T. J. Griesbach Senior Nuclear Engineer, Combustion Engineering, Inc., Windsor, Conn. 06095; presently, Project Manager, Nuclear Safety Analysis Center, Palo Alto, Calif. Mem.ASME Dynamic Elastic-Plastic Behavior of Circumferential Cracks in a Pipe Subject to Seismic Loading Conditions An analytical study is performed to investigate the structural stability, and inherent integrity, of a Pressurized Water Reactor primary coolant loop cold leg pipe containing a through-wall circumferential crack. The purpose of this study is to gain a better understanding of the mechanisms and extent of crack opening behavior in a real piping system, and, thus, establish the basis for improved pipe break criteria. Cracks extending one-half the circumference or greater are considered in the pipe. Combined operating pressure plus external seismic loads are applied simultaneously to cause a maximum crack opening effect. A dynamic elastic-plastic analysis is performed to calculate stress intensity factors at the crack tip. The results are compared with experimental fracture toughness data to assess the material's capability to resist crack extension. A fatigue crack growth study is also performed to determine the range of initial flaw sizes which could grow and extend during normal operation to threaten the integrity of the cold leg pipe. 1 Introduction In the design of nuclear power plants to withstand a loss of coolant accident (LOCA), regulatory guidelines [1] and industry standards [2] require that pipe whip restraint devices be installed to mitigate the effects of an instantaneous guillotine type of pipe failure. The present pipe break criteria [3] presume that an instantaneous gillotine pipe break can occur without determining the likelihood of such an event from a consideration of the physical mechanisms of crack growth and crack opening behavior in a real piping system. By choosing the guillotine failure as the worst case accident, it is assumed that this will "envelope" any instance of a circumferentially propagating crack in a pipe. However, in the design of piping systems to prevent pipe whip, the required pipe whip restraints could cause interference with the system during normal operation. In addition, the size of such restraint mechanisms hinder access for in-service inspection of the piping and maintenance of adjacent components. This may reduce plant safety while increasing cost and complexity. Determination of the margin of safety against a large break in the cold leg piping system of a Pressurized Water Reactor (PWR) power plant has been the subject of a study at Battelle [4]. Their results conclude that initial defects in the piping system could possibly grow through the wall and cause a leak in less than one plant life (40 yr). The calculated leakage rate from such a crack in the pipe was predicted to be large enough to be detectable prior to the formation of a large pipe break. It was determined that the time between leak and large pipe break would be sufficient for plant shutdown even if a Safe Shutdown Earthquake (SSE) occurs immediately after formation of leak. Probabilistic fracture mechanics analysis was performed by Lawrence Livermore Laboratory as part of the USNRC Load Combination Program [5]. The purpose of the study was to estimate the probability of a seismic induced loss-of-coolant accident (LOCA) in the primary system of a commercial PWR. The results indicate that the probability of a doubleended guillotine pipe break directly caused by a seismic event during the plant life is very small, on the order of 10 ~12. The purpose of the present analysis is to further investigate the integrity of the discharge leg pipe in a PWR under severe loading conditions using deterministic methods. In particular, the behavior of a partially cracked pipe subjected to the combined effects of normal operating loads plus external seismic loads is examined to determine the largest stable through-wall circumferential crack size. Furthermore, a fatigue crack growth study is performed to evaluate the mechanism and extent to which initially present inside surface flaws could grow to be critical in size during the operating plant life. The results of this analysis emphasize the need, and provide a basis, for more realistic pipe break criteria in the design of nuclear piping systems. Contributed by the Pressure Vessels and Piping Division for publication in 'he JOURNAL OF PRESSURE VESSEL TECHNOLOGY. Manuscript received by the Pressure Vessel and Piping Division, October 28, 1980; revised manuscript received December 6,1982. Journal of Pressure Vessel Technology 2 Method of Analysis A previous study by Griesbach and Ayres [6] considered the Copyright © 1983 by ASME FEBRUARY 1983, Vol. 105/63 Downloaded From: http://pressurevesseltech.asmedigitalcollection.asme.org/ on 10/26/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use crack opening effects of a circumferential crack at the reactor vessel inlet nozzle end of the pipe. Such a crack was presumed to initiate at a time during the Safe Shutdown Earthquake loading transient which would produce the most severe loading condition at the crack tip. The results of the previous analysis demonstrated several significant effects: A/—NV-PUMP IB © (a) The end constraint afforded by the reactor vessel, the reactor coolant pump and the support structures severely limit the displacements and rotations in the pipe which contribute to circumferential crack opening. (b) Under such constraint conditions, seismic loading has only a small influence on the amount of crack opening as well as the crack-tip stress intensity factor resulting from a circumferential crack in the pipe. (c) A circumferential crack larger than two-thirds of the way around the pipe would be necessary before the effects of operating pressure plus SSE loading could cause crack instability and, thus, produce a full circumference pipe break at the inlet nozzle. The present study is a continuation of the effort described in the foregoing to demonstrate that seismic loading cannot cause a guillotine break in the middle of the pipe where the end constraint effects are at a minimum. The method of analysis used here is the same as that which was established and utilized in the previously described work [6], The details of this method will be discussed further in Section 3. Briefly, a three-dimensional finite element model of one leg of the primary system is constructed, including the reactor vessel, the reactor coolant pump, and the vertical and horizontal structure supports. A circumferential through-thickness crack is postulated to occur in the discharge leg pipe half-way between the reactor vessel inlet nozzle and the reactor coolant pump. Static operating pressure loading is applied, as well as a dynamic time history loading function representing a Safe Shutdown Earthquake. The crack is presumed to initiate at the most severe time during the SSE loading transient. A detailed elastic-plastic dynamic analysis is performed to evaluate the behavior of the piping system containing a crack. The value of the crack-tip stress intensity factor, K,, is calculated as a function of time using the /-integral method. For values of K, which are below the measured fracture toughness, KIC, the crack is assumed to remain stable. By applying this technique for various different crack sizes, the critical crack size is determined as the minimum crack size for which the calculated stress intensity factor exceeds the fracture toughness of the material. All finite element computations are performed using the MARC general purpose nonlinear finite element program. The second phase of this study evaluates the fatigue crack growth mechanisms by which initial flaws could enlarge and grow to threaten the integrity of the piping system. Various initial flaw sizes are hypothesized and the stress intensities for design basis operating transients are calculated. Crack growth rates are determined by performing an iterative process considering the frequency and severity of operating cycles, PUMP i A / ^ S j T o o -PUMP IA PUMP 2B-\V^> STEAM GENERATOR No. 1 Fig. 1 STEAM GENERATOR No. 2 Nuclear steam supply system arrangement and the flaw size is updated and monitored to the point of first leak when the flaw depth exceeds the wall thickness. By continuing the analysis for circumferential crack growth, the required time for a through-thickness crack to grow to be critical in size is determined. Critical crack size is defined as the minimum circumferential through-thickness crack which could propagate unstably to become a full circumference pipe break during a Safe Shutdown Earthquake. The margin between the point of leak and possible break during SSE is calculated for a wide range of initial (pre-service) flaw depths and lengths. 3 Model Studies The primary system for a typical Combustion Engineering two-loop PWR contains the reactor vessel and two heat transfer loops, each loop containing a steam generator and two recirculating reactor coolant pumps. Figure 1 illustrates the arrangement of the components, the primary system piping, and the horizontal and vertical structural supports. The reactor vessel is supported vertically by four rectangular columns, each column is bolted to a pad under a vessel inlet nozzle. Each reactor coolant pump is supported by a set of Nomenclature K, --= crack-tip stress intensity factor J --= /-integral value G --= strain energy release rate E == elastic modulus v == Poisson's ratio g == acceleration due to gravity t == time P == period of vibration 64 / Vol. 105, FEBRUARY 1983 w = natural frequency of vibration Kic = plane strain fracture toughness Jre = critical /-integral value for crack growth a0 = initial surface flaw depth C„ = initial circumferential halflength of flaw da dN da/dN C n j3,7 = = = = = = change in crack depth number of fatigue cycles fatigue crack growth rate scaling constant fatigue growth rate exponent parameters of Newmark dynamic operator A = increment Transactions of the ASME Downloaded From: http://pressurevesseltech.asmedigitalcollection.asme.org/ on 10/26/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use Fig. 3 System arrangement showing finite element model Fig. 2 Finite element model four vertical columns, four horizontal columns, and a horizontal snubber. The steam generator is supported vertically on a base plate which slides on low-friction bearings. A system of hydraulic snubbers and keys with mating keyways are attached to the upper portion of the steam generator to provide horizontal support. The arrangement of the supports allows for essentially free thermal expansion of the components and piping (excluding friction), while providing support for static weight, seismic, and pipe break effects. The three different types of piping runs which are shown in Fig. 1 are the "hot leg piping," "suction leg piping," and "discharge leg piping." Only one leg of the discharge leg piping is considered in this analysis since, by symmetry conditions, each leg is identical. The piping is made from SA516 Grade 70 Carbon Steel. The discharge leg piping is 30 in. (762 mm) inside diameters with a nominal wall thickness of 3 in. (76.2 mm). The pipes are of relatively short length and large diameter, resulting in a stiff piping system. In analyzing the dynamic behavior of the discharge leg pipe, the mass and stiffness associated with the major components and the structural supports have a significant effect on the overall response of the piping system. This phenomenon if often ignored when considering the integrity of a pipe containing a cracklike defect; the discharge leg is a single component in a more complex system, and it is not valid to analyze the dynamic response of this component without including the interacting effects with the adjacent structural members. Taking these effects into account the finite element representation used in this analysis is presented in Fig. 2. The model is made up of a combination of 169 beam and shell-type elements with approximately 1800 degrees-offreedom. Three-dimensional beam elements, with the appropriate section properties, were used to model the reactor vessel, the reactor coolant pump, the horizontal and vertical supports, and the snubber. Lumped masses were used for these main components in accordance with the mass distribution from a system flexibility anlaysis [7]. The discharge leg was modeled using a combination of beam elements and shell elements with uniform distributed mass being used for the elements representing the pipe. The threedimensional rectangular curved shell element was chosen to model the section of the pipe containing a crack for several Journal of Pressure Vessel Technology Fig. 4 Schematic showing finite element representation reasons: It is a rapidly convergent element, it can handle rigid-body motions exactly, distributed mass terms are accurately represented, through-thickness cracks can be modeled with relative ease, localized plasticity effects can be included, and the /-integral technique can be utilized to calculate the stress intensity at the crack tip. The choice of element mesh size represents a reasonable compromise between using a very coarse mesh near the crack tip which would be too crude to model the localized effects in this region, and the prohibitive constraint (in terms of computer time) of using a more refined crack-tip mesh. The crack-tip stress intensity factor, K,, was calculated directly using the /-integral technique. J is an energy term which is used to express the change in potential energy per unit change in crack extension. For the case of linear elastic, nonlinear elastic, and small-scale yield fracture mechanics analyses, the parameter J is identical to the strain energy release rate, G, defined for a linear elastic body. (1-v2) J=G= K,2 (for plane strain) (1) E FEBRUARY 1983, Vol. 105/65 Downloaded From: http://pressurevesseltech.asmedigitalcollection.asme.org/ on 10/26/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use 10.0 MAGNIFIED CRACK OPENING DISPLACEMENT Fig. 5 Displaced view showing crack opening displacement for onehalf circumference crack in pipe 0.1 1.0 Fig. 6 10.0 FREQUENCY, CPS SSE in-structure response spectrum 100.0 where K, is the stress intensity factor, E is Young's modulus, and v is Poisson's ratio. Writing K, in terms of / gives the relation: the finite element model containing a one-half circumference crack under static pressure loading. A "bowing-out" of the J>E (assuming plane strain) (2) pipe, and the corresponding crack opening effect, is apparent K,= in this figure for a crack occurring in the middle of the The validity of the /-integral approach has been demon- discharge leg pipe. The maximum deflection for the static strated in its ability to produce accurate results in the load case with a one-half circumference crack was determined determination of crack-tip stress intensity factors without the to be less than 0.1 in. (2.54 mm) as compared to the total need for special crack-tip elements using the stiffness length of the pipe which is 218 in. (8.58 m). These results derivative technique [8]. Furthermore, in the absence of gros,s confirm the kinematic basis of the analysis in that the plastic deformation, the value of the /-integral is only slightly deflections and rotations of the pipe are justifiably small so affected by mesh size variation provided the /-integral that large displacement effects need not be considered. The static analysis for a one-half circumference crack in the contour is taken far enough away from the crack tip [9]. Since the pipe is treated as a thin shell, the calculated value for / , or middle of the discharge leg pipe produced a crack tip stress Vm). This correKj, represents the mean value across the thickness of the pipe intensity value, K,, of 106 ksi Vin (117 MPa 2 2 wall. This is consistent with the formulation of the /-integral sponds to a crack opening area of 1.98 in (1278 mm ) due to which is established for two-dimensional geometries, the pipe pressure loading only. For comparison purposes, the results in this case being considered as a two-dimensional reference from [6] for a one-half circumference crack at the inlet nozzle ksi surface in the Gaussian (surface) coordinate system. Although end of the discharge leg pipe gave a value for K, of 92 MPa Vm) and a crack opening area of 1.36 in2 (877 transverse shear effects at the crack tip are not accounted for Jin (101 2 in this formulation, the thin shell approximation is fairly mm ) due to static pressure loading. good for long cracks predominantly under pressure (i.e., Considering the static behavior of the structure containing membrane) loading [10] as is the case in this analysis. a two-thirds circumference crack in the middle of the pipe, the Figure 3 is a plan view and Fig. 4 is a perspective view calculated value for the stress intensity at the crack tip was superimposing the finite element representation and the determined to be 183 ksi Vin (202 MPa Vm). A crack opening corresponding system components. Compatibility between area of 7.142 (4607 mm2) resulted from this geometry and the intersection of the beams and shells was accomplished by a loading condition. In comparing the results for a two-thirds set of imposed constraint equations (i.e., nodal point circumference crack at the inlet nozzle end of the pipe [6], the "trying") to maintain the Euler-Bernoulli condition that calculated value for K, of 132 ksi Vin (145 MPa Vm) and the plane sections remain plane before and after deformation. crack opening area of 2.36 in2 (1520 mm2) show that the Also, a similar application of nodal point trying between tendency for crack opening is considerably less for a crack at nodes on the shell surface permitted the introduction of a the end of the pipe than if such a crack existed in the middle of crack in the pipe by the releasing of tide nodes. the pipe. This demonstrates the constraint effect produced by The kinematic behavior of the finite element model was the system components and the structural supports to limit the evaluated under static conditions to verify the overall range of motion and restrict any large opening effects due to a response of the system to operating pressure loading. Internal circumferential crack in the pipe. pressure of 2250 psi (15.5 MPa) was applied as a distributed The upper shelf, dynamic fracture toughness for SA-516 load to the shell elements forming the pipe section which Gr. 70 material is expected to exceed the static, initiation produced the state of axial and circumferential stresses toughness value of 250 ksi Vin (275 MPa Vm) assumed in the present in the pipe during normal operating conditions. It was analysis. This is based upon two experimental observations: assumed that the presence of a through-thickness leaking initiation toughness measurements underestimate the real crack would not depressurize the system and reduce the stress fracture toughness of ductile materials; and, the upper shelf level in the pipe. dynamic fracture toughness for ductile materials exceeds the For both the static and dynamic analyses, circumferential static toughness value. Due to specimen size limitations, there cracks were chosen to occur around the outer side of the pipe are no valid Klc measurements for this material on the upper where the resulting deflections and crack opening effects shelf. However, a conservative lower-bound estimate for Krc would ba at a maximum. Figure 5 shows a displaced plot of can be made from JIC measurements [11] of SA-516 Gr. 70 66/Vol. 105, FEBRUARY 1983 Transactions of the ASME Downloaded From: http://pressurevesseltech.asmedigitalcollection.asme.org/ on 10/26/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use 2.0 1 i i i 300 i ACCELERATION 270 - 1.0 i ,IM Jr\M.ltak 0 r -1.0 1 -2.0 100 i 1 'C 240 wry 1 1 i i 1 i VELOCITY 50 0 -50 -100 i 0 1 1 2 1 i 1 3 - 1 5 TIME, SECONDS Fig. 7 20 Time histories generated from reference spectrum 40 60 80 100 TIME, MILLISECONDS Fig. 9 K; versus time (following appearance of crack) for a one-half circumference crack in the middle of the pipe 4 0.2 0.3 STRAIN, IN/IN Fig. 8 Stress-strain curve for SA 516-Grade 70 carbon steel at 550°F and similar steels which indicate a static, initiation toughness in excess of 250 ksi Vin (275 MPa Vm) [12, 13]. The tests demonstrate that these steels have steep Jrcsistance curves and a resulting true fracture resistance significantly higher than the assumed value. A second conservative assumption is the use of the static toughness for the calculation in lieu of the dynamic fracture toughness SA-516 Gr. 70. The fracture toughness of ferritic materials shows a significant increase with loading rate on the material upper shelf when the cleavage fracture mode is precluded, as is demonstrated in reference [14]. For these reasons, the assumed fracture toughness for SA-516 Gr. 70 is appropriate for this analysis. By comparing the static results of the analysis with the value for the critical fracture toughness of the piping material, both a one-half and a two-thirds circumferential crack in the middle of the pipe are determined to remain stable during normal operation. This is a significant result when compared to the finding for the critical crack size in a pipe under operating pressures and having "free-end" conditions [8], which showed that the largest stable crack size is only one-half circumference with a corresponding crack opening area of 5.3 in2 (3420 mm2). Thus, when considering the pipe as an integral part of the reactor coolant system, the "in-system" behavior of the pipe results in a larger tolerable crack size Prior to instability for a circumferential crack in the pipe. Journal of Pressure Vessel Technology Seismic Loading Conditions In evaluating the dynamic response of the system of seismic loading, a seismic excitation was applied to the model as support motion time histories at the structural attachments to the foundation. The loading function for a seismic event is defined by "ground response spectra" corresponding to the peak ground accelerations. The model evaluated here is considered to be a subsystem of a much more complex configuration of nuclear power plant basemat, containment building, internal structure, and pressurized water reactor coolant system. It has been demonstrated that an uncoupled subsystem analysis produces accurate results provided that the excitations applied to the uncoupled model are derived from a coupled system model to account for interaction effects [15]. For this analysis, "in-structure" response spectra were determined at support locations from a complex threedimensional structural model of the building and reactor coolant system [7], and a conservative envelope of the response spectra at the various support locations was determined for SSE conditions, as shown in Fig. 6. From the envelope which defines the spectral input of the seismic event, and using the Fourier transform method [16, 17], it is possible to generate an artifical time history which maintains the identical spectrum over the frequency range of interest. The resulting acceleration and velocity time histories for horizontal support motion are given in Fig. 7. From this figure it is noted that peak accelerations greater than 1.0 g are present in the SSE loading function. Typically, maximum ground accelerations on the order of 0.2-0.4 g are used for design basis earthquakes [15]. By comparison, the seismic loading used in this analysis represents a "very severe" earthquake. A more detailed description of the seismic loading procedure is given in [6]. 5 Dynamic Elastic-Plastic Analysis The combined effects of pressure plus seismic loading on the behavior of the discharge leg pipe are evaluated by an incremental dynamic analysis. The purpose of the dynamic analysis is to examine the overall behavior of the system following initiation of a through-wall circumferential crack. An earlier study by Ayres considered the dynamic response of a free-end pipe following the instantaneous appearance of a stable circumferential crack [18]. Similar studies have FEBRUARY 1983, Vol. 105/67 Downloaded From: http://pressurevesseltech.asmedigitalcollection.asme.org/ on 10/26/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use Table 1 Loading transients analyzed and life occurrences Life occurrences 500 500 15,000 15,000 2000 2000 10s 400 200 10 40 40 5 200 Loading transients Plant heatup, 100°F/hr Plant cooldown, 100°F/hr Plant loading, 5 percent/min Plant unloading, 5 percent/min 10 percent step load increase 10 percent step load decrease Normal plant variation (± 100 psi, ± 10°F) Reactor trip Leak test, 2250 psia, 100-400°F Hydrostatic test, 3125 psia, 100-400°F Loss of reactor coolant flow <a) (o) Loss of turbine generator load Loss of secondary pressure (a) Operating basis earthquake (a> PRESSURE (<0Abnormal transient conditions SSE LOADING 60 80 100 TIME, MILLISECONDS 120 140 Fig. 10 K/ versus time (following appearance of crack) for a two-thirds circumference crack in the middle of the pipe T 1—I I M i l ! 1 1—I 1 I 1 I I J 1 1—I I I I 11! o >^ £ 10 -3 S 10" DATA UPPER B0UNC / / o AS ME SECTION XI "WATER" LINE - 1—1 t— < < o Q- o o; Q. < o ZD O 10' 10 \ i i i i nl | i l i i i ill | ' i i i i II 1 10 100 1000 STRESS INTENSITY FACTOR RANGE, A K , ksi-in 1/2 TIME, HOURS PLANT HEATUP Fig. 11 TIME, HOURS Fig. 12 Reference fatigue crack growth curve P U N T COOLDOWN Plant heatup and cooldown loading transients examined the propagation phenomena of unstable cracks produced by an instantaneous initiation [19], as well as the fluid-structure interaction effects due to fluid depressurization [20]. While fluid depressurization effects may be significant for some piping systems in consideration of stability, particularly in pipes with large length-to-diameter ratios, these effects are judged to be small in this case since L/D = l, and including them is beyond the scope of the present study. In the present analysis, the response of the system due to an impulse load will be understandably different than the freeend pipe. The large stiffness contribution of the end constraints, and the associated inertia of the system components, will have a dominant effect over such very short duration events. Thus, the crack-opening behavior evaluated in this study is the results of the fundamental frequency displacement and rotations of the pipe following the sudden appearance of a crack. It was determined that the natural frequency of the pipe without a crack is 16-17 Hz, which is within the range of frequencies which would be active during seismic loading. The pipe is initially considered to be pressurized and un68/V01.105, FEBRUARY 1983 cracked (at time / = 0.0), and the motion time history is applied as a loading function to all supports. Dynamic time steps of 0.1 s were used during the "buildup" phase of the seismic event, and direct integration of the dynamic equations was performed using the Newmark /3 method, with 7 = 1/2, (3 = 1/4 (trapezoid rule). From the time history plots in Fig. 7, it is apparent that the maximum positive seismic excitation occurs at a time of t = 1.0 s as noted by the coincident peaks in acceleration and velocity. Because the discharge leg is a high-energy pipeline, and the seismic oscillations contribute additional kinetic energy to the system, the pipe is presumed to remain uncracked until the time of peak seismic loading for which the stored energy is at a maximum. The initiation of the crack at this point in time causes the largest amount of pipe whip behavior. Since the ends of the pipe are not free to whip, the greatest degree of loading is directed toward the middle of the pipe and, ultimately, to the crack tip. The integration time step was reduced to .01 s just prior to the time of crack initiation to trace the crack opening behavior of the pipe. The choice of time step for this part of the analysis was based on the criterion that: Af=l/6p=l/6«l/w (3) Transactions of the ASME Downloaded From: http://pressurevesseltech.asmedigitalcollection.asme.org/ on 10/26/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use • * • SSE f ! —~"~1 III 1M Through Wall Crack • 1' , I U-2c —1 Surface Crack / / a0-.50IN Z CQ - 39.0 IN / ' ' ' 20 YEARS Fig. 13 Fatigue crack growth versus years of operation - a 0 = 0.50 in.,2C 0 = 39.0 in. - 11 - 7 1 SSE a M • < cc <-> x u 40 - Fig. 15 Fatigue crack growth versus year of operation-a 0 = 0.35 in., 2Cn 45.5 in. h—2c c — | /- T] "I Through Wall Crack o • 0 i t • / 1 U^ M -J . | y a 0 = 1.0 IN 2C f l -3d.0IN 2c S u rface C rack 25 £ < • 20 YEARS Fig. 14 Fatigue crack growth versus years of operation - a 0 2C„ = 34.0 in. a. 0 1.0 in, where p is the period and w is the natural frequency of the pipe. Frequencies above 20-25 Hz would be filtered out by the coarseness of the time step. However, because of the large inertia of the system, the higher frequencies do not have a significant effect on crack opening behavior. A small amount of stiffness damping was included with a damping factor of 1.0 x 10"5 which imposes less than 0.05 percent damping over the frequency range of interest. No artificial damping is induced in using the Newmark /3 operator; however, small periodicity errors may be introduced in the dynamic solution as a function of the time step size. Localized plasticity effects are considered when stresses in the pipe exceed the yield strength of the material. An initial yield point value of 35 ksi was determined experimentally for SA-156 Gr. 70 carbon steel at 550°F (288°C), and the corresponding work hardening behavior used in the analysis is as shown in the stress-strain curve given in Fig. 8. The crack tip stress intensity factor, Kj, is determined as a function of time for both a one-half and a two-thirds circumference crack, and the results are compared with the material fracture Journal of Pressure Vessel Technology Fig. 16 Fatigue crack growth results for a range of initial flaw sizes - 2 C 0 versus A0. toughness, KIC. Using this criterion, a critical crack size is determined for the onset of crack instability due to the combination of operating pressure plus external seismic loading. 6 Results of Dynamic Analysis Stress levels exceeding the yield strength were calculated near the crack-tip region following the appearance of the crack. The development of a plastic zone near the tip of the crack was very localized, and the calculated value for plastic FEBRUARY 1983, Vol. 105/69 Downloaded From: http://pressurevesseltech.asmedigitalcollection.asme.org/ on 10/26/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use 1 1 - >S. \ 1 TIMETO CAUSE LEAK ^ T I M E T O CAUSE ^ BREAK DURING ^CvMAXSSE -* a „ - .50 IN N^ - i 1 20 YEARS Fig. 17 Margin between time to cause leak and large pipe break during SSE for various initial flaw lengths, 2C0(a0 = 0.50 in) strain in the locally yielded zone ahead of the crack tip was less than 1 percent. No other portion of the pipe experienced stresses large enough to cause plastic deformation. The dynamic response of the pipe showed a noticeable decrease in the natural frequency following initiation of a crack, which indicates a corresponding change in the stiffness of the system as a result of the crack. This is consistent with previous findings for the effects of a circumferential crack at the inlet nozzle end of pipe [6]. The dynamic crack opening effects are described in terms of the crack-tip stress intensity factor, KIt and the calculated values for K, versus time are shown in Fig. 9 for a one-half circumference crack in the middle of the pipe. The influence of seismic loading produces a peak value for K, of 150 ksi Vin (166 MPa Vm), which is a 57 percent increase in the stress intensity factor K, above the static value due to pressure loading only. By comparison, the results of the previous study [6] for a one-half circumference crack at the reactor vessel inlet nozzle end of the pipe showed an increase due to seismic loading of only 16 percent above the static value due to pressure. The fact that K, is less than KIC indicates that the crack would remain stable under these conditions. The calculated values for K, versus time for a two-thirds circumference crack are shown in Fig. 10. It is noted that the dynamic behavior of the pipe containing a two-thirds circumference crack produces a peak value for K, of 272 ksi Vin (300 MPa Vm). This is significantly above the static value due to pressure of 183 ksi Vin (202 MPa Vm), and, in fact, exceeds the fracture toughness of the material which indicates that such a crack would not remain stable. The results of the dynamic analysis are significant in that the critical crack size is identified to be a very large crack greater than one-half the circumference. Furthermore, the existence of such a crack would have the greatest effect on the integrity of the discharge leg if the crack occurred in the middle of the pipe rather than at the ends and was subjected to the combination of pressure plus seismic loading conditions. 7 Fatigue Crack Growth Study The results of the dynamic analysis are significant in the determination of the critical defect size. Extensive pre-service and in-service inspections are conducted to ensure the quality of the piping against such flaws. However, the fact that 70/Vol. 105, FEBRUARY 1983 uncertainties exist in the performance of such inspections, and the possibility that initially small flaws can enlarge during normal operation by fatigue crack growth, poses an additional concern. While it has been demonstrated that a significantly large (i.e., greater than one-half circumference), through-wall crack would be required before crack instability could occur during an SSE, a fatigue crack growth study was performed to determine the range of initial defect sizes that could grow to be critical in size during the 40-yr design life of the plant. The primary piping system and related components must be designed to withstand both the normal and abnormal loading transients as outlined in Table 1. The stress levels due to pressure and thermal loads in the pipe are determined by ASME code accepted procedures for pressure vessels and piping from the pressure and temperature design. Typical design curves for plant heatup and cooldown as a function of time are shown in Fig. 11. The effects of stress concentration due to a flaw in the pipe are evaluated using the methods for K, determination in the ASME Code [21]. Section XI of the ASME Code [22] defines a fatigue crack growth rate law of the form: da = C'(AKI)n ~dN (4) where n is the slope of the log {da/dN) versus log (AK,) curve, and C" is a scaling constant. This material property curve has been determined experimentally, and the material constants for fatigue crack growth in a water environment are: C" = 3.795 x 10" 10 and n = 3.726. The rate of crack growth (da/dN) is measured in inches per cycle from this relationship. This crack growth law is intended to be a conservative upper bound to the experimental data, however, recent fatigue crack growth studies have produced data which lie above this curve [23]. The solid line in Fig. 12 shows the da/dN versus AK, curve which has been proposed as a revision to Section XI of the ASME Code and is seen to envelope all of the fatigue crack growth data [24]. A threshold stress intensity of 2.4 ksi Vin (2.6 MPa Vm) was used to bound the lower range of the fatigue crack growth rate curve based on data for A-106-B piping steel [25]. The results of this study include the upper bound to the crack growth rate curve as given in Fig. 12. Semi-elliptical shaped inner surface flaws were hypothesized for various initial crack depth, a0, and lengths, 2C0. A computer methodology was used to evaluate the stress intensity factor for a given flaw size and loading function and then compute the growth rate of the flaw under cyclic loading conditions. The method of analysis is based on the Section XI, Appendix A flaw evaluation procedure which calculates the stress intensity factor, K,, as a function of flaw geometry and stress state [26]. Using this method, the AK/ level for a loading cycle is calculated based on the crack size and loading conditions. From the number of cycles of loading in a given time period, crack growth rates are calculated and the corresponding changes in crack size. The time to produce first leak is determined when an existing flaw enlarges and, subsequently, "pops-through" the thickness of the pipe. This "pop-through" phenomenon is what is meant by a suddenlyappearing through-thickness crack. In relating these results to the dynamic analysis, the circumferential length of the through-wall crack is important to the determination of crack stability. For cracks which penetrate the wall thickness, the subsequent calculation of the stress intensity factor, K,, was evaluated using the finite element method since the Section XI flaw evaluation procedure does not extend to through-wall cracks. The finite element technique enabled the determination of Kj as a function of the circumferential crack length, 2C, and the applied load, and this information was Transactions of the ASME Downloaded From: http://pressurevesseltech.asmedigitalcollection.asme.org/ on 10/26/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use incorporated into the crack growth procedure. In this manner, the fatigue crack growth study was continued for circumferential growth of through-wall cracks. Using the criterion for crack instability during SSE loading, the margin between leak and possible large pipe break is determined for a given initial defect size. A wide range of initial flaw sizes and shapes were considered, and the resulting crack growth rates were calculated for the design basis loading transients and corresponding frequencies of occurrence given in Table 1. An example of the predicted growth behavior for a defect with an initial depth of 0.50 in. (12.7 mm) and an initial length of 39.0 in. (990 mm) is shown in Fig. 13. For the prescribed cyclic loading history the flaw was calculated to become a leaking crack in 21 yr of operation, which is much less than the normal (40 yr) plant life. It should be emphasized that the loading histories used in this analysis are a conservative representation of the design transients and are intended to describe the upper limit of possible reactor operating experience. If, after formation of a through-wall crack, the defect remains undetected and operation of the reactor continues, the calculated fatigue crack growth rate is such that it would require another 18 yr for the crack to extend circumferentially to become a large pipe break in the event of a Safe Shutdown Earthquake occurring near the end of the reactor plant life. This illustrates that a significant leak-before-large-break margin exists for a initial defect of this size. Figure 14 shows a similar plot of crack size versus years of operation for an initial flaw with dimensions a0 = 1.0 in. (25.4 mm) and 2C0 = 34.0 in. (863 mm). This initial flaw size also results in the formation of a large circumferential through-wall crack which could become a large pipe break during SSE loading within one plant life of 40 yr. However, it was determined that an initial flaw 1.0 in. deep and 34.0 in. long would grow to become a leaking crack in only 4 yr of reactor operation. This produces a leak-before-large-break margin of almost 36 yr in which to detect and repair the leaking crack. The fatigue crack growth results for a 0.35-in. (8.9-mm) deep and 45.5-in. (1156-mm) long initial flaw size are presented in Fig. 15. The time required to cause a leaking crack for this case is 38 yr, and the time to produce a critical length circumferential crack during SSE loading would be 40 yr of reactor life. The calculated leak-before-large-break margin for this initial defect size is only 2 yr. It is possible to construct a curve describing the range of initial flaw sizes (2C0 versus a0) which could produce a leaking crack in 40 yr of reactor operation, as well as the locus of initial flaw lengths and depths which could grow to become a large pipe break during a Safe Shutdown Earthquake in the 40th year of plant life as shown in Fig. 16. It is seen from this plot that for initial flaws less than 0.33 in. (7.6 mm) in depth there could be no through-wall penetration by fatigue crack growth to become a leaking crack. Similarly, for initial flaws greater than 0.33 in. (7.6 mm) in depth, but less than 30.0 in. (762 mm) in length, the results indicate that a leak could develop but no large pipe break during the plant operating life. For flaws which are initially deeper than 0.33 in. (7.6 mm) but less than 60 in. (1524 mm) in length, a sufficient leak-before-large-break margin would exist to insure detectability by leakage rate prior to the development of an unstable through-thickness crack. For example, considering an initial flaw depth of 0.50 in. (12.77 mm) and a range of initial flaw lengths, the time required to produce a leaking crack and the time for which a circumferential crack could grow to become a possible large break during SSE loading are shown in Fig. 17. It is noted that initial flaws must exceed 60 in. (1524 mm) in length before little or no leak-before-largebreak margin exists. However, for initial defects less than 60 Journal of Pressure Vessel Technology in. (1524 mm) in length the margin is substantial. Considering an initial flaw depth of 0.50 in. (12.7 mm) and an initial length of 40 in. (1016 mm), the margin between leak and possible break during SSE is determined to be 14 yr. The major concern is for those flaws which could grow to leak and, within a short period of time, cause a large pipe break during SSE loading. The results shown here demonstrate that such a flaw have to initially exceed 60 in. (1524 mm) in length and be greater than 0.33 in. (7.6 mm) in depth. The Code allowable limit for an inside surface indication of very long length (a0/2C0 « 0.0) is less than 0.15 in. (3.8 mm) depth for flaws detected during pre-service inspection [27]. Because the magnitude of a potentially dangerous flaw size is greater than twice the Code allowable limit, the ability to demonstrate that no such flaw could exist in the piping system prior to operation rules out the practical possibility of the guillotine pipe break failure. 8 Conclusions From this study it can be concluded that a throughthickness crack would have to extend more than halfway around the circumference in the middle of the discharge leg pipe before the effects of pressure plus SSE loading could cause unstable crack propagation. A range of initial defect sizes were identified which could cause a primary system pipe to leak, or cause a pipe to break in the event of a Safe Shutdown Earthquake, as based on conservative design basis plant operating conditions and crack growth rate data. The results of this study indicate that no leak or pipe break could occur for initial (pre-service) inside surface defects in the piping system less than 0.33 in (7.6 mm) deep. A significant margin exists between the time to cause a leaking crack and the time for a crack to become critical in size to produce a possible pipe break (caused by the combination of pressure plus SSE) for initial flaws greater than 0.33 in. (7.6 mm) deep and less than 60 in. (1524 mm) in circumferential length. The range of initial flaw sizes which could grow to threaten the integrity of the system represent large defects which should be easily detected during in-process inspection. On the basis of the large critical crack sizes and, similarly, the large initial defect sizes required before significant fatigue crack growth could occur, the results of this study provide evidence that the occurrence of a guillotine type of pipe break in the discharge leg is virtually impossible. Acknowledgments The author would like to acknowledge the contributions of N. A. Lebedinsky for helpful discussions in dynamic modeling, R. J. Fabi for providing programming assistance, and T. U. Marston for assistance with fracture toughness determination. References 1 "Protection Against Pipe Whip Inside Containment," Regulatory Guide 1.46, U.S. Atomic Energy Commission, May, 1973. 2 "Design Basis for Protection Against Pipe Whip," ANSI N176, American Nulcear Society, June, 1973. 3 "Design Basis Pipe Breaks for the Combustion Engineering Two Loop Reactor Coolant System," CENPD-168-A, Combustion Engineering, Windsor, Conn., June 1977. 4 Mayfield, M. E., Forte, T. P., Rodabaugh, E. C , Leis, B. M., andEiber, R. J., "Cold Leg Integrity Evaluation," Battelle Columbus Laboratories Report to USNRC, NUREG/CR-1319, Feb. 1980. 5 Lu, S., Streit, R. D., and Chou, C. K., "Probability of Pipe Fracture in the Primary Coolant Loop of a PWR Plant, Vol. 1, Summary Load Combination Program," Project I Final Report, Lawrence Livermore Laboratory, NUREG/CR-2189, Vol. 1, Sept. 1981. 6 Griesbach, T. J., and Ayres, D. J., "Opening and Extension of Circumferential Cracks in a Pipe Subject to Dynamic Loads," Nuclear Engineering and Design, Vol. 57, No. 1,1980, pp. 141-152. FEBRUARY 1983, Vol. 105/71 Downloaded From: http://pressurevesseltech.asmedigitalcollection.asme.org/ on 10/26/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use 7 Kassawara, R. P., Austin, S. C , and Izor, R. C , "The Effects of Reactor Coolant System Pipe Rupture Motion on Tributary Piping and Attached Equipment," presented at 5th International Conference on Structural Mechanics in Reactor Technology, Berlin (West), Germany, Aug. 1979. 8 Parks, D. M., " A Stiffness Derivative Finite Element Technique for Determination of Elastic Crack Tip Stress Intensity Factors," International Journal of Fracture, Vol. 10, No. 4, Dec. 1974. 9 Shih, C. F., et al., "Crack Initiation and Growth Under Fully Plastic Conditions: A Methodology for Plastic Fractor," EPRI Ductile Fracture Research Review Document, EPRI NP-701-SR, Feb. 1978. 10 Barsoum, R. S., Loomis, R. W., and Stewart, fi. D., "Analysis of Through Cracks in Cylindrical Shells by the Quarter-Point Elements," International Journal of Fracture, Vol. 15, No. 3, June 1979, pp. 259-280. 11 "Standard Test for JIc, A Measure of Fracture Toughness," ASTM StandSLvdESn-Sl, Annual Book of ASTM Standards, Part 10, ASTM, 1981. 12 Menke, B. H., Hiser, A. L., Hawthore, J. R., and Loss, F. J., "R Curve Characterization of Low Strength Structural Steels," Materials Engineering Associates, Inc., MEA-EPRI Research Program RP2055-7, EPRI NP-2715, Nov. 1982. 13 Oldfield, F. M., Strickler, T., and Oldfield, W., "Description and Catalogue of the Nuclear Reactor Material Databases," Materials Research and Computer Simulation Corp., MRCS-EPRI Research Program RP2055-2, Topical Report, Apr. 1982. 14 Server, W. L., Oldfield, W., and Wullaert, R A., "Experimental and Statistical Requirements for Developing a Well-Defined Kjg Curve," Fracture Control Corp., FCC-EPRI Research Program RP696-1, EPRI NP-372, May 1977. 15 Gerdes, L. D., "Dynamic Structural Analysis of Uncoupled Subsystems," Paper K6/18, 4th International Conference on Structural Mechanics in Reactor Technology, San Francisco, Aug. 1977. 16 Scanlan, R. H., and Sachs, K., "Earthquake Time Histories and Response Spectra," Journal of Engineering Mechanics Division, ASCE, Volume 100, Aug. 1974, pp. 635-655. 17 Scanlan, R. H., and Sachs, K., "Floor Response Spectra for MultiDegree-of-Freedom Systems by Fourier Transform," Paper K5/5, 3rd International Conference on Structural Mechanics in Reactor Technology, London, U.K., Sept. 1975. 18 Ayres, D. J., "Determination of the Largest Stable Suddenly Appearing Axial and Circumferential Through Cracks in Ductile Pressurized Pipe," Paper F7/1, 4th International Confernce on Structural Mechanics in Reactor Technology, San Francisco., Aug. 1977. 19 Emery, A. F., Kobayashi, A. S., and Love, W. J., "An Analysis of the Propagation of a Brittle Circumferential Crack in a Pipe Subjected to Axial Stresses," Paper No. 78-PVP-101, Joint ASME/CSME Pressure Vessel and Piping Conference, Montreal, Canada, June 1978. 20 Emery, A. F., Kobayashi, A. S., Love, W. J., and Jain, A., "Dynamic Propagation of Circumferential Cracks of Two Pipes with Large-Scale Yielding,'' ASME JOURNAL OF PRESSURE VESSEL TECHNOLOGY, Vol. 102, No. 1, Feb. 1980, pp. 28-32. 21 ASME Boiler Pressure Vessel Code, Section XI, Article A-3000, "Method forKj Determination," 1977. 22 ASME Boiler and Pressure Vessel Code, Section XI, Article A-4000, "Definition of Material Properties," 1977. 23 Bamford, W. H., "Application of Corrosion Fatigue Crack Growth Rate Data to Integrity Analyses of Nuclear Reactor Vessels," ASME Journal of Engineering Materials and Technology, Vol. 101, July, 1979, pp. 182-190. 24 Minutes of ASME Section XI Evaluation Working Group Meeting, Bethesda, Maryland, Nov. 1979. 25 Mukherjee, B., and Vanderglas, M. L., "Fatigue Threshold Stress Intensity and Life Estimation of ASTM-A106B Piping Steel," ASME JOURNAL OF PRESSURE VESSEL TECHNOLOGY, Vol. 102, Aug. 1980, pp. 294 -302. 26 Cipolla, R. C , "Computational Method to Perform the Flaw Evaluation Procedure as Specified in the ASME Code, Section XI, Appendix A , " EPRINP-1181, Part 1, Electric Power Research Inst., Palo Alto, Calif., Sept., 1979. 27 ASME Boiler Pressure Vessel Code, Section XI, Article IWB-3000, Table IWB-3514-2, "Acceptance Standards for Flaw Indications," 1977. plications, and components (reliability, qualification and testing, seismic qualification, valves, pump piping, piping supports, flow-induced vibration, fluid structure interaction, inspection, maintenance, repair, and behavior of cracks); 1984 PVP Conference and Exhibit lifeline earthquake engineering (seismic design of oil and gas pipelines and storage facilities and refineries, telecomThe 1984 Pressure Vessel and Piping Conference and munications, experiments and field observations in lifelines, Exhibit, sponsored by ASME's Pressure Vessels and Piping modes of failure in fault movements, slope instability and Division, will be held June 17-21, 1984, in San Antonio, liquidation, post-earthquake recovery in water supply and natural gas systems, offshore oil and gas platforms); and high Texas. Papers are solicited in the following area: design and pressure technology (modes of failure, fabrication practices, analysis (design methods for pressure vessels and piping, testing, high temperature effects, system safety, and in-service process equipment design, elevated temperature analysis, inspection). Ideas for and developers of poster sessions are limit analysis, stress analysis, seismic analysis, dynamic also sought. Abstracts of the proposed papers are due August 30, 1983. analysis, code requirements, dynamic stress criteria, testing technology, field services, fatigue, creep, and fracture damage Manuscripts will be required by December 15, 1983, for analysis); materials and fabrication (modes of failure, review. Address inquiries and send abstracts to: nondestructive examination, environmental effects, bimetallic G.E.O. Widera, welds, fabrication methods, quality assurance, specifications, Technical Program Chairman, technology transfer, fatigue, and elevated temperature efMechanical Engineering Department, fects); computer technology (structural analysis software, University of Illinois at Chicago, optimum design methods, graphics, vertification, water Box 4348, hammer analyses, data base usage, analysis of welds, and Chicago, IL 60680; parameter identification techniques); operations, apTel: (312)996-5317 Call for Papers 72 / Vol. 105, FEBRUARY 1983 Transactions of the ASME Downloaded From: http://pressurevesseltech.asmedigitalcollection.asme.org/ on 10/26/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use

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