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Effect of residual stress on creep crack growth behavior in ASME P92 steel
Accepted Manuscript Effect of residual stress on creep crack growth behavior in ASME P92 steel Lei Zhao, Hongyang Jing, Lianyong Xu, Yongdian Han, Junjie Xiu PII: DOI: Reference:
S0013-7944(13)00265-8 http://dx.doi.org/10.1016/j.engfracmech.2013.07.020 EFM 4102
To appear in:
Engineering Fracture Mechanics
Received Date: Revised Date: Accepted Date:
8 July 2012 27 April 2013 23 July 2013
Please cite this article as: Zhao, L., Jing, H., Xu, L., Han, Y., Xiu, J., Effect of residual stress on creep crack growth behavior in ASME P92 steel, Engineering Fracture Mechanics (2013), doi: http://dx.doi.org/10.1016/j.engfracmech. 2013.07.020
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Effect of residual stress on creep crack growth behavior in ASME P92 steel Lei Zhao1, 2, Hongyang Jing1, 2, Lianyong Xu1, 2*, Yongdian Han1, 2 , Junjie Xiu1, 2 1. School of Materials Science and Engineering, Tianjin University, Tianjin 300072, China 2. Tianjin Key Laboratory of Advanced Joining Technology, Tianjin 300072, China * Tel.: +86 022 27402439; fax: +86 022 27402439. *E-mail address：[email protected]
Abstract: Effect of residual stress on creep crack growth behavior in ASME P92 steel was investigated using compact tension (CT) specimen. Tensile residual stresses were generated ahead of crack tip by loading in compression beyond yield and then unloading. The maximum region of residual stress was obtained by numerical simulations which calculated the models with various notch radiuses and penetration loads. After pre-compression, creep crack growth tests were carried out on pre-compressed and original CT specimens to study the effect of residual stress. Furthermore, the corresponding approach on predicting creep crack growth behavior for components with residual stress was also investigated.
Keywords:
residual
stress;
creep
crack
pre-compression; ASME P92 steel.
1
growth;
numerical
simulation;
Nomenclature： a: current crack length b: uncracked ligament length a0: initial crack length r: radial distance from the crack tip In: integration constant in the HRR stress field distribution P: applied load in tests B: specimen thickness Bn: net specimen thickness between the bottoms of side grooves W: specimen width Kp: strain hardening parameters np: strain hardening exponent E: Young’ s modulus υ: Poisson ratio A: coefficient in the power-law creep strain rate expression n: power-law creep stress exponent C*: steady state creep fracture mechanics parameter D, φ : material constants in a correlations with C* K: stress intensity factor rc: creep process zone size tr : time to rupture in a uniaxial creep test t : the current creep time
σ : the stress value at the current creep time Y0: half the distance between the output terminals V0 : initial voltage of specimen before creep 2
V : output value of the potential at any time. MSF : appropriate multiaxial stress factor σy: yield stress σm : hydrostatic stress and a measure of a mean principle stress state σe : equivalent stress σref : reference stress σ22 :stress normal to the crack εe : elastic strain part εp : plastic strain part ε22 :strain normal to the crack
εref : creep strain rate at reference stress K0, σref0 : initial values of K and σref at the creep time of 0 h Kapp : stress intensity factor due to the applied loading Kres : stress intensity factor due to the residual stress Kcomb : combined stress intensity factor ω, ω : creep damage parameter and creep damage rate εf: uniaxial creep failure strain
ε * : multiaxial creep failure strain f
εAc : average creep strain a : creep crack growth rate
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1. Introduction ASME P92 steel as a potential material capable of high creep strength and high corrosion resistance at elevated temperature has been extensively applied in the Ultra Super Critical (USC) Power Plants which operate at 600-650 °C and 30 MPa with the aim of enhancing thermal efficiency and reducing CO2 emission [1, 2]. Components employed in these power generation plants are continually exposed to high temperatures and high steam pressures. Hence, failures such as creep crack growth could occur within these high temperature regimes [3]. In these situations, creep crack growth occurs by nucleation, growth and coalescence of creep voids ahead of crack tip and can impose a limit on the remained service life of P92 steel components. Previous researches studied the creep crack growth properties of ASME P92 steels to assess the reliability of these components at high temperature [4-6]. However, the effect of residual stress on the creep crack growth property of ASME P92 steel has not been studied in detail. Residual stress is inevitable during the fabrication processes for many mechanical or thermal operations. They can be introduced into P92 steel components by bending, forging and welding [7, 8]. The inhomogeneous deformation presents in these processes and could make the material generate plastic formation which is constrained by the surrounding material within elastic formation. The magnitudes of residual stress often exceed the yield strength of material. The residual stresses would be superimposed by any applied loading and generate a complex stress state acting on in-service components. They may significantly affect the load carrying capacity and resistance to creep and fracture for
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these components made of P92 steels [9]. As a result, the creep crack incubation time and propagation time at high temperature are affected and then early creep crack failures may occur [10]. Some of these failures are driven by the residual stress alone while some are driven by the residual stress combined with primary tensile load. In particular, tensile residual stresses combined with external applied tensile stresses can have a detrimental effect on the structural integrity and accelerate the growth of the crack-like defects such as micro-cracks and creep voids. Stress relief heat treatment is often employed to reduce the magnitude of residual stresses, but the residual stress can not be completely removed. Hence, understanding the effect of residual stress on the creep crack growth properties plays an important role in assessing the reliability of high-temperature structural components. The aim of the present study is to investigate the effect of residual stress on the creep crack growth behavior of P92 steel. The residual stress is generated in compact tension (CT) specimen by pre-compressing and then unloading. The maximum zone of tensile residual stress ahead of crack tip is calculated using numerical simulations. Furthermore, the creep crack growth prediction approach considering the effect of residual stress is also studied in order to assess the integrity of P92 steel components at high temperature. 2 Experimental procedures 2.1 Materials The material investigated in the present study is extracted from an ASME P92 steel pipe, with an inner diameter of 390 mm and a thickness of 80 mm. The pipe was
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heat-treated by the following normalizing and tempering. Normalizing was carried out at 1040 °C for 4 h followed by air-cooling. The subsequent tempering was carried out at 960 °C for 11 h. The chemical composition of the studied ASME P92 steel is given in Table 1. 2.2 Specimen In order to introduce a significant hydrostatic tensile residual stress in a simple and repeatable manner, a CT specimen was used in the present study. CT specimens have been normally used in fracture or creep crack growth tests under external tensile loading. The tensile residual stress field can be generated by loading in compression beyond yield and then unloading [8]. In the present study, CT specimen with a thickness of 15 mm was used. The geometry and dimension of the CT specimen adopted is illustrated in Fig. 1. Side-grooves were not introduced into the CT specimen to increase the constraint conditions ahead of crack tip. Although these modifications in the adopted specimens reduced the constraint of the CT specimen at the notch, it was judged that the residual stress field at the mid-thickness plane would be sufficiently triaxial. Hence, it can be used to investigate the effect of residual stress on the creep crack growth behavior. 2.3 Creep crack growth test The first stage of the study is to identify appropriate notch radius and pre-compression load magnitude, which can determine the residual stress distribution. The goal is to obtain a relatively high magnitude of the tensile residual stress over a significant distance ahead of the notch. This is achieved using finite element method
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(FEM) analyses with various notch radiuses and penetration load magnitudes. Subsequently, the CT specimen was machined and then pre-compressed at room temperature with the appropriate notch radius and load magnitude determined from FEM analyses. After pre-compression, a 1.0 mm pre-crack was introduced into the notch of CT specimen with pre-compression (CT1) and that without pre-compression (CT2), respectively. This was achieved by first spark eroding a 0.08 mm wide starter slot to a depth of 0.5 mm into the notch root, and then producing a sharp crack of 0.5 mm at the slot tip by fatigue load cycling at room temperature. On the basis of ASME E1457-07 code [11], these two CT specimens were tested at 650 °C using a lever arm high temperature creep machine. The temperatures were kept within ±1 °C during test. The experimental conditions are shown in Table 2. The creep crack growth length was measured by an electrical potential method. An electric current was applied to the specimen and then the value of an electric potential drop was measured. The creep crack growth length is usually calculated using Johnson’s equation for CT specimen [12, 13], as shown in follow:
a=
cosh ( π Y0 2W ) cos −1 π cosh (V / V0 ) cosh −1 ( cosh (π Y0 2W ) / cos ( π a0 2W ) )
2W
(1)
3. Finite element method analysis 3.1 FEM model The tensile crack-opening residual stress field was introduced in the vicinity of the notch of the CT specimens using a pre-conditioning compression treatment. Turski [8] had reported that the extent of the tensile residual stress field can be maximized by increasing the notch radius and the pre-compression load. In order to obtain the 7
maximum extent of the tensile residual stress field in the notch region, FEM simulations were carried out to determine the appropriate notch radius and pre-compression load. The commercial FEM software ABAQUS was used for all FEM analyses. It was assumed that there were two symmetry planes along the ligament and the mid-thickness plane in the CT specimen. Consequently, a one-quarter geometry of the CT specimen was modeled using first order (linear) interpolation 8-node hexahedral brick elements with reduced integration and hourglass control (ABAQUS C3D8R), as shown in Fig. 2. The finite element mesh is refined in the vicinity of notch tip to obtain accurate results and to eliminate mesh dependency effects in the analyses. The smallest size is 20 µm, which is designed according to the average grain size of P92 steel and this size has previously obtained accurate creep crack growth prediction for CT specimens of carbon manganese steel [14]. An analytical rigid body was used to simulate the punch tool in the FEM model to apply the compression load. A concentrated force was applied at the center of the rigid body in the 2 direction to simulate the punching process and then unloaded. The rigid body was constrained in all directions except the 2 direction of the CT model. Frictionless contact was assumed between the rigid body and the CT model. The symmetry boundary conditions were applied on the mid-thickness plane and the ligament plane of CT specimen. The pre-crack of CT specimen is carried out by releasing the constraint of the elements on the ligament during FEM analysis. 3.2 Constitutive material behavior
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During the pre-compression process, the plastic deformation occurs in CT specimen. Hence, an elastic-plastic analysis is carried out to simulate the pre-compression process. In this paper, the material is assumed to be isotropic and homogenous and the plastic deformation is assumed to follow the von Mises flow theory with power-hardening relationship, which can be written as follows:
σ = Eε e + K p ( ε p )
np
(2)
where εe and εp demonstrate the elastic and plastic parts, respectively; Kp is the power-hardening parameter; np is the strain hardening exponent. The mechanical properties of ASME P92 steel at room temperature and at 650 °C employed in the present study are shown in Table 3. The temperature dependent material properties provided in Table 3 at 650 °C are used for the subsequent thermal exposure and creep analyses. After the residual stress fields were introduced into the CT specimens, creep crack growth tests were carried out on these specimens to investigate the effect of residual stress. Hence, the relaxation of residual stress and the accumulation of creep damage ahead of crack tip during creep crack growth process were also investigated using FEM analyses. An elastic-plastic power creep law is employed, and the average creep strain rate ε Ac is employed and is given by [15]:
εAc =
εf = Aσ en tr
(3)
At 650 °C, for ASME P92 steel, A is 2.6353E-16 MPa-n/h and n is 5.23, which are determined from the relationship between the average creep strain rate and stress level obtained from the corresponding uniaxial creep tests that were carried out on samples 9
taken from the same ASME P92 steel pipe [16]. In order to study the creep damage accumulation and to predict the creep crack growth behavior, an uncoupled single damage theory based on the creep ductility exhaustion approach is adopted [17]. The damage rate ω is defined to depend on the equivalent creep strain rate ε c as shown:
ω =
ε c ε c = ε *f MSFε f
(4)
where ε *f is the critical multiaxial failure strain, which depends on the uniaxial creep fracture strain ε f and the appropriate multiaxial stress factor MSF. ε f depends on the material and is 18 % for the present ASME P92 steel, which is the measured value of uniaxial creep tests. The form of the MSF can be written as [18]:
ε *f n − 0.5 σ m 2 n − 0.5 MSF = = sinh sinh 2 εf 3 n + 0.5 n + 0.5 σ e
(5)
Furthermore, the total damage at any time is calculated from the time integral of creep damage rate:
ε c dt 0 ε* f
t
ω = ∫ ω dt = ∫ 0
t
(6)
When the creep damage of an integration point reaches to 0.999, this point is assumed to be failed. Then, the elastic modulus of this point is set to zero and the remaining forces exerted by the adjacent nodes are relaxed to zero. This creep damage model was implemented in the ABAQUS using the corresponding user defined subroutines [19]. Besides, it can be noted that the creep deformation is independent of the creep damage accumulation, which means that the creep strain rate can not be accelerated by the damage evolution. Hence, the convergence problems are reduced 10
and the very high strain rates are avoided during the FEM analyses when the damage approaches unity. 4. Results and discussion 4.1 Effect of notch radius on the residual stress The FEM models with various notch radiuses of 1, 1.5 and 2.5 mm are calculated, respectively. The peak load applied on the punch tool is 36 kN for three cases. During the pre-compression process, after the required load is applied, the cylinder is raised and then the specimen is unloaded. If the compressive load is sufficiently high, the material near the notch undergoes yielding in compression followed by elastic unloading. The normalized stress-strain response for the first element in the crack tip during the pre-compression process is shown in Fig. 3, where σ22 is the stress normal to the crack, ε22 is the strain normal to the crack and σy is the yield stress at room temperature. As shown in Fig. 3, it can be observed that the yield in compression is followed by the yield in tension and finally the plastic deformation is generated in the crack tip region. The variations of tensile residual stress distribution in the mid-thickness plane of the specimen with the increasing notch radius are shown in Fig. 4. It can be noted that as the notch radius increases, the value of the peak σ22 decreases while the size of tensile residual stress region in the crack notch increases. The maximum peak σ22 is approximately 1.5 σy. The tensile residual stresses zone increases from 2.0 mm to 3.0 mm as the notch radius increases from 1 mm to 2.5 mm. In addition, the peak σ22 is located at about 0.5 mm away from crack tip, which is independent of the notch
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radius. The corresponding magnitude of stress triaxiality ahead of crack tip with different notch radiuses is shown in Fig. 5. As a rule, stress triaxiality can be used to demonstrate the constraint condition. It can be seen that the highest stress triaxiality is located in the specimen with a small notch radius, which corresponds to the maximum peak tensile residual stress location as shown in Fig. 4. This phenomenon means that a small notch radius can cause a high constraint ahead of crack tip. The peak stress triaxiality is also located at about 0.5 mm ahead of the crack tip irrespective of the notch radius. The residual stress distribution in the specimen with notch radius of 2.5 mm and peak penetration load of 36 kN through the thickness of the specimen is shown in Fig. 6. It reveals that the tensile residual stress is generated in the whole crack tip region. However, the peak tensile residual stress decreases from the center plane to the outer surface. 4.2 Effect of penetration load on the residual stress The effect of maximum penetration load on the tensile residual stress in the crack tip was also explored. It can be noted that the extent of the tensile residual stress in the model with notch radius of 2.5 mm is largest. Therefore, the model with 2.5 mm notch radius is adopted and the peak penetration loads are 24, 31, 34, 36, 38, and 41 kN, respectively. The peak load depends on the penetration depth. The residual stress distributions in the crack tip with different maximum penetration loads are shown in Fig. 7. It can be observed that the peak value and the region of the tensile residual stress increase as the applied load increases from 24 to
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36 kN. The peak stress in the specimen after 36 kN pre-compression is near two times as that of yield strength at room temperature. When the stress exceeds 36 kN, only the peak stress increases while the size of the tensile residual stress region changes little. Fig. 8 shows the stress triaxiality distribution ahead of crack tip with different penetration loads. The stress triaxiality increases as the penetration load increases. In addition, the stress triaxiality changes little when the penetration stress exceeds 36 kN. 4.3 Effect of temperature on the residual stress After pre-compression, the creep crack growth tests at high temperature would be carried out on CT specimens, where creep deformation would be dominant ahead of crack tip. Hence, the effect of the temperature on the residual stress was investigated. Following pre-compression, the specimen is heated up to high temperature of 650 °C. Fig. 9 shows the variation of residual stress distribution in the specimen when it is heated from 20 to 650 °C. Due to the reduction in yield strength at high temperature as shown in Table 3, it leads to an instantaneous reduction in the residual stress. However, the peak residual stress is still about 1.5 times as the yield strength at 650 °C, the response of which is similar to that at room temperature. This demonstrates that the residual stress remains after heated to high temperature. 4.4 Effect of residual stress on the creep crack growth According to the above analysis, the peak penetration load of 36 kN and the notch radius of 2.5 mm are adopted for the pre-compressing process, which can be employed to generate the largest extent tensile residual stress in the notch tip. Two CT
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specimens are employed in this paper. The initial crack length and initial stress intensity factor for all of the cases are kept constant to assure the same experimental condition, which are 11 mm and 15 MPam1/2, respectively. The variation of the penetration load versus the load line displacement during the pre-compression process is shown in Fig. 10, where the FEM result is also given for comparison. The response of load as the load line displacement increases for experiment and FEM is the same, which demonstrates that the numerical simulation results are reasonable. Turski [8] and Withers [20] had also reported that the FEM predicted residual stress distributions were in excellent agreement with that measured by X-ray synchrotron diffraction. As a rule, the residual stress is the stress that remains after the original cause of the stresses (external forces, heat gradient) has been removed. Residual stresses occur for a variety of reasons, including inelastic (plastic) deformations, temperature gradients (during heat treatment) or structural changes (phase transformation). In this paper, the residual stress is introduced into the CT specimen through pre-compression and then unloading. This approach is simple and repeatable. The residual stress is generated due to the plastic deformation and the accuracy of the residual stress magnitude mainly depends on the elastic-plastic property, which can be accurately obtained from the tensile tests. Hence, the calculated residual stress through FEM can be employed to represent the actual residual stress distribution and to investigate its effect on the creep crack growth. Following pre-compression, the creep crack growth tests were conducted. If the pre-compressed CT specimen is maintained at 650 °C with no external applied tensile
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load, the residual stresses ahead of crack tip would gradually relax to a smaller value, as shown in Fig. 11. In particular, the deep decline of stress occurs within 100 h. Finally, the strains in the specimen would be completely converted into creep strains. It can be deduced that the residual stress only affects the creep crack initiation stage, which was also reported by Webster [21]. Hence, in the present study, the effect of residual stress on the creep crack growth behavior focuses on the creep crack initiation stage. During creep crack growth test, as the creep crack growth length reaches to the specified length, the test will be interrupted. Fig. 12 illustrates the variation of creep crack growth length against time for pre-compressed and original CT specimens. It can be observed that the creep crack growth rate of the specimen with residual stress is much higher than that of the specimen without residual stress. For the specimen without pre-compression, the creep crack growth length increases little when the creep time is less than 400 h while for the specimen with pre-compression the creep crack growth length grows to about 0.7 mm. Figs. 13 (a) and (b) shows the variation of stress ahead of crack tip for CT1 and CT2 specimens during creep. It can be noted that as the creep time increases the stress gradually relaxes due to creep deformation. When the creep time increases from 0 h to 10000 h, the peak stress at crack tip of CT1 specimen relaxes from 450 to 200 MPa while the peak stress of CT2 specimen relaxes from 360 to 200 MPa. This demonstrates that the peak stress of CT1 specimen with residual stress is higher than that of CT2 specimen. In addition, the difference of the stress distribution between CT1 and CT2 specimens mainly occurs when the creep time is less than 100 h, which
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corresponds to the steep decline stage of stress. As the creep time exceeds 100 h, the difference of the stress distribution between CT1 and CT2 specimens is insignificant. This phenomenon also reveals that the residual stress only affect the creep crack initiation stage. The applied tensile stress combined with tensile residual stress enhances the stress level ahead of crack tip. Hence, the stress level and the stress triaxiality ahead of crack tip in the specimen with pre-compression are higher than those in the specimen without pre-compression. The high stress and stress triaxiality can accelerate the diffusion of vacancies, which is the major reason to the creep voids nucleation [22, 23]. Then, the nucleation, growth and coalescence of creep voids ahead of crack tip are accelerated. As a result, the creep damage accumulation is accelerated, which leads to a high creep crack growth rate. Furthermore, plastic deformation can reduce the creep resistance and the creep ductility [24, 25], which also accelerates the creep damage accumulation further. Due to the accelerated creep damage accumulation, the creep crack initiation time is declined. Fig.14 shows the comparison of the creep crack behavior between FEM results and experimental data. It can be observed that the creep crack growth tendency is accurately demonstrated by the FEM results. At beginning, the calculated creep crack growth behavior exhibits a good agreement with the corresponding experimental data. Nevertheless, as the creep increases further, the calculated creep crack growth length for CT specimen with residual stress is smaller than that of experimental result while that for CT specimen without residual stress is higher than that of corresponding experiment data. This may be ascribed to two reasons. Firstly, the residual stress in
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FEM relaxes more quickly than that in experimental CT specimen due to the average creep strain rate employed to demonstrate the whole creep curve. Secondly, the material of FEM is assumed to be isotropic and homogenous while the material of the experimental CT specimen owns inhomogeneity. Furthermore, the phenomenon that the creep crack growth behavior will be accelerated as the residual stress remains in the CT specimen is also clearly observed. 4.5 Predicting creep crack growth behavior with residual stress As a rule, the C* is always used to correlate the creep crack growth behavior [15, 26]. For the aim of understanding the effect of residual stress on the creep crack, it is necessary to interpret the variation of C* during creep crack process. Parameter C* can be determined in the terms of a reference stress σref and the stress intensity factor K as follows [27]:
C* = σ ref εref R′ K R′ = σ ref
(7)
2
(8)
where εref is the creep strain rate at the reference stress. The value of R′ depends on the stress distribution ahead of crack tip and the specimen geometry and the crack length. Because K and σref are determined by the stress magnitude ahead of crack tip, the value of K and σref both decline as the stress relaxes during creep. In general, K is proportional to the stress magnitude ahead of crack tip. Hence, it can be assumed that the value of R′ nearly keeps constant during creep crack growth process, which can be calculated by:
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K R′ = 0 σ ref 0
2
(9)
where K0 and σref0 are the initial value of K and σref at the creep time of 0 h, respectively. For the specimens with residual stress, Webster [21] had proposed that a combined stress intensity factor K, due to the applied loading Kapp and that due to the residual stress distribution Kres, was employed to demonstrate the stress level ahead of crack tip, which is defined as follows: K = K app + K res
(10)
In the present study, Kapp is 15 MPam1/2. Kres is directly determined from the FEM results of the CT specimen only with residual stress. The distribution of Kres through the thickness of the CT specimen only with residual stress at 650 °C is shown in Fig. 15. The Kres is calculated after the pre-cracking and heating to 650 °C, where the relaxation of the residual stress occurs. The Kres is not a constant value and varies across the thickness and the peak value is located at a distance from the center plane, which is also observed in literature [10]. Hence, it is assumed that an average value of Kres of 13.6 MPam1/2 is employed to represent the stress intensity level ahead of crack
tip. In addition, the σref0 is also obtained from the FEM results. Because the creep crack growth process is mainly determined by the tensile stress field ahead of crack tip, the average value of the tensile residual stress magnitude ahead of crack tip is employed to represent the reference stress level of the CT specimen [10]. The average stress across the tensile stress field as shown in Fig. 15 (a) is 230 MPa. The stress would relax during creep, as shown in Fig. 11. For the material 18
obeying the power creep law, the stress relief would obey [10]:
σ = σ 0 [1 + AE ( n-1) σ 0n −1t ]1/( n−1)
(11)
where σ 0 is the initial stress value at the creep time of 0 h; t is the current creep time;
σ is the stress value at the current creep time. Fig. 16 shows the relaxation of the reference stress σref0 of 230 MPa during creep process. It can be observed that most of the stress relief occurs in the primary creep stage, the creep time of which is less than 1000 h. As defined in Eq.7, the C* also relaxes as the creep time increases. According to the high temperature fracture mechanics, the creep crack growth rate can be determined in the terms of C* by an expression of form [28]： φ
a = D0 ( C *)
(12)
For ASME P92 steel at 650 °C, D0 is 0.0141 and φ is 0.8606. The creep crack growth at any time can be obtained from the time integral of creep crack growth rate. The comparison of the predicted creep crack growth length and the experimental result for the CT specimen with residual stress is shown in Fig. 17. It can be observed that the predicted creep growth curve has the similar shape as that of experiment but the predicted creep length is larger than that of experiment at the same creep time. This phenomenon demonstrates that this method overestimates the creep crack growth rate. As stated in the above, the crucial feature of the creep crack growth prediction is to obtain the reliable K and σref0 value. After heated to 650 °C, the residual stress is higher than the yield stress. In addition, when the external tensile load is applied on the CT specimen with residual stress, the plastic deformation must occur ahead of
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crack tip and the corresponding increase of the stress is not linear. Hence, the combined stress intensity K defined as the summation of Kapp and Kres has limitation on the assessment of remained creep life. Under plastic deformation, it would overestimate the stress intensity level ahead of crack tip. To obtain a more accurate estimation of creep crack growth behavior, a modified approach is employed. In this approach, it is assumed that the combined K should be directly determined from the calculated stress field of the FEM model with residual stress and external applied load. Fig. 18 shows the distribution of the combined K through the thickness for the CT1 specimen with residual stress. The average value of Kcomb is about 18.7 MPam1/2, which is less than the summation of Kapp and Kres. The corresponding predicted creep crack growth length versus creep time is shown in Fig. 19. It is apparent from this figure that the predicted creep crack curve using Kcomb value directly obtained from FEM result is more accurate. At the same creep time, the predicted creep crack growth is a little higher than that of experiment. Hence, it can be concluded that the modified method is reasonable. 6. Conclusions In this work, the effect of tensile residual stresses that were introduced in CT specimen by pre-compression on the creep crack growth properties of ASME P92 steel at 650 °C was investigated by numerical simulation and experiment. (1) A three dimensional FEM analysis of the pre-compression on the CT specimen with various notch radiuses and penetration loads was performed. The FEM results revealed that the extent of tensile stress region ahead of crack tip increased as
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the notch radius and the penetration load increased. The largest extent was obtained as the notch radius was 2.5 mm and the peak penetration load was 36 kN. The largest region of tensile residual stress ahead of crack tip was about 3 mm and the peak tensile residual stress value was about 1.5 times as yield strength at room temperature. In addition, the tensile residual stress presented in the whole CT specimen, where the value of the mid-thickness plane was higher than that of the outer surface. (2) After the CT specimen was heated to 650 °C, the value of tensile residual stress decreased, but the extent of tensile residual field changed little. The peak tensile residual stress value was 1.5 times as yield strength at 650 °C. During creep, the stress relaxed greatly in the initial creep stage. Hence, the residual stress had great influences on the creep crack initiation stage. (3) Creep crack growth tests revealed that CT specimen with tensile residual stress and external applied stress exhibited a fast creep crack growth tendency compared with CT specimen only with the external applied stress. This was due to the fact that a high tensile stress state ahead of crack tip could stimulate the nucleation, growth and coalescence of creep voids and even could decline the creep ductility. As a result, the creep damage accumulation ahead of crack tip was accelerated. (4) A prediction approach on the basis of the combined K and the reference stress σref directly obtained from the FEM results could be employed to give a more accurate
creep crack growth prediction for the components with residual stress. Acknowledgement: This research work was financially supported by the Project of the National
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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). Reference: [1] Vaillant JC, Vandenberghe B, Hahn B, Heuser H, Jochum C. T/P23, 24, 911 and 92: New grades for advanced coal-fired power plants--Properties and experience. Int J Pres Ves Pip. 2008;85:38-46. [2] Kern T-U, Staubli M, Scarlin B. The European efforts in material development for 650°C USC power plants - COST522. ISIJ Int. 2002;42:1515-9. [3] Davies C, Odowd N, Nikbin K, Webster G. An analytical and computational study of crack initiation under transient creep conditions. Int J Solids Struct. 2007;44:1823-43. [4] Sugiura R, Toshimitsu Yokobori Jr A, Suzuki K, Tabuchi M. Characterization of incubation time on creep crack growth for weldments of P92. Eng Fract Mech. 2010;77:3053-65. [5] Yatomi M, Fuji A, Tabuchi M, Hasegawa Y, Kobayashi KiI, Yokobori T. Evaluation of creep crack growth rate of P92 welds using fracture mechanics parameters. Journal of Pressure Vessel Technology. 2010;132:041404 (8 pp.). [6] Sawada K, Hongo H, Watanabe T, Tabuchi M. Analysis of the microstructure near the crack tip of ASME Gr.92 steel after creep crack growth. Mater Charact. 2010;61:1097-102.
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[7] Lee H, Biglari F, Wimpory R, Nikbin K. Treatment of residual stress in failure assessment procedure. Eng Fract Mech. 2006;73:1755-71. [8] Turski M, Bouchard PJ, Steuwer A, Withers PJ. Residual stress driven creep cracking in AISI Type 316 stainless steel. Acta Mater. 2008;56:3598-612. [9] Soanes T, Bell W, Vibert A. Optimising residual stresses at a repair in a steam header to tube plate weld. Int J Pres Ves Pip. 2005;82:311-8. [10] Webster GA, Davies CM, Nikbin KM. Assessment of creep crack growth due to stress relief. Int J Solids Struct. 2010;47:881-6. [11] ASTM. ASTM E1457-07. Standard Test Method for Measurement of Creep Crack Growth Times in Metals. United States:West Conshohocken: ASTM International; 2007. p. 1012-35. [12] Saxena A. Electrical potential technique for monitoring subcritical crack growth at elevated temperatures. Eng Fract Mech. 1980;13:741-50. [13] Schwalbe KH, Hellmann D. Application of the electrical potential method to crack length measurements using Johnson's formula. J Test Eval. 1981;9:218-20. [14] Yatomi M, O'Dowd NP, Nikbin KM, Webster GA. Theoretical and numerical modelling of creep crack growth in a carbon-manganese steel. Eng Fract Mech. 2006;73:1158-75. [15] Yatomi M, Tabuchi M. Issues relating to numerical modelling of creep crack growth. Eng Fract Mech. 2010;77:3043-52. [16] Zhao L, Jing H, Xu L, An J, Xiao G. Numerical investigation of factors affecting creep damage accumulation in ASME P92 steel welded joint. Mater Design.
23
2012;34:566-75. [17] Nikbin KM, Smith DJ, Webster GA. Prediction of Creep Crack Growth from Uniaxial Creep Data. Proceedings of The Royal Society of London, Series A: Mathematical and Physical Sciences. 1984;396:183-97. [18] Cocks ACF, Ashby MF. Intergranular fracture during power-law creep under multiaxial stresses. Met Sci. 1980;14:395-402. [19] ABAQUS. Abaqus 6.9 standard user manual. USA: ABAQUS, Inc; 2009. [20] Withers PJ, Turski M, Edwards L, Bouchard PJ, Buttle DJ. Recent advances in residual stress measurement. Int J Pres Ves Pip. 2008;85:118-27. [21] Webster GA. Trends in high temperature structural integrity assessment. Journal of ASTM International. 2006;3. [22] Li D, Shinozaki K, Kuroki H. Stress-strain analysis of creep deterioration in heat affected weld zone in high Cr ferritic heat resistant steel. Mater Sci Technol. 2003;19:1253-60. [23] Tabuchi M, Ha J, Hongo H, Watanabe T, Yokobori T. Experimental and numerical study on the relationship between creep crack growth properties and fracture
mechanisms.
Metallurgical
and
Materials
Transactions
A.
2004;35:1757-64. [24] Loveday MS, Dyson BF. Prestrain-induced particle microcracking and creep cavitation in IN597. Acta Metall. 1983;31:397-405. [25] Willis M, McDonaugh-Smith A, Hales R. Prestrain effects on creep ductility of a 316 stainless steel light forging. Int J Pres Ves Pip. 1999;76:355-9.
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[26] Yamamoto M, Miura N, Ogata T. Applicability of C* parameter in assessing Type IV creep cracking in Mod. 9Cr-1Mo steel welded joint. Eng Fract Mech. 2010;77:3022-34. [27] Ainsworth RA. Practical aspects of the calculation and application of C*. Mater High Temp. 1992;10:119-26. [28] Yatomi M, Yokobori Jr AT, Nikbin KM. Comparison of two creep crack growth parameters, C* and Q*, with FE analysis. Strength Fract Complex. 2006;4:83-92.
25
Table captions: Table 1 Chemical composition of used ASME P92 steel in wt. %. Table 2 Experimental conditions of creep crack growth tests. Table 3 Mechanical properties of ASME P92 steel at room temperature and 650 °C. Figure captions: Fig. 1 Geometry and dimension of the designed CT specimen. Fig. 2 One quarter FEM model of the used CT specimen. Fig. 3 Response of normalized stress against strain during pre-compression process. Fig. 4 Residual stress distribution after pre-compression of the FEM models with different notch radiuses. Fig. 5 Stress triaxiality distribution after pre-compression of the FEM models with different notch radiuses. Fig. 6 Residual stress distribution across the thickness of the specimen. Fig. 7 Normalized residual stress distribution after pre-compression of the FEM models with different penetration loads. Fig. 8 Stress triaxiality distribution after pre-compression of the FEM models with different penetration loads. Fig. 9 Variation of residual stress distribution in the specimen heated from 20 °C to 650 °C. Fig. 10 Comparison of the development of the load line displacement between experimental data and FEM result. Fig. 11 Response of stress against the time during the pre-compression, heated and
26
followed creep processes. Fig. 12 Comparison of creep crack growth behavior for the pre-compressed and original CT specimens. Fig. 13 Stress relaxation during creep process for (a) CT1 specimen with tensile residual stress and external applied stress and (b) CT2 specimen only with external applied stress. Fig. 14 Comparison of creep crack growth behavior between FEM calculated results and experimental data. Fig. 15 Stress intensity factor K distribution across the thickness of CT specimen only with residual stress. Fig. 16 Relaxation of reference stress σref0 of 230 MPa during creep process. Fig. 17 Comparison of the creep crack growth length for prediction and experiment using the combined K determined by the summation of Kapp and Kres. Fig.18 Stress intensity factor K distribution across the thickness of CT specimen with residual stress and external applied stress. Fig. 19 Comparison of the creep crack growth length for prediction and experiment using the combined K determined by the FEM results.
27
Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6
Figure 7
Figure 8
Figure 9
Figure 10
Figure 11
Figure 12
Figure 13(a)
Figure 13(b)
Figure 14
Figure 15
Figure 16
Figure 17
Figure 18
Figure 19
Table 1 Chemical composition of used ASME P92 steel in wt. %. Material
C
Si
Mn
S
P
Cr
Ni
Mo
W
V
Nb
B
Al
N
Bal.
P92 steel
0.10
0.47
0.40
0.001
0.008
8.77
0.12
0.38
1.48
0.16
0.054
0.001
0.02
0.043
Fe
Table 2 Experimental conditions of creep crack growth tests. Specimen
a0 (mm)
W (mm)
B (mm)
K (MPam1/2)
P (N)
CT1
11.08
30
15.08
15
5824
CT2
11.02
30
15.08
15
5830
Table 3 Mechanical properties of ASME P92 steel at room temperature and 650 °C. Temperature Elastic modulus E (MPa) Poisson ratio υ Yield strength σy (MPa) Ultimate strength σu (MPa) Material coefficient Kp (MPa) Strain hardening exponent np
20 °C
650 °C
206000 110000 0.3 0.3 402 180 625 280 861 311 0.155 0.0657
Research Highlights: 1) Residual stress was generated in CT specimen notch using pre-compression. 2) Maximum extent of tensile residual stress in CT specimen was obtained by FEM. 3) Residual stress combined with external stress led to a fast creep crack growth. 4) Effect of residual stress on creep damage evolution was studied. 5) Predicting creep crack growth for specimen with residual stress was studied.
S0013-7944(13)00265-8 http://dx.doi.org/10.1016/j.engfracmech.2013.07.020 EFM 4102
To appear in:
Engineering Fracture Mechanics
Received Date: Revised Date: Accepted Date:
8 July 2012 27 April 2013 23 July 2013
Please cite this article as: Zhao, L., Jing, H., Xu, L., Han, Y., Xiu, J., Effect of residual stress on creep crack growth behavior in ASME P92 steel, Engineering Fracture Mechanics (2013), doi: http://dx.doi.org/10.1016/j.engfracmech. 2013.07.020
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Effect of residual stress on creep crack growth behavior in ASME P92 steel Lei Zhao1, 2, Hongyang Jing1, 2, Lianyong Xu1, 2*, Yongdian Han1, 2 , Junjie Xiu1, 2 1. School of Materials Science and Engineering, Tianjin University, Tianjin 300072, China 2. Tianjin Key Laboratory of Advanced Joining Technology, Tianjin 300072, China * Tel.: +86 022 27402439; fax: +86 022 27402439. *E-mail address：[email protected]
Abstract: Effect of residual stress on creep crack growth behavior in ASME P92 steel was investigated using compact tension (CT) specimen. Tensile residual stresses were generated ahead of crack tip by loading in compression beyond yield and then unloading. The maximum region of residual stress was obtained by numerical simulations which calculated the models with various notch radiuses and penetration loads. After pre-compression, creep crack growth tests were carried out on pre-compressed and original CT specimens to study the effect of residual stress. Furthermore, the corresponding approach on predicting creep crack growth behavior for components with residual stress was also investigated.
Keywords:
residual
stress;
creep
crack
pre-compression; ASME P92 steel.
1
growth;
numerical
simulation;
Nomenclature： a: current crack length b: uncracked ligament length a0: initial crack length r: radial distance from the crack tip In: integration constant in the HRR stress field distribution P: applied load in tests B: specimen thickness Bn: net specimen thickness between the bottoms of side grooves W: specimen width Kp: strain hardening parameters np: strain hardening exponent E: Young’ s modulus υ: Poisson ratio A: coefficient in the power-law creep strain rate expression n: power-law creep stress exponent C*: steady state creep fracture mechanics parameter D, φ : material constants in a correlations with C* K: stress intensity factor rc: creep process zone size tr : time to rupture in a uniaxial creep test t : the current creep time
σ : the stress value at the current creep time Y0: half the distance between the output terminals V0 : initial voltage of specimen before creep 2
V : output value of the potential at any time. MSF : appropriate multiaxial stress factor σy: yield stress σm : hydrostatic stress and a measure of a mean principle stress state σe : equivalent stress σref : reference stress σ22 :stress normal to the crack εe : elastic strain part εp : plastic strain part ε22 :strain normal to the crack
εref : creep strain rate at reference stress K0, σref0 : initial values of K and σref at the creep time of 0 h Kapp : stress intensity factor due to the applied loading Kres : stress intensity factor due to the residual stress Kcomb : combined stress intensity factor ω, ω : creep damage parameter and creep damage rate εf: uniaxial creep failure strain
ε * : multiaxial creep failure strain f
εAc : average creep strain a : creep crack growth rate
3
1. Introduction ASME P92 steel as a potential material capable of high creep strength and high corrosion resistance at elevated temperature has been extensively applied in the Ultra Super Critical (USC) Power Plants which operate at 600-650 °C and 30 MPa with the aim of enhancing thermal efficiency and reducing CO2 emission [1, 2]. Components employed in these power generation plants are continually exposed to high temperatures and high steam pressures. Hence, failures such as creep crack growth could occur within these high temperature regimes [3]. In these situations, creep crack growth occurs by nucleation, growth and coalescence of creep voids ahead of crack tip and can impose a limit on the remained service life of P92 steel components. Previous researches studied the creep crack growth properties of ASME P92 steels to assess the reliability of these components at high temperature [4-6]. However, the effect of residual stress on the creep crack growth property of ASME P92 steel has not been studied in detail. Residual stress is inevitable during the fabrication processes for many mechanical or thermal operations. They can be introduced into P92 steel components by bending, forging and welding [7, 8]. The inhomogeneous deformation presents in these processes and could make the material generate plastic formation which is constrained by the surrounding material within elastic formation. The magnitudes of residual stress often exceed the yield strength of material. The residual stresses would be superimposed by any applied loading and generate a complex stress state acting on in-service components. They may significantly affect the load carrying capacity and resistance to creep and fracture for
4
these components made of P92 steels [9]. As a result, the creep crack incubation time and propagation time at high temperature are affected and then early creep crack failures may occur [10]. Some of these failures are driven by the residual stress alone while some are driven by the residual stress combined with primary tensile load. In particular, tensile residual stresses combined with external applied tensile stresses can have a detrimental effect on the structural integrity and accelerate the growth of the crack-like defects such as micro-cracks and creep voids. Stress relief heat treatment is often employed to reduce the magnitude of residual stresses, but the residual stress can not be completely removed. Hence, understanding the effect of residual stress on the creep crack growth properties plays an important role in assessing the reliability of high-temperature structural components. The aim of the present study is to investigate the effect of residual stress on the creep crack growth behavior of P92 steel. The residual stress is generated in compact tension (CT) specimen by pre-compressing and then unloading. The maximum zone of tensile residual stress ahead of crack tip is calculated using numerical simulations. Furthermore, the creep crack growth prediction approach considering the effect of residual stress is also studied in order to assess the integrity of P92 steel components at high temperature. 2 Experimental procedures 2.1 Materials The material investigated in the present study is extracted from an ASME P92 steel pipe, with an inner diameter of 390 mm and a thickness of 80 mm. The pipe was
5
heat-treated by the following normalizing and tempering. Normalizing was carried out at 1040 °C for 4 h followed by air-cooling. The subsequent tempering was carried out at 960 °C for 11 h. The chemical composition of the studied ASME P92 steel is given in Table 1. 2.2 Specimen In order to introduce a significant hydrostatic tensile residual stress in a simple and repeatable manner, a CT specimen was used in the present study. CT specimens have been normally used in fracture or creep crack growth tests under external tensile loading. The tensile residual stress field can be generated by loading in compression beyond yield and then unloading [8]. In the present study, CT specimen with a thickness of 15 mm was used. The geometry and dimension of the CT specimen adopted is illustrated in Fig. 1. Side-grooves were not introduced into the CT specimen to increase the constraint conditions ahead of crack tip. Although these modifications in the adopted specimens reduced the constraint of the CT specimen at the notch, it was judged that the residual stress field at the mid-thickness plane would be sufficiently triaxial. Hence, it can be used to investigate the effect of residual stress on the creep crack growth behavior. 2.3 Creep crack growth test The first stage of the study is to identify appropriate notch radius and pre-compression load magnitude, which can determine the residual stress distribution. The goal is to obtain a relatively high magnitude of the tensile residual stress over a significant distance ahead of the notch. This is achieved using finite element method
6
(FEM) analyses with various notch radiuses and penetration load magnitudes. Subsequently, the CT specimen was machined and then pre-compressed at room temperature with the appropriate notch radius and load magnitude determined from FEM analyses. After pre-compression, a 1.0 mm pre-crack was introduced into the notch of CT specimen with pre-compression (CT1) and that without pre-compression (CT2), respectively. This was achieved by first spark eroding a 0.08 mm wide starter slot to a depth of 0.5 mm into the notch root, and then producing a sharp crack of 0.5 mm at the slot tip by fatigue load cycling at room temperature. On the basis of ASME E1457-07 code [11], these two CT specimens were tested at 650 °C using a lever arm high temperature creep machine. The temperatures were kept within ±1 °C during test. The experimental conditions are shown in Table 2. The creep crack growth length was measured by an electrical potential method. An electric current was applied to the specimen and then the value of an electric potential drop was measured. The creep crack growth length is usually calculated using Johnson’s equation for CT specimen [12, 13], as shown in follow:
a=
cosh ( π Y0 2W ) cos −1 π cosh (V / V0 ) cosh −1 ( cosh (π Y0 2W ) / cos ( π a0 2W ) )
2W
(1)
3. Finite element method analysis 3.1 FEM model The tensile crack-opening residual stress field was introduced in the vicinity of the notch of the CT specimens using a pre-conditioning compression treatment. Turski [8] had reported that the extent of the tensile residual stress field can be maximized by increasing the notch radius and the pre-compression load. In order to obtain the 7
maximum extent of the tensile residual stress field in the notch region, FEM simulations were carried out to determine the appropriate notch radius and pre-compression load. The commercial FEM software ABAQUS was used for all FEM analyses. It was assumed that there were two symmetry planes along the ligament and the mid-thickness plane in the CT specimen. Consequently, a one-quarter geometry of the CT specimen was modeled using first order (linear) interpolation 8-node hexahedral brick elements with reduced integration and hourglass control (ABAQUS C3D8R), as shown in Fig. 2. The finite element mesh is refined in the vicinity of notch tip to obtain accurate results and to eliminate mesh dependency effects in the analyses. The smallest size is 20 µm, which is designed according to the average grain size of P92 steel and this size has previously obtained accurate creep crack growth prediction for CT specimens of carbon manganese steel [14]. An analytical rigid body was used to simulate the punch tool in the FEM model to apply the compression load. A concentrated force was applied at the center of the rigid body in the 2 direction to simulate the punching process and then unloaded. The rigid body was constrained in all directions except the 2 direction of the CT model. Frictionless contact was assumed between the rigid body and the CT model. The symmetry boundary conditions were applied on the mid-thickness plane and the ligament plane of CT specimen. The pre-crack of CT specimen is carried out by releasing the constraint of the elements on the ligament during FEM analysis. 3.2 Constitutive material behavior
8
During the pre-compression process, the plastic deformation occurs in CT specimen. Hence, an elastic-plastic analysis is carried out to simulate the pre-compression process. In this paper, the material is assumed to be isotropic and homogenous and the plastic deformation is assumed to follow the von Mises flow theory with power-hardening relationship, which can be written as follows:
σ = Eε e + K p ( ε p )
np
(2)
where εe and εp demonstrate the elastic and plastic parts, respectively; Kp is the power-hardening parameter; np is the strain hardening exponent. The mechanical properties of ASME P92 steel at room temperature and at 650 °C employed in the present study are shown in Table 3. The temperature dependent material properties provided in Table 3 at 650 °C are used for the subsequent thermal exposure and creep analyses. After the residual stress fields were introduced into the CT specimens, creep crack growth tests were carried out on these specimens to investigate the effect of residual stress. Hence, the relaxation of residual stress and the accumulation of creep damage ahead of crack tip during creep crack growth process were also investigated using FEM analyses. An elastic-plastic power creep law is employed, and the average creep strain rate ε Ac is employed and is given by [15]:
εAc =
εf = Aσ en tr
(3)
At 650 °C, for ASME P92 steel, A is 2.6353E-16 MPa-n/h and n is 5.23, which are determined from the relationship between the average creep strain rate and stress level obtained from the corresponding uniaxial creep tests that were carried out on samples 9
taken from the same ASME P92 steel pipe [16]. In order to study the creep damage accumulation and to predict the creep crack growth behavior, an uncoupled single damage theory based on the creep ductility exhaustion approach is adopted [17]. The damage rate ω is defined to depend on the equivalent creep strain rate ε c as shown:
ω =
ε c ε c = ε *f MSFε f
(4)
where ε *f is the critical multiaxial failure strain, which depends on the uniaxial creep fracture strain ε f and the appropriate multiaxial stress factor MSF. ε f depends on the material and is 18 % for the present ASME P92 steel, which is the measured value of uniaxial creep tests. The form of the MSF can be written as [18]:
ε *f n − 0.5 σ m 2 n − 0.5 MSF = = sinh sinh 2 εf 3 n + 0.5 n + 0.5 σ e
(5)
Furthermore, the total damage at any time is calculated from the time integral of creep damage rate:
ε c dt 0 ε* f
t
ω = ∫ ω dt = ∫ 0
t
(6)
When the creep damage of an integration point reaches to 0.999, this point is assumed to be failed. Then, the elastic modulus of this point is set to zero and the remaining forces exerted by the adjacent nodes are relaxed to zero. This creep damage model was implemented in the ABAQUS using the corresponding user defined subroutines [19]. Besides, it can be noted that the creep deformation is independent of the creep damage accumulation, which means that the creep strain rate can not be accelerated by the damage evolution. Hence, the convergence problems are reduced 10
and the very high strain rates are avoided during the FEM analyses when the damage approaches unity. 4. Results and discussion 4.1 Effect of notch radius on the residual stress The FEM models with various notch radiuses of 1, 1.5 and 2.5 mm are calculated, respectively. The peak load applied on the punch tool is 36 kN for three cases. During the pre-compression process, after the required load is applied, the cylinder is raised and then the specimen is unloaded. If the compressive load is sufficiently high, the material near the notch undergoes yielding in compression followed by elastic unloading. The normalized stress-strain response for the first element in the crack tip during the pre-compression process is shown in Fig. 3, where σ22 is the stress normal to the crack, ε22 is the strain normal to the crack and σy is the yield stress at room temperature. As shown in Fig. 3, it can be observed that the yield in compression is followed by the yield in tension and finally the plastic deformation is generated in the crack tip region. The variations of tensile residual stress distribution in the mid-thickness plane of the specimen with the increasing notch radius are shown in Fig. 4. It can be noted that as the notch radius increases, the value of the peak σ22 decreases while the size of tensile residual stress region in the crack notch increases. The maximum peak σ22 is approximately 1.5 σy. The tensile residual stresses zone increases from 2.0 mm to 3.0 mm as the notch radius increases from 1 mm to 2.5 mm. In addition, the peak σ22 is located at about 0.5 mm away from crack tip, which is independent of the notch
11
radius. The corresponding magnitude of stress triaxiality ahead of crack tip with different notch radiuses is shown in Fig. 5. As a rule, stress triaxiality can be used to demonstrate the constraint condition. It can be seen that the highest stress triaxiality is located in the specimen with a small notch radius, which corresponds to the maximum peak tensile residual stress location as shown in Fig. 4. This phenomenon means that a small notch radius can cause a high constraint ahead of crack tip. The peak stress triaxiality is also located at about 0.5 mm ahead of the crack tip irrespective of the notch radius. The residual stress distribution in the specimen with notch radius of 2.5 mm and peak penetration load of 36 kN through the thickness of the specimen is shown in Fig. 6. It reveals that the tensile residual stress is generated in the whole crack tip region. However, the peak tensile residual stress decreases from the center plane to the outer surface. 4.2 Effect of penetration load on the residual stress The effect of maximum penetration load on the tensile residual stress in the crack tip was also explored. It can be noted that the extent of the tensile residual stress in the model with notch radius of 2.5 mm is largest. Therefore, the model with 2.5 mm notch radius is adopted and the peak penetration loads are 24, 31, 34, 36, 38, and 41 kN, respectively. The peak load depends on the penetration depth. The residual stress distributions in the crack tip with different maximum penetration loads are shown in Fig. 7. It can be observed that the peak value and the region of the tensile residual stress increase as the applied load increases from 24 to
12
36 kN. The peak stress in the specimen after 36 kN pre-compression is near two times as that of yield strength at room temperature. When the stress exceeds 36 kN, only the peak stress increases while the size of the tensile residual stress region changes little. Fig. 8 shows the stress triaxiality distribution ahead of crack tip with different penetration loads. The stress triaxiality increases as the penetration load increases. In addition, the stress triaxiality changes little when the penetration stress exceeds 36 kN. 4.3 Effect of temperature on the residual stress After pre-compression, the creep crack growth tests at high temperature would be carried out on CT specimens, where creep deformation would be dominant ahead of crack tip. Hence, the effect of the temperature on the residual stress was investigated. Following pre-compression, the specimen is heated up to high temperature of 650 °C. Fig. 9 shows the variation of residual stress distribution in the specimen when it is heated from 20 to 650 °C. Due to the reduction in yield strength at high temperature as shown in Table 3, it leads to an instantaneous reduction in the residual stress. However, the peak residual stress is still about 1.5 times as the yield strength at 650 °C, the response of which is similar to that at room temperature. This demonstrates that the residual stress remains after heated to high temperature. 4.4 Effect of residual stress on the creep crack growth According to the above analysis, the peak penetration load of 36 kN and the notch radius of 2.5 mm are adopted for the pre-compressing process, which can be employed to generate the largest extent tensile residual stress in the notch tip. Two CT
13
specimens are employed in this paper. The initial crack length and initial stress intensity factor for all of the cases are kept constant to assure the same experimental condition, which are 11 mm and 15 MPam1/2, respectively. The variation of the penetration load versus the load line displacement during the pre-compression process is shown in Fig. 10, where the FEM result is also given for comparison. The response of load as the load line displacement increases for experiment and FEM is the same, which demonstrates that the numerical simulation results are reasonable. Turski [8] and Withers [20] had also reported that the FEM predicted residual stress distributions were in excellent agreement with that measured by X-ray synchrotron diffraction. As a rule, the residual stress is the stress that remains after the original cause of the stresses (external forces, heat gradient) has been removed. Residual stresses occur for a variety of reasons, including inelastic (plastic) deformations, temperature gradients (during heat treatment) or structural changes (phase transformation). In this paper, the residual stress is introduced into the CT specimen through pre-compression and then unloading. This approach is simple and repeatable. The residual stress is generated due to the plastic deformation and the accuracy of the residual stress magnitude mainly depends on the elastic-plastic property, which can be accurately obtained from the tensile tests. Hence, the calculated residual stress through FEM can be employed to represent the actual residual stress distribution and to investigate its effect on the creep crack growth. Following pre-compression, the creep crack growth tests were conducted. If the pre-compressed CT specimen is maintained at 650 °C with no external applied tensile
14
load, the residual stresses ahead of crack tip would gradually relax to a smaller value, as shown in Fig. 11. In particular, the deep decline of stress occurs within 100 h. Finally, the strains in the specimen would be completely converted into creep strains. It can be deduced that the residual stress only affects the creep crack initiation stage, which was also reported by Webster [21]. Hence, in the present study, the effect of residual stress on the creep crack growth behavior focuses on the creep crack initiation stage. During creep crack growth test, as the creep crack growth length reaches to the specified length, the test will be interrupted. Fig. 12 illustrates the variation of creep crack growth length against time for pre-compressed and original CT specimens. It can be observed that the creep crack growth rate of the specimen with residual stress is much higher than that of the specimen without residual stress. For the specimen without pre-compression, the creep crack growth length increases little when the creep time is less than 400 h while for the specimen with pre-compression the creep crack growth length grows to about 0.7 mm. Figs. 13 (a) and (b) shows the variation of stress ahead of crack tip for CT1 and CT2 specimens during creep. It can be noted that as the creep time increases the stress gradually relaxes due to creep deformation. When the creep time increases from 0 h to 10000 h, the peak stress at crack tip of CT1 specimen relaxes from 450 to 200 MPa while the peak stress of CT2 specimen relaxes from 360 to 200 MPa. This demonstrates that the peak stress of CT1 specimen with residual stress is higher than that of CT2 specimen. In addition, the difference of the stress distribution between CT1 and CT2 specimens mainly occurs when the creep time is less than 100 h, which
15
corresponds to the steep decline stage of stress. As the creep time exceeds 100 h, the difference of the stress distribution between CT1 and CT2 specimens is insignificant. This phenomenon also reveals that the residual stress only affect the creep crack initiation stage. The applied tensile stress combined with tensile residual stress enhances the stress level ahead of crack tip. Hence, the stress level and the stress triaxiality ahead of crack tip in the specimen with pre-compression are higher than those in the specimen without pre-compression. The high stress and stress triaxiality can accelerate the diffusion of vacancies, which is the major reason to the creep voids nucleation [22, 23]. Then, the nucleation, growth and coalescence of creep voids ahead of crack tip are accelerated. As a result, the creep damage accumulation is accelerated, which leads to a high creep crack growth rate. Furthermore, plastic deformation can reduce the creep resistance and the creep ductility [24, 25], which also accelerates the creep damage accumulation further. Due to the accelerated creep damage accumulation, the creep crack initiation time is declined. Fig.14 shows the comparison of the creep crack behavior between FEM results and experimental data. It can be observed that the creep crack growth tendency is accurately demonstrated by the FEM results. At beginning, the calculated creep crack growth behavior exhibits a good agreement with the corresponding experimental data. Nevertheless, as the creep increases further, the calculated creep crack growth length for CT specimen with residual stress is smaller than that of experimental result while that for CT specimen without residual stress is higher than that of corresponding experiment data. This may be ascribed to two reasons. Firstly, the residual stress in
16
FEM relaxes more quickly than that in experimental CT specimen due to the average creep strain rate employed to demonstrate the whole creep curve. Secondly, the material of FEM is assumed to be isotropic and homogenous while the material of the experimental CT specimen owns inhomogeneity. Furthermore, the phenomenon that the creep crack growth behavior will be accelerated as the residual stress remains in the CT specimen is also clearly observed. 4.5 Predicting creep crack growth behavior with residual stress As a rule, the C* is always used to correlate the creep crack growth behavior [15, 26]. For the aim of understanding the effect of residual stress on the creep crack, it is necessary to interpret the variation of C* during creep crack process. Parameter C* can be determined in the terms of a reference stress σref and the stress intensity factor K as follows [27]:
C* = σ ref εref R′ K R′ = σ ref
(7)
2
(8)
where εref is the creep strain rate at the reference stress. The value of R′ depends on the stress distribution ahead of crack tip and the specimen geometry and the crack length. Because K and σref are determined by the stress magnitude ahead of crack tip, the value of K and σref both decline as the stress relaxes during creep. In general, K is proportional to the stress magnitude ahead of crack tip. Hence, it can be assumed that the value of R′ nearly keeps constant during creep crack growth process, which can be calculated by:
17
K R′ = 0 σ ref 0
2
(9)
where K0 and σref0 are the initial value of K and σref at the creep time of 0 h, respectively. For the specimens with residual stress, Webster [21] had proposed that a combined stress intensity factor K, due to the applied loading Kapp and that due to the residual stress distribution Kres, was employed to demonstrate the stress level ahead of crack tip, which is defined as follows: K = K app + K res
(10)
In the present study, Kapp is 15 MPam1/2. Kres is directly determined from the FEM results of the CT specimen only with residual stress. The distribution of Kres through the thickness of the CT specimen only with residual stress at 650 °C is shown in Fig. 15. The Kres is calculated after the pre-cracking and heating to 650 °C, where the relaxation of the residual stress occurs. The Kres is not a constant value and varies across the thickness and the peak value is located at a distance from the center plane, which is also observed in literature [10]. Hence, it is assumed that an average value of Kres of 13.6 MPam1/2 is employed to represent the stress intensity level ahead of crack
tip. In addition, the σref0 is also obtained from the FEM results. Because the creep crack growth process is mainly determined by the tensile stress field ahead of crack tip, the average value of the tensile residual stress magnitude ahead of crack tip is employed to represent the reference stress level of the CT specimen [10]. The average stress across the tensile stress field as shown in Fig. 15 (a) is 230 MPa. The stress would relax during creep, as shown in Fig. 11. For the material 18
obeying the power creep law, the stress relief would obey [10]:
σ = σ 0 [1 + AE ( n-1) σ 0n −1t ]1/( n−1)
(11)
where σ 0 is the initial stress value at the creep time of 0 h; t is the current creep time;
σ is the stress value at the current creep time. Fig. 16 shows the relaxation of the reference stress σref0 of 230 MPa during creep process. It can be observed that most of the stress relief occurs in the primary creep stage, the creep time of which is less than 1000 h. As defined in Eq.7, the C* also relaxes as the creep time increases. According to the high temperature fracture mechanics, the creep crack growth rate can be determined in the terms of C* by an expression of form [28]： φ
a = D0 ( C *)
(12)
For ASME P92 steel at 650 °C, D0 is 0.0141 and φ is 0.8606. The creep crack growth at any time can be obtained from the time integral of creep crack growth rate. The comparison of the predicted creep crack growth length and the experimental result for the CT specimen with residual stress is shown in Fig. 17. It can be observed that the predicted creep growth curve has the similar shape as that of experiment but the predicted creep length is larger than that of experiment at the same creep time. This phenomenon demonstrates that this method overestimates the creep crack growth rate. As stated in the above, the crucial feature of the creep crack growth prediction is to obtain the reliable K and σref0 value. After heated to 650 °C, the residual stress is higher than the yield stress. In addition, when the external tensile load is applied on the CT specimen with residual stress, the plastic deformation must occur ahead of
19
crack tip and the corresponding increase of the stress is not linear. Hence, the combined stress intensity K defined as the summation of Kapp and Kres has limitation on the assessment of remained creep life. Under plastic deformation, it would overestimate the stress intensity level ahead of crack tip. To obtain a more accurate estimation of creep crack growth behavior, a modified approach is employed. In this approach, it is assumed that the combined K should be directly determined from the calculated stress field of the FEM model with residual stress and external applied load. Fig. 18 shows the distribution of the combined K through the thickness for the CT1 specimen with residual stress. The average value of Kcomb is about 18.7 MPam1/2, which is less than the summation of Kapp and Kres. The corresponding predicted creep crack growth length versus creep time is shown in Fig. 19. It is apparent from this figure that the predicted creep crack curve using Kcomb value directly obtained from FEM result is more accurate. At the same creep time, the predicted creep crack growth is a little higher than that of experiment. Hence, it can be concluded that the modified method is reasonable. 6. Conclusions In this work, the effect of tensile residual stresses that were introduced in CT specimen by pre-compression on the creep crack growth properties of ASME P92 steel at 650 °C was investigated by numerical simulation and experiment. (1) A three dimensional FEM analysis of the pre-compression on the CT specimen with various notch radiuses and penetration loads was performed. The FEM results revealed that the extent of tensile stress region ahead of crack tip increased as
20
the notch radius and the penetration load increased. The largest extent was obtained as the notch radius was 2.5 mm and the peak penetration load was 36 kN. The largest region of tensile residual stress ahead of crack tip was about 3 mm and the peak tensile residual stress value was about 1.5 times as yield strength at room temperature. In addition, the tensile residual stress presented in the whole CT specimen, where the value of the mid-thickness plane was higher than that of the outer surface. (2) After the CT specimen was heated to 650 °C, the value of tensile residual stress decreased, but the extent of tensile residual field changed little. The peak tensile residual stress value was 1.5 times as yield strength at 650 °C. During creep, the stress relaxed greatly in the initial creep stage. Hence, the residual stress had great influences on the creep crack initiation stage. (3) Creep crack growth tests revealed that CT specimen with tensile residual stress and external applied stress exhibited a fast creep crack growth tendency compared with CT specimen only with the external applied stress. This was due to the fact that a high tensile stress state ahead of crack tip could stimulate the nucleation, growth and coalescence of creep voids and even could decline the creep ductility. As a result, the creep damage accumulation ahead of crack tip was accelerated. (4) A prediction approach on the basis of the combined K and the reference stress σref directly obtained from the FEM results could be employed to give a more accurate
creep crack growth prediction for the components with residual stress. Acknowledgement: This research work was financially supported by the Project of the National
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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). Reference: [1] Vaillant JC, Vandenberghe B, Hahn B, Heuser H, Jochum C. T/P23, 24, 911 and 92: New grades for advanced coal-fired power plants--Properties and experience. Int J Pres Ves Pip. 2008;85:38-46. [2] Kern T-U, Staubli M, Scarlin B. The European efforts in material development for 650°C USC power plants - COST522. ISIJ Int. 2002;42:1515-9. [3] Davies C, Odowd N, Nikbin K, Webster G. An analytical and computational study of crack initiation under transient creep conditions. Int J Solids Struct. 2007;44:1823-43. [4] Sugiura R, Toshimitsu Yokobori Jr A, Suzuki K, Tabuchi M. Characterization of incubation time on creep crack growth for weldments of P92. Eng Fract Mech. 2010;77:3053-65. [5] Yatomi M, Fuji A, Tabuchi M, Hasegawa Y, Kobayashi KiI, Yokobori T. Evaluation of creep crack growth rate of P92 welds using fracture mechanics parameters. Journal of Pressure Vessel Technology. 2010;132:041404 (8 pp.). [6] Sawada K, Hongo H, Watanabe T, Tabuchi M. Analysis of the microstructure near the crack tip of ASME Gr.92 steel after creep crack growth. Mater Charact. 2010;61:1097-102.
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[7] Lee H, Biglari F, Wimpory R, Nikbin K. Treatment of residual stress in failure assessment procedure. Eng Fract Mech. 2006;73:1755-71. [8] Turski M, Bouchard PJ, Steuwer A, Withers PJ. Residual stress driven creep cracking in AISI Type 316 stainless steel. Acta Mater. 2008;56:3598-612. [9] Soanes T, Bell W, Vibert A. Optimising residual stresses at a repair in a steam header to tube plate weld. Int J Pres Ves Pip. 2005;82:311-8. [10] Webster GA, Davies CM, Nikbin KM. Assessment of creep crack growth due to stress relief. Int J Solids Struct. 2010;47:881-6. [11] ASTM. ASTM E1457-07. Standard Test Method for Measurement of Creep Crack Growth Times in Metals. United States:West Conshohocken: ASTM International; 2007. p. 1012-35. [12] Saxena A. Electrical potential technique for monitoring subcritical crack growth at elevated temperatures. Eng Fract Mech. 1980;13:741-50. [13] Schwalbe KH, Hellmann D. Application of the electrical potential method to crack length measurements using Johnson's formula. J Test Eval. 1981;9:218-20. [14] Yatomi M, O'Dowd NP, Nikbin KM, Webster GA. Theoretical and numerical modelling of creep crack growth in a carbon-manganese steel. Eng Fract Mech. 2006;73:1158-75. [15] Yatomi M, Tabuchi M. Issues relating to numerical modelling of creep crack growth. Eng Fract Mech. 2010;77:3043-52. [16] Zhao L, Jing H, Xu L, An J, Xiao G. Numerical investigation of factors affecting creep damage accumulation in ASME P92 steel welded joint. Mater Design.
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2012;34:566-75. [17] Nikbin KM, Smith DJ, Webster GA. Prediction of Creep Crack Growth from Uniaxial Creep Data. Proceedings of The Royal Society of London, Series A: Mathematical and Physical Sciences. 1984;396:183-97. [18] Cocks ACF, Ashby MF. Intergranular fracture during power-law creep under multiaxial stresses. Met Sci. 1980;14:395-402. [19] ABAQUS. Abaqus 6.9 standard user manual. USA: ABAQUS, Inc; 2009. [20] Withers PJ, Turski M, Edwards L, Bouchard PJ, Buttle DJ. Recent advances in residual stress measurement. Int J Pres Ves Pip. 2008;85:118-27. [21] Webster GA. Trends in high temperature structural integrity assessment. Journal of ASTM International. 2006;3. [22] Li D, Shinozaki K, Kuroki H. Stress-strain analysis of creep deterioration in heat affected weld zone in high Cr ferritic heat resistant steel. Mater Sci Technol. 2003;19:1253-60. [23] Tabuchi M, Ha J, Hongo H, Watanabe T, Yokobori T. Experimental and numerical study on the relationship between creep crack growth properties and fracture
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2004;35:1757-64. [24] Loveday MS, Dyson BF. Prestrain-induced particle microcracking and creep cavitation in IN597. Acta Metall. 1983;31:397-405. [25] Willis M, McDonaugh-Smith A, Hales R. Prestrain effects on creep ductility of a 316 stainless steel light forging. Int J Pres Ves Pip. 1999;76:355-9.
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[26] Yamamoto M, Miura N, Ogata T. Applicability of C* parameter in assessing Type IV creep cracking in Mod. 9Cr-1Mo steel welded joint. Eng Fract Mech. 2010;77:3022-34. [27] Ainsworth RA. Practical aspects of the calculation and application of C*. Mater High Temp. 1992;10:119-26. [28] Yatomi M, Yokobori Jr AT, Nikbin KM. Comparison of two creep crack growth parameters, C* and Q*, with FE analysis. Strength Fract Complex. 2006;4:83-92.
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Table captions: Table 1 Chemical composition of used ASME P92 steel in wt. %. Table 2 Experimental conditions of creep crack growth tests. Table 3 Mechanical properties of ASME P92 steel at room temperature and 650 °C. Figure captions: Fig. 1 Geometry and dimension of the designed CT specimen. Fig. 2 One quarter FEM model of the used CT specimen. Fig. 3 Response of normalized stress against strain during pre-compression process. Fig. 4 Residual stress distribution after pre-compression of the FEM models with different notch radiuses. Fig. 5 Stress triaxiality distribution after pre-compression of the FEM models with different notch radiuses. Fig. 6 Residual stress distribution across the thickness of the specimen. Fig. 7 Normalized residual stress distribution after pre-compression of the FEM models with different penetration loads. Fig. 8 Stress triaxiality distribution after pre-compression of the FEM models with different penetration loads. Fig. 9 Variation of residual stress distribution in the specimen heated from 20 °C to 650 °C. Fig. 10 Comparison of the development of the load line displacement between experimental data and FEM result. Fig. 11 Response of stress against the time during the pre-compression, heated and
26
followed creep processes. Fig. 12 Comparison of creep crack growth behavior for the pre-compressed and original CT specimens. Fig. 13 Stress relaxation during creep process for (a) CT1 specimen with tensile residual stress and external applied stress and (b) CT2 specimen only with external applied stress. Fig. 14 Comparison of creep crack growth behavior between FEM calculated results and experimental data. Fig. 15 Stress intensity factor K distribution across the thickness of CT specimen only with residual stress. Fig. 16 Relaxation of reference stress σref0 of 230 MPa during creep process. Fig. 17 Comparison of the creep crack growth length for prediction and experiment using the combined K determined by the summation of Kapp and Kres. Fig.18 Stress intensity factor K distribution across the thickness of CT specimen with residual stress and external applied stress. Fig. 19 Comparison of the creep crack growth length for prediction and experiment using the combined K determined by the FEM results.
27
Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6
Figure 7
Figure 8
Figure 9
Figure 10
Figure 11
Figure 12
Figure 13(a)
Figure 13(b)
Figure 14
Figure 15
Figure 16
Figure 17
Figure 18
Figure 19
Table 1 Chemical composition of used ASME P92 steel in wt. %. Material
C
Si
Mn
S
P
Cr
Ni
Mo
W
V
Nb
B
Al
N
Bal.
P92 steel
0.10
0.47
0.40
0.001
0.008
8.77
0.12
0.38
1.48
0.16
0.054
0.001
0.02
0.043
Fe
Table 2 Experimental conditions of creep crack growth tests. Specimen
a0 (mm)
W (mm)
B (mm)
K (MPam1/2)
P (N)
CT1
11.08
30
15.08
15
5824
CT2
11.02
30
15.08
15
5830
Table 3 Mechanical properties of ASME P92 steel at room temperature and 650 °C. Temperature Elastic modulus E (MPa) Poisson ratio υ Yield strength σy (MPa) Ultimate strength σu (MPa) Material coefficient Kp (MPa) Strain hardening exponent np
20 °C
650 °C
206000 110000 0.3 0.3 402 180 625 280 861 311 0.155 0.0657
Research Highlights: 1) Residual stress was generated in CT specimen notch using pre-compression. 2) Maximum extent of tensile residual stress in CT specimen was obtained by FEM. 3) Residual stress combined with external stress led to a fast creep crack growth. 4) Effect of residual stress on creep damage evolution was studied. 5) Predicting creep crack growth for specimen with residual stress was studied.