STRESS-CORROSION CRACK GROWTH IN ALUMINUM ALLOYS P. S. THEQCARISand G. A. PAPADOPOULOS Departmentof Theoreticaland Applied Mechanics,The National TechnicalUniversity, A&ens (629, Greece &&act-A maaoscopic stody of the growth of a stress corrosion crack in an ahuninumalloy was u&taken by usiog the opticalmethodof caustics.The dependenceof the crack-tipstress intensityfactors K, on the applied stress,as well as on the mohrity of a Nat3 aqueous solution was studied in detail. The calculationof these quantitieswas made by taLiDgiota account the tbickaess variationof the specimendoe to the corrosive enviroament. A criterion of the crack growth in terms of the caustics obtained by illthe cracked specimen by a light beam was formulatedand the correspondingvalues of the thresholdstress intensityfactor KIsc were accurately determined.Piiy, the creahm and the evolution of the pits developedat the vicioity of the cracktip was studiedand theirsigni6canceon the mechanismsof fractureof the specimens was examined.
Dun TOthe great complexity of the stress corrosion phenomena, which are afFected by a number of parameters, attempts were made toward the separation of the many interdependent variables. In combination with the large number of the contributing factors to these phenomena, corrosion cracking was studied from a number of diirerent points of view, such as the electrochemical, the physical and the mechanical points of view. In the present paper stress corrosion crack growth phenomena in aluminum alloys are studied from the mechanical point of view. A comprehensive discussion of the various factors affecting the kinetics of a corrosion crack in an aqueous solution under sustained loads has been given by Speidel[l]. As it is stated in this study relative to the threshold stress intensity K 19cc,below which crack growth does not occur, the existence of this limit is due to the rather arbitrary cut-off times of the experiments and there is no experimental evidence supporting such a limit value for K1. It is, however, possible to detine a conventional value for Klsn~, that is the value of K1 corresponding to a definite crack-growth rate (for example lo-” msec-‘). As it is self-evident, the experimental determination of K19cT is of major importance in practical applications. In this study the conventional values of KIscc for an aluminum alloy were determined accurately, by using an optical method very suitable for the solution of crack problems, the so-called method of caustics[2,3]. According to this method the stress singularity at the near to the crack tip region is transformed into an optical curve on a screen, which can be very much enlarged by receding the screen from the specimen, so that very accurate measurements on it can be made. In addition to the determination of the threshold values KIscc of KI, the variation of the stress intensity K, for the same ahuninum alloy with the applied stress, as well as with the [email protected]
of a NaCl aqueous solution was also studied. In all these studies the values of KI were determined by taking into account the thickness variation of the specimen due to the corrosive environment. Finally, the study was directed towards the mechanism of crack growth by studying the creation, evolution and growth of pits developed near the crack tip, due to the corrosive environment and the applied stress. The significance of the role of pits on the stress-corrosion cracking was emphasized by several authors [4,5]. It was pointed out the superior role of pitting in the field of stress corrosion, which, in a way, may be regarded as an extreme case of pitting, leading to a slow mechanism of growth of the primary crack by the progressive coalescence with it of the deeply advanced pits at the vicinity of the crack tip. DJYl=MNA’YION OF SYRRSS INTRNSlYY FACTOR St BY CAUSl’ICS The stress intensity factor KI, which is the governing quantity for the near to the crack-tip region, can be accurately determined by the optical method of caustics. According to this 781
P. S. THEOCARIS and G. A. PAPADOPOULOS
-=thndf7 31 the more interesting region of the specimen at the vicinity of the crack-tip is illuminated by a light beam and the reflected light rays are received on a reference screen at some distance from the specimen. When a certain load is applied to the specimen the reflected light rays at the vicinity of the crack tip, where there is a steep thickness variation due to the singularity existing, are scattered and they are concentrated along a curve, the so-called caustic, when projected on a reference screen placed at some distance from the specimen. As it has already been indicated, when the crack axis is normal to the tensile load, applied to the specimen, the transverse diameter 9 of the caustic is directly related to the stress intensity factor K1 through the relation:
where z. is the distance between the specimen and the screen, where the caustic is formed, d is the thickness of the specimen, c is a constant, which for the case when the light rays reflected from the front face of the specimen are considered, is given by:
with Y Poisson’s ratio and E the elastic modulus of the material of the specimen, and A, is the magnification factor of the optical arrangement, defmed by: A,=-
with zl the distance between the specimen and the point-lit source S illuminating it. Positive values of zi correspond to positions of the liit source S in front of the specimen and negative values for S behind the specimen. By using relations (l)-(3) the values of the stress intensity factor KI for a cracked tension specimen in a corrosive environment can be determined. As it is well-known, the value of Kr for a tension specimen with a transverse crack of length u is equal to:
where P is the applied load, b and d are the width and the thickness of the specimen respectively and k is a constant expressing the inlhtence of specimen’s geometry on KI. If the load P, applied to the specimen, is kept constant, then from relation (4) it is concluded that, if the crack does not propagate the quantity (K,d) is constant, which by taking into account relation (1) means that the diameter a of the caustic is constant. Thus, any increment of the diameter D, means that the crack starts to propagate. This provides another means of visualizing the crack growth, instead of the conventional measurements made up to now on the crack-tip by a travelling microscope. By comparing these two methods of the crack growth veritlcation and localization of the progressing crack-tip, it can be observed that the method of caustics gives a twofold magnification of the crack propagation while the magnification of the crack growth in the conventional method, is only single. Indeed, the crack growth, which inlhrences the crack-tip stress field, is depicted on the caustic generated by illuminating the specimen by a light beam, thus providing a ftrst magnitlcation since the caustic can be highly magnified accordii to the particular arrangement of the experimental apparatus used. Purthermore the increase of the diameter of the caustic can be measured afterwards by a travelling microscope, thus providing with a second magnification and higher precision. Besides this twofold magnification, which is provided by the method of causticsin the crack growth measurement, this method presents a further advantage over the conventional methods. Indeed, in the latter methods, where the crack tip propagation is observed through a
Stress-corrosioncrack growth in aluminumalloys
microscope, it is very difllcult to determine the exact position of the crack tip, due to the usual crack blunting, because of the corrosive environment. In addition the particles of the aqueous solution may fill the crack tip region, so that to make difhcult the localization of the crack tip. Contrary to these conventional methods using a travelling microscope, in the method of caustics all these factors do not influence the measurement of the crack length. Indeed, in this method, the crack growth influences the near to the crack tip stress field, which is transformed into an optical curve. This transformation is made with hii accuracy, as it has already been proved by a series of publications by the 6rst author[2,3,73. The above described very accurate determination of the crack tip growth enables the exact below which the crack does not propagate. This can be calculation of the limiting value K,, achieved by applying on the specimen small increments of load and determining the particular load for which we have a prescribed crack growth velocity. The corresponding value of C presents the threshold value I&~. EXPERIMENTAL EVIDENCE The experiments
were undertaken in a 57s aluminum alloy whose composition and mechanical properties are given in Table 1. Tension specimens of width w = 69 mm and length I = 390 mm were prepared from a uniformly thick large plate, whose thickness was C= 1 mm. Two symmetrical artificial “ V” notches of angle and length equal to 9 = 30“ and a = 10 mm respectively were accurately sawn. The one lateral surface of each specimen was mechanically polished to become reflective by using a O-type emery paper. The thus prepared cracked tension specimens were subjected to a constant load by using a creep universal-testing machine. The non-reflective surface of the specimens was exposed in a NaCl aqueous solution while the reflective surface was covered by greasing substance so as to be protected by the corrosive environment. The molarity M of the NaCl-aqueous solution was varied for, ditferent batches of specimens and it had the following values: M = 0.6, 1.0 and 2.0 m. The specimens were also loaded with an anodic current of density j = 2 mA cm-’ in order to accelerate the corrosion process. The temperature T of the environment was kept constant during the experiments and was equal to T = 23°C. The tension specimens were interposed in a light beam emitted from a 15 mW He-Ne laser. The laser light was widened by a lens system, so that the magnification factor A,,,,defined by relation (3), was equal to A, = 6.5. Otherwise, the experimental apparatus was similar to that described in Ref. . Three different initial stress levels were applied to the specimens, so that the stress intensity factor K,, defined by relation (4), takes the following three initial values equal to IG’ = 15.62,21.68 and 27.86 Kpmm-“‘*. The load applied to the specimen was kept constant and the caustic formed on a reference screen by illuminating the specimen was photographed at detlnite intervals of time. Figure 1 shows the patterns obtained on the reference screen by illuminating a cracked tension specimen with a coherent He-Ne laser light beam. The values of the initial stress intensity factor &’ of the specimens and the molar&y M of the NaCl aqueous solution were equal to: KI’ = 21.68 kpmm-uz and M = 2 m. The two photographs of this ligure correspond to times t from the beginning of the application of the load t = 0 and t = 16 hr. It can be observed from these two photographs that at the tip of the “V” notch a strongly illuminated curve the so-called caustic is formed. By measuring the transverse diameter of this curve the values of the stress intensity factor Kr can be calculated through relations (l)-(3), as described above. It can be remarked fror6 these two photographs, that the diameter of the caustic is larger for the Table 1. Compositionand mechanicalpropertiesof 57s alumimm~alloy
.. comrbn luccbanical propertics
2.2-2.8 Mg. 0.15-0.35Cr Elastic modulus
0.45Fe + Si
Poisson’s ratio 0.;3
9 NO. 4-c
O.lOCu O.lOMn O.lOZn Yield stress
P. S. THEOCARISand G. A. PAPADOPOULOS
second photograph corresponding to a time interval t = 16hr from the photograph corresponding to the besinning of the experiment (t = 0). We can also mark on the surface of the corroded specimen some other strongly illuminated lines tending to form closed curves, as the time interval increases. These marks are distinctly observed in the following two photographs shown in Fii. 2. These photographs correspond to times from the beginning of the application of the load t = 38.25 and 49.00 hr respectively. It can be observed from these two photographs that as time increases the above closed, strongly illuminated curves, start to become more and more distinguishable, while their size increases. These secondary caustics are created by local irregularities, called pits, formed on the ill~ted surface of the specimen, which is exposed to the corrosive environment. In addition to the creation of these secondary caustics we can see that the main caustic, formed at the crack tip, becomes indistinguishable and is confused,with the secondary caustics. Finally, Fii. 3 shows the primary and the secondary caustics in an alumimun specimen with an initial stress intensity factor equal to Kj = 15.62kpmm-” immersed in a NaCl aqueous solution with molarity M = 2 m. Photograph (a) corresponds to a time interv~ t from the beginning of the experiment equal to t = 49.74 hr, while photograph (b) to t = 76.24 hr. Both these photographs correspond to a near to fracture stage of the specimen. We can see that the secondary caustics formed from the pits have been significantly enlarged, while their shapes become oblong to the direction of the crack propagation. In addition, the secondary caustics are confused with the primary caustic formed at the tip of the “V” notch. CRACK-TIP STKKSS INTKNSlTY FACTORS & From the experimentally obtained caustics and by using relations (l)-(3) the crack-tip stress intensity factors KI were determined. Since the thickness d of the specimens varies considerably during the corrosion process stress intensity factors were calculated by determining the actual specimen’s thickness during the experiment. This determination was made by using a microscope, measuring the specimen thickness at a number of points at the vicinity of the crack tip and taking the mean value of all these measurements. The variation of the gross specimen thickness d near the crack tip during the corrosion process for a precracked specimen in a M = 2 m NaCl aqueous solution for three diierent values of the initial stress intensity factor, equal to Ki = 27.86, 21.68 azd 15.62kpmm-“‘2 respectively is shown in Fii. 4. It can be observed from this 6gure that a strong thickness variation of the specimen happens, as the time t increases. We can also remark the paradox phenomenon, at 6rst sight, that the gross thickness variation is lower for higher values of the initial stress intensity for the same time interval from the begimring of each test. This
30 t (hours) -
~4.V~noftbcgrossthickneasdofthespecimeonearthecracktip,wrmalizedtothe~~ thickncas4. as well as of the stress intensityfactor K,, normal&d to its initialvalue Ki, v8 time 1 from the bcgimhg of the test for a doubly notched alumh~~~tcmdoospecimenin a 2 m NaCl aqueoussolutionfor three difhcat values of the initial strcm intensity factor K,’ and equal to ICi = 15.62, 21.68 and 27.86kpmm-*.
Fig. 1. Caustic patterns obtained on a reference screen by ihninatiog a doubly notched ahninum specimen by a He-Ne laser light. Specimen is immersed in a 2m NaCLaqueous solution and is loaded by a constant load P = 473kp. so that the initial value of stress intensityfactor K,’ is equal to K,’ = 21.68kpmm-*. Cases (a) sod (b) correspond to times t = 0 and 16 hours from the beghing of the test. We cao observe the main caustic at the crack tip and secondary strongly ihninated curves on the specimen’s surface crea+d by light rays reflected from pits.
FQ. 2. Caustic patterns on a reference scan for the same as in Fu. 1 specimen at times f = 38.25III (a) and 49.00br (b). The secondary caostics formed by pits become more distinguishable and increase in their size as timef increases. The shape of main caustic formed at crack tip is different to the typical epicycloid formed by brittle materials, which indicates that some plasticity is introduced at the crack-tip.
Fig.3. Caustic patterns on a reference screen for a doubly notched aluminum specimen with: K,’ = 15.62kpmmeSn, M = 2 m at times t = 49.76hr (a) and 76.24hr (b) respectively. Secondary caustics become oblong to the direction of primary crack propagation, while the primary caustic at crack tip is coalescing with secondary caustics.
Stresscorrosion crack growth inixhmhum alloys
phenomenon is in contradiction with the conventional thickness variation by loading the specimen by in-plane forces due to Poisson’s effect. The thickness variation of the specimen at the present case, however, is not due to Poisson’s effect only but also to the existence of pits created on the face of the specimen, which is exposed to the corrosive environment. Thus, it can be concluded that the bigher stress level increases the area of pits rather than their depths. In the same Ft. 4 the variation of the stress intensity factor K, vs time for the above three initial values of the stress intensity factor K,’ is also given. The corresponding curves terminate at the points where the specimen breaks. We can see that the critical time of fracture for each specimen is reduced as the initial stress intensity factor increases. It is worthwhile indicating here the rapid and high increase of K, as the time t irmeases. The inlhtence of the molarity of the NaCl-aqueoussolution on the gross-thickness variation of the specimen and on the crack-tip stress intensity factor KI is shown in IQ. 5. Again, it is worthwhile indicating the strong thickness variation of the specimen as well as the progressive increase of the stress intensity factor during the evolution of the experiment. The increase of the molarity of the corrosive environment increases the variation of the thickness of the specimen, as well as the stress intensity factor. Finally, Pii. 6 shows the variation of the diameter of the caustic vs time t for four d&rent values of the initial stress intensity factor which were equal to K,’ = 11.94, 15.62,21.68 and
Fii 5. Variationof (did,,) and (KJK,‘) vs time t for a doubly notched aluminumtension specimen with K:=~.lMkpmm-“forthreevalneaofthemolarityoftheN~laauaoussolotionandbcmaltoM=0.6,l.0 ad 2.0m. _
~6.V~oottbedhmter4ottbc~~fmmedattbc~tip,~to~~ vdmefortimer~O,vstiwtfor3d~~aotcbcd~~specimen,withM~2mfoPf~ [email protected]
of the initial stress intensity factor K: andequal toK,‘=1194. 15.62, 21.68 & 27.86kpmm-” lespachely. (Points on the comspondiql curveafor whfehdiamar 4 of causticincreasw give times for which crack start to propagate.)
P. S. THEOCARIS and G. A. PAPADOPOULOS
27.86 kpmmSw2.As it has already been indicated above the increment of the diameter of the caustic ensures that the threshold value K ,- of K, has been reached for the particular cut-off time of the experiment considered. We can see that for the smallest value of the initial stress intensity factor and equal to Ki = 11.94kpmm-3n there is a large interval of time t for which the diameter of the caustic is kept constant. This interval extends up to t = 45 hr. Thus, if the cut-off time of the experiment is smaller than t = 45 hr the value of KIis equal to = 11.94kpmm-3n. By increasing the initial stress level, the time interval over which the K zter of the caustic is constant is shrinked. Thus, for K,’ = 21.68 kpmm-” there is not any such interval. As it has already been proved above, the localization of the crack growth takes place with high accuracy by studying the variation of the diameter of the caustic formed by illuminating the specimen by a light beam. Thus, in each of the (DJD,,,)= f(t) curves in Fii. 6 there is a limit from which the diameter of the canstic start to increase. This limit gives the appropriate time limit for the initiation of propagation of the crack.
MACROSCOPIC STUDV OF PITSBY CAUSTICS As it has previously been indicated (see Fiis. l-3), besides the primary caustic formed at the tip of the notch and after a definite time interval from the beginning of the experiment, some other highly ilhuninated curves are created on the image of the surface of the specimen. These secondary caustics aie generated by the light rays reflected from the surface of the specimen at the vicinity of the pits which are created on the specimen. As it can be derived from Figs. l-3 the secondary caustics are bhured at the early stages of the initiation of pits, but as the time increases these caustics become progressively distinct and coalesce between them to form larger caustics. The successive evolution of the secondary caustics for a cracked aluminum specimen with an initial value of the stress intensity factor equal to K,’ = 15.62kpmm-3n in a 2m NaCl aqueous solution is shown in Fii. 7. Five successive stages of the secondary caustics, corresponding to times equal to t = 43.83, 67.83, 89.58, 100.58 and 114.58hr from the beginning of the test are drawn under identical scales. It can be remarked from this figure that at the early stages of the corrosion process the shape and the orientation of the secondary caustics is rather random (see Figs. 7(a) and 7(b)), while as time t increases these caustics are coalescing to form larger and more intensitve caustics which are progressively becoming oblong with their longer axes oriented toward the direction of the propagation of the primary crack. The variation of the characteristic time t. of appearance of pits on the surface of specimens vs the molarity of the NaCl-aqueous solut& for four values of the initial stress intensity factor Ki and equal to K,’ = 15.62,21.68,25.08 and 27.86 kpmme3” is shown in Fii. 8. It can be seen that the time t., is reduced as the molarity and the initial stress intensity factor increases. Finally, Fii. 9 shows the variation of the area A covered by the secondary caustics normalized to an initial area A,,, which was covered by these caustics near to the crack axis at the beginning of each test and in the direction of the primary crack propagation vs time t for two different values of the initial stress intensity factor and equal to Ki = 15.62 and 21.68 kpmm-3’2respectively.
DISCUSSIONOF EXPERIMRNTAL RESULTS The in8uence of the stress level and the molarity of a NaCl aqueous solution on the characteristics of the crack growth in an aluminum alloy was studied by using the optical method of caustics. The stress intensity factor KI, characterkingthe near to the crack-tip stress field, was evahrated for various initial stress levels and molarities of the aqueous solutions, vs time. The variation of Kr with these parameters was depicted in Figs. 4 and 5. From these figures it can be concluded that the rate of variation of K1 vs time t is not constant, but increases with time. This increment becomes larger as the initial stress intensity values or the molarities of the corrosive environment increase. All these results indicam the sign&ant role of the mechanical (expressed by the stress intensity factor) as well as of the environmental, (expressed by the molarity of the solution) factors on the crack-tip stress field. As it is well-known from the theory of elastic fracture mechanics, the stress components at the
Stress-corrosioo crack growth in alumioum alloys AOUEOUS NaCl SOLUTION K;
j i 2mAkm2
( c )
t = 89.58
(d 1 t= 100.58
7. Evolutionof secondary caustics formed by pits for a doubly notched aluminum tension specimen with Kk = 15.62kpmm-“, aad M = 2 m at the ~~~n~ times # from the begin!& of the test. (It can be observed that the secondary caustics, while at the early stages of the corrosioo process are arbitrarily oriented, they become oblong to the direction of the primary crack propagation, as time t increases.) Fii.
M (moles) ----+ Fii. 8. Variationof the time &,of the appearance of pits on specimen vs the molar&yM of the NaCI aqueous solutioa for four diierent values of the i&ii stress intensity factor and equal to Ki = 15.62,21.68,25.08and 27.86 respectively.
P. S. THEGCARIS andG. A. PAPADGPGUI_.GS
75 Bo 10s 120 thowdpie. 9. Variationof theareaA coveredby secondarycausticsformedby pitanormalizedto aninitialareaA, nearthe crackaxis vs time t for two d&rent valuesof the initial stress intensityfactorK,’ and equal to K,’ = 15.62and 21.68kpmm-* rcspcctively.
crack-tip region are directly related to stress intensity factor &, so that the value of the critical stress for which the material of the specimen fails can be determined. The study was then directed towards the determination of the value of the particular time, for which the crack starts to propagate. This was done with a high accuracy and simplicity by measuring the diameter of the caustic formed on a reference screen. As it has been already proved, any increment in the diameter of the caustic means that a crack starts to propagate. The crack does not propagate with a high velocity, as it occurs with brittle or semi-brittle fracture cases. This is due to the fact that the crack propagation procedure is largely assisted by the corrosive environment and not from the applied load, which corrosive environment, contributes mainly in breaking the bonds between the molecular structure of the material, while any increase of stress is of secondary importance. It is worthwhile observing from Fw. 2 and 3 that the main caustic, formed at the crack tip, is not symmetric to the crack axis, as in FQ. 1, but there is a distortion of the axis of symmetry of the caustic.. This ensures, as it has been previously pointed out[71, that shear stresses are introduced at the crack tip. Thus, it is concluded that the crack does not propagate along its initial axis, but follows a zig-zag path. From the angle of distortion of the axis of symmetry of caustic it can be readily determined the amount of contribution of the sliding-mode stress intensity factor IL, which characterizes the near to the crack tip stress field of a cracked plate subjected to shear forces. The variation of (K&G‘) vs time t for M = 2 m and IG’ = 15.62,21.68 and 27.86 kpmm-m respectively, as well as for &’ = 27.86 kpmm-” and M = 1 m and 2.0 m respectively are shown in Figs. 10(a) and 10(b). We can see that shear stresses become appreciable after a definite time interval from the beginning of the test and that the ratio (JL/&‘) takes larger values as the initial value of stress intensity factor K,’ decreases. This peculiar behaviour can be explained by the fact that microcracks and pits are oriented mainly parallel to the crack axis, as the applied stresses increase, so that for these stresses the shearing stress intensity factor becomes smaller. Moreover, it can be concluded from Fig. 10(b) that the value of sliding-mode stress intensity factor Kn increases as the molar&yit4 of the solution increases. We can also observe that for large values of A4 the time at which appreciable shear stresses are introduced is shortened. This indicates that the molarity of the solution plays a particular importance for the creation of microcracks and pits through which the primary crack propagates. Another interesting remark is the significant role in the mechanism of crack growth with corrosive environment played by the pits developed on the surface of the specimen after a period of time from the beginning of each test. The variation of the time t, of appearance of the first pit on the specimen vs the molarity M of the NaCl aqueous solution for four values of the initial stress intensity factor was shown in Fig. 8. The strong dependence of t,, on the values of
Stress-corrosioncrack growth ia ahmhum alloys
Fii 10. Variationof the ratio (K&C/) of the sliding mode stress intensity factor Kn to the initial stnss intensityfactor K: vs time I for K/ = IS.62 23.68and 27.86kpmmVwz aad M = 2 m (Fig. lO(a) for M = 1 and 2 m attd K: = 27.86kpmm-= (Pi. M(b)).
the stress intensityfactorKj and on the [email protected]
of the NaCisoiution,shown in this fisute, provesthe sign&ant roIeof IG’and A4on the mechanismof growthof crack,which startsto propagatewith the assistanceof pits. The majorrole of the stressintensityon creationof pits is shown by the fact thatthey arefirstlycreatedin the nearto the cracktip region,due to the high
Fe. il. Vatiationof the ratio(419) of the longitudinalD, to the w&verse 4 diameterof the primary eausticvstimetforX~=15.62,21.68awl~.86kpmm~~~~-2m(Pig.It(a))andforM~ImaMf2m for K,’ = 27.86kpmm-)” Fi. 1l(b)).
P. S. THEOCARISand G. A. PAPADOPBULOS
values of stresses at that region. However, although pits are formed at lirst very near to the crack tip there are selective positions on the specimen for which they are developed more rapidly than in others. This observation shows the increasing role of the crystallographic structure of the material of the specimen on its resistance to stress corrosion cracking. It can also be observed (see Figs. l-3) that, while at the beginning of the creation of pits they are arbitrarily oriented, as time increases they become oblong to the direction of the crack propagation and they are progressively coalescing with the primary caustic formed at the crack tip. From the photographs of the reflected,images of the specimen on the screen we can see that, while at the beginning of the experiment the main caustic at the crack tip has the form of the usual epicycloid form of brittle or semi-brittle materials, after a while the caustic becomes oblong to the direction of the crack. This shows that some plasticity is introduced near to crack tip. As it has already been shown [8,9] the primary caustic, formed at the crack tip, can be successfully used for the study of the form of the stress distribution in the cracked specimen, as well as for the determination of the crack opening displacement and the elastic-plastic boundary. This is in accordance with Swann’s [ 101predictions that in a corrosive specimen some initial fracture occurs, which is accompanied by small plastic deformation. The variation of the ratio of the longitudinal D, to the transverse D,diameter of the primary caustic is shown in Figs. 1l(a) and 1l(b) for three different values of the initial stress intensity factor K,’ (Fii. 11(a)) and two values of molarity M (Fig. 11(b)) vs time t. It is clear from these two figures that there is an important role played by the applied stress and the molarity of the corrosion environment on the plasticity introduced at the crack tip.
REFZRENCES [l] hf. 0. Speidel, Currentuuderstandingof stress corrosioncrackgrowthin ahuninumalloys. NATO Science Committee. Research Eooluation Conf., pp. 28-344. Brussels (1971).  P. S. llteocaris, Plastic strainat the roots of sharp notches in perspex. Exper. stress analysis and its influenceon design. Proc. of the 4th Int. Conj. on Stress Analysis, pp. 513-523.Cambridge,England(1970).  P. S. Theo&s, Local yieldingarounda crack-tipin Plexiglas.J. Appt.Mech. Tmns, ASME, Ser. E, 37 (2), 409-415 (1970). 141C. Edeleanuand T. J. Law, The propagationof corrosionpits in metals. I. Instit. Metals. 89,90 (1961).  E. C. Pearson, H. J. HuR and R. H. Hay, Can. L T&m., Jo, 311 (1952).  P. C. Paris and G. C. Sii, Stress analysis of cracks. ASTM STP J81, 30-81 (1964). [71 P. S. l’heocaris and E. E. Gdoutos, An optical methodfor determiningopening-modeand edge-slidii mode stress intensityfactors. J. Appl. Mech. Trans.ASME Ser. E, 39 (l), 91-97 (1972). [II]P. S. Theocaris,Stress intensityfactors in yieldingmaterialsby the methodof caustics. Int. J. Fmcture Mech.9 (2), 185-197(1973).  P. S. Theocarisand E. E. Gdoutos,The modifiedDugdale-Barenblatt modeladapt’edto variousfractureconfigurations in metals. Int. J. Fmcture Mech. M(3), 549-664(1974). [lo] P. R. Swann, Morphologicalaspects of stress corrosionfailure,NATO Sci. CommitteeResearchEualwtion Conf, pp. 113-126.Brussels (1971). (Received21 June 1976)