Study on the Establishment Method of Service-Induced Crack Acceptance Standards for Reactor Pressure Vessels

Wang Dasheng¹, Duan Yuangang¹, Xiang Wenxin², Jin Ting¹, Qi Lei², Liu Pan¹, Hou Fan³
¹. State Key Laboratory of Nuclear Power Safety Technology and Equipment, China Nuclear Power Engineering Co., Ltd., Shenzhen, Guangdong, 518172, China
². Taishan Nuclear Power Joint Venture Co., Ltd., Taishan, Guangdong, 529200, China
³. China Nuclear Power Operation Co., Ltd., Shenzhen, Guangdong, 518172, China

Abstract

To meet the rapid assessment requirements for cracks discovered during in-service inspection of reactor pressure vessels (RPVs)—referred to as service-induced cracks—it is necessary to develop a methodological framework for establishing acceptance standards. This paper analyzes the principles and methodologies proposed by the Electric Power Research Institute (EPRI) for developing service-induced crack acceptance criteria. Using the postulated crack from RPV design-stage fracture resistance analysis as a benchmark, and incorporating the safety criteria for acceptance standard formulation, we propose a mechanical analysis approach based on design postulated cracks and design safety factors. Application of this method to an RPV shell yields acceptance standards that closely align with those specified in the ASME Code. The proposed mechanical analysis methodology is also applicable to other nuclear power pressure equipment.

Keywords: Reactor pressure vessel; service-induced crack; acceptance standard; safety criterion

1. Introduction

The reactor pressure vessel (RPV) represents a critical and non-replaceable component in nuclear power plants, and its safe and reliable operation constitutes the most important guarantee for nuclear power plant safety [1-2]. During manufacturing, installation, and commissioning, microscopic cracks that are either negligible or undetectable during the design stage may exist within the equipment. Under harsh operating conditions—including high temperature, high pressure, and corrosive environments—and due to gradual material degradation, these microscopic cracks may progressively propagate while new cracks initiate [3-4], posing potential threats to the safe operational status and service life of RPVs. To ensure long-term safe, efficient, and reliable operation of nuclear power plants, both the French RSE-M [5] and American ASME [6] codes require regular non-destructive examinations (NDE) of RPVs during service to analyze and evaluate the impact of detected cracks on equipment safety and operational life. To satisfy engineering demands for rapid assessment of service-induced cracks, research on acceptance standard formulation methods and the development of corresponding acceptance criteria are essential.

Appendix 5.2 of the RSE-M code and IWB-3500 of ASME Section XI provide acceptance standards for service-induced cracks to meet these rapid engineering assessment needs. However, the crack acceptance criteria in RSE-M Appendix 5.2 lack extensive engineering practice documentation, and their development methodology has not been reported in literature. The service-induced crack acceptance standards in ASME Section XI were primarily developed based on EPRI research [7] and are applicable to nuclear plants designed and constructed according to the ASME Code [8]. Chu Qibao et al. [9] investigated the formulation principles of ASME Section XI "service-induced crack acceptance tables," studied the methodology for establishing allowable crack size acceptance criteria for austenitic piping surface cracks, and presented calculation methods for pre-service and service-induced crack allowable dimensions. Chen Mingya et al. [10] adopted plastic limit load as the critical state for austenitic pressure piping structures and, based on the principle of maintaining structural design plastic limit load, proposed acceptance standards for austenitic stainless steel piping service-induced cracks, comparing the results with acceptable crack sizes in ASME and RSE-M codes. EPRI [7,11] conducted comprehensive studies on service-induced crack acceptance standard development, using a postulated crack with depth equal to one-quarter of wall thickness (t/4) and length equal to 1.5 times wall thickness (1.5t) as the benchmark crack for RPV design-stage fracture analysis per ASME Section III Appendix G, incorporating appropriate safety factors to establish service-induced crack acceptance standards that were subsequently incorporated into ASME Section XI.

This paper draws upon EPRI's formulation philosophy and safety criteria for service-induced crack acceptance standards, proposing a mechanical analysis methodology based on design postulated cracks and design safety factors. Using this method, we develop acceptance standards for RPV shell components and compare the results with existing standards in ASME and RSE-M codes.

2. Discussion of EPRI's Methodology for Service-Induced Crack Acceptance Standards

In reference [7], EPRI employs mechanical analysis as the core approach to determine acceptable service-induced crack dimensions, while simultaneously comparing these mechanically derived acceptable crack sizes with equivalent crack sizes from manufacturing-stage NDE acceptable indications to select reasonably conservative values as the final acceptance standards. EPRI established the primary safety criteria and development methodology for nuclear plant equipment service-induced crack acceptance standards [7], which were subsequently applied to the formulation of ASME Section XI acceptance criteria [6].

For RPV service-induced crack acceptance standard development, EPRI utilized the postulated crack from fast fracture analysis conducted during the design stage per ASME Section III Appendix G—a crack with depth t/4 and length 1.5t (designated as aIII)—as the benchmark crack. By incorporating design stress intensity safety margins, they developed the acceptable crack size aXI for Section XI acceptance standards. This methodology ensures that the accepted crack aXI and the design-stage postulated crack aIII possess equivalent crack driving forces when safety factors are considered, representing the key safety principle underlying EPRI's approach.

Since ASME Section III Appendix G's fast fracture analysis methodology remains unchanged, EPRI's RPV service-induced crack acceptance standard development method remains applicable to nuclear plants designed according to the ASME Code. However, for RPVs designed per RCC-M [12] (2007 edition and later), the design-stage postulated crack size was revised from t/4 to 20mm (approximately t/10), which differs significantly from EPRI's benchmark crack size. Consequently, the mechanical analysis method employed in EPRI's acceptance standard development is no longer directly applicable, although the underlying safety philosophy and criteria remain valuable references.

3. Methodology Based on Design Crack and Design Safety Factor

Based on fracture mechanics theory and the safety criteria for service-induced crack acceptance standard formulation presented in EPRI report [7], this section proposes a mechanical analysis methodology for establishing service-induced crack acceptance standards using the postulated crack ad from equipment design-stage fracture resistance analysis as the benchmark crack and the design safety margin Fm from fracture evaluation criteria as the safety factor fs. Employing the design safety margin Fm as the safety factor aligns with EPRI's safety criterion that "the structural integrity safety margin for components containing cracks should not be lower than the safety margin requirements related to material toughness behavior used in equipment design under normal plant operating conditions."

According to fracture mechanics theory [13], the general method for calculating stress intensity factor (SIF) at a crack tip is given by equation (1):

$$K_I = Y\sigma\sqrt{\pi a}$$

where Y is the crack shape factor (related to crack depth, shape, and structural geometry, obtainable from SIF calculation handbooks or code-specified methods), σ is the stress distribution at the crack location, and a is the crack size.

The methodology for developing service-induced crack acceptance standards is as follows:

(1) From equation (1), the design-stage postulated crack ad is expressed by equation (2):

$$a_d = \frac{1}{\pi}\left(\frac{K_{Id}}{Y_d\sigma}\right)^2$$

where KId is the SIF for crack ad and Yd is the shape factor for crack ad.

(2) Maintaining crack driving force KId consistent with that used in design-stage fracture resistance analysis and applying safety factor fs to the crack driving force, the allowable crack size aa for in-service acceptance standards is given by equation (3):

$$a_a = \frac{1}{\pi}\left(\frac{K_{Id}}{fs \cdot Y_a\sigma}\right)^2$$

Conservatively assuming in-service operating loads are identical to design loads, combining equations (2) and (3) yields the allowable crack aa for service-induced acceptance standards as shown in equation (4):

$$a_a = \left(\frac{Y_d}{fs \cdot Y_a}\right)^2 a_d$$

Using equation (4) with design-stage postulated crack sizes ad under various loading conditions and the corresponding safety margins Fm from code requirements, and by consulting shape factors Y for different crack geometries, service-induced crack acceptance standards can be established.

4. Case Study

Using an RPV designed per the 2007 edition of RCC-M as the analysis object, we apply the methodology proposed in Section 3 to develop acceptance standards for RPV shell surface cracks. The RPV shell has wall thickness t = 200mm and inner radius Ri = 1995mm [14].

4.1 Stress Intensity Factor Calculation

Per RCC-M's influence function method for SIF calculation, the stress distribution at the crack location is first fitted using a polynomial as shown in equation (5):

$$\sigma(x) = \sigma_0 + \sigma_1\left(\frac{x}{L}\right) + \sigma_2\left(\frac{x}{L}\right)^2 + \sigma_3\left(\frac{x}{L}\right)^3 + \sigma_4\left(\frac{x}{L}\right)^4$$

where x represents the distance from the point to the vessel wall (0 ≤ x ≤ L), and L represents the distance for stress polynomial fitting (0 ≤ L ≤ t), with t being the structural wall thickness.

The SIF is then calculated using equation (6):

$$K_I = \sqrt{\pi a}\sum_{i=0}^{4}\sigma_i i_j$$

where i0, i1, i2, i3, and i4 are influence functions, and a is the crack depth.

Assuming the stress on the crack plane as membrane stress conservatively equal to the maximum stress at the crack cross-section, the SIF calculation simplifies to equation (7):

$$K_I = i_0\sigma\sqrt{\pi a}$$

Transforming equation (7) yields the crack size expression in equation (8):

$$a = \frac{1}{\pi}\left(\frac{K_I}{i_0\sigma}\right)^2$$

According to fracture mechanics theory, the influence coefficient i0 in equation (8) is equivalent to the shape factor Y in equation (4).

4.2 Benchmark Crack Size and Safety Margin

Using the postulated crack from RPV design-stage fracture resistance analysis per RCC-M Appendix ZG as the benchmark crack ad, the benchmark crack has depth ad = 20mm and aspect ratio a/2c = 1/6. The design safety margins Fm for various loading conditions in fracture evaluation criteria are shown in [TABLE:1]. Conservatively using the maximum design safety margin from normal operating conditions (Level A criteria) as the safety factor fs, we take fs = 2.

[TABLE:1]

4.3 Service-Induced Crack Acceptance Standard Results

Based on equation (8) and the relationship between allowable crack aa and benchmark crack ad from equation (4), the allowable crack size aa in the acceptance standard is given by equation (9):

$$a_a = \left(\frac{i_{0d}}{fs \cdot i_{0a}}\right)^2 a_d$$

where i0d is the influence coefficient for the benchmark crack and i0a is the influence coefficient for the acceptable crack. In this analysis, the wall thickness to radius ratio is approximately t/Ri = 1/10. Influence coefficients for cracks of various depths and aspect ratios can be obtained from tables provided in RSE-M Appendix 5.4 [5]. For shell surface cracks, interpolation yields i0d = 0.9827. The resulting service-induced acceptance standard is presented in [TABLE:2].

[TABLE:2]

A comparison between the RPV shell service-induced crack acceptance standard developed using the proposed method and those specified in ASME and RSE-M codes is shown in [TABLE:3] and illustrated in [FIGURE:1].

[TABLE:3]

[FIGURE:1]

The comparative analysis demonstrates that the acceptance standard developed using the proposed method is essentially consistent with the ASME Code acceptance standard, validating the rationality of the methodology. The minor differences from the ASME standard primarily arise from the use of shape coefficients from RSE-M (versus ASME) for SIF calculations and because ASME's acceptance criteria also consider equivalent crack sizes from acceptable NDE indications. Additionally, the analysis reveals that RSE-M acceptance standards are more lenient than ASME standards.

This case study focused on RPV shells; however, the proposed mechanical analysis methodology for developing service-induced crack acceptance standards is equally applicable to other nuclear pressure equipment.

Conclusions

To ensure long-term safe and efficient operation of nuclear power plants, acceptance standards for RPV service-induced cracks must be established to meet engineering requirements for rapid assessment. This paper proposes a mechanical analysis methodology for developing equipment service-induced crack acceptance standards. Applying this method to RPV shells yielded acceptance standards that were compared with existing nuclear code requirements.

1) Due to differences between equipment design-stage postulated crack sizes and EPRI's benchmark crack size for service-induced crack acceptance standard development, EPRI's acceptance tables are not directly applicable to RPVs designed per RCC-M 2007 and later editions.

2) Drawing upon EPRI's formulation philosophy and safety criteria, this paper presents a mechanical analysis methodology for establishing service-induced crack acceptance standards based on design postulated cracks and design safety factors.

3) Application of the proposed method to RPV shells produced acceptance standards that show close agreement with ASME Code requirements, thereby validating the methodology's rationality.

It should be noted that while the proposed method addresses service-induced crack acceptance standard development from a mechanical analysis perspective, practical engineering implementation should also incorporate appropriate modifications based on NDE requirements. Further research will continue in this area.

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