Mechanical factors in primary water stress corrosion cracking of cold-worked stainless steel

Nuclear Engineering and Design 301 (2016) 24–31

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Mechanical factors in primary water stress corrosion cracking of cold-worked stainless steel Rashid Al Hammadi a , Yongsun Yi b,∗ , Wael Zaki c , Pyungyeon Cho b , Changheui Jang d a

Nuclear Security Division, Federal Authority for Nuclear Regulation, Abu Dhabi, United Arab Emirates Department of Nuclear Engineering, Khalifa University, Abu Dhabi, United Arab Emirates Department of Mechanical Engineering, Khalifa University, Abu Dhabi, United Arab Emirates d Nuclear and Quantum Engineering Department, Korea Advanced Institute of Science and Technology, Daejeon, South Korea b c

h i g h l i g h t s • • • • •

PWSCC of cold-worked austenitic stainless steel was studied. Finite element analysis was performed on a compact tension specimen. Mechanical fields near a crack tip were evaluated using FEA. The dependence of mechanical factors on KI and yield stress was investigated. The crack tip normal stress was identified as a main factor controlling PWSCC.

a r t i c l e

i n f o

Article history: Received 12 November 2015 Received in revised form 17 February 2016 Accepted 20 February 2016 Classification: B. Materials engineering

a b s t r a c t Finite element analysis was performed on a compact tension specimen to determine the stress and strain distributions near a crack tip. Based on the results, the crack tip stain rates by crack advance and creep rates near crack tip were estimated. By comparing the dependence of the mechanical factors on the stress intensity factor and yield stress with that of the SCC crack growth rates, it was tried to identify the main mechanical factor for the primary water stress corrosion cracking (PWSCC) of cold-worked austenitic stainless steels. The analysis results showed that the crack tip normal stress could be the main mechanical factor controlling the PWSCC, suggesting that the internal oxidation mechanism might be the most probable PWSCC mechanism of cold-worked austenitic stainless steels. © 2016 Elsevier B.V. All rights reserved.

1. Introduction Austenitic stainless steels (ASS) have been widely used for reactor vessel internals because of their corrosion resistance, toughness, ductility, strength, and fatigue characteristics in the primary water conditions of pressurized water reactors (IAEA, 1999). The operating experience of ASS indicates that they have shown good performance in the primary water (PW) conditions (Tice et al., 2009) while intergranular stress corrosion cracking (IGSCC) of ASS has been reported as a generic problem in oxygenated water (Roychowdhury et al., 2011). However, some cases of IGSCC were reported on cold-worked ASS in the primary water conditions and

∗ Corresponding author. Tel.: +971 567338652. E-mail addresses: [email protected] (R.A. Hammadi), [email protected] (Y. Yi), [email protected] (W. Zaki), [email protected] (P. Cho), [email protected] (C. Jang). http://dx.doi.org/10.1016/j.nucengdes.2016.02.031 0029-5493/© 2016 Elsevier B.V. All rights reserved.

cold-work was found as a possible cause of the IGSCC (Couvant et al., 2007; Raquet et al., 2007). Since then, many studies have been performed on cold-worked ASS in the primary water conditions to examine the effects of mechanical, electrochemical, and material factors on the IGSCC (Tice et al., 2009; Lu et al., 2009). It has been identified that the IGSCC crack growth rate (CGR) of ASS increases with the degree of cold-work and consequently with the yield stress (Gómez-Briceno et al., 2009). Also, there are clear similarities in the primary water stress corrosion cracking (PWSCC) phenomena between ASS and nickel base alloys such as Alloy 600. For example, in the PW conditions, both types of materials show lower susceptibility to the IGSCC in sensitized conditions (Tice et al., 2009). For this reason, it has been tried to explain the IGSCC phenomenon of cold-worked ASS using the SCC mechanisms proposed for the PWSCC of Ni-base alloys such as slip dissolution, internal oxidation, and creep damage model. But, it seems that no mechanisms have fully explained the observations about the IGSCC occurring on cold-worked ASS and Ni-base alloys. This lack of

R.A. Hammadi et al. / Nuclear Engineering and Design 301 (2016) 24–31

understanding of the IGSCC mechanism of both alloys in the PW conditions is attributed to many factors involved in the PWSCC phenomena (Rebak and Szklarska-Smialowska, 1996). Although clear correlations have been found between the SCC crack growth rates of ASS in the PW conditions and the stress intensity factor or the degree of cold-work, only a few results have been reported on the mechanical factors near/at a crack tip as a function of the degree of cold-work. Shoji et al. (2010) compared qualitatively crack tip strain values between yield stresses of 160 MPa and 500 MPa calculated by different crack tip strain field formulations. But their further analysis was only on the crack tip strain rates. Several different mechanical factors that govern the IGSCC kinetics are identified in the proposed PWSCC mechanisms. The SCC crack growth rate (CGR) in the slip dissolution model (Andresen and Ford, 1988) is mainly governed by the crack tip strain rate (CTSR) among the mechanical factors. Through an analysis using a Weibull distribution of PWSCC damages, Shah et al. (1992) proposed the tensile stress as one of the main factors determining the crack growth rate of PWSCC. Also, in the internal oxidation model, the local tensile stress at a crack tip plays a main role in crack advance (Herbelin et al., 2009). Since the mechanical stress and strain fields near/at a crack tip control the PWSCC, analyzing the main mechanical factor would be an important step in identifying the possible PWSCC mechanism of cold-worked ASS. In this study the mechanical factors around a crack tip were evaluated to investigate their effects on the PWSCC of cold-worked ASS. Finite element analysis (FEA) on a compact tension specimen was performed to calculate the stress and strain fields near a crack tip as a function of stress intensity factor, KI , and yield stress,  ys . Other mechanical factors near a crack tip were estimated based on the FEA results. Along with the main mechanical factors, the possible mechanisms for the PWSCC of cold-worked ASS are discussed.

2. Finite element model and analysis The finite element analysis was performed using ABAQUS (Version 6.11) on a 1/2 in. compact tension (CT) specimen (ASTM E647-08) with a crack length (a) of 12.16 mm shown in Fig. 1. For finite element analysis the sample model was meshed with two zones having different mesh shapes and sizes as shown in Fig. 2. Theoretically, crack tip asymptotic fields have been expressed as a function of r that is a distance from the crack tip on the crack plane. According to Shoji et al. (2010) the characteristic distance ro where the mechanical factors for SCC are evaluated was estimated to have a micrometric level. Therefore, near the crack tip, the geometry model for a CT specimen was finely meshed as an element with 20 ␮m × 20 ␮m size and square shape while the remaining portion of the model was meshed as randomized quadrangle shape. The element applied to the whole region of a CT specimen was 8-node biquadratic plane strain quadrilateral element, ABAQUS element CPE8, which has 8 nodes and fully 9 integration points as shown in Fig. 3. The distributions of the stress and strain fields in the compact tension specimen were determined numerically by means of FEA. For this purpose, a finite element model was constructed to solve the boundary value problem representing the CT specimen containing a crack with traction-free lips. The upper pin was modelled as a rigid body because of the usually very small strains experienced by the pin during proper tensile testing. The opening of the crack was obtained by subjecting the upper pin to an upward concentrated force F, with rigid and frictionless contact conditions defined at the interface between the pin and the hole.

25

Fig. 1. Geometrical model of compact tension specimen.

The constitutive behaviour of the steel alloy was considered elastoplastic with isotropic hardening, for which the stress-strain relation is given by



 = C : ε − εp



(1) εp

is the plastic strain and C is the where ε is the total strain, elastic stiffness tensor of the material, function of Young’s modulus E and Poisson’s ratio v assuming isotropic stress-strain behaviour. The isotropic strain hardening beyond the onset of plastic deformation is determined from tensile stress vs. plastic strain data provided to the FEA software as user input. The time integration of the above equations is accomplished by means of FEA where the load defined by the upward force F acting on the upper pin is discretized into increments and the boundary value problem is solved iteratively for each load increment. This procedure gives access to the displacement field at the nodes of the mesh elements and to stress and strain fields at the integration points within. The calculation results were compared with experimental SCC crack growth rates of 316 stainless steel measured by Terachi et al. (2012). Therefore, the material properties of 316 stainless steel available in literature were used. The stress–strain behaviour of 316 stainless steel was expressed by the Ramberg–Osgood equation (Xue et al., 2009):



ε=

 + ˛× E

     n ys E

×

ys

(2)

where E is the Young’s modulus,  ys is the yield strength, ˛ is the dimensionless material constant, and n is the strain hardening exponent of the material. The input parameters used in this analysis are shown in Table 1. 3. Effect of mechanical factors on PWSCC 3.1. KI and  ys dependence of SCC crack growth rates By comparing the respective dependence of mechanical factors near a crack tip determined by the finite element analysis on KI and

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Fig. 3. Integration points and nodes in an element.

 ys with that of PWSCC CGRs, the significance of each mechanical factor was evaluated. First, using PWSCC CGR data from literature, their dependence on KI and  ys was determined. Terachi et al. (2012) performed PWSCC tests on cold-worked 304 and 316 stainless steels in PW conditions over wide ranges of temperature, stress intensity factor, and the degree of cold-working. They reported that the crack growth rates could be empirically described in terms of the apparent stress intensity factor and yield stress as follows: B CGR ∝ KIA and CGR ∝ ys .

Fig. 2. Finite element mesh used in the stress and strain analysis.

Table 1 Input parameters of cold-worked 316 stainless steel for finite element analysis. Parameters

Values

References

Yield stress

200–800 MPa

˛ in Ramberg–Osgood relationship n in Ramberg–Osgood relationship Young’s modulus

1.0

Terachi et al. (2012) Xue et al. (2009)

190 GPa

Poisson’s ratio

0.28

3.5

Xue et al. (2009) Kim et al. (2002) and Outeiro (2008) Outeiro (2008)

(3)

In Eq. (3), depending on materials (304 vs. 316 stainless steels), temperatures (290 ◦ C vs. 320 ◦ C), and the degree of cold work, the exponents of A and B range 0.6–3.2 and 2–3, respectively. This analysis indicates that the logarithms of the CGR values are linearly correlated with those of KI and  ys . Based on this observation, a multiples regression analysis on the CGRs was performed against the two variables, KI and  ys . To isolate the effects of the two variables, only the CGRs for 316 stainless steel tested at 320 ◦ C with different degrees of cold-work were selected, which are shown in Table 2. The multiple regression result is expressed as:





log(CGR) = 2.57 log (KI ) + 2.71 log ys − 21.25. √

(4)

where CGR is in m/s, KI in MPa m, and  ys in MPa. The calculated CGRs by Eq. (4) are compared with the measured CGRs in Fig. 4, which shows that they are in good agreement. Also, the proportional constants, A and B in Eq. (3), are close each other, suggesting that KI and  ys , have similar contributions to the SCC CGRs over the ranges of the selected experimental conditions.

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Table 2 PWSCC CGR data of 316 SS at 320 ◦ C excerpted from the work by Terachi et al. (2012). √

Cold-work (%)

 ys (MPa)

Apparent KI (MPa

5

256

10

377

26.1 33.9 31.9 27.9 34.6 25.8 28.2

5.5 × 10−12 1.5 × 10−11 1.7 × 10−11 1.8 × 10−11 4.4 × 10−11 3.6 × 10−11 4.7 × 10−11

15

501

27.9 34.6 25.8 28.2 20.8

4.4 × 10−11 6.9 × 10−11 1.2 × 10−10 4.5 × 10−11 4.1 × 10−12

20

575

25.8 39.3 29.6 21.6 31.1 41.7 32.4

9.5 × 10−11 1.4 × 10−10 1.1 × 10−10 6.5 × 10−11 1.1 × 10−10 1.7 × 10−10 1.1 × 10−10

m)

CGR (m/s)

Fig. 5. Crack tip normal stresses at the crack tip as a function of (a) stress intensity factor and (b) yield stress.

Fig. 4. Comparison between measured CGR and calculated CGR by multiple regression of 316 stainless steel in 320 ◦ C primary water.

3.2. Stress and strain fields around a crack tip As mentioned earlier, the available oxidation rate constants on stainless steel in pure water with different dissolved oxygen levels give the characteristic distance at a micrometric level (Shoji et al., 2010). The values of the normal stresses and total normal strains at the crack tip were determined from the nearest integration point (Point 1 in Fig. 3) that is located at 2.25 ␮m from the crack tip on the crack plane and designated as the crack tip normal stresses ( yy ) and crack tip normal strains (εyy ), respectively. Fig. 5 shows the crack tip normal stresses as a function of KI and  ys . The stress values are quite higher than the yield stresses used for the calculations, which is consistent with the calculation results by Davies et al. (2005). According to their calculation, depending on the applied loads and calculation methods, the ratio of the maximum normal stress at a crack tip to yield stress ranges from 2 to 9, which is due to the plane strain condition. In Fig. 5 the crack tip stresses increase as the yield stress increases at a constant KI and the stress intensity factor increases at a constant  ys . Fig. 6(a) shows that the crack tip normal strain increases with the stress intensity factor. However, the value of εyy decreases up to the yield stress of 500 MPa and shows almost no change between 500 and 800 MPa

[see Fig. 6(b)]. The normal strain distributions inside an element along the crack plane were determined from Integration points 1 √ through 3 in Fig. 3. The strain distributions at KI = 30 MPa m are shown in Fig. 7 for different yield stresses. Assuming that the strains vary linearly inside the first element at the crack tip, the strain gradients were calculated and their absolute values, |εyy,x |, are shown as a function of the stress intensity factor and yield stress in Fig. 8(a) and (b), respectively. The dependence of the strain gradient on KI and  ys shows a similar trend to that of the normal strain in Fig. 6. Among the three mechanical factors analysed near a crack tip, only the crack tip normal stresses increase with both of the stress intensity factor and yield stress while the crack tip strain and absolute values of crack tip strain gradient increase with the stress intensity factor and decrease with the yield stress. The determined crack tip stresses and strain gradients are used for estimating other mechanical factors near a crack tip. 3.3. KI and  ys dependence of mechanical factors The effects of cold-working on the crack tip creep rates, CTSRcreep , and crack tip strain rates by crack advance, CTSRCA , of a material were evaluated following the analysis procedure used by Hall (Hall, 2008; Hall, 2009). For a growing crack, the crack tip strain rate (CTSR) has two components expressed by



∂ε (r, t) ε˙ (r, t) = ∂t





∂ε (r, t) − ∂r r

CGR (t) . t

(5)

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Fig. 6. Crack tip normal strains at the crack tip as a function of (a) stress intensity factor and (b) yield stress.

Fig. 8. Strain gradient near the crack tip as a function of (a) stress intensity factor and (b) yield stress.

The first term as a quasi-stationary component refers to the time dependent strain (creep) rate at a fixed distance from the moving crack tip and the second term represents the contribution of the crack advance to the crack tip strain rate (Hall, 2009). First, the time-dependent creep term, CTSRcreep , in Eq. (5) is discussed. Noel et al. (1996) performed creep tests on nickel base alloys in the primary water conditions and proposed an empirical creep model as follows:



ε˙ = k ×

Fig. 7. Crack tip strain distribution inside the first element from the crack tip at √ KI = 30 MPa m.

true − ys ys

0.86

 Q

× t −0.47 × exp −

RT

(6)

where ε˙ is the creep rate (10−6 h−1 ), k is a constant depending only on materials,  true is the true stress (MPa) after loading,  ys is the yield stress (MPa), and t is the time (h). Since test data for the creep rates on cold-worked ASS in the primary water conditions are not available, the KI and  ys dependence of the creep rates of ASS was evaluated based on the empirical model expressed by Eq. (6). Defining  eff = [( true −  ys )/ ys ]s that has no unit as an empirical effective stress and assuming that k and Q are constants for coldworked materials, the KI and  ys dependence of the effective stress was compared. In the definition of  eff , s is a constant that might be related to materials and equal to 0.86 for nickel base alloys. The values of  eff were calculated by substituting the crack tip normal stresses as  true from Fig. 5 and 0.86 as the exponent s for different values of KI and  ys into  eff = [( true −  ys )/ ys ]s , which are shown in Fig. 9. The values of  eff is increasing with KI and decreasing with  ys . Since the value of s is not available for stainless steel, the values of  eff were calculated with different values of s from 0.1 to

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Table 3 Comparisons of KI and  ys dependence of mechanical factors in log-log plots. Mechanical factors

A (in KI A )

B (in  ys B )

Crack growth rate, CGR (m/s) Crack tip normal stress,  yy (MPa) Effective stress in creep rate,  eff Crack tip strain rate by crack advance, CTSRCA

2.57 0.49 0.53 3.88

2.70 0.48 −0.57 2.33

appears as the product of the strain gradient at a crack tip and the crack growth rate. To calculate the values of CTSRCA , the strain gradients from Fig. 8 were used and the crack growth rates were calculated using Eq. (4). Then, multiple regression was applied to the calculated CTSRCA , which resulted in:





log (CTSRCA ) = 3.88 log (KI ) + 2.33 log ys − 19.21

Fig. 9. KI and  ys dependence of  eff in creep rate.

2.0, which showed the same KI and  ys dependence. This suggests that the higher yield stress the smaller creep rate. It is well known that high temperature creep in metals is controlled by the effective stress rather than the applied stress (Groisböck and Jeglitsch, 1992; Yi and Was, 2001). The internal stress (=the applied stress − the effective stress) plays as internal resistance to creep and depends on the dislocation configuration (Chen et al., 2014). From this consideration, it would be obvious that the higher yield stress results in relatively smaller effective stress. Since in Eq. (6) the parameter k is mainly dependent on the carbide precipitation and its distribution (Noel et al., 1996) it can be assumed to be a constant when only mechanical factors are compared. According to Eq. (6) the creep rates are linearly proportional to the effective stress defined as  eff = [( true −  ys )/ ys ]s above and therefore it can be concluded that the increase in the yield stress decreases the creep rate or it does not contribute to the enhancement of creep. This is consistent with the creep behaviour of stainless steel in air. Kassner and Smith (2015) reported that the creep resistance of 403 stainless steel increased by cold-work at low temperatures as well as elevated temperatures. Also, it was found that the creep strain for different ASS including 316L stainless steel at medium and low temperatures up to 573 K could be prevented by plastic pre-straining (Usami and Mori, 2000). Second, the crack tip strain rate component by crack advance, CTSRCA , which is the second term of Eq. (6), is discussed. CTSRCA

(7)

√ where KI and  ys are in the units of MPa m and MPa, respectively. For the crack tip normal stresses shown in Fig. 5, the KI and  ys dependence was evaluated by the same approach using the multiple regression. The KI and  ys dependence of the measured CGRs and calculated mechanical factors are summarized in Table 3. The exponents, A and B, were determined using multiple regression analysis and thought to represent the dependence of each mechanical factor on KI and  ys , respectively. By comparing the KI and  ys dependence between the mechanical factors and the crack growth rate, the significance of each mechanical factor was evaluated. The exponent B for  eff was determined to be a negative value since the creep rates decrease with the cold-work as discussed earlier. For the crack tip strain rate by crack advance, CTSRCA , both of the exponents are positive values but the value of A is almost twice that of B, suggesting that the yield stress contributes to the increase in the CTSRCA , but not as much as the stress intensity factor. Finally, the values of A and B for the crack tip normal stress,  yy , are very close each other, which is the same trend as the crack growth rate. Comparison of the KI and  ys dependence between the SCC CGRs and the mechanical factors implies that the crack tip normal stress can be the most suitable mechanical factor governing the PWSCC of cold-worked austenitic stainless steels. 4. PWSCC mechanism of cold-worked austenitic stainless steels When the slip dissolution SCC model is considered, the crack growth rate of PWSCC may be expressed as a function of the crack tip strain rate (Vankeerberghen et al., 2009, Shoji et al., 2010): a˙ cal = A × fEC × ε˙ m

(8)

where A is a calibration factor, fEC is a function of electrochemical factors, ε˙ is the CTSR, and m is the current decay constant. The CTSR as the primary factor induces periodical rupture of the surface oxide, which sustains the crack growth. Considering the theoretical plastic strain distribution at a growing crack tip, Shoji et al. (1995) proposed a CTSR formulation and also a CGR formulation by combining the oxidation kinetics and the CTSR at a crack tip. The crack advance strain rate component, CTSRCA , calculated in the previous section corresponds to the CTSR by Shoji et al. (2004). In Table 3, compared with the  ys dependence of the CGR, the calculated CTSRCA by the increase in  ys does not seem to be sufficient to explain the observed CGRs of the cold-worked 316 stainless steel in the primary water conditions. Furthermore, this model has some limitation in explaining the effects of sensitization or cathodic treatment on the PWSCC of iron and nickel base alloys while it has been well predicting the SCC CGRs in oxygenated environments such as boiling water reactors (Hua and Rebak, 2004).

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Hall proposed a thermally activated dislocation creep model for the PWSCC of nickel base alloys (Hall, 1995). Assuming that the creep is the primary mechanical factor of SCC, Yang et al. (2014) developed a quantitative prediction model by finite element analysis. It has been confirmed by many researchers (Magnin et al., 1993; Thaveeprungsriporn et al., 1993) that the creep is enhanced in the primary water, indicating that the creep rate at a crack tip could be the primary factor of the PWSCC. The KI and  ys dependence of the creep rate in Table 3 was evaluated using the experimental data on nickel base alloys. Therefore, it is necessary to evaluate the effect of  ys on the creep rates of cold-worked ASS through more accurate experiments or analysis. Nevertheless, since the creep rates were estimated to decrease with the increase in the yield stress from Table 3, the creep component does not seem to be playing a main role in the enhanced PWSCC CGRs of cold-worked ASS. As one of the probable PWSCC mechanisms of Alloy 600, Scott (1999) proposed the internal oxidation mechanism. In the mechanism, oxygen diffuses down the grain boundaries of the alloy, resulting in selective oxidation of Cr. This process occurs ahead of the tip of an active crack and is responsible for embrittlement and subsequent crack growth (Was and Capell, 2007). In this mechanism, the tensile stress can play a role in the following two aspects: (i) enhancement of oxygen diffusion (Krupp et al., 2005) and (ii) fracture of internal oxide. Since the embrittled grain boundaries by oxygen can fracture when the tensile stress at a crack tip is sufficient, this internal oxidation mechanism could be supported by this study. It should be noted that in the finite element analysis the yield stress was used as a mechanical property affected by cold-work with a constant strain hardening coefficient, n. Since by cold-work the values of n as well as  ys are changed, further work should be carried out considering the effect of cold-work on the strain hardening behaviour to more accurate analyses.

5. Conclusions Using finite element analysis, mechanical factors influencing the PWSCC of cold-worked austenitic stainless steels were evaluated. The main conclusions are summarized as follows: (1) The crack tip normal stress increased with KI and  ys while the strain gradient increased with KI but decreased with  ys . (2) The KI and  ys dependence of PWSCC crack growth rates of coldworked 316 stainless steel from literature was evaluated by a multiple regression analysis. In log-log plots, the exponents of KI and  ys were close each other, suggesting that KI and  ys have similar contributions to the PWSCC CGRs. (3) The crack tip strain rates by crack advance and creep rates were estimated by the calculated strain gradients and normal stresses at a crack tip. Evaluated in terms of the KI and  ys dependence, both of the factors do not seem to explain fully the effects of KI and  ys on the measured PWSCC CGRs. (4) The KI and  ys dependence of the crack tip normal stress at a crack tip calculated by multiple regression analysis showed similar trend to that of the PWSCC CGRs, implying that the crack tip normal stress may be the main mechanical factor of the PWSCC of the cold-worked ASS. Also, this study supports the internal oxidation mechanism as the most probable mechanism of the PWSCC.

Acknowledgements The authors are grateful for the financial support and test facilities provided by Khalifa University Internal Research Funding

(KUIRF I - 210029) and the support from Federal Authority for Nuclear Regulation (FANR) for Al Hammadi.

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