- Email: [email protected]
Analysis of creep crack growth behavior of P92 steel welded joint by experiment and numerical simulation
Materials Science & Engineering A 558 (2012) 119–128
Contents lists available at SciVerse ScienceDirect
Materials Science & Engineering A journal homepage: www.elsevier.com/locate/msea
Analysis of creep crack growth behavior of P92 steel welded joint by experiment and numerical simulation Lei Zhao a,b, Hongyang Jing a,b, Lianyong Xu a,b,n, Yongdian Han a,b, Junjie Xiu a,b a b
School of Materials Science and Engineering, Tianjin University, Tianjin 300072, China Tianjin Key Laboratory of Advanced Joining Technology, Tianjin 300072, China
a r t i c l e i n f o
abstract
Article history: Received 17 March 2012 Received in revised form 1 June 2012 Accepted 23 July 2012 Available online 31 July 2012
High temperature creep crack growth tests were carried out on standard compact specimens machined from the welded joint of ASME P92 steel pipe. The creep crack growth behaviors of the distinct subregions of welded joint were investigated to clarify the ability of creep crack resistance under high temperature. In addition, good correlations between creep crack growth rate and C* for different microzones of welded joint were obtained. The tested results revealed that the sub-regions of welded joint exhibited different creep crack behaviors and at the same value of C* the highest creep crack growth rate occurred in the fine grained heat affected zone (FGHAZ) which was known as Type IV cracking zone. Furthermore, finite element method analyses coupled with continuum damage mechanics were conducted to predict the creep crack growth behavior and to study the effect of multistress state on crack propagation. & 2012 Elsevier B.V. All rights reserved.
Keywords: Creep crack growth Finite element method analysis Multistress state ASME P92 steel Type IV cracking
1. Introduction In consideration of reduction in CO2 emission and energy saving for thermal power plants, high strength heat resistant steels have been developed to meet the requirements of the boiler components under increased steam pressure and temperature condition [1]. Several types of 9–12% Cr boiler steels with high creep strength have been developed [2,3]. In recent times, P92 steels strengthened by tungsten addition have become the candidate materials for application to ultra-supercritical (USC) power plants components, such as superheater and reheater headers and steam pipes, chests and valves operating at about 600–650 1C [4–6]. Most of these components are made of weldments, which consist of several distinct regions with different microstructures, such as the welded metal (WM), the base metal (BM) and the heat affected zone (HAZ). The HAZ is commonly composed of the coarse grain HAZ (CGHAZ), the fine grain HAZ (FGHAZ) and the intercritical HAZ (ICHAZ) [7]. Even for these steel welded joints with high creep strength serviced at high temperature, fracture often occurs in the FGHAZ adjacent to the base metal, known as Type IV cracking, and decreases the creep lives of welded joints [8–10]. This failure is mainly caused by creep crack growth, which
n Corresponding author at: School of Materials Science and Engineering, Tianjin University, Tianjin 300072, China. Tel./fax: þ86 22 27402439. E-mail address: [email protected] (L. Xu).
0921-5093/$ - see front matter & 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.msea.2012.07.094
is most likely to take place in components with pre-existing defects or stress concentration. Creep crack growth (CCG) imposes a limit on the service lives of components at elevated temperature [11]. Understanding of CCG properties of the welded joint is important for the reliability assessment of high-temperature structural components. For the welded joint, microstructure inhomogeneity exists among these distinct zones leading to different creep deformation properties. As a result, the constraint is always generated in the fusion zone and HAZ zone during creep. Then, the multiaxial stress state is always created. These phenomena make it difficult to estimate the creep crack behavior for the welded joint. To date, some previous researches have investigated the CCG properties of base metal and welded joint of high chromium steels [12–16]. However, the CCG behaviors of distinct sub-regions of ASME P92 steel welded joint have not been studied in detail. Therefore, it is crucial to investigate the CCG properties of sub-regions in the welded joint and to clarify factors affecting the crack propagation property of ASME P92 steel welded joint so as to accurately assess the safety of power plants under long-term servicing at high temperature. In the present study, creep crack growth tests were conducted on compact tension (CT) specimens with cracks in WM, BM, fusion zone and FGHAZ (zone of HAZ adjacent to base metal) at 650 1C. Creep crack propagation behaviors in the different subregions of the welded joint were investigated. Based on the experimental results, the finite element method (FEM) analysis coupled with the continuum damage mechanics was conducted
120
L. Zhao et al. / Materials Science & Engineering A 558 (2012) 119–128
Table 1 Chemical composition (wt%) of ASME P92 steel and welded metal used (bal. Fe). Material
C
Si
Mn
S
P
Cr
Ni
Mo
W
V
Nb
B
Al
N
Base metal Welded metal
0.10 0.12
0.47 0.29
0.40 0.71
0.001 0.008
0.008 0.009
8.77 9.08
0.12 0.49
0.38 0.42
1.48 1.72
0.16 0.19
0.054 0.06
0.001 0.003
0.02 0.01
0.043 0.06
Table 2 Welding conditions of ASME P92 steel pipe. Groove
As shown in left figure
Number of weld passes Preheating temperature (1C) Interpass temperature (1C) Welding current (A) Arc voltage (V) Welding heating input (kJ/cm) Welding speeding (mm/min)
27–30 150 200–250 100–120 11–15 15–20 150
to simulate the creep crack extension and then to analyze the effect of stress multiaxiality in the welded joint on creep crack growth.
2. Experimental procedures 2.1. Materials The material investigated in the present study is ASME P92 steel pipe, with an inner diameter of 390 mm and a thickness of 80 mm, which was subjected to normalizing at 1040 1C for 4 h and then tempering at 760 1C for 11 h. The chemical composition of the parent P92 steel is given in Table 1. The pipes were fabricated using a multilayer gas tungsten arc welding (GTAW) method with single J grooves. Welding consumable used for GTAW was matching filler wire developed recently for welding this class of steel. The chemical composition of the welded metal is also given in Table 1. After welding, the post weld heat treatment (PWHT) was carried out at 760 1C for 4 h to assure that the residual stresses in the welded joint were reduced to a level that it could be ignored during the analyses. The welding conditions are shown in Table 2, which are the same as the fabrication process for the actual large diameter steam pipes in fossil power plants. The Vickers hardness (HV10) distribution across the welded joint is shown in Fig. 1. The measurements of Vickers hardness were conducted on the welded joint specimen before the creep crack growth test. The hardness of WM is higher than that of BM about 30 HV. The highest hardness is located at the fusion zone. A sharp reduction in hardness can be seen within the HAZ. It is well known that the HAZ of 9%Cr steel is mainly composed of FGHAZ adjacent to base metal and CGHAZ adjacent to welded metal [7], and these two regions correspond to the softer and harder region, respectively. In the present study, the CGHAZ shows higher hardness about 30 HV than that in the WM. The FGHAZ shows slightly higher hardness than the BM.
Fig. 1. Distribution of Vickers hardness across ASME P92 steel welded joint before creep crack.
2.2. Specimen Creep crack growth tests were carried out on standard compact tension specimens. All specimens were machined from the
Fig. 2. Schematic of CT specimens extracting from ASME P92 steel welded joint.
L. Zhao et al. / Materials Science & Engineering A 558 (2012) 119–128
P92 steel welded joint in the longitudinal orientation (welding orientation), as shown in Fig. 2. The geometries and dimensions of CT specimen adopted are shown in Fig. 3, which are chosen in accordance with the ASTM E1457-07 requirements [17]. The precracks were introduced in all specimens using the electric discharge machining (EDM) and fatigue pre-cracking. The width and the length of EDM pre-crack were 0.08 mm and 2 mm, respectively. After EDM pre-cracking, the fatigue pre-cracking was carried out at room temperature and under a stress ratio of 0.05 according to the requirements in the ASTM E1457-07 [17]. The fatigue pre-crack was grown to about 2 mm away from the EDM pre-crack. Then they were used for the creep crack propagation experiments. 2.3. Test methods Creep crack growth tests were performed in lever arm constant load tensile creep machines equipped with split tubes. In general, according to the ASTM standard E1457-07 [17], the tests were performed and the data obtained were analyzed. The crack length and load line displacement were measured. Load line displacement was monitored by attaching capacitance gauges to the lower and up pull rods that were tied with the specimen by the pins. Then, the displacement was measured by the change in distance between the up and the lower pull rods during testing. Creep crack length was measured by an electrical potential drop method. An electrical current was applied to the specimen and the value of the electric potential drop was measured. The crack length is usually calculated using Johnson’s equation for CT specimen given by [18,19] a¼
2W
p
( cos1
)
cos hðpY 0 =2WÞ 1
cos h½ðV=V 0 Þ cos h
121
where a is the current crack length, a0 is the initial crack length, Y0 is half the distance between the output terminals, W is the width of the specimen, V0 is the initial voltage and V is the actual value of the potential.
2.4. Test conditions All of the creep tests were performed in air at 650 1C. Table 3 shows the conditions of creep crack propagation experiments. The applied load was determined from the value of initial stress intensity factor K by the following equation: a P 2 þa0 =W 0 K ¼ pffiffiffiffiffiffiffiffiffi 1=2 f 3=2 W ð1a0 =WÞ BBN W
ð2Þ
where P is the applied load; B is the specimen thickness, BN is the net specimen thickness between the bottoms of side grooves and f(a0/W) is obtained from: f
a 0
W
a a 2 a 3 a 4 0 0 0 0 ¼ 0:886 þ 4:64 13:32 þ 14:72 5:6 W W W W ð3Þ
In the present study, to analyze the CCG property of the distinct microzones of the welded joint, four different crack tip positions are considered, with the cracks placed within BM region, WM region, FGHAZ (the zone of HAZ adjacent to the base metal) which corresponds to Type IV cracking zone and fusion zone (see Fig. 2). For specimens with the WM, the effects of different initial crack lengths and initial K values on the creep crack growth were also investigated.
ðcos hðpY 0 =2WÞ=cosðpa0 =2WÞÞ
ð1Þ
Fig. 4. Representative morphology of creep crack behavior for CT specimen with crack in FGHAZ.
Fig. 3. Dimension and size of CT specimen used in the testing.
Table 3 Experimental conditions of creep crack growth test. Specimen
Crack location
Crack depth a0/W
Load P (N)
Initial stress intensity factor K (MPa m1/2)
Duration time tf (h)
CT1 CT2 CT3 CT4 CT5 CT6
BM WM WM WM FGHAZ Fusion zone
0.50 0.50 0.59 0.47 0.46 0.46
2030 2030 1510 2850 2288 2243
14 14 14 18 14 15
1001 336.5 219.5 45.5 536 214.5
122
L. Zhao et al. / Materials Science & Engineering A 558 (2012) 119–128
Fig. 5. Microscopic feature of creep crack tip in FGHAZ specimen (a) crack tip feature and (b) microscopic crack feature.
Fig. 6. Relationship between creep crack growth length and time.
Fig. 7. Relationship between creep crack growth length and normalized time.
3. Experimental results A typical representation of the creep crack propagation path for the FGHAZ specimen is shown in Fig. 4. It is seen that the creep crack grows towards the interface between FGHAZ and BM. Because the CT specimens without the side grooves are used in the present study, it leads to the crack growth towards the softer zone. In addition, the mechanical strength and the creep strength in the region adjacent to the FGHAZ/BM interface are low. As a
result, the fatigue pre-crack declines to the EDM pre-crack. Further, during creep, the creep crack also grows at an angle (about 451) to the fatigue pre-crack. When the crack reaches to the zone near the FGHAZ/BM interface, the crack then grows through this region. Fig. 5 shows the microscopic features of creep cracks in the FGHAZ specimen. As shown in Fig. 5(a), irregular cracks surrounded by creep voids are observed. These irregular cracks may be caused by the nucleation and subsequent growth and coalescence of creep voids. At elevated temperature creep voids always occur at the interface between the matrix and grain boundary or near the coarse precipitated carbides such as M23C6 and Laves phase [9], as shown in Fig. 5(b). As the creep time increases, the creep voids grow up. When many creep voids have reached a critical size, they will coalesce to form microscopic cracks along grain boundaries. Because the observed creep voids are mainly located at the grain boundaries, the formed cracks are also located at grain boundaries, which can be clearly noted in Fig. 5(b). After that, some microscopic cracks gradually link to each other and finally form macroscopic cracks distributed along the grain boundaries. It can be deduced that the failure mechanism in FGHAZ specimen is intergranular crack. Then, under the effect of the external applied stress on the crack tip, the crack tip would link to macroscopic cracks and the creep crack would propagate further. Furthermore, for P92 steel welded joint, creep voids are more likely to occur in the FGHAZ adjacent to the FGHAZ/BM interface. The phenomenon may make the creep crack propagate towards this interface. Creep crack growth extension, Da, was derived from the tested data and Eq. 1. The relationship between creep crack length and time for BM, FGHAZ, fusion zone and WM specimens is shown in Fig. 6. It can be observed that theses curves show an initial period with reduced crack growth rate and follow by a lengthy period of a constant crack growth rate and then a rapid tertiary region. The CCG life of the FGHAZ specimen is about half of that of the BM specimen at the same value of initial K. The fatigue pre-crack of the FGHAZ specimen is less than the designed 2 mm. Otherwise the CCG life of the FGHAZ specimen would be much shorter than that of the BM specimen. In addition, it can be deduced that the FGHAZ is much more brittle than the BM from the view point of creep crack growth. Fig. 7 shows the relationship between creep crack length and non-dimensional time t/tf for different sub-regions in the welded joint, where t is the current time of load application and tf is the life of creep crack growth for each specimen. It is observed that the crack propagation is steeply increased at the final stage. More than 50% of crack extension is made in the final 10% period in all the experiments. Furthermore, the value of the initial K can affect the creep crack propagation. For the cases of fusion zone and WM specimens with a higher value of the initial K, the accelerated region of the creep crack growth rate takes larger portion of the total creep crack propagation life. However, for the cases of WM, BM and FGHAZ specimens with a lower value of the initial K, the
L. Zhao et al. / Materials Science & Engineering A 558 (2012) 119–128
linear relationship between creep crack length and non-dimensional time takes a major portion of the total creep crack growth life, approximately 80%.
4. Finite element creep crack growth prediction 4.1. Creep damage constitutive equations In the present study, the ABAQUS software coupled with continuum damage mechanics is used to predict the creep crack growth behavior in CT specimens [20]. A modified Karchanov–Rabotnov equation for the creep damage is employed to calculate stress distribution and creep crack growth of CT specimen, and the constitutive equation can be expressed in the multiaxial form as follows [21]: decij dt
¼
3 n1 Bs Sij ð1r þ rð1DÞn Þ 2 e
ð4Þ
dD A ðas1 þ ð1aÞse Þv ¼ gU U dt fþ1 ð1DÞf
ð5Þ
Dcr ¼ 1ð1gÞð1=ðf þ 1ÞÞ
ð6Þ
c ij
where e is the creep strain tensor; se and s1 are the equivalent stress and the maximum principal stresses, respectively; Sij is the stress deviation tensor; D is the damage variable; Dcr is the critical damage, while D/Dcr ¼0.99 means that the material is damaged completely; a is the multiaxial stress parameter (0o a o1); B, n, A and v are the material constants related to the minimum creep strain rate and rupture behavior; g, r and f are the constants accounting for the
123
inhomogeneity of the damage, where r represents the volumetric ratio of the damage phase. The material constants B, n, A, v, g, r and f can be obtained by curve fitting to the uniaxial creep curves. Table 4 shows the material constants of the distinct sub-regions in the welded joint for modified Karchanov–Rabotnov equation. The material constants of FGHAZ and CGHAZ are derived from simulated FGHAZ and simulated CGHAZ which are obtained by the heat treatment simulating and then crept at 650 1C with various applied stresses. 4.2. FEM model In order to investigate the creep crack behavior in detail, a three-dimensional model of the CT specimen is used for the FEM calculation. According to the geometry and property of the CT specimen, one quarter of the CT specimen with BM and WM and one half of the CT specimen with HAZ are modeled, as shown in Figs. 8 and 9, respectively. The load is applied to the center of the upper hole using a pin. The pin is modeled as an analytical rigid. Its geometry and dimension are the same as those of the actual pin in the creep crack growth test. This pin is joined to the center of the hole from one side and to the inner nodes of the hole from the other side. Contact pairs are created between the shell and the inner nodes of the hole. The center of the upper hole is applied load and constrained in all directions except the Y-direction. For one quarter model, the symmetry boundary condition is applied to the center plane of the specimen while for one half model the center of the lower hole is constrained in X- and Y-directions. This is to prevent rigid body translation and rotation of the model. The symmetry plane of the model is constrained in the Z-direction. Continuum elements C3D8R and C3D6 are used. Refined elements
Table 4 Material properties for distinct sub-regions of P92 steel welded joints at 650 1C. Material constants
FGHAZ
CGHAZ
Base metal
Welded metal
E
90 GPa 0.3 8.5969E 038 16.4339 0.95668 7.31333 0.43 5.7511E 039 18.81762 0.076309
110 GPa 0.3 1.15375E 040 16.4476 0.998283 12.2481 0.43 3.734E 032 13.271 0.126224
125 GPa 0.3 1.05906E 038 15.746 0.995211 11.0108 0.43 2.65748E 037 15.7096 0.099287
120 GPa 0.3 6.7001E 040 16.4518 0.966615 7.20317 0.43 1.21767E 035 15.1317 0.0471326
m B n g
f
a A v
r
Fig. 8. One quarter 3D FEM model for CT specimens with BM and WM materials (a) meshes in whole model and (b) local meshes in crack tip.
124
L. Zhao et al. / Materials Science & Engineering A 558 (2012) 119–128
Fig. 9. One half 3D FEM model for CT specimens with crack tip in HAZ (a) meshes in whole model and (b) local meshes in crack tip.
Fig. 10. Comparison of creep crack growth between FEM results and experimental results.
are used in crack tip and crack propagation area (see Figs. 8 and 9). The size of smallest element at the crack tip is 0.02 mm, which is the same as the mean size of grain in the FGHAZ. For the specimens with HAZ, the FEM model consists of four materials: BM, WM, FGHAZ and CGHAZ (see Fig. 9). The pre-crack inserted in FEM model was realized by the elements that were not constrained. 4.3. FEM results For FEM models with BM and WM materials, the initial crack lengths and the initial K values are the same as those of CT1, CT2 and CT3 specimens in the experimental investigations that are listed in Table 3. Fig. 10 compares the creep crack growth evolution of the experiment and simulation results using BM specimen (CT1 specimen listed in Table 3) and WM specimens (CT2 and CT3 specimens listed in Table 3). It can be observed that the tendency of the creep crack propagation is well predicted. In addition, the FEM results only show the steady creep crack growth and accelerated creep growth stages. This is due to the fact that Karchanov–Rabotnov creep damage equation only demonstrates the secondary and tertiary stages of creep behavior, ignoring the creep deformation of the primary creep stage. At beginning the calculated creep crack growth length is a little shorter than that of the experiment as the creep time increases
the calculated creep crack propagation shows agreement with the experimental results. Furthermore, the calculated creep crack failure time of these specimens is almost the same as those of experiment, as shown in Fig. 10. Generally speaking, the FEM analyses in this paper are reasonable, which can be employed to predict the creep crack behavior. Fig. 11 shows the contours of the creep damage accumulation on the crack plane with various creep times for the WM specimen (CT2 specimen listed in Table 3). When the damage of the element reaches to 0.99 Dcr, the element is assumed to be failed and then the element stiffness is set to zero and the remaining forces exerted by the element on adjacent nodes are relaxed to zero. The red area in Fig. 11 means the failed element. The crack length is assumed to calculate the length of the failed element. As shown in Fig. 11, it can be observed that at beginning the creep crack propagates slowly as the creep time increases further the number of failed element increases at an accelerated rate. When the creep time reaches to the creep crack life tf for each specimen, the extent of failed element increases dramatically. In addition, the length of failed element decreases towards the outer surface, which is known as crack tunneling effect and is also found in the tested specimens [22]. This trend is to be expected with a decrease in constraint from approximately plane strain condition at the center plane to plane stress condition at the outer surface. Stress triaxiality is defined as sm/se, where sm is the hydrostatic stress or mean principle stress and se is the equivalent stress. It is always used to demonstrate the constraint condition. Fig. 12 shows the variation of stress triaxiality in the crack tip from the center plane to the outer surface. It can be observed that the crack tip stress triaxiality in the center plane is higher than that in the outer surface. The high stress triaxiality is likely to stimulate the nucleation and growth of creep voids and accelerate the accumulation of creep damage [23]. As a result, a larger extent of failed element is located at the center plane of the specimen.
5. Discussions 5.1. Characterization of CCG rata using C* In the present study, the steady state creep integral parameter C* is calculated, which is analogous to J-integral in elastic–plastic mechanics. It is also a line or surface integral that encloses the crack front. According to ASTM E1457-07 [17,24], for CT specimens, the parameter C* can be calculated using load line displacement rate and corresponding creep crack extension length.
L. Zhao et al. / Materials Science & Engineering A 558 (2012) 119–128
125
Fig. 11. Contours of creep damage accumulation for CT specimen with crack in welded metal. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 12. Distribution of stress triaxiality along the crack tip plane.
The relation is described as follows: PV_ c n 2 þ0:522 Cn ¼ Bn ðWaÞ n þ 1 1a=W
Fig. 13. Relationship between creep crack growth rate and parameter C* for specimens with cracks in distinct zones of welded joint.
ð7Þ
where P is the applied load, Bn is the net specimen thickness between the bottoms of side grooves, a is the current creep crack length, W is the width of specimen, n is the creep exponent, V_ c is the creep load line displacement rate and is given as follows: V_ c ¼ V_ t V_ e V_ p
ð8Þ
where V_ t , V_ e and V_ p are the total, elastic and plastic load line displacement rates, respectively 2K 2 Bn a_ V_ e ¼ PE
ð9Þ
and ðm þ 1ÞJp Bn a_ V_ p ¼ P
ð10Þ
where a_ is the CCG rate, E is Young’ s modulus, m is the exponent in a Ramberg–Osgood fit to the tensile data and Jp is the plastic component of the J-integral [17]. The relationship between CCG rate a_ and C* parameter for WM, BM, fusion zone, and FGHAZ specimens is shown in Fig. 13. It can be observed that each curve has a tail part. For all the CCG test data, the CCG rates are high at the start of the tests and then decrease with decrease in the C*. After that CCG rates increase linearly with increasing the values of C*, as shown in Fig. 13. Furthermore, it can be observed that the relationships between CCG rate and C* among the distinct sub-regions in the welded joint are different from each other although the difference is unremarkable. It has been reported that for the low alloy steel, the creep crack growth rate is five times higher than that of the base metal [25]. However, for advanced 9%Cr heat resistant steel, it has a high resistance to creep and creep crack growth [25,26]. Hence, the creep crack growth property of the high creep strength steel is different from that of the low alloy steel. Although the
126
L. Zhao et al. / Materials Science & Engineering A 558 (2012) 119–128
difference of CCG rate and C* is unremarkable, it is still clearly observed that in the linear characteristic region, the CCG rate at the same value of C* for the FGHAZ specimen is highest, and followed is the WM specimen and then is the fusion zone specimen and last is the BM specimen. At the same value of C*, the CCG rate of the FGHAZ specimen is about two times higher than that of the BM specimen. The highest CCG rate occurring in the FGHAZ is caused by two main reasons. For one thing, the fine gains are formed in this zone due to the low peak temperature and short dwell time at the peak temperature during welding. It is known that when all the other service parameters are constant, the creep strength reduces as the grain size decreases. Hence, the resistance to creep crack growth of FGHAZ is lower than the rest sub-regions in the welded joint, which in turn accelerates the creep crack growth in this zone. For another, due to the low creep strength, the FGHAZ creeps easier than the rest zones of the welded joint. The creep deformation in the FGHAZ is large while that in the adjacent zones is small. The FGHAZ is constrained by the surrounding zones (BM and CGHAZ). As a result, a high stress concentration is generated in this zone, which can accelerate the creep damage accumulation and in turn stimulate the creep crack growth. The creep crack growth in this zone is accelerated further. As shown in Fig. 13, it can be noted that in the tail part the CCG rate is almost constant, which makes it hard to predict the CCG rate using the C* parameter. The relationship between the CCG rate and the C* parameter is needed to evaluate the creep crack behavior in the components. If two CCG rates can be assumed for a value of C*, precise prediction cannot be achieved. Hence the only valid data for the C* parameter is the data where the tail part in Fig. 13 is removed. Using this approach, the relationships between CCG rate and C* for WM, BM, fusion zone and FGHAZ specimens, are shown as follows: a_ ¼ 0:0195ðC n Þ0:8856
for FGHAZ
a_ ¼ 0:0143ðC n Þ0:7359
for fusion zone
a_ ¼ 0:0193ðC n Þ0:7843
for welded metal
n 0:8606
a_ ¼ 0:0141ðC Þ
for base metal
Fig. 14 shows the variation of relation between a_ and C* for the WM specimens with different initial crack lengths a0 or initial K values. It can be observed that these three specimens show
Fig. 14. Variation of creep crack growth rate against parameter C* for various specimens with crack in welded metal.
similar linear characteristic relation between CCG rate and C*. It can be deduced that the relationship between the CCG rate and C* is independent of the initial creep crack length and the initial K value. These two factors only have effect on the initiation time of the creep crack growth behavior. A high initial a0 and K would cause a high constraint in the crack tip, which can accelerate the creep damage accumulation and in turn reduce the initiation time of the creep crack propagation. 5.2. Effectiveness of C* parameter The C* parameter is applicable for the condition that the material shows creep-ductile behavior, where the creep region near the crack tip is extensively wide compared with the crack propagation rate. In the ASTM E1457-07 standard [17], some specific terms of conditions are defined to ensure the applicability of C* parameter. At first, the total load line displacement rate and the creep load line displacement rate should be in the ratio of V_ c =V_ t Z0:5. This ratio represents the degree of creep area spread. The stress intensity factor K will be the dominant parameter at V_ c =V_ t r0:2. Fig. 15 shows the relationship between the load line displacement rate ratio V_ c =V_ t and the C* parameter. V_ c =V_ t is in the range of 0.81–0.99 at all the duration in all the experiments, and satisfies the condition specified in ASTM E1457-07 [17]. It can be observed that as the value of C* is too high and is greatly accelerated in the tertiary stage, the V_ c =V_ t declines steeply. Therefore, the creep crack growth should not be terminated until the specimen fractures. The specimen should be interrupted when the creep crack growth have been in the accelerated stage for some time. In the tertiary stage, considerable plastic deformation is experienced. As the creep crack propagates, the plastic deformation becomes large. When the plastic deformation exceeds the creep deformation, the creep brittle fracture occurs in the CT specimen. Therefore, in the present study, all tests are interrupted as CCG rate is enough high without the fracture. The second restrictive condition to ensure the applicability of C* is to remove the transient creep crack region from the result data. The transient time tT is defined as follow: tT ¼
K 2 ð1u2 Þ Eðn þ 1ÞC n ðt T Þ
ð11Þ
where C*(tT) is the value of C* at the time of tT. The calculation of tT depends on the value of C*(tT). Because tT cannot be obtained directly, C*(tT) also cannot be obtained explicitly. In ASTM 1457-07 [17], it is recommended that the following procedure must be
Fig. 15. Distribution of load line displacement rate ratio against parameter C*.
L. Zhao et al. / Materials Science & Engineering A 558 (2012) 119–128
127
Table 5 Transient time tT and initiation time ti of creep crack growth test. Specimen
Crack location
Duration time tf (h)
Transient time tT (h)
tT/tf
Initiation time ti (h)
ti/tf
CT1 CT2 CT3 CT4 CT5 CT6
BM WM WM WM FGHAZ Fusion zone
1001 336.5 219.5 45.5 536 214.5
2.65 1.49 0.79 0.11 2.02 0.51
0.0026 0.0044 0.0036 0.0024 0.0038 0.0023
134 85 50 3.5 80 24
0.134 0.253 0.228 0.226 0.149 0.112
used for its estimation. For the time tT, corresponding to each date point, t0 T is calculated using the above equation but substituting C*(t) for C*(tT). tT is then the largest value of t0 T in the entire date set. Table 5 shows the tT, ti and tf of all tests. The creep crack initiation time, ti, is defined as the time to achieve a measurable amount of crack extension. In the current experiments, the time for 0.2 mm crack extension has been determined as the creep crack initiation time ti [13]. It can be noted that tT/tf is sufficiently small. The data before tT have been removed from the figures shown in Section 4.1. During creep crack extension, creep damage known as creep voids gradually accumulates from the beginning of the tests and leads to little crack extension. These phenomena make the crack growth rate change little while the C* is low. As a result, the plotted curves have a tail. It gives rise to a reduced CCG rate at beginning of test, which is less than the steady state creep crack growth rate. This ‘‘tail’’ can be avoided by excluding data prior to the onset of a steady state of damage. In most cases it would appear before the creep crack initiation time [13,27]. In addition, the crack growth life and the creep crack initiation time for fusion zone and FGHAZ specimens are much shorter than those for BM specimens. It can be deduced that the prediction of creep crack initiation time plays an important role in evaluating of fracture life of the welded joints.
Fig. 16. Distribution of stress triaxiality across the specimen with crack in HAZ at various creep crack growth lengths.
5.3. Effect of multiaxial stress for welded joint As analyzed above, the stress concentration in the crack tip may play an important role in the creep crack growth. Hence, in the present study, the variation of the stress distribution in the crack tip of the specimen with HAZ is investigated on the basis of the FEM coupled with continuum damage mechanics. As mentioned in Section 3, a half model is adopted. As shown in Fig. 9, the width of FGHAZ is the same as that of CGHAZ, which is assumed to be 1 mm. A circular arc with 0.025 mm is used to idealize the actual crack tip. The initial cracks are assumed to be located at the FGHAZ/BM interface, CGHAZ/FGHAZ interface and WM/CGHAZ interface, respectively. In these analyses, the initial crack length a0 and the initial K value are assumed to be the same for all the calculated cases, which are 10 mm and 14 MPa m1/2, respectively. Thus, the initial crack depth a0/W and the applied load P for these models are 0.5 and 2050 N, respectively. Fig. 16 shows the variation of stress triaxiality distribution across the welded joint in the center plane of CT specimen with cracks located at the CGHAZ/FGHAZ interface. It can be observed that the highest stress triaxiality is located at the interface before creep crack extension. As the creep crack propagates, the stress triaxiality in the HAZ containing CGHAZ and FGHAZ increases and the location of highest triaxiality moves towards to the FGHAZ. In addition, when the crack length exceeds 1 mm the stress triaxiality increases slowly. This increase is due to the multiaxial stress state induced by the creep deformation. The creep strength of distinct sub-regions in welded joint is different, where the lowest creep strength is in the FGHAZ and the highest creep strength is in the BM. During creep, the deformation of FGHAZ is larger than those of adjacent zones i.e. CGHAZ and base metal. As a result,
Fig. 17. FEM results of creep propagation for specimens with different initial crack locations.
the deformation of FGHAZ is constrained by the adjacent zones, which leads to a high stress triaxiality occurred. The high multiaxial stress will accelerate the creep crack growth rate. The comparison among the creep crack growth behaviors for the CT models with different crack tip positions is clarified in Fig. 17. The results of FEM models with BM and WM material are also given for comparison. It can be observed that the specimen with crack tip located at FGHAZ/BM interface exhibits a high creep crack growth rate compared with those with crack tip located in other microzones of welded joint. It reveals that the
128
L. Zhao et al. / Materials Science & Engineering A 558 (2012) 119–128
creep damage accumulation is accelerated in this interface due to a high constraint in this zone. As a result, in the creep crack tests, the crack growth declines to the FGHAZ/BM interface for the specimens with cracks located at the FGHAZ, as shown in Fig. 3. Compared with the experimental results as shown in Fig. 5, the calculated creep crack growth behaviors in Fig. 17 exhibit a little difference from those of experiment. This is due to the fact that the initial crack length a0 and initial stress intensity factor K in these simulations are set to be different from those of experiment. For the calculated cases they are kept constant, while for the experimental cases they are different from each other. As a rule, high a0 and initial K value would accelerate the creep crack growth and then decline the corresponding creep crack failure life. Hence, some differences between FEM results and experimental data present. However, the above comparison among the calculated creep crack growth behaviors for the specimens with different crack tip positions in the present study are conducted under the same conditions, so the obtained conclusions are reasonable.
6. Conclusions In the present study, a series of creep crack growth tests on the CT specimen for the distinct sub-regions of ASME P92 steel welded joint were carried out at 650 1C. The relationship of creep crack growth rate and parameter C* for the different sub-regions of the welded joint was obtained. It was found that C* could be used to correlate the creep crack growth rate for the microzones of welded joint. Furthermore, the high CCG rate occurred in the specimens with cracks located in the FGHAZ, due to the high constraint and the low creep strength in this zone. At the same value of C*, the CCG rate of the FGHAZ specimen is about two times higher than that of the BM specimen. FEM analysis coupled with continuum damage mechanics was used to predict the creep crack behavior. The calculated creep crack extension behaviors of the BM and WM specimens were in agreement with those of experiment. In addition, the constraint in the crack tip induced by the different material properties around the crack tip played an important role in creep crack growth, which could accelerate the creep damage accumulation. The specimen with crack tip in FGHAZ/BM interface exhibited a higher creep crack growth rate compared with those with crack tip in other microzones of welded joint.
Acknowledgment This research work was financially supported by the Project of the National Natural Science Foundation of China (50805103, 50975196 and 51175375) and Key Project in the Science & Technology Pillar Program of Tianjin (Grant No. 11ZCKFGX03000) and Research Fund for the Doctoral Program of Higher Education of China (20090032110026 and 20110032130002).
References [1] [2] [3] [4]
[5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27]
J.A. Francis, W. Mazur, H.K.D.H. Bhadeshia, ISIJ Int. 44 (2004) 1966–1968. T.-U. Kern, M. Staubli, B. Scarlin, ISIJ Int. 42 (2002) 1515–1519. T. Fujita, Adv. Mater. Process. 141 (1992) 42–45. P.F. Giroux, F. Dallea, M. Sauzay, G. Pereza, I. Tournie, V. Rabeau, J. Malaplate, T. Van Den Berghe, A.F. Fournier, B. Gourgues-Lorenzon, Mater. High Temp. 27 (2010) 29–34. B. Kim, B. Lim, D. Ki, Int. J. Mod. Phys. B 20 (2006) 4231–4236. K. Sawada, K. Kubo, F. Abe, Mater. Sci. Eng. A 319–321 (2001) 784–787. B. Kim, C. Jeong, B. Lim, Mater. Sci. Eng. A 483 (2008) 544–546. K. Shinozaki, H.K. Dejun Li, H. Harada, K. Ohishi, T. Sato, Sci. Technol. Weld. Joining 8 (2003) 289–295. L. Zhao, H.-Y. Jing, L.-Y. Xu, J.-C. An, G.-C. Xiao, D.-L. Xu, Y.-C. Chen, Y. Han, J. Mater. Res. 26 (2011) 934–943. H. Tezuka, T. Sakurai, Int. J. Pres. Ves. Pip. 82 (2005) 165–174. B. Dogan, B. Petrovski, Int. J. Pres. Ves. Pip. 78 (2001) 795–805. R. Sugiura, A.T. Yokobori Jr., M. Tabuchi, T. Yokobori, Eng. Fract. Mech. 74 (2007) 868–881. C.M. Davies, D.W. Dean, K.M. Nikbin, N.P. O’Dowd, Eng. Fract. Mech. 74 (2007) 882–897. S. Maleki, Y. Zhang, K. Nikbin, Eng. Fract. Mech. 77 (2010) 3035–3042. V.A. Vainshtok, M.V. Baumshtein, I.A. Makovetskaya, I.V. Kramarenko, Eng. Fract. Mech. 40 (1991) 1147–1163. K. Sawada, H. Hongo, T. Watanabe, M. Tabuchi, Mater. Charact. 61 (2010) 1097–1102. ASTM E1457-07, Standard Test Method for Measurement of Creep Crack Growth Times in Metals, ASTM, 2007. K.H. Schwalbe, D. Hellmann, J. Test. Eval. 9 (1981) 218–220. G.A. Hartman, D.A. Johnson, Exp. Mech. 27 (1987) 106–112. ABAQUS, Abaqus 6.9 Standard User Manual, ABAQUS, Inc., USA, 2009. S.-T. Tu, P. Segle, J.-M. Gong, Int. J. Pres. Ves. Pip. 81 (2004) 199–209. T.H. Hyde, M. Saber, W. Sun, Eng. Fract. Mech. 77 (2010) 2946–2957. N. Roy, S.C. Bose, R.N. Ghosh, Mater. Sci. Eng. A 527 (2010) 4810–4817. S. Taira, R. Ohtani, T. Kitamura, J. Eng. Mater. Technol. 101 (1979) 154–161, ASME. M. Tabuchi, T. Watanabe, K. Kubo, M. Matsui, J. Kinugawa, F. Abe, Int. J. Pres. Ves. Pip. 78 (2001) 779–784. A.T. Yokobori Jr., S. Takmori, T. Yokobori, Y. Hasegawa, K. Kubota, K. Hidaka, Key Eng. Mater. 171–174 (2000) 131–138. O. Kwon, K.M. Nikbin, G.A. Webster, K.V. Jata, Eng. Fract. Mech. 62 (1999) 33–46.
Contents lists available at SciVerse ScienceDirect
Materials Science & Engineering A journal homepage: www.elsevier.com/locate/msea
Analysis of creep crack growth behavior of P92 steel welded joint by experiment and numerical simulation Lei Zhao a,b, Hongyang Jing a,b, Lianyong Xu a,b,n, Yongdian Han a,b, Junjie Xiu a,b a b
School of Materials Science and Engineering, Tianjin University, Tianjin 300072, China Tianjin Key Laboratory of Advanced Joining Technology, Tianjin 300072, China
a r t i c l e i n f o
abstract
Article history: Received 17 March 2012 Received in revised form 1 June 2012 Accepted 23 July 2012 Available online 31 July 2012
High temperature creep crack growth tests were carried out on standard compact specimens machined from the welded joint of ASME P92 steel pipe. The creep crack growth behaviors of the distinct subregions of welded joint were investigated to clarify the ability of creep crack resistance under high temperature. In addition, good correlations between creep crack growth rate and C* for different microzones of welded joint were obtained. The tested results revealed that the sub-regions of welded joint exhibited different creep crack behaviors and at the same value of C* the highest creep crack growth rate occurred in the fine grained heat affected zone (FGHAZ) which was known as Type IV cracking zone. Furthermore, finite element method analyses coupled with continuum damage mechanics were conducted to predict the creep crack growth behavior and to study the effect of multistress state on crack propagation. & 2012 Elsevier B.V. All rights reserved.
Keywords: Creep crack growth Finite element method analysis Multistress state ASME P92 steel Type IV cracking
1. Introduction In consideration of reduction in CO2 emission and energy saving for thermal power plants, high strength heat resistant steels have been developed to meet the requirements of the boiler components under increased steam pressure and temperature condition [1]. Several types of 9–12% Cr boiler steels with high creep strength have been developed [2,3]. In recent times, P92 steels strengthened by tungsten addition have become the candidate materials for application to ultra-supercritical (USC) power plants components, such as superheater and reheater headers and steam pipes, chests and valves operating at about 600–650 1C [4–6]. Most of these components are made of weldments, which consist of several distinct regions with different microstructures, such as the welded metal (WM), the base metal (BM) and the heat affected zone (HAZ). The HAZ is commonly composed of the coarse grain HAZ (CGHAZ), the fine grain HAZ (FGHAZ) and the intercritical HAZ (ICHAZ) [7]. Even for these steel welded joints with high creep strength serviced at high temperature, fracture often occurs in the FGHAZ adjacent to the base metal, known as Type IV cracking, and decreases the creep lives of welded joints [8–10]. This failure is mainly caused by creep crack growth, which
n Corresponding author at: School of Materials Science and Engineering, Tianjin University, Tianjin 300072, China. Tel./fax: þ86 22 27402439. E-mail address: [email protected] (L. Xu).
0921-5093/$ - see front matter & 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.msea.2012.07.094
is most likely to take place in components with pre-existing defects or stress concentration. Creep crack growth (CCG) imposes a limit on the service lives of components at elevated temperature [11]. Understanding of CCG properties of the welded joint is important for the reliability assessment of high-temperature structural components. For the welded joint, microstructure inhomogeneity exists among these distinct zones leading to different creep deformation properties. As a result, the constraint is always generated in the fusion zone and HAZ zone during creep. Then, the multiaxial stress state is always created. These phenomena make it difficult to estimate the creep crack behavior for the welded joint. To date, some previous researches have investigated the CCG properties of base metal and welded joint of high chromium steels [12–16]. However, the CCG behaviors of distinct sub-regions of ASME P92 steel welded joint have not been studied in detail. Therefore, it is crucial to investigate the CCG properties of sub-regions in the welded joint and to clarify factors affecting the crack propagation property of ASME P92 steel welded joint so as to accurately assess the safety of power plants under long-term servicing at high temperature. In the present study, creep crack growth tests were conducted on compact tension (CT) specimens with cracks in WM, BM, fusion zone and FGHAZ (zone of HAZ adjacent to base metal) at 650 1C. Creep crack propagation behaviors in the different subregions of the welded joint were investigated. Based on the experimental results, the finite element method (FEM) analysis coupled with the continuum damage mechanics was conducted
120
L. Zhao et al. / Materials Science & Engineering A 558 (2012) 119–128
Table 1 Chemical composition (wt%) of ASME P92 steel and welded metal used (bal. Fe). Material
C
Si
Mn
S
P
Cr
Ni
Mo
W
V
Nb
B
Al
N
Base metal Welded metal
0.10 0.12
0.47 0.29
0.40 0.71
0.001 0.008
0.008 0.009
8.77 9.08
0.12 0.49
0.38 0.42
1.48 1.72
0.16 0.19
0.054 0.06
0.001 0.003
0.02 0.01
0.043 0.06
Table 2 Welding conditions of ASME P92 steel pipe. Groove
As shown in left figure
Number of weld passes Preheating temperature (1C) Interpass temperature (1C) Welding current (A) Arc voltage (V) Welding heating input (kJ/cm) Welding speeding (mm/min)
27–30 150 200–250 100–120 11–15 15–20 150
to simulate the creep crack extension and then to analyze the effect of stress multiaxiality in the welded joint on creep crack growth.
2. Experimental procedures 2.1. Materials The material investigated in the present study is ASME P92 steel pipe, with an inner diameter of 390 mm and a thickness of 80 mm, which was subjected to normalizing at 1040 1C for 4 h and then tempering at 760 1C for 11 h. The chemical composition of the parent P92 steel is given in Table 1. The pipes were fabricated using a multilayer gas tungsten arc welding (GTAW) method with single J grooves. Welding consumable used for GTAW was matching filler wire developed recently for welding this class of steel. The chemical composition of the welded metal is also given in Table 1. After welding, the post weld heat treatment (PWHT) was carried out at 760 1C for 4 h to assure that the residual stresses in the welded joint were reduced to a level that it could be ignored during the analyses. The welding conditions are shown in Table 2, which are the same as the fabrication process for the actual large diameter steam pipes in fossil power plants. The Vickers hardness (HV10) distribution across the welded joint is shown in Fig. 1. The measurements of Vickers hardness were conducted on the welded joint specimen before the creep crack growth test. The hardness of WM is higher than that of BM about 30 HV. The highest hardness is located at the fusion zone. A sharp reduction in hardness can be seen within the HAZ. It is well known that the HAZ of 9%Cr steel is mainly composed of FGHAZ adjacent to base metal and CGHAZ adjacent to welded metal [7], and these two regions correspond to the softer and harder region, respectively. In the present study, the CGHAZ shows higher hardness about 30 HV than that in the WM. The FGHAZ shows slightly higher hardness than the BM.
Fig. 1. Distribution of Vickers hardness across ASME P92 steel welded joint before creep crack.
2.2. Specimen Creep crack growth tests were carried out on standard compact tension specimens. All specimens were machined from the
Fig. 2. Schematic of CT specimens extracting from ASME P92 steel welded joint.
L. Zhao et al. / Materials Science & Engineering A 558 (2012) 119–128
P92 steel welded joint in the longitudinal orientation (welding orientation), as shown in Fig. 2. The geometries and dimensions of CT specimen adopted are shown in Fig. 3, which are chosen in accordance with the ASTM E1457-07 requirements [17]. The precracks were introduced in all specimens using the electric discharge machining (EDM) and fatigue pre-cracking. The width and the length of EDM pre-crack were 0.08 mm and 2 mm, respectively. After EDM pre-cracking, the fatigue pre-cracking was carried out at room temperature and under a stress ratio of 0.05 according to the requirements in the ASTM E1457-07 [17]. The fatigue pre-crack was grown to about 2 mm away from the EDM pre-crack. Then they were used for the creep crack propagation experiments. 2.3. Test methods Creep crack growth tests were performed in lever arm constant load tensile creep machines equipped with split tubes. In general, according to the ASTM standard E1457-07 [17], the tests were performed and the data obtained were analyzed. The crack length and load line displacement were measured. Load line displacement was monitored by attaching capacitance gauges to the lower and up pull rods that were tied with the specimen by the pins. Then, the displacement was measured by the change in distance between the up and the lower pull rods during testing. Creep crack length was measured by an electrical potential drop method. An electrical current was applied to the specimen and the value of the electric potential drop was measured. The crack length is usually calculated using Johnson’s equation for CT specimen given by [18,19] a¼
2W
p
( cos1
)
cos hðpY 0 =2WÞ 1
cos h½ðV=V 0 Þ cos h
121
where a is the current crack length, a0 is the initial crack length, Y0 is half the distance between the output terminals, W is the width of the specimen, V0 is the initial voltage and V is the actual value of the potential.
2.4. Test conditions All of the creep tests were performed in air at 650 1C. Table 3 shows the conditions of creep crack propagation experiments. The applied load was determined from the value of initial stress intensity factor K by the following equation: a P 2 þa0 =W 0 K ¼ pffiffiffiffiffiffiffiffiffi 1=2 f 3=2 W ð1a0 =WÞ BBN W
ð2Þ
where P is the applied load; B is the specimen thickness, BN is the net specimen thickness between the bottoms of side grooves and f(a0/W) is obtained from: f
a 0
W
a a 2 a 3 a 4 0 0 0 0 ¼ 0:886 þ 4:64 13:32 þ 14:72 5:6 W W W W ð3Þ
In the present study, to analyze the CCG property of the distinct microzones of the welded joint, four different crack tip positions are considered, with the cracks placed within BM region, WM region, FGHAZ (the zone of HAZ adjacent to the base metal) which corresponds to Type IV cracking zone and fusion zone (see Fig. 2). For specimens with the WM, the effects of different initial crack lengths and initial K values on the creep crack growth were also investigated.
ðcos hðpY 0 =2WÞ=cosðpa0 =2WÞÞ
ð1Þ
Fig. 4. Representative morphology of creep crack behavior for CT specimen with crack in FGHAZ.
Fig. 3. Dimension and size of CT specimen used in the testing.
Table 3 Experimental conditions of creep crack growth test. Specimen
Crack location
Crack depth a0/W
Load P (N)
Initial stress intensity factor K (MPa m1/2)
Duration time tf (h)
CT1 CT2 CT3 CT4 CT5 CT6
BM WM WM WM FGHAZ Fusion zone
0.50 0.50 0.59 0.47 0.46 0.46
2030 2030 1510 2850 2288 2243
14 14 14 18 14 15
1001 336.5 219.5 45.5 536 214.5
122
L. Zhao et al. / Materials Science & Engineering A 558 (2012) 119–128
Fig. 5. Microscopic feature of creep crack tip in FGHAZ specimen (a) crack tip feature and (b) microscopic crack feature.
Fig. 6. Relationship between creep crack growth length and time.
Fig. 7. Relationship between creep crack growth length and normalized time.
3. Experimental results A typical representation of the creep crack propagation path for the FGHAZ specimen is shown in Fig. 4. It is seen that the creep crack grows towards the interface between FGHAZ and BM. Because the CT specimens without the side grooves are used in the present study, it leads to the crack growth towards the softer zone. In addition, the mechanical strength and the creep strength in the region adjacent to the FGHAZ/BM interface are low. As a
result, the fatigue pre-crack declines to the EDM pre-crack. Further, during creep, the creep crack also grows at an angle (about 451) to the fatigue pre-crack. When the crack reaches to the zone near the FGHAZ/BM interface, the crack then grows through this region. Fig. 5 shows the microscopic features of creep cracks in the FGHAZ specimen. As shown in Fig. 5(a), irregular cracks surrounded by creep voids are observed. These irregular cracks may be caused by the nucleation and subsequent growth and coalescence of creep voids. At elevated temperature creep voids always occur at the interface between the matrix and grain boundary or near the coarse precipitated carbides such as M23C6 and Laves phase [9], as shown in Fig. 5(b). As the creep time increases, the creep voids grow up. When many creep voids have reached a critical size, they will coalesce to form microscopic cracks along grain boundaries. Because the observed creep voids are mainly located at the grain boundaries, the formed cracks are also located at grain boundaries, which can be clearly noted in Fig. 5(b). After that, some microscopic cracks gradually link to each other and finally form macroscopic cracks distributed along the grain boundaries. It can be deduced that the failure mechanism in FGHAZ specimen is intergranular crack. Then, under the effect of the external applied stress on the crack tip, the crack tip would link to macroscopic cracks and the creep crack would propagate further. Furthermore, for P92 steel welded joint, creep voids are more likely to occur in the FGHAZ adjacent to the FGHAZ/BM interface. The phenomenon may make the creep crack propagate towards this interface. Creep crack growth extension, Da, was derived from the tested data and Eq. 1. The relationship between creep crack length and time for BM, FGHAZ, fusion zone and WM specimens is shown in Fig. 6. It can be observed that theses curves show an initial period with reduced crack growth rate and follow by a lengthy period of a constant crack growth rate and then a rapid tertiary region. The CCG life of the FGHAZ specimen is about half of that of the BM specimen at the same value of initial K. The fatigue pre-crack of the FGHAZ specimen is less than the designed 2 mm. Otherwise the CCG life of the FGHAZ specimen would be much shorter than that of the BM specimen. In addition, it can be deduced that the FGHAZ is much more brittle than the BM from the view point of creep crack growth. Fig. 7 shows the relationship between creep crack length and non-dimensional time t/tf for different sub-regions in the welded joint, where t is the current time of load application and tf is the life of creep crack growth for each specimen. It is observed that the crack propagation is steeply increased at the final stage. More than 50% of crack extension is made in the final 10% period in all the experiments. Furthermore, the value of the initial K can affect the creep crack propagation. For the cases of fusion zone and WM specimens with a higher value of the initial K, the accelerated region of the creep crack growth rate takes larger portion of the total creep crack propagation life. However, for the cases of WM, BM and FGHAZ specimens with a lower value of the initial K, the
L. Zhao et al. / Materials Science & Engineering A 558 (2012) 119–128
linear relationship between creep crack length and non-dimensional time takes a major portion of the total creep crack growth life, approximately 80%.
4. Finite element creep crack growth prediction 4.1. Creep damage constitutive equations In the present study, the ABAQUS software coupled with continuum damage mechanics is used to predict the creep crack growth behavior in CT specimens [20]. A modified Karchanov–Rabotnov equation for the creep damage is employed to calculate stress distribution and creep crack growth of CT specimen, and the constitutive equation can be expressed in the multiaxial form as follows [21]: decij dt
¼
3 n1 Bs Sij ð1r þ rð1DÞn Þ 2 e
ð4Þ
dD A ðas1 þ ð1aÞse Þv ¼ gU U dt fþ1 ð1DÞf
ð5Þ
Dcr ¼ 1ð1gÞð1=ðf þ 1ÞÞ
ð6Þ
c ij
where e is the creep strain tensor; se and s1 are the equivalent stress and the maximum principal stresses, respectively; Sij is the stress deviation tensor; D is the damage variable; Dcr is the critical damage, while D/Dcr ¼0.99 means that the material is damaged completely; a is the multiaxial stress parameter (0o a o1); B, n, A and v are the material constants related to the minimum creep strain rate and rupture behavior; g, r and f are the constants accounting for the
123
inhomogeneity of the damage, where r represents the volumetric ratio of the damage phase. The material constants B, n, A, v, g, r and f can be obtained by curve fitting to the uniaxial creep curves. Table 4 shows the material constants of the distinct sub-regions in the welded joint for modified Karchanov–Rabotnov equation. The material constants of FGHAZ and CGHAZ are derived from simulated FGHAZ and simulated CGHAZ which are obtained by the heat treatment simulating and then crept at 650 1C with various applied stresses. 4.2. FEM model In order to investigate the creep crack behavior in detail, a three-dimensional model of the CT specimen is used for the FEM calculation. According to the geometry and property of the CT specimen, one quarter of the CT specimen with BM and WM and one half of the CT specimen with HAZ are modeled, as shown in Figs. 8 and 9, respectively. The load is applied to the center of the upper hole using a pin. The pin is modeled as an analytical rigid. Its geometry and dimension are the same as those of the actual pin in the creep crack growth test. This pin is joined to the center of the hole from one side and to the inner nodes of the hole from the other side. Contact pairs are created between the shell and the inner nodes of the hole. The center of the upper hole is applied load and constrained in all directions except the Y-direction. For one quarter model, the symmetry boundary condition is applied to the center plane of the specimen while for one half model the center of the lower hole is constrained in X- and Y-directions. This is to prevent rigid body translation and rotation of the model. The symmetry plane of the model is constrained in the Z-direction. Continuum elements C3D8R and C3D6 are used. Refined elements
Table 4 Material properties for distinct sub-regions of P92 steel welded joints at 650 1C. Material constants
FGHAZ
CGHAZ
Base metal
Welded metal
E
90 GPa 0.3 8.5969E 038 16.4339 0.95668 7.31333 0.43 5.7511E 039 18.81762 0.076309
110 GPa 0.3 1.15375E 040 16.4476 0.998283 12.2481 0.43 3.734E 032 13.271 0.126224
125 GPa 0.3 1.05906E 038 15.746 0.995211 11.0108 0.43 2.65748E 037 15.7096 0.099287
120 GPa 0.3 6.7001E 040 16.4518 0.966615 7.20317 0.43 1.21767E 035 15.1317 0.0471326
m B n g
f
a A v
r
Fig. 8. One quarter 3D FEM model for CT specimens with BM and WM materials (a) meshes in whole model and (b) local meshes in crack tip.
124
L. Zhao et al. / Materials Science & Engineering A 558 (2012) 119–128
Fig. 9. One half 3D FEM model for CT specimens with crack tip in HAZ (a) meshes in whole model and (b) local meshes in crack tip.
Fig. 10. Comparison of creep crack growth between FEM results and experimental results.
are used in crack tip and crack propagation area (see Figs. 8 and 9). The size of smallest element at the crack tip is 0.02 mm, which is the same as the mean size of grain in the FGHAZ. For the specimens with HAZ, the FEM model consists of four materials: BM, WM, FGHAZ and CGHAZ (see Fig. 9). The pre-crack inserted in FEM model was realized by the elements that were not constrained. 4.3. FEM results For FEM models with BM and WM materials, the initial crack lengths and the initial K values are the same as those of CT1, CT2 and CT3 specimens in the experimental investigations that are listed in Table 3. Fig. 10 compares the creep crack growth evolution of the experiment and simulation results using BM specimen (CT1 specimen listed in Table 3) and WM specimens (CT2 and CT3 specimens listed in Table 3). It can be observed that the tendency of the creep crack propagation is well predicted. In addition, the FEM results only show the steady creep crack growth and accelerated creep growth stages. This is due to the fact that Karchanov–Rabotnov creep damage equation only demonstrates the secondary and tertiary stages of creep behavior, ignoring the creep deformation of the primary creep stage. At beginning the calculated creep crack growth length is a little shorter than that of the experiment as the creep time increases
the calculated creep crack propagation shows agreement with the experimental results. Furthermore, the calculated creep crack failure time of these specimens is almost the same as those of experiment, as shown in Fig. 10. Generally speaking, the FEM analyses in this paper are reasonable, which can be employed to predict the creep crack behavior. Fig. 11 shows the contours of the creep damage accumulation on the crack plane with various creep times for the WM specimen (CT2 specimen listed in Table 3). When the damage of the element reaches to 0.99 Dcr, the element is assumed to be failed and then the element stiffness is set to zero and the remaining forces exerted by the element on adjacent nodes are relaxed to zero. The red area in Fig. 11 means the failed element. The crack length is assumed to calculate the length of the failed element. As shown in Fig. 11, it can be observed that at beginning the creep crack propagates slowly as the creep time increases further the number of failed element increases at an accelerated rate. When the creep time reaches to the creep crack life tf for each specimen, the extent of failed element increases dramatically. In addition, the length of failed element decreases towards the outer surface, which is known as crack tunneling effect and is also found in the tested specimens [22]. This trend is to be expected with a decrease in constraint from approximately plane strain condition at the center plane to plane stress condition at the outer surface. Stress triaxiality is defined as sm/se, where sm is the hydrostatic stress or mean principle stress and se is the equivalent stress. It is always used to demonstrate the constraint condition. Fig. 12 shows the variation of stress triaxiality in the crack tip from the center plane to the outer surface. It can be observed that the crack tip stress triaxiality in the center plane is higher than that in the outer surface. The high stress triaxiality is likely to stimulate the nucleation and growth of creep voids and accelerate the accumulation of creep damage [23]. As a result, a larger extent of failed element is located at the center plane of the specimen.
5. Discussions 5.1. Characterization of CCG rata using C* In the present study, the steady state creep integral parameter C* is calculated, which is analogous to J-integral in elastic–plastic mechanics. It is also a line or surface integral that encloses the crack front. According to ASTM E1457-07 [17,24], for CT specimens, the parameter C* can be calculated using load line displacement rate and corresponding creep crack extension length.
L. Zhao et al. / Materials Science & Engineering A 558 (2012) 119–128
125
Fig. 11. Contours of creep damage accumulation for CT specimen with crack in welded metal. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 12. Distribution of stress triaxiality along the crack tip plane.
The relation is described as follows: PV_ c n 2 þ0:522 Cn ¼ Bn ðWaÞ n þ 1 1a=W
Fig. 13. Relationship between creep crack growth rate and parameter C* for specimens with cracks in distinct zones of welded joint.
ð7Þ
where P is the applied load, Bn is the net specimen thickness between the bottoms of side grooves, a is the current creep crack length, W is the width of specimen, n is the creep exponent, V_ c is the creep load line displacement rate and is given as follows: V_ c ¼ V_ t V_ e V_ p
ð8Þ
where V_ t , V_ e and V_ p are the total, elastic and plastic load line displacement rates, respectively 2K 2 Bn a_ V_ e ¼ PE
ð9Þ
and ðm þ 1ÞJp Bn a_ V_ p ¼ P
ð10Þ
where a_ is the CCG rate, E is Young’ s modulus, m is the exponent in a Ramberg–Osgood fit to the tensile data and Jp is the plastic component of the J-integral [17]. The relationship between CCG rate a_ and C* parameter for WM, BM, fusion zone, and FGHAZ specimens is shown in Fig. 13. It can be observed that each curve has a tail part. For all the CCG test data, the CCG rates are high at the start of the tests and then decrease with decrease in the C*. After that CCG rates increase linearly with increasing the values of C*, as shown in Fig. 13. Furthermore, it can be observed that the relationships between CCG rate and C* among the distinct sub-regions in the welded joint are different from each other although the difference is unremarkable. It has been reported that for the low alloy steel, the creep crack growth rate is five times higher than that of the base metal [25]. However, for advanced 9%Cr heat resistant steel, it has a high resistance to creep and creep crack growth [25,26]. Hence, the creep crack growth property of the high creep strength steel is different from that of the low alloy steel. Although the
126
L. Zhao et al. / Materials Science & Engineering A 558 (2012) 119–128
difference of CCG rate and C* is unremarkable, it is still clearly observed that in the linear characteristic region, the CCG rate at the same value of C* for the FGHAZ specimen is highest, and followed is the WM specimen and then is the fusion zone specimen and last is the BM specimen. At the same value of C*, the CCG rate of the FGHAZ specimen is about two times higher than that of the BM specimen. The highest CCG rate occurring in the FGHAZ is caused by two main reasons. For one thing, the fine gains are formed in this zone due to the low peak temperature and short dwell time at the peak temperature during welding. It is known that when all the other service parameters are constant, the creep strength reduces as the grain size decreases. Hence, the resistance to creep crack growth of FGHAZ is lower than the rest sub-regions in the welded joint, which in turn accelerates the creep crack growth in this zone. For another, due to the low creep strength, the FGHAZ creeps easier than the rest zones of the welded joint. The creep deformation in the FGHAZ is large while that in the adjacent zones is small. The FGHAZ is constrained by the surrounding zones (BM and CGHAZ). As a result, a high stress concentration is generated in this zone, which can accelerate the creep damage accumulation and in turn stimulate the creep crack growth. The creep crack growth in this zone is accelerated further. As shown in Fig. 13, it can be noted that in the tail part the CCG rate is almost constant, which makes it hard to predict the CCG rate using the C* parameter. The relationship between the CCG rate and the C* parameter is needed to evaluate the creep crack behavior in the components. If two CCG rates can be assumed for a value of C*, precise prediction cannot be achieved. Hence the only valid data for the C* parameter is the data where the tail part in Fig. 13 is removed. Using this approach, the relationships between CCG rate and C* for WM, BM, fusion zone and FGHAZ specimens, are shown as follows: a_ ¼ 0:0195ðC n Þ0:8856
for FGHAZ
a_ ¼ 0:0143ðC n Þ0:7359
for fusion zone
a_ ¼ 0:0193ðC n Þ0:7843
for welded metal
n 0:8606
a_ ¼ 0:0141ðC Þ
for base metal
Fig. 14 shows the variation of relation between a_ and C* for the WM specimens with different initial crack lengths a0 or initial K values. It can be observed that these three specimens show
Fig. 14. Variation of creep crack growth rate against parameter C* for various specimens with crack in welded metal.
similar linear characteristic relation between CCG rate and C*. It can be deduced that the relationship between the CCG rate and C* is independent of the initial creep crack length and the initial K value. These two factors only have effect on the initiation time of the creep crack growth behavior. A high initial a0 and K would cause a high constraint in the crack tip, which can accelerate the creep damage accumulation and in turn reduce the initiation time of the creep crack propagation. 5.2. Effectiveness of C* parameter The C* parameter is applicable for the condition that the material shows creep-ductile behavior, where the creep region near the crack tip is extensively wide compared with the crack propagation rate. In the ASTM E1457-07 standard [17], some specific terms of conditions are defined to ensure the applicability of C* parameter. At first, the total load line displacement rate and the creep load line displacement rate should be in the ratio of V_ c =V_ t Z0:5. This ratio represents the degree of creep area spread. The stress intensity factor K will be the dominant parameter at V_ c =V_ t r0:2. Fig. 15 shows the relationship between the load line displacement rate ratio V_ c =V_ t and the C* parameter. V_ c =V_ t is in the range of 0.81–0.99 at all the duration in all the experiments, and satisfies the condition specified in ASTM E1457-07 [17]. It can be observed that as the value of C* is too high and is greatly accelerated in the tertiary stage, the V_ c =V_ t declines steeply. Therefore, the creep crack growth should not be terminated until the specimen fractures. The specimen should be interrupted when the creep crack growth have been in the accelerated stage for some time. In the tertiary stage, considerable plastic deformation is experienced. As the creep crack propagates, the plastic deformation becomes large. When the plastic deformation exceeds the creep deformation, the creep brittle fracture occurs in the CT specimen. Therefore, in the present study, all tests are interrupted as CCG rate is enough high without the fracture. The second restrictive condition to ensure the applicability of C* is to remove the transient creep crack region from the result data. The transient time tT is defined as follow: tT ¼
K 2 ð1u2 Þ Eðn þ 1ÞC n ðt T Þ
ð11Þ
where C*(tT) is the value of C* at the time of tT. The calculation of tT depends on the value of C*(tT). Because tT cannot be obtained directly, C*(tT) also cannot be obtained explicitly. In ASTM 1457-07 [17], it is recommended that the following procedure must be
Fig. 15. Distribution of load line displacement rate ratio against parameter C*.
L. Zhao et al. / Materials Science & Engineering A 558 (2012) 119–128
127
Table 5 Transient time tT and initiation time ti of creep crack growth test. Specimen
Crack location
Duration time tf (h)
Transient time tT (h)
tT/tf
Initiation time ti (h)
ti/tf
CT1 CT2 CT3 CT4 CT5 CT6
BM WM WM WM FGHAZ Fusion zone
1001 336.5 219.5 45.5 536 214.5
2.65 1.49 0.79 0.11 2.02 0.51
0.0026 0.0044 0.0036 0.0024 0.0038 0.0023
134 85 50 3.5 80 24
0.134 0.253 0.228 0.226 0.149 0.112
used for its estimation. For the time tT, corresponding to each date point, t0 T is calculated using the above equation but substituting C*(t) for C*(tT). tT is then the largest value of t0 T in the entire date set. Table 5 shows the tT, ti and tf of all tests. The creep crack initiation time, ti, is defined as the time to achieve a measurable amount of crack extension. In the current experiments, the time for 0.2 mm crack extension has been determined as the creep crack initiation time ti [13]. It can be noted that tT/tf is sufficiently small. The data before tT have been removed from the figures shown in Section 4.1. During creep crack extension, creep damage known as creep voids gradually accumulates from the beginning of the tests and leads to little crack extension. These phenomena make the crack growth rate change little while the C* is low. As a result, the plotted curves have a tail. It gives rise to a reduced CCG rate at beginning of test, which is less than the steady state creep crack growth rate. This ‘‘tail’’ can be avoided by excluding data prior to the onset of a steady state of damage. In most cases it would appear before the creep crack initiation time [13,27]. In addition, the crack growth life and the creep crack initiation time for fusion zone and FGHAZ specimens are much shorter than those for BM specimens. It can be deduced that the prediction of creep crack initiation time plays an important role in evaluating of fracture life of the welded joints.
Fig. 16. Distribution of stress triaxiality across the specimen with crack in HAZ at various creep crack growth lengths.
5.3. Effect of multiaxial stress for welded joint As analyzed above, the stress concentration in the crack tip may play an important role in the creep crack growth. Hence, in the present study, the variation of the stress distribution in the crack tip of the specimen with HAZ is investigated on the basis of the FEM coupled with continuum damage mechanics. As mentioned in Section 3, a half model is adopted. As shown in Fig. 9, the width of FGHAZ is the same as that of CGHAZ, which is assumed to be 1 mm. A circular arc with 0.025 mm is used to idealize the actual crack tip. The initial cracks are assumed to be located at the FGHAZ/BM interface, CGHAZ/FGHAZ interface and WM/CGHAZ interface, respectively. In these analyses, the initial crack length a0 and the initial K value are assumed to be the same for all the calculated cases, which are 10 mm and 14 MPa m1/2, respectively. Thus, the initial crack depth a0/W and the applied load P for these models are 0.5 and 2050 N, respectively. Fig. 16 shows the variation of stress triaxiality distribution across the welded joint in the center plane of CT specimen with cracks located at the CGHAZ/FGHAZ interface. It can be observed that the highest stress triaxiality is located at the interface before creep crack extension. As the creep crack propagates, the stress triaxiality in the HAZ containing CGHAZ and FGHAZ increases and the location of highest triaxiality moves towards to the FGHAZ. In addition, when the crack length exceeds 1 mm the stress triaxiality increases slowly. This increase is due to the multiaxial stress state induced by the creep deformation. The creep strength of distinct sub-regions in welded joint is different, where the lowest creep strength is in the FGHAZ and the highest creep strength is in the BM. During creep, the deformation of FGHAZ is larger than those of adjacent zones i.e. CGHAZ and base metal. As a result,
Fig. 17. FEM results of creep propagation for specimens with different initial crack locations.
the deformation of FGHAZ is constrained by the adjacent zones, which leads to a high stress triaxiality occurred. The high multiaxial stress will accelerate the creep crack growth rate. The comparison among the creep crack growth behaviors for the CT models with different crack tip positions is clarified in Fig. 17. The results of FEM models with BM and WM material are also given for comparison. It can be observed that the specimen with crack tip located at FGHAZ/BM interface exhibits a high creep crack growth rate compared with those with crack tip located in other microzones of welded joint. It reveals that the
128
L. Zhao et al. / Materials Science & Engineering A 558 (2012) 119–128
creep damage accumulation is accelerated in this interface due to a high constraint in this zone. As a result, in the creep crack tests, the crack growth declines to the FGHAZ/BM interface for the specimens with cracks located at the FGHAZ, as shown in Fig. 3. Compared with the experimental results as shown in Fig. 5, the calculated creep crack growth behaviors in Fig. 17 exhibit a little difference from those of experiment. This is due to the fact that the initial crack length a0 and initial stress intensity factor K in these simulations are set to be different from those of experiment. For the calculated cases they are kept constant, while for the experimental cases they are different from each other. As a rule, high a0 and initial K value would accelerate the creep crack growth and then decline the corresponding creep crack failure life. Hence, some differences between FEM results and experimental data present. However, the above comparison among the calculated creep crack growth behaviors for the specimens with different crack tip positions in the present study are conducted under the same conditions, so the obtained conclusions are reasonable.
6. Conclusions In the present study, a series of creep crack growth tests on the CT specimen for the distinct sub-regions of ASME P92 steel welded joint were carried out at 650 1C. The relationship of creep crack growth rate and parameter C* for the different sub-regions of the welded joint was obtained. It was found that C* could be used to correlate the creep crack growth rate for the microzones of welded joint. Furthermore, the high CCG rate occurred in the specimens with cracks located in the FGHAZ, due to the high constraint and the low creep strength in this zone. At the same value of C*, the CCG rate of the FGHAZ specimen is about two times higher than that of the BM specimen. FEM analysis coupled with continuum damage mechanics was used to predict the creep crack behavior. The calculated creep crack extension behaviors of the BM and WM specimens were in agreement with those of experiment. In addition, the constraint in the crack tip induced by the different material properties around the crack tip played an important role in creep crack growth, which could accelerate the creep damage accumulation. The specimen with crack tip in FGHAZ/BM interface exhibited a higher creep crack growth rate compared with those with crack tip in other microzones of welded joint.
Acknowledgment This research work was financially supported by the Project of the National Natural Science Foundation of China (50805103, 50975196 and 51175375) and Key Project in the Science & Technology Pillar Program of Tianjin (Grant No. 11ZCKFGX03000) and Research Fund for the Doctoral Program of Higher Education of China (20090032110026 and 20110032130002).
References [1] [2] [3] [4]
[5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27]
J.A. Francis, W. Mazur, H.K.D.H. Bhadeshia, ISIJ Int. 44 (2004) 1966–1968. T.-U. Kern, M. Staubli, B. Scarlin, ISIJ Int. 42 (2002) 1515–1519. T. Fujita, Adv. Mater. Process. 141 (1992) 42–45. P.F. Giroux, F. Dallea, M. Sauzay, G. Pereza, I. Tournie, V. Rabeau, J. Malaplate, T. Van Den Berghe, A.F. Fournier, B. Gourgues-Lorenzon, Mater. High Temp. 27 (2010) 29–34. B. Kim, B. Lim, D. Ki, Int. J. Mod. Phys. B 20 (2006) 4231–4236. K. Sawada, K. Kubo, F. Abe, Mater. Sci. Eng. A 319–321 (2001) 784–787. B. Kim, C. Jeong, B. Lim, Mater. Sci. Eng. A 483 (2008) 544–546. K. Shinozaki, H.K. Dejun Li, H. Harada, K. Ohishi, T. Sato, Sci. Technol. Weld. Joining 8 (2003) 289–295. L. Zhao, H.-Y. Jing, L.-Y. Xu, J.-C. An, G.-C. Xiao, D.-L. Xu, Y.-C. Chen, Y. Han, J. Mater. Res. 26 (2011) 934–943. H. Tezuka, T. Sakurai, Int. J. Pres. Ves. Pip. 82 (2005) 165–174. B. Dogan, B. Petrovski, Int. J. Pres. Ves. Pip. 78 (2001) 795–805. R. Sugiura, A.T. Yokobori Jr., M. Tabuchi, T. Yokobori, Eng. Fract. Mech. 74 (2007) 868–881. C.M. Davies, D.W. Dean, K.M. Nikbin, N.P. O’Dowd, Eng. Fract. Mech. 74 (2007) 882–897. S. Maleki, Y. Zhang, K. Nikbin, Eng. Fract. Mech. 77 (2010) 3035–3042. V.A. Vainshtok, M.V. Baumshtein, I.A. Makovetskaya, I.V. Kramarenko, Eng. Fract. Mech. 40 (1991) 1147–1163. K. Sawada, H. Hongo, T. Watanabe, M. Tabuchi, Mater. Charact. 61 (2010) 1097–1102. ASTM E1457-07, Standard Test Method for Measurement of Creep Crack Growth Times in Metals, ASTM, 2007. K.H. Schwalbe, D. Hellmann, J. Test. Eval. 9 (1981) 218–220. G.A. Hartman, D.A. Johnson, Exp. Mech. 27 (1987) 106–112. ABAQUS, Abaqus 6.9 Standard User Manual, ABAQUS, Inc., USA, 2009. S.-T. Tu, P. Segle, J.-M. Gong, Int. J. Pres. Ves. Pip. 81 (2004) 199–209. T.H. Hyde, M. Saber, W. Sun, Eng. Fract. Mech. 77 (2010) 2946–2957. N. Roy, S.C. Bose, R.N. Ghosh, Mater. Sci. Eng. A 527 (2010) 4810–4817. S. Taira, R. Ohtani, T. Kitamura, J. Eng. Mater. Technol. 101 (1979) 154–161, ASME. M. Tabuchi, T. Watanabe, K. Kubo, M. Matsui, J. Kinugawa, F. Abe, Int. J. Pres. Ves. Pip. 78 (2001) 779–784. A.T. Yokobori Jr., S. Takmori, T. Yokobori, Y. Hasegawa, K. Kubota, K. Hidaka, Key Eng. Mater. 171–174 (2000) 131–138. O. Kwon, K.M. Nikbin, G.A. Webster, K.V. Jata, Eng. Fract. Mech. 62 (1999) 33–46.