On the length of crack advance during hydrogen-assisted cracking

5cripta M E T A L L U R G I C A et M A T E R I A L I A

Vol. 25, pp. 847-852, 1991 Printed in the U.S.A.

ON THE L E N G T H OF C R A C K

Pergamon Press plc All rights reserved

A D V A N C E DURING H Y D R O G E N - A S S I S T E D C R A C K I N G

E. I. Meletis" and E. C. A i f a n t i s ÷ " L o u i s i a n a State University, Baton Rouge, LA 70803, USA ÷ M i c h i g a n T e c h n o l o g i c a l university, Houghton, MI 49931, USA (Received November

8, 1990)

Introduction It has been e s t a b l i s h e d that the p r e s e n c e of h y d r o g e n in m a n y alloy systems (steels, t i t a n i u m - and n i c k e l - b a s e alloys) causes e m b r i t t l e m e n t resulting in subcritical c r a c k g r o w t h at loading levels s i g n i f i c a n t l y lower than those a s s o c i a t e d w i t h u n s t a b l e c r a c k motion. H y d r o g e n can be i n t r o d u c e d in the material in the atomic form ~H) in two ways. These are, e l e c t r o l y t i c a l l y through a d i s c h a r g e r e a c t i o n (H + e ~ ~ H) or from a g a s e o u s a t m o s p h e r e through m o l e c u l a r dissociation, followed in both cases by H absorption. In the presence of a crack, a c c e l e r a t e d H p e n e t r a t i o n is a c c o m p l i s h e d in the region in front of the crack tip by two d i f f e r e n t mechanisms: stress-assisted d i f f u s i o n and d i s l o c a t i o n transport. It is e v i d e n t that the zone in the immediate v i c i n i t y of the crack tip is of utmost i m p o r t a n c e since this is where the critical stress f i e l d / e n v i r o n m e n t interaction occurs leading to e m b r i t t l e m e n t and c r a c k propagation. The a f o r e m e n t i o n e d region is c o m m o n l y referred to as the process zone (PZ). It is expected then, that the s i n g u l a r a s y m p t o t i c forms p r e v i o u s l y obtained for e l a s t o p l a s t i c m a t e r i a l s to d e s c r i b e the stress d i s t r i b u t i o n in the neighborhood of the c r a c k tip (within the PZ), should not hold since this region has been m o d i f i e d as a result of the stress f i e l d / e n v i r o n m e n t interaction. It is a n t i c i p a t e d that the stress field and the a s s o c i a t e d s i n g u l a r i t y are relaxed within this m o d i f i e d zone and this region should be e x c l u d e d from the continuum description. In spite of the widely r e c o g n i z e d i m p o r t a n c e of the PZ as a result of Barenblatt's early work [i], very little has been done for its precise description. Neimitz and A i f a n t i s [2] adopted the PZ c o n c e p t and d e v e l o p e d a method e n a b l i n g the c a l c u l a t i o n of the PZ size and shape and the stress d i s t r i b u t i o n w i t h i n it d u r i n g h y d r o g e n - a s s i s t e d c r a c k i n g (HAC) in e l a s t o p l a s t i c materials. Based on that and c o n s i d e r i n g a d i s c o n t i n u o u s c r a c k p r o p a g a t i o n process, the same authors [3] p r o p o s e d a model to p r e d i c t the length of the individual c r a c k jumps during HAC. The p u r p o s e of the p r e s e n t paper was to compare experimental observations of HAC in 2090 A1 with theoretical predictions. The s e l e c t e d material had a flattened, p a r a l l e l grain boundary structure w h i c h is typical of commercial h i g h - s t r e n g t h rolled A1 alloys. E n v i r o n m e n t - a s s i s t e d c r a c k i n g (EAC) studies u n d e r t a k e n p r e v i o u s l y by Meletis [4] on 2090 A1 u n d e r plane strain conditions, have shown that testing in the short t r a n s v e r s e d i r e c t i o n (stress axis v e r t i c a l to g r a i n boundaries) results in a p u r e l y i n t e r g r a n u l a r c r a c k i n g mode. C r a c k i n g occurs on parallel but d i s p l a c e d grain b o u n d a r i e s s e p a r a t e d by u n f r a c t u r e d ligaments. Failure of the ligaments p r o d u c e s "river patterns" similar to those o b s e r v e d in t r a n s g r a n u l a r EAC. In addition, r e c e n t l y it has been e s t a b l i s h e d by M e l e t i s and Huang [5] that alloy 2090 is s u s c e p t i b l e to HAC under c a t h o d i c c h a r g i n g conditions. T h e o r e t i c a l M o d e l l i n q of the PZ u n d e r HAC C o n d i t i o n s In this section a special case of the N e i m i t z - A i f a n t i s PZ model [2,3] under HAC c o n d i t i o n s is o u t l i n e d involving an elastic material. M o r e details on this and r e m a i n i n g t h e o r e t i c a l model d e v e l o p m e n t s are c o n t a i n e d in a forthcoming

847 0036-9748/91 $3.00 + .00 Copyright (c) 1991 Pergamon Press plc

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paper [6]. The above PZ model refers in general, to a blunted crack tip in an elastoplastic material and is not directly applicable to HAC in A1 2090 in which there is limited crack tip plasticity. It should be noted that under these conditions and without the influence of hydrogen the model reduces to the Barenblatt-Dugdale model. Following the procedure by Neimitz and Aifantis[2,3] the conditions for the cancellation of singularity and smooth closure at the crack tip are expressed by the relations stated in terms of the appropriate J integral as J" = J ~ 6r = -

Jpz

G O6pz(X)

) ~ (x) -~ -x

(2.1) dx

(2.2)

O

( l-v 2) J.=

2.

- - K

(2.3)

E

where J., J-z denotes t h e J i n t e g r a l a t infinity and along the PZ, respectively. The symbol ~ •6_ denotes the crack opening displacement due t o t h e cohesive stresses a In the PZ of length r and an expression for it is provided from elastic solutions at crack tips. K. is the stress intensity factor due to the applied loads, v is the Poisson's ratio and E is the elastic modulus. For an elastic material as in this case eqn. (2.1) is equivalent to writing K.= K.pz where K is the stress intensity due to the cohesive stress distribution in the PZ~ TM For simplicity is assumed that the cohesive stress is constant and independent of the crack opening displacement in the PZ. The cohesive stress can be as high as the theoretical strength (u=E/lO) for brittle materials or equal to the yield strength u ~ for ductile materials. It then follows (in analogy to the small-scale yielding problem) that . K. z . Kpzz r . . . . (2.4) 8 oz 8 oz

Now i n t h e p r e s e n c e o f h y d r o g e n t h e s i z e , distribution i n t h e PZ a r e e x p e c t e d t o be m o d i f i e d interactions in the PZ as suggested, for example by proposed a specific reduction of u. Neimitz and approach that under the influence of hydrogen the be determined by a proper scaling with those under rN = ~ l r ,

6" = % 6 ,

oN = ~3o

shape and c o h e s i v e s t r e s s due t o t h e s t r e s s - h y d r o g e n Oriani and Josephic [7] who Aifantis [8,9] adopted the modified PZ parameters can ambient conditions, i.e. (2.5)

where t h e s u p e r s c r i p t H d e n o t e s t h e p r e s e n c e o f h y d r o g e n and~At , ~2, 4 3 a r e t h e scaling coefficients w h i c h , i n g e n e r a l , depend on t h e a p p l i e d l o a d , h y d r o g e n concentration, t e m p e r a t u r e _ etc. However, while in the Neimitz and Aifantis case determination of ~I, 42, ~ 3 requires the simultaneous solution of three equations for three unknowns, here specification of ~ 3 determines'~1 a n d S 2 from the available elastic solutions. For the elastoplastic case under the influence of hydrogen Neimitz and Aifantis proposed that the cohesive stress at the trailing edge of the PZ decreases with respect to the mean hydrogen concentration CH in the PZ. In the elastic case for a uniform cohesive stress distribution in the PZ, this can be written in terms of material constants Z and B as 0"

=

O

-

Z ( C H )i

(2.6)

Once the size, shape and cohesive strength of the PZ under the influence of hydrogen are known a condition for crack initiation can be determined. Crack growth in HAC occurs at lower load levels than under ambient conditions. Assuming the crack growth occurs when J. obtains a critical value, then an energy balance at the crack tip gives a fracture criterion of the form Jo = O"¢ 6N¢ = JNc

(2.8)

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where o"¢ is the critical cohesive stress, 6"c is the critical crack tip opening displacement and J"c is the critical energy release rate in the presence of hydrogen. When eqn. (2.8) is satisfied, the PZ ruptures and the crack "jumps" a distance Aa equal to the PZ length, i.e., ~ a = r" (2.9) and arrests. Hydrogen diffuses to the PZ again, reduces the cohesive strength until eqn.(2.8) is satisfied and the crack "jumps" again. The cycle repeats itself after a time interval of At(time required for sufficient hydrogen build up within the PZ) and HAC proceeds in a step-wise fashion with the average crack tip velocity given by V = ~a/At

(2.10)

A similar argument can be made to extend the aforementioned PZ mechanism to model the "discontinuous" process of crack "growth" and "arrest". Now, however, Aa is the length of the region behind the crack tip where unfractured ligaments restrain the crack faces. This region is called the ligament zone LZ and the cohesive stress distribution within LZ is given by the strength, dimensions and distribution of the ligaments. In this way the concept of the PZ can be extended in a self-similar way to propose the LZ mechanism for modelling crack growth and arrest over larger space and time scales. ExDerimental Study Materials and procedure Commercial 2090 A1 (AI-2.2Li-2.9Cu-0.12Zr) in the T8 condition was selected for the experimental study. The material was produced in the form of rolled plate and its microstructure consisted of flattened grains with average dimensions ll00~m x 240~m x ll~m. Double cantilever beam(DCB) specimens were prepared from the plate in the SL orientation, which is the most sensitive orientation since the crack plane lies parallel to the flattened grain boundaries. The DCB specimens were 2.54 cm high (plate thickness), 1.3cm wide and 12.5cm long providing valid plane strain conditions. The specimens were first fatigue precracked to develop a sharp and straight crack front and subsequently the side surfaces bearing the crack were polished down to 1 ~m finish using diamond paste to obtain mirror-like surfaces. Hydrogen embrittlement testing was conducted by attaching a container around the specimen in such a way that one of the side crack bearing surfaces was not in contact with the electrolyte, but exposed to laboratory air. The specimen was first loaded in lab air to a K s = 8.6 MPa~m and then cathodically charged at -1500 mV(SCE) in 3.5% NaCl + 450 mg/l As203. Under this loading level, kinetic crack growth prevails which is commonly known as Stage II in the crack velocity vs K s curve. Crack propagation events were monitored on the unexposed specimen side surface by using a travelling optical microscope and caustic observations. Following hydrogen testing, the fracture surfaces were examined by scanning electron microscopy (SEM). Results The observations on the specimen surface showed that the crack advanced in a stepwise (discontinuous) mode. In total, four crack-advance events were monitored on the specimen surface and the two methods (travelling microscope and caustics) showed excellent agreement. The jump length, a i and corresponding waiting time interval, t i as well as the calculated crack growth velocity, da/dt, for each of the above events are shown in Table I. SEM examination of the fracture surfaces showed that they had a flat, brittle appearance indicative of the low-energy HAC process. Detailed fracture surface observations revealed the presence of two types of crack-arrest markings (CAM); micro- and macro-CAM. These markings are produced by the blunting (arrest) of the crack front during the individual crack jumps. Both types of CAM run perpendicular to the direction of crack propagation and had a curved appearance due to plane stress conditions prevailing at the specimen surfaces. Figure 1 shows the appearance of macro- and micro-CAM. The macro-CAM were widely spaced and composed of a large number of micro-CAM. Measurements of the spacing

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between macro-CAM showed that they corresponded to the jump events monitored on the specimen surface. Therefore, the calculated da/dt values above reflect the overall crack velocity rather than the velocity of individual crack events which are represented by the micro-CAM. The spacing between subsequent microCAM was found to vary with an average value of 30 ~m. This distance represents the length of the individual crack jump and is equal to the PZ size. The macro-CAM are a result of longer crack-front arrest periods. These occur for the reason that the cracks propagate on parallel but displaced grain boundaries and as a consequence they are separated by unfractured ligaments. The length of the unfractured ligaments increases with crack advance, the ligaments become increasingly load bearing and thus decreasing the stress intensity at the crack-tip and eventually they result in crack arrest. The crack front resides at these sites (macro-CAM) until the ligaments are fractured by stress/ environment interactions and the crack propagation process resumes. The SEM observations showed that the most probable ligament fracture mechanism is low-energy tearing under the applied shear stress. This is supported by our recent results which indicate that the presence of hydrogen in this material causes significant yield strength reduction and enhanced dislocation mobility [i0]. In addition, the localized shear of ligaments connecting coplanar cracks gives rise to "river patterns" that can be used to identify the actual crack growth direction. The existence of the unfractured ligaments also provides an explanation for the striking similarity in the calculated overall crack growth rates in spite of the variation in the spacing of the macro-CAM. This is that further spaced macro-CAM are associated with longer unfractured ligaments that require longer stress/environment interaction time for their fracture. This of course presumes a time-dependent ligament fracture process in agreement with the experimental evidence. Theoretical Analysis and Discussion In this section the quantitative description of both micro (- 30~m) and macro (-0.25-i mm) CAM is considered along with the corresponding threshold stress intensity factors by using the PZ and LZ models, respectively. In particular, the model used to investigate the restraining effect of the ligaments and the condition for crack arrest is of a semi-cohesive zone type. The crack is imagined to be a physical crack with two regions in front of it; that is, the ligament or semi-cohesive zone (LZ) of length L and cohesive process zone of length r. Maintaining smooth closure at the tip of the PZ we can express the condition for finite stress at the effective crack tip by K, - KLZ : ~ z

(4.1)

where KLz is the restraining stress intensity factor due to compressive forces in the LZ. Smith [ll] did a detailed investigation of the restraining effect of the ligaments on the crack (without the PZ zone) and using his approach an expression for ~ z is obtained in the form 2 V~2af h KLZ

L~r

~]/2

¢R n ~d X 2 + (nd/2) z dx

(4.2)

where af is the uniform stress distribution in the LZ equal to the fracture strength of the ligaments, h is the width of the ligaments, d is the spacing between the ligaments and n is the number of discrete ligaments across the thickness of the specimen. If b denotes the specimen thickness and (h, L) <
%z =

(~-

~)

(4.3)

2~d Now that there is an expression for the restraining effect of the ligaments on the crack tip, the PZ length r is given by eqn. (2.4) except that now K, is

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replaced by K. - ~ z to include the r e s t r a i n i n g effect of the ligaments. Eqn. (4.3) shows that as the LZ increases in length, ~ z increases w h i c h in turn decreases the PZ length. C r a c k arrest occurs w h e n the LZ reaches a critical length L¢ and PZ length d e c r e a s e s to a v a l u e ~ such that the stress intensity factor due to the cohesive stress a c in the PZ (or e n e r g y in the PZ) decreases to its critical value K,, i.e., 4a c

Kpz = - -

= K,

~

(4.4)

,2J~V From eqns. (4.1), (4.3) and e x p r e s s e d in the form 4af h

Y,,,

( ~

(4.4)

-

the

condition

¢-<~) = K.

for

crack

arrest

can

be

(4.5)

~'2-~-" d Next the q u e s t i o n of when the crack will "jump" a d i s t a n c e the length of the LZ is addressed. It is p r o p o s e d that under the influence of h y d r o g e n and sufficient e x p o s u r e time, the fracture (yield) s t r e n g t h of the ligaments d e c r e a s e s from its value u n d e r ambient c o n d i t i o n s af to af" and the ligaments fail p o s s i b l y by a m i c r o p l a s t i c i t y m e c h a n i s m as p r o p o s e d by B e a c h e m [12]. Thus under the influence of h y d r o g e n the ligaments fracture p r o g r e s s i v e l y and ~z starts decreasing. Under these c o n d i t i o n s the length of PZ increases to a critical v a l u e r ~ and ~z ~ncreases to a critical t h r e s h o l d value Kth , i.e.,

4ac This is p r e c i s e l y eqn. (2.8) in terms of the stress intensity factor rather than the J integral. It can be shown that K~h = ~EJcN/(l-v~. For HAC in 2090 A1 K.h = 6.4 MPa ~ [I0]. A s s u m i n g rc" equal to the d i s t a n c e b e t w e e n m i c r o - C A M (30~m) ac" can be e s t i m a t e d from eqn. (4.6) to be 730 MPa. This means that ac" = E/100 w h i c h is a p p r o x i m a t e l y one tenth of the t h e o r e t i c a l fracture strength, i.e., a r e a s o n a b l e value. From eqns. written as

(4.1),

(4.3) and

(4.6)

a condition

for c r a c k initiation can be

4afNh (4.7) -(~Lc + re" - r~c") = K~, ~2~ d A s s u m i n g ofH = 0.9af [i0] and taking ~ = 1.138mm (the length of the first crack increment), d= 240~m (the average w i d t h of flattened grains), a t =307 MPa or 485 MPa (the intergranular or t r a n s g r a n u l a r fracture s t r e n g t h respectively) and rc" = 30~m (the average d i s t a n c e between micro-CAM) the w i d t h of the ligaments h can be e s t i m a t e d from eqn. (4.7). D e p e n d i n g on w h e t h e r there is intergranular or t r a n s g r a n u l a r failure of the ligaments, it is e s t i m a t e d that h= 26-42~m which is 2-4 grains thick. S u b s t i t u t i n g this value of h b a c k into eqn. (4.5) and c h o o s i n g r c as 30~m (or less) K, is found to be 6.2 MPa~-~. This shows that the c r a c k arrests at a stress intensity factor b e l o w that r e q u i r e d for crack i n i t i a t i o n and the "extra" energy to start crack g r o w t h is p r o v i d e d by the s t r e s s - h y d r o g e n interactions in both the LZ and PZ. K,

When a s u f f i c i e n t number of the l i g a m e n t s fail eqn. (4.7) is satisfied and the c r a c k "jumps" a d i s t a n c e equal to the LZ length L c. The r e s t r a i n i n g stress intensity factor ~ z is now reduced and the crack enters the stage II regime again. It will continue until the second LZ r e a c h e s a c r i t i c a l length and arrests the c r a c k again. The cycle repeats itself so that HAC p r o c e e d s in a step-wise fashion. It can be seen that s u b s e q u e n t c r a c k jumps are s i g n i f i c a n t l y less t h a n the first c r a c k jump. This s u g g e s t s that some l i g a m e n t s still remain even a f t e r the s u b s e q u e n t crack advance that is equal to the length of the LZ. These residual ligaments will c o n t i n u e to r e s t r a i n the c r a c k tip so that the critical length of the next LZ for c r a c k a r r e s t will be smaller. For example, the r e s t r a i n i n g stress intensity factor due to the forces in both ligament zones is given by

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H-ASSISTED CRACKING

4~

%z =

h

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Z5, No.

4 f~" h

( ~ -

~r)

(VL, + ~

~d

+ r - ~

+r)

(4.8)

2~-~d

where f is the f r a c t i o n of l i g a m e n t s u n f r a c t u r e d in the first LZ, af"=O.9~f and and I~ are the lengths of the first and second LZ respectively. I n t r o d u c i n g eqns. (4.8) and (4.4) into eqn. (4.1) the c o n d i t i o n for crack arrest of the s e c o n d LZ can be e x p r e s s e d as 4~f h

(V-~0÷r c - ~

+ 0.gf(VLI0

+ ~ 0 ÷r0 - V - ~

+r~)~

-- ~.

(4.9)

~ d A s s u m i n g that K, increases s l i g h t l y as the crack grows, it can be estimated that f• 0.80. This suggests that only a r o u n d 20% of the l i g a m e n t s failed after the first c r a c k arrest. From this it can be e s t i m a t e d that after this fraction of l i g a m e n t s failed (K, - ~z) = 6.9 M P a ~ w h i c h is above t h r e s h o l d and high enough a g a i n resume stage II cracking. This a n a l y s i s can be e x t e n d e d to the s u b s e q u e n t c r a c k g r o w t h increments. This will be d o n e in a f o r t h c o m i n g p a p e r [6] w h e r e the length of each c r a c k advance, the c o r r e s p o n d i n g w a i t i n g times and the c r a c k tip v e l o c i t i e s are studied in detail. The a n a l y s i s will indicate the t r a n s p o r t and c r i t i c a l a c c u m u l a t i o n of h y d r o g e n into the LZ and PZ as well as the h y d r o g e n - i n d u c e d d a m a g e d e v e l o p m e n t in these regions. Acknowledqement The a s s i s t a n c e in the t h e o r e t i c a l a n a l y s i s and e x p e r i m e n t a l work by Mr. T.W. Wedd and Mr. W e i j i Huang is g r a t e f u l l y acknowledged. References i. 2. 3. 4. 5.

G. I. Barenblatt, PMM 23, 434 (1959). A. Neimitz and E. C. Aifantis, Engng F r a c t u r e Mech. 26, 491 (1987). A. Neimitz and E. C. Aifantis, Engng. Fracture Mech. 26, 505 (1987). E. I. Meletis, Mat. Sci. Eng. 93, 235 (1987). E. I. M e l e t i s and W. Huang, A l u m i n u m - L i t h i u m Alloys V, T.H. Sanders, Jr. and E. A. Starke, Jr. Eds., pp. 1309, McPE, B i r m i n g h a m UK(1989). 6. T.W. Webb, W.Huang, E.I. Meletis and E.C. Aifantis, f o r t h c o m i n g paper. 7. R.A. Oriani and P.H. Josephic, Acta Metall. 25, 979 (1977). 8. A. Neimitz and E.C. Aifantis, Engng. F r a c t u r e Mech. 31, 9 (1988). 9. A. Neimitz and E.C. Aifantis, Engng. F r a c t u r e Mech. 31, 19 (1988). I0. W. Huang, M. S. Thesis, L o u i s i a n a State University, 1990. Ii. E. Smith, Engng. F r a c t u r e Mech. 19, 601 (1984). 12. C.D. Beachem, Metall. Trans. 3, 437(1972).

TABLE 1 E x p e r i m e n t a l M e a s u r e m e n t s of C r a c k Growth u n d e r C a t h o d i c a l l y - C h a r g e d Hydrogen. Crack Event

~i 2 3 4

iJump iLength ai, IBm

Waiting Time ti, s

1.138 0.243 0.269 0.511

23,400 7,200 4,500 9,300

Crack Velocity da/dt, m/s 4.86 x 10-8 3.38 x 10-8 5.98 x 10-8 5.5 x 10-8

Fig. 1 S c a n n i n g e l e c t r o n m i c r o g r a p h showing m a c r o - and micro-CAM.

4