a fracture model for hydride-induced embrittlement

$: A fracture model for hydride-induced embrittlement$
Pergamon Acta metall, mater. Vol. 43, No. 12, pp. 43254335, 1995

Elsevier Science Ltd Copyright �9 1995 Aeta Metallurgica Inc.

0956-7151(95)00133-6 Printed in Great Britain. All rights reserved 0956-7151/95 $9.50 + 0.00

A FRACTURE MODEL FOR HYDRIDE-INDUCED EMBRITTLEMENT

K. S. CHAN Southwest Research Institute, San Antonio, TX 78238, U.S.A.

(Received 22 July 1994; in revised form 8 March 1995)

Abstract--The presence of hydrides in the microstructure can substantially reduce the tensile ductility of Zr and Ti alloys. For treating hydride-induced embrittlement in these alloys, a fracture model has been developed by considering the hydrides to crack readily under tensile loading so that an array of microcracks form in the microstructure. Interaction of the plastic fields of the microcracks leads to fracture of the matrix ligaments, and a loss in the tensile ductility. Application of the proposed model to Zircaloys reveals that hydride-induced embrittlement depends on the hydride size, morphology, and distribution, as well as the continuity of the hydride network, in accordance with experimental observations.

INTRODUCTION

The formation of hydrides in Zr-[l-20] and Ti-base alloys [21-26] can be detrimental to mechanical properties, including tensile ductility [1-6, 21-24], fracture toughness [1, 17], ultimate fracture strength, and sus- tained-load cracking, or slow crack growth resistance [18-20, 25, 26]. Many aspects of hydride-induced embrittlement in these alloys are well understood, par- ticularly the role of hydride in the embrittlement process [1-3, 21, 22]. Reviews of previous work on the effects of hydrides on the mechanical properties of Zr- and Ti-alloys can be found in Northwood and Kosasih [1], Ells [2], Coleman and Hardie [3], and Paton and Williams [22].

Extensive studies have shown that a substantial loss of tensile ductility can occur in Zr-alloys as the result of hydride precipitation [1-16]. The amount of ductility degradation depends on the hydride orientation, morphology, and distribution. Hydride platelets oriented normal to the stress axis have been found to cause large reductions in strength and ductility, while hydride platelets oriented parallel to the stress axis have little effect. Closely spaced hydride platelets lead to brittle fracture, but ductile fracture prevails in materials containing widely spaced hydrides [3]. Furthermore, hydride- induced embrittlement is significantly higher for plate-like hydrides than for spheroidal hydrides [8].

The prevailing view on hydride-induced embrittlement in Zr-alloys is that both the metastable, 7, and the equilibrium, 6, phases are intrinsically brittle at temperatures less than 150~ [1, 13]. During tensile loading at a temperature less than 150~ the hydrides that are aligned normal to the stress axis fracture readily and form microcracks that accelerate

the plastic failure process in the matrix [10, 13]. Closely spaced hydride platelets are more damaging than their widely spaced counterparts because of shorter distances for link-up of hydride microcracks [3]. A brittle fracture behavior results when a continuous hydride network exists in the microstructure [14, 15]. In many cases, observed heat-treatment and microstructural effects on hydride-induced embrittlement can be traced to the formation of a hydride network with a high degree of continuity, which provides a continuous path for easy crack propagation once a crack is initiated [14, 15].

The initiation of fracture at hydrides has been the subject of several recent investigations [10-13]. These investigations, however, were concerned with determining the critical stress and strain conditions at the initiation of microcracks at hydride platelets and the role of the matrix strength in the cracking process. Little effort has been made to model the flow localization and fracture in the matrix ligament, the link-up of microcracks, and the resulting loss of tensile ductility. There is also a need for a fracture model that can predict the influence of hydride morphology and distribution on tensile ductility.

The objective of this article is to present a fracture model for treating hydride-induced embrittlement in metals with a particular emphasis on the Zr-base alloys. Motivated by experimental observations, the proposed approach is to model the plastic fracture process of the matrix ligaments located between hydride microcracks as a function of the size, volume fraction, morphology, and distribution of the hydrides, as well as the continuity of the hydride network. For model evaluations, the proposed model is applied for predicting hydride embrittlement in Zircaloys. The results are compared against experimental data in the literature.

4325

4326 CHAN: HYDRIDE-INDUCED EMBRITTLEMENT

o'.

e e e

@ e e e e

t

T ..L ~g_ ALL,_

o. O .

(a) (b)

Fig. I. Schematic shows cracked hydride particles are modeled as an array of well-aligned microcracks of length 2a, center-to-center spacing, L, and stacking spacing, s, sub-

jected to a remote stress, aoo.

THE FRACTURE MODEL

Physical view of the fracture process

The approach taken for treating hydride-induced embrittlement is illustrated schematically in Fig. 1. A uniform distribution of hydrides of a characteristic dimension, 2a, exists in a Zr- or Ti-base alloy. During loading of the hydrided alloy, the hydrides fracture readily to form microcracks that are aligned normal to the applied stress axis. All of the microcracks are penny-shaped cracks of length, 2a, whose in-plane and stacking spacings are L and s, respectively, as shown in Fig. 1. The morphologies of hydrides considered include disk-like, spheroidal, plate-like, and oblate spheroidal particles.

Under elastic-plastic loading, each of the microcracks is subjected to a remote stress ~ , and a crack extension driving force represented by the J-integral [27]. An elastic-plastic strain field occurs ahead of the tips of each of the microcracks, whose amplitude

Creek A Crack B D

r+ J Distance

Fig. 2. The strain concentration process postulated in the fracture model for describing failure of the matrix ligament connecting two adjacent microcracks in an array of uni- formly aligned microcracks subjected to a remote stress, ~ .

decreases with increasing distance from the tip of the microcrack, e.g. microcrack A in Fig. 2. Overlapping of the strain fields of microcrack A with a neighbour- ing microcrack, B, results in elevated strain values within the matrix ligament, as shown in Fig. 2. When the local effective strain at a distance, r, ahead of the microcrack reaches the matrix ductility, Era, the microcrack extends and propagates in an unstable man- ner, resulting in final fracture of the hydrided solid.

Treatment of the hydrided-induced fracture process requires a knowledge of the size of the matrix ligament separating the tips of interacting microcracks and the strain concentrations at the crack tips and within the ligament. Construction of the proposed fracture model can be separated in two parts. The first part involves modeling the size of the matrix ligament in terms of a microstructural parameter, (, which represents a measure of the continuity of the hydride network in the microstructure. The second part concerns the calculation of strain concentration and the failure of the ligament connecting two interacting microcracks under a remote tensile load.

L ]-( s /i

(a) (b) Fig. 3. Unit cells utilized to model idealized hydride networks containing: (a) disk-like hydrides; and (b)

spheroidal hydrides.

CHAN: H Y D R I D E - I N D U C E D E M B R I T T L E M E N T 4327

" I. S / b" / ] / I .

l - f - - 3 ( )

l

i 2a

(a) Co) Fig. 4. A network of plate-like hydrides: (a) unit cell; and (b) top view of the plate-like hydrides.

Continuity o f hydride network

Several hydride networks based on idealized morphologies are examined, including: (1) disk-like; (2) spheroidal; (3) plate-like; and (4) oblate-spheroidal hydrides. For disk-like hydrides, the continuity of the hydride network is modeled in terms of the unit cell shown in Fig. 3(a), which shows that the hydrides are modeled as circular disks of length, 2a, height, h, and an in-plane spacing,/, in a rectangular unit cell L in width and s in height; the latter also corresponds to the stacking spacing of the hydride disks. Based on this arrangement of hydrides, the volume fraction, VH, of the hydride is given by

V Va = L2 s (1)

where V is the volume of the hydride. Since L = l + 2a, the in-plane spacing, 1, can be obtained from equation (1), and

l = 2a(r _ 1) (2)

where

VHS ( = - - (3)

~r2

is the continuity parameter; 2 = V/4rra 2 is a characteristic length dimension for the hydride morphology

Table 1. Summary of the critical volume fraction, V~, of hydride for the formation of a continuous hydride network for four idealized hydride morphologies. The hydride network becomes continuous

when the continuity parameter, ( = V H S/n2, reaches unity

2/" ~ V Morphology Dimensions / = - 7 ~ / V:~ \ 4 h a - ~

Disk 2a: diameter h nh h: height 4 4-~

a na Spheroid 2a: diameter 3 3"~

Platelet b: height bc nbc 2a: thickness - - - - 2c: width 4a 4as

Oblate spheroid 2a: minor diameter c __rcc 2c: major diameter 3 3s

considered, and 2 = h/4 for a thin disk. According to equation (2), the in-plane spacing is very large when

approaches zero, but the in-place spacing becomes nil when ~ = 1. Thus, a hydride network is continuous when ( = 1, and discontinuous for 0 < ( < 1 since l > 0 .

The continuity of the hydride network for spheroidal hydrides is modeled in terms of the unit cell shown in Fig. 3(b). As in the case for disk-like hydrides, the spheroidal hydrides, of radius 2a, are separated by an in-plane spacing,/, in a rectangular unit cell L in width and s in height, where s is also the stacking spacing of the spheroidal hydrides measured from the center of the spheroids. Similar procedures are used to construct the networks containing plate-like and oblate-spheroidal hydrides. The unit cell for the plate-like hydride network is shown in Fig. 4(a). The cross-section of the plate-like hydrides of height, b, is described in terms of an ellipse with major and minor diameters of 2c and 2a, respectively, as shown in Fig. 4(b). The relevant dimension parameters for the various hydride morphologies are summarized in Table 1. When the procedure described above is applied for disk-like hydrides, the same expression, equation (2), is obtained for the in-plane spacing for all hydride networks, but the length parameter, 2, varies with the hydride shape. The critical hydrogen volume fraction, V*, at which a continuous hydride network occurs (( = 1) also varies with the hydride morphology. The appropriate expressions for these parameters are presented in Table 1.

The morphology of the hydride plays a significant role in determining the volume fraction of hydride at which a continuous network is formed. Figure 5 shows a comparison of the microstructural conditions for the formation of a continuous hydride network for disk-like and spheroidal hydrides. The comparison is presented in terms of volume fraction of the hydride vs stacking spacing, s, of the hydride normalized by the grain size, d, of the matrix. Since the radius of the spheroidal hydrides is likely to be larger than the thickness of the disk-like hydrides, the


1'0 / ~ Continuous Networkh = 0.5 gm | \ a=3 gm

0.8 ~ ~ d = 10 gm

\ "10

,.-'I"o 0.6 \ N,~pheroidaJHydride

.o ~ V. ~a "6 isk-Like Hydride 0

,.,- 0.4

0.2

Unconnected Hydrides

0 . 0 i I , I , I , I , I

0.0 0.2 0.4 0.6 0.8 1.0

,/d Fig. 5. Volume fraction of hydride required to form a continuous hydride network as a function of

stacking spacing, s, normalized by the grain size, d, for disk-like and spheroidal hydrides.

critical condition for forming a continuous hydride network of disk-like hydrides is more easily attained, i.e. at a lower volume fraction of a hydride, as shown in Fig. 5.

Failure of matrix ligaments

The concentration of plastic strain in the matrix ligament located between two interacting penny- shaped microcracks, A and B, as shown in Fig. 2, is considered here. At a distance, r, ahead ofmicrocrack A, the strain tensor, E~, is given by [28--30]

r J ] ''~l +" A _ O ~ E , / - - , Q(O) (4) % - L~Ey%lor j

where J is the J-integral, ~y is the yield strain, O'y is the yield stress, n is the inverse of the strain hardening exponent, e is the material constant in the Ram- berg-Osgood constitutive relation [31], and In and ~(0) are normalized parameters in the HRR-field (Hutchinson [28], Rice and Rosengren [29]). Simi- larly, the strain tensor at r due to microcrack B is given by

L _7 l+" % Lc%%I,(l - r)J g~ (5)

which is added to equation (4) to give

+n OCE[ QJ 1 n/l E~(0) (6) E~= yL0%ay/~rj

where

9= [ " Y"+q'+""j (7)

represents the increase in the near-tip strains at r due to the interactions of microcracks A and B.

The J-integral can generally be separated into elastic and plastic components. For the problem considered here, the elastic component, Jr, is much smaller than the plastic one, Jp, and can be ignored. For a penny-shaped crack of length, 2a, in a solid of Young's modulus, E, subjected to a remote stress, cro~, the J-integral for large-scale yielding is given by [32]

h /Ep'~

where Ee and % are the elastic and plastic strains, respectively,

3 h (9)

2~/1 + 3/n

and

which can be combined with equation (8) to give

J 0.405rcho.ya[Ep]l +./n - ( l l ) [~Ey] TM

when the Osgood-Ramberg equation [31]

E_p_p

Ey kay//

with a =ooo, Ee = alE, and Ey = %/E is used. Substi- tuting equation (11) into equation (6) leads to

Jr-1 " / ' ' C / r v1-q ~ l+b__z7 ) .j 03)

CHAN: HYDRIDE-INDUCED EMBRITTLEMENT 4329

with g, being the local effective strain at r, and

_ 1 f ,o Tin+, c -- ~ L ~ _ [ (14)

after the expression for Q, equation (7), is incorporated. In equation (14), gn(0) is the effective value for the normalized coefficient, gu(0).

Equation (13) relates the local effective strain, ~,, at location r in the matrix ligament to the nominal plastic strain, %. Fracture of the hydrided material is taken to commence when the local effective strain, ~r, reaches the matrix fracture strain, Era, at r = d/fl and 0 = 0 ~ where d is the grain size, and fl is a constant, usually 2. The nominal fracture strain, Ef, or tensile ductility at the onset of fracture, is then obtained from equation (13) by setting g,=em, Ep~--/~f, and r = d/fl , leading to

CEmZn/, + n Ef = ,/~ +, (15) ( z )

1 + -2((_1/2- 1)--z

where z = d/(f la) . In one defines Er(~0) as the refer- ence fracture strain, one obtains a normalized fracture strain ratio, R, by dividing Er(~) by El(fro), resulting in

1+ R = ~:r(~) ((01/2 -- 1) - z (16)

( z )"/"+~ s 1 Jr "2(~_1/2~ - l) - -Z

which is zero when ~/2 = 2/2 + z, but has a value of unity when ( = ~0. Since r cannot be set to zero, ~0 = 1 x 10 -4 is generally used. Such a small value of ~0 means the solid is essentially free of any hydrides,

and El((0) approximates the matrix fracture strain. The advantage offered by equation (16) is that the values for En(0 = 0), I . , and Era, are not explicitly required.

For elliptical cracks in plate-like hydrides, the J-integral, Jmaj, in the major crack direction is taken as

J a Jm~j = ~-5 ( c ) (17)

while the J-integral, Jm~,, in the minor crack direction is approximated as

J Jmin = ~--5 (18)

where q~ is an elliptical integral of the second kind. Equations (17) and (18) are obtained by assuming that the geometry correction factor for elastic elliptical cracks [33] also applies to plastic elliptical cracks.

Normal i zed tensile ductility

The tensile ductility of the hydrided material can be considered to contain two contributions: one from the hydrides and one from the matrix ligaments. By summing these two components, the tensile ductility of the hydrided material normalized by tensile ductility of the matrix, Er/Em, is obtained as

E r = ( I_EH']R 'H + - - (19) Em \ Em// Em

where R, given by equation (16), represents the normalized ductility of the matrix ligament, and En is the tensile ductility of the hydride. According to equation (19), E r / E m = 1 when ( = (0, and ErIE m = EH/Ern when (1/2= 2/(2 + z), a condition that occurs when the hydride network is almost continuous.

Z

w N

n. 0 Z

10'

10-'

10 -z

s = a

/

large s l small l _ _ m

i I ~ I ~ I

0.0 2.0 4.0 6.0

Disk-Like Hydrides a = 3,Ltm d= lOltm h = 0.5 txm

f ' sma. s ' large l

I .. i I 1

8.0 10.0

VOLUME FRACTION OF HYDRIDE, Fig. 6. Calculated normalized tensile ductilities for closely spaced (large s, small l) and widely spaced (small s, large l) hydride networks. The closely spaced hydrides are more detrimental to tensile ductility

than the widely spaced hydrides.

4330 CHAN: HYDRIDE-INDUCED EMBRI'IYI'LEMENT

(/1

r~ t.d N "1 .<

n.. 0 z

lO 0

10-'

Spherodial Hydrides

\

a= 3p.m d= 10 pm s = a

10 " I , I , I , I , I , I

0 . 0 3.0 6.0 9.0 12.0 15.0

VOLUME FRACTION OF HYDRIDE, % Fig. 7. Calculated normalized tensile ductilities for networks of disk-like and spheroidal hydrides~

Disk-Iike hydrides are more detrimentaI to tensile ductility than spheroidal hydrides.

DEGRADATION OF TENSILE DUCTILITY BY HYDRIDE EMBRrUI'LEMENT

The model has been utilized to examine the dependence of the tensile ductility of a hydrided material as a function of volume fraction, morphology, and distribution of hydrides. Figure 6 shows comparison of calculated normalized tensile ductility as a function of volume fraction of hydrides for two different distribution patterns of disk-like hydrides, which are: (1) large stacking spacing, s, and small in-plane

spacing, 1 (a = 3 #m, s = 10 #m, and h = 0.5 pm); and (2) small stacking spacing, s, and large in-plane spacing, l ( a = s = 3 #m, h = 0.5 #m). The former hydride configuration leads to a lower tensility for a given volume fraction of hydrides when compared to the latter configuration. In both cases, the normalized tensile ductility decreases precipitously when the hydride network becomes almost continuous. The pre- cipitous drop in tensile ductility was triggered by the overlapping strain fields of the microcracks and a

lo 0 >..

5

i10-' E3 Ld N "1 .<

rv" O Z 10 -=

Fine Grain

Large Grain ~ ~b =3.75 b " 2a

Large Grain \ ~ \ I " u u . "1

E - 7 7 7 " = 1 ~ I - - - - I I a = c . 0 . e ~ a n .tuuu~uI I a .e .z~ I n-ew.

�9 " l . . . = , l ~ b.6~" I ~;lo~ L%L i i o a.r I I

s=d=10pm

Rod-Like Hydrides

0.0

, I i I , I i I , i 1

8.0 16.0 24.0 52.0 40.0

VOLUME FRACTION OF HYDRIDE, % Fig. 8. Dependence of calculated normalized tensile ductility on the aspect ratio, b/2a, and grain size for

rod-like hydride networks.

CHAN: HYDRIDE-INDUCED EMBRITTLEMENT

lO 0

__i 10-'

"1 '<C ~E i v , o Z

10 -=

Minor Axis Direclion

Plate-Uke Hydrides s=d=10 tm / I n= 0 I ; = ' = ' I

\ ~ 12ac::) C:>--l-- MajorAxis \ I Direc~on

\ \

n t n I Front View I Side view

a= 0.8 rtm a= 0.81un c =31,tin c =0.81~ b = 61.tin b=61Jtm

0 .0

, I , I , I , I , I

3 . 0 6 . 0 9 . 0 12 .0 15 .0

VOWME FRACTION OF' HYDRIDE, % Fig. 9. Calculated normalized tensile ductilities for plate-like hydrides fracturing in the major and minor

directions of the platelets. The latter case was calculated using a = c = 0.8 #m.

4331

ligament size less than d/fl, where ]~ = 2 unless stated otherwise.

Calculated normalized tensile ductility results for disk-like and spheroidal hydrides are shown in Fig. 7. The appropriate values for the microstructural parameters are indicated in the figure. As expected, the spheroidal hydrides are less prone to hydride embrittlement than the disk-like variety because a continuous network of spheroidal hydrides is more difficult to form and requires a higher hydrogen content per unit crack length.

Comparison of calculated tensile ductilities for rod-like (b/2a = 3.75) and cylindrical (b/2a = 1) hydrides is presented in Fig. 8. The result indicates that the material with cylindrical hydrides is less prone to embrittlement than rod-like hydrides, which is analogous to the behavior observed in the materials containing spheroidal and disk-like hydrides. Figure 8 also shows comparison of the calculated tensile ductilities in large-grained and fine-grained materials with rod-like hydrides. The calculation shows that the fine-grained material is less susceptible to hydride embrittlement because the critical strain at fracture is monitored at r = d/2.

The degradation of tensile ductility by plate-like hydrides is illustrated in Fig. 9, which shows the calculated tensile ductilities for fracture in the major and minor directions of the plate-like hydride network. The tensile ductility has been found to be smaller in the major axis direction when compared to that for the minor axis. The latter case was computed using a = c = 0.8 #m. Again, the difference in the ductility behavior is caused by a longer crack front,

and a smaller link-up distance in the former hydride orientation.

MODEL APPLICATIONS FOR ZIRCALOYS

The validity of the proposed model is examined by comparing model calculations with experimental data for Zircaloys in the literature. Lin et aL [8] have reported experimental results of reduction in area for Zircaloy-4 as a function of hydrogen content. The hydrides in this material had a plate-like morphology. Fracture strain, Ef, and volume fraction of hydrides were calculated from reduction-in-area and hydrogen content, respectively. Furthermore, Lin et aL [8], also reported the total elongation of Zircaloy-2 for various hydrogen contents. In recent papers, Bai et aL [14, 15] presented experimental data of reduction-in- area as a function of volume fraction of hydrides for Zircaloy-4 in the stress-relieved, recrystallized, and fl-treated conditions. In the former two conditions, the hydrides were aligned either parallel to the stress- axis or randomly aligned. In the fl-treated conditions, the hydrides were localized in the interfaces of the or-phase (Zr) platelets. The fl-treated microstructure contained a continuous hydride network that led to a substantial loss in tensile ductility. These experimental data have been used as the basis for comparison against model calculation.

Input to the model includes hydride diameter, 2a; stacking spacing, s; grain size, d; thickness, h, for hydride platelets; and the inverse of the strain hardening exponent, n. A wide range of hydride size has


,3

"1 Or) Z

(:3

N " i

rv" O Z

lO*

10-'

10 -~ O.O

�9 o

o o o ?; ,,.,v,,, o,..,r,,,=,,y.,., 25"C a = 3 pm

o Experimental Data (Lin eta/.) d = 10 I.tm

Model h = 0.5 ~rn s =3 p.rn n=10

= I = I i I , I , l

2.0 4,0 6.0 8 .0 tO.O

VOLUME FRACTION OF HYDRIDE, % Fig. 10. Comparison of calculated normalized tensile ductility against experimental data from Lin et al.

[8] for Zircaloy-2 containing hydride platelets.

been reported in the literature. Using transmission electron microscopy, Carpenter [34] determined that the size of y hydride in Zr ranged from 0.15 to 8/~m in length, 0.05 to 2 ~m in width, and 0.01 to 0.04 #m in thickness. L ine t al. [8], did not report any information on the hydride size for the Zircaloy-2 and Zircaloy-4 materials tested in their study. The hydride sizes for the Zircaloy-4 studied by Bai e t al. [14, 15], were 15-20 #m in length and 0.1-1 p m in thickness. Hydride thickness in the range of 0.1-2.5 #m has also been reported by others [11, 16, 35]. For Zr-2.5 Nb, Choubey and Puls [13] have reported hydride 50-100#m in length and 1 #m in thickness. Since

there is no information about the hydride size in the material tested by Lin et al. [8], the hydride size was chosen to be in the lower range of the size distribution spectrum. In particular, hydride platelets were modeled as disk-like hydride with a = 3/~m, h = 0.5/~m, and d = 10/lm. For spheroidal hydrides, a = 3 gm, s = 8.5 #m, and d = 10 #m. For the Zircaloy-4 studied by Bai e t al. [14, 15], the hydride size reported by the authors was used, i.e. a = 10 #m, h = 1 #m; and s = 6 - 3 0 # m and d = 30#m were assumed. In all calculations, a value of n = 10 was used to reflect the lack of hardening in the hydrided materials, and fl = 2. The value ofs m = 0.0154.037 was obtained

--I

5 Z) rm

(/)

r~ Ld N --I

n-

O Z

io

10-'

Zircaloy, 25"C I Spheroidized Hydn'de

o Experimental Data (Lin et al.) Model

a = 3.0 I.tm s = 8.5 I.tm d = 10 l.tm n=10

1 0 - I , I , I , l , I , I

O.0 3.0 6.0 9.0 12.O 15.0

VOLUME FRACTION OF HYDRIDE, % Fig. 1 l. Comparison of calculated normalized tensile ductility against experimental data from Lin et al.

[8] for Zircaloy-4 containing spheroidal hydrides.

(:3 i , i N "3 <I:

I:E O Z

lo*

10-'

CHAN:

Zircaloy-4, 25"C Experimental Data (Bai et al.) o reerystalized A stress relieved $ beta-annealed

HYDRIDE-INDUCED EMBRITTLEMENT

0 & &O

large s small 1

Model a= 10 I.tm d = 20 lam h= lt.tm n= lO

small s large l

/ s = 6 g m s = 30 lam

- - # - e - # - - ~ $ o c e e

1 0 -2 , I , I , I , I , I

0 . 0 2 .0 4 . 0 6 .0 8 . 0 10.0

VOLUME FRACTION OF" HYDRIDE, % Fig. 12. Comparison of calculated normalized tensile ductility against experimental data from Bai et al.

[14, 15] for Zircaloy-4 containing hydride platelets in three different microstructures.

4333

based on experimental data reported by Lin et al. [8], and Bai e t al. [14, 15].

Comparison of the calculated results with the experimental results of Zircaloy-4 from Linet al. [8], is shown in Fig. 10. Disk-like hydrides were assumed in the model calculation. The good agreement between model calculation and experiment in Fig. 10 suggests that the tensile ductility of a zirconium alloy containing hydrides depends on the hydride morphology and distribution. Specifically, a continuous hydride network is detrimental to the tensile ductility of zirconium alloys.

One of the means for mitigating hydride embrittlement in Zircaloy-2 is to form the hydrides into spheroids using heat-treatment techniques. Lin et al.

[8], have reported such an experiment. They have found that as expected, the spheroid hydrides are less detrimental to tensile ductility when compared to the plate-like hydrides. Comparison of the calculated normalized tensile ductility for Zircaloy-2 against the experimental result of Line t al. [8], is presented in Fig. 11. Both the experimental and theoretical results indicate that Zircaloy-2 can tolerate more than 6 vol.% in hydrides without suffering from a severe loss of tensile ductility when the hydrides are in the form of spheroids. In comparison, Zircaloy-2 suffers a severe loss of tensile ductility when the plate-like hydrides are more than 6 vol.%, as shown in Fig. 10.

AM43/12--1

Recent investigations by Bai e t al. [14, 15], indicate that the tensile ductility of hydrided Zircaloy-4 sheets is substantially lower in the /~-treated condition (1030~ than in either the stressrelieved (460~ h) or the recrystallized condition (650~ h), because of the formation of a continuous hydride network in the /~-treated material. The model has been used to calculate the normalized tensile ductility of the Zircaloy-4 in the three heat-treated conditions by using the microstructural parameters described earlier. In particular, the stacking spacing, s, has been varied to reflect the larger prior grain size and interface precipitation in the /~-treated material. The larger value results in a smaller in-plane spacing, l, for a given volume function. Comparison of the calculated and observed tensile ductilities as a function of volume fraction of hydrides is presented in Fig. 12. In accordance with experimental observations, the lower tensile ductility in the //- treated material is the consequence of a more continuous hydride network with a smaller in-plane spacing for the hydrides. The observed microstru- ture/fracture relationship is somewhat analogous to the idealized situation considered in the calculations shown in Fig. 6, which shows a more closely spaced hydride network is more susceptible to a loss of tensile ductility than one with widely spaced hydrides.


DISCUSSION

The present analysis reveals that hydrides reduce tensile ductility in three ways: (1) by lowering the plastic strain for initiation of microcracks to En; (2) by increasing plastic flow concentration within the matrix; and (3) by providing a crack path for easy crack propagation if the hydride network is continuous. The loss in tensile ductility occurs even though the intrinsic ductility of the matrix, which is taken to be the tensile ductility of the matrix alloy in the absence of hydrides, has not been altered and remains at E m throughout the various calculations. The implication is that hydride-embrittlement is essentially a flow localization phenomenon in which the hydrides act as initiation sites for microcrack formation. Whether a loss of ductility occurs or not depends on the flow localization process in the matrix ligaments connecting the hydride microcracks and the continuity of the hydride network.

The effects of hydride size, spacing, and distribution on tensile ductility are basically a manifes- tation of the distance that the crack-tip plastic zones of the microcracks must extend in order to overlap, concentrate, and accelerate the flow localization process in the matrix ligament. In contrast, the influence of hydride morphology on tensile ductility is a reflec- tion of the amount of hydride required per unit microcrack formation. For example, the volume of hydride associated with fracturing a spheroid of diameter 2a is considerably larger than that for a thin disk of diameter 2a. As a result, a thin film of continuous hydride is most detrimental as far as tensile ductility is concerned, as demonstrated in Fig. 6 and experimentally by Bai et al., using a fl-treated Zircaloy-4.

While developed mainly for Zr-alloys, the proposed model should also be applicable to Ti- [21, 22], Ti3A1- [36-39], and TiAl-alloys [39] where the formation of hydrides often leads to a loss in tensile ductility and fracture toughness. Previous work [40] indicated that titanium hydrides exhibited a limited ductility of about 2% plastic strain prior to fracture in compression. This finding was contrary to the observation of zero ductility for zirconium hydrides tested in compression at temperatures below 100~ [41]. Because of the tensile ductility in the titanium hydrides, application of the proposed fracture model to hydride-induced embrittlement in Ti-base alloys might require a fracture criterion (e.g. a critical strain criterion) for the formation of microcracks. This can be readily incorporated into the fracture model by a proper choice of the value of the EH/E m

ratio in equation (19). The application of the proposed model to Ti3Al-base alloys might also be complicated by the formation of an orthorhombic phase in the microstructure. The model should also be applicable to treating the well-known detrimental effects of graphite flakes on the ductility of cast irons.

In this case, the graphite network in cast iron is very similar to the hydride network in Zr-alloy~ Grain boundary embrittlement [42-44] resulting from the, segregation of tramp elements to form a semicontin- uous or continuous brittle layer along grain boundaries might also be addressed using the proposed model.

CONCLUSIONS

1. A fracture model has been developed for treating hydride-induced embrittlement in Zr-alloys. The model is successful in predicting the dependence of tensile ductility of Zircaloys on hydride morphology, volume fraction, and distribution.

2. Hydrides instigate a loss of tensile ductility in Zircaloys by providing microcrack initiation sites, accelerating the flow localization process in the matrix, and creating an easy path for crack propagation.

3. The reduction in tensile ductility by hydride embrittlement increases with the continuity of the hydride network. The most damaging hydride network morphology is a continuous thin film along grain boundaries or interfaces.

Acknowledgements--This research was sponsored by the Internal Research Program of Southwest Research Institute. K. S. Chan is grateful for the support provided by the Advisory Committee for Research. Clerical assistance by Ms Julie McCombs is appreciated.

REFERENCES

1. D. O. Northwood and U. Kosasih, Int. metall. Rev. 2,8, 92 (1983).

2. C. E. Ells, The Metallurgical Society of CIM. Annual Volume (1978).

3. C. E. Coleman and D. Hardie, J. less-common Metals 11, 168 (1966).

4. C. J. Beevers, Electrochem. Technol. 4, 221 (1966). 5. W. Evans and G. W. Parry, Electrochem. Technol. 4,

231 (1966). 6. R. P. Marshall and M. R. Louthan Jr, Trans. Am. Soc.

Metals 56, 693 (1963). 7. B. J. Gill, J. E. Bailey and P. Cotterill, J. less-common

Metals 40, 129 (1975). 8. S-C. Lin, M. Hamasaki and Y-D. Chuang, Nucl. Sci.

Engng 71, 251 (1979). 9. D. O. Pickman, Nucl. Engng Design 21, 212 (1972).

10. L. A. Simpson, Metall. Trans. 12A, 2213 (1981). 11. M. P. Puls, Metall. Trans. 19A, 1507 (1988). 12. M. P. Puls, Metall. Trans. 22A, 2327 (1991). 13. R. Choubey and M. P. Puls, Metall. Trans. 25A, 993

(1994). 14. J. B. Bai, C. Prioul and D. Francois, in Proc. ICM 6

(edited by M. Jono and T. Inouoe), Vol, 731. Kyoto, Japan (1991).

15. J. B. Bai, C. Prioul and D. Francois, Metall. Trans. 25A, 1185 (1994).

16. Y. Fan and D. A. Koss, Metall. Trans. 16A, 675 (1985). 17. C. K. Chow and L. A. Simpson, in Case Histories

Involving Fatigue and Fracture Mechanics (edited by C. M. Hudson and T. P. Rich), ASTM STP 918, 78. ASTM, Philadelphia, Pa (1986).

18. R. Dutton, K. Nuttall, M. P. Puls and L. A. Simpson, Metall. Trans. 8A, 1553 (1977).

CHAN: HYDRIDE-INDUCED EMBRITTLEMENT 4335

19. L. A. Simpson and M. P. Puls, Metall. Trans. 10A, 1093 (1979).

20. M. I . Puls, Metall. Trans. 21A, 2905 (1990). 21. R. I. Jaffee and D. N. Williams, Trans. Am. Soc. Metals

51, 820 (1959). 22. N. E. Paton and J. C. Williams, in Hydrogen in Metals

(edited by I. M. Bernstein and A. W. Thompson), p. 409. ASM, Materials Park, Ohio (1974).

23. C. J. Beevers and D. V. Edmonds, Trans. Am. Inst. Min. Engrs 245, 2391 (1969).

24. R. C. Bourcier and D. A. Koss, Seripta metall. 16, 515 (1982).

25. J. E. Hack and G. R. Leverant, Metall. Trans. 13A, 1729 (1982).

26. H. G. Nelson, Metall. Trans. 4A, 364 (1973). 27. J. R. Rice, J. appl. Mech. 35, 379 (1968). 28. J. W. Hutchinson, J. Mech. Phys. Solids 16, 13 (1968). 29. J. R. Rice, J. Mech. Phys. Solids 16, 1 (1968). 30. J. W. Hutchinson, J. appl. Mech. Trans. ASME SO, 1042

(1983). 31. M. F. Kanninen and C. H. Popelar, in Advanced

Fracture Mechanics, pp. 299 300. Oxford University Press, New York (1985).

32. N. E. Dowling, Engng Fract. Mech. 26, 333 (1987).

33. G. R. Irwin, Trans. ASME, J. appl. Mech. 29, 651 (1962).

34. G. J. C. Carpenter, Acta metall. 26, 1225 (1978). 35. X. Q. Yuan and K Tangri, J. nucl. Mater. 105, 310

(1982). 36. W-Y. Chu, A. W. Thompson and J. C. Williams, in

Hydrogen Effects on Material Behavior (edited by N. Moody and A. W. Thompson), p. 543. TMS, Warren- dale, Pa (1990).

37. W-Y. Chu and A. W. Thompson, Metall. Trans. 23A, 1299 (1992).

38. K. S. Chan, Metall. Trans. 24A, 1095 (1993). 39. D. Legzdina, I. M. Robertson, and H. K. Birnbaum,

J. Mater Res. 6, 1230 (1991). 40. P. E. Irving and C. J. Beevers, J. Mater. Sci. 7, 23

(1972). 41. K. G. Barraclough and C. J. Beevers, J. Mater. Sci. 4,

518 (1969). 42. D. F. Stein, A. Joshi and R. P. Laforce, Trans. ASM 62,

776 (1969). 43. A. Joshi and D. F. Stein, J. Inst. Metal. 99, 178

(1971). 44. R. G. Thompson, C. L. White, J. J. Wert and D. S.

Easton, Metall. Trans. 12A, 1339 (1981).

a fracture model for hydride-induced embrittlement

Documents