NASA Technical Reports Server (NTRS) 19910012245: Elastic response of zone axis (001)-oriented PWA 1480 single crystal: The influence of secondary orientation

14 Pages·0.69 MB·English

by  NASA Technical Reports Server (NTRS)

NASA Technical Memorandum 103782 ..... /_ _
Elastic Response of [001]-Oriented
PWA 1480 Single Crystal--The
Influence of Secondary Orientation
Sreeramesh Kalluri and Ali Abdul-Aziz
Sverdrup Technology, Inc.
Lewis Research Center Group
Brook Park, Ohio
and
Michael A. McGaw .
National Aeronautics and Space Administration
Lewis Research Center
Cleveland, Ohio
Prepared for the
1991 Aerospace Atlantic Meeting
......... sponsored by the Society of Automotive Engineers
Dayton, Ohio, April 23-26, 1991
NASA
N91-21558
(NA,_A-TM-I03782) ELASTIC RF3PGNSE OF ZONE
AXIS (OF)I)-,']RIENTFO PWA 1480 SINGLE C_Y_TAL:
THE INFLUgNCZ OF SECONDARY ORIENTATION
CSCL 2OK
(NASA) 13 p
G3139

Elastic Response of [O01]-Oriented PWA 1480 Single Crystal -
The Influence of Secondary Orientation
Sreeramesh Kalluri and Ali AbduI-Aziz
Sverdrup Technology, Inc.,
NASA Lewis Research Center Group
Cleveland, Ohio 44135
and
Michael A. McQaw
NASA Lewis Research Center
Cleveland, Ohio 44135
Abstract fatigue resistance. The directional solidific3-
tlon process usually generates a secondary crys-
The influence of secondary orientation on tallographic direction, [010] that is randomly
the elastic response of a [O01]-oriented nickel- oriented with respect to fixed geometric axes in
base single-crystal superalloy, PWA 1480, was the turbine blade. However, orientation of the
investigated under mechanical, thermal, and com- secondary crystallographic direction can be
bined thermal and mechanical loading conditions controlled by using a seed crystal during solid;-
by applying finite element techniques. Elastic flcation (4). Since single crystals exhibit
stress analyses were performed with a commer- anlsotropic elastic behavior, the stress-strain
cially available finite element code. Secondary response and dynamic characteristics of a turbine
orientation of the single-crystal superalloy was blade that is directionally cast along the [001]
offset with respect to the global coordinate crystal orientation bend to vary with the orien-
system in increments from 0° to 90° and stresses tation of the secondary crystallographic
developed within the single crystal were deter- direction within the blade (5-6).
mined for each loading condition. The results The main objective of this study was to
indicated that the stresses were strongly influ- determine the influence of secondary orientation
enced by the angular offset between the secondary on the elastic response of [O01]-oriented, single
crystal orientation and the global coordinate crystal PWA 1480 under mechanical, thermal, and
system. The degree of influence was found to combined thermal and mechanical loading condl-
vary with the type of loading condition (mechani- tions by applying finite element stress analyses.
cal, thermal, or combined) imposed on the single- A parametric study was conducted in which the
crystal superalloy. secondary orientation angle was varied in incre-
ments of 10° from 0e to go ° for each loading
Introduction condition. The stresses developed within the
single crystal PWA 1480 superalloy for all the
Single crystal (SC) superalloys were iden- cases of the parametric study are presented.
tified as potential blade materials that war- The turbine blade of a rocket engine turbo-
ranted further development for advanced liquid pump is schematically represented in Fig. 1.
propellant rocket engine turbopumps by Chandler This is a hollow SC PWA 1480 turbine blade that
(1), After subsequent development, materials is directionally cast such that the [001] crys-
scientists evaluated the mechanical properties of tallographic direct;on (primary orientation) is
several single crystal superalloys (2,3) to find parallel to the span of the blade. In this par-
a suitable candidate replacement blade material tlcular design the hollow core extends below the
for the burbopumps of the Space Shuttle Main platform into the shank region. In Fig. 1, XYZ
Engine (SSME) and advanced rocket engines. A is the global coordinate system, with Z-axis
well characterized, nickel-base cubic single along the span of the blade, Y-axis along the
crystal superalloy, PWA 1480, was selected by chord of the blade, and X-axis along the thick-
Pratt & Whitney as the blade material for the ness of the blade,
Alternate Turbopump Development (ATD) program for In a cryogenic liquid propellant rocket
the SSME. engine turbopump, the blade attachment region may
Turbine blades of nickel-base single crys- be actively cooled. Since the turbine blade air-
tal superalloys (including PWA 1480) are direc- foil is exposed to the hot gas flow path, thermal
tionally solidified along the low modulus [001] gradients are induced both along the span of the
crystallographic direction to enhance thermal blade as well as through the thickness, for the
full length of the hollow core. These gradients
may be especially severe through the thlckness Dn Dz2 Cn 0 0 D16
(of the order of 875 °C/cm), while being milder
along the span. These gradients are substan- O'xx Dz2 Dn Cz2 0 0 D26 e xx
cr
tially higher than those in typical aircraft gas
YY eyy
turbine blades. To examine the role which the Cn C12 Ci_ 0 O 0
secondary crystal orientation may play in such O'zz Czz (2)
cases, an analysis of a square plate subjected to yz 0 0 0 C44 0 0 "Yy=
slmilsr loadings will be employed (Fig. 1).
"F "Yzx
A square plate with the dimensions of 25.4 ZX 0 0 0 0 C44 0
by 25.4 by 3.2 mmwas selected for the parametric
xy,
finite element stress analyses. The crystal
D16 D26 0 0 0 D66
(XcYcZc) and global (XYZ) coordinate systems for
the plate are shown in Fig. 1. The global
coordinate system is obtained by rotating the where,
crystal coordinate system about the Z -axis by
an angle of 8. Since the axes Z an_ Z are
C ,
both oriented along the [001] crystallographic
direction, the angle 8 between the crystal and Dn = Cn - 2(C11 - C12 - 2C44 ) (3)
global coordinate systems represents the orien-
X sin28 cos28
%atlon of the secondary crystallographic direc-
tion. The matrix of direction cosines that
relates the global coordinate system to the
crystal coordinate system (Fig. 1) is as follows:
D12 = C12 + 2(Clz - Cz2 - 2C44) i4)
cos.iinl/ei ]
x sin2@ cos2e
-sin@ cos@ (z)
0 0
D16 = (C n -C12 -2C44)(sin_@cos8 (5)
ELASTIC STIFFNESS COEFFICIENTS
- sinScos_)
Three independent elastic stiffness coeffi-
clenbs (CN, CI. and C44; Eq. (2)) are required to
describe %he e{asbic behavior of a cubic single D_ = -D_ (6)
crystal such as SC PWA 1480 within the crystal-
lographic coordinate sys%em (7). To describe the
elastic behavior in the global coordinate system
the stiffness tensor must be transformed from the
crystal coordinate system to the global coor-
D_s = C_ + 2(C_ - C _ - 2C ) (7)
dinate system (Fig. 1) according to the law of
transformation of fourth rank bensors. Lieberman
X sin_ cos_@
and Zirinsky (8) developed a simplified method
for transforming the stiffness coefficients of
single crystals between two coordinate systems In Eq. (2), _ o , G and F , F , T are
that are related by a matrix of direction cosines the englneeri_ noyrymal,ZZano. sh.earyZsD--resZxses, xy
(Eq. (1)). Their method was used together with respect;vely, and •x , • , _ and 7 , 7zx
Eq. (1) to obtain the elastic stiffness coeffi- 7_y are the engin.eering _ ynyorma_Z and shearyz '
clenbs of a cubic single crystal in the global strains, respectively. Thus, Eqs. (2) to (7)
coordinate system. The stiffness matrix of the define the stiffness matrix in a global
cubic single crystal within the global coordinate coordinate system (XYZ) that is offset by an
system and its relablonship to the engineering (arbitrary) angle 8 %o the crystal coordinate
stresses and engineering strains is as follows: system (XcYcZ¢; Fig. 1).
Thethree independent elastic stiffness finite element code enforcing the assigned tem-
coefficients (applicable within the crystal coor- peratures to the specific faces of the plate in
dinate system) for SC PWA 1480 at various temper- Fig. 4, while insulating all other faces. Ther-
atures are listed in Table 1. These coefficients mal gradients shown in Fig. 5 were used in the
were determined by the Engineering Division of second and third loading cases. These data
Pratt & Whitney, United Technologies Corporation represent temperatures at the centroids of the
under the NASA Lewis Research Center contract elements. The thermal output feature of MARC
NAS3-2393g. The variations of stiffness coeffi- code was used to generate the input subsequent
cients Dzl , Dz2, Die , D2e and D._o with. the stress analysis.
secondary orientation angle 8, _termlned from For each loading case in the parametric
Eqs. (2) to (7) for SC PWA 1480 at 38 °C, are study, the secondary orientation angle 8 was
shown in Fig. 2. Z¢ is evident from this figure varied from 0° to gO° in _ncremenbs of 10° . I_
that the variation in the elastic stiffness addition, all loading cases were studied for
coefficients has a periodicity of go° in 8, and = 45a to obtain the data at the symmetric loca-
therefore, a range of 0 to gO° was selected for tion (Fig. 2). The stiffness matrices for the
the secondary orientation angle in the parametric various secondary orientations were incorporated
study. in the finite element analyses by programming
Eq. (2) in the MARC user's subroutine HODKLW (9).
FINITE ELEMENT ANALYSES Variations in the physical and elastic properties
of the material with temperature were accounted
Elastic stress analyses were conducted on for in the analyses.
the plate model shown in Fig. 3 by using the MARC The variations in the different components
finite element structural analysis code (g). The of stress with secondary crystal orientation
finite element model of the plate contained a angle 8 were documented for three elements shown
total of 500 isoparametric eight-noded solid in Fig. 3. These elements were selected to
elements with ten elements along the side and capture the extreme as well as reference stress
five elements through the thickness of the plate. locations for the five different loading cases
The boundary conditions used were as follows: considered in this study. For example, under the
(1) the node at D was fixed in X, Y, and Z second loading case in which a thermal gradient
directions, (2) nodes along the edge AD were was imposed along the Z-direction (Fig. 4(b)),
fixed in Y and Z directions, (3) nodes along extreme thermal stresses could be generated in
the edge DC were fixed in X and Z directions faces ABCD and EFOH. Hence, the selection of
and (4) nodes along edges AB and BC were element 295 (Fig. 3) which was near surface EFCH
fixed in the Z direction. All boundary for this loading case. Similar reasoning was
conditions were enforced by specifying the fixed used in selecting element 445 (Fig. 3), for the
boundary option of the MARC code. A total of third Joading case in wh}ch a thermal gradient
five different loading cases were considered in was imposed along the X-direction. Finally, a
this study. In these cases mechanical, thermal centrally located, element 245 (Fig. 3) was
and combined mechanical and thermal loads were selected for the first loading case in which only
applied separately to the model. The previously the mechanical loading was imposed. Another con-
described boundary conditions were employed in sideration that led to the choice of these spe-
all five loading cases. cific locations was mitigation of the constraint
The first loading case involved a distrib- effects on the stresses generated within the
uted mechanical load of 137.g MPa along the elements.
Z-direction (Fig. 4(a)). In the second and third For the five loading cases considered in
loading cases thermal gradients were imposed this study, the values of the six stress compo-
along the Z- and X-dlrecbion, respectively nents ab the centroid of the selected elements
(Figs. 4(b) and (c)). Imposition of thermal are listed in Table 3 for a secondary orientation
gradients along the Z and X directions was an angle of _ = 0°, In all loading cases the
attempt to simulate the thermal gradients that stresses developed within the three selected
occur along the span and through the thickness of elements were well within the elastic regime of
the actual turbine blade. Finally, the fourth SC PWA 1480. In loading Case 1, which involved
and fifth loading cases were obtained by combin- only mechanical loading, values of the six stress
ing the first loading case with the second and components in the three selected elements were
third loading cases, respectively. very similar. However, in loading Cases 2 and 3
The physical properties of SC PWA 1480 which involved thermal gradients along the Z-
including mean coefficient of thermal expansion, and X-axis, respectively, elements 295 (near the
thermal conductivity and specific heat were hot side of a thermal gradient along Z-axls) and
obtained from Ref. 10. For the loading cases 445 (near the cold side of a thermal gradient
involving thermal gradients, thermal boundary alon 9 X-axis) were subjected to large normal
conditions represented by the temperatures in compressive and tensile stresses, respectively,
Fig. 4 were applied to the finite element model compared to the normal stresses in element 245
considered. These thermal boundary conditions which was nearly at the center of the mesh. The
may be representative of cryogenic rocket engine magnitudes of the tensile normal stresses of
turbomachinery turbine blade applications. Ther- element 445 in loading Case 3 were larger than
mal boundary conditions were introduced into the the magnitudes of compressive normal stresses in
element295underloadingCase2 becausethe DISCUSSION
square plate was subjected to a more severe
thermal gradient along the thickness (X-axis) In this study, the elastic stress compo-
than along the length (Z-axis). Finally, in nents were normalized to determine the influence
loading Cases 4 and 5 which involved both mech- of secondary orientation angle 8, under differ-
anical and thermal loading, the stresses devel- ent loading conditions. In Figs. 6 to 8 the
oped within the selected elements were very normalized stress components indicate that, on a
nearly equal to those expected from the super- relative basis, all six components of stress are
position of stresses developed in the individual influenced by the secondary orientation angle, 8.
mechanical and thermal Ioadings (loading Case 1 However, the importance of secondary orientation
with loading Cases 2 and 3, respectively). These effects cannot be evaluated by consideration of
results are in agreement with the principle of the variation in the normalized stress components
superposition for the linear elastic analysis. (with 8) alone. The magnitudes of the
The influence of secondary orientation on individual components must also be taken into
the stresses developed within the selected consideration for accurate assessment of the
elements are shown in Figs. 6 to 8. For each influence of secondary orientation. For example,
element and loading case, the individual stress one normalized stress component, (_)_/(T )-,
components at a given secondary orientation angle exhibited a range as large as ±166 _ %lemX_n{ 295
8 were normalized with the corresponding stress under loading Case 2, in which thermal loading
components obtained for 8 = 0°, i.e. was imposed along the Z-axis (Fig. 7(a)(ii)).
(Gx,)8/(G x)e , (GvX) R/(Gyy)e , and (_xy)8/(rxv) e and However, it is clear from Table 3 that the value
so on. THe indi_,dual _s well as normali_ed of Txy at 8 = 0° is only 0.005 Mpa. For this
stress components were then plotted against the loading condition, multiplying this stress com-
secondary orientation angle 8 for each element ponent by a factor of 166 yields 0.830 MPa, a
and loading condition. If there was no influence relatively small value compared to the other
of secondary orientation on the elastic response normal components of stress within this element
of SC PWA 1480, then all six normalized stress (Fig. 7(a)(i)). By comparison, the normalized
components should remain at a fixed value of stress component (G )^/(G )_ increased only
Y _ YY.
unity as 8 is varied from 0° to go°. Any from 1.0 to 1.4 as _ was ,ncreased from 0°
deviation from unity is an indication that the to 90 ° under thermal loading along the X-axis
elastic response of PWA 1480 SC is affected by (Fig. 7(b)(ii)). However, this represented an
the secondary orientation angle 8. The influ- increase in G from 2042 MPa at 8 = 0° to
ence of secondary orientation on individual and 286.3 MPa at _= 45 ° (Fig. 7(b)(ii)). Thus, the
normalized stress components under imposed variations in the normalized stress components
mechanical loading (Case 1) is shown in Fig. 6 with 8, while indicative of the influence of
for the three selected elements. The variation secondary orientation on She elastic response of
of individual and normalized stress components SC PWA 1480, alone are not sufficient to assess
with secondary orientation angle 8 are shown in the importance of secondary orientation effects.
Figs. 7 and 8 for thermal loads (loading Cases 2 The variation of actual magnitudes of the indi-
and 3) and combined thermal and mechanical loads vidual components of stress also must be consid-
(loading Cases 4 and 5), respectively. ered to determine the quantitative significance
The influence of the secondary orientation of the secondary orienSation effects.
angle on both the individual and normalized Among the mechanical, thermal and combined
stress components was dictated by the type (mech- loading cases considered in this study, the case
anical or thermal or combined) of loading imposed of a thermal gradien_ along the X-axis (through
on the SC PWA 1480 square plate. For example, no the thickness of the square plate) produced large
significant influence of secondary orientation stresses (Table 3; In Case 3, element 445 is
was observed for the individual stress components under biaxial tension). This is due to the fact
under mechanical loading (Fig. 6). However, in that the thermal gradient through the thickness
cases involving thermal gradients along X- and of the plate is more severe than the thermal
Z-axis the individual normal stress components gradient along the length of the square plate
exhibited significantly larger influence of sec- (Fig. 5). In loading case 5, the mechanical load
ondary orientation than the individual shear which was superimposed on the thermal load of
stresses (Figs. 7 and 8). The normalized stress Case 3, nearly doubled the a component of
components exhibited a substantial dependence on stress within the square plat_ (Table 3; Case 5,
the secondary orientation angle, 8 under all element 445).
five loading cases. In all of the loading cases The state of maximum biaxial tension
except those involving thermal gradient along the occurred for loading Case S at a secondary
X-axis, largest influence of secondary orienta- orientation angle 8 = 46 ° (Table 3, element 445
tion was observed for the normalized stress com- and Fig. 8(b)(i)). This is to be expected
ponent (_)_/(_ )-. For the cases involving because in this instance the stiffness coeffi-
xy . xy
thermal gradient a_ong the X-ax,s the normalized cient D_I (which reaches a maximum at 8 = 45° ,
components (Oxx) R/(G..), and (_xx) 8/(_,y) @ Fig. 2) Is coupled with a steep thermal gradient
exhibited about%heCate order o_ variation with through the thickness of the square plate and a
the secondary orientation angle, 8. mechanical load along the Z-axis. Thus, large
thermal gradients perpendicular to the primary significance of secondary orientation in
orientation [001] of the turbine blade may be engineering design.
expected to produce very high stresses, if they 2. The type of loading (mechanical, ther-
occur near the secondary orientation of 8 = 45° . mal, or combined) imposed on the square plate
However, these stresses can be minimized by dictated the variation in the individual stress
controlling the secondary orientation so that components with the secondary orientation angle.
thermal gradients perpendicular to [001] occur 3. For the same temperature boundary condi-
near 8 = 0° . tions, thermal gradients through the thickness of
Some normalized stress components shown in the square plate produced higher stresses than
Figs. 6 to 8 exhibit a lack of symmetry about the thermal gradients along the length (primary
secondary orientation angle, 8 = 45 °, For exam- orientation of [001]) of the square plate. Thi_
was due to a higher thermal gradient through t.,_
ple, the normalized stress component (G)_/(Gxx)a
is not symmetric about # = 45 ° . S;m;I;_ thickness of the plate. If it is required to
behavior is also exhibited by the normalized impose thermal gradients perpendicular to the
stress components, (_)g/(_.,)e and (rz)_/(_,,)e primary [001] orientation, a secondary
orientation of 0° tends to minimize the thermal
in Fig. 6(c) (ii) and b_ _axx)_/COxx),, ".....
(_)elC_)e, and (r=)AIC%T e inFig.. 8(b)(;;). stresses developed within the plate, whereas a
The main _eason for lac_ of symmetry about secondary orientation of 45 ° tends to produce
8 = 45 ° is the coupling between G and G much larger thermal stresses.
wx yy
and 7 as well as between r and e and
• •unXy the s:n,gle crystal st,f_,ness matrixX_
(_Vq. (2)). The coupling elastic coefficients
D_q and D2e change sign about 8 = 45 ° (Fig. 2)
which creates a lack of symmetry in the stress
components. A small amount of observed lack of REFERENCES
symmetry may also have been caused by numerical
round off errors. This may especially be the 1. Chandler, W.T., "Materials for Advanced
reason for the observed asymmetry in Rocket Engine Turbopump Turbine Blades, w
Advanced High Pressure O_/H. Technology,
:n_h__(_/(Y_=)s"ung/e bcreycsatuasle st_iffnesshas nmoatrcixo.upling terms S.F. Morea and S.T. Wu, _ds_, NASA CP-2372,
In this study the influence of secondary 1985, pp. 110-132.
orientation was studied under purely elastic
conditions and steady state thermal gradients. , Dreshfield, R.L., and Parr, R.A.,
In actual service, turbine blades are subjected "Application of Single Crystal Superalloys
to severe thermal transients due to start up and for Earth-to-Orbit Propulsion Systems, w AIAA
shutdown, which can produce localized plasticity Paper 87-1976, 1987. (Also, NASA TM-89877.)
and creep in the turbine blades. The influence
of secondary orientation on the stresses produced 3, Fritzemeler, L.C., WAdvanced Single Crystal
within the actual blade under conditions of plas- for SSME Turbopumps, w RI/RD 88-273, Rockwell
ticity and creep will be different from the International Corp., NASA CR-182244, 1989,
influence determined under fully elastic condi- pp. 1-44.
tions. To determine the influence of secondary
orientation on the stresses developed within the 4. Duhl, D.N., "Single Crystal Superalloys,"
turbine blades, nonlinear, transient thermal Superalloys, Supercomposites and Super-
structural analyses must be conducted with appro- ceramics, J.K. Tien and T. Caulfleld, ads.,
priate boundary conditions. Academic Press, Inc., 1989, pp. 149-182.
CONCLUSIONS 5. Bowen, K., Nagy, P., and Parr, R. A., aThe
Evaluation of Single Crystal Superalloys for
A parametric study was conducted with Turbopump Blades in the SSME,u AIAA Paper
elastic finite element analyses to determine the 86-1477, 1986.
influence of secondary orientation angle on the
elastic behavior of a [O01]-oriented nickel-base 6. AbduI-Aziz, A., August, R., and Nagpal, V.,
single crystal superalloy, PWA 1480 under "Design Considerations for a Space Shuttle
mechanical, thermal and combined mechanical and Main Engine (SSME)Turbine Blade Made of
thermal loads. The secondary orientation angle Single Crystal Material, w AIAA Paper 89-2149,
was varied from 0° to go° and the stresses 1989.
developed within a square plate of SC PWA 1480
under different loading conditions were computed. 7, Nye, J.F., Physical Properties of Crystals:
The following conclusions were drawn from the Their Representation by Tensors and Matrices,
parametric study. Calendron Press, Oxford, 1957, pp. 131-149.
1. Under the loading conditions studied,
the normalized stress components showed a sub-
stantial variation with the secondary orientation
angle. However, the normalized stress components
should be considered along with the magnitudes of
the individual stress components to determine the
8.
Lieberman, D.S., and Zirinsky, S., WASimpli- 10. Swanson, G.A., Linsak, I., Nissley, D.M.,
fied Calculation for the Elastic Constants of Norris, P.P., Meyer, T.G., and Walker, K.P.,
Arbibrarily Oriented Single Crystals," Acta _Life Prediction and Constitubive Models for
_, vol. g, 1956, pp. 431-436. Engine Hot Section Anisotropic Materials,"
PWA-Sg68-47, Pratt and Whitney Aircraft
g. MARC General Purpose Finite Element Analysis Group, NASA CR-179594, 1987. (Avail. NTIS,
Program, Vol. A: User Information Manual; AD-A173875.)
Vol. B: Marc Element Library; Vol. F:
Theoretical Manual. MARC Analysis Corp.,
Palo Alto, CA, 1988.
TABLE 1.- INDEPENDENT ELASTIC
STIFFNESS COEFFICIENTS
FOR SC PWA 1480
Temperature, C11, CI2 , C44 ,
°C GPa GPa GPa TABLE 2 - PHYSICAL PROPERTIES OF SC PWA 1480
[From Ref (9).]
-18 252 163 131
38 250 163 129 Temperature, Thermal Thermal Specific
93 248 161 128 °C coefficient conductlviby, heab,
149 246 160 126 of expansion, k, C_
204 244 159 124 W/m °C kJ/kg °C
260 242 158 123 m/m/°C
316 240 157 121
93 00000107 9.2 0.406
371 238 157 119
204 0000111 10.8 .440
427 235 156 117
316 0000115 12.4 .465
482 233 154 115 427 .0000119 13.7 .477
538 230 154 113 538 .0000124 15.3 .481
593 228 152 111
649 .0000129 16.9 .490
649 225 152 109 760 0000134 18.5 .511
704 223 151 107
871 0000140 20.0 .569
760 219 150 105
982 .0000147 21.5 .687
816 217 150 102 1093 .0000157 22.8 .917
871 213 149 100
927 210 148 97
982 206 146 95
1038 201 145 92
1093 197 143 88
1149 192 143 85
1204 186 142 81
TABLE 3. - STRESSES DEVELOPED IN SINCLE CRYSTAL PIA 1480 PLATE UNDER MECHANICAL,
THERMAL AND COIIBINEO LOADING CASES SECONDARY ORIENTATION ANGLE, 8 = O"
Case Type of Element
OXX P O'yy *}'yz ' 7"j[ xI
loading MPa MPa MPa MPa
Mechanical 245 0.655 1.310 136.9 0.001 O. 316 -().047
(Z-axis) 295 •012 .053 137.g .001 --.003 _,00_
445 -.0_0 1.234 136.6 .005 .385 -. 182
245 .043 --15.78 19.98 -0•017 -5.475 -.296
295 --19.44 _20.34 -1.88 .005 .043 -0.034
Thermal 245 •034 3.020 6.847 1.496 --. 270 --12.41
(X-axis) 445 •993 204.2 130.0 1.214 15.56 -3. 744
Mechanical 245 .697 -14.47 156.9 .018 -5,167 - .343
and thermal 295 --19.43 40.29 136.0 .006 •040 --.041
(Z-axi s)
Mechanical 245 .687 143.7 1.496 .046 12.46
(Z-axis) 445 .903 266.4 1. 220 15.95 -3. 923
and thermal
(X-axis)
6
I Z, Z¢ [001]
H G
.,,-_-7.,_ 2s.4_m -_
[01Ol [oto]
x x [1oo]
XYZ :Global co-ordinate system,
XcYcZc:Crystal co-ordinate system.
Figure 1.--Schematics of SSME turbine blade and the square plate considered for the analysis,
350 I I I '1 I t I 'I I I I I I I I I ---I_
300-
250 -
200- Primary orientation: [001]
(.9
._ 150-
u_
_100-
50-
-50,
-100 I I I I I t--I I I _ I ' I ' I --+---
20 40 60 80 100 120 140 160 180
Secondary orientation angle, degrees
Figure 2.-Variation ofelastic stiffness coefficients of SC PWA 1480 with the
secondary orientation angle 9.
Z [ooi}
Element295
G
XZ
/
Y
D
Element 445
YZ
IZ
....y
X
X
Figure 3.-Finite element mesh of the square plate.
8