Fatigue crack growth behavior of a 170 mm diameter stainless steel straight pipe subjected to combined torsion and bending load

Abstract

In a nuclear powerplant, the rotary equipment, such as a pump directly fitted with hanger in the piping system, experiences torsional and bending loads. Higher crack growth rate occurs because of this torsional load in addition to the bending load. Hence, it is necessary to study the fatigue behavior of piping components under the influence of combined torsional and bending load. In this study, experimental fatigue life evaluation was conducted on a notched stainless steel SA312 Type 304LN straight pipe having an outer diameter of 170 mm. The experimental crack depth was measured using alternating current potential drop technique. The fatigue life of the stainless steel straight pipe was predicted using experiments, Delale and Erdogan method, and area-averaged root mean square–stress intensity factor approach at the deepest and surface points of the notch. Afterward, the fatigue crack growth and crack pattern were discussed. As a result, fatigue crack growth predicted using analytical methods are in good agreement with experimental results.

Graphical abstract

Keywords

fatigue life / Delale and Erdogan method / RMS–SIF approach / stainless steel / torsion and bending load / fatigue crack growth

1 Introduction

Fatigue failure is an accumulative damage of a material under repeated or fluctuating load. Efforts to prevent fatigue failure may have different objectives such as infinite lifespan and reliability depending on the importance of the structural system under consideration. For a circumferentially cracked pipe, the effect of axial force and bending moment are provided in the American Society of Mechanical Engineers Boiler and Pressure Vessel Code (ASME BPVC) Section XI [1] or the Japan Society of Mechanical Engineers Fitness-For-Service Code [2]. However, torsional moment has not yet been considered. Generally, nuclear powerplant pipelines are subjected to pressure as well as torsional and bending moments owing to seismic or mechanical loads. Therefore, loading conditions such as combined torsional and bending moments may influence the failure of a piping system. In design and construction codes, the combined torsional and bending moments need to be considered for pipes without cracks. Various studies on piping components in nuclear powerplants have shown that the piping components may experience combined bending and torsional moments during operation. Thus, the flaw evaluation of pipes under the influence of combined bending and torsional moments with the local wall thinning flaws needs guidance. Currently, the flaw evaluation procedure for a pressurized piping component under the influence of combined torsional and bending moments with local wall thinning flaws has been developed by ASME BPVC Section XI Working Group.

Li et al. [3] conducted failure analysis for 4–24-inch (100–600 mm) diameter pipes, and introduced an equivalent moment that combined bending and torsional moments by a vector summation. Another analysis was performed by Hasegawa et al. [4] on 24-inch (600 mm) diameter straight pipes with local wall thinning under the influence of combined bending and torsional moments. It was found that the equivalent moment, defined as the root of the sum of the squares (RSS) of the torsional and bending moments, was equal to the pure bending moment when the wall thinning depth was shallow. Meanwhile, Pukazhendhi et al. [5] conducted experimental studies on piping components under the influence of combined torsional and bending loads with different load ranges. They concluded that further studies need to be done on combined torsional and bending moments in piping components under different loadings with various moment-to-torsion (M/T) ratios. Additionally, Paris and Erdogan [6] proposed a crack propagation law, and Delale and Erdogan [7] introduced a method that is widely used for fatigue crack growth analysis. Moreover, Cruse and Besuner [8] introduced a powerful analytical method in which root mean square–stress intensity factor (RMS–SIF) was used to study fatigue crack growth. Arora et al. [9] successfully utilized the RMS–SIF method to study the fatigue crack growth behavior of piping components. In summary, fatigue crack growth analysis has been performed using various experimental and analytical investigations based on different methods [9,10], sizes of piping components [11–16], environmental conditions [17,18], and loading values [19-22].

In this study, the effects of combined torsional and bending loads on notched stainless steel straight pipes were investigated. An experimental study was conducted on a pipe with a circumferential outer surface notch under the influence of combined torsional and bending loads, and the results were compared with the fatigue crack growth and fatigue life estimation results obtained using analytical calculation. In this paper, the experimental and analytical (Delale and Erdogan method and RMS–SIF approach) investigations of the fatigue crack growth behavior of a stainless steel pipe subjected to combined torsional and bending loads are reported.

2 Experimental conditions and analytical methods

2.1 Details of the pipe specimen

The pipe specimen employed in the fatigue test was SA 312 Type 304LN austenitic stainless steel pipe. Tables 1 and 2 summarize the mechanical properties and chemical composition of the stainless steel pipe, respectively. The mechanical properties and chemical composition for the Type 304LN stainless steel pipe based on the American Society for Testing and Materials specifications are also provided.

The pipe specimen (referred to as SSTB 6-1) had a machined part-through circumferential notch on the outer surface, and its initial depth and length were 4.4 and 42.0 mm, respectively. The details of the pipe specimen and the notch dimensions are tabulated in Table 3.

2.2 Fatigue test

Fatigue test was conducted at room temperature (27°C±5°C). Combined torsional and bending loads were applied via the loading arms, which were welded upright to the pipe in the horizontal plane, and the test was conducted under a four-point bending loading condition without internal pressure. The schematic diagram of the fatigue test is shown in Figure 1. The notch was located at the maximum bending moment of the pipe specimen. The lengths of the outer and inner spans were 1700 and 680 mm, respectively. Figure 2 depicts a top view of the fatigue test. The angle between the torsional moment of the loading beam and the center line of the pipe was 45°. The center point of the loading beam was set up to coincide with the center point of the pipe specimen. Figure 3 shows a photograph of the pipe specimen and the testing machine. The length of the load connector was approximately 300 mm, and it did not touch the top of the pipe specimen during the test. The capacity of the hydraulic actuator was ±1000 kN.

The details of the loading and fatigue life are given in Table 4. The fatigue test was conducted under a load control condition with a M/T of 1.45. The bending moment M was calculated for the 680 mm span of the straight pipe, whereas the torsional moment T was calculated for the 275 mm distance between the loading arm and the center of the straight pipe. The test frequency was varied from 0.2 to 0.5 Hz, and the stress ratio was 0.1. Furthermore, the crack depth was measured using alternating current potential drop technique at different intervals. To measure the crack depth and crack length, the notch portion was divided into A and B as shown in Figure 4. The crack length was considered as zero at both tips of the notch and the crack length has measured using high quality video microscope. A strain gauge was fixed along the longitudinal and outer surface of the pipe such that it was diametrically opposite to the notch location. Afterward, the notch was subjected to a combined bending and torsional stress. A typical experimental stress wave phase at 0.5-Hz test frequency is shown in Figure 5.

2.3 Analytical studies

2.3.1 Method I: Fatigue life prediction using Delale and Erdogan approach

A pipe specimen with a semi-elliptical outer surface notch was considered for fatigue life analysis using Delale and Erdogan method [7]. The equivalent moment on the pipe specimen due to both applied pure bending and torsional loads was computed using:

(1)M_{\mathrm{equ}}={\displaystyle \frac{\mathrm{1}}{\mathrm{2}}}[M+\sqrt{M^{\mathrm{2}}+T^{\mathrm{2}}}],

where M is the applied bending moment, T is the torsional moment, and M_{\mathrm{equ}} is the equivalent bending moment. The bending and torsional moments were calculated for the applied load P. The maximum and minimum applied stresses developed on the pipe owing to the corresponding equivalent moment were calculated using:

(2)\sigma ={\displaystyle \frac{\mathrm{32}D{M}_{\mathrm{equ}}}{\mathrm{\pi }(D^{\mathrm{4}}-d^{\mathrm{4}})}},

where σ, D, and d represent the applied stress, outer diameter of the pipe, and inner diameter of the pipe, respectively.

Furthermore, the SIF was calculated [24] using:

(3)K_{\mathrm{0}}={\displaystyle \frac{\mathrm{6}{M}_{\infty }}{t^{\mathrm{2}}}}\sqrt{t}{g}_{\mathrm{b}}({\xi }_{\mathrm{0}}),

where K_{\mathrm{0}} represents the stress intensity factor of the corresponding two-dimensional plane strain crack geometry and t represents the pipe thickness. Thus, {\xi }_{\mathrm{0}}={\displaystyle \frac{a}{t}}. The geometry factor g_{\mathrm{b}}(\xi ) was calculated as follows:

(4)g_{\mathrm{b}}(\xi )=\sqrt{\pi \xi }(\mathrm{1.1202}-\mathrm{1.8872}\xi +\mathrm{18.0143}{\xi }^{\mathrm{2}}-\mathrm{87.3851}{\xi }^{\mathrm{3}}+\mathrm{241.9124}{\xi }^{\mathrm{4}}-\mathrm{319.9402}{\xi }^{\mathrm{5}}+\mathrm{168.0101}{\xi }^{\mathrm{6}}),

The normalizing SIF value K/K₀ was obtained from Murakami and Keer [24]. Additionally, the SIFs of K_max and K_min were calculated from their corresponding maximum and minimum principal stresses.

It is well known that fatigue crack growth rate da/dN is expressed as a function of the SIF range. This function is generally of the form:

(5){\displaystyle \frac{\mathrm{d}a}{\mathrm{d}n}}={\displaystyle \frac{C{(\mathrm{1}+\beta )}^m{(\mathrm{\Delta }K)}^{\alpha }}{K_c-(\mathrm{1}+\beta )\mathrm{\Delta }K}},

where C, m, and α are material constants. The unit of ΔK, K_max, and K_min is MPa/m, whereas that of da/dN is mm/cycle. Meanwhile, experimental investigations of fatigue crack growth on six compact tension C(T) specimens (CT-22-T, CT-19-T, CT-16-T, CT-22-F, CT-19-F, and CT-16-F) have been conducted at room temperature to determine the material constants C, m, and \alpha [25]. The number of cycles was calculated until the crack depth reached 80% of the wall thickness of the pipe specimen.

2.3.2 Method II: Root mean square-stress intensity factor approach

A powerful method that accounts for the area-averaged RMS–SIF (K_RMS) at the deepest and surface points of a pipe was proposed by Cruse and Besuner [8]. The K_RMS values in the thickness and circumferential directions were calculated using the following procedure.

(i) Evaluation of K_RMS in the thickness (a) direction

Figure 6 shows a crack profile in the thickness direction, where a is the initial crack depth, c is one-half the total crack length, and Δa is the incremental crack depth in the thickness direction.

The square of the RMS–SIF in the thickness direction is expressed as

(6)K_{\mathrm{rms,a}}^{\mathrm{2}}={\displaystyle \frac{\mathrm{1}}{\mathrm{\Delta }{S}_{\mathrm{a}}}}{\displaystyle {\int }_{\mathrm{\Delta }{S}_{\mathrm{a}}}{K}^{\mathrm{2}}}(\varphi )\mathrm{d}{S}_{\mathrm{a}},

where ΔS_a represents an incremental crack depth area and dS_a is the variable of integration, which are given by

(7)\mathrm{\Delta }{S}_{\mathrm{a}}={\displaystyle \frac{\mathrm{1}}{\mathrm{2}}}\mathrm{\pi }c\mathrm{\Delta }a,

(8)d{S}_{\mathrm{a}}=c\mathrm{\Delta }a{\sin }^{\mathrm{2}}\varphi \mathrm{d}\varphi ,

Substituting Eqs. (7) and (8) into Eq. (6), K_{\mathrm{rms,a}}^{\mathrm{2}}and K_{\mathrm{rms,a}} become:

(9)K_{\mathrm{rms,a}}^{\mathrm{2}}={\displaystyle \frac{\mathrm{2}}{\mathrm{\pi }c\mathrm{\Delta }a}}{\displaystyle {\int }_{\mathrm{\Delta }{S}_{\mathrm{a}}}{K}^{\mathrm{2}}}(\varphi )c\mathrm{\Delta }a{\sin }^{\mathrm{2}}\varphi \mathrm{d}\varphi ,

(10)K_{\mathrm{rms,a}}=\sqrt{{\displaystyle \frac{\mathrm{2}}{\mathrm{\pi }}}{\displaystyle \underset{\mathrm{0}}{\overset{\mathrm{\pi }}{\int }}{K}^{\mathrm{2}}(\varphi ){\sin }^{\mathrm{2}}\phi \mathrm{d}\varphi }},

where K_rms,a represents the RMS–SIF in the a direction, K_rms,a,max, and K_rms,a,min are the maximum and minimum values of K_rms in the a direction corresponding to the maximum and minimum loadings, and ϕ is the angle of the crack front.

(11)\mathrm{\Delta }{K}_{\mathrm{rms,a}}=K_{\mathrm{rms,a,max}}-K_{\mathrm{rms,a,min}},

Using Eq. (11), the values of ∆K_rms in the thickness direction were calculated.

(ii) Evaluation of K_RMS in the crack circumferential (c) direction

Figure 7 shows a crack profile in the circumferential direction, where a is the initial crack depth, c is one-half the total crack length, and Δc is the incremental surface crack length.

The square of the RMS–SIF in the circumferential direction is expressed as

(12)K_{\mathrm{rms,c}}^{\mathrm{2}}={\displaystyle \frac{\mathrm{1}}{\mathrm{\Delta }{S}_{\mathrm{c}}}}{\displaystyle {\int }_{\mathrm{\Delta }{S}_{\mathrm{c}}}{K}^{\mathrm{2}}}(\varphi )\mathrm{d}{S}_{\mathrm{c}},

where ΔS_c represents an incremental crack length area and dS_c is the variable of integration, which are given by

(13)\mathrm{\Delta }{S}_{\mathrm{c}}={\displaystyle \frac{\mathrm{1}}{\mathrm{2}}}\mathrm{\pi }a\mathrm{\Delta }c,

(14)\mathrm{d}{S}_{\mathrm{C}}=a\mathrm{\Delta }c{\cos }^{\mathrm{2}}\varphi \mathrm{d}\varphi ,

where Δc represents an incremental crack length.

Substituting Eqs. (13) and (14) into Eq. (12), K_{\mathrm{rms,c}}^{\mathrm{2}}and K_{\mathrm{rms,c}} become:

(15)K_{\mathrm{rms,c}}^{\mathrm{2}}={\displaystyle \frac{\mathrm{2}}{\mathrm{\pi }a\mathrm{\Delta }c}}{\displaystyle {\int }_{\mathrm{\Delta }{S}_{\mathrm{C}}}{K}^{\mathrm{2}}}(\varphi )a\mathrm{\Delta }c{\cos }^{\mathrm{2}}\varphi \mathrm{d}\varphi ,

(16)K_{\mathrm{rms,c}}=\sqrt{{\displaystyle \frac{\mathrm{2}}{\mathrm{\pi }}}{\displaystyle \underset{\mathrm{0}}{\overset{\mathrm{\pi }}{\int }}{K}^{\mathrm{2}}(\varphi ){\cos }^{\mathrm{2}}\phi \mathrm{d}\varphi }},

where K_rms,_c represents the RMS–SIF at c, and K_rms,c,max, and K_rms,c,min are the maximum and minimum values of K_rms in the circumferential direction corresponding to the maximum and minimum loadings, respectively.

(17)\mathrm{\Delta }{K}_{\mathrm{rms,c}}=K_{\mathrm{rms,c,max}}-K_{\mathrm{rms,c,min}},

The number of cycles corresponding to the K_RMS values in the thickness and circumferential directions were calculated using Paris’ law [6].

(18){\displaystyle \frac{\mathrm{d}a}{\mathrm{d}N}}=C{(\mathrm{\Delta }{K}_{\mathrm{rms,a}})}^m\mathrm{and}{\displaystyle \frac{\mathrm{d}c}{\mathrm{d}N}}=C{(\mathrm{\Delta }{K}_{\mathrm{rms,c}})}^m,

where da/dN is the rate of fatigue crack propagation per cycle, ∆K_rms,a and ∆K_rms,c represent the RMS–SIF range obtained by Eqs. (11) and (17) in the thickness and circumferential directions, respectively.

3 Results and discussion

Fatigue crack growth analyses were performed on the notched stainless-steel straight pipe subjected to combined torsional and bending loads by experimental and analytical (Delale and Erdogan method and RMS–SIF approach) investigations. Here, the primary assumption that crack growth is mainly in-depth direction [26] was examined by conducting an experimental study on the combined torsional and bending loadings. The SIFs were analytically evaluated as the crack depth increased at 0.5 mm intervals. Meanwhile, an increase in SIF led to an increase in the crack growth rate under constant loading.

The experimental number of loading cycles required for the pipe specimen to have a crack depth of 11.2 mm (80% of the pipe wall thickness) was 105715, whereas the analytical number of loading cycles obtained from Delale and Erdogan method and RMS–SIF approach were 76207 and 90996, respectively. As a result, a reduction in fatigue life was observed at 27.9% and 13.9% from the Delale and Erdogan method and K_RMS approach, respectively, compared with the experimental values.

Figure 8 shows the photographic view of a cracked section of the pipe after fatigue and fracture tests. Figure 9(a) shows the variation of the crack depth vs. number of cycles for the pipe specimen using Delale and Erdogan method, RMS–SIF approach, and experiments. The experimental surface crack lengths for notch tips A and B were 9.4 and 14.38 mm, respectively, whereas the corresponding analytical surface crack lengths were 7.5 and 9.0 mm. From the analytical results, the crack length of tips A and B of the pipe specimen decreased to 20.3% and 32.7% (Methods I and II) compared to the experimental values.

Figures 9(b) and 9(c) show the comparison of crack length vs number of cycles for tips A and B of the pipe specimen obtained from experiments and analytical calculations. To observe the crack profile from the beginning to the end, we chose several lines at a particular interval. The experimental crack growth profile is shown in Figure 10(a). The shape of the semi-elliptical notch was slightly changed during the analysis because of the increasing crack depth at 0.5 mm intervals. The analytical crack growth profile is shown in Figure 10(b).

4 Conclusions

In this work, an experimental fatigue crack growth study was conducted on a Type 304LN stainless steel straight pipe with a circumferential outer surface notch subjected to a combined torsional T and bending M load. The test was conducted under a load control condition with M/T ratio of 1.45. Analytical fatigue crack growth studies were also carried out on the same pipe specimen using Delale and Erdogan method and RMS–SIF approach. Based on the comparisons of the experimental and analytical results, the following conclusions are made:

The predicted analytical fatigue life from the Delale and Erdogan method and RMS–SIF approach reached 74.4% (78714 cycles) and 86.1% (90996 cycles), respectively, compared with that of the experimental fatigue life (105715 cycles). Furthermore, surface crack growth was observed in the diagonal direction with respect to both notch tips A and B owing to the effect of torsional loading on the pipe specimen. Therefore, the RMS–SIF method is more reliable for analytical fatigue life prediction compared to Delale and Erdogan method.

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