EQUILIBRIUM ASPECTS OF HYDROGEN-INDUCED CRACKING OF STEELS*

R. A. ORIANIZ and P. H. JOSEPHIC:

The threshold pressures, p*, of hydrogen and of deuterium gases necessary to cause crack propagation in AISI 4340 steel of 250 ksi yield strength have been determined as functions of plane-strain stress- intensity factor K at room temperature. The functional p*(K) is shown to be well fitted by an analytical expression derived from the unstable equilibrium form of the decohesion theory plus some reasonable ad hoc assumptions for the neceswry functional relationships. From the fitting of the theoretical equation to the esperimental data are obtained numerical values for the hydrostatic component of stress at the crack front, for the equilibrium enhancement of concentration of hydrogen, and for the reduction by the hydrogen of the masimum cohesive resistive force. The msgnitudes of these numbers and their trends with K are in agreement with expectations from the decohesion theory but with no other extant point of view.

ASPECTS D’EQUILIBRE DE LA FISSURATIOX DUE _i L’HYDROGEXE DANS LES ACIERS

Les pressions limites, p*, d’hydrogene et de deuterium gazeux necessaires pour provoquer la propaga- tion de fissures dans l’acier AISI 4340 de 250 ksi de limite Blastique sont determinees en fonction du facteur K d’intensite de contrainte en deformation plane a la temperature ambiante. Les auteurs montrent que la fonction p*(K) est bien exprimee par une expression analytique d&iv&s de la forme d’equilibre instable de la theorie de d&oh&ion a laquelle s’ajoutent quelques hypotheses ad hoc raisonnables sup les relations fonctionelles necessaires. 11s obtiennent, par application de l’equation theorique aux resultats experimentaux, des valeurs numeriques pour la composante hydrostatique de la contrainte au front de fissure, pour l’augmentation d’equilibre de la concentration en hydrogene, et pour la diminution par l’hydrogene de la force maximale de resistance. Si les ordres de grandeur de ces valeurs et leur variation avec K sont en accord avec les previsions tirees de la theorie de la d&oh&ion, elles ne s’accordent avec aucun autre point de vue present.6 jusqu’ici.

GLEICHGEWICHTSdSPEIiTE BE1 DER WASSERSTOFFVERSPRGDUNG VOX STABLES

Die Schwellwerte p* des Wasserstoff- und Deuteriumdruckea, oberhalb dessen sich in NISI-4340- Stahl mit 250 ksi Streckgrenze Risse ausbreiten, wurden als Funktion des Spannungsintensitatsfaktors K bei ebener Dehnung bestimmt. Das Funktional p*(K) l&t sich sehr gut durch eine analytische Gleichung anpassen, die aus der instabilen Gleichgewichtsform der Dekohilsionstheorie und einigen plslusiblen ad hoc Annahmen fur die notwendigen funktionalen Beziehungen hergeleitet wurde. Sume- rische Werte fiir die hydrostatische Spannungskomponente an der RiDfront werden fur eine Zunahme des Wasserstoffdruckes im Gleichgemicht und fiir eine Reduktion der maximalen kohasiven Wider- standskraft au3 der Anpassung der theoretischen Gleichung an die experimentellen Daten gewonnen. Die Groflenordnung dieser Werte und ihre K-_abhangigkeit sind in Ubereinstimmung mit Erwartungen, die sich aus der Dekohasionstheorie ergeben, jedoch nicht mit anderen Gesichtspunkten.

INTRODUCTION

The decohesion theory(l*2) for hydrogen-induced crack propagation in steels postulates that regions exist at crack fronts where non-Hookean elast,ic stresses attain significant fractions of the elastic modulus. In such regions the chemical potential of dissolved hydrogen is lowered sufficiently so that dissolved hydrogen attains concentrations that are several orders of ma,titude larger than the normal concentration in equilibrium with the given environing hydrogen fugacity. The abnormally large hydrogen accumulation lowers the maximum resistive cohesive force, F,, between the atoms so that oz’, the local maximum tensile stress normal to the plane of the crack, which is controlled by the esternally applied load and the crack-front geometry, can equal t.he maximum lattice cohesive force. The crack propa- gates when oz’ = nF,,,(cH’), where n is the number of atoms per unit area of crystallographic plane, at a rate described by a differential equation involving the kinetically controlling transport mechanism for hy- drogen from its source to the site of bond breaking.

* Received October 30, 1973; revised Januarv 9, 195-l. -i U.S. Steel Research Laboratory, Xonroevtie, Pennsyl-

vania 15146, U.S.A.

To quantitatively describe the variation of crack velocity with stress-intensity factor, temperature, and environing hydrogen fugacity, one must have explicit knowledge of the relation F,(c,‘), of the elastic stress field within atomic distances from the crack-front, of the functional between chemical potential and elastic stress state in the non-Hookean region, of how the relaxation phenomena in the st,eel act to fix a macroscopic mean crack-tip radius p, of the kinetically controlling transport mechanism for hydrogen, and of how all these properties vary with temperature. Clearly, quantitative experimental vali- dation of the decohesion model is a formidable problem.

Nevertheless, some progress can be made in that direction by concentrating on the non-kinetic aspects of the theory, since then one need not be concerned with non-existent information on the kinetics of the overall transport of hydrogen from it’s source (am- bient gas phase, cathodic charging, acid pickling, rust.ing reaction) to the point of maximum tensile stress. One important feature of the theory is that an immobile crack for which crz’ = nF,(cH”) under a given external hydrogen fugacity is a situation of unst,able chemical and mechanical equilibrium. A necessary corollary is that (in the absence of any

ACTA MET_~LURGICA, VOL. 22, SEPTEMBER 197-l 1065

other mechanism of cracking, such as plastic tearing) at a giren est,ernaI hydrogen fugacity, f, t,here exists a threshold stress-inter&~- factor, .K, below which a crack will not propagate, and similarly, that for a given K there exists a threshold f below which the crack will not propagate. Thus, one concludes that there exist.s a functional, f*(K), for a given steel under a given mode of loading at a given temperature but independent of t,he nature of the source of the hydrogen which separates the crack propagat.ion domain from that of t,he st,atic crack. The asterisk is meant to emphasize that this functional is an equi- librium property (although of unstable character) of the steel-hy~ogen-mecha~cal loading s-y&em, and as such it contains information on Fm(cE”), hydrogen concentrat,ion as a function of t,he elast,ic stress state, and t.he mean crack-front radius of curvature as

determined by bhe plastic properties of the steel. Accounts have already been given(2*3) of euperi-

ments which demonstrated the correctness of a simple inference from the above ideas: namely, that a crack which has been allowed to come to a halt either by achieving a smaller .K (by crack advance in a WOL-type specimen) or by reducing the environing hydrogen-gas pressure can be restarted simply by increasing the hydrogen pressure slightly. It has been sh~wn(~l that this result eliminates all models which depend on dislocations for the intrinsic mecha- nism of hydrogen-induced cracking and t,hat it is consistent only with the decohesion mechanism and with the Petch adsorption criterion. The latter, however, is in ikeIf not a mechanism but only a thermodynamic, necessary, but insufficient con- dition for crack propagatGon. The present paper gives the result of more careful work nit.h an improved apparatus to establish p*(K) for hydrogen and for deuterium in a high-stren~h steel and also describes an analysis of the data xvhich strongly supports the decohesion theory. In addition, sonic emissions were monitored during crack propagation.

EXPERIMESTAL DETAILS

Modified ?VOL specimens(“) have the characteristic that as the crack propagates, the plane-strain stress- intensity factor K decreases continuously, so that the self-arrest of a crack under constant pressure of hydrogen gas may be assured and it is easy to control the progress of a crack. As in former ~orli,(~) such a specimen, I in. thick, was held rigidly within a stainless st,eel vessel (see Fig. I), which could be evacuated and filled with hydrogen gas. The ma@- tude of mode-l loading could be changed at will whenever the crack was stationary by appl>-ing

FIG. I, Schemetic diagram of specimen chamber; sight glasses in the cover are not shown.

torque to the loading bolt of the specimen by means of a shaft protruding through an O-ring. Strain gages sensed t,he loading force, which was recorded con- tinuously; a computSer progmmt enabled t.he stress- intensity factor and t,he crack length to be quickly calculated from the sensed bolt loading and the compliance of t,he specimen. which was measured as a function of artificial crack length in separate experiments on similar specimens. A differential transducer to detect sonic emissions n-as affixed directly to the specimen, the output of which was coupled t,o a preamplifier with a gain of 60 dB. This signal in turn was fed to a recording oscilloscope and an audio amplifier and speaker system, whereby the sonic bursts could be seen and heard simulta- neousfy.

The environment.al chamber was evacuable by a mechanical pump. Hydrogen gas purified by passage through a molecular sieve at liquid nitrogen tem- perature could be let in. Pressures 5vere measured either by a simple mercury manometer operable up to 2 atm absolute or by a McLeod gage for pressures between lo-* and 15 t,oir. Gold foil was placed within the connecting tubing in order to avoid contamination of the crack surface by mercury.

To establish the p*(K) functional (p being the hydrogen-gas pressure), one must Fait for a period of time to make sure that the crack is static at a set of values of K and p, and then to increase p by a small amount to observe whether or not the crack begins to mote. The accuracy of locating p*(.lK,) depends then on the smallness of the pressure increment needed to restart the crack at the value K,. The manner in which the chemical and mechanical heterogeneity of a steel presents an intrinsic limitation on the smallness

T The writers are grateful to A. W. Loginom of the Research Laboratory for the computer program.

ORI_kSI ASD JOSEPHIC: ASPECTS OF H-ISDt-CED CR_ICKISG OF STEELS 106;

of the necessary pressure increment has been pre- viouslv discussed.(*) Experimental limitations also arise from blunting of the crack by plastic relaxation and from chemical contamination of the crack surface during the waiting period. Blunting of the crack (namely, increase of p) can be reduced to a negligible degree by using a steel of very high yieId strength. As in prior \vork,(2) we employed AfSI 4340 steel heat-treated to a yield strength of 250 ksi (1.7 x

109 S/ms) and having a K, in air of about 60 ksi t/K (62 x 106X/m3’s). That plast,ic relaxation was of negligible consequence was demonstrated by the fact that a waiting period of 16 hr with an immobile crack led to about the same hydrogen pressure for restarting the crack as did a waiting period of 1rS min. Such a result is also a good indication that the measures that me have used to avoid chemical contamination of the crack surfaces were effective. In previous worh -(Go) we obtained evidence that very small amounts of contamination by air necessitate much larger hydrogen-pressure increments to restart a static crack. In the present work we have again surrounded the specimen wit,h a large volume of highly adsorbent iron poxvderi so that any residual oxygen, water vapor, carbon dioxide, etc. in the purified hydrogen or which entered into the chamber from t.he air would be adsorbed by the powder and thereby prevented from adsorbing on the crack surfaces where they would impede the ingress of hydrogen into the steel. We have ample evidence that the use of this getter, or of some other equally effective stratagem, is necessary to prevent residual impurities in the hydrogen from affecting the kinetics of crack propagation under hydrogen gas, especially at low propagation rates.

The main experiment was begun by applying torque to t.he WOL specimen within the environmental chamber and under 710 torr (5.32 S/m2) of hydrogen

$ We are indebted to H. H. Podgurski of this Laboratory both for the original suggestion to use such an adsorbent and for specific recommendations for its preparation from a commercial catalyst for the synthesis of ammonia. The powdered catalyst is placed within a silica vessel through which hydrogen can be flowed. The silica vessel is held within a furnace and is connected to the specimen chamber by a flesible metal tube. Commercially pure H, is flowed through at about 1 min-1 at 400°C for 3 days, then 8t 0.3 mm-1 for 1 week at 45O”C, then at 0.2 min-” for 5 days at 500°C. Following this, hydrogen purified by passage through a motecular sieve at liquid nitrogen temperature is flowed through the catalyst for 2 days at 500%. The molecular sieve is prepared bv baking zeolite at 110°C for 3.5 hr in a hydrogen flow of Or2 mm-l. After this reduction treatment, the reduced catalyst is transferred into the specimen chamber and onto and around the specimen by means of the flesible metal tube. Prior to the transfer, the specimen chamber is flushed with hydrogen and evacuated repeatedly. The trans- fer mechanism is then seaIed off by cold-welding shut a copper tubing that forms part of the transfer system.

gas. Cracking initiated at. a stress intensity of some-

what over 57 ksi t&., whereupon the gas pressure was decreased as quick157 as possible to stop the crack. Thereafter, the threshold pressures were determined at various values of stress int,ensity, which was changed up or down in random fashion. After the bulk of the measurements u-ith hydrogen had been carried out, the gas -R&S changed to deuterium of 99.9 per cent isotopic purity, care being taken to thoroughly flush out the hydrogen from t.he getter. After the measurements nith deuterium were com- pleted, more measurements were made with hydrogen. At all stages of the experiments, sonic emissions were monitored both with a loudspeaker and with an oscilloscope.

RESULTS ASD ANALYSES

Figure 2 displays the results of these experiments for both hydrogen and deuterium. The lower t,er- minus of a vertical line, marked by a horizontal dash, indicates the gas pressure at one value of stress- intensity factor at which t,he crack remained immobile for a t,ime and after which the gas pressure \vas raised and the crack was observed to propagate. The latter pressure is at the upper terminus of the vertical

i_

100:

5 -_ 10 P

1.0

FIG. 2. Pressures of hydrogen and deuterium, marked by a short dash, at which the crack remained stationary prior to the pressures at vrhich the crack propagated, marked by a circle for H, and a square for D, at various stress-intensity factors, K. The curves are the result

of fitting equation (S) to the experimental points.

1068 ACTA METALLURGICA, VOL. -72, 1974

line and is marked by a circle or a square. In some cases, show-n by a dot without any vertical line, the pressure so marked represents the self-arrest of a formerly moving crack. The duration of wait,ing at the lower gas pressure to make sure of the immobility of the crack can be judged to have been sufficient for this purpose by the following argument. Williams and Selson(j) have found that crack-propagation velocity, r, in a high-strength steel under gaseous hydrogen varies as p” ; and the largest value of n

they observed is 312. Adopting the relation v CC Sp3J2

we can say that had the crack been moving at thi lower pressure, p,, prior to raising the pressure to p,

and observing motion at velocity vug, the velocity at p, would be given by v1 = vup(p,/pf)3/2. Hence, knowing r, and knowing the minimum perceptible crack displacement as limited by the noise in the system (1O-4 in.), one can estimate the minimum necessary lvaiting time at p, to have perceived motion. In all cases, the durations at p, were from 5 to 100 t,imes longer than the minimum times. In addition, since p1 \vas approached by small increments from lower pressures, the crack was observed not to move at pressures <p, < p, for much longer times than t,he waiting period at p,. We consider, therefore, that the reality of a threshold gas pressure, p*, below which t.he crack n-ill not propagat,e at a given value of K, has been established and that p*(K) lies within the scatter band of the data in Fig. 2.

The pressure increment necessary to cause a self-arrested crack to move again should bevanishingly small, according to our theory applied to a mechani- cally and chemically homogeneous steel (an “ideal steel”). The magnitudes of the pressure increments shown in Fig. 2 are due to the noise in the system and, more importantly, to the intrinsic heterogeneity of the steel leading to a spatial distribution of values of (F,p’/2), as has been previously(2) discussed. We did not observe any trend of pressure increment with time of waiting at lower pressures, nor did we observe any variation due to the history of the experimental sequence (except for one feature that is discussed below). The inference t,hat may be drawn, therefore, is that any effects due to crack blunting or to chemical contamination of the crack surfaces are negligible. The present experiments abundantly demonstrated the extreme rapidity with which a change in gas pres- sure is reflected in a change in crack velocity if the pressure change is made when the crack is already moving. This was noted and discussed previously.(‘) Such rapid responses, a fraction of a second, were not observed in the absence of t,he chemical getter, shoq-ing that a surface impedance had to be overcome.

Sonic emissions, both large and small “spikes” on the oscilloscope trace, were sometimes observed as the crack propagated. Sometimes there seemed to be a positive correlation between the frequency and mag- nitude of the ‘%pikes” and the crack velocity, and other times not. Most of the crack growth was not accompanied by any observable sonic emission, whereas sonic emissions were sometimes observed when the crack was static. When this happened after t,he load on the specimen had been changed, the noise could have arisen from plastic mechanisms within the specimen and from sporadic slipping of the loading bolt wit,hin the threaded hole. How-ever, sometimes sonic emissions were observed with the crack stationary and at times long removed from the moments when the load was changed. From the point of view of the decohesion mechanism, which asserts that in an “ideal steel’ crack propagation induced by low-pressure gaseous hydrogen is an atom-by-atom process and therefore should be noise- less and that sonic emissions are evidence of certain deviations from “idealitv “(l,~ the most s@ificant finding is the absence of-s’onic emissions beyond our detection threshold during most of the crack propa- gation. We have not been able to find an?- account in the literature of similar experiments under lom- pressure hydrogen gas; clearly, much more needs to be done in this area before any definitive conclusions can be drawn.

Figure 3 reproduces scanning electron microscope photographs of the fracture surface of the 4340 steel specimen, the results on which have been presented elsewhere.(2) We find a gradual change in the charac- ter of the fracture under hydrogen as K is increased, and this is illustrated in Fig. 3. At low stress-intensity factors, the fracture is very clearly and sharply intergranular. At higher K values, although the fracture remains intergranular, there is also a con- tribution from a tearing mode that serves to blur the outlines of the grains.

The ability to restart a self-arrested crack, and the existence of a curve p*(K) which separates the static- crack domain from that of the propagating crack are predictions of the decohesion theoF which are supported by experiment. The separation between the p*(K) curve for hydrogen from that for deuterium, already observed in former work(*) and here con- timed, is consistent with the decohesion model but not consistent with any ot’her extant idea for hydrogen-induced crack propagation. As discussed before, the relative position of the curves indicates that the partial molal volume of deuterium in x-iron is smaller than that of hydrogen, as expected from the

ORIASI ASD JOSEPHIC: ASPECTS OF H-ITDUCED CRACKISG OF STEELS 1069

A. K W 17 ksi Jinch 500 x

0. K “N49 ksi ?/inch 500::

FIG. 3. SE11 photomicrograph$ of the fructure surface

at x x0. (a) Cracliing nnder H, at K * 17 ksi \ g. (h) Craclring under H, at K =x 49 kai \ in.

relative magnitudes of the zero-point. energies? and;or

that the lighter mass is more effective in reducing F,

for the same concentration. The decohesion theory

asserts that thep*(K) curve is associated with a crack

that is in unstable chemical nnd mechanical equilib-

rium and for which the local tensile stress is in the

non-Hookean elastic region and is equal to the masi-

mum cohesive force of the lattice as reduced b>- the stress-induced large concentration of hydrogen. K-e will now examine the data as much as is possible at present for these aspects of the theory.

The basic equation for the equilibrium crack kin

0:’ = k’G(L,/py = nF,(c”) (1)

where G is the esternally applied tensile stress, k’ is a

numerical parameter, and L is the length of the crack.

Since the stress-intenaitv factor is proportional to

GL'!~, one can write equation (1) as

I< = kP”‘nF,,,(c”). (2)

In the total absence of any information. we assume the simplest possible dependence of F, upon hydrogen concentration :

I’, = ‘F,,!O - xc (3)

in which F,O is the masimum coheAve resistive

force of the relevant (that is, with the occurring alloying components) hydrogen-free lattice. and x is an unknown nutnber.

To relate the hydrogen solubility to the elastic stress state, we will consider only the effect of the hydrostatic component of stress. @: in the non- Hookean region immediately at the crack-tip; con- sidering the effect of the shear stresses operating on the non-isotropic distortion produced by hydrogen in the b.c.c. lattice’“) would ire an unwarranted com- plication in the present approsimate treatment. Because either in plane stress or in plane strain @ cc Go at distances much larger than p. u-e surmise that immediately at. the crack tip also such a propor- tionality holds so that 3 CC G:‘. Hence one can write

in which q1 is an unknown number. XOK, the ordinary approximate relation for the concentration of dissolved hydrogen in a lattice in the elastic state 9 in equilib- rium with hydrogen at concentration cu in the same lattice, but stress-free, i@ RT In (c/co) = ST, where F is the partial molal volume of the dissolved

hydrogen. This relation is \vell obeyed in the domain of low elastic stresses and low interstitial concentra-

tions. In the present case, non-Hookean (i.e. non- linear) elastic stresses and hence concentrations > c,, are presumed to be involrecl. The concept of continuitv(2) leads to the inference that the stress- ” induced concentration of an interstitial solute must deviate negatively from the above equation in the region of large strain. This deviation is related to the

strain energy term in the expression for the chemical potential,C6) which grows in importance as the elastic

stresses increase. Thus, to remain as simple as possible

we write

In2 _ 07 t19'

CO RT RT

n-here ‘1~ is an unknown coefficient.

(9

lij;f_l ACT_% SIETALLTTRGICA, I-OL. 3’. 19;;

The last relation that v-e need is one betTeen the 'hBLE 1. \-aim?.- Or" J?iWmI!?Wr~ idW.dtltW.~ f?Onl CqUati;;II ! 3)

stress-free hykgen concentration, co, in equilibrium iittrct to e_xprinmml &EU

xith the ewironing hydrogen gas at pressure, y. 4 c

We can use Siererts’ lam for this: cg = +‘2, where 9 K

kdi t 2

Ib;k.” $Fe F,cr’)

is the Siererts’ coefficient. for the relevant lattice. ( :; ll:l” ) C *i’ilg ;s( :;: lil-i) F.%@

Our experiments hare shon?l that the hydrogen. 9 1.12 1%) t3.m lj.16

induced crack propagates along grain boundaries and 10 I “4 31Nj 8.45 !I). ii 12 1:;s ;of> d. 10 0.21

interphase boundaries, and so Fe need a Siertrta’ :i

1.74 I,.iitit _ _” I.14 1) J& ._

parameter for hydrogen at such boundaries where I.99 ~.9.x ;.a 0.2;

IS ., ;I * _.-t ,5.9.3.~ 7.10 0.30 there are experimental reasons(i) to beliere that the 20 2.49 8,xm 6.i.5 0.3.k

22 -. hydrogen solubility is much larger than in the normal

r?., . 3 l“,si?Cj 6.40 (j.37

lattice. Hence, \Tre will IT-rite developed from the basic theory, plus the reasonable

EU = ,3pl’” =; ,&~$.J_g 2 (6) assu~n~tioi~s (3-6) inc~ependelltl~- of the erperimental

where .yL is Siererts’ parameter for the normal lattice data, the fit encourages us to make further calcnla.

of b.c.c. iron, and $ is a multiplicative factor >l. tions. The regression analysis furnishes LIS ujth

These equations may be combined to yield values of the coefficients of K tt1K1 P. in which the only unknowns are q ttncl !G ( f; for H in x-iron is

2&T ri 3qr2 P 2.0 cmg/mole P). Hence, these parameters become lnp=‘3In(I;;,‘--K)---L------

RT p’-” RT p calculable and map be used in equation (4) to calcnlate

9, and then in equation {.?I to calcuktte tic,,. This - In p - 2 In (RX’X,%~) (7) has been done and the results are given in Table 1.

where K1,O is the plane-strain stress intensity factor \J*e note that the magnitude of the hydrostatic

at Tvhith a crack propagates in the hydrogen-free component Of stress attains values many times larger

steel, 611 ksi Z‘G. for our experimental material, and ttwn the orerall yield strength of the steel, and that

x-here p can be a function of K. However, to simplify c/co: the ratio of the local liydrogen ConeeIltr~~t~f~rl to

the problem, we ~~-ill assume that p is constant over the stress-free solubility, attains 111agt~iCi~des as large

the range of I< inrolved; this assumption x-ill be us 1V in qualitatire agreement with the conceptual

examined subsequently. Equation (i) then becomes busis of the theory. We can take another 3tep toward evaluating the low1 hydrogen concentration by adopting a Siererts’ parameter, aL = 126 :=; 10-9, deduced from Gonzalezfs[s) equation for the solubility of hydrogen in x-iron; the units of dL are (atom

- 2 In ( nkpl%~sL) 1 2

(8) H/atom Fe) (torr)- . Then equation (6) and column

3 of Table 1 yield C” in terms of the unknon-n param-

in d~ieh q = ql/p*‘*, and an asterisk has been placed eter @. These values are listed in column 4 of the

on the p to &OK that equation (8) represents the same table, from which one sees that as she applied

function p*(K), subject to the assumptions of stress intensity is increased the absolute value of

equations (3-6). We see that equation (8) expresses hydrogen concentration at unstable mechanicul

the left sicle as a polynomial of degree 2 in K, and and chemical equilibrium decreases someT&at, de.

thus it is an easy matter to fit this expression to the spite the accompanying nearly exponential decrease in

data in Fig. 2 for H, and thereby to obtain best gsts pressure (see Fig. 2). At this time, the rake of p values for the coefficient of K and of li”, as well areraged over the grain and interphase boundaries

as of the last term on the right., which is independent in our steel cannot be specified. Holrever, noting

of both K and p. In carrying out this fitting, p* at that Podgurski and Oriani(‘O) measured about

any one ralue of A VGUS arbitrarily taken at the -25 kcaljmole H, for the enthalpy of adsorption of midpoint of the .Ap represented by the rertical lines hydrogen at the interphase boundary between x-iron

in Fig. ‘7. and AlX particles, one can assert that $ cortld well The curves dra-xn in Fig. 3 are the results of the he >lV.

regres$on analysis using 30 y*-_K pairs for Irl, and 11-e can also estimate the amoont by rrhich the

18 for D,. It is clear from the goodness of the fit local hydrogen concentration reduces the F,,, of the

between the curres and the data points that. equation relevant portion of the lattice. Ke fist note that

(S) is of the right form, and since equation (Y) was equations (2) and (3) predict a Iinear relationship

ORIAXI ASD JOSEPHIC: ASPECTS OF H-ISDUCED CRACKISG OF STEELS 1Oil

between K and c” when the parameters are connected by the p*(K) functional :

K = (-gnkpl;‘)c” + nkpl~2p,ov (9)

The slope divided by the intercept yields -u/F,O. Furthermore,

F,(c”) _

In Fig. f: we have plotted column 1 vs column 4 of Table 1, obtaining the predicted linearity. From the slope and intercept one obtains x/F,@ = 0.98 x lOj@-a-‘, and using this in equation (10) one obtains the Falues tabulated in the last column of Table 1. We note that these values for the fractional reduction of the maximum cohesive force do not depend on assumptions about the magnitudes of either Pm0 or of /?. Although the actual numerical values of Fm(c”)fFmo shouId not be taken too seriously in view of the nnE hoc nature of reIations (3-5), it is gratifUying that the values are reasonable and more or less in

aemeement with our theoretical expectations. In addition, the trend with increasing K is the one to be espected, since for K - RICO, F~(c*)~~~O -+ unity.

It should be emphasized that after choosing the functional relations (3-6) as described above, no assumptions at all as to the values of the unknown parameters were necessary to obtain the entries in columns 4 and 3 of Table 1, and only the known value

of ‘SL was additionally needed for the calculated

FIG. 4. Relation between the stress-intensity factor K and the hvdronen concentration. c*. in units of H atom &r Fe a&m, a’t the position of &&mum tensile stress. Since c” is the concentration slang the p*(K) curve, it may be regarded as the critical coticentration required for onset of crack propagation at the given value of IL.

values in col~mm 4 and 5. Further calculations a-ould require the adoption of arbitrary numerical values, and only one such calculation will be pre. sented. From a plot of cc rs K (the inverse of Fig. A), one can calculate that the ratio of slope to intercept

is -0.0167 (ksi .t/iz)-l, and from equation (9) one sees that this ratio equals -(TJ+PF,,,~)-~. Eence, one has a numerical value for the product of two unknown quantities, pX/2 and (nF,O), the latter of which is the maximum cohesive force of the hydrogen. free lattice in lb/S. If one assumes the reasonable vaIue of lo-” in. for p, one obtains F,O = 6 x 10” lb/ in.2, a reasonable value for this quantity.

DISCUSSION

The good fit (Fig. 2) of the experimental p*(K) data by means of an equation derived from the basic decohesion theory plus some reasonable assumptions as to functional relationships, the excellent linearity of K vs c” (Fig. 4) in agreement with theory, and the agreement with theoretical expectations of the numerical vaiues (Table 1) and of their trends with K deduced from the fitting of the theoretical equation to the data, give strong support to the credibility of the decohesion theory, although proof cannot be claimed. Of the functional relationships (2-6) used to derive equation (S), (3 and 5) are the most ad hoc. Whereas the parabolic term of (5) is not very impor- tant, the logarithmic nature of this relation is neces- sary for obtaining good fitting of the data of Fig. 2; however, such a relationship between c/co and @ is on a firm theoretical foundation.@) The form assumed for relation (3j is not critical, and indeed it. can be shown that the use of F, = Fmo - XP, with & I m < 3, leads only to trivial changes in the numerical values of the quantities tabulated inTable 1.

It has already been pointed out that the restarting of a self-arrested crack simply by a small increase of hydrogen pressure invalidates all extant ideas relative to the mechanism of hydrogen-induced crack prope- gation in st.eels except t,he decohesion theory and the Petch adsorption point of view. The latter is not competitive as a mechanistic description since it is only a necessary but not sufficient thermod~amic criterion for crack propagation. It is nevertheless of interest to inquire how well the experimental data for p*( K) given in Fig. 2 may be fitted by an expression derived from the Petch modification of the GriEth criterion. In the presence of plastic strain, the Griffith criterion may be written(ll)

C7= W

107” ACT_% ~IETALLURGICI, VOL. 22, 19i-t

where E and Y are the Young’s modulus and Poisson ratio, respectively, of the lattice; a, is the inter-

atomic spacing; and y is the specific surface-free

energy of the crack surface as covered by adsorbate in equilibrium with the environing medium. The Petch concept is that because y is decreased by the adsorp- tion from the gaseous hydrogen environment, the threshold stress, o, that must be externally applied to cause crack propagation decreases. In terms of K, equation (11) may be written as

K=k (

“l+ p I,“?

x(1 - Y2) a, 1 * (1”)

To express h’ as a function of p of hydrogen, we need a functional for the surface free energy- pressure relation. Employing first the Freundlich isotherm,

r = npy (13) \POJ

where p, and b are fixed parameters of the system, and.P is the surface excess of hydrogen, and using the Gibbs adsorption isotherm, equation (12) becomes

h’2 = k~(*(l~$J(Yo - $Pb). 14)

The prediction of K linear in pbf2 is clearly very dif- ferent from that displayed by the data of Fig. 2. Consider now the Langmuir isotherm, written for a diatomic gas that dissociates upon adsorbing:

II2

r =

P ,,f,“P I,2 *

-f PO (15)

With the justifiable assumption that p/p0 > 1, incorporation of (15) through the Gibbs adsorption isotherm equation into (12) yields

1nP = 41 - ~2bolP [(h’i,)? _ K23

2k2En(RjX)T (16)

PO in which iV is the Avogadro number. The prediction of linearity between Inp and K2 is not well borne out by the experimental data, but if one draws t,he average chord through the curve, its slope is about

-0.025 (ksi l/%)-2. The slope espected from. equa- tion (16) using Y = f, E = 30 x lo3 ksi, k = 1, T = 298 Ii, and n = 1Or6 atoms/in.? is -0.505ao/p. Since a,/p w lo-‘, th ere is a very large discrepancy between the experimental data and the prediction from t.his variant of the Petch-Griffith criterion.

We turn now to an examination of the assumpt.ion of constancy of the mean radius of curvature p that Fe used in simplifying equation (i) to obtain equa- tion (8). A phenomenon was observed during experi- mentation that sheds light on this question and which

is interesting in its own right. Upon increasing the stress-intensity factor K by manually applying torque to the loading bolt of the specimen when the crack was static, we were able to make the crack propagate again bv raising the hydrogen pressure to values that were subsequently established to be very close to the threshold values, p*(K). The behavior upon lowering K of the static crack was much different. To cause the crack to run directly after such a lowering, it was necessary to raise the pressure of hydrogen to values considerably above those subae- quently established as the threshold values. Subse- quent values of p for restarting the crack were lower than the initial restarting pressure, were reproducible, and fall on a single p*(K) curve. The only way in which we can understand this transient irreversibility is by supposing that p is indeed an increasing function of K. When the K of a static crack is manually increased, the mean radius of curvature also increases, because of plastic mechanisms activated by the externally applied stress increment, to the value characteristic of that value of K for that particular steel. However, when the K of a static crack is decreased by manually decreasing the tensile stress exerted by the bolt, the p charact,erist,ic of the higher K persists at the lower K because there is no driving force on the dislocations to move so as to decrease p. Consequently, after the lowering of K the hydrogen pressure must first be raised to a value much higher than p* because the crack is initially blunter than it should be at the new value of K. Once the crack is thus made to move, it acquires the value of p charac- teristic of the existing K.

Confirmation that this description is essentially correct may be obtained by considering Fig. 5, in which is plotted the ratio, against Ki, of the pressure, p,, initially required to restart the crack directly after K has been lowered from a higher value Ki. over the equilibrium (threshold) pressure p* characteristic of the lower K. The logarithmic nature of this plot is consistent with the above explanation, as is apparent by recognizing that in equation (7) the dominant term on the right is that containing K/p”“. Hence, keeping p constant at the too-large value characteristic of Ki will affect the initial p at the lower K in an exponential way, as demonstrated in Fig. 5. Indeed, it is easy to see from equation (7) that

the same h Inp may be achieved either by a change in K at constant p, or by a change in p at constant K, and that these are related approximately as

ORIASI AXD JOSEPHIC: _%SPECTS OF H-IXDIICED CRACKISG OF STEELS lOi

Ki,kri~

FIG. 5. After manually decreasing the stress intensity from a value I&, the initial pressure p, required to propa- gate the crack et the lower K is larger than p*, the re- producible, threshold pressure corresponding to unstable

equilibrium.

Thus, we are forced to recognize that the simplification represented by equation (8) is not correct in principle; we note, however, that the maximum variation of p over our experimental range is relatively small, being given approximately by Ap/p M 0.8. This plus the good fitting of the data of Fig. 2 justify in a practical way the use of equation (8).

The fact that the hy~ogen-induced cracking path in this steel is inter~anular means that the calculated values of 8/c,, and of ~~(c~‘~~~~* pertain to the boundaries between grains and between phases. In particular, the critical concentration for the onset of cracking at a given value of K (Fig. 4) is the one at the

boundaries. Since fi can easily be larger than 103, the boundary concentrat.ion, H/Fe, of hydrogen at. the crack tip reaches the order of 10m2 or higher. Lest there be any misunderstanding, we remark that this huge concentration does not at all imply a corre- spondingly huge supersaturation or activity of dis- solved hydrogen ; rather, it is in thermodynamic equi~brium with the environing gaseous hydrogen at pressures below 1 atm. We remark also that, the c”(K) relation of Fig. 4 depends on the p that charac- terizes the crack front and which is itself a function of the plastic properties of the steel. In addition, in the analysis of our experiments F,,,O pertains to grain and interphase boundaries.

The question then arises: Do the boundaries crack because the larger hydrogen accumulation at the boundaries than in the grain interior (since p > 1) causes a larger decrease of cohesive resistive force there t,han is produced in the interior, or is the effect of the large hydrogen concentration at the boundaries aggravated by a lower P,,,O at the hydrogen-free

boundaries due to the atomic geometry or to the alloying elements segregated there! Two recent researches attest to the importance of alloying ele- ments in presumably lo\rering F,“. JIcXahon et al.“?) found that the heat treatment that rendered an HY- 130 steel susceptible to temper embrittIement also markedly increased the susceptibility to intergranular hydrogen embrittlement under cathodic charging at room temperature; they also prored by -Auger spectroscopy that the temper-embrittled grain bound- aries had concentrations of several alloying elements much larger than in the bulk. The interpretation by these workers of their results is that the segregated allouying elements lowered F,O. Bernstein(i3) x$-as able to change the cracking mode from intergranular to transgranular “in iron subjected to high-fugacity

cathodic charging by changes in the heat-treating

temperature, cooling rate. and interstitial content,

and he found that these changes are similar to those

in the fracture path of iron tested in tension at IOK

temperature. His interpretation of this result is that. the changes in mode in both phenomena are related to

the partitioning of solutes between the bulk and the grain boundaries. Bernstein’s work(14’ also shon-s

the importance of grain-boundary orientation for hydrogen-induced, intergnanular crack propagation,

but, whether susceptibility changes with orientation

because of a change of Fngo due to a change in the intrinsic atomic geometry, or because F,* changes

because of an accompanying change in the segregation

of alloying elements is not known at present.

CONCLUSIONS .\ND SUMM_%RY

Using a high-strength steel, we have esperimentally demonstrated the existence in hydrogen-induced crack propagation of threshold hydrogen pressures and stress-intensity factors, in agreement with the basic postulates of our decohesion theory. This theory holds that the threshold functional p*(K) corresponds to an unstable chemical and mechanical equilibrium characterized by equality between the local maximum tensile stress and the maximum

cohesive resistive force of the lattice, as reduced by

the stress-induced large concentration of hydrogen, lying in the path of the crack. An approximate

analytical expression, derived from the equilibrium portion of the theory plus reasonable but ad hoc relations, has been found to give e ve9 good fit with the experimental p*(K), and from the fit are obtained numerical values for the hydrostatic component of stress at the crack tip, the stress-induced concentra- tion enhancement, and the fractional reduction of the maximum cohesive force at grain boundaries ~vhich, together kth the trends nith K of these quantities,

1074 ACT.1 XETALLURGICA, VOL. 22, 1974

are reasonable and agree with the basic concepts of the theory. These results give strong support to the decohesion theory. Similar agreement with the experimental data and similar predictive ability are not found from any other point of view.

SEX examination shows that in the presently used steel, cracking under hydrogen is cleanly intergranular at low Ii’ values, and still intergranular but acquiring a “tearing” component at higher Ii values. Clearly, we have here the operation of two mechanisms during craching : the decohesion at grain boundaries and at interphase boundaries, and plastic tearing. Only the former appears to be aided by hydrogen and is characteristic of hydrogen-induced cracking.

The latter contributes more as R increases toward Kleo at the same temperature. Indeed, the spebimen in an air environment at the temperature of liquid nitrogen produces the mixed mode that we have observed at. the higher 6 values under hydrogen at room temperature. We surmise that, although softer steels exhibit a larger contribution from the plastic mode that will make the present type of experimen- tation and analysis much more difficult, the contri- bution of hydrogen to the crack propagation is also through the decohesion mode in the softer steels.

It is clear that although the decohesion theory as a whole has been given strong support by the present work, essentially no progress has yet been made toward developing from the theory explicit relations to describe the velocity of craclr propagation. The

chief reason for this is the current ignorance of the detailed kinetics of hydrogen transport from the ambient to the point of maximum tensile stress. When esperimental information is developed on this topic, it will be useful to attempt computer solutions of the equations of Ref. (1).

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