EVALUATION OF TORSION AND BENDING COLLAPSE MOMENTS FOR PIPES WITH LOCAL WALL THINNING

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1 Proceedings of the ASE 11 Pressure Vessels & Piping Division Conference PVP11 July 17-1, 11, Baltimore, aryland, USA Proceedings of the ASE Pressure Vessel and Piping Division Conference PVP11 July 17-1, 11, Baltimore, aryland, USA PVP EVALUATION OF TORSION AND BENDING COLLAPSE OENTS FOR PIPES WITH LOCAL WALL THINNING Kunio Hasegawa Japan Nuclear Energy Safety Organiation (JNES) Toranomon , inatoku, Tokyo 15-1, Japan jnes.go.jp Bostjan Beensek Hunting Energy Service (UK) Ltd. Badentoy Avenue, Badentoy Industrial Park Portlethen, Aberdeen, Scotland AB1 4YB, UK Yinsheng Li Japan Nuclear Energy Safety Organiation (JNES) Toranomon 4-3-, inatoku, Tokyo 15-1, Japan Phuong Hoang Sargent & Lundy LLC 55E. onroe Street, Chicago, IL 663, USA ABSTRACT ASE B&PV Code Section XI provides fully plastic bending fracture evaluation procedures for pressuried piping components containing flaws subjected to bending and membrane loads. The piping components in power plants may eperience only bending moments but also occasionally small torsion moments, simultaneously. Currently, there is a lack of guidance in the Section XI for combined loading modes including torsion. Finite element analyses were conducted in this paper for 4-inch diameter straight pipes with local wall thinning. The pipe was subject to combined bending and torsion moments. It is shown that the effect of torsion moment on plastic collapse bending moment for the pipes depends on the local wall thinning sies. In addition, it is found that the equivalent moments defined as the root of the sum of the squares (RSS) of the torsion and bending moments is equal to pure bending moments, when wall thinning depth is shallow. INTRODUCTION Piping items in power plants may eperience combined bending and torsion loading during operation. Local wall thinning may be detected in piping systems and assessed using fitness-for-service procedures. Currently, there is a lack of guidance in the Boiler Code, Section XI for such case. The Working Group on Pipe Flaw Evaluation of ASE (American Society of echanical Engineers) Boiler and Pressure Vessel Code Section XI is currently developing guidance for crack-like flawed pipes subjected to combined torsion and bending moments [1-4]. These moments were obtained by Finite Element (FE) analysis under elastic-fully plastic conditions. The guidance for a pipe containing crack-like flaw pipe has almost been completed, and codification is under discussion at the Working Group. Net step to consider is a pipe with local wall thinning. This paper focuses on the collapse bending moments at small torsion moments for large diameter pipes with local wall thinning. Guidance is given on equilibrium collapse moment for combined torsion and bending moments together in the presence of the internal pressure for a pipe with local wall thinning in this paper. FINITE ELEENT ANALYSIS FOR PIPES SUBJECTED TO TORION AND BENDING OENTS Finite Element Analysis Conditions Plastic collapse bending moments for large diameter pipes with local wall thinning inside the pipe were calculated for the condition of torsion moments and internal pressure by Finite Element (FE) analysis. The model is illustrated in Fig. 1. The pipe is a 4-inch (6A) schedule 8 pipe, where the outer diameter D is 69.6 mm, and the wall thickness is 3.9 mm. 8D Wall thinning D T Fig. 1 odel of locally wall thinned pipe subjected to torsion and bending moments B 1 Copyright 11 by ASE 1 Copyright 11 by ASE Downloaded From: on 11/5/14 Terms of Use:

2 The length of the pipe is eight times larger than the outer diameter. The center of the wall thinning is at pipe mid-length. All of the displacements at one end of the pipe are fied, and torsion moment and bending moment are applied at the other end of the pipe. Internal pressure of 8 Pa is also applied for the pipe, where 8 Pa corresponds to hoop stress of 74.9 Pa. The wall thinning area is located in tensile stress side during bending. Table 1 shows the calculation conditions for the FE analysis. The FE analysis was conducted by ABAQUS Standard v The large deformation of geometry change is invoked in order to obtain plastic collapse moment accurately under large deformation. The material in this analysis has elastic-fully plastic stress-strain curve with the yield stress of 338 Pa, which is identified with the flow stress of the material. The geometries of the wall thinning region in the calculations are as follows. The thinning angle θ is ranged from 3 o to 36 o, and the ratios of wall thinning depth to wall thickness a/t are.5 and.75, where a is the wall thinning depth and t is the pipe wall thickness. The wall thinning length ranges from.5d to 5. D. Calculation matri is tabulated in Table. Table 1 Calculation conditions for FE analysis. Aial direction R i θ D / R i π Circumferential direction r y ξ r y r = 1 y ξ=d o / a/t=.75 t (1) Round concave in a plate 8D Program ABAQUS Stress-strain curve Elastic fully plastic Geometrical non-linearity Considered Yield (flow) stress, σ y,(σ f ) 338 Pa Young s modulus, E 3 GPa Strain hardening, H Pipe outer diameter, D 69.6 mm Pipe wall thickness, t 3.9 mm Thinning depth, a/t.5 and.75 Thinning angle, θ o 3, 9, 18, 7, 36 Thinning length, L/D.5, 1.,., 3., 4., 5. Internal pressure (hoop stress) 8. Pa (74.9 Pa) Wall Thinning Conditions The shape of the wall thinning is a round concave. Figure illustrates the formation of a local round wall thinning in a pipe. Round concave is a part of sphere which is epressed by, y ξ =1 (1) r ry r where is the ais of the circumferential direction, y the ais of the radius direction, the ais of the aial direction, ξ is the length between the center of the sphere and the inside radius of the pipe, as shown in Fig. (1). The concave shape is immersed on a flat plate and the plate is subsequently transformed into a pipe as shown in Fig. (), such that the wall thinning forms inside the pipe. For the wall thinning angle of 36 o, the above procedure is not used and the wall thickness is simply reduced and kept uniform around the circumference. Details of the FE mesh for the local wall thinning is shown in Fig. 3. Aial cross section of the pipe mesh is depicted in Fig. 3(1) and the shape of the round wall thinning is shown in Fig. 3(). The loading was applied in three steps: first pressuriing the pipes to the pressure of 8 Pa, then applying the given torsion moment T on the pipe end, and finally the bending moment was imposed by rotation of the remote end, as illustrated in Fig. 1. The applied torsion moment is calculated from the corresponding shear stress τ. The relation between nominal torsion moment T and shear stress not taking the account of the wall thinning is epressed by, T () Round wall thinning in a pipe Fig. Formation of a local round wall thinning inside a pipe = πr tτ () where R is the pipe mean radius. The wall thinning is located such that its center coincides with the plane of the maimum tensile stress due to bending. The bending was imposed in small increments until the maimum bending moment was obtained as observed by the reaction moment vs. bending rotation plot. Copyright 11 by ASE Copyright 11 by ASE Downloaded From: on 11/5/14 Terms of Use:

3 CALCULATION RESULTS Plastic Collapse Bending and Torsion oments The pure bending moments and pure torsion moments at collapse are shown in Table, where B is the collapse bending moment without torsion moments and T is the pure torsion moment at collapse. These B and T moments decrease with increasing wall thinning depths, angles and lengths. any of bending tests have been performed on ductile carbon steel pipes with local wall thinning. From these test data, plastic collapse moments based on limit load criteria can be estimated by ultimate tensile strength of the pipe materials [5]. In this paper, the plastic collapse moment B obtained by the FE analyses are not compared with the moments derived from the limit load criteria. This is because the present results are based on the material s yield stress whereas the limit load criteria use the ultimate tensile strength. Figure 4 shows the relationship between the bending moment and the bending angle for a pipe with local wall thinning of a/t =.75, L/D = 1. and θ = 9 o, as a function of torsion stress. Torsion stress is epressed as a ratio of the flow (1) Aial cross section of pipe with wall thinning stress, where the flow stress is 338 Pa. The moment angle curve is shown in Fig. 5 for the case of a longer wall thinning of a/t =.75, L/D =. and θ = 9 o. The moment-angle pattern for the pipe with the longer wall thinning is similar to the pipe with the shorter wall thinning of L/D = 1.. It can be seen that, from Figs. 4 and 5, the bending moment b increases with increasing bending angle θ b and attains the maimum bending moment. After the maimum bending moment, applied bending moment decreases with increasing bending angle θ b. The maimum bending moment corresponds to the plastic collapse moment B. The plastic collapse moment B decreases with increasing torsion stress. Table Pure bending and torsion moments at collapse. a/t L /D θ, o B, kn-m T, kn-m () Shape of wall thinning inside a pipe. Fig. 3 FE mesh break down for locally wall thinned pipe. A moment-rotation curve between pure torsion moment t and torsion angle θ t are shown in Figs. 6 and 7. Figure 6 shows the results for the pipe with wall thinning of a/t =.75, L/D = 1. and θ = 9 o, and Fig. 7 for the a/t =.75, L/D =. and θ = 9 o. Torsion moment t increases with increasing torsion angle θ t and shows the maimum moment T. When the wall thinning length increases from L/D = 1. to., the maimum moment T decreases slightly. Torsion Effect on the Plastic Collapse Bending oment Calculation results for locally thinned pipes subjected to bending moments under torsion moment were calculated by FE 3 Copyright 11 by ASE 3 Copyright 11 by ASE Downloaded From: on 11/5/14 Terms of Use:

4 analyses. The plastic collapse bending moments were obtained as a function of torsion moments. Table 3 shows one case of the calculation results of the plastic collapse bending moments for a pipe with local wall thinning of a/t =.75, L/D = 1. and θ = 9 o. Nominal torsion moments T given by the ratio of the torsion stress to the flow stress τ/σ f were calculated by Eq. (). When τ/σ f =, the bending moment B becomes pure bending moment B, and when B =, T becomes pure torsion moment T. It can be seen that the plastic collapse moment B decreases with increasing torsion moment T. Plastic collapse bending moments for pipes with longer wall thinning are shown in Table 4. The shape of the wall thinning is 3 a/t =.75, L/D =. and θ = 9 o. The torsion moments T epressed as a function of the stress ratio τ/σ f are the same as those tabulated in Table 3, because they are calculated using the Eq. () and remain independent for the flaw geometry. The plastic collapse bending moments also decrease with increasing the torsion moments. The pure torsion moment T decreases, when the wall thinning length is long from L/D = 1. to L/D =.. EQUIVALENT PLASTIC COLLAPSE OENTS It is shown that the plastic collapse bending moments for pipes with local wall thinning are affected by the torsion moments. In accordance with the construction codes [6, 7], 3 Bending moment, b, kn-m a/t =.75 θ = 9 o L = D τ/σf=. τ/σf=.1 τ/σf=.15 τ/σf=. τ/σf=.5 τ/σf=.3 τ/σf=.35 τ/σf= Bending angle, θ b, rad Fig. 4 Relationship between bending moment and angle for a pipe with wall thinning of a/t =.75, θ = 9 o and L/D =1.. 3 Torsion moment, t, kn-m Fig. 6 Relationship between torsion moment and angle for a pipe with wall thinning of a/t =.75, θ = 9 o and L/D =1.. 3 Pure torsion Torsion angle, θ t, rad a/t =.75 θ = 9 o L = D Bending moment, b, kn-m τ/σf=. a/t =.75 τ/σf=.1 τ/σf=.15 θ = 9 o τ/σf=. 5 L = D τ/σf=.5 τ/σf= Bending angle, θ b, rad Fig. 5 Relationship between moment and angle for a pipe with wall thinning of a/t =.75, θ = 9 o and L/D =.. 4 Torsion moment, t, kn-m Pure torsion Torsion angle, θ t, rad a/t =.75 θ = 9 o L = D Fig. 7 Relationship between torsion moment and angle for a pipe with wall thinning of a/t =.75, θ = 9 o and L/D =.. Copyright 11 by ASE 4 Copyright 11 by ASE Downloaded From: on 11/5/14 Terms of Use:

5 Table 3 Calculation results for equivalent moments for a pipe with wall thinning of a/t =.75, θ = 9 o and L/D =1.. τ/σ f T, kn-m B, kn-m eq, kn-m a/t = L /D = θ = 9 o Table 4 Calculation results for equivalent moments for a pipe with wall thinning of a/t =.75, θ = 9 o and L/D =.. τ/σ f T, kn-m B, kn-m eq, kn-m a/t = L /D = θ = 9 o combination of bending and torsion loads are resolved into orthogonal moment components and summed into an equivalent load by vector summation. The equivalent moment eq is given by, = (3) eq y where the equivalent moment eq is a resultant moment applied in the calculation to combine the orthogonal moment components,, y and at a given position in a piping system. In the construction code, the assumption is that these piping items do not have cracks or local wall thinning. This approach is eamined below for the analyed case of pipes with local wall thinning. An engineering approach of combined torsion with the bending load for a pipe with a circumferential crack is proposed in reference [8] as follows; eq = ( C ) (4) B e T where C e is the weighting factor. Using ABAQUS finite element modeling to calculate the J-integral at the crack tip of a circumferential through-wall cracked pipe, the weighting factor of C e = 3 / is added on the torsion moment to accurate combine bending and torsion moments into an effective moment. 5 The reference [3] shows that the weighting factor becomes a function of the torsion moment for a pipe containing crack-like flaws. In many cases, the C e = 1. was found. By using C e =1., the equivalent moment for Ref. [8] becomes the equivalent moment of the construction code given by Eq. (3). = (5) eq B T When there is no torsion load, the equivalent moment B is equal to the pure bending moment B. On the contrary, the equivalent moment becomes pure torsion moment, when B =. The relationship between the collapse bending moments and the torsion moments shown in Table 3 is depicted in Figure 8, together with the equivalent moment calculated by Eq. (5). This is the case for the pipe with a/t =.75, L/D = 1. and θ = 9 o. The torsion stresses in nuclear piping are generally small at many positions in piping systems, compared with the bending stress. Torsion stresses are relatively high at Tee joints or pipes near nole safe ends. Based on the plant survey, it is sufficient for the present investigation to limit the torsion stress to % of the flow stress. The plastic collapse moment decreases with increasing torsion moment. However, the equivalent moment given by Eq. (5) is almost constant over the range of the actual plant torsion moment. Plastic collapse moments for longer wall thinning of a/t =.75, L/D =. and θ = 9 o is shown in Fig. 9. By comparing the bending moment to that in Fig. 8, it can be seen that the equivalent moment decreases more rapidly for a deeper flaw over the entire range of the torsion moment. A criteria for acceptance of the equivalent moment at C e = 1. is defined as follows. When the difference of the equivalent moment eq against pure bending moment B is within the 1% of the pure bending moment at the torsion stress of τ/σ f =., then the equivalent moment B is regarded as constant at Collapse bending moment, B, eq, kn-m Bo Actual plant range eq = B T τ / σ B To 1 3 Collapse torsion moment, T, kn-m f.5 3 Fig. 8 Collapse bending moment and equivalent moment for a pipe with wall thinning of a/t =.75, θ = 9 o and L/D =1.. Copyright 11 by ASE 5 Copyright 11 by ASE Downloaded From: on 11/5/14 Terms of Use:

6 Collapse bending moment, B, eq, kn-m the range of τ/σ f.. Table 3 shows one of the eamples on equivalent moment eq. The equilibrium moments between the τ/σ f =. and. are almost constant. This is consistent observation for wall thinning depth of a/t =.5 such that the equivalent moments eq are constant under the range of < θ 36 o and < L/D 5.. However, the equivalent moments for wall thinning depth of a/t =.75 depends on the flaw geometry and the validity of the equivalent moment of Eq. (5) depends on the wall thinning angles and lengths. One eample is shown in Table 4. The eq at τ/σ f =. is less than 9% of that at τ/σ f =.. It can not be said that the equivalent moments eq = B are constant between τ/σ f =. and at.. DISCUSSION Bo Actual plant range eq = B T B τ / σ To Collapse torsion moment, T, kn-m Allowable wall thinning sies are derived from the plastic collapse bending moments. When the equivalent moments eq consisting of the bending and torsion loads are within the 1% of the collapse moments B, the allowable wall thinning sies can be assessed by using the plastic collapse pure bending moments B. All equivalent moments given by Eq. (5) for wall thinning depth of a/t =.5 can be presented by the pure bending moments, just like Table 3. Table 3 is the case for a/t =.75. The eq ranges from 67.3 kn-m to kn-m, and this is regarded as constant for τ/σ f.. For a/t =.5, all the eq are also constant between τ/σ f.. Figure 1 illustrates constant equivalent moment area for a/t =.5. On the other hand, equivalent moments given by Eq. (5) are limited for wall thinning depth for a/t =.75. Figure 11 shows the boundary of equivalent moment area applied by Eq. (5) for a/t =.75. The equivalent moments shown with the open circles f.5 3 Fig. 9 Collapse bending moment and equivalent moment for a pipe with wall thinning of a/t =.75, θ = 9 o and L/D =.. Wall thinning angle, θ o Wall thinning angle, θ o Wall thinning length, L /D a/t =.5 Fig. 1 Area of constant equivalent moments eq for pipes with wall thinning of a/t = a/t = Wall thinning length, L /D Fig. 11 Area of constant equivalent moments eq for pipes with wall thinning of a/t =.75. are within the 1% criteria and open triangles are without the 1% criteria. Longer the wall thinning and larger the wall thinning angle, the equivalent moments can not be eplained by the pure bending moment. When considering allowable wall thinning, the depth of a/t =.5 is close to minimum required wall thickness determined by construction codes. Therefore, it is a good result that Eq. (5) is applicable to use B for a/t =.5. However, for wall thinning depth of a/t =.75, Eq. (5) is limited to be applicable for the case of the wall thinning length of L/D 1.. When L/D > 1., Eq. (5) is not applicable to determine allowable wall thinning sies. Several fitness-for-service codes provide allowable wall thinning sies, and if the wall thinning is 8% deeper than the nominal wall thickness, that is a/t >.8, codes do not allow any further analytical evaluation [9, 1, 11]. Wall thinning depth of a/t =.75 for large angle and long length might not be allowed for piping items. 6 Copyright 11 by ASE 6 Copyright 11 by ASE Downloaded From: on 11/5/14 Terms of Use:

7 CONCLUSIONS Pipes containing local wall thinning subjected to combined torsion and bending moments in the presence of internal pressure were investigated. It is concluded that the equivalent moments combining torsion and bending loads by a vector summation are comparable with the pure collapse bending moments for wall thinning depth of 5% of nominal wall thickness of the pipe. Conversely, for the pipe with wall thinning depth of 75% of nominal wall thickness, this analogy is limited to the wall thinning sie. References 1. Li, Y., Hasegawa, K., Hoang, P., and Beensek, B., Prediction method for plastic collapse of pipe subjected to combined bending and torsion moments, ASE PVP1, July 18-, 1,Bellevue, WA, PVP Li, Y., Ida, W., Hasegawa, K., Hoang, P., and Beensek, B., Effect of pressure on plastic collapse under the combined bending and torsion moments for circumferentially surface flawed pipes, ASE PVP1, July 18-, 1,Bellevue, WA, PVP Hoang, P., Hasegawa, K., Beensek, B., and Li, Y., Effect of torsion on equivalent bending moment for limit load and EPF circumferential pipe flaw evaluations, ASE PVP 1, July 18-, 1, Bellevue, WA, PVP Beensek, B., Li, Y., Hasegawa, K., and Hoang, R., Proposal for inclusion of torsion in Section XI flaw evaluation procedures for pipes containing surface crack-like flaws, ASE PVP 1, July 18-, 1, Bellevue, WA, PVP iyaaki, K., Kanno, S., Ishiwata,., Hasegawa, K., Ahn, S. H., and Ando, K., Fracture and general yield for carbon steel pipes with local wall thinning, Nuclear engineering & Design, Vol. 11,, pp ASE Boiler and Pressure Vessel Code section III, Rules for Construction of Nuclear Facility Components, Division I, Subsection NB, NB-368, RSE-, In-service Inspection Rules for the echanical Components of PWR nuclear Power Islands, Chapter IV, Appendi 5.4, AFCEN, Addendum NUREG/CR-699, Effect of toughness anisotropy and combined tension, torsion and bending loads on fracture behavior on ferritic nuclear pipe, British Standards, Guide to methods for Assessing the acceptability of flaws in metallic structures, BS 791, Kocak, S. Webster, J.J. Janosch, R.A. Ainsworth and R. Koers, FITNET, January ASE(American Society of echanical Engineers) B&PV Code Section XI, Code Case N-597- Requirements for analytical evaluation of pipe wall thinning, November, 3. 7 Copyright 11 by ASE 7 Copyright 11 by ASE Downloaded From: on 11/5/14 Terms of Use: