Nucleation and Growth of Flow and Fracture Markings W A L L E R GEORGE N A V A L R E S E A R C H LABORATORY. W A S H I N G T O N , D . C.
Macroscopic observations of t h e temporal and spatial development of localized plastic flowing and fracturing i n polymeric solids (and metals) are used t o suggest “models” of t h e physical character of t h e microscopic processes of plastic flowing. T h e nature of delayed yielding i n metals and polyamides is reviewed. Special emphasis is placed upon t h e advance nucleation of macroscopic flow and fracture elements in t h e region of stress concentration i n advance of t h e primary flow or fracture event. T h i s effect is illustrated i n t h e growth of fatigue fractures, creepy fracture, horizontal flow markings, or craze cracks, Fracture pairs and showers are illustrated and it is suggested t h a t these phenomena similarly involve advance nucleation w i t h i n t h e contracted stress fields associated w i t h rapidly advancing primary flow or fracture elements.
T
HE most obvious characteristic of a plast,ically deformed solid
is the appearance on it,s traction-free surfaces of often highly regular and alyays singular markings-clear, unambiguous evidence of the spatially local character of the processes involved. These flow markings are largely irreversible, for it. is rarely possible to significantly alter them by reversal of the sign of the surface tractions which lead to their initial appearance. Significant advance in the understanding of the processes of plastic flowing did not occur unt,il flow markings on the surfaces of deformed single crystals were studied. I t was then possible to correlate the average atomic configuration of the crystal with the orientation of t,he flow marking. I t was a study of these correlations yhich independently led Taylor (28), Polanyi ( 2 6 ) ,and Orowan ($4)to int,roduce the concept of the dislocation as a fundamental aspect of crystal plasticity. I n his original paper, Taylor presented a brief piscussion of the dynamics of dislocations which LYas largely motivated by macroscopic observations of the formation of flow markings in rock salt single crystals. Under polarized light the formation of these flow markings is observed to be accompanied by a short thin pencil of light which quickly propagat,es from one edge of the loaded crystal to t,he other in a manner which suggested to Taylor t,he propagation of a fracture across the crystal. Furt,her development of dislocation dynamics was not made unt’il rather recently, when Frank (8) and Eshelby ( 6 ) among others gave ext,ended discussions of the dynamics of the mathematical models of t,he dislocation commonly used in semiquant.itative studies of single crystal plasticity. (The nonlinear models of Frenkel and PeierlsIiabarro are expected from this discussion.) At, present, it appears necessary for new experimental studies to develop guides for extensions of these models from their present mathematical form, which is simply the well-known Volterra (30) “distorsioni,” renamed “dislocation” by Love ($1). Mathematically, dislocations are singular solutions of the two-dimensional equations of the classical elastic field for small displacements and are closely relat.ed to the solut’ion for an isolated force a t a point in a threedimensional field given by Kelvin (16) in 1882. The adoption of the Volterra mathematical model for a fundamental microscopic aspect of plastic flowing (the dislocation) was the result of physical intuition and association fed by macroscopic observations of flow markings on single crystals. Accordingly, the experimentalist may xell ask, are there other macroscopic characteristics of flow markings to be seen on plastically deformed solids which may similarly be used to obtain further insight into the complex of phenomenon called plastic flowing? I t is the purpose of this paper to examine the formation of flow markings on plastic and metallic solids with this question in mind.
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In part.icular, it will be concerned with the temporal development of these markings. In this connection polymeric solids are of special interest, since the time effects exhibited by these materials are usually slower by t,wo or more orders of magnitude than comparable effects in metallic or ionic solids. Obviously, there are certain essential difficulties with this approach which are associated with known differences between the micro and atomic structures of metals and polymers. In part,ial defense for neglecting these in the present paper it is noted that the polymers discussed here are a t least partially crystalline y i t h “grain” and “mosaic” boundaries, which are gross as compared with t,hose normally found in metals, this difference being perhaps more one of degree than of kind. Although it may be inferred from earlier experiments of Andrade ( I ) , Gough and coworkers ( 1 3 ) , and Bridgeman (g) among others, Clark and Wood ( 4 )were the first to clearly demonstrate in a simple loading experiment the existence of a time int,erval bet’weenthe application of an essentially constant tensile load and the response of the specimen by plastic flowing. They studied the dependence of these Raiting times for plastic flowing in a mild steel as a function of t’emperature and carbon content. Shortly after, Kauffman and George (16) were able t o show t’hat polyamide and polyethylene films of low orientation exhibited similar time d e l a p . I n these materials, delays approximately 1000 times those observed by Clark and Wood ( 4 ) for mild steel may be readily observed. In the polymer films a macroscopic creep is observed to occur within the time delay. Closer examination of t5hedeforming specimen under polarized light reveals the existence of arrays of flow markings apparently analogous to the Luder’s lines commonly seen in mild steel. Experiments on the polymer films using repetitions of alternate epochs of load and rest enable one to measure a form of an upper and lower limit for a delay time for the development and release of isolated flow markings bound initially to a free edge or imperfection. This time delay for “nucleation” of single flow markings appears to be of the order of 0.10 of that for the development of gross necking or a plastic shock wave in the polyamide films a t a given load. Thus, there is experimental evidence for the existence of time delays for the format,ion of flow markings and gross local necking in polymers. The dependence of t.he delay time for gross necking in polyamide film upon stress is quite similar to that observed by Wood and Clark in mild steel except for the magnitude 0: the time delay. This is illustrated in Figure 1. Wood and Clark (31)have studied mild steels which have been treated with wet hydrogen to alter their carbon content. Since the initial gross yielding is known from the work of Cottrell ( 5 ) and others t o be affected by the carbon content, it is not surprising
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1
I
Figure 1.
I
I
I
Delay T i m e versus Stress
Nylon data f r o m ( 1 5 ) , m i l d steel data f r o m ( 4 )
the relative humidity a t which the specimens are conditioned prior to testing. These effects are illustrated in Figure 2. I n both the polymers and metals examples can be found of a time delay which is apparently related to the concentration of a molecule or atom present in some form within the structure of the solid. In this connection the increase of carbon and nitrogen content of the mild steel increases the delay time, while the increase in water content decreases the magnitude of the delay time. Fracturing is the end point of plastic flowing. Time intervals analogous to those described may also be observed prior to the
Sol ids
development of fast fracturing in a simple experiment by the writer (10, I,%?),first described by Irwin (14). A centrally notched foil or film is loaded in dead weight. Under proper conditions the initial notch or slot is seen to elongate slowly to a critical length, a t which point rapid fracturing quickly develops by accelerating at the expense of strain energyreleased from the field of the specimen by its growth. Discussions of the development of this instability in terms of a generalized Griffith theory have been independently given by Orowan (23) and Irwin (14). Measurements of the writer ( 1 0 , l Z )and Smith (28) confirm these descriptions. George and Irwin ( 1 1 ) have suggested that the rapid development of plastic shock waves in nylon film involves a collapse of flow markings in a manner a t least grossly analogous t o the development of rapid fracturing. The advance of a fracture, both within the delay time and while accelerating a t the expense of strain energy stored within the specimen, is not as simple a process as it might appear a t first sight in terms of the foil model used for illustration. Independently, Kies et al. (10), Kies and Sullivan (1Q Zappfe (SS), and Smekal(26) have described the structure of fracture markings t o be observed on the fracture surfaces of glasses; plastics, metals, and other solids. A particularly simple and striking example of the structure to be observed is shown in Figure 3, which represents a section of a fracture surface in a polymethyl methacrylate
Figure 3.
Fracture Surface of Lucite (20)
Fracture traveled f r o m left t o r i g h t
I
l
2500
2000
\
plate. The various traces reminiscent of conic sections represent the intersection of level differences, which apparently grew into each other as the macroscopic fracture traveled from left t o right. The centers of the various subelements are clearly visible. This type of observation illustrates the discontinuous, complex, fine structure of the fracturing process. The centers of the subelements can be shown to develop in advance of Bhe main fracture front, a kind of advance nucleation of fracture elements. Kies (17, 18) has prepared a remarkable motion picture of this advance nucleation of subelements of fracture in a special specimen subjected to cyclic loading with a mean tension. A set of four pictures of this process, selected to illustrate an apparent time delay for the appearance of the advance fracture elements, is shown in Figure 4. The nuclei of two advance elements are clearly visible in the original negative. Another example of advance nucleation of fracture elements is found in the case of the foil model referred to previously. Zinc foils, in particular, show the advance nucleation of fracture elements ( 2 2 ) . Figure 5 shows a complex array which is typical of the creepy development of fracture in this material. (Creepy fracturing is a quasi-stable growth of fracture which does not necessarily accelerate a t the expense of released elastic strain energy stored in the specimen as a whole.)
j ,
10000
Effect of Water on Delay Time-Stress for Nylon (15)
Relation
10
1000
100
Delay Time (sec)
Figure 2.
Tests performed a t
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23' C.
.
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From Sol ids
A
E
c Figure4. Advance Nucleation of Fatigue Fractures i n Cast Cellulose Acetate (18) Sequence from 16 frames per second motion picture Of three nuclei t o right of principal fracture region i n B and develop into fracture elements i n D
A. B.
C.
D.
C,two
Frame1 Frame2 Frame29 Frame30
These examples of the disontinuous advance of fractuiing have a counterpart in the case oi localized plastic flowing. Craze little-studied type of floir cracks exhibit this type of advance. marking, which is here termed '.horizontal," also exhibits thiR discontinuous development. While the ordinary flow marking assumes orientations very roughly of 45 with respect to the initial prinripal tension, the hoiizontnl flow marking is rather accuratrlv oriented
Figure 5. Advance Nucleation of Creepy Fracture i n Zinc Foil (22) Fracture growing from left t o right
films, commercially known as bIYlar. Figure 6 shows a
Figure 7. Figure 6. Advance Nucleation of Horizontal Flow Markings i n M y l a r Film (Tensile Stress Vertical)
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typical example of this type of flow marking. The irregular and incomplete character of the markings is particularly clear. This structure is due to advance nucleation i n regions slightly above or below the primary stimulus. What may be another t l p e of advance nucleation process can be observed in the formation of fracture showers. The splitting of a fast fracture into two separate fractures may be ternied a fract'ure pair. Figure 7 illustrates such splitting in a 1,uoite plate. The production of fracture pairs occurs, as shown b y Smith and Ferguson ( 2 7 ) ,Tvheii the velocity of the primitr>- fracture approaches the velocity of sound in the medium. F i m i two-dimensional dynamic elast,icity ( 2 7 ) it is possible to show for either a Volterra (Burger's edge-type) dislocation or a cei%:tin model of a crack that the stress concentration of the dist,urbance n-ill contract with increasing velocity around the head of the disturbance and split into two separate parts in much the same manner that an electric field contracts ahead of a fast moving elect,ron. This tendency of the stress ahead of the moving disturhance to split develops rapidly as the velocity of motion ai)proaches the velocity of sound, c, in the medium. Siniilarly the strain energy contained in the field surrounding the disturh:mre increases rapidly as the velocity of the disturbance approachrs c. For isotropic elasticity it can be shown (9) for a s c r e ~ dislocation (Burger's Type II), that the energy for the uniformly moving dintul,bance pattern, E , is given 113-
ahere Eois the strain energy of the disturbance when the vcxlocity of motion, u, approaches zero. Orowan ( 2 5 ) and XiIanri ( 3 2 )have suggested that a similar relation is valid for fracture. This view of the production of fracture pairs is stimulating and the analogy with well-known formulas of special relativity is striking. Unfortunately, in practice one does not usually observe just a simple pair formation when a primary fracture is moving a t nearly sonic velocities, but rather a shower as show1 in Figure 8. Kies (17, 18) hnx cleai,ly denionstrnted in the c,nw of c.ert:Lin el a s t o m e r s that the tendencv to
t,ions suggest -- that each fracture elem e n t of t h e shower i n v o l v e s nucleation \I ithiri
Fracture Pair i n Lucite (27)
Exposure 116000 second Fracture b a s traveling from left t o right a t about 1000 feet per second prior t o rupture
Figure 8.
Fracture Shower in Nylon Film
Exposures, about 3600 per second Shower created by unstable horizontal flow marking
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the contracted stress field catalyzed by flaws. Lowering of the test temperature appears t o increase appreciably the elastic strain energy available to accelerate the fracturing. From this view, the possible role of microconstruction of the medium is dual in character. It may either act t o provide flaws or catalyzing agents or t o alter the availability of strain energy. These two characteristics would be expected to have different temperature dependencies. The temporal development of flow markings and fractures, when viewed in their simpler aspects, strongly suggest a process which is at least grossly analogous to the nucleation of a new from a parent phase. I n fact, Fisher, Hollomon, and Turnbull ( 7 ) have ventured the speculation that the origins of fracturing and plastic flowing may be generally regarded as a nucleation phenomena. The discontinuous, fine structure illustrated here represents a more complex series of processes than that suggested by the delay time experiments. If the simpler aspects of plastic flowing and fracturing may be regarded as nucleation phenomena, then these advance nucleations of fracture and flow elements may be analogous to the advance stimulation of recrystallization nuclei which has been described by Burgers (3) in studies of the recrystallization of aluminum. I n general conclusion, the illustrations cited here provide a number of new and interesting features of the development of macroscopic flow and fracture markings. At present it appears that some of these may be useful from the model point of view in extending understanding of the microscopic processes of plastic flowing. The nucleation of new flow and fracture elements in advance of primary flow and fracture may prove to be of particular importance. If a similar process does exist on the microscopic scale it may well be the major source of slow speed dislocation multiplication and hence the answer to the very old question of how dislocations multiply and pile up to form the macroscopically observed flow marking. ACKNOWLEDGMENT
The writer wishes to acknowledge many stimulating and clarifying discussions with G. R. Irwin and E. Orowan on numerous aspects of the general topic of this paper. Special acknowledgment is due W. H. Charch, E. I. du Pont de Nemours & Co., Inc., for gift of Mylar film.
LITERATURE C I T E D
(1) Andrade, E. N. da C., Proc. Roy. Soc. (London), A84, 1 (1911). (2) Bridgeman, P. W., J. Applied Phys., 17, 225 (1946). (3) Burgers, W. G., Nature, 157, 76 (1946). (4) Clark, D. S., and Wood, D. S., Am. Soc. Testing Materials, P , o c . ,
49, 717 (1949). (5) Cottrell, A. H., Proc. P h y s . SOC.( L o n d o n *) ,60, 30 (1948).
(6) Eshelby, J. D., Ibid., A62, 307 (1949). (7) Fisher, J. C., Hollomon, J. H., and Turnbull, D., J . Apuplaed * Phys., 19, 775 (1948). (8) Frank, F. C., Proc. P h y s . SOC.( L o n d o n ) ,60, 46 (1948). (9) Ibid., A62, 131 (1949). (10) George, W., P h y s . Rev., 73, 1262A (1948). (11) George, W., and Irwin, G., MIT Plastics Symposium, available on microfilm, June 1950. (12) George, W., and Irwin, G., P h v s . Rev.,73, 12308 (1948). (13) Gough, H. J., Hanson, D., and Wright, S. J., Trans. R o y . Soc. ( L o n d o n ) ,A226, 1 (1928). (14) Irwin, G. R., “Fracturing of Metals,” p. 147, Cleveland, Am. Soc.‘ Metals, 1948. (15) Kauffman, J. W., and George, W., J . Colloid Sci., 6, No. 5, 450 (1951). (16) Kelvin, Lord (Thomson, W,), “Math. and Phys. Papers,” Vbl. 1, p. 97, Cambridge, England, Cambridge University Press, 1882. (17) Kies, J. A., MIT Symposium on Plastics, available on microfilm, June 1950. (18) Kies, J. A,, and Hauver, C., unpublished. (19) Kies, J. A., and Sullivan, A. M., J . Metals, 188, 1090 (1950). (20) Kies, J. A , , Sullivan, A. M., and Irwln, G . R., J . Applied Phys., 21, 716 (1950). (21) Love, A. E. H., “Treatise on Mathematical Theory of Elasticity,” 4th ed., p. 221, New Yolk, Dover Publishing Co., 1944. (22) MoLean, E., Hauver, C., and George, W., unpublished. (23) Orowan, E., MIT Conference on Fatigue, in press, June 1980. (24) Orowan, E., 2.Physzk, 89, 634 (1934). (25) Polanyi, M., 2. Physsk, 89, 660 (1934). (26) Smekal, A., Glastech. Ber., 23, No. 3, 57 (1950). (27) Smith, H. L., and Ferguson, W. J., N a v . Research Lab. Progiess Rept., 11 (April 1950),unclassified. (28) Smith, H. L., Kies, J. A., and Irwin, G. R., Phys. Rev., 83, 872A (1951). (29) Taylor, G. I., Proc. R o y . SOC.( L o n d o n ) , A145, 372 (1934) (30) Volterra, V., Ann. Bco2e norm. (Paris),Ser. 3, 24, 401 (1907). (31) Wood, D. S., and Clark, D. S.,33rd Annual Convention Am. Soc. Metals, to be published. (32) Yoffe, E. H. (nee Mann, E.), Phil. Mag., 42,739 (1950). (33) Zappfe, C. A., Trans. Am. Soc. Metals, 41, 396 (1949). RECEIVED for review Deoembxr 21, 1951.
ACCEPTEDApril 3, 1052.
The Photographic latent Image As a Nucleation Process from the Solid Phase J. H. W E E E K O D A K RESEARCH LABORATORIES, ROCHESTER, N. Y .
T h e nucleation process, which occurs in t h e individual grains of t h e photographic emulsion, is referred t o as t h e formation of t h e l a t e n t image. T h e l a t e n t image and i t s format i o n are discussed f r o m t h e standpoint of t h e electronic and ionic properties of crystals. T h e m i n u t e size of t h e latent-image nuclei, together w i t h t h e discrete structure of t h e photographic emulsion, makes possible t h e tremendous amplification factor which is i n herent in t h e photographic process.
T
HE macroscopic image obtained on a photographic emulsion is
initiated by a brief exposure t o a geometrical pattern of light and is brought up t o the visible stage by a subsquent chemical development process. This paper shows t h a t the photographic process depends on a primary nucleation mechanism t h a t occurs in the solid crystalline grains of the emulsion under the action of light. The nuclei thus formed act t o ‘%rigger” the chemical reduction of a grain when i t is placed in a so-called developing solution. The minute size of these nuclei which initiate developJune 1952
ment, together with the grainy structure of the emuIsion, makeer possible the tremendous amplification factor which is inherent in the photographic process. By development, the original nuclei are magnified some billionfold t o produce the black and white image ordinarily observed. The nucleation process, which occurs in t h e individual grains of the photographic emulsion, is generally referred to as Iatent-image formation. Other aspects of the action of light include the direct photolysis of silver halide, whereby gross overexposure produces a
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