DUCTILE TEARING ANALYSIS OF A CUSTOM PIPE TO FLANGE Greg Thorwald, Ph.D. Principal Consulting Engineer, Quest Integrity Group, USA Michael Rock Engineering Project Manager, Mighty River Power Limited, New Zealand THEME Durability, Fatigue & Fracture KEYWORDS Ductile tearing, crack stability, 3D crack mesh, J-integral, J-R diagram, J-T diagram, fracture mechanics, finite element analysis, FEACrack, Warp3D SUMMARY A ductile tearing analysis of a postulated crack is analyzed to evaluate crack stability and determine the critical crack length. The through-thickness circumferential crack is located in the pipe-to-flange connection in a mixing tee piping component in a geothermal power plant. The pipe-to-flange geometry has an overall cylindrical shape with a 90-degree corner between the pipe and the flange at the outer fillet weld. High stresses are expected at that location, which could initiate a crack and cause it to grow. Material testing data available from another recent project is used to improve this analysis. Twelve 3D crack meshes are generated for a range of crack lengths from short to long, and are used to compute the crack front J-integral values by elastic-plastic finite element analysis. An automated crack mesh generation software is used to reduce the time and effort needed to generate all the crack mesh input files. Many crack meshes are needed to provide enough data points on the applied J result curve to compute an accurate J derivative by simple differences or a polynomial curve-fit. The crack front J values and the material J-R resistance curve are used to compute the tearing modulus and obtain the J-T diagram. The crack ductile instability point is evaluated on the J-T diagram to obtain a critical J value. The critical J value is then used to obtain the critical crack length. The initial crack length to cause the unstable tearing is obtained by shifting the J-R material curve until the tangent instability point intersects with
the applied J results curve, and indicates the amount of stable ductile tearing before failure. Compared with using a single toughness value, the ductile tearing analysis takes advantage of stable tearing and the higher J-R resistance values, giving a longer critical crack length, which may be beneficial in deciding upon a course of action for inspecting, maintaining, or repairing a damaged component. 1: INTRODUCTION A ductile tearing analysis is used to examine a postulated circumferential through-thickness crack at the pipe-to-flange fillet weld connection in a piping mixing tee component. The goal of the analysis is to compute the critical crack length that would cause unstable crack growth and structural failure in this piping component. Material testing data is available from a recent analysis of another section of the pipe and is used to improve this analysis (Rowson, 2010). Other items needed for the ductile tearing analysis include the fracture mechanics theory and equations describing ductile crack stability (Anderson, 2005), a 3D crack mesh generator such as FEACrack (Quest Integrity, 2010) to quickly create the finite element analysis (FEA) input files of the pipe-to-flange model, and a non-linear FEA solver with the J-integral calculation such as Warp3D available in the public domain from the University of Illinois (Dodds, et al, 2009). 2: MIXING TEE PIPING COMPONENT The mixing tee is a piping component in the Mighty River Power Rotokawa geothermal power plant (Figure 1). The Rotokawa geothermal field is located in the Taupo Volcanic Zone in New Zealand, roughly 13km northeast of Taupo Township. This resource is a high temperature geothermal field with down hole temperatures of up to 320 C. Rotokawa Geothermal Power Station generates 33 MW and is one of two electricity generating power stations on this field. It is a combined cycle plant with a back pressure topping steam turbine and binary Organic Rankine Cycle bottoming and brine units. Twophase geothermal fluid is piped from the production wells to a centrifugal type separator where the steam and brine phases are separated. The steam phase is used to power the turbine (and subsequently the bottoming units). The brine phase is piped directly to a separate brine binary unit. The cooled brine is then mixed with the condensed steam from the bottoming units. The resultant fluid is then injected back into the ground. Under normal operation, all of the separated brine passes through the brine unit. Under some circumstances, some hot brine bypasses the binary unit and is mixed with the cooled brine. A mix tee is installed where the two fluids combine. The mix tee s purpose is to control how the fluids are mixed so that the likelihood of steam condensation induced water hammer is reduced.
Crack location Flow Out: Mixed Brine Flow In: Cooled Brine Region for FEA model Pipe: 250 NPS x 9.27 ASTM A53 Gr B steel Flow In: Bypass Hot Brine Figure 1: Crack located at the pipe-to-flange connection in the mixing tee. The pipe is 250 NPS x 9.27 (Nominal Pipe Size), which has an outside diameter of 273.1 mm, and a 9.27 mm thickness. The pipe is made of ASTM A53 Gr B steel. The recent material tests give the yield strength of 325 MPa, a tensile strength of 463 MPa, and a modulus of elasticity of 162 GPa at the operating temperature of 230 o C. The pipe is designed for 32 bar internal pressure (3.2 MPa), including additional loads on the pipe of 67 kn axial force and 24.3 MN-mm bending moment. The circular flange plate is 50 mm thick with a 560 mm outside diameter, and is made of AS1548-7-460 R steel (similar to ASTM A662 Gr B). The flange material was not tested, so the minimum specified values are used for the yield strength of 119 MPa, tensile strength of 198 MPa, and modulus of elasticity of 190 GPa. The pipe is connected to the flange by internal and external circumferential fillet welds. Since the connection forms a square corner, higher stresses are expected near the outer fillet weld, which could cause a crack to initiate and grow. 3: CRACK MESHES Stress intensity or J values are generally known only for cracks in standard geometric shapes like plates, cylinders, and spheres. To account for the pipeto-flange geometry in the ductile tearing analysis, custom 3D crack meshes are needed. The crack meshes for this analysis includes the pipe and flange on the left side of the mixing tee. The crack meshes are half symmetric with appropriate symmetry constraints, internal pressure, crack face pressure, and axial loads. Weld residual stress was not included in this analysis to keep the example concise, but could be included if desired (Thorwald, 2008).
The user-defined geometry method in the FEACrack software is used with a definition mesh to quickly generate the needed crack meshes. The definition mesh describes the desired pipe-to-flange geometry as a general 6-sided volume, and the elements within the definition mesh are used to transform the crack mesh primitive into the final shape (Thorwald, 2006), (Figure 2). Since the definition mesh is used only to create the analysis crack mesh, refinement is needed only along surface curvatures, such as around the circumference for this model. A single element is sufficient across the flange or along the pipe to describe the flat surface geometry in those regions. Use many elements to capture surface curvature around circumference Flange: 560 mm OD 50 mm thickness Pipe: 250 NPS x 9.27 Single element is sufficient if no surface curvature Figure 2: Definition mesh for the pipe-to-flange pipe geometry. The pipe-to-flange 3D crack meshes are shown with color-coded mesh zones, which are used to help adjust the mesh refinement near the crack (Figure 3). The circumferential crack is located in the pipe at the toe of the fillet weld. The crack front uses the typical focused mesh pattern needed to support the J- integral contour calculations. A ductile tearing analysis reveals some of the typical crack meshing challenges: needing many crack meshes, putting the crack into the component geometry, creating the focused mesh at the crack front, and post processing and tabulating the numerous crack front results. Using automated crack mesh generation software reduces the modelling effort. Twelve pipe-to-flange crack meshes were generated with crack lengths from 25 mm to 275 mm. The crack meshes use 20-node brick elements. Hiding the pipe region gives a cut-away view that reveals the crack plane and crack front location in the mesh (Figure 4). The half-symmetric model
includes half of the through-thickness crack length, measured around the circumference on the pipe outside diameter. The mesh zone sizes near the crack plane were adjusted to follow the fillet welds and give a mesh line at the weld-to-flange junction. Fix x DOF Symmetry plane, fix y DOF Pressure, axial loads Crack tip focused mesh Figure 3: Views of the through-thickness 3D crack mesh and a close-up of the crack tip focused mesh. Flange Half crack length, c Ligament Symmetry plane Crack front Figure 4: Crack plane in the pipe (light blue) Remove the pipe to view the through-thickness crack plane. 4: FEA RESULTS The FEA results show that the flange plate stiffens the end of the pipe and the crack has opening and shearing displacement (Figure 5). The color scale bar
upper limit has been set to the yield strength of 325 MPa to show the high stress region at the toe of the fillet weld at the maximum loading. The elasticplastic FEA used 20 analysis steps with equal increments to increase the applied loading to its maximum value, and for equilibrium convergence. A comparison analysis of the pipe alone with a through-thickness crack shows the crack opening, but does not have the shear displacement (Figure 6), which helps to understand the effect of the flange plate. The pipe-only models use quarter symmetric cylinder through-thickness crack meshes with the same pipe dimensions, materials, and loads. YS = 325 MPa Crack opening and shear displacement 5x displacement scale Figure 5: Pipe-to-flange Warp3D Von Mises stress results, 2c = 100 mm case. Symmetry YS = 325 MPa Crack opening displacement Symmetry 5x displacement scale Figure 6: Cylinder model Warp3D Von Mises stress results, 2c = 100 mm. The left plot in Figure 7 shows the crack front J values versus the distance through the pipe thickness (from the pipe outside diameter through the
Crack front J-integral (N/mm) Max crack front J-integral (N/mm) DUCTILE TEARING ANALYSIS OF A CUSTOM PIPE TO FLANGE thickness to the inside diameter) in the pipe-to-flange model at the maximum load. The right plot in Figure 7 shows the maximum crack front J values versus the half crack length, c, and compares the pipe-to-flange results with the cylinder results. Each data point is from a crack mesh FEA at the given crack length. The higher stress at the pipe-to-flange connections appears to increase the crack front J values for shorter cracks compared with the cylinder model. The extra stiffness from the flange appears to reduce the crack front J values by limiting the displacement of the back crack face at the longer crack lengths compared with the pipe-only cylinder model. 700.0 600.0 500.0 Pipe to flange through crack, J results, step 20 800.0 700.0 600.0 500.0 J results: pipe to flange and cylinder cylinder 400.0 300.0 200.0 100.0 0.0 2c = 275 mm 2c = 25 mm 0 2 4 6 8 10 pipe OD distance through thickness (mm) pipe ID J versus distance through the pipe wall thickness 400.0 300.0 200.0 100.0 0.0 Pipe to flange 0 20 40 60 80 100 120 140 160 c, half crack length (mm) pipe to flange, max J (N/mm), step 20 cylinder, max J (N/mm), step 20 Max J versus half crack length, c Figure 7: Crack front J-integral results for a range of crack lengths. 5: TEARING RESISTANCE The material testing data provides the J-R resistance curve for the ASTM A53 pipe material (Figure 8). The data points between the exclusion lines are curve-fit to a power-law equation with coefficients C 1 and C 2, Equation (1), (Anderson, pp 405-408). The crack length difference (a-a 0 ) gives the crack extension in the specimen from an initial crack length a 0 during the testing. J R C C2 a a 174. a a 0. 5574 1 0 08 0 (1) The J 1C value on the J-R plot indicates the nominal material toughness of 93.4 N/mm. The single toughness value could be used in a linear elastic fracture mechanics (LEFM) evaluation to obtain a critical crack size. The tearing modulus, T, is a non-dimensional value computed using the modulus of elasticity, E, yield stress, 0, and the derivative of a J curve, Equation (2). The tearing modulus is computed for both the material resistance and crack front curves.
J-Integral (N/mm) DUCTILE TEARING ANALYSIS OF A CUSTOM PIPE TO FLANGE E T 2 0 dj da (2) The tearing resistance, T R, from the J-R material curve, is computed using a chain-rule derivative of the power-law equation to get T R in terms of J R and the curve-fit exponent, Equation (3). T R E C J 2 R 2 0 a a0 (3) 300 250 200 J-Integral Tearing Resistence Curve Test result for ASTM A53 ASTM E1820 Standard y = 174.08x 0.5574 150 100 J 1C =93.4 N/mm 50 0 0 0.5 1 1.5 2 2.5 Crack extension, delta a (mm) Test Data Construction Line 0.15mm Exclusion line 0.2mm Offset line 1.5mm Exclusion line Data within exclusion lines (for trend line) J1C, intersection of 0.2 offset and tend line Power law within exclusion lines Figure 8: J-R material testing results for the pipe ASTM A53 Gr B material. The applied tearing modulus, T app, from the crack front J versus crack length results is computed using either simple differences, J/ c, or a polynomial curve-fit to compute the derivative of J. The 5 th order polynomial curve-fit of the J results in the left plot in Figure 9 provides an easy to compute J derivative, Equation (4), for comparison to the differences (the exponent values have been left as constants in each term to indicate the derivative calculation). dj app dc 4 3 2 5*7.52E 8 c 4* 2.28E 5 c 3* 2.82E 3 c 2*0.162 c 5. 59 (4) In either approach, sufficient data points are needed for accurate derivative values. More crack meshes at various lengths can be added as needed to provide more data points. The same modulus and yield stress values (from the pipe) in both tearing modulus calculations are used for consistency.
Tearing modulus Max crack front J-integral (N/mm) Max crack front J-integral (N/mm) DUCTILE TEARING ANALYSIS OF A CUSTOM PIPE TO FLANGE The T R and T app tearing modulus curves are plotted together to get the J-T diagram (Figure 10). A crack length is stable for a tearing modulus value below the T R tearing resistance curve, and unstable above the T R curve. Typically the T app curve will intersect with the T R curve, and the J-T diagram is convenient to identify the intersection at the ductile instability. However, the pipe material test specimen was sub-size, which gives a limited range of values in the T R curve. The extrapolated T R curve (green dashed line) is shown only to suggest where the curves might eventually intersect if more data were available. Since the tearing modulus curves do not intersect, the maximum available material J-R value of 262 N/mm is used as the critical J to determine the critical crack length, since using extrapolated J-R material values may be unreliable. 800.0 700.0 600.0 500.0 400.0 300.0 200.0 100.0 0.0 Pipe to flange in the mixing tee J results y = 7.52E-08x 5-2.28E-05x 4 + 2.82E-03x 3-1.62E-01x 2 + 5.59E+00x R² = 1.00E+00 0 20 40 60 80 100 120 140 160 c, half crack length (mm) pipe to flange, max J (N/mm), step 20 Poly. (pipe to flange, max J (N/mm), step 20) Pipe flange: 5 th order polynomial curve-fit 800.0 700.0 600.0 500.0 400.0 300.0 200.0 100.0 0.0 Cylinder through-thickness crack y = 2.56E-05x 4-5.32E-03x 3 + 3.81E-01x 2-8.65E+00x R² = 9.99E-01 0 20 40 60 80 100 120 140 160 c, half crack length (mm) cylinder, max J (N/mm), step 20 Poly. (cylinder, max J (N/mm), step 20) Cylinder: 4 th order polynomial curve-fit Figure 9: Use polynomial curve-fit to the J versus crack length plots. 200 180 160 140 120 J 1C 100 80 60 40 20 0 Tearing modulus, pipe to flange model and cylinder T R ASTM A53 extrapolated J = 262 cylinder pipe to flange 0 100 200 300 400 500 600 J-integral (N/mm) T_R for ASTM A53 pipe T_app pipe to flange, differences T_app cylinder, differences T_R extrapolation using cuve-fit T_app pipe to flange, curve-fit T_app cylinder, curve-fit Figure 10: Look for intersection of T R and T app tearing modulus curves to get the critical J at ductile instability; curves do not intersect in the available data range.
Max crack front J-integral (N/mm) 2c total crack length (mm) DUCTILE TEARING ANALYSIS OF A CUSTOM PIPE TO FLANGE The applied tearing modulus curves in Figure 10 are computed using both the simple differences and the polynomial curve-fit for comparison. There is close agreement between the two approaches for most of the curve. Additional data points at the higher J values may improve the agreement for the higher J values by generating more crack meshes. The left plot in Figure 11 shows where the critical J max from the J-T diagram intersects with the pipe-to-flange and cylinder J curves. Interpolation gives the pipe-to-flange through-thickness critical crack length of 211 mm. Coincidentally, the pipe-only cylinder model critical crack size is nearly the same when using the J max value. The J result trends in Figure 11 show that for a different critical J material value, the cylinder and pipe-to-flange models would give different critical crack lengths. 300 Interpolate for critical crack size at given J 2c = 211 mm 225 Critical crack length, 2c 250 J max 200 200 Pipe to flange 175 150 150 100 J 1C Cylinder 125 100 50 75 50 0 0 25 50 75 100 125 c, half crack length (mm) pipe to flange, max J cylinder, max J J1C toughness J-R max value c 25 0 pipe to flange cylinder J1C toughness J-R Jmax Figure 11: Use the critical J value to interpolate the critical crack length. If the J 1C single toughness value were used, the critical crack length for the pipe-to-flange model would be 77 mm. The extra effort of a ductile tearing analysis takes advantage of the higher material J-R value at the ductile instability, and gives a larger critical crack size. Knowing these critical crack lengths may help a client decide on a safe but not overly conservative course of action to inspect, maintain, or repair a damaged component. The initial critical crack length, 2c 0, to initiate the unstable ductile tearing is obtained by shifting the material J-R curve on the J versus crack length plot until the tangent instability point just meets the analysis J results curve (Figure 12). With the limited J-R data available, the tangent instability point is approximated by the maximum J-R value. The critical initial crack length 2c 0 is 206 mm, which allows for 5 mm of stable ductile crack growth until the
J_app and J_R (N/mm) DUCTILE TEARING ANALYSIS OF A CUSTOM PIPE TO FLANGE crack length reaches the ductile instability point and the component is predicted to fail. 700.0 600.0 500.0 400.0 300.0 200.0 100.0 0.0 Pipe to flange through-crack, find initial c 0 Approximate tangent instability point 0 20 40 60 80 100 120 140 160 pipe to flange max J 2c 0 = 206 mm Pipe to flange c, half crack length (mm) J-R ASTM A53 J-R ASTM A53 data Figure 12: Adjust the initial critical crack length to shift the J-R curve so the tangent instability point meets the applied J results curve. Another consideration is the possible yield rupture failure as the crack length increases. The increasing crack length is reducing the available pipe crosssection to carry the load, which could also cause the component to fail. The limit load calculation is not included in this analysis to keep the example concise. 6: CONCLUSION A postulated circumferential through-thickness crack in the pipe-to-flange connection in the mixing tee was examined using a ductile tearing analysis, and compared with a pipe-only analysis. The ductile tearing analysis used twelve 3D crack meshes with a range of crack lengths, from short to long, to compute the crack front J-integral values by elastic-plastic finite element analysis. The material J-R curve and analysis J results were used to compute the tearing modulus curves to get the J-T diagram. Each crack mesh provides a data point on the applied tearing modulus curve, and enough crack meshes are needed to compute an accurate J derivative. The critical J value for ductile instability was used to interpolate the critical crack length. The initial critical crack length that initiates the unstable ductile tearing was obtained by shifting the J-R curve to match the ductile instability point to the crack front J results curve. Compared with using a single toughness value, the ductile tearing analysis takes advantage of stable tearing and higher J-R values giving a longer critical crack length, which may be beneficial in deciding upon a course of action to inspect, maintain, or repair a damaged component.
REFERENCES Rowson, Q. and Rock M., 2010. Tearing Analysis Employing Finite Element Analysis With Crack Mesh In Comparison To Standardised Methods. NAFEMS World Congress 2011, Boston, May 23-26. Anderson, T. L., 2005. Fracture Mechanics: Fundamentals and Applications. 3 rd ed. Boca Raton, FL: CRC Press, Taylor & Francis Group. Quest Integrity Group, 2010. FEACrack User s Manual, version 3.2. Available at: <http://www.questintegrity.com/products/feacrack/> [Accessed 7 December 2010]. Dodds, R. et al., 2009. WARP3D-Release 16.2: 3-D Dynamic Nonlinear Fracture Analyses of Solids Using Parallel Computers. Available at: <http://cern49.cee.uiuc.edu/cfm/warp3d.html> [Accessed 7 December 2010]. Thorwald, G., 2006. Necessary Analysis Ingredients For FEA Models With Multiple Cracks. 2006 West Regional ABAQUS User s Meeting, San Francisco Bay Area, October 24-25. Thorwald, G. 2008. Fatigue Analysis Using a Custom Profile 3D Crack Front Including Weld Residual Stress. 2008 International ANSYS Conference, Pittsburgh, August 26-28.