2] or 1 10 11 m/cycle [3]. The values of dCT ODth;ox and k p;true = f for the three steels at di erent temperatures are plotted in Figure 11. It is acknowledged that the values of dc are uncertain for the three steels. Nevertheless, a good correlation is observed between dCT ODth;ox and k p;true = f which may indicate that the values of dc vary little for the adopted materials. It is also noticed that the slope of the regression line is 1/3 lower than in Equation (11). This is assumed to be caused by some compression of the oxide layer during unloading. The relationship between dCT ODth;ox and k p;true = f is then used for the prediction of dKth;ox . The values of Kth for 1%Cr steel have been reported in [20, 29] where Kth at 550 C and room temperature with di erent loading frequencies were discussed. It is acknowledged that the values of k p;true and dc are unknown in [20, 29], and that dc will influence the intercept term of the regression equation in Figure 11. However, taking the data in [29] as an example and assuming dc is constant for the adopted material, the regression equation may be applied as log(dCT ODth;ox ) f =0:5Hz
= 0:36 log(k p;true =0:5) + const = 0:36 log(k p;true =5) 1 + const = 0:36 log(k p;true =5) + const 0:36 = log(dCT ODth;ox ) f =5Hz 0:36 = log(dCT ODth;ox ) f =50Hz 2 0:36
(12)
Therefore, given dCT ODth;ox;50Hz at 550 C, the values of dCT ODth;ox;5Hz and dCT ODth;ox;0:5Hz can be predicted by Equation (12). Values of dKth;ox at 5Hz and 0.5Hz may be predicted from dCT ODth;ox by Equation (9) assuming Kth at R=0.9 and room temperature as Kth;e f f . The same logic can be applied to the data in [20], where the dKth;ox value at 10Hz may be used to predict the values of dKth;ox of the same material at other frequencies. Predicted and observed values of dKth;ox are compared in Figure 12, where good accordance is observed. 3.4. Practical implications It has been acknowledged that there are two international standards, ASTM [2] and ISO [3] covering the determination of Kth with di erent criteria of threshold da=dN. While this is unlikely to have a big influence at room temperatures for steels, the situation is di erent at elevated temperatures. Kth may be strongly influenced by the choice of standards due to creep cracking. Creep crack initiation has already been observed at high-R and high temperature with da/dN below 0.3nm/cycle, after which the crack growth becomes time dependent. Figure 13 shows 10
Table 2: Summary of oxide layer thickness and CTOD at R=0.9 FCG tests
Material
T
k p;true
R p;0:2
E
dCT ODth;ox
dKth;ox
C
mm2 =h
MPa
MPa
m
MPa m
445
160,800
1.366
2.3
1%Cr
550
1 10
6
9%Cr
550
4 10
9
9%Cr
600
18%Cr 18%Cr
p
483
159,078
0.183
0.5
2:84 10
8
410
132,338
0.362
0.7
550
3:37 10
10
197
165,405
0.086
0.1
650
3:81 10
9
193
135,814
-0.09
-0.1
Figure 11: The relationship between dCT ODmin and k p = f at R=0.9
the da/dN(K) response of 9CrMoCo steel at 600 C. When the pASTM threshold da/dN criteria of 0.1nm/cycle is adopted, the measured crack growth threshold is around 3.7MPa m. However, the crack growth rate increases due to creep cracking and drops afterwards, and if the ISO criteria of 0.01nm/cycle threshold growth rate is adopted, the p resultant Kth is around 3MPa m. A significant di erence of the measured Kth according to di erent standards is discovered. The incidence of creep cracking at the crack tips of quasi-static fatigue cracks at high temperatures may be efc fectively predicted using a TDFAD construction for steels with chromium contents up to 18%. The Kmat parameter is not recommended as the most appropriate measure of creep toughness in the TDFAD construction for a full range of ferritic, martensitic and austenitic steels for the determination of Kr . Instead, KIi values determined from the CT specimen of the same section size as used for K determination tests in the current application appear to be more appropriate. High temperature FCG in air is also influenced by oxidation interactions, e.g. the preferential di usion of oxygen along grain boundaries located at the fatigue crack tip, oxide-induced crack closure etc.. While the values of dKth;ox are strongly influenced by the low crack growth rate near Kth , the case is di erent at higher crack growth rate. For 8 example, the value p of dKth;ox for 1%Cr steel at the crack growth of 5 10 m/cycle at 550 C and R=0.9 is only around 0.1MPa m according to Equation (11).p Similar results may be obtained for the 9%Cr and 18%Cr steel, where p the values of dKth;ox are both below 0.1MPa m at 550 C and 600 C for the 9%Cr steel, and below 0.01MPa m at 550 C for the 18%Cr steel. Oxide induced crack closure is therefore negligible when the crack growth rate is above 5 10 8 m/cycle for the three steels at elevated temperatures. Similar result has also been reported by Zhu [30]. 11
Figure 12: Comparison of predicted and observed [20, 29] values of Kth ox ;
4. Conclusion The prediction of creep crack development in high frequency fatigue crack growth tests involving CT specimens of three power plant steels at temperatures between 550 C and 650 C has been performed. Experiments have shown that creep cracking can only be observed in CT specimens at high R in FCG tests when the fatigue crack is quasistationary, i.e. when fatigue crack growth rate is below 0.3nm/cycle. Below this velocity the crack mode turns from fatigue dominated to creep dominant at high temperatures for the respective alloys. The da/dN(K) response may give an indication of creep crack initiation in FCG tests, showing that crack growth rate increases even if K decreases when the crack is quasi-stationary. However, for the purpose of convincingly assessing the creep crack initiation in FCG tests, a TDFAD approach is introduced. Results show that by adapting the maximum force during cyclic loading to TDFAD, it succeeds in assessing CCI in FCG tests of 1CrMoV, 9CrMoCo and 18Cr8Ni steel at temperatures in between 550 C and 650 C. In this application KIi (determined using 12.5mm c thick CT specimens) appears to give a better prediction of creep cracking than in the R5 Kmat approach. Oxide-induced crack closure is influential on Kth in high-R cyclic load tests at high temperatures. The thick oxide layer on the fracture surface causes variation of CTOD, whose relationship with K is used to evaluate the Kth enhancement due to oxidation dKth;ox . The relationship between dCT ODth;ox , k p;true and f has been studied. The relationship has later been used to predict dKth;ox of 1%Cr steel in two publications. Good accordance is found between the predicted and observed dKth;ox . It is acknowledged that the conceptual parameter dc is uncertain currently and will be studied in further work. There exist two widely used standards for Kth determination, ASTM and ISO. While their respective da/dN criteria are unlikely to be influential on the Kth determined at ambient temperature, the case is di erent in high-R tests at elevated temperatures mainly due to creep cracking. References [1] [2] [3] [4] [5]
P. Paris, F. Erdogan, A critical analysis of crack propagation laws, Journal of basic engineering 85 (1963) 528–533. ASTM, E647 Standard test method for measurement of fatigue crack growth rates, Annual Book of ASTM Standards (2013). ISO, 12108-2012 Metallic materials-fatigue testing-fatigue crack growth method, British Standards Institution, London (2012). Code, RCC-MRx, Design and constriction rules for mechanical components of FBR nuclear islands, AFCEN (2007). J. Ewald, S. Sheng, A. Klenk, G. Schellenberg, Engineering guide to assessment of creep crack initiation on components by two-criteriadiagram, International Journal of Pressure Vessels and Piping 78 (2001) 937–949. [6] R. A. Ainsworth, D. G. Hooton, D. Green, Failure assessment diagrams for high temperature defect assessment, Engineering Fracture Mechanics 62 (1999) 95–109.
12
Figure 13: da/dN(K) response of a 9%Cr steel involving creep cracking, for which di erent Kth values associated with the criteria proposed in the ASTM and ISO standards are detected
[7] R6, Assessment of the integrity of structures containing defects, EDF Energy Nuclear Generation Ltd Procedure 32 (2013) 3–104. [8] BS, 7910:2013 Guide to methods for assessing the acceptability of flaws in metallic structures, BSI, British Standards Institution, London, 2013. [9] R5 Issue 3, Assessment procedure for the high temperature response of structures, BEGL Procedure (2003). [10] D. Dean, R. Patel, A. Klenk, F. Mueller, Comparison of procedures for the assessment of creep crack initiation, in: Int. Proc. HIDA-4 Conference, Cambridge, UK. [11] C. M. Davies, Predicting creep crack initiation in austenitic and ferritic steels using the creep toughness parameter and time-dependent failure assessment diagram, Fatigue & Fracture of Engineering Materials & Structures 32 (2009) 820–836. [12] W. Elber, Fatigue crack closure under cyclic tension, Engineering Fracture Mechanics 2 (1970) 37–45. [13] G. Gray, J. Williams, A. Thompson, Roughness-induced crack closure: an explanation for microstructurally sensitive fatigue crack growth, Metallurgical Transactions A 14 (1983) 421–433. [14] P. Liaw, T. Leax, R. Williams, M. Peck, Influence of oxide-induced crack closure on near-threshold fatigue crack growth behavior, Acta Metallurgica 30 (1982) 2071–2078. [15] R. Ritchie, S. Suresh, Some considerations on fatigue crack closure at near-threshold stress intensities due to fracture surface morphology, Metallurgical Transactions A 13 (1982) 937–940. [16] S. Suresh, G. Zamiski, D. R. Ritchie, Oxide-induced crack closure: an explanation for near-threshold corrosion fatigue crack growth behavior, Metallurgical Transactions A 12 (1981) 1435–1443. [17] A. Vasudeven, K. Sadananda, N. Louat, A review of crack closure, fatigue crack threshold and related phenomena, Materials Science and Engineering: A 188 (1994) 1–22. [18] Y. Yamada, J. Newman, Crack closure behavior on a variety of materials under high stress ratios and k max test conditions, Journal of ASTM International 9 (2011) 1–12. [19] Y. Yamada, J. Newman Jr, Crack closure under high load-ratio conditions for inconel-718 near threshold behavior, Engineering Fracture Mechanics 76 (2009) 209–220. [20] SR. Holdsworth, Z. Chen, Oxidation and creep interactions during high temperature, high-R fatigue crack growth threshold determination, Materials at High Temperatures 34(5/6) (2017). [21] SR. Holdsworth, Initiation and early growth of creep cracks from pre-existing defects, Materials at High Temperatures 10(2) (1992) 127–137. [22] M. Nazmy, W. Ho elner, C. Wuthrich, Elevated-temperature creep-fatigue crack-propagation in nickel-base alloys and 1Cr-Mo-V steel, Metallurgical Transactions a-Physical Metallurgy and Materials Science 19 (1988) 855–862. [23] N. E. Frost, K. J. Marsh, L. P. Pook, Metal fatigue, Courier Corporation, 1974. [24] W. Ramberg, W. R. Osgood, Description of stress-strain curves by three parameters (1943). [25] Z. Azari, M. Abbadi, H. Moustabchir, M. Lebienvenu, The influence of fatigue cycling on the oxidation kinetics and crack initiation of a Cr-Mo steel, International Journal of Fatigue 30 (2008) 517–527. [26] AA Wells, Application of fracture mechanics at and beyond general yield, British Welding J 10 (1963) 563–570. [27] P. Liaw, T. Lea, W. Logsdon, Near-threshold fatigue crack growth behavior in metals, Acta Metallurgica 31 (1983) 1581–1587. [28] R. Pippan, C. Zelger, E. Gach, C. Bichler, H. Weinhandl, On the mechanism of fatigue crack propagation in ductile metallic materials, Fatigue and Fracture of Engineering Materials and Structures 34 (2011) 1–16. [29] S. Matsuoka, E. Takeuchi, S. Nishijima, A. J. Mcevily, Near-threshold fatigue crack-growth properties at elevated-temperature for 1Cr-1Mo0.25V steel and 12Cr stainless-steel, Metallurgy and Materials Transaction A 20 (1989) 741–749.
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[30] M.-L. Zhu, F.-Z. Xuan, S.-T. Tu, E ect of load ratio on fatigue crack growth in the near-threshold regime: A literature review, and a combined crack closure and driving force approach, Engineering Fracture Mechanics 141 (2015) 57–77.
14
Highlight 1. The values of ∆ܭ௧ of three power plant steels at elevated temperatures and high stress ratios have been discussed 2. The creep crack initiation during high cycle fatigue at elevated temperatures is discussed 3. The oxide-induce crack closure at elevated temperatures is studies from the view of crack tip opening displacement
S0142-1123(17)30349-3 https://doi.org/10.1016/j.ijfatigue.2017.08.020 JIJF 4445
To appear in:
International Journal of Fatigue
Received Date: Accepted Date:
4 July 2017 21 August 2017
Please cite this article as: Chen, Z., Holdsworth, S., High-R low growth rate fatigue crack propagation at elevated temperatures, International Journal of Fatigue (2017), doi: https://doi.org/10.1016/j.ijfatigue.2017.08.020
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High-R low growth rate fatigue crack propagation at elevated temperatures Zhen Chen,Stuart Holdsworth ¨ EMPA:Swiss Federal Laboratories for Materials Science and Technology, Uberlandstrasse 129, 8600 D¨ubendorf, Z¨urich, Switzerland
Abstract While fatigue cracking is widely considered as the primary cracking mode under cyclic loading conditions, this is not the case for high-R (Kmin =Kmax ) low growth rate fatigue crack propagation at elevated temperatures. Creep cracks can sometimes be observed in such situations when the stress intensity factor range K is around the fatigue crack growth threshold stress intensity factor Kth . A Time Dependent Failure Assessment Diagram (TDFAD) has been adopted in this study for predicting creep cracking in high-R cyclic loading conditions at elevated temperatures. In addition, attention is also paid to oxide-induced crack closure which is greatly influential at high temperatures. Three power plant steels with di erent chromium contents, namely 1%Cr, 9%Cr and 18%Cr steels, have been investigated at temperatures between 550 C and 650 C. The experiments were performed by reducing K continuously to Kth . Good accordance has been found between fracture surface observations and the TDFAD approach predictions of creep crack initiation. Apart from creep cracking, high-R Kth values have also been found to be influenced by oxideinduced crack closure at elevated temperatures. The enhancement is studied through the relationship between the crack tip opening displacement and stress intensity factor. Keywords: Fatigue, High temperature, Creep cracking, High R, Oxide induced crack closure
1. Introduction High cycle fatigue crack growth may be described in terms of cyclic stress intensity factor K (Kmax Kmin ), as shown schematically in Figure 1. Conventionally, the diagram is considered in three regimes, namely a low-K regime in which K is close to the fatigue crack growth (FCG) threshold Kth , a mid-K regime in which crack growth rate da=dN and K obey a power law [1], and a high-K regime in which crack propagation approaches conditions for unstable fracture or plastic collapse. The standard ASTM E647 [2] defines the fatigue crack growth threshold Kth as the cyclic stress intensity factor K that corresponds to 1 10 10 m/cycle fatigue crack growth rate. The ISO standard [3] uses a similar definition but with a threshold crack growth rate criterion of 1 10 11 m/cycle. In the mid-K and high-K regimes, fatigue cracks propagate at rates greater than 10 nm/cycle and dominate the crack growth process. However, this is not the case in the low-K regime near Kth where fatigue crack growth is close to arrest. Other fracture modes can become more influential in this regime. For example, during high frequency high-R FCG at elevated temperatures, creep cracks were detected during post-test inspection in the current study on the fracture surfaces of the test pieces as K drops to near Kth . This is despite the generally perceived notion that high frequency fatigue crack growth is exempt from creep cracking. To the author’s knowledge, this has not been addressed before in the literatures. Therefore a method for predicting creep crack initiation in these circumstance has been devised. Methods have been developed for the assessment of creep crack initiation (CCI). A d approach [4] determines the crack initiation time by evaluating the stress state at a characteristic distance ’d’ from the crack tip. A Two Criteria Diagram (2CD) approach [5] has been developed in Germany. The 2CD approach requires two material properties, the creep rupture strength Rr and the creep crack initiation stress intensity factor KIi . By normalizing the operating stress and stress intensity factor respectively with the two material properties, the 2CD approach predicts if creep crack extension is likely to occur. Preprint submitted to International Journal of Fatigue
September 28, 2017
The Time Dependent Failure Assessment Diagram (TDFAD) concept [6], which is developed from the Failure Assessment Diagram (FAD) approach [7, 8], is incorporated into the R5 procedure [9] for the assessment of creep failure at high temperatures. The approach also requires few material properties, and it avoids calculation of the elastic-plastic stress state at the crack tip. It also has the advantage that the failure envelope is time dependent. The approach has been applied to predict the creep crack initiation in ferrtic and austenitic steels at elevated temperatures, where slightly non-conservative predictions may be found for the ferritic steels [10, 11]. For high-R low growth rate FCG at elevated temperatures, a more proper parameter is proposed in the TDFAD approach for a conservative prediction of creep cracking at the crack tip. The concept of crack closure was introduced by Elber [12] as an influential factor determining the magnitude of Kth . A large number of authors have proposed various mechanisms of crack closure [13–17] at ambient temperature, which are regarded mainly as a consequence of the plastic wake at the crack tip, but also with contributions from surface roughness and oxide wedging. Crack closure was noticed to have less impact on Kth at high-R. However, in recent years the evidence of crack closure at high-R has been observed and measured in the experiments, which may be attributed to surface roughness or oxide debris [18, 19]. At the crack tips of specimens tested to give high-R Kth at elevated temperatures, thicker oxide layers can be generated and significant enhancement of Kth due to oxide-induced crack closure may be observed. The enhancement of the crack tip opening displacement (CTOD) caused by the oxide layer is therefore used to study the oxide-induced crack closure at high-R.
Figure 1: High cycle fatigue crack growth behaviour from low to high K regions
2. Experiment and Methods 2.1. Test Details and Materials A dynamic resonance testing machine was used to carry out a series of FCG experiments. The test were performed at frequencies between 50 and 60Hz and at temperatures ranging from 25 to 650 C. The crack length was continuously monitored using the electrical direct current potential drop (DCPD) method [2]. To achieve low growth rate FCG, K was decreased continuously following Equation (1)
K = Kini e
ca
(1)
where Kini is the initial stress intensity factor, a is the length of crack extension and c is the load reduction rate. After the experiments, the specimens were broken open in order to visually measure the crack length and to verify the 2
Figure 2: Dimension of the compact tension specimen
(a) R constant K decrease mode
(b) Kmax constant K decrease mode
Figure 3: Two control mode for Kth determination test, both with K decreasing
DCPD crack length calibration. In addition, this step also allowed the fracture surface detail to be characterised, e.g. for any evidence of creep cracking. Three power plant steels with di erent chromium levels were investigated, namely a low alloy 1CrMoV steel, a martensitic 9CrMoCo steel and an austenitic 18Cr8Ni steel. With reference to typical power plant operating temperatures, the 1%Cr steel was tested only at 550 C, the 9%Cr steel was tested at 550 C and 600 C, and the 18%Cr steel was tested at 550 C and 650 C. In addition, the values of Kth at room temperature were also determined for the three steels. The tests were conducted using standard compact tension (CT) specimens with thickness B=12.5mm and width W=25mm. This is accord to the standard ASTM E647 [2], where the thickness of the compact tension specimen may be up to half of the width. Figure 2 shows the dimensions of the adopted CT specimen geometry. Experiments were performed with either a constant stress ratio R = 0:1, 0:3, 0:7 or 0:9, or a constant Kmax = p 35MPa m [2, 3]. According to Equation (1), K decreases as the crack extends, and this was achieved by adjusting Kmax and/or Kmin during the experiments. Figure 3 schematically shows how Kmax , Kmin , and K change with crack extension for (a) the constant-R and (b) the constant Kmax control modes.
3
Figure 4: Oxide layer observed in SEM with tilt angle 52 after polishing the vertical face of the FIB trench
2.2. Oxide layer thickness measurement An SEM-FIB drilling technique was adopted for the measurement of oxide layer thickness, with the thickness being measured adjacent to the final crack tip of each FCG specimen. This involved FIB drilling a small trench of 20m depth with one vertical face and one stepped face. Prior to drilling, a platinum coating of 0.1m thickness was locally electron sputter-deposited on the fracture surface to provide edge protection, and another platinum layer of 1m thickness was deposited on the former platinum layer by means of ion-sputtering to act as a marker. After rough drilling, the ion beam was used to polish the vertical face of the trench. By tilting the sample, the oxide layer thickness was measured directly in the SEM as shown in Figure 4. The observed oxide layer from FIB drilling is not always above the original metal surface [20]. In 1%Cr steel, the oxide composition is mostly Fe3 O4 with a thin outer layer of Fe2 O3 and 100% of the oxide scale forms above the original metal surface [20]. For 9% steel the oxide is composed of Fe3 O4 +Fe2 O3 above, and (Fe,Cr)3 O4 spinel below the original metal surface. Typically only 50% of the whole oxide scale forms above the original metal surface [20]. In the case of 18%Cr steel, the oxide is composed of (Fe,Cr)2 O3 where only 30% forms above the original metal surface [20]. Only the proportion of oxide scale above the original surface is later adopted to study the oxide induced crack closure. 2.3. TDFAD approach The TDFAD approach was adopted for the prediction of creep crack initiation during FCG experiments. The approach proposes the construction of a creep crack initiation assessment diagram in terms of two parameters, Kr and c Lr . While the approach suggests using creep toughness Kmat to calculate Kr and proved to be sucient for austenitic steels [10, 11], evidence has shown that this parameter can be non-conservative for high strength lower Chromium containing martensitic and bainitic steels [20]. In this study, the parameter KIi adopted in the 2CD approach [5] c appeared to be a more appropriate representation of the material creep toughness. Conventionally the Kmat and KIi parameters used in the TDFAD and 2CD approaches, respectively, are determined using 25mm thick CT specimens. However, it should be recognised that both parameters are section size dependent. It is acknowledged that thicker specimens exhibit lower fracture toughness at ambient temperatures. However, this is in contrast with our measurements of creep toughness as tabulated in Table 1, in which the CT specimen of 25mm thickness exhibits higher creep toughness than that from the 12.5mm thick CT specimen. The determined values using 25mm thick CT specimen were non-conservative relative to those obtained with the 12.5mm thick CT specimens which were adopted in the current study. The KIi values for 12.5mm thick specimens were therefore adopted in the TDFAD analysis conducted, where KIi was determined for a crack initiation criterion (d) of 0.5mm according to the experience reviewed in [21]. Two material properties, Rc0:2 and Rr , are required to perform the creep crack initiation assessment. Rc0:2 denotes the stress corresponding to 0.2% inelastic (plastic plus creep) strain taken from the isochronous stress-strain curve for
4
Figure 5: Schematic isochronous stress strain curve
the assessment time and temperature, as illustrated in Figure 5, and Rr denotes the creep rupture stress at the same time and temperature as for which Rc0:2 is evaluated. For the case of a single primary load, Kr and Lr are calculated as Kr where K denotes stress intensity factor, and Lr
= K=KIi
(2)
= re f =Rc0:2
(3)
where re f [10] denotes the reference stress. Apart from Kr and Lr , a cut-o point Lrmax
Lrmax
is required and is defined as
= Rr =Rc0:2
(4)
Rr should not be higher than the flow strength, i.e. the average of the yield strength R p;0:2 and the ultimate tensile strength Rm . In the case of lack of data, the flow strength may be taken as Rr . The TDFAD [6] is defined as 2 6 6 6 6 4
Kr
=
Kr
=0
E re f Lr Rc0:2
+
3 0:5
Lr3 Rc0:2 777 7 5 2E re f
Lr 6 Lrmax
(5)
Lr > Lrmax
(6)
where E is Young’s modulus, and re f is the total strain from the isochronous curve at the reference stress re f , as illustrated in Figure 5. The loading condition for the assessment with reference stress re f and stress intensity factor K are converted to Lr and Kr according to Equations (2) and (3). The assessment point (Lr ,Kr ) is plotted in the assessment diagram, as schematically shown in Figure 6. If it lies within the envelope formed by Equation (5) and (6), which is denoted by the square square data point in Figure 6, the assessed structure is predicted not to be vulnerable to creep cracking. In contrast, if (Lr ,Kr ) falls outside the envelope as denoted by the triangle data point in Figure 6, creep crack development is expected. The stress intensity factor K for calculating Kr took the value of the maximum threshold stress intensity factor Kmax;th , which was the maximum stress intensity factor when K equalled Kth . Similarly, re f was calculated from the maximum load Fmax;th at the fatigue threshold. As an essential parameter for creep crack initiation assessment, re f depends on the choice of deformation state, namely plane strain or plane stress, and the yield criterion, e.g. Tresca or Von Mises. The evidence from all the tests conducted in this study indicated that the 12.5mm thick CT specimens deformed in plane strain during the FCG tests at elevated temperatures. The assessment in this study adopted the plane strain Von Mises reference stress.
5
Figure 6: A schematic TDFAD
(a) SEM photo of the smooth transgranular fracture surface
(b) SEM photo of the dark and rough fracture surface at the crack tip, indicating a ductile intergranular cracking mechanism
Figure 7: Examples of fracture surface detail
3. Results and Discussion 3.1. da dN(K) response /
Figure 8 shows an example of the da/dN(K) p response of apK reducing FCG experiment and its corresponding fracture surface. As K decreases from 5MPa m to 2.9MPa m, the crack growth rate drops first to 0.3nm/cycle after which it turns to increase up to 0.5nm/cycle. The fracture surface is smooth for the first 5mm crack extension, but becomes dark and rough thereafter until the crack tip. The smooth surface, which is an indication of transgranular fracture, reflects a fatigue dominated cracking mechanism during the first 5mm before it changes to creep dominated fracture as indicated by the rough surface, i.e. intergranular fracture. The fracture modes were later confirmed by the SEM, which were shown in Figure 7. The fracture mechanism highly depends on the loading frequency, stress and temperature. At frequencies greater than 10Hz and high cyclic stress, the fracture mode at elevated temperatures is likely to be transgranular and fatigue dominated [22]. This is exactly the case when the crack growth rate is greater than 0.3nm/cycle, where high load reversals in a short time lead to planar slip inside grains resulting in transgranular fracture [23]. The crack tip is blunted and resharpened rapidly due to high frequency loading, leading to fatigue dominated crack propagation. In 6
(a) da/dN(K) response
(b) CT specimen fracture surface (B=12.5mm)
Figure 8: An example of an FCG test which involves creep cracking
contrast, the fracture mode at high temperature, high peak stress and low cyclic stress is more likely to be intergranular and creep dominated. When the fatigue crack growth rate drops to ∼ 0.3nm/cycle, cracking is assumed to be quasistationary and the low reversal load is no longer able to blunt and resharpen the crack tip. Creep damage has enough time to accumulate on the grain boundary in the form of ductile intergranular cracking. The cracking mode changes to creep dominated, leading to an increasing overall crack growth rate. It is acknowledged that the creep crack initiation during high temperature FCG tests cannot always be identified from the da/dN(K) response. Figure 9 shows the fracture surface of another test piece which involves creep cracking. In this case, evidence of creep cracking could hardly be discerned from its da/dN(K) response. This evidence indicated that a reliable method is essential for predicting creep crack initiation. For a non-destructive assessment, the TDFAD approach is then adopted. 3.2. Creep crack initiation assessment Construction of the TDFAD envelope requires the material’s isochronous stress-strain curve ( ) and KIi , which are both functions of time and temperature. The K reducing FCG test at high temperature takes around 30 hours until the crack growth rate meets the ASTM E647 criteria. During this period, the crack tip is at a low growth rate below 0.3nm/cycle for about 24 hours. The material properties for this period are summarized in Table 1 with the appropriate isochronous stress strain curves modelled by the Ramberg-Osgood relationship [24], Equation (7). Table 1 c also summarizes the Kmat and KIi measured using 25mm thick CT specimen, and KIi values measured using a 12.5mm c c thick CT specimen. The Kmat values are much higher than those for KIi in short term tests mainly because Kmat is a toughness parameter which incorporates the consequence of both instantaneous plastic and creep deformation. The section size sensitivity of KIi has also been observed. The KIi values for a 12.5mm thick CT specimen were adopted for the TDFAD approach. = + 0 (7) E k Figure 10 shows assessment envelopes for the 1%Cr, 9%Cr and 18%Cr steels held for 24 hours after fatigue cracks became quasi-stationary at various temperatures between 550 C and 650 C. The filled points represent the FCG tests involving creep cracking observed at the fatigue crack tip, while the unfilled points represent FCG tests without creep cracking detected on the fracture surface. The filled point falls outside the assessment envelope, while all unfilled points stay inside the envelope. The predictions fit well with the fracture surface observations.
7
(a) da/dN(K) response
(b) CT specimen fracture surface (B=12.5mm)
Figure 9: Unexpected da/dN(K) response from an FCG test where creep cracking is involved
Table 1: Summary of time dependent material properties of three steels
Material
T
k0
C
c Kmat (CT25)
KIi (CT25)
KIi (CT12.5)
Rc0:2
MPa m
MPa m
MPa m
MPa m
p
p
p
p
1%Cr
550
730
9
>100
48
< 40
366
9%Cr
550
1280
5
>110
65
< 40
345
9%Cr
600
400
10
>100
55
< 40
410
18%Cr
550
368
8.2
>130
55
< 40
123
18%Cr
650
373
5.94
>130
48
< 40
121
8
(a) 1%Cr steel at 550 C
(b) 9%Cr steel at 550 C
(d) 18%Cr steel at 550 C
(c) 9%Cr steel at 600 C
(e) 18%Cr steel at 650 C
Figure 10: TDFAD of 1%Cr, 9%Cr and 18%Cr steels loaded in quasi-stationary state for 24 hours at temperatures between 550 C and 600 C
3.3. Oxide induced crack closure The increase in thickness of the oxide layer in many steels at elevated temperatures in air may be predicted by assuming parabolic growth kinetics [20, 25] x2 = k p t (8) where k p is the parabolic oxidation constant, x is the oxide layer thickness and t is the time. At high R, the plasticity induced crack closure sets the crack opening load at the Kmin load level, and any small amount of oxide layer may cause earlier contact of fracture surfaces during the unloading portion of the loading cycle [18], i.e. the actual crack tip opening displacement (CTOD) at minimum load is higher than anticipated. A widely adopted CTOD formulation is proposed by Wells [26] K 2 (1 2 ) (9) CT OD = 2ER p;0:2 where R p;0:2 is the material yield strength, E is the material Young’s modulus, K is the stress intensity factor and is the material Poisson ratio. The early crack face contact due to oxidation, i.e. oxide-induced crack closure, causes an enhancement of Kth . This enhancement due to oxidation (dKth;ox ) equals the di erence between the e ective closure load Kcl and the nominal minimum load Kmin at the fatigue crack growth threshold. According to Equation (9), Kmin and Kcl correspond to two crack tip opening displacements, namely CT ODmin and CT ODcl . Their di erence at the fatigue crack growth threshold, i.e. dCT ODth;ox = CT ODcl CT ODmin , is twice the e ective oxide layer thickness. It should be noticed that only the proportion of oxide scale above the original metal surface is e ective for dCT ODth;ox , which for 1%Cr steel is 100%, for 9% Cr steel is 50% and for 18%Cr steel is 30% of the total observed [20]. The material properties of the three steels are summarized in Table 2, where k p;true denotes the parabolic constant associated with oxide layer development above the original metal surface, as determined by FIB drilling. Tests have shown that dKth;ox may be observed in high-R tests at elevated temperatures. Table 2 summarizes dKth;ox and dCT ODth;ox values for the three steels at temperatures between 550 C and 650 C. Unlike the Kth measured at high temperatures Kth;HT , the Kth measured at room temperature Kth;RT and high R is merely influenced by crack closure, it is therefore adopted as Kth;e f f at elevated temperatures for the calculation of dKth;ox , i.e. dKth;ox = Kth;HT Kth;RT , and the corresponding dCT ODth;ox by Equation p (9). The 1%Cr steel, which has the highest k p;true of the three steels, shows an enhancement of Kth;ox of 2.3MPa m at 550 C, while for the 9%Cr and 9
p
18%Cr steels the dKth;ox values are both below 1MPa m at the same temperature. For the 9%Cr steel the dKth;ox is higher at 600 C than at 550 C. Higher k p has been shown to result in higher dKth;ox . It has also been noticed that 18%Cr steel shows lower Kth at 650 C than at room temperature which results in negative dKth;ox . This is probably due to the drop in Young’s modulus that lowers Kth [27], while the thin oxide layer contributes little enhancement from oxide-induce crack closure. When performing a Kth test, K is slightly reduced to Kth , such that the crack propagates at threshold crack growth rates according to di erent standards [2, 3]. The oxide scale is formed on the newly exposed fracture surface, and the newly formed oxide scale thickens following Equation (8). Due to thicker oxide scale at elevated temperatures, the crack faces close at the early contact point before unloading to the minimum load at high R. The oxide layer thickness at the early contact point, which is several micrometers behind the crack tip [28], is then related to dCT ODth;ox according to Equation (8) dCT ODth;ox
=2
and
q q
q
k p;true t
k p;true 4dc =(da=dt)
(10)
k p;true = f 4dc =(da=dN)
log(dCT ODth;ox ) = 1=2 log(k p;true = f ) + 1=2 log 4dc =(da=dN)
(11)
where dc is the distance between the early contact point and the crack tip, and f is loading frequency. Depending on the standard, da=dN is either 1 10 10 m/cycle [2] or 1 10 11 m/cycle [3]. The values of dCT ODth;ox and k p;true = f for the three steels at di erent temperatures are plotted in Figure 11. It is acknowledged that the values of dc are uncertain for the three steels. Nevertheless, a good correlation is observed between dCT ODth;ox and k p;true = f which may indicate that the values of dc vary little for the adopted materials. It is also noticed that the slope of the regression line is 1/3 lower than in Equation (11). This is assumed to be caused by some compression of the oxide layer during unloading. The relationship between dCT ODth;ox and k p;true = f is then used for the prediction of dKth;ox . The values of Kth for 1%Cr steel have been reported in [20, 29] where Kth at 550 C and room temperature with di erent loading frequencies were discussed. It is acknowledged that the values of k p;true and dc are unknown in [20, 29], and that dc will influence the intercept term of the regression equation in Figure 11. However, taking the data in [29] as an example and assuming dc is constant for the adopted material, the regression equation may be applied as log(dCT ODth;ox ) f =0:5Hz
= 0:36 log(k p;true =0:5) + const = 0:36 log(k p;true =5) 1 + const = 0:36 log(k p;true =5) + const 0:36 = log(dCT ODth;ox ) f =5Hz 0:36 = log(dCT ODth;ox ) f =50Hz 2 0:36
(12)
Therefore, given dCT ODth;ox;50Hz at 550 C, the values of dCT ODth;ox;5Hz and dCT ODth;ox;0:5Hz can be predicted by Equation (12). Values of dKth;ox at 5Hz and 0.5Hz may be predicted from dCT ODth;ox by Equation (9) assuming Kth at R=0.9 and room temperature as Kth;e f f . The same logic can be applied to the data in [20], where the dKth;ox value at 10Hz may be used to predict the values of dKth;ox of the same material at other frequencies. Predicted and observed values of dKth;ox are compared in Figure 12, where good accordance is observed. 3.4. Practical implications It has been acknowledged that there are two international standards, ASTM [2] and ISO [3] covering the determination of Kth with di erent criteria of threshold da=dN. While this is unlikely to have a big influence at room temperatures for steels, the situation is di erent at elevated temperatures. Kth may be strongly influenced by the choice of standards due to creep cracking. Creep crack initiation has already been observed at high-R and high temperature with da/dN below 0.3nm/cycle, after which the crack growth becomes time dependent. Figure 13 shows 10
Table 2: Summary of oxide layer thickness and CTOD at R=0.9 FCG tests
Material
T
k p;true
R p;0:2
E
dCT ODth;ox
dKth;ox
C
mm2 =h
MPa
MPa
m
MPa m
445
160,800
1.366
2.3
1%Cr
550
1 10
6
9%Cr
550
4 10
9
9%Cr
600
18%Cr 18%Cr
p
483
159,078
0.183
0.5
2:84 10
8
410
132,338
0.362
0.7
550
3:37 10
10
197
165,405
0.086
0.1
650
3:81 10
9
193
135,814
-0.09
-0.1
Figure 11: The relationship between dCT ODmin and k p = f at R=0.9
the da/dN(K) response of 9CrMoCo steel at 600 C. When the pASTM threshold da/dN criteria of 0.1nm/cycle is adopted, the measured crack growth threshold is around 3.7MPa m. However, the crack growth rate increases due to creep cracking and drops afterwards, and if the ISO criteria of 0.01nm/cycle threshold growth rate is adopted, the p resultant Kth is around 3MPa m. A significant di erence of the measured Kth according to di erent standards is discovered. The incidence of creep cracking at the crack tips of quasi-static fatigue cracks at high temperatures may be efc fectively predicted using a TDFAD construction for steels with chromium contents up to 18%. The Kmat parameter is not recommended as the most appropriate measure of creep toughness in the TDFAD construction for a full range of ferritic, martensitic and austenitic steels for the determination of Kr . Instead, KIi values determined from the CT specimen of the same section size as used for K determination tests in the current application appear to be more appropriate. High temperature FCG in air is also influenced by oxidation interactions, e.g. the preferential di usion of oxygen along grain boundaries located at the fatigue crack tip, oxide-induced crack closure etc.. While the values of dKth;ox are strongly influenced by the low crack growth rate near Kth , the case is di erent at higher crack growth rate. For 8 example, the value p of dKth;ox for 1%Cr steel at the crack growth of 5 10 m/cycle at 550 C and R=0.9 is only around 0.1MPa m according to Equation (11).p Similar results may be obtained for the 9%Cr and 18%Cr steel, where p the values of dKth;ox are both below 0.1MPa m at 550 C and 600 C for the 9%Cr steel, and below 0.01MPa m at 550 C for the 18%Cr steel. Oxide induced crack closure is therefore negligible when the crack growth rate is above 5 10 8 m/cycle for the three steels at elevated temperatures. Similar result has also been reported by Zhu [30]. 11
Figure 12: Comparison of predicted and observed [20, 29] values of Kth ox ;
4. Conclusion The prediction of creep crack development in high frequency fatigue crack growth tests involving CT specimens of three power plant steels at temperatures between 550 C and 650 C has been performed. Experiments have shown that creep cracking can only be observed in CT specimens at high R in FCG tests when the fatigue crack is quasistationary, i.e. when fatigue crack growth rate is below 0.3nm/cycle. Below this velocity the crack mode turns from fatigue dominated to creep dominant at high temperatures for the respective alloys. The da/dN(K) response may give an indication of creep crack initiation in FCG tests, showing that crack growth rate increases even if K decreases when the crack is quasi-stationary. However, for the purpose of convincingly assessing the creep crack initiation in FCG tests, a TDFAD approach is introduced. Results show that by adapting the maximum force during cyclic loading to TDFAD, it succeeds in assessing CCI in FCG tests of 1CrMoV, 9CrMoCo and 18Cr8Ni steel at temperatures in between 550 C and 650 C. In this application KIi (determined using 12.5mm c thick CT specimens) appears to give a better prediction of creep cracking than in the R5 Kmat approach. Oxide-induced crack closure is influential on Kth in high-R cyclic load tests at high temperatures. The thick oxide layer on the fracture surface causes variation of CTOD, whose relationship with K is used to evaluate the Kth enhancement due to oxidation dKth;ox . The relationship between dCT ODth;ox , k p;true and f has been studied. The relationship has later been used to predict dKth;ox of 1%Cr steel in two publications. Good accordance is found between the predicted and observed dKth;ox . It is acknowledged that the conceptual parameter dc is uncertain currently and will be studied in further work. There exist two widely used standards for Kth determination, ASTM and ISO. While their respective da/dN criteria are unlikely to be influential on the Kth determined at ambient temperature, the case is di erent in high-R tests at elevated temperatures mainly due to creep cracking. References [1] [2] [3] [4] [5]
P. Paris, F. Erdogan, A critical analysis of crack propagation laws, Journal of basic engineering 85 (1963) 528–533. ASTM, E647 Standard test method for measurement of fatigue crack growth rates, Annual Book of ASTM Standards (2013). ISO, 12108-2012 Metallic materials-fatigue testing-fatigue crack growth method, British Standards Institution, London (2012). Code, RCC-MRx, Design and constriction rules for mechanical components of FBR nuclear islands, AFCEN (2007). J. Ewald, S. Sheng, A. Klenk, G. Schellenberg, Engineering guide to assessment of creep crack initiation on components by two-criteriadiagram, International Journal of Pressure Vessels and Piping 78 (2001) 937–949. [6] R. A. Ainsworth, D. G. Hooton, D. Green, Failure assessment diagrams for high temperature defect assessment, Engineering Fracture Mechanics 62 (1999) 95–109.
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Figure 13: da/dN(K) response of a 9%Cr steel involving creep cracking, for which di erent Kth values associated with the criteria proposed in the ASTM and ISO standards are detected
[7] R6, Assessment of the integrity of structures containing defects, EDF Energy Nuclear Generation Ltd Procedure 32 (2013) 3–104. [8] BS, 7910:2013 Guide to methods for assessing the acceptability of flaws in metallic structures, BSI, British Standards Institution, London, 2013. [9] R5 Issue 3, Assessment procedure for the high temperature response of structures, BEGL Procedure (2003). [10] D. Dean, R. Patel, A. Klenk, F. Mueller, Comparison of procedures for the assessment of creep crack initiation, in: Int. Proc. HIDA-4 Conference, Cambridge, UK. [11] C. M. Davies, Predicting creep crack initiation in austenitic and ferritic steels using the creep toughness parameter and time-dependent failure assessment diagram, Fatigue & Fracture of Engineering Materials & Structures 32 (2009) 820–836. [12] W. Elber, Fatigue crack closure under cyclic tension, Engineering Fracture Mechanics 2 (1970) 37–45. [13] G. Gray, J. Williams, A. Thompson, Roughness-induced crack closure: an explanation for microstructurally sensitive fatigue crack growth, Metallurgical Transactions A 14 (1983) 421–433. [14] P. Liaw, T. Leax, R. Williams, M. Peck, Influence of oxide-induced crack closure on near-threshold fatigue crack growth behavior, Acta Metallurgica 30 (1982) 2071–2078. [15] R. Ritchie, S. Suresh, Some considerations on fatigue crack closure at near-threshold stress intensities due to fracture surface morphology, Metallurgical Transactions A 13 (1982) 937–940. [16] S. Suresh, G. Zamiski, D. R. Ritchie, Oxide-induced crack closure: an explanation for near-threshold corrosion fatigue crack growth behavior, Metallurgical Transactions A 12 (1981) 1435–1443. [17] A. Vasudeven, K. Sadananda, N. Louat, A review of crack closure, fatigue crack threshold and related phenomena, Materials Science and Engineering: A 188 (1994) 1–22. [18] Y. Yamada, J. Newman, Crack closure behavior on a variety of materials under high stress ratios and k max test conditions, Journal of ASTM International 9 (2011) 1–12. [19] Y. Yamada, J. Newman Jr, Crack closure under high load-ratio conditions for inconel-718 near threshold behavior, Engineering Fracture Mechanics 76 (2009) 209–220. [20] SR. Holdsworth, Z. Chen, Oxidation and creep interactions during high temperature, high-R fatigue crack growth threshold determination, Materials at High Temperatures 34(5/6) (2017). [21] SR. Holdsworth, Initiation and early growth of creep cracks from pre-existing defects, Materials at High Temperatures 10(2) (1992) 127–137. [22] M. Nazmy, W. Ho elner, C. Wuthrich, Elevated-temperature creep-fatigue crack-propagation in nickel-base alloys and 1Cr-Mo-V steel, Metallurgical Transactions a-Physical Metallurgy and Materials Science 19 (1988) 855–862. [23] N. E. Frost, K. J. Marsh, L. P. Pook, Metal fatigue, Courier Corporation, 1974. [24] W. Ramberg, W. R. Osgood, Description of stress-strain curves by three parameters (1943). [25] Z. Azari, M. Abbadi, H. Moustabchir, M. Lebienvenu, The influence of fatigue cycling on the oxidation kinetics and crack initiation of a Cr-Mo steel, International Journal of Fatigue 30 (2008) 517–527. [26] AA Wells, Application of fracture mechanics at and beyond general yield, British Welding J 10 (1963) 563–570. [27] P. Liaw, T. Lea, W. Logsdon, Near-threshold fatigue crack growth behavior in metals, Acta Metallurgica 31 (1983) 1581–1587. [28] R. Pippan, C. Zelger, E. Gach, C. Bichler, H. Weinhandl, On the mechanism of fatigue crack propagation in ductile metallic materials, Fatigue and Fracture of Engineering Materials and Structures 34 (2011) 1–16. [29] S. Matsuoka, E. Takeuchi, S. Nishijima, A. J. Mcevily, Near-threshold fatigue crack-growth properties at elevated-temperature for 1Cr-1Mo0.25V steel and 12Cr stainless-steel, Metallurgy and Materials Transaction A 20 (1989) 741–749.
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[30] M.-L. Zhu, F.-Z. Xuan, S.-T. Tu, E ect of load ratio on fatigue crack growth in the near-threshold regime: A literature review, and a combined crack closure and driving force approach, Engineering Fracture Mechanics 141 (2015) 57–77.
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Highlight 1. The values of ∆ܭ௧ of three power plant steels at elevated temperatures and high stress ratios have been discussed 2. The creep crack initiation during high cycle fatigue at elevated temperatures is discussed 3. The oxide-induce crack closure at elevated temperatures is studies from the view of crack tip opening displacement