the mechanisms of crack initiation and crack propagation in metal-induced embrittlement of metals

The Mechanisms of Crack Initiation and Crack Propagation in Metal-Induced Embrittlement of Metals

PAUL GORDON and HENRY H. AN

Metal-induced embrittlement (MIE) of 4140 steel by indium has been studied using delayed failure tensile tests. The temperature and stress dependence of the kinetics of crack initiation and crack propagation in both liquid metal-induced and solid metal-induced cracking have been examined in the same system for the first time in MIE. This was done using electrical potential-drop measurements along the indium-covered portion of the sample gage length to record the start and progress of cracking, and also through fractographic observations. In Part I of the report on this work, the experimental results are presented, and their implications with regard to crack propagation are discussed. In Part II, various mechanisms proposed in the literature for crack initiation are evaluated in the light of the experimental results and other known characteristics of MIE. It is concluded that crack initiation in the embrittlement of 4140 steel by indium can best be explained by a mechanism involving stress-aided embrittler diffusion penetration of the base-metal grain boundaries, and it is suggested this may also be more generally true.

I N T R O D U C T I O N

W H E N normally ductile solid metals are placed under tensile stress and simultaneously into intimate contact with certain lower-melting metals, they tend to fracture at abnor- mally low stresses. Since the lowered fracture stress can be below the normal yield stress and since the effect has been most commonly noted when the low-melting metal actually was in the liquid state, the phenomenon was labeled liquid- metal embrittlement (LME). It is now clear, however, that the embrittler can produce a similar effect when in the solid state (see, e .g., Reference 1); the phenomenon is, thus, more appropriately called metal-induced embrittlement (MIE) or, as the case may be, liquid metal-induced embrittlement (LMIE) or solid metal-induced embrittlement (SMIE).

There have been several different theories proposed to account for MIE (actually for LMIE) on an atomic level. These include the atomic bond-breaking model of Stoloff and Johnston 2 and Westwood and Kamdar, 3 in which it is proposed that the adsorption of the embrittler atoms at the tip of a crack in the base metal lowers the cohesive bond energy of the base metal surface atoms sufficiently to make tensile decohesion at the crack tip easier than crack blunting by dislocation flow when stress is applied, leading to brittle fracture; the stress-assisted dissolution model of Robertson,4 later also proposed by Glikman et al,5 in which it is hypoth- esized that a crack propagates because the highly stressed atoms at its leading edge are dissolved into, and carried away by diffusion through, the liquid embrittler; the surface- structure model of Lynch 6 in which it is proposed that the role of the embrittler atoms adsorbed at the crack tip is to so alter the atomic structure of the base metal surface atoms as to lower considerably the normally high stress necessary to generate and move dislocations at the tip, thus lowering the stress for fracture by slip; and the Krishtal 7 model which proposes that brittle fracture takes place only after the grain

PAUL GORDON is Professor, Department of Metallurgical and Materi- terials Engineering, Illinois Institute of Technology, Chicago, IL 60616. HENRY H. AN, formerly Graduate Student, lllinois Institute of Tech- ogy, is Engineer ing Specialist , Electronics and Space Divis ion, Emerson Electric Company, Florissant, MO.

Manuscript submitted February 9, 1981.

METALLURGICAL TRANSACTIONS A

boundaries of the base metal have been embrittled by solid state diffusion of embrittler atoms some tens of atom diameters into and along base metal grain boundaries. (The potential role of grain boundary diffusion embrittlement was earlier suggested by Arkharov 8 and by Flegentova et al 9

as a possible effect supplementary to the major surface- active embrittlement effect.)

None of these models has received universal acceptance, though the bond-breaking model has been most generally accepted because it seems to account for more of the experimental observations than the others. The paper presented here is a report on the first phase of an effort to help identify the correct MIE model by taking advantage of a little- studied feature of MIE, namely, delayed failure. If a metal in contact with an embrittler is placed under a fixed tensile load of a magnitude less than that necessary to fracture it at once, it will, in most cases, undergo a form of static fat igue--delayed f a i l u r e - in which fracture takes place at constant load after a substantial length of t i m e - - u p to several hours, or even longer, depending on the load and the temperature. For a given embrittlement couple (the base metal-embrittler combination), we have found that the time to failure is both stress and temperature dependent. The phenomenon thus presents a clear opportunity to study the kinetics of the cracking process and consequently to obtain significant information on the underlying mechanisms. Until the present work, however, only a few delayed failure studies have been carried out (References 10 to 18) and of these only three published works 1~ used techniques capa- ble of distinguishing the initiation from the propagation of the embrittlement crack. In addition, the temperature and stress dependencies have not been thoroughly studied.

In the present work, pure indium (melting point 156 ~ has been used as the embrittler applied to smooth (un- notched) tensile samples of commercial 4140 steel quenched and tempered to a room temperature ultimate tensile strength of 1500 _ 12 MPa (218 ---2 ksi). The samples were tested under various fixed initial stresses ranging from about the proportional limit to just above the 0.2 pct offset yield strength at temperatures in the range 107 to 182 ~ Thus, for the first time in SMIE, the same embrittlement system has been studied extensively both in the SMIE and the LMIE

ISSN 0360-2133/82/0311-0457500.75/0 �9 AMERICAN SOCIETY FOR METALS AND VOLUME 13A, MARCH 1982 - - 457

THE METALLURGICAL SOCIETY OF AIME

range. In each test, the electrical potential drop produced by a constant current over that portion of the sample gage length covered by indium was monitored. When a crack formed, the otherwise constant potential drop increased and continued to do so during crack propagation; the data thus provided a measurement of both the crack initiation time and the crack propagation time as a function of test temperature and initial stress, again for the first time in MIE studies.

In the main body of this paper, the first part presents the experimental results o f the delayed failure tests and a discussion of their implications with respect to crack propagation. In the second part, theoretical considerations on crack initiation are presented.

PART I. DELAYED FAILURE IN THE EMBRITTLEMENT OF 4140 STEEL BY INDIUM

I. EXPERIMENTAL DETAILS

The indium used in this investigation was reported by the supplier (Indium Corporation of America) to be 99.999 pct pure. The steel was obtained in the form of i5,9 mm (actually 0.63 inch) round bars of commercial 4140 steel, all from the same heat, having the composition indicated in Table I. Cylindrical delayed failure tensile samples were rough- machined from these bars, heat treated, and then final- machined to a gage length of 42 mm and a gage diameter of 5.84 mm. The gage surface was given a mechanical polish to 600 grit followed by electropolishing. The final gage diameter was just under 5,84 mm, measured to within 0.1 pct.

Preliminary work indicated that the most convenient delayed failure test temperatures and times would be obtained with samples having a tensile strength of 1500 MPa (218 ksi); thus, all samples were heat treated to produce this strength. Only two samples were actually tensile tested (continuous loading) to failure at room temperature; the strength of the others was checked by hardness mea- ments and all were found to be Rc 45.5 +--0.3, which is equivalent to a tensile strength of 1500 • MPa (218 -+2 ksi). This close control of the strength was obtained by carefully regulating all heat treatment conditions. Austenitizing was done in air in a muffle furnace containing a heavy steel cylinder to smooth out temperature variations. The austenitizing treatment was 60 minutes in the preheated furnace followed by oil quenching. During the final 20 minutes the sample was at 846 ~ -+1 ~ (1555 -+2 ~ Tem- pering was carried out in a lead bath for 60 minutes at 427 -+0.5 ~ (800 -+ 1 ~ The average fracture grain size of the heat treated samples was about 0.01 mm (see later, Figure 4).

Table I. Chemical Composition of 4140 Steel Samples

wt Pct Element Heat Analysis Bar Analysis

C 0.41 0.39 Mn 0.87 0.86 P 0.014 0.01 S 0.016 0.03 Si 0.23 0.25 Ni 0.11 Cr 0.96 0.92 Mo 0.18 0.15 Cu 0.1

458 - - VOLUME 13A, MARCH 1982

The preliminary testing and previous work, e.g. ,is, revealed that the most serious source of scatter in the results was improper application of the embrittler. We have found that the main requirements of proper application are: (a) thorough "wet t ing"- - if this was not accomplished, cracking tended to be very late, and, in SMIE, many small "thumbnail" cracks formed around the periphery of the sample surface; with good wetting, on the other hand, there was always only a single crack, in both SMIE and LMIE, which in SMIE formed a ring of almost uniform depth all around the sample periphery (see later, Figure 3); (b) the good flow that comes with good wetting had to be confined to an annular band of uniform thickness and length (along the gage length)-- free flow formed regions of very thin indium coverage in which cracks appeared to initiate prematurely but then stopped propagating into the steel when the crack broke through the indium to the atmosphere (presumably because of oxidation of the crack surface). The technique finally devised to produce these requirements consisted of the following steps: (1)application of a heat resistant silicone-phenolic resin to the gage length leaving uncovered only a 4 mm wide band at the center of the gage length; (2) initial application of the indium to this band by electro- plating; (3)melting of the electroplated indium under a soldering flux by torch-heating while spinning the sample on a lathe; (4) removal of the resin, cleaning, and filing of the indium band to a final thickness of 0.25 mm. A typical prepared sample is shown in Figure 1. The flux used in the melting of the indium was a commercial soft-solder flux containing zinc chloride, tin chloride, and ammonium chloride. Previous embrittlement testing ~7 had shown that the flux did not in itself produce embrittlement. We also carried out standard hydrogen embrittlement tests at room tem- ture on indium-plated samples to show that no effect of this kind was introduced by our plating procedure.

Delayed failure tensile testing was carried out on a dead- load stress-rupture machine provided with a temperature- controlled furnace (air atmosphere) and universal type specimen gripping devices to minimize bending. During testing, the temperature of the sample was measured with a chromel-alumel thermocouple spot welded to the sample surface next to the indium band. The temperature was continuously recorded and held constant to better than---0.5 ~ The uncertainty in the indicated initial stress levels was ---3 MPa, due largely to the error associated with sample diameter measurement.

Crack initiation and propagation were monitored by pass- ing a 15-ampere electric current along the sample and mea- suring the potential drop along a 5 to 6 mm gage length of the sample centered on the indium band. The power supply was both current and voltage regulated to 0.1 pct of load. The usual total potential drop was 1.8 to 2.0 mv, which was continuously recorded. The smallest detectable potential change was 0.001 to 0.002 mv, whereas the total potential change during the brittle crack developmen t was approximately 0.1 my.

II. RESULTS AND DISCUSSION

A. General Characteristics of the Fractut:es

Fracture in our delayed failure tensile tests was found to take place in three stages. The first stage consisted of an

METALLURGICAL TRANSACTIONS A

(a)

Fig. 1 --Typical specimen, with indium applied. Approximately 2.2 times magnification.

incubation, or initiation, period during which there was no detectable crack, both in SMIE and in LMIE. The presence of this incubation period was noted for all samples, primar- ily by the initial constancy in the electrical potential drop vs time curves obtained (see Figures 6 to 8). It was recognized, however, that the sensitivity of the electrical measurements to very small cracks was not h i g h - - i t is estimated that a crack of cross sectional area about 0.15 mm 2 (say, 1.5 mm long by 0.1 mm deep) would be the smallest detectable by these measurements. To discover whether much smaller cracks were present during the incubation period, for both SMIE and LMIE several interrupted delayed failure tests were run in which the samples were held under load for up to 90 pct or more of the expected incubation time, the load released, and the indium removed.* The samples were then

*Indium was removed by reheating and brushing the molten indium off.

deep-acid etched (50 pct HCI-H20 at 70 ~ for 0.5 hour) and the surfaces examined in the scanning electron microscope (SEM) for cracks. None was observed; a repre- sentative sample surface is shown in Figure 2. An estimate of the size of crack which could easily have been observed had it been present can be obtained by noting that the inclusions in the steel can readily be observed in Figure 2 as small, longitudinal, elongated etch pits. The smallest of these which we could readily identify were about

i

(b)

Fig. 2--Deep-etched surface of sample after interrupted delayed failure test. Longitudinal lines (vertical) are inclusion markings. (a) 13.6 times magnification, showing full width of sample (horizontal), (b) 93.0 times magnification.

0.02 x 0.002 mm in size; since MIE cracks would be trans, verse to the inclusions and the etch exaggerates their size, we could undoubtedly have detected the presence of cracks considerably smaller than this had they existed, say, 0.01 mm long by 0.001 mm deep. Thus, if we designate as ti the time at which the potential drop curve first is detected to change, then we conclude that any crack present prior to ti could have been at 0.9 ti no larger than about 10-5/0.15, or about 10 -4 times the size of the crack at tl. This point will be discussed further later.

In the literature only three publications and two unpublished works bear on the question of an incubation period for crack initiation in MIE. Rostoker, et a l l~ concluded from LMIE delayed failure tensile tests that (a) in an incubation period in which the tensile properties did not change, no cracks were present, and (b) the incubation period con- sumed most of the time to failure. Nichols and Rostoker 12

METALLURGICAL TRANSACTIONS A VOLUME 13A, MARCH 1982 - - 459

showed one di la tometer curve in which, during an 18-minute delayed failure test in LMIE, changes in specimen length occurred only during the last minute. They also carried out interrupted delayed failure tests and found no cracks on the sample surface before final failure. Zych, 16 in high strain-rate LMIE tensile tests with total failure times between 10 -3 and 10 3 seconds, found initiation times were always a large fraction of the failure times. These findings agree with ours. On the other hand, Iwata, et a113 present one length-change curve and Lynn 17 in unpublished work Carded out one interrupted-delayed failure series, both in SMIE, in which crack propagation was reported to have started immediately on loading. Kassner, TM also in unpublished work using delayed failure tensile tests found a substantial incubation period in LMIE but not in SMIE. We believe the latter SMIE result was due to experimental diffi- culties. All of the other apparently inconsistent results from different investigators can be rationalized on the basis of the mechanism for MIE proposed in Part II of this report on our present work.

The second stage of delayed failure is the embrittler- dependent propagation of the initiated crack. It has long been established (e.g. ,19) that the crack propagates during this stage only so long as embrittler is available at the crack tip. A detailed discussion of the nature of the possible embrittler transport processes and predictions of the probable operative ones have been given by Gordon; 2~ one purpose of the present work is to check these predictions. The macroscopic appearance of this stage of the fracture is illustrated in the fractographs of Figures 3 through 5 for SMIE and LMIE. In SMIE (Figure 3), the embrittler-dependent crack forms a ring at the periphery of the fracture surface. In every case this ring was found to be about 0.6 to 0.8 mm deep at its greatest depth and, on the opposite side of the periphery, the crack usually showed a radial ledge or step. This is interpreted to mean the nucleation event took place on the cylindrical surface at the point of greatest crack depth, that the crack then grew circumferentially in both directions, meeting at the ledge, and at the same time grew radially, with the rate in this direction being the propagation bottle- neck and being determined by the rate at which the embrittler could be transported to the advancing crack tip. (With good wetting, indium is always immediately available at the sample surface, so that the rate of circumferential propagation near the sample surface is always much greater than that radially.) No indium could be seen on the crack surface and none could be detected by the X-ray energy dispersive capability of the SEM; there is no doubt, however, from the literature, from theoretical considerations, and from the appearance of the crack surface itself that the indium is there in a thin layer, as discussed later. The thickness of the layer is below the detectability of the SEM-EDX. The intergranular nature of the apparently brittle portion of the fracture is illustrated in Figure 4(a).

In LMIE the embrittler-dependent portion of the crack tends to be less regular in shape, appears on 0nly one side of the fracture surface, and is covered with a layer of indium thick enough to be seen readily by eye (Figure 5). This appearance is due to the very rapid rate of embrittler transport radially, as discussed later. It has been shown many times in the literature that such LMIE fractures in poly- crystalline steel are also intergranular.

Fig. 3- -Typica l fracture surface, SMIE. Approximately 8.1 times magnification.

The third stage of the failure process is reached in both SMIE and LMIE when the stress intensity at the crack tip has exceeded the critical stress intensity for normal ductile failure. The crack then propagates independently of the embrittler--essentially "runs away" from the embrittler-- producing the final catastrophic failure; the central region of the fracture surface in SMIE (Figure 3) and that portion not covered by indium in LMIE (Figure 5) correspond to this final stage of fracture. Figures 4(b) and (c) illustrate the dimpled rupture characteristics of this fracture stage.

B. Typical Delayed Failure Potential-Drop Curves

Figure 6 presents a typical potential drop-time curve for a delayed failure test in LMIE. It is clear that no detectable potential change takes place for an extended time period after loading-- in this case, 511 seconds-- and then the potential drop increases precipitously as fracture takes place in a time shorter than the lower limit of our experimerital sensitivity. The crack p ropaga t ion - -bo th embrittler- dependent and embrittler-independent stages--takes place during the period of less than one second of precipitous potential rise (later experiments narrowed this to 0.1 second). The embrittler transport rate along the fracture surface

460 - - VOLUME 13A, MARCH 1982 METALLURGICAL TRANSACTIONS A

(a)

(a)

(b) (c) Fig. 4 - - S E M fractographs in (a) embritt ler-controlled portion of SMIE fracture, 605 times magnification; (b) ductile portion of fracture, 880 times magnification; (c) at brittle-to-ductile change-over, 880 times magnification.

(b) Fig. 5 - -Typ ica l fracture surface, LMIE. Approximately 8.3 times magnification.

Fig. 6--Typical potential drop-time curve in LMIE.


Fig. 7--Typical potential drop-time curve in SMIE.

Fig. 8--Typical potential drop-time curve in SMIE.

must be extremely high, confirming the deduction that the transport can only be by bulk liquid embrittler flow, as discussed by Gordon. 2~

Typical potential drop-time curves for delayed failure tests in SMIE are shown in Figures 7 and 8. Here, again, there is an incubation period--for4.50 x 104S (12.5 hours) in Figure 7 and 4.07 • 103S (1.13 hours) in Figure 8. Then

the potential drop rises and continues to do so at an increasing rate for 0.43 x 10as (1.2 hours) in Figure 7 and 0.24 • 104s (0.67 hours) in Figure 8. This is the embrittler transport-controlled stage of the crack propagation. There is, alternatively, some possibility that in this stage the propagation is discontinuous, as in hydrogen embrittlement cracking, and that, therefore, the propagation rate is deter-


mined by crack reinitiation rather than embrittler transport. Our curves, however, do not exhibit discontinuous propagat ion--we have been able to show that any apparent propagation discontinuities which appear are in fact inherent in our recorder. This was done by noting the curve characteristics during temperature increase before testing and temperature decrease after failure. In every case, any jogs no- ticed during the crack propagation stage were duplicated in size and shape during the heat-up or cool-down period when the only change taking place was the smooth change in temperature. We, therefore, conclude that any crack reinitiation taking place during the crack propagation (such as at grain boundaries) was unimportant compared to actual crack movement itself. Again, as in LMIE, we define the initiation time as that time at which the shape and magnitu~le of the potential drop curves begin to change detectably. Tl~e end of the embrittler-dependent propagation period is indicated by the final precipitous rise in potential drop which accompanies the much faster final ductile fracture stage.

C. Crack Propagation and Embrittler Transport

Figure 6 demonstrates that in LMIE once the crack gets underway, both the embrittler-controlled and the ductile portions of the crack formation are over in less than about one second. (This was narrowed to 0.1 second in other tests.) This was found to be true at all temperatures and at all loads (for which failure took place) in our LMIE tests (13 tests in the temperature range of 158 o to 183 ~ and initial stresses from 1068 to 1226 MPa (155 to 178 ksi). As shown by Gordon, 2~ the only feasible embrittler transport mechanism consistent with such a high propagation rate in the indium is bulk liquid flow.*

*The actual transport time, according to Gordon, 2~ is of the order of 10 -3 seconds. Experimental measurements of crack propagation rates in LMIE (for example, References 14, 16, 19, 21) indicate the time for transport in our LMIE tests would be in the range 0.03 to 0.003 seconds.

In SMIE the embrittler-controlled crack propagation rate is much lower, as shown in Figures 7 and 8. The curves in Figures 7 and 8 are typical of all our SMIE tests-to-failure-- some 26 tests in the temperature range 114 o to 154 ~ and the initial stress range 1068 to 1226 MPa (155 to 178 ksi). The propagation times from initiation to catastrophic failure at various stress levels are plotted in Figure 9 as a function of temperature and in Figure 10 as a function of stress. Though there is a substantial scatter in the data, certain trends are clear:

(a) There is a large, discontinuous increase in propagation time at the indium melting point from times of less than 0.1 second in LMIE to times in the range 500 to 2000 seconds in SMIE. Thus, the transport mechanism in SMIE is clearly different and much slower than that in LMIE. Since bulk liquid flow and vapor phase transport are not possible here (for the latter the vapor pressure of indium is much too l o w - - s e e Reference 20), some diffusion mechanism must be responsible. An approximate experimental diffusion coefficient can be obtained from the transport times by using the expression (see, for example, Reference 22)

X 2 D ~ - -

2t

and the known crack depth of about 0.7 mm. At 156 o in

(/)

z 0 u

I -

z 0

(.9

o n- O,.

IO000

I000

I00

I0

TEMPERATURE, *C 156

I10 130 150 I 170 190 I I I l I I

[ Q = 54Tin p Joules

�9 ---_____ . ~ . ~ . ~ mole > MELTING POINT ~ / OF INDIUM

ALL POINTS AT 154~

INITIAL STRESS M P o ksi

-- 1226 178 0 1208 175 & 1192 173 <] 1178 171 %7 1158 168 0

- - 1109 161 [3 1089 158

1 . 0 - -

0.1 2.7

I 2.6

LMIE

TO < 0.1 SECOND WHEN INDIUM IS MOLTEN

I I I I 2.5 2.4 2.3 2.2

TEST TEMPERATURE,

- - I 0 hrs

hr

2.1

Fig. 9--Propagation time v s temperature at various initial stress levels.

ks i 160 170 180

~, ,o 4

uJ

Z o io a

0.. 0 Q..

,d

I I I

0

S M I E (:It 1 5 4 " C

o o

o

I I I

o 8

1060 I I 0 0 1140 1180

INITIAL STRESS, MPa

I 1220 1260

Fig. 10--Propagation time v s initial ~ stress in SMIE at 154 ~

SMIE, this gives D ~ 2 • 10 -4 mm 2 per second. Of the various conceivable diffusion mechan i sms- -vo lume or grain boundary diffusion of indium through the steel, first monolayer surface diffusion of indium over the steel crack surface, or surface self-diffusion of indium over indium already deposited on the steel crack surface by a "waterfall" mechanism--a l l but the last are expected to be too slow by many orders of magnitude at these temperatures (see Refer- ence 20). Following the ideas Of Gjostein, 23 the surface self-diffusion coefficient of solid indium at its melting point can be expected to have a value of the order 10 -1 to 10 -3 mm 2 per second. This is within reasonable range of our experimental value of 2 x 10 -4. The factor of approximately 50 discrepancy can be accounted for in one or more


of the following ways: (i) Since it is postulated that the indium transport proceeds by indium atom diffusion over a number of indium atom layers which themselves are laid down at the advancing edge of the indium by a "waterfall" effect, then the appropriate diffusion time to be used is not the total propagation time, but rather this divided by the number of indium atom layers. Thus, if there were 50 atom layers of indium, the discrepancy would disappear, and such a coating of indium on the crack surface would still not be visible to the unaided eye or detectable by SEM-EDX. (It would, however, be detectable by Auger measurements; such experiments would be very useful on this point.) (ii) If there are only one or two atom layers of indium, the dif- fusing atoms might "feel" the slowing effect of the relatively stationary iron atoms below; (iii) oxygen or other gas atoms may be slowing the indium diffusion--our experiments are carded out in air and we depend on the good wetting of the applied indium to the steel to keep the air from contacting the fresh crack surface. However, we know that in a few tests this did not work. Occasionally we found that a growing crack would slow and stop. A typical potential drop curve in one such test is shown in Figure 11. In such cases, examination under a microscope revealed that the crack had opened to the atmosphere, that is, broken through the indium, as shown in Figure 12. Propagation data from such tests were discarded; it seems possible, however, that even in our successful tests, some gas may have leaked through the apparently unbroken indium coating over the crack and slowed the crack growth somewhat.*

*Additional experiments are being carded out in vacuum.

(b) The propagation times in SMIE are roughly independent of the initial stress applied in the tests (Figures 9

and 10). ~ This argues in favor of a surface diffusion trans-

*Actually, there should probably be a small negative slope to the data in Figure 10, since at higher applied stress the crack depth at final failure is somewhat shorter than at lower stress. However, the stress range is too small and the data scatter too large for this to be observable.

port mechanism, for there is no reason to expect the rate of movement of surface atoms on a crack surface to be influ- enced by the stress level at the crack tip or within the bulk sample.

(c) The propagation times in SMIE decrease slowly with increasing temperature. The line drawn through the data in Figure 9 was drawn both to represent best the data and to fit Gjostein's 23 ideas for surface self-diffusion on solid metals. In these ideas, at temperatures below about 0.8 to 0.9 Tmp, the surface self-diffusion data should fit an Arrhenius type equation

( 54 Tmp~ D = D0exp ~-~ ] ,

where the activation energy 54 Trap is given in joules per mole when T~ is in degrees Kelvin; somewhere above 0.8 to 0.9 T~p, the D values should rise at an increasing rate with temperature up to the melting point. The straight-line portion of the curve in Figure 9 through the data was given a slope of - 5 4 Trap(-23,100 jou les /mole or -5600 ' cals/mole for indium); both the fit here and the higher temperature curvature of the line support the idea that indium self-diffusion is the controlling transport mechanism in SMIE.

D. Crack Initiation

The meaning of the time, t~, which we have defined as the

Fig. 11---Typical potential drop-time curve in SMIE for sample in which crack formed and stopped growing.


(a)

(b)

Fig. 12--Crack broken through indium coating on sample in which crack formed and stopped growing. (a) Approximately 2.2 times magnification, (b) l l l times magnification.

crack initiation time, needs some further clarification. Strictly, this is the time at which the crack first reaches a size--about 0.15 mm 2 in area---detectable by our potential drop measurements. However, the interrupted delayed failure tests showed that any crack existing at 0.9 ti could be no larger than about 10 -4 times the size at t i , whereas in SMIE at 1.1 t~ the potential drop curves (Figures 7 and 8) show that the crack size is no more than about three to four times that at t~. Thus, in SMIE, there is clearly a drastic decrease in crack growth rate between 0.9 t~ and ti. We interpret this to mean that at this point there is a change in the rate- controlling mechanism of crack formation from control by some crack initiating process to control by the embrittler transport process. This is illustrated schematically in the upper diagram of Figure 13. Here, the time for the crack initiating process (line df) and for embrittler transport from source to crack tip (line ac) are plotted v s crack size. At

Fig. 13--Schemat ic representation of crack growth paths in SMIE and LMIE.

crack sizes below the point of intersection, b, of thes.e two lines, the time for transport is much shorter than that for the crack initiation process, so the latter gives the crack formation time; beyond point b, the opposite is true. As a result, the crack formation time is given by the path dbc in the figure. In LMIE, the situation is as indicated schematically in the lower diagram of Figure 13. Here, the embrittler transport time (line ac) is very short throughout crack formation; therefore, the initiation process controls crack formation at all times, leading to the growth path dbf. In both SMIE and LMIE, then, ti is a measure of the point b. We know that at earlier times, the curve drops precipitously to below point e, the point delineated by the interrupted delayed failure tests; the shape of the curve at nucleation of the crack is not known. We have made the assumption, however, that whatever its shape, this is constant from sample to sample, and have, thus, taken t~ as a measure of the initiation process kinetics. The discussion of crack initiation below is based on this assumption;

The experimentally determined crack initiation times at two different stress levels are plotted v s temperature for both SMIE and LMIE in Figure 14. Again, within the experimental scatter a number of clear characteristics can be seen:

(a) The data for both stress levels and for both SMIE and LMIE can be represented by Arrhenius type equations. This suggests strongly that the underlying process involved during the crack-incubation period is thermally activated.


I0 5

104 t/) E3 z 0 L3 kU tn t~ 103

I-.-

z 0

~ 1 0 2 I-

TEMPERATURE, *C

I10 120 130 140 150 116.5

\ 0 I i I I T

INDIUM MELTING

POINT

- IOhrs 1 2 2 ~ S M I E j

(178 ksi) - I hr j f

time .-/-scale

-0,1 hr

- I rain

I0 2.7 2.6

170 I~0 I I

I 0 0 hrs--

I0 h rs -

O ~ Ihr--J

I I time

N ~ I j .~ 1158 MPo

0 " ~ {168 ksi)

O ~ I rain -- &

I zx I L~7 LMIE

2.5 2.4 2.3 2 2 2.1 I000 .K-I TEST TEMPERATURE,

Fig. 14--1nitiation time v s temperature stress levels.

io e

10 5 (/3 (:3 Z O L) UJ U)

,o" V- z 9 F- <~

~o 3 E Z

102

in SMIE and LMIE at two

Further, since the slopes of all the straight lines through the data are the same within experimental error, the process is indicated to be basically the same for both LMIE and SMIE, and for the different stress levels. From the slopes, the average apparent activation energy* of this process is

*The activation energy is "apparent" because, as described in Part II of this presentation, we believe it is actually the sum of two activation energies.

155 ---3.5 kJ/mole (37.0 • kcals/mole).*

:~The experimental errors given in this paper for activation energies are actually reproducibilities based on the three lines in Figure 13. For one standard deviation, the errors of the activation energies, based on the variance in regression analysis, are about ---19 kJoules/mole (-+4.5 kcals/mol).

(b) Since the lines in Figure 14 are displaced upward on decrease in stress, it is clear that the rate of the underlying process is stress dependent, increasing with increasing stress.

(c) At the melting point, the initiation time increases dis- continuously by a factor of about 6.5 in going from LMIE to SMIE, though the slopes of the corresponding lines do not differ. To confirm the presence of this gap, a series o f tests was run at several other stress levels at the two temperatures 154 ~ (just below the indium melting point) and 158 ~ Oust above the indium melting point); the results are given in Figure 15. It may be seen that the ratio of initiation times across the gap at the melting point persists unchanged, within a substantial scatter, for all stress levels at which delayed failure takes place, that is, down to 1068 MPa (155 ksi). Below this stress level, no failure took place at a l l - - at least within the patience of the experimenters (to times of about 11 days). Thus, there is a "threshold" stress l e v e l - - as found

20

1 5

(n

Z 0 t.) LU tn 5

~3 ' 0

X

ILl ~E 7-

3 Z 0 I--

7- 2 Z

~ ~) [ ] AVE. OF 3 TESTS

(~ AVE. OF 2 TESTS

S M I E

at 154* i n W O: I I.--

LMIE

at 158*

I I I000 I100 1200

STRESS, MPo

I I I I 150 160 170 180

STRESS, ksi

Fig. 15--Initiation time vs stress level in SMIE and LMIE near indium melting temperature.

in most previous MIE s tudies--below which MIE delayed failure does not take place. In the present case, the threshold stress is just above the macroscopic proportional limit of 1040 MPa (151 ksi). Above the threshold stress, the initiation times decrease approximately linearly with increasing stress both in SMIE and LMIE.

PART II. T H E O R E T I C A L ASPECTS OF CRACK INITIATION

I. EVALUATION OF PREVIOUSLY PROPOSED MECHANISMS

A. Rober tson Disso lu t ion M e c h a n i s m

Robertson 4 has proposed (later also Glikman, et al 5) that a crack propagates in LMIE because the highly stressed atoms at its leading edge are dissolved into, and are car- fled away by diffusion through, the liquid embrittler. In this theory, crack initiation and crack propagation are one and the same process; our work shows that for indium embrittlement of steel this is not true. In addition, the Robertson


theory, if it can account for the existence of SMIE at all, would predict an abrupt and substantial change in temperature dependence of crack initiation at the embrittler melting point, since its main temperature dependence derives from the activation energy for the diffusion of the base metal atoms in the embrittler; this diffusion activation energy would change sharply at the embrittler melting temperature. This we have shown not to be true for indium embrittlement of steel; thus, we conclude that the dissolution mechanism is not valid for MIE in the indium-4140 steel system. We expect that, on a similar basis, it will also be found to be invalid generally.

B. Lynch 6 Ductile-Failure Mechanism

In this model it is suggested that the role of the embrittler is to so alter the surface layer atomic structure of the base metal as to lower considerably the normally high stress necessary to generate and move dislocations at a crack tip, thus allowing fracture by microvoid coalescence and slip with very limited plastic flow. Though this is certainly a viable possibility in a general sense, by itself it seems to offer no ready mechanism for delayed crack initiation-- the alteration of the structure in the one or two atom layers composing the surface should be virtually instantaneous if it is caused by embrittler atom adsorption as suggested. Though the question of whether delayed failure is the rule in MIE systems has not yet been conclusively settled; the evidence in the literature is preponderately in the affirmative. The systems in v~hich at least some measurement of delayed failure (though not its temperature dependence) has been attempted are listed in Table II. Two general types of behavior have been found. In the first, designated Type A in Table II, delayed failure is observed. In the second, designated Type B in Table II, there appears to be in each case a stress above which failure takes place "virtually instantaneously" but below which failure does not take place at all. Of the 23 embrittlement couples reported in Table II, five show Type B behavior, all in LMIE. It should be recognized that, in these five, "virtually instantaneously" means a time below the lower limit of one to two seconds which was measur- able. The study by Zych 16 (see also Gordon2~ however, established that for liquid Hg on 2024 aluminum even in the stress range where total failure times were 10 -1 to 10 -3

seconds a substantial fraction of this time was spent in crack initiation. Thus, it seems possible that some or all of the Type B couples listed in Table II actually involve very rapid delayed failure and, therefore, thermal activation. A satis~ factory explanation for the existence of these two types of behavior has not to now been offered, particularly in the case of LMIE where the delay cannot be attributed to embrittlement transport time; a possible rationalization will be suggested later in the present discussion.

Thus, the Lynch proposal that MIE cracking is really ductile rather than brittle, though not ruled out, does not seem by itself to be able to account for important aspects of MIE.

C. SJWK Tensile-Decohesion Mechanism

Crack formation in MIE by brittle tensile decohesion at a crack tip as proposed by Stoloff and Johnston 2 and West- wood and Kamdar 3 (referred to hence as the SJWK theory) again seems to be a reasonable possibility in a general sense

Table II. Delayed Failure in MIE Systems

Type A Behavior-Delayed Failure Observed Embrittler

Base Metal Liquid Solid Ref.

4130 steel Li 10 4340 steel Cd Cd 13 4140 steel In In this work 4140 steel Cd 17 4140 steel Pb 17 4140 steel Sn 17 4140 steel In 17 4140 steel Zn 17 Zn (Monoxtals) Hg 11 2024 A1 Hg 16 2024 A1 Hg-3 pct Zn 10 7075 A1 Hg-3 pct Zn ~ 10 5083 A1 Hg-3 pct Zn 10 A1-4 pct Cu Hg-3 pct Zn ', I0 Cu-2 pct Be Hg 12 Cu-2 pct Be Hg 14

Type B Behavior-Delayed Failure Not Observed Embrittler

Base Metal Liquid Solid Ref.

Zn Hg 11 Cd Hg 11 Cd Hg + In 15 Ag Hg + In 15 AI Hg 15

- - lower ing of 3' by the embrittler is expected both to lower the stress for such fracture and to favor crack extension over crack blunting (see, e .g . , References 10, 11, 24, 25, 26). However, such a mechanism, though it may be involved, does not appear to have the appropriate thermal activation characteristics to be the rate controlling mechanism in crack initiation in the indium-4140 system. To show this, we may start with the Griffith 27 equation for the change, AW, in total energy of an elastic, infinitely wide, plate under tensile stress o" when a crack of elliptical cross section with major axis 2a is introduced into the plate (the crack front is in the plate thickness direction). Per unit length of crack front, this is

~.o.2a 2

A W -- E + 4 y a , [1]

where E is Young's modulus. Fracture mechanics has demonstrated that an equation of the same form is (approximately) valid fo r samples in which there is some limited plastic flow in a zone at the crack front and which also have more general crack and sample geometries. The quantity K = Yo-%/a, called the stress intensity at the crack front, is delineated, where Y is a numerical constant determined by the specific geometries of the loading system, the sample, and the crack (and is equal to %/7r in the special case of Eq. [1]). In addition, the SJWK theory shows that when a plastic zone is present, 3' in Eq. [1] should include the work of plastic flow, and this can be done by replacing 3" with %ff, where

%ff ~ T P , [2] ao


p is the tip radius of the blunted crack, and a0 is the base metal lattice parameter. Considering now that the crack is at the sample surface (depth = one-half the major axis, 2a), then Eq. [1] becomes

y2o.2 a 2

AW - E + 2voffa. [3]

The crack can now grow unstably due to the applied stress alone only if the depth, a , is greater than a critical value, a*, given by maximizing AW with respect to a (at constant or, Y, and E). The critical value, a*, and the corresponding critical energy, AW*, so obtained are

ETaf a* = y2or-"-'~ [4]

and

E'y2eff AW* = y2o---- ~ . [5]

If it is assumed that incipient cracks of maximum depth a = am < a * preexist in a sample (due to topological discontinuities which, on an atomic scale, must exist at the surface of a sample, especially at surface-grain boundary intersections), then at constant stress such a crack could be postulated to extend to a depth just beyond a* by thermal activation. The thermal activation energy in this case would be

Ey2eff y202a2 Va = A W * - A W a . = V2-"-~ + T 2%ft~m �9 [6]

In principle, then, Eqs. [2] through [6] may account for thermal activation in the SJWK mechanism for crack initiation. It may be seen, however, that according to Eq. [6], the activation energy will be expected to vary strongly with both y and or, whereas this was found not to be true for indium embrittlement of 4140 steel. The dependency of U on y and or from Eq. [6] may be found to be

where

and

Y2 or2 aoa m A = - - [8]

Ep

(dU) (y + A~ do" [9] = - 2 \~/-'----,~/ -~"

With respect first to the variation of U with y, from Eqs. [7] and [8] it follows that:

(a) the smallest possible value of (dU/U),, corresponds to am = 0, for which

or y

(b) designating the energy of the liquid indium-solid steel interface YLS and that of the solid indium-solid steel interface Yss, and integrating Eq. [10] across the indium melting point, we have

USMIE (Yss ) 2 " [111 ~LUm \'YLs/

Though there is no experimental data for either Yss or "YLs in the case of indium on steel, we may estimate the order of magnitude of their ratio by noting that in those few metal systems where such data are available (see, e .g., Refer- ence 28), the energy of the solid-solid interface is several times that of the liquid-solid interface. It seems reasonable to assume this is also true for indium on steel. If the ratio in this case were only two- -p robab ly an underest imate-- from F_x I. [11] the activation energy for crack initiation in SMIE of 4140 steel by indium would, according to the SJWK mechanism, be expected to be four times that in LMIE. This is clearly far larger than our experimental finding of a difference between UsMm and ULMm of less than the experimental error (+-two pct on the basis of repro- ducibility, +- 12 pct on the basis of the variance in regression analysis for one standard deviation).*

*It is true that equilibrium may not prevail at the indium-steel interface, and that this may lower Yss/yLs. However, the validity of the SJWK theory itself demands a state of near-equilibrium at the interface to produce the lowering of y and its accompanying embrittlement, so that we may for the purposes of testing the theory also assume near-equilibrium.

(c) if am is greater than 0, as is likely, the value of USMm/ULMIE from Eq. [11] increases and the argument above is even stronger, though for reasonable values of the quantities in A, its magnitude is small relative to y.

Essentially the same deduction may be made on the basis of the dependency of U on o', though here our evidence is not conclusive because the range of o" over which we determined U for indium embrittlement of 4140 steel was too small. Experimentally it was found that U in SMIE for o- = 1158 and 1226 MPa (168 and 178 ksi) was the same within experimental error. From Eq. [9] the smallest change in U predicted by the SJWK theory is, taking am = O,

o r

= - 2 - - [121 Y or

Uuss _ (1226] 2 \1158] = 1.12.

Since am may well have been finite, UII58/UI226 is predicted to be somewhat larger than 1.12. This difference is close to our experimental error, but we feel we might well have been able to detect such a change if it had existed.

From these arguments on the variation of U with y and or it seems unlikely that tensile decohesion at the tip of a sharp crack, as predicted by the SJWK theory, can be the rate-controlling process in the initiation of MIE cracks, at least in the case of indium on 4140 steel.

D. Krishtal Mechanism In 1970 M.A. Krishtal 7 proposed that in order for an

embrittler to produce LMIE, the embrittler atoms must first diffuse into grain boundaries in the base metal to some critical depth (tens of atom diameters) and concentration. He also proposed that the energy gained by the lowering of the base metal surface energy was somehow converted into dislocations which aided the diffusion penetration, that the


strains resulting from the embrittler atoms' presence produced more dislocations, and the sum total effect embrittled the boundaries to the point of nucleating a crack. Little attention has been given Krishtal's ideas and Krishtal him- self made no detailed attempt to test these ideas by considering them in the light of the known characteristics of LMIE. We, however, have done just that with regard to the basic suggestion of embrittler grain boundary diffusion penetration, and have found it makes possible not only an appropriate interpretation of our data on the indium-4140 steel system, but also an easy qualitative rationalization of virtually all the known LMIE and SMIE characteristics. We therefore have borrowed this idea, elaborated on it, and present it below as a mechanism for MIE which should be reckoned with. We do not, however, profess to judge the validity of the remaining aspects of his ideas with respect to dislocation motion and production; they may or may not be involved--our data do not allow a test of this.

II. PROPOSED MECHANISM

The concept proposed is that the actual crack nucleation event is not the rate-controlling step in crack initiation, but rather that during an incubation period there is a preparation process which is rate-controlling. During this period embrittler atoms penetrate by stress-aided (and possibly dislocation-aided) diffusion a short distance into base metal grain boundaries (or, in single crystals, into subboundaries or other dislocation arrays). In the penetration zones the presence of the embrittler atoms lowers the crack resistance and increases the difficulty of slip. When a sufficient concentration of embrittler atoms has been built up to some critical depth (tens of atom diameters, according to Krishtal 7) in one of the penetration zones, crack nucleation takes place, probably at the head of already-existing dislocation pileups where the stress has become supercritical for the lowered crack resistance.

The embrittler atom penetration process consists of two steps, namely:

1. The change of the embrittler atoms from the adsorbed to the dissolved (in the surface) state; 2. Subsequent diffusion penetration along preferred paths--usually grain boundaries.

The rates of both these steps are accelerated by increased stress. The probability of an embrittler atom finding its way into a grain boundary is equal to the product of the probabi- lities of the two steps; the corresponding nucleation time, t,, will be inverse to this, so that

t, "-~exp (AG~% exp (AGd~ \ RT / \ RT / '

[13]

where AGs and AGd are the activation free energies for steps (1) and (2), respectively. Our model and our data do not at this point indicate what the atomic details of the nucleation process itself are, but apparently once the crack has formed, it grows extremely rapidly (see Part I of this report) either (a) up to (and beyond) the time we have defined as the initiation time, t~, at which time it becomes detectable by our potential drop measurements, or (b) until the crack is deep enough so that the time for transport of the embrittler

atoms along the crack surfaces from source to crack tip becomes longer than the time for the continued penetration process, at which point the transport process becomes rate- controlling. The relationship of tl to the crack growth history is illustrated schematically in the upper diagram of Figure 13 for SMIE and the lower diagram for LMIE. In SMIE there is a sharp change in slope of the crack growth curve between 0.9 ti and ti; we know this from the observed slope of the potential drop curve at ti and the fact that no crack is seen on interrupted delayed failure sample surfaces at 0.9 t~ at 150 magnifications (see Part I). We interpret this to mean that at some point between 0.9 ti and t~ the time for embrittler atom transport to the crack tip (line ac in Figure 1) has become longer than that for the crack initiation process (line df) and the former takes over rate control from the latter. In LMIE (lower diagram in Figure 1) the embrittler transport time is so short that the crack initiation process may be rate-controlling throughout. Though we do not know what the crack growth curve looks like at times earlier than 0.9 t~, we have made the assumption that whatever its shape it is constant from sample to sample; thus, we have taken t~ as a measure of the initiation process kinetics.

On the basis of this concept, the way in which the crack initiation time, t~, may be expected to vary with stress and temperature may be deduced from the schematic diagram in Figure 16. This diagram represents the effect of temperature and stress on the total time to produce penetration zones during the crack initiation stage. Each of the curved lines indicates the effect of stress on this time at a given temperature, T, where Tg>Ts>---T~. Superimposed on the diagram is a dotted line marked threshold stress, ~h, which gives (r~ vs temperature (not a function of time), o-~ is the stress below which no MIE failure takes place. (We have no good explanation for the generally observed experimental fact that such a stress exists; in our work it was found to be just above the proportional limit of the 4140 steel, suggesting the

IT, T7 Ts Ta 1"1 I ~ ~ \ \ \ NX N ~TIME TO PRODUCE PENETRATION ZONES

I~ ~ \ \ \ ~ x ~ ~ REGION OF DELAYED OZ. I t \ \ \ \ ~ / ~ ~ ~ /.CRACK INITIATION AT

i 4 . . . . T 4

l r ~ " - ~ - - ~ - - ~ ' - ~ ~ x ' ~ THRESHOLD ' I \ \ \ \,// '~%.~'A ~ ~ ~ STRESS

(~ CT I \ \ \ ? ~ ( / / ~ / / / / ' x \ \ \ O'th vs T" 03 I . . . .

. . . . . . . . . " ' " 1"1

T 3 T4 T 5 T6 T7 T 8

T9

TIME

Fig. 16- - Schematic diagram showing time to develop penetration zones as a function of stress and temperature of test, and relationship to crack initiation time. Crack initiation time at T4 and trl is t~l---~t,. T9 > 7"8 > ---T~.

METALLURGICAL TRANSACTIONS A VOLUME I3A, MARCH 1982 - - 469

threshold in this case may be associated with the movement of dislocations. If this is so, its magnitude may well decrease with increasing temperature, as shown in Figure 16. There is some experimental support for a negative temperature dependence of O'th in the unpublished Ph. D. thesis work of Lynn.17) The diagram in Figure 16 is drawn for a given value of y , the interfacial energy of the base metal as affected by the embrittler. Lower y, for example, would lower the penetration time isotherms through the effect of y on AG,, and might also have a substantial effect on o-~.

The prediction of initiation times from Figure 16 may be illustrated as follows: Consider a set of delayed failure tests in which the o- vs t curve during loading is as shown in Figure 16. If a sample preheated to any selected temperature above T8 is loaded, crack initiation will take place "instantaneously" upon reaching the threshold stress level, oh, for that temperature. This is because at the loading rate shown the time to reach the O'th for these temperatures is equal to, or greater than, the time to develop the penetration zones at grain boundaries. As a result, in LMIE there will be immediate f a i l u re - - a s for type B couples in Table I I - - s ince LMIE crack propagation rates are extremely high; in SMIE, there will be delayed failure, with the failure time equal to the time during the embrittler transport-controlled stage of crack growth. For a sample preheated to a temperature below Ts, say T4, upon continuous loading "instantaneous" crack initiation would take place at the stress level, marked 0"/4 in Figure 16, for which the loading time equals the penetration zone formation time at T4, i.e., where the orvs t line meets the T4 isothermal line. This stress is well above O'th for/'4, the stress below which no failure will take place at T4. If a sample preheated to T4 is tested at any fixed or level between 0"/4 and 0"~, such as, for example, 0"1 in Figure 16, delayed crack initiation will occur. The initiation time will be equal to tl - t~ where t~ is the time to load to 0"1 and tl is the time to form penetration zones at T4 and stress level or1.* If the stress level at which

*For simplicity, the fact that the sample is not at cr~ during the entire loading time is ignored in the use of Figure 16. The qualitative validity of the reasoning is not affected.

the sample is tested increases, the initiation time decreases. The shaded area in Figure 16 is the region within which delayed failure takes place at T4. The delayed failure time for tests at temperatures below Ts and stresses between crth and cri would be the sum of the crack initiation times given by Figure 16 and the transport controlled growth time.

The proposed concept for crack initiation can readily account qualitatively for all the MIE phenomenological characteristics reported in the literature and in our present study (with the exception of the threshold stress, as noted above). These are each discussed briefly below:

1. Delayed failure. In LMIE, delayed failure is due to delayed crack initiation while penetration zones develop. In SMIE, delayed failure additionally can occur even with "instantaneous" crack initiation because of the time for slow embrittler transport along the crack surfaces by embrittler surface self-diffusion. 2. The apparent activation energy found for crack initiation (for In/4140 s tee l - -155 kJoules/mol (37kcals/mol)) is consistent with semiquantitative estimates which can be made for the proposed mechanism. Eq. [ 13] can be rewritten

t exp( AS )exp A + R \ RT ] '

where AS,, ASd, AHs, and AHd are the activation entropies and enthalpies for the solution and diffusion steps in crack initiation. From our measured activation energy, then

AHs + AHd --~ 155 kJ/mol (37 kcals/mol).

The activation energy for self-diffusion in the grain boundaries of bcc iron can be estimated from Gjostein's 23 equation, AH~ ~ 84Trap joules per mole, giving 151 kJ/mol (36.2 kcals/mol). The corresponding activation energy for stress-aided diffusion of indium in 4140 steel might well be somewhat below this, so that the experimental value of 155 kJ/mol for AHs + M-/a is quite reasonable. 3. The occurrence of Type B behavior (Table II). This oc- curs only in LMIE when the test temperature is high enough so that the penetration zone development time is shorter than the time to load the sample. The applied stress must also be above the "threshold" stress, and if the latter changes, the stress level for type B failure will also change. 4. Specificity--the fact that the severity of embrittlement depends on the nature of the embrittler and the base metal. The lowering of y is specific, for reasons which our model does not address (see, for example, Reference 29). How- ever, the lowering of y, in addition to possible effects of the type discussed in Reference 29, lowers AG, and in turn, therefore, the crack initiation time. It also could affect AGa if dislocation production as proposed by Krishtal is involved. 5. The relatively mild dependence of the activation energy for crack initiation on y. y affects only AGs, and only through the change of the surface layer structure of the base metal. This effect is undoubtedly not as drastic as the effect y would have on crack formation if brittle tensile decohesion were rate-determining. Our experimental finding was that the initiation activation energy was little, if at all, changed as between LMIE and SMIE. It should be noted that this is consistent with the finding of a ratio of 6.5 for SMIE/LMIE crack initiation times at the indium melting temperature. This ratio must, in our model, be due to a difference in AGs as between SMIE and LMIE. If it is assumed that the ratio of 6.5 is entirely due to the AH, term in the free energy, then, according to Eq. [13],

Ratio ~ 6.5 = exp \ RT /

where 8 AHs = (AHsMIE -- AHLMIE),. This gives 8 AH~ ~ 6.7 kJoules/mol (1.6 kcals/mol), which is within our experimental error. Further, there may be a 8 ASs, which would make the necessary 8 z~H, even smaller. 6. Occurrence of transition temperature. In continuous loading tensile tests it is found that MIE does not set in unless the test temperature is sufficiently h igh-- tha t is, a ductile-to-brittle transition temperature exists (see, for example, Reference 30). Also, at higher test temperatures a brittle-to-ductile transition takes place (Reference 30). In our proposed model the occurrence of MIE depends on the development of high concentrations of embrittler atoms at grain boundaries (or other rapid diffusion paths); as the testing temperature is raised, the rates of solution and of grain boundary diffusion first become sufficient at the


ductile-to-brittle transition temperature. At higher temperatures, volume diffusion from the boundaries into the adja- cent grains becomes effective, tending to reduce the grain boundary concentrations; also, as the temperature increases, the equilibrium Gibbs adsorption ratio of solute concentration in the boundary to solute concentration in the grains approaches unity, again tending to eliminate the grain boundary concentrations. These latter two effects produce the high temperature brittle-to-ductile transition. 7. Strain rate effects. In continuous loading tensile tests, it is found that increasing the strain rate raises the brittle-to- ductile transition temperature, a~ At the higher strain rates, higher temperatures are required to provide sufficient volume diffusion to dissipate the grain boundary penetration zones. 8. Solute effects. Solutes in either the embrittler or the base metal are frequently found to increase the severity of embrittlement, al In our proposed model a solute can increase both the rate of solution and the rate of diffusion of the embrittler in the base metal, or actually become an even more effective embrittler itself with its own solution and diffusion rates. 9. Grain size effects. Decreasing grain size is found to lower the severity of MIE. Lower grain size means lower stress concentrations at dislocation pile-ups at grain boundaries, and therefore a greater amount of embrittler penetration is required to accomplish the greater lowering of crack resistance needed. 10. Effects of cold work. It has been found that cold work decreases susceptibility to MIE. a2 Increasing cold work would increase dislocation density in the base metal grains, providing many more "pipes" to dissipate embrittler concentrations at grain boundaries, thus lowering MIE susceptibility.

C. Concluding Remarks

It is clear that much more data is needed for a definitive and general check of the proposed mechanism-- data of the type obtained here on crack initiation and propogation but in other embrittlement couples, and over wider stress ranges in both LMIE and SMIE. In addition, data is needed on the solubilities, diffusion rates, and interfacial energies involved. With such information, the proposed mechanism could be tested quantitatively and more generally. In the meantime, serious consideration of the proposed concepts and some possible revision of the more generally accepted ideas on MIE would seem warranted.

brittler transport which takes place by indium surface self-diffusion.

5. Crack initiation in both LMIE and SMIE exhibits an incubation period; at constant stress the initiation time increases with decreasing temperature according to an Arrhenius-type relation; it also increases with decreasing stress.

6. The apparent activation energy for crack initiation time is the same, within experimental error, in LMIE and SMIE, having a value of 155 + 3 . 5 k J / m o l (37 - 0.8 kcals/mol). This apparent activation energy showed no change on raising the applied stress from 1158 to 1226 MPa (168 to 178 ksi).

7. At constant stress, the initiation time at the melting point of indium is larger by a factor of 6.5 in SMIE than in LMIE. This time gap at the melting point persists at about the same value over the stress range tes ted-- f rom 1068 to 1226 MPa (155 to 178 ksi).

8. Theoretical considerations indicate that for indium embrittlement of 4140 steel crack initiation can best be explained by a mechanism which is an extension and elaboration of the embrittler grain boundary diffusion concept proposed by M. A. Krishtal.

ACKNOWLEDGMENTS

The experimental material in Part I of this paper is based largely on the Ph. D. thesis research of H.H. An in the Department of Metallurgical Engineering at Illinois Institute of Technology.

We are indebted to the National Science Foundation for financial support of this research from its inception under contracts DMR 7704272 and DMR 7908674, and to the Office of Naval Research for financial support during its last year under Contract No. 0014-79-C0580.

Thanks are also due to Professors Sheldon Mostovoy and J .S. Kallend of the Department of Metallurgical and Materials Engineering, Illinois Institute of Technology, for helpful discussions; to A. P. Druschitz, a Ph.D. candidate in the Department of Metallurgical and Materials Engineering, Illinois Institute of Technology, for supplying the fractographs of Figure 4, and for carrying out the hydrogen embrittlement tests referred to in the description of experimental details; and to M. E. Kassner, who did a considerable amount of the preliminary work as a Master's thesis which helped lay the groundwork for the research reported.

III. CONCLUSIONS

In the fracture of 4140 steel due to MIE by indium:

1. Crack initiation and crack propagation are separate stages in crack formation, each being thermally activated with quite different activation energies.

2. In LMIE, crack propagation is extremely rapid, taking place in less than 0.1 second (for crack depths of the order of 1 to 2 mm).

3. Theory and the experimental results indicate embrittler transport to the crack tip LMIE is by bulk liquid flow.

4. In SMIE, crack propagation is much slower (500 to 2000 seconds for a depth of 0.7 mm); it is controlled by em-

REFERENCES

1. J.C. Lynn, W. R. Warke, and Paul Gordon: Mater. Sci. Eng., 1975, vol. 18, pp. 51-62.

2. N.S. Stoloff and T.L. Johnston: Acta Met . , 1963, vol. 11, pp. 251-56.

3. A.R.C. Westwood and M.H. Kamdar: Phil. Mag., 1963, vol. 8, pp. 787-804.

4. W.M. Robertson: Trans. TMS-AIME, 1966, vol. 236, pp. 1478-82. 5. E.E. Glikrnan, Y.V. Goryunov, V.M. Demin, and-K. Y. Sarycher:

Izvest. Vyss. Ueheb. Zav. Fizika, May 1976, no. 5, pp. 7-15, 15-23; ibid, July 1976, pp. 17-22, 22-29.

6. S.P. Lynch: ARL Mat. Reports No. 101, 102, Dept. of Defense, Melbourne, Victoria, Australia, 1977.

7. M.A. Krishtal: Sov. Phys. Dokl., 1970, vol. 15, no. 6, pp. 614,17. 8. V.I. Arkhaxov: Trudi IFM UF Akad. Nauk SSSR. Sverdlovsk, 1946,

vol. 8, p. 54; 1949, vol. 12, p. 94; 1954, vol. 14, p. 15; 1955, vol. 16, p. 7.


9. N.I. Flegontova, B.D. Summ, and Y.V. Goryunov: Phys. Metals and Metall. (Eng. Trans.), 1964, vol. 18, no. 5, pp. 724-29.

10. W. Rostoker, J.M. McCaughey, and H. Markus: Embrittlement of Liquid Metals, Reinhold Publ. Co., New York, NY, 1960.

11. L.S. Bryukhanova, I .A. Andreeva, and V.I. Likhtman: Sov. Phys.-Solid State, 1962, vol. 3, pp. 2025-28.

12. H. Nichols and W. Rostoker: Trans. ASM, 1965, vol. 58, pp. 155-63. 13. Y. Iwata, Y. Asayama, and A. Sakamoto: Nippon Kinzaku Gakkaishi

(J. Japan Inst. Met. ), 1967, vol. 31, pp. 77-83. 14. J.V. Rinnovatore, J.D. Corrie, and H. Markus: Trans. ASM, 1966,

vol. 59, pp. 665-71. 15. C.M. Preece and A. R. C. Westwood: Fracture, Proc. Sec. Intl. Conf.

on Fracture, P. L. Pratt, ed., Chapman and Hall, London, England, 1969, pp. 439-50.

16. J. Zych: M.S. Thesis, Illinois Institute of Technology, Chicago, IL, 1977.

17. J.C. Lynn, Ph.D. Thesis, Illinois Institute of Technology, Chicago, IL, 1974.

18. M.E. Kassner: M.S. Thesis, Illinois Institute of Technology, Chicago, IL, 1977.

19. F.N. Rhines, J. A. Alexander, and W. E Barclay: Trans. ASM, 1962, vol. 55, pp. 22-44.

20. Paul Gordon: Metall. Trans. A, 1978, vol. 9A, pp. 267-73.

21. B.D. Summ, P. A. Rutman, Y. V. Goryunov: Fiziko-Khim. Mekban. Mater., 1973, vol. 9, pp. 50-53.

22. E Shewmon: Diffusion in Solids, McGraw Hill, New York, NY, 1963, p. 8.

23. N.A. Gjostein: Diffusion, ASM, Metals Park, OH, 1973, pp. 241-74. 24. J.R. Rice and R. Thomson: Phil. Mag., 1974, vol. 29, pp. 73-96. 25. J.R. Rice: in Effect of Hydrogen on Behavior of Materials, A. W.

Thompson and I.M. Bemstein, eds., 1976, AIME, pp. 455-66. 26. D.D. Mason: Phil. Mag. A., 1979, vol. 39, pp. 455-68. 27. A.A. Griffith: Phil. Trans. Roy. Soc. London, 1920, vol. 221,

pp. 163-98. 28. L.E. Murr: Interfacial Phenomena in Metals and Alloys, Addison-

Wesley, Reading, MA, 1975, pp. ~101, 124, 126, 155. 29. M.J. Kelley and N.S. Stoloff: Metall. Trans. A, 1975, vol. 6A,

pp. 159-66. 30. K.L. Johnson, N.N. Breyer, and J.W. Dally: Proc. of Conf. on

Environmental Degradation of Engr. Marls., Blacksburg, VA, 1977, pp. 91-103.

31. N.N. Breyer and K.L. Johnson: J. Test. and Eval., 1974, vol. 2, pp. 471-77.

32. N.N. Breyer and E Gordon: Proc. Third Intl. Conf. on Strength of Metals and Alloys, Cambridge, England, 1973, vol. 1, pp. 493-97.


the mechanisms of crack initiation and crack propagation in metal-induced embrittlement of metals

Documents