Internal Stresses Due to Dislocation Walls Around Second Phase Particles C. CARRY, S. DERMARKAR, J. L. STRUDEL, AND B. C. WONSIEWICZ Nickel base superalloys with large y' volume fractions exhibit a high threshold stress duringa tensile test, and a large internal stress when tested in high temperature creep. Arrays of regularly spaced edge dislocations which develop duringthe first stages of creep have been observed. They lie in the y-y' interfaces and form dipolar arrangements on opposite sides of the ),' cuboids. The various components of the stress tensor are cal- culated for such a dipolar wall configuration and mappedby drawing equistress lines. The stressfieldresultingfrom such dislocation configurations has a very strong com- ponent along the tensile axis and opposes the applied stress. The shear component in the glide plane of similar dislocations is also very large between the precipitates and would tend to repel any new dislocation, in the absence of an external stress. The structural in- stability of these alloys under creep strain is also interpreted by this model. RECENT studies of creep at intermediate and high temperatures of oriented nickel base superalloy single crystals, 1,2 have revealedthe formation of near edge dislocation walls around second phase particles. These walls start developing during the incubation period1 and take their full extension in secondary creep.2 Their contribution to the internal stress of the material can be clearly established if we consider the various com- ponents of the stress field they generate. Li3 and Marcinkowski 4 studied the short range and longrange stresses associated with infinite and with finite edge dislocation walls. In this paper we consider a dipolar arrangement of regularly spaced infinite arrays of such dislocations. Resolvedclimb and glide compo- nents resultingfrom the cumulative action of two walls of opposite signs lead to a strong internal stress be- tween the two walls and to a very rapidly decreasing stress field outside the dipolar wall. This configura- tion is probably quite general in two phase alloys and is more easily identified when the volume fraction of the hardening phase reaches 50 to 70 pct. It is likely to be found in oriented eutectics submitted to high temperature creep. EXPERIMENTAL PROCEDURE The nickel base superalloy used here and the crys- tal growingand orienting procedures have been de- scribed previously.1 The volume fraction of the V' phase at the creep temperature is about 60 pct. After proper heat treatments, the ~' precipitates appear as rounded cuboids, 3000A in size and leaving 400A wide passages for dislocations gliding in the matrix. The ~' phase is in perfect epitaxy with the matrix but a slight lattice mismatch leads to a misfit parameter 5 ~- -4 × 10-3 in this particular alloy. Computer simulations of the dipoles arrays were conducted on a Digital Equipment Corporation 11/45 C. CARRY is Assistant Professor,Ecole Polytechnique, 1007 Lausanne, Switzerland, S. DERMARKAR and J_ L. STRUDEL are Graduate Student and Professor,respectively,Ecole des Mines de Paris Centre des Mat6riaux,91003 Evry,France, and B. C. WONSIE- WICZ is Member, Technical Staff, Bell Laboratories, Murray Hill, N.J. 07940. Manuscript submitted May 2, 1978. METALLURGICAL TRANSACTIONSA computer running under the UNIX* time sharing sys- *UNIX isa trademark of Bell Laboratories. tern. The programs were written in Cprogramming language .5 EXPERIMENTAL OBSERVATIONS Creeptests were conducted in tension at 850°Cunder a stress of 150 to 200 MPa on (127} oriented single crystals, i.e. 18 deg from J001L• This asymmetric orientation was chosen in order to minimize the num- ber of slip systems operating simultaneously. At this temperature and at low strain rates, deformation takes place in the matrix, by activated glide of a/2(l10} dis- locations in {1i0} type planes.6 The leading segment of the dislocation is ha screw orientation and bows out between the ~' precipitates, leavingbehindtwo edge dislocations of opposite signs in the y-7' interface. This configuration is clearly observed in HV-TEM micrographs (Fig. 1) andrepresented schematically in Fig. 2. Their edge character was determined in TEM by use of the partial extinction rule g .b = 0 and a stereographic projection as d e s c r i b e d e l s e w h e r e .1'7 During secondary creep, complex walls containing dislocation arrays with several Burgers vectors, move in opposite directions along opposite faces of the y' precipitates. Their glide takes place under the ef- fective shear stress. Their climb, on the other hand, is the rate controlling process in the course of second- ary creep,z The position of the extra half-plane for these dislocations is represented in Fig. 2 for a speci- men testedin tension. Also shown in B, are the posi- tion of the extra half-plane of edge dislocations which would compensate the lattice misfit when 5 is negative. Note that the deformation dislocations representedin A on vertical cube faces tend to aggravate the lattice mismatchbetweenthe two phases. The mean spacing° between y' precipitates is originally about 200 to 300A. Enhanced diffusion along dislocation cores will ac- celerate the coalescence and also modify the shape of the ~' phase which will tend to form thin plates or needles as described and interpreted indetailby Carry a n d S t r u d e l8'9 a n d f i r s t r e p o r t e d b y W e b s t e r and SullivanI° and later by Tien and Copley.n Thus, ISSN 0360-2133 / 79 / 0711-0855500.75 /0 © 1979 AMERICAN SOCIETY FOR METALS AND VOLUME 10A, JULY 1979 855 THE METALLURGICAL SOCIETY OF AIME