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Strain-rate effects on turbine missile casing impact
Computers & Smcrures, Vol 13. pp. 311-318.1981 Printed in Great Britain All rights reserved
STRAIN-RATE
004~7949/81p10311-onso2.00/0 Copyri&bt @ 1981 Pergpmon Pm Ltd.
EFFECTS ON TURBINE CASING IMPACT
MISSILE
JA~IEST. CiOFtDON,JR. and JOHNE. REAUOH science Applications, Inc., 2450 Washington Avenue, Suite 120,San Leandro, CA 94577, U.S.A. (Receiued 11 May 1980) Abstract-Results from two-dimensional plane stress and plane strain computations simulating the impact of a 1u)’ turbine disk fragment on a turbine internal stator blade ring are presented and compared with data obtained in recent full-scale experiments. These computations were performed using the nonlinear explicit finite-difference computer code STEALTH developed for the Electric Power Research Institute. The numerical model employed represents the turbine missile as a rigid body which acts as a kinematic boundary condition on the stator ring. A work hardening, strain-rate dependent material model was used to character& the strength behavior of the stator ring. Friction effects were not modeled. Predictions of the deformed shape of the stator ring, line-of-flight displacement of the missile cg., missile rotation angle and rotational velocity agreed well with experimental values. Predicted values of missile kinetic energy and line-of-flight velocity were lower than observed experimentally, but showed reasonable agreement up to about 3.3 msec after impact, at which time the hold-down bolts were observed to move in the experiment. These bolts were not modeled in the analysis. For times leas than 3.0 msec, the predicted strains compared reasonably well with measured values.
INTRODUCTION The
capability to predict the effect of turbine missile impact due to the rare failure of a shrunk-on disk is a necessity in the design and safe operation of both nuclear and fossil-fueled power plants. Recent fullscale experiments [l] have demonstrated the large plastic deformations resulting from turbine missile impact and the extent to which a simulated internal stator blade ring and a simulated steam turbine outer wall can slow the velocity of 120” turbine disk fragments in two orientations-blunt and piercing. The objective was to provide benchmark data on both the energyabsorbing mechanisms of the impact process and, if break-through occurred, the exit conditions of the fragment. This paper documents numerical studies conducted using the explicit finite-difference computer code STEALTH t to simulate and predict the transient. large strain, nonlinear behavior resulting from the blunt orientation impact of a turbine disk fragment on the internal stator blade ring in the full-scale experiment. The goals of this numerical simulation were to aid in understanding the process by which missile fragments are slowed by the stator blade ring, and to demonstrate the applicability of the STEALTH code in determining the energy absorption of the stator blade ring (due principally to plastic flow), by comparison with the experiments. TARGET STRUCTURE The
target structure being modeled is shown in Fig. 1. The inner structure, representing the last-stage stationary-blade support ring was 12.7 cm (5 in.) thick, 50.8 cm (20 in.) wide and 431.8 cm (170 in.) in dia. The outer tSolids and Thermal hydraulics codes for EPRI Adapted from Lagrange TOODY and HEMP”, developed for Electric Power Research Institute by Science Applications, Inc. under EPRI Contract RP307. 311
I
I
-_1~3.2a”
I
I
PUNVIEW
LA TRACK
ICK
Fig. 1. Target structure, missile and impact orientations. a casing cover, was 3.2 cm (1.26 in.) thick, 182.9 cm (72 in.) wide and 635 cm (250 in.) in dia. The ring and the shell were fabricated from ASTM A515, Grade 65 cold-rolled steel with a tensile yield of 300 MPa (43.6 ksi), a tensile ultimate of 491 MPa (71.4 ksi), and an elongation of 26% at room temperature. The ring and the shell were bolted to a massive concrete structure and soil overburden weighting 1633 metric tons (1800 tons). The bolted connections simulated as closely as practicable the horizontal joints in an actual turbine. Twelve bolts that were 3.8 cm (1.5 in.) in diameter held down each end of the ring; these had shell, representing
JAMES T. GORDON. JR. and JOHN E. RFXGH
312
an ultimate strength of 11.5 MN (2.6 x 10” Ibn and an active length of 25.4 cm (10 in.). Fourteen bolts 2.54 cm (1 in.) in diameter held down each end of the shell; these had an ultimate strength of 6.7 MN (1.5 x lo6 lbf) and an active length of 15.2 cm (6 in.). The bolts were fabricated from A490 steel.
MISSILE IMPACT CONDITIONS
The missile was a 120” sector ofa last-stage shrunk-on disk. Dimensions and mass properties of the 1527-kg (3366-lb) missile are given in Fig. 2. The missile was made from high-strength alloy steel (ultimate strength of 896 MPa or 130 ksi). Note that the turbine sector has no blades: it is assumed that the blades break off or are crushed during exit.
SECTION
MATERIAL
MODEL
The material model used in these calculations was a work hardening, strain-rate dependent representation for A515 steel. Static tensile stress-strain data from the A.515 steel used to fabricate the experimental test ring are given in Table 1 in terms of true stress u = gt( 1+ C, I and true strain E = ln t 1+ cC) Since no data were found m the literature on the dynamic behavior of A5 15 steel. published dynamic data
for similar types of mild cold-rolled steels were taken as the basis for the strain-rate law used. The strain-rate dependence of the dynamic flow stress or, used for these calculations is aven by
A-A
Fig. 2. Dlmenslons and mass properttes of steel missile segment ( 120”hub sectIon).
The missile was mounted on a lightweight support sled. which was pushed by a rocket sled. After the acceleration stage the rocket sled was braked, allowing the missile and support sled to coast toward the target. Activation of explosive bolts just before impact separated the missile from the support sled, which was diverted by a striker plate beneath the target structure. The missile then traveled in free flight before its 15.5 cm wide (6.1 in.) edge struck the center of the 50.8 cm wide (20 in.) ring. As indicated in Fig. 1, the flight path of the missile’s center of gravity was offset 51.3 cm (20.2 in.) from the centerline of the track and the structure. This simulated the trajectory of a turbine segment that leaves the shaft translating tangentially from a circle through the segment’s center of gravity. The rotation of the segment, which would be at the rotational velocity of the turbine at failure, was not simulated in the tests. Instead, the total translational and rotational energy of the hypothetical turbine segment was included in the translational energy of the test missile. The nominal impact velocity was 151 m/set (495 ft/sec). This translational velocity gave the same total kinetic energy (17.4 x 106J, or 12.8 x lo* ft-lbf) as a segment leaving a shaft spinning at 2160 rpm. or 120”; of operating speed (the so-called design overspeed condition).
Table 1. True stress vs true strain for A5 15steel
uC(MPa) ---. 0 258.893 413.893 491.614 954.958
rr(psi) 0 37,548 60,000 71,300 138.500
-0
E
0.001293 0.050 0.095 0.75
where u. is the static yield stress. This simple strainrate law has been used to characterize the behavior of mild steel by Bodner and Symonds [Z] using experimental data from Manjoine [3]. The stress invariant u2 = 35: is calculated assuming the stress changes are elastic. Then. if u <0(&P.0)
(2)
the elastic state is appropriate. and no plasticity results. The fundamental equation for plasticity, using the Prandtl-Reuss flow rule to second order accuracy is - cl(&P,eP) eP= Q ~__ 3/1At
(3)
where p is the shear modulus. This equation is solved by Newton’s
method
to obtain the consistent
yield stress
Strain-rate effects on turbine missile casing impact
and plastic strain rate.
The first guess $, is taken to be
where C is the total equivalent strain rate. In all cases, the plastic strain dependence is evaluated at the value of plastic strain from the previous time-step. The calculations were performed using the inelastic portion of the true stress vs true strain curve defined in Table l.Table2 showsthevaluesofYoung’smodulus E, bulk modulus K, Poisson’s ratio Y. and shear modulus G, used in these calculations where K = E/3( I- 2v) and G=E/2il+v). Table 2. Elastic constants used for A515 steel E
Mbar(psi)
P*is&‘s ratio 0.287
(2.9ck0x 10’)
K
G
Mbanpsi)
Mbarfpsi)
0.777700077 1.5649452 (2.2694 x 10’) (1.1268842 x 10’)
The mean stress (eq~tion-of-bate) model was considered to be a linear function of the compression fl where p=K/l=K@,ip-1)
(6)
where p is the pressure, p the density and p0 a reference density (7.85 gm/cm3).
PROBLEM SIMU~~ON The
geometry of blunt impact in plan view is shown in Fig. 3. The turbine missile is considered to be a rigid body which acts as a kinematic boundary condition on the 6nitedifference grid representing the stator ring. Although the STEALTH code does allow for multi-material impact (using slidelines), the approximation of a rigid missile would seem to be a good one since missile deformation was not observed in the fullscale blunt o~en~tion tests. Furthermore, to simulate the missile with a finite-difference grid would double the computer cost.
Fig. 3. Undeformed stator ring and turbine missile. The turbine missile. is represented
as a rigid body by
straight line segments describing the impact face and perimeter of the disk. The disk center of mass is shown
313
in Fig. 3 as the end point of the line segment perpendicular to the inner arc of the disk to aid in visualization of missile rotation. The stator ring is represented by a (4 x 111) iinitedifference grid consisting of 3 zones through the thickness of the ring and 110 zones circumferentially. As indicated in Fig. 1, each end of the test ring was attached to a thick base plate by eight thick flanges. Each base plate was attached to the back-up structure by 12 pretorqued bolts. Early examination of teat results indio ated that these bolts failed at about 9 msec after impact. Inspection of the failed bolts showed little or no inelastic elongation before failure. This suggested that the supports displaced little during the impact response of the ring prior to bolt failure (the base plate would have no motion at all until the reaction load exceeded the pre-load). In consideration of these factors, the numerical calculations were performed with theassumption of rigid fixed supports. Subsequent teat data evaluation has indicated that the base plates had begun to lift as early as 3.3 msec after impact. Thus, this fixed support boundary condition is strictly applicabie only to about 3.3 msec after impact. COMPUTATIONAL ALGORITMM The
STEALTH computer code solves the partial differential equations of continuum mechanics using an explicit &n&e-difkrence me&d formulated in a Lagrange (moving) coordinate frame. The STEALTH code is based entirely on the computer code technology published by Lawrence Livermore Laboratory, Livermore, Calif. and Sandia Laboratories, Albuquerque, New Mexico. The description that follows has been summarized from a descriptive report [4]. The computer code documentation is a separate report [S-S]. In the Lagrange system, fixed mass units translate, rotate compress, expand and distort. Momentum is associated with the motion of the mass and internal energy is fixed to the mass unit. The STEALTH solutions are second-order accurate in space and time. A complete description of the Lagrangian equations solved by the STEALTH code is given in the user’s manual [S]. Several rezoning options are available in STEALTH for updating grid point locations and variables in problems with large mesh distortion or grid tangling. Pressure ~~ontin~ties are handled by smearing out the discontinuity with a von Neumann quadratic artificial viscosity [93; zone-to-zone oscillations may be damped out by using a linear artificial viscosity [lo]: grid instability (hourglassing) is controlled by a “tensor-triangle” artificial viscosity [lo]. Stability of the differential equations is automatically regulated by the Courant stability criterion [S]. The computational procedure used in modeling the blunt o~entation impact process can be summarized as follows: On a given cycie. n: *The disk perimeter acts as a fixed boundary for the finite-difference grid. &TEALTH computes the stresses in the ring and new grid point positions due to the blunt orientation impact. No rezoning is used in the calculation. aThe forces acting on the disk perimeter due to stresses in the ring are computed and summed to give the resultant x and y forces and torque acting on the disk center
JAMEST. GORDON,JR. and
314
of mass. Frictionless contact is assumed between the disk and ring. *Rigid body motion of the disk center of mass is computed and new positions for the disk perimeter points are determined. These new locations are then used as the fixed boundary for the next cycle of the computation. Complete details ‘of this numerical procedure are documented in [ 111.
JOHN E. REAUGH
stator ring and turbine missile position at 2 msec for strain-rate independent (static tensile data) and rate dependent yield models. The effect of rate dependency is particularly evident on the right side of the ring where less bending occurs with a rate dependent yield model.
250. 200. 2 150.
DYNA.iWC RESPONSE CALCULATIONS
CaIculations were done in both plane stress and plane strain symmetries. The plane stress calculations were carried to 9.0 msec. The plane strain calculation was carried to 3.3 msec, the approximate time at which the hold-down bolts and plates were first observed to move in the experiment. Results were quite close for the two symmetries with the ptane stress values being generally closer to the experimental data than the plane strain results. Unless otherwise noted all results presented here are From plane stress calculations with a rate dependent yield model.
100. 50.0
-200.
-100.
0.00
cm
100.
zoo.
Fig. 6. Companson of deformed stator ring and turbine missile position at 0.0 and 9.0 msec.
250.
200. E 150. 0 100. -200.
50.0
-100
0
30
100
200
Cfll
-2bo.
-IbO.
0100 em
IbO.
zbo.
Fig. 7. Deformed stator ring and turbine missile position at 2 msec for rate independent yield model.
Fig. 4. Deformed stator ring and turbine missile at 3.3 msec.
250. 200. 150. 100. cm
50.0
-2bo.
-lb0
0’.00
tbo.
cm
Fig. 5. Deformed stator ring and turbine missile position at 9.0 msec.
Figures 3-S show mesh plots of the undeformed stator ring and turbine missile position at 0. msec (about 8 @ec prior to impact), and the deformed ring and missile position at 3.3 msec (time at which the holddown bolts move) and 9.0 msec (time at which the hold-down bolts break), respectively. Figure 6 shows mesh plots comparing the deformed ring position at 9.0 msec with the undeformed position at 0. msec Inspection of mesh plots between 3.0 and 9.0 msec (not shown here) indicates that bending of the ring begins to predominate over stretching after 3.3 msec. Missile cg. position is indicated by the end point of the line perpendicular to the turbine disk’s inner radius. Missile rotation is indicated by the orientation of this same line. Figures 7 and 8 show mesh plots of the deformed
Fig. 8. Deformed stator ring and turbine missile position at 2 msec for rate dependent yield model.
The experimental deformed ring shape was very similar to that exhibited in the rate dependent calculation. Figure 9 shows a comparison of experimental and computed missile line-of-flight cg. displacement histories. Both rate dependent and rate independent results are shown. The rate independent calculation was carried only to 2 msec. The rate independent displacements are seen to be greater than those observed in the experiment while the rate dependent displacements are lower than and closer to the experimental values. Thus, the slowing of the turbine missile is better simulated by the rate dependent calculation. The rate dependent displacements are seen to agree quite well with the experimental data up to about 3.3 msec (the time at which the holddown bolts were first observed to move), the difference being 3.0% at 1.0 msec. 8.8% at 2.0 msec, and 9.09;, at 3.3 msec. However, considerably better agreement could probably be obtained by using a dynamic effects factor with the rate independent model.
315
Strain-rate effects on turbine missile casing impact
Figure 10 presents a comparison of computed (plane stress and plane strain) and experimental deformed shapes at 3.3 msec for the ring midsurface. The plane stress and plane strain results are soen to be quite close, particularly in the missile-ring contact region. The plane strain calculation showsa slightly greater bending of the ring near the right hand support and the upper left portion of the ring (-60 in. cx 60) than for the plane stress cases.
r-
A
)-
T A
c
)-
A )-
A Experiment -
Steulth @onesees5 ymk
-.mt&~h 0
~
I
I
IO
20
I 30
Stealth plane strasr rate w-dependent yicaldmodel
fte dawn bolts mavlng I 40
Time-
I 50
I co
.
1
I
70
80
!
ms8t
Fig. 9. Comparison of expertmental and computed missile line-of-flight c.g. displacement histories.
Line-of-flight missile cg. velocity vs time is present& in Fig. 11. The computed velocities are in good agreement with measured values at early times. At 1.Omsec, the computed velocity is less than 5% below that observed experimentally. At 2.0 msec, the difierence is about 20% and at 3.3 msec about 24%. Thereafter, the calculated results show a steady drop in velocity, whereas in the experiment, missile velocity decmases at a much slower rate probably due to the hold-down bolts moving at 3.3 msec and &rally failing at about 9.0 msec. Figure 12 presents plots of missile kinetic energy (rotational plus translational), stator ring kinetic energy, ring internal (strain) energy and total energy as functions of time from the STEALTH calculations. The monitoring of these quantities provides a good means of assessing the reliability of the BnitedSerence solution as the calculation proceeds. In particular, the plots of total system energy show that the calculation is conserving energy (as the energy is transferred from the disk to the ring). For example, at 3.3 msec, the total ring energy is 123.9 in-lb and the change in kinetic energy of the disk is 123 in-lb, less than 1% difference. The greatest difference occurs at about 2 msec where the total system energy has dropped by about 10%. At 9.0 msec, the difference is only 4%. These difIerences in energy are we11 within the variation shown in most ~it~ff~~~ impact calculations with similar grid zoning and would be reduced by using a finer grid with additional zones through the ring thickness. Figures 13 and 14 show plots of STEALTH computed circumferential strains at the left support (80” left of the ring centerline) and at a position lo” left of the ring centerline. respectively. The strains are defined as (f-lo)& where (I-1,) is the stretch of an element of original length I,. The stretches are computed directly from the coordinates of the finite difference grid points. In Fig. 13, note the transition from small to large strains at about 5 msec. A similar change occurs in Fig. 14 at
Experwnentol deformed shape at 3.3 msec lJnd@frJm=dshope (mldpkme)----
x,
Fig. 10. Comparison CA5731-5- ”
of computed
and experimental
In
deformed shapes at 3.3 msec for ring midsurface.
JAMEST.
316
GORDON, JR. and JOHN E. REAUGH
2 and 5 msec. Figures 15 and 16 present comparisons of experimental and computed strain histories on the inner and outer surfaces near the left support. For the outer surface, the agreement between experimental and STEALTH computed values is good to about 2.5 msec. For the inner surface, the peak computed strains up to about 5 msec are two to three times the experimental values. Circumferential stram data was obtained at five additional radial locations and is given m [l I]. Computed strains were generally higher than recorded in the experiment with characteristics similar to the results shown in Figs. 1%16. For the right support. however. the agreement between experimental and computed strains was much poorer, especially after 2 msec. and reqmres further study to resolve the discrepancy. Comparisons of experimental and computed time histories of missile rotation angle and rotational velocity are given in [ 111. The experimental values of
I
I
--Tie-down -----Bolt
bolts rrwng
failure
1 o Stealth
I
L
’I
31
3j
0 0200
Time -
00400
oo600
set
Fig. Il. Comparison of experimental and computed rnissde ling-of-flight c.g. velocity histories.
0
I
2
rotation angle agree well with the computed values, particularly for times less than 4 msec. The experlmental
4
3
5
7
6
9
8
Time -set
Fig. 11. Turbine missile energy hIstones--STEALTH
-10
I 0
I
I 2
plane stress
I
I
I
I
I
I
1
3
4
5
6
7
8
9
1
Time-msec
Fig. 13. Circumferential
stiams at left support
(80
lefr ofnng
centerlmet-STEALTH
plane stress.
317
Strain-rate effects on turbiine missile easing impact values of rotational velocity remain approximately constant rather than falling off as found in the STEALTH calculations. This discrepancy is perhaps due in part to the bolt motion and subsequent failure in the experiment, whereas the STEALTH calculation used fixed supports. The computer time required for the entire plane stress calculation from 0. to 9.0 msec was 850 cp set on a CDC 7600. This calculation time includes restart and archive tape writing.
employed represented the turbine missile as a rigid body which served as a kinematic boundary condition on the stator ring. A work hardening, strain-rate dependent material model was used to characterize the strength behavior of the stator ring. Friction effects were neglected. Tie-down bolt flexibility was not modeled and the stator ring ends were assumed fixed. Incorporation of a constraint model with a bolt-failure would undoubtedly bring the representation STEALTH results closer to the experimental data.
160
,,Abter
14.0
*
C
e
iFI
I’
/-----__/’
120
.’
too 60 60 40
T0nSkUl + comptxWon
20 -0 -20 -40 0
I I
I 2
I 3
I
I 4
I 6
5
I 7
I
I
9
9
Tome- msec Fig. 14. Circumferential strains 10” left of ring eenterlino
STEALTH plane stress.
oStealth
.E g g lam
-
plane
stess
J
4 I 0 Compression -lcm + Tensm
0
0002
0004
0006
Ttme
om
OCXO
0.012
0014
,
316
In seconds
Fig. 15. Comparison of experimental and computed strains at left support outer surface.
CONCLUSION
Results from numerical simulation of the blunt impact of a 120‘ turbine disk fragment on the turbine internal stator blade ring have been presented. Comparison of these results with experimental data has successfully demonstrated the applicability of the nonlinear explicit &rite-difference code STEALTH in determining the energy absorbtion of the stator blade ring. Calculations were performed in both plane stress and plane strain symmetries. The numerical mode1
Predicted histories of line-of-flight missile c.g. displacement, missile rotation angle, rotational velocity and deformed shape of the stator ring agreed well with the experiment. Missile energy and line-of-flight velocity predictions were lower than observed experimentally but agreed reasonably well to about 3.3 msec. For times less than 3.0 msec, the predicted strains compared reasonably well with measured values. In order to insure increased confidence in the prediction of turbine missile impact, several items merit
318
JAMEST.GORWN,JR.
and
JOHN E. REAUCH
o Stealth
-4ccQ
b
0002
ocm4
occ6
Ocm8
0010
-plane stress
0012
0014
0016
Time IIJseccds
Fig. 16. Comparison of experimental and computed strams at left support mner surface.
investigation. Among these are: *Inclusion of a hold-down bolt model. *Numerical simulation of the piercing orientation impact and comparison with experimental data. This would require a dynamic fracture model. *Simulation of three-dimensional effects in the piercing impact process, and the turbine model. *Incorporation of stator blade models into the impact analysis. (The blades were assumed to be broken off in the current studies.)
continued
5.
6
7. work was performed under the auspices of the EPRI, Palo Alto, Calif., Dr. George Sliter, Turbine Missile Research Program Manager. Acknowledgement-This
8
1. H. R. Yoshimura and J. T. Schamaun, Preliminary results of turbine missile casina tests. EPRI Research Project 399 Preli~~ry Rep&t, EPRI, Palo Aho, Calif. (19781. S. R. Bodner and P. S. Symonds, Experimental and theoretical investigation of the plastic deformation of cantilever beams subjected to impulsive loading. J. Appl. Mech. 29,719728 (1962). M. J. Manjoine, Influence of rate of strain and temperature on yield stress of mild steel. J. Appl. Mech. 66. 211-218 (19441. R. Hofmann, STEALTH. A lagrange exphcrt finite-
9
10.
11.
difference code for solids. structural, and thermohydraulic analysis. EPRI NP-176, Summary, EPRI, Palo Alto, Calif. 119761. R. Hofmann, STEALTH, A lagrange explicit finitedifference code for solids, structural and thermohydraulic analysis. EPRI NP-260. Vol. 1, Useis Manual. Palo Alto. Calif. (19761. R. Hofmann, STEALTH, A lagrange explicit hrutedifference code for solids. structural and thermohydraulICanalysis. EPRI NP-260, Vol. 2. Sample and &i$cation Probers. EPRI. R. Hofmann, STEALTH, A lagrange explicit finitedifference code for solids, structural and thermohydra&c analysis. EPRI NP-260, Vol. 3. Programmer’s Manual. EPRI, Palo Alto, Calif. (1976). B. I. Gerber, STEALTH, A lagrange explicit finite-dilference code for solids, structural and thermohydraulic analysis. EPRI NP-260. Vol. 4, GRADIS Manual. EPRI, Palo Alto, Calif. (1976). J. Von Neumann and R. D. Richtmyer, A method for the numerical calculation of hydrodynamic shocks. J. Appl. Phps. 21,232-237 f 1950). M. L. Wilkins, The use of artificial viscosity in multidimensional fluid dynamic calculations. USRL-78348 (Preprint), Lawrence Livermore Laboratory, Livermore, Calif. (19761. J. T. Gordon, Jr. and J. E. Reaugh, STEALTH Calculations of turbine missile casing impact. EPRI Project 399-4 Final Report. Science Applications, Inc., San Leandro, Calif. (19791.
STRAIN-RATE
004~7949/81p10311-onso2.00/0 Copyri&bt @ 1981 Pergpmon Pm Ltd.
EFFECTS ON TURBINE CASING IMPACT
MISSILE
JA~IEST. CiOFtDON,JR. and JOHNE. REAUOH science Applications, Inc., 2450 Washington Avenue, Suite 120,San Leandro, CA 94577, U.S.A. (Receiued 11 May 1980) Abstract-Results from two-dimensional plane stress and plane strain computations simulating the impact of a 1u)’ turbine disk fragment on a turbine internal stator blade ring are presented and compared with data obtained in recent full-scale experiments. These computations were performed using the nonlinear explicit finite-difference computer code STEALTH developed for the Electric Power Research Institute. The numerical model employed represents the turbine missile as a rigid body which acts as a kinematic boundary condition on the stator ring. A work hardening, strain-rate dependent material model was used to character& the strength behavior of the stator ring. Friction effects were not modeled. Predictions of the deformed shape of the stator ring, line-of-flight displacement of the missile cg., missile rotation angle and rotational velocity agreed well with experimental values. Predicted values of missile kinetic energy and line-of-flight velocity were lower than observed experimentally, but showed reasonable agreement up to about 3.3 msec after impact, at which time the hold-down bolts were observed to move in the experiment. These bolts were not modeled in the analysis. For times leas than 3.0 msec, the predicted strains compared reasonably well with measured values.
INTRODUCTION The
capability to predict the effect of turbine missile impact due to the rare failure of a shrunk-on disk is a necessity in the design and safe operation of both nuclear and fossil-fueled power plants. Recent fullscale experiments [l] have demonstrated the large plastic deformations resulting from turbine missile impact and the extent to which a simulated internal stator blade ring and a simulated steam turbine outer wall can slow the velocity of 120” turbine disk fragments in two orientations-blunt and piercing. The objective was to provide benchmark data on both the energyabsorbing mechanisms of the impact process and, if break-through occurred, the exit conditions of the fragment. This paper documents numerical studies conducted using the explicit finite-difference computer code STEALTH t to simulate and predict the transient. large strain, nonlinear behavior resulting from the blunt orientation impact of a turbine disk fragment on the internal stator blade ring in the full-scale experiment. The goals of this numerical simulation were to aid in understanding the process by which missile fragments are slowed by the stator blade ring, and to demonstrate the applicability of the STEALTH code in determining the energy absorption of the stator blade ring (due principally to plastic flow), by comparison with the experiments. TARGET STRUCTURE The
target structure being modeled is shown in Fig. 1. The inner structure, representing the last-stage stationary-blade support ring was 12.7 cm (5 in.) thick, 50.8 cm (20 in.) wide and 431.8 cm (170 in.) in dia. The outer tSolids and Thermal hydraulics codes for EPRI Adapted from Lagrange TOODY and HEMP”, developed for Electric Power Research Institute by Science Applications, Inc. under EPRI Contract RP307. 311
I
I
-_1~3.2a”
I
I
PUNVIEW
LA TRACK
ICK
Fig. 1. Target structure, missile and impact orientations. a casing cover, was 3.2 cm (1.26 in.) thick, 182.9 cm (72 in.) wide and 635 cm (250 in.) in dia. The ring and the shell were fabricated from ASTM A515, Grade 65 cold-rolled steel with a tensile yield of 300 MPa (43.6 ksi), a tensile ultimate of 491 MPa (71.4 ksi), and an elongation of 26% at room temperature. The ring and the shell were bolted to a massive concrete structure and soil overburden weighting 1633 metric tons (1800 tons). The bolted connections simulated as closely as practicable the horizontal joints in an actual turbine. Twelve bolts that were 3.8 cm (1.5 in.) in diameter held down each end of the ring; these had shell, representing
JAMES T. GORDON. JR. and JOHN E. RFXGH
312
an ultimate strength of 11.5 MN (2.6 x 10” Ibn and an active length of 25.4 cm (10 in.). Fourteen bolts 2.54 cm (1 in.) in diameter held down each end of the shell; these had an ultimate strength of 6.7 MN (1.5 x lo6 lbf) and an active length of 15.2 cm (6 in.). The bolts were fabricated from A490 steel.
MISSILE IMPACT CONDITIONS
The missile was a 120” sector ofa last-stage shrunk-on disk. Dimensions and mass properties of the 1527-kg (3366-lb) missile are given in Fig. 2. The missile was made from high-strength alloy steel (ultimate strength of 896 MPa or 130 ksi). Note that the turbine sector has no blades: it is assumed that the blades break off or are crushed during exit.
SECTION
MATERIAL
MODEL
The material model used in these calculations was a work hardening, strain-rate dependent representation for A515 steel. Static tensile stress-strain data from the A.515 steel used to fabricate the experimental test ring are given in Table 1 in terms of true stress u = gt( 1+ C, I and true strain E = ln t 1+ cC) Since no data were found m the literature on the dynamic behavior of A5 15 steel. published dynamic data
for similar types of mild cold-rolled steels were taken as the basis for the strain-rate law used. The strain-rate dependence of the dynamic flow stress or, used for these calculations is aven by
A-A
Fig. 2. Dlmenslons and mass properttes of steel missile segment ( 120”hub sectIon).
The missile was mounted on a lightweight support sled. which was pushed by a rocket sled. After the acceleration stage the rocket sled was braked, allowing the missile and support sled to coast toward the target. Activation of explosive bolts just before impact separated the missile from the support sled, which was diverted by a striker plate beneath the target structure. The missile then traveled in free flight before its 15.5 cm wide (6.1 in.) edge struck the center of the 50.8 cm wide (20 in.) ring. As indicated in Fig. 1, the flight path of the missile’s center of gravity was offset 51.3 cm (20.2 in.) from the centerline of the track and the structure. This simulated the trajectory of a turbine segment that leaves the shaft translating tangentially from a circle through the segment’s center of gravity. The rotation of the segment, which would be at the rotational velocity of the turbine at failure, was not simulated in the tests. Instead, the total translational and rotational energy of the hypothetical turbine segment was included in the translational energy of the test missile. The nominal impact velocity was 151 m/set (495 ft/sec). This translational velocity gave the same total kinetic energy (17.4 x 106J, or 12.8 x lo* ft-lbf) as a segment leaving a shaft spinning at 2160 rpm. or 120”; of operating speed (the so-called design overspeed condition).
Table 1. True stress vs true strain for A5 15steel
uC(MPa) ---. 0 258.893 413.893 491.614 954.958
rr(psi) 0 37,548 60,000 71,300 138.500
-0
E
0.001293 0.050 0.095 0.75
where u. is the static yield stress. This simple strainrate law has been used to characterize the behavior of mild steel by Bodner and Symonds [Z] using experimental data from Manjoine [3]. The stress invariant u2 = 35: is calculated assuming the stress changes are elastic. Then. if u <0(&P.0)
(2)
the elastic state is appropriate. and no plasticity results. The fundamental equation for plasticity, using the Prandtl-Reuss flow rule to second order accuracy is - cl(&P,eP) eP= Q ~__ 3/1At
(3)
where p is the shear modulus. This equation is solved by Newton’s
method
to obtain the consistent
yield stress
Strain-rate effects on turbine missile casing impact
and plastic strain rate.
The first guess $, is taken to be
where C is the total equivalent strain rate. In all cases, the plastic strain dependence is evaluated at the value of plastic strain from the previous time-step. The calculations were performed using the inelastic portion of the true stress vs true strain curve defined in Table l.Table2 showsthevaluesofYoung’smodulus E, bulk modulus K, Poisson’s ratio Y. and shear modulus G, used in these calculations where K = E/3( I- 2v) and G=E/2il+v). Table 2. Elastic constants used for A515 steel E
Mbar(psi)
P*is&‘s ratio 0.287
(2.9ck0x 10’)
K
G
Mbanpsi)
Mbarfpsi)
0.777700077 1.5649452 (2.2694 x 10’) (1.1268842 x 10’)
The mean stress (eq~tion-of-bate) model was considered to be a linear function of the compression fl where p=K/l=K@,ip-1)
(6)
where p is the pressure, p the density and p0 a reference density (7.85 gm/cm3).
PROBLEM SIMU~~ON The
geometry of blunt impact in plan view is shown in Fig. 3. The turbine missile is considered to be a rigid body which acts as a kinematic boundary condition on the 6nitedifference grid representing the stator ring. Although the STEALTH code does allow for multi-material impact (using slidelines), the approximation of a rigid missile would seem to be a good one since missile deformation was not observed in the fullscale blunt o~en~tion tests. Furthermore, to simulate the missile with a finite-difference grid would double the computer cost.
Fig. 3. Undeformed stator ring and turbine missile. The turbine missile. is represented
as a rigid body by
straight line segments describing the impact face and perimeter of the disk. The disk center of mass is shown
313
in Fig. 3 as the end point of the line segment perpendicular to the inner arc of the disk to aid in visualization of missile rotation. The stator ring is represented by a (4 x 111) iinitedifference grid consisting of 3 zones through the thickness of the ring and 110 zones circumferentially. As indicated in Fig. 1, each end of the test ring was attached to a thick base plate by eight thick flanges. Each base plate was attached to the back-up structure by 12 pretorqued bolts. Early examination of teat results indio ated that these bolts failed at about 9 msec after impact. Inspection of the failed bolts showed little or no inelastic elongation before failure. This suggested that the supports displaced little during the impact response of the ring prior to bolt failure (the base plate would have no motion at all until the reaction load exceeded the pre-load). In consideration of these factors, the numerical calculations were performed with theassumption of rigid fixed supports. Subsequent teat data evaluation has indicated that the base plates had begun to lift as early as 3.3 msec after impact. Thus, this fixed support boundary condition is strictly applicabie only to about 3.3 msec after impact. COMPUTATIONAL ALGORITMM The
STEALTH computer code solves the partial differential equations of continuum mechanics using an explicit &n&e-difkrence me&d formulated in a Lagrange (moving) coordinate frame. The STEALTH code is based entirely on the computer code technology published by Lawrence Livermore Laboratory, Livermore, Calif. and Sandia Laboratories, Albuquerque, New Mexico. The description that follows has been summarized from a descriptive report [4]. The computer code documentation is a separate report [S-S]. In the Lagrange system, fixed mass units translate, rotate compress, expand and distort. Momentum is associated with the motion of the mass and internal energy is fixed to the mass unit. The STEALTH solutions are second-order accurate in space and time. A complete description of the Lagrangian equations solved by the STEALTH code is given in the user’s manual [S]. Several rezoning options are available in STEALTH for updating grid point locations and variables in problems with large mesh distortion or grid tangling. Pressure ~~ontin~ties are handled by smearing out the discontinuity with a von Neumann quadratic artificial viscosity [93; zone-to-zone oscillations may be damped out by using a linear artificial viscosity [lo]: grid instability (hourglassing) is controlled by a “tensor-triangle” artificial viscosity [lo]. Stability of the differential equations is automatically regulated by the Courant stability criterion [S]. The computational procedure used in modeling the blunt o~entation impact process can be summarized as follows: On a given cycie. n: *The disk perimeter acts as a fixed boundary for the finite-difference grid. &TEALTH computes the stresses in the ring and new grid point positions due to the blunt orientation impact. No rezoning is used in the calculation. aThe forces acting on the disk perimeter due to stresses in the ring are computed and summed to give the resultant x and y forces and torque acting on the disk center
JAMEST. GORDON,JR. and
314
of mass. Frictionless contact is assumed between the disk and ring. *Rigid body motion of the disk center of mass is computed and new positions for the disk perimeter points are determined. These new locations are then used as the fixed boundary for the next cycle of the computation. Complete details ‘of this numerical procedure are documented in [ 111.
JOHN E. REAUGH
stator ring and turbine missile position at 2 msec for strain-rate independent (static tensile data) and rate dependent yield models. The effect of rate dependency is particularly evident on the right side of the ring where less bending occurs with a rate dependent yield model.
250. 200. 2 150.
DYNA.iWC RESPONSE CALCULATIONS
CaIculations were done in both plane stress and plane strain symmetries. The plane stress calculations were carried to 9.0 msec. The plane strain calculation was carried to 3.3 msec, the approximate time at which the hold-down bolts and plates were first observed to move in the experiment. Results were quite close for the two symmetries with the ptane stress values being generally closer to the experimental data than the plane strain results. Unless otherwise noted all results presented here are From plane stress calculations with a rate dependent yield model.
100. 50.0
-200.
-100.
0.00
cm
100.
zoo.
Fig. 6. Companson of deformed stator ring and turbine missile position at 0.0 and 9.0 msec.
250.
200. E 150. 0 100. -200.
50.0
-100
0
30
100
200
Cfll
-2bo.
-IbO.
0100 em
IbO.
zbo.
Fig. 7. Deformed stator ring and turbine missile position at 2 msec for rate independent yield model.
Fig. 4. Deformed stator ring and turbine missile at 3.3 msec.
250. 200. 150. 100. cm
50.0
-2bo.
-lb0
0’.00
tbo.
cm
Fig. 5. Deformed stator ring and turbine missile position at 9.0 msec.
Figures 3-S show mesh plots of the undeformed stator ring and turbine missile position at 0. msec (about 8 @ec prior to impact), and the deformed ring and missile position at 3.3 msec (time at which the holddown bolts move) and 9.0 msec (time at which the hold-down bolts break), respectively. Figure 6 shows mesh plots comparing the deformed ring position at 9.0 msec with the undeformed position at 0. msec Inspection of mesh plots between 3.0 and 9.0 msec (not shown here) indicates that bending of the ring begins to predominate over stretching after 3.3 msec. Missile cg. position is indicated by the end point of the line perpendicular to the turbine disk’s inner radius. Missile rotation is indicated by the orientation of this same line. Figures 7 and 8 show mesh plots of the deformed
Fig. 8. Deformed stator ring and turbine missile position at 2 msec for rate dependent yield model.
The experimental deformed ring shape was very similar to that exhibited in the rate dependent calculation. Figure 9 shows a comparison of experimental and computed missile line-of-flight cg. displacement histories. Both rate dependent and rate independent results are shown. The rate independent calculation was carried only to 2 msec. The rate independent displacements are seen to be greater than those observed in the experiment while the rate dependent displacements are lower than and closer to the experimental values. Thus, the slowing of the turbine missile is better simulated by the rate dependent calculation. The rate dependent displacements are seen to agree quite well with the experimental data up to about 3.3 msec (the time at which the holddown bolts were first observed to move), the difference being 3.0% at 1.0 msec. 8.8% at 2.0 msec, and 9.09;, at 3.3 msec. However, considerably better agreement could probably be obtained by using a dynamic effects factor with the rate independent model.
315
Strain-rate effects on turbine missile casing impact
Figure 10 presents a comparison of computed (plane stress and plane strain) and experimental deformed shapes at 3.3 msec for the ring midsurface. The plane stress and plane strain results are soen to be quite close, particularly in the missile-ring contact region. The plane strain calculation showsa slightly greater bending of the ring near the right hand support and the upper left portion of the ring (-60 in. cx 60) than for the plane stress cases.
r-
A
)-
T A
c
)-
A )-
A Experiment -
Steulth @onesees5 ymk
-.mt&~h 0
~
I
I
IO
20
I 30
Stealth plane strasr rate w-dependent yicaldmodel
fte dawn bolts mavlng I 40
Time-
I 50
I co
.
1
I
70
80
!
ms8t
Fig. 9. Comparison of expertmental and computed missile line-of-flight c.g. displacement histories.
Line-of-flight missile cg. velocity vs time is present& in Fig. 11. The computed velocities are in good agreement with measured values at early times. At 1.Omsec, the computed velocity is less than 5% below that observed experimentally. At 2.0 msec, the difierence is about 20% and at 3.3 msec about 24%. Thereafter, the calculated results show a steady drop in velocity, whereas in the experiment, missile velocity decmases at a much slower rate probably due to the hold-down bolts moving at 3.3 msec and &rally failing at about 9.0 msec. Figure 12 presents plots of missile kinetic energy (rotational plus translational), stator ring kinetic energy, ring internal (strain) energy and total energy as functions of time from the STEALTH calculations. The monitoring of these quantities provides a good means of assessing the reliability of the BnitedSerence solution as the calculation proceeds. In particular, the plots of total system energy show that the calculation is conserving energy (as the energy is transferred from the disk to the ring). For example, at 3.3 msec, the total ring energy is 123.9 in-lb and the change in kinetic energy of the disk is 123 in-lb, less than 1% difference. The greatest difference occurs at about 2 msec where the total system energy has dropped by about 10%. At 9.0 msec, the difference is only 4%. These difIerences in energy are we11 within the variation shown in most ~it~ff~~~ impact calculations with similar grid zoning and would be reduced by using a finer grid with additional zones through the ring thickness. Figures 13 and 14 show plots of STEALTH computed circumferential strains at the left support (80” left of the ring centerline) and at a position lo” left of the ring centerline. respectively. The strains are defined as (f-lo)& where (I-1,) is the stretch of an element of original length I,. The stretches are computed directly from the coordinates of the finite difference grid points. In Fig. 13, note the transition from small to large strains at about 5 msec. A similar change occurs in Fig. 14 at
Experwnentol deformed shape at 3.3 msec lJnd@frJm=dshope (mldpkme)----
x,
Fig. 10. Comparison CA5731-5- ”
of computed
and experimental
In
deformed shapes at 3.3 msec for ring midsurface.
JAMEST.
316
GORDON, JR. and JOHN E. REAUGH
2 and 5 msec. Figures 15 and 16 present comparisons of experimental and computed strain histories on the inner and outer surfaces near the left support. For the outer surface, the agreement between experimental and STEALTH computed values is good to about 2.5 msec. For the inner surface, the peak computed strains up to about 5 msec are two to three times the experimental values. Circumferential stram data was obtained at five additional radial locations and is given m [l I]. Computed strains were generally higher than recorded in the experiment with characteristics similar to the results shown in Figs. 1%16. For the right support. however. the agreement between experimental and computed strains was much poorer, especially after 2 msec. and reqmres further study to resolve the discrepancy. Comparisons of experimental and computed time histories of missile rotation angle and rotational velocity are given in [ 111. The experimental values of
I
I
--Tie-down -----Bolt
bolts rrwng
failure
1 o Stealth
I
L
’I
31
3j
0 0200
Time -
00400
oo600
set
Fig. Il. Comparison of experimental and computed rnissde ling-of-flight c.g. velocity histories.
0
I
2
rotation angle agree well with the computed values, particularly for times less than 4 msec. The experlmental
4
3
5
7
6
9
8
Time -set
Fig. 11. Turbine missile energy hIstones--STEALTH
-10
I 0
I
I 2
plane stress
I
I
I
I
I
I
1
3
4
5
6
7
8
9
1
Time-msec
Fig. 13. Circumferential
stiams at left support
(80
lefr ofnng
centerlmet-STEALTH
plane stress.
317
Strain-rate effects on turbiine missile easing impact values of rotational velocity remain approximately constant rather than falling off as found in the STEALTH calculations. This discrepancy is perhaps due in part to the bolt motion and subsequent failure in the experiment, whereas the STEALTH calculation used fixed supports. The computer time required for the entire plane stress calculation from 0. to 9.0 msec was 850 cp set on a CDC 7600. This calculation time includes restart and archive tape writing.
employed represented the turbine missile as a rigid body which served as a kinematic boundary condition on the stator ring. A work hardening, strain-rate dependent material model was used to characterize the strength behavior of the stator ring. Friction effects were neglected. Tie-down bolt flexibility was not modeled and the stator ring ends were assumed fixed. Incorporation of a constraint model with a bolt-failure would undoubtedly bring the representation STEALTH results closer to the experimental data.
160
,,Abter
14.0
*
C
e
iFI
I’
/-----__/’
120
.’
too 60 60 40
T0nSkUl + comptxWon
20 -0 -20 -40 0
I I
I 2
I 3
I
I 4
I 6
5
I 7
I
I
9
9
Tome- msec Fig. 14. Circumferential strains 10” left of ring eenterlino
STEALTH plane stress.
oStealth
.E g g lam
-
plane
stess
J
4 I 0 Compression -lcm + Tensm
0
0002
0004
0006
Ttme
om
OCXO
0.012
0014
,
316
In seconds
Fig. 15. Comparison of experimental and computed strains at left support outer surface.
CONCLUSION
Results from numerical simulation of the blunt impact of a 120‘ turbine disk fragment on the turbine internal stator blade ring have been presented. Comparison of these results with experimental data has successfully demonstrated the applicability of the nonlinear explicit &rite-difference code STEALTH in determining the energy absorbtion of the stator blade ring. Calculations were performed in both plane stress and plane strain symmetries. The numerical mode1
Predicted histories of line-of-flight missile c.g. displacement, missile rotation angle, rotational velocity and deformed shape of the stator ring agreed well with the experiment. Missile energy and line-of-flight velocity predictions were lower than observed experimentally but agreed reasonably well to about 3.3 msec. For times less than 3.0 msec, the predicted strains compared reasonably well with measured values. In order to insure increased confidence in the prediction of turbine missile impact, several items merit
318
JAMEST.GORWN,JR.
and
JOHN E. REAUCH
o Stealth
-4ccQ
b
0002
ocm4
occ6
Ocm8
0010
-plane stress
0012
0014
0016
Time IIJseccds
Fig. 16. Comparison of experimental and computed strams at left support mner surface.
investigation. Among these are: *Inclusion of a hold-down bolt model. *Numerical simulation of the piercing orientation impact and comparison with experimental data. This would require a dynamic fracture model. *Simulation of three-dimensional effects in the piercing impact process, and the turbine model. *Incorporation of stator blade models into the impact analysis. (The blades were assumed to be broken off in the current studies.)
continued
5.
6
7. work was performed under the auspices of the EPRI, Palo Alto, Calif., Dr. George Sliter, Turbine Missile Research Program Manager. Acknowledgement-This
8
1. H. R. Yoshimura and J. T. Schamaun, Preliminary results of turbine missile casina tests. EPRI Research Project 399 Preli~~ry Rep&t, EPRI, Palo Aho, Calif. (19781. S. R. Bodner and P. S. Symonds, Experimental and theoretical investigation of the plastic deformation of cantilever beams subjected to impulsive loading. J. Appl. Mech. 29,719728 (1962). M. J. Manjoine, Influence of rate of strain and temperature on yield stress of mild steel. J. Appl. Mech. 66. 211-218 (19441. R. Hofmann, STEALTH. A lagrange exphcrt finite-
9
10.
11.
difference code for solids. structural, and thermohydraulic analysis. EPRI NP-176, Summary, EPRI, Palo Alto, Calif. 119761. R. Hofmann, STEALTH, A lagrange explicit finitedifference code for solids, structural and thermohydraulic analysis. EPRI NP-260. Vol. 1, Useis Manual. Palo Alto. Calif. (19761. R. Hofmann, STEALTH, A lagrange explicit hrutedifference code for solids. structural and thermohydraulICanalysis. EPRI NP-260, Vol. 2. Sample and &i$cation Probers. EPRI. R. Hofmann, STEALTH, A lagrange explicit finitedifference code for solids, structural and thermohydra&c analysis. EPRI NP-260, Vol. 3. Programmer’s Manual. EPRI, Palo Alto, Calif. (1976). B. I. Gerber, STEALTH, A lagrange explicit finite-dilference code for solids, structural and thermohydraulic analysis. EPRI NP-260. Vol. 4, GRADIS Manual. EPRI, Palo Alto, Calif. (1976). J. Von Neumann and R. D. Richtmyer, A method for the numerical calculation of hydrodynamic shocks. J. Appl. Phps. 21,232-237 f 1950). M. L. Wilkins, The use of artificial viscosity in multidimensional fluid dynamic calculations. USRL-78348 (Preprint), Lawrence Livermore Laboratory, Livermore, Calif. (19761. J. T. Gordon, Jr. and J. E. Reaugh, STEALTH Calculations of turbine missile casing impact. EPRI Project 399-4 Final Report. Science Applications, Inc., San Leandro, Calif. (19791.