On the notch sensitivity of the ductile intermetallic Ni3Al containing boron

Pergamon

0956-7151(95)00252-9

Acra mafer. Vol. 44, No. 4, pp. 1601-1612, 1996 Elsevier Science Ltd Copyright 0 1996 Acta Metallurgica Inc. Printed in Great Britain. All rights reserved 1359-6454/96 $15.00 + 0.00

ON THE NOTCH SENSITIVITY OF THE DUCTILE INTERMETALLIC Ni,Al CONTAINING BORON Y. XU and E. M. SCHULSON Thayer School of Engineering, Dartmouth

College, Hanover, NH 03755, U.S.A.

(Received 13 March 1995; in revised form 5 June 1995) Abstract-Experiments and calculations have shown that the notch sensitivity of the ductile aluminide N&Al(B) is related to the suppression of plastic flow by the triaxial state of tensile stress produced by the notch. Cracks initiate at the tip of the notch, where stress and strain are concentrated, and then propagate intergranularly when the degree of triaxiality exceeds a critical level.

1. INTRODUCTION As intermetallics enter engineering service, it becomes important to understand the effects of notches and holes on their mechanical behavior. Such features, while usually avoided in the laboratory, are often part of design. A case in point, and the subject of this paper, is the strongly ordered Ll, aluminide N&Al. It has now been established that by alloying Ni-rich derivatives of this alloy with a small amount of boron a large amount of ductility can be imparted to otherwise brittle polycrystals [ 1,2]. Boron segregates to the grain boundaries where, through a process or processes still under debate, it suppresses intergranular fracture. Global flow ensues and elongation of 40% or more is realized before fracture occurs trans-granularly under a tensile stress around 1500 MPa. It has also been established that a notch re-activates intergranular fracture [3,4]. Material, which has smooth bars exhibits the properties noted, fractures when notched under low stresses after less deformation. N&Al(B), in other words, is notch sensitive, which is to say that a notch (and presumably a hole) reduces its loadbearing capacity by more than the reduction in area. A notch intensifies stress and strain, introduces a triaxial state of tensile stress, and raises the strain rate at its tip. It may also exacerbate environmental embrittlement. Which of these factors accounts for the notch sensitivity of N&Al(B) is the question addressed in this paper. While the discussion is limited to N&Al, the findings may be relevant to Zr, Al, an isostructural ductile aluminide that is also notch sensitive [5]. 2. PROCEDURES

wise noted) Ni-24 at.% Al-O.3 at.% B of 9.5 pm grain size. The specimens were prepared from the same extrusion of an alloy used in an earlier study [6] where the effect of grain size on the yield stress was investigated. The preparation and processing of the material were described in the earlier work. Both smooth bars and double-edge V-notched bars of the material were tested in tension using a floormodel Instron machine and an MTS servohydraulic system. The smooth bars were either cylindrical (2.5 mm dia x 25 mm) or prismatic (2.5 x 2.5 x 25 mm) in shape; the notched bars were prismatic in shape and had the dimensions noted in Fig. 1 (except one larger specimen shown in Fig. 4). The notches were freshly cut prior to testing using a milling machine, as might be done in practice. It is assumed that the hardened layer caused by the milling has no significant effect on the behavior, because the tensile strength and ductility of smooth bars having freshly milled surfaces was found to be essentially indistinguishable from the strength and ductility of smooth bars having electrochemically polished surfaces. The deformation field near the notch tip was examined using several techniques. Two pairs of well spaced (> 8 mm) notches were cut into some specimens and the surviving sections were examined using optical and scanning electron microscopy, Vickers microhardness indentations (25 g, 15 s) and transmission electron microscopy. The hardness measurements were made on metallographically polished sections through the center of the specimen (i.e. at x3 = 0, Fig. 2), and the TEM foils were prepared as described elsewhere [6]. Also, metallic grids were deposited on the surface across the reduced sections, as described elsewhere [7], and then examined in a scanning electron microscope after various levels of loading.

2.1. Experimental

2.2. Calculations

Experiments were performed at room temperature on randomly oriented polycrystals of (unless other-

The stresses and strains throughout region were estimated from numerical 1601

the notched calculations.

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XU and SCHULSON:

NOTCH

test series variable

desig-

SENSITIVITY

OF INTERMETALLIC

N&AI

I

dimensions

t (mm) w (mm) a (mm) p (mm) 0 (“) I -1 I

8

/

?!i W

e

P

a

Q

Fig. 1. Dimensions

and shape

These were performed using the ABAQUS” finite element code. The alloy was modeled as an elasticplastic solid that work hardens linearly, more or less n keeping with its behavior [6]. Young’s modulus was taken as 200 GPa [8], Poisson’s ratio as 0.4 [8], the yield stress as 450 MPa [6] and the work-hardening rate as 5000 MPa [6]. Meshes were used comprised of eight-node, linear displacement, brick-like elements and six-node, linear displacement triangular prisms, Fig. 2. Owing to symmetry, only one-eighth of the specimen was modeled. The procedure was checked by performing calculations of the stress and strain

of the notched

specimens.

distribution around notches in elastic-perfectly plastic solids and by finding that the results [7j compared very well with those obtained from analytical solutions [9, lo] of this case. Also, the calculated deformation fields were found to be in good agreement with the observed fields, as described in Section 4. That the elements were small enough to allow convergence was established by performing calculations (of plane strain deformation, &jj = 0) using elements 25% larger than shown in Fig. 2 and finding that the results were essentially indistinguishable from those obtained using the finer mesh.

I I / / /

x1

k ‘\

\

x3

I

,/I

x2

4 I I

>

(4 Fig. 2. Meshes used in numerical

(cl calculations for: (a) the sharply; The coordinate system is shown

and (b) the bluntly in (c).

notched

specimens.

XU and SCHULSON:

3. EXPERIMENTAL RESULTS 3.1. The dominant factor 3.1.1. Strain rate? The strain rate at the root of a notch is greater than elsewhere, approximately by a factor of L/2p, where J is the nominal gauge length of the bar and p is the radius of curvature of the notch. In the present work this ratio was as high as 300. If the strain rate were the dominant factor underlying the notch sensitivity, then smooth bars should be less ductile when rapidly deformed. This, however, was not observed. Instead, the tensile ductility in air at a strain rate of 7 s-i (imparted using the MTS system equipped with an accumulator) was essentially the same as that at 10m4s-l, Table 1. Also, the yield strength, the tensile strength and the fracture mode were essentially the same as measured at the lower rate. The elevated notch-tip strain rate, therefore, is not the dominant factor underlying the notch sensitivity of N&Al(B). This is not a surprising conclusion, because N&Al is not rate sensitive at room temperature. 3.1.2. Environment? Moisture embrittles boronfree Ni-rich N&Al [ll-141 but has little effect on boron-doped material [15,16], implying that the external environment should have little effect on the present alloy. To confirm this point, tests were performed in both air and dry oxygen on notched bars of the dimensions noted in Fig. 1. The displacement velocity was 10-3mm.s-‘, giving a notch-tip strain rate of about 10-2s-1. The notched bars behaved in the same manner in both environments: they broke through an approx. 50/50 mixture of intergranular and transgranular fracture at a notchsection stress between 1020 and 1050 MPa after a reduction in area between 14 and 15%. That the environment was dry enough was established from separate tests on smooth bars of boron-free material of similar grain size and Ni:Al ratio, prepared as described elsewhere [6], which reproducibly showed greater elongation (4-5% vs 2-3%) in the dry oxygen. Moisture, therefore, is not the factor that re-activates intergranular fracture. 3.1.3. Triaxial stress state? This leaves the stress state. Owing to its triaxial character, the stress state introduced by a notch exerts a constraint on plastic deformation. This raises the whole stress-strain curve for the sub-surface elements. The surface elements, however, still yield at the uniaxial yield stress because the stress state there is only biaxial and biaxial stresses do not raise the yield stress of plastically isotropic materials like N&Al(B). Thus, while yield-

Table 1. Tensile properties of N&AI(B) tested at two different strain rates at room temperature Smooth bar strain rate (SC’) Elongation to fracture (%) Yield strength (MPa) Tensile strength (MPa)

10-a 33 390 1480

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NOTCH SENSITIVITY OF INTERMETALLIC N&Al

7.1 36 430 1540

ing can begin at the notch tip when the axial stress reaches the uniaxial yield stress, it cannot extend much beyond the tip until the axial stress increases. Should fracture intervene, the overall ductility would be reduced. It follows that if the notch sensitivity is related to the triaxial tension, then it should be more pronounced in large sections; i.e. in sections both thick enough and wide enough to support large tensile stresses across the width and through the thickness. Tensile tests were thus performed in air on wide (w = 2 mm) notched bars of different thicknesses (0.2-2 mm, Series B, Fig. 1). To avoid variations in microstructure, the specimens were sliced from the same parent extrusion. Again, the displacement rate was 10m3mm. SK’, leading to a notch-tip strain rate of about lo-’ SK’. Figure 3 shows the results. Upon increasing the thickness, the fracture plane changed from slanted (by about 45” to both xi and x3) to flat, except near the notch root where, as noted earlier [4], shear zones about 50-100pm wide developed owing to the largely biaxial stress state there. Correspondingly, the fracture mode changed from predominantly ductile transgranular to the 50/50 mixture of intergranular and ductile transgranular noted above. Only a small amount (about 10%) of intergranular fracture was detected on the fracture surface of the thinner specimens. The fracture mode transition occurred somewhat abruptly, at a thickness of about 1.5 mm. This corresponds to about twice the size of the notch-tip plastic zone for plane stress deformation, as calculated from the relationship: tC=2rp=2(K,,/a,)*/27C

= 1.4mm

(1)

where K,= is the fracture toughness (30 MPa . ml’*, [17]) and CT~is the yield stress (450 MPa, [6]). Equation (1) suggests that for the specimens thinner than about 1.4 mm, the plastic zones at the notch tips may overlap throughout the entire thickness. This overlap will be eliminated in the thicker specimens, the center of which undergoes more plane-strain-like deformation. Accompanying the transition of the fracture mode was a decrease in ductility, from a reduction in area (RA) of about 20-24% to about 14-16%, Table 2. The fracture stress was significantly lower than that Table 2. Summary

Thickness (mm) 0.20 0.24 0.41 0.44 0.52 1.09 1.13 1.29 2.51

of tensile properties of notched different thickness

Width (mm) 2.01 2.02 1.93

1.96 1.91 1.93 2.10 2.11 2.00

Fracture stress (MPa) 908 880 907 1020 1020 1080 1070 1070 1120

Reduction in area (%) 19.7 20.5 23.6 23.1 16.5 15.5 14.7 16.0

specimens Intergranular fracture (%) 10.2 12.8 5.5 17.7 14.9 27.6 31.9 44.2 53.1

with

1604

XU and SCHULSON:

NOTCH SENSITIVITY OF INTERMETALLIC

Ni,Al

i

0

0 0

.l

1

10

tc

Thickness (mm)

of smooth bars (i.e. 1010 f 70 MPa vs about 1500 MPa, Table 1) but showed little systematic variation with thickness. It is concluded, therefore, that the notch sensitivity of N&Al(B) and the attendant re-activation of intergranular fracture are related to the tensile triaxiality of the stress state. 3.2. Effect of notch acuity The behavior was affected by the notch tip radius. An increase from p = 0.04 to 0.5mm (Series C, Fig. 1) raised the fracture stress of a wide Table 3. The notch-section

B = WP (T, (MPd

p = l/O.04 = 25 1010 + 90

(W = 2 mm), thick (t = 2 mm) bar from about 1000 o 1520 MPa. Correspondingly, only about the central third of the specimen broke via the SO/SOmixed mode fracture, compared with about three-quarters for the more sharply notched bars. On the other hand, the behavior was not significantly affected by the depth of the notch, at least when varied by a factor of two. This point was established from an experiment in which the notch depth, a, but not its radius of curvature (p = 0.04 mm), was reduced from 0.5 to 0.25 mm in a wide, thick bar (W = t = 2 mm) (Series D, Fig. 1). Fracture occurred at a notch

fracture stress versus notch acuity f3

p = 0.5jo.04 = 13 1090

/3 = p;.g.,,=

2.5

j3 = l/O.5 = 2 1500

p=o 1510 + 40

XU and SCHULSON:

NOTCH SENSITIVITY OF INTERMETALLIC N&Al

section stress of 1090 MPa at RA = 15%, again through the SO/SOmixture. These observations indicate that the notch acuity can affect the behavior of thick bars. If notch acuity is defined as /I = 2n/p, then it appears that as the acuity decreases from around 25 to a value between 13 and 2.5 the fracture stress increases from around 1000 MPa to that of the smooth bar, Table 3. Presumably, the transition to the smooth-bar-like behavior corresponds to the

1605

triaxiality of the stress state falling below a critical level (more below). 3.3. Notch-tip

deformation

Figure 4 shows a sharp @ = 0.04 mm) and a blunt (p = 0.5 mm) notch in two double-notched specimens. It is assumed that the sections shown were on the verge of breaking, because the specimens were loaded until they broke at the other notch. From the

Fig. 4(a-c). See caption overleaf.

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XU and

SCHULSON:

NOTCH

SENSITIVITY

patterns of reflected light, it can be seen that plastic strain was concentrated near the tip of the sharper notch, within four lobe-like regions, but was more uniformly distributed throughout the reduced section in the more bluntly notched bar. Microhardness measurements confirmed these impressions. The hardness of the more sharply notched bar reached about 240 at around 100 pm from the notch root and then, within three notch radii across the smallest section, fell to about 150; i.e. to the level of the undeformed material, Fig. 5(a). The hardness near the more bluntly notched tip reached

OF INTERMETALLIC

N&Al

a similar level, of about 230, but decreased less rapidly across the section and never fell to the level of the undeformed material, Fig. 5(b). These measurements also indicate that just prior to fracture the plastic strain near the notch tip (i.e. at x2 = 100 pm) reached about 0.2, independent of the notch acuity. This estimate was obtained from the hardness of about 240 obtained from a smooth bar specimen lengthened by 20%. That plastic strain was confined to the region near the tip of the sharp notch was further confirmed using transmission electron microscopy. Within a thin foil

/--_ /.I;: u

‘1

/ . -----

Fig. 4. Notch

tip deformation

\

/

of (a-c) a sharp and (d+) a blunt notch. Note the sharp-notched has the dimensions 5.7 x 5.7 x 50 mm.

1

specimen

XU and SCHULSON:

NOTCH SENSITIVITY

taken a few notch radii from the tip the dislocation structure was essentially the same as that within a foil taken through the center of the specimen, Fig. 6. In both regions, the dislocation density was similar to that within a smooth bar shortened by about 2% [6]. Further examination showed that the fracture of both the sharply and the bluntly notched specimens initiated at the root of the notch. This point was evident from the existence of short cracks emanating from the roots, Fig. 4(b) and (e). The cracks nucleated intragranularly and were parallel to the slip plane in a number of grains, Fig. 4(c). This implies that they formed through dislocation interactions once sufficient plastic strain had been imparted, a point currently being examined using notched single crystals. The cracks became oriented approximately normal to the axial stress as they entered the region of triaxial tension behind/beneath the notch [Fig. 4(c)]. Presumably a similar scenario occurred at the broken notch and the crack there propagated in a mode-1 manner when the stress intensity factor reached its critical value; i.e. K, = K,, . Supporting this view is the fact that in the more sharply notched specimen shown in Fig. 4 (a+): K, = YCJ (nc)“‘=

1.1 x 937

x (n x 0.25 x 10-3)1/2 = 29 MPa . ml/‘,

(2)

which is close to K,, of about 30 MPa rn1j2 [17]. Curiously, Khadkikar et al. [4] reported that cracks initiated near the center of their specimens. In the present tests, cracks were not detected there after

(a) 00 Q 0

0

o

1.50 -

100 -0.5

Oo o0.0

0.5

1.0

1.5

OF INTERMETALLIC

1607

carefully preparing and polishing sections through the center of both the sharply and bluntly notched bars, perpendicular to the notch. The difference may be related to a difference in notch acuity and strain gradients. Their specimens were circumferentially notched and the ratio of section diameter to notch radius was 7, compared with our ratio of section width to notch radius of 25 to unity. The difference may also be related to a difference in microstructure, for their material contained pores which could have acted as sites for crack initiation. Returning to the deformation field, a more quantitative measure was obtained from the distortion of the metallic grids, Fig. 7. These were deposited at three locations (at x2 = 80, 300 and 500 pm) across two reduced sections (x1 = 0) of the more bluntly notched bar described above. The lines on the grids were not parallel to the coordinate axes defined in Fig. 2, and so corrections were made using the transformation law for second order tensors to obtain the strains w.r.t. the coordinate system defined. Local averages were obtained from distortions measured over a set of 9 x 9 cells which embraced about 35-40 grains. The error in strain was estimated to be about kO.02. It was found that upon loading the specimen to an average axial stress of 667 MPa [point A, Fig. 7(a)] across the notch, distortion was not apparent in the grid nearest the root [Fig. 7(c)]. This means that, owing to its constraint on plastic flow, the notch effectively increased the axial stress for yielding at this site to above 667 MPa from 450 MPa for smooth bars. Upon increasing the axial stress to 892 MPa Lpoint B, Fig. 7(a)] distortion was apparent in the grid nearest the root, corresponding to a], = 0.03; no distortion, however, was seen at the center of the specimen. Upon increasing the stress further the strain increased at all points, including the center. It reached E,~ = 0.15 nearest the root when fracture occurred across the other notched section. Figure 7(e) summarizes the observations. These measurements, although made at the free surface, confirm that plastic flow spread from the notch tip as the load increased and confirm the microhardness-based estimate of the sub-surface strain at a similar site. 4. NUMERICAL

Fig. 5. Microhardness measured from the reduced section of: (a) the sharply; and (h) the bluntly notched specimens.

N&Al

CALCULATIONS

To obtain further information on the stress and strain distribution around a notch near the onset of fracture and on the triaxiality of the stress state, calculations were made using finite elements. As already noted, the procedure was checked against analytical solutions for the case of non-hardening deformation. It was also checked against the real behavior of N&Al(B). The latter check was made by calculating the equivalent plastic strain, 5, for both the sharply notched and the bluntly notched bars described above (w = t = 2 mm, a = 0.5 mm) deformed under plane stress (in recognition of the stress state at the free surface) and then by comparing

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XU and SCHULSON:

NOTCH SENSITIVITY OF INTERMETALLIC

Fig. 6. Microstructure

Ni,Al

near the tip of the sharply notched specimen.

the calculated fields with the observed fields. The calculations were performed for far-field or boundary axial stresses (on the meshes of Fig. 2) of 500 and 750 MPa for the sharply notched and the bluntly notched bars, respectively; these stresses correspond to notch-section axial stresses at fracture of 1000 and 1500 MPa. Figure 8 shows that the calculated fields compare favorably with those observed (Fig. 4). Figure 9 summarizes the calculations for the sharply notched bars of different thicknesses of Section 3.1.3. They were performed for a far-field stress of 500 MPa to simulate the conditions just prior to fracture. Shown are the equivalent plastic strain 5, the maximum principal stress CT,and the equivalent stress C. They were computed across the notched section (x, = 0) through the mid-plane (x3 = 0) of the specimens, vs the distance ahead of the notch tip, x2. The orientation of the principal axes across the smallest section is very close to the xi co-ordinate axes, because the shear stresses were much smaller than the normal stresses [7]. Note that for all specimens 5 and 0, were highest at the tip where their values were about 0.3 and 2500 MPa, respectively. These values were relatively independent

of the specimen thickness. Also, they were similar to those of the smooth bar at fracture, as seen upon converting the engineering values reported above to true values, taking into account the slight necking [i.e. E=/n (1 +a,,& =en (1 +0.34) = 0.3 and CJ,= 1510 x 1.34 = 2110 MPa]. Note also that the stress decreased quite rapidly ahead of the tip, but varied only slightly with thickness. The plastic strain also fell rapidly, but at any point within about one-to-three notch radii from the tip was higher for the thinner bars. These gradients, when coupled with the apparent constancy of the notch-tip stress and strain, account for the absence of a significant effect of thickness on the notched-bar strength and for the greater reduction in area of the thinner bars (Section 3.1.3). Figure 10 shows the calculated values of the same parameters for the more bluntly notched bar of Section 3.2 (W = t =2mm, a =0.5mm, p = 0.5 mm). The far-field stress in this case was 750 MPa, to simulate the higher fracture stress of 1500 MPa. The stress and strain gradients were lower and the strain at the center of the specimen was higher than for the more sharply notched bar at fracture, in

XU and SCHULSON:

NOTCH

SENSITIVITY

OF INTERMETALLIC

3000

1609

N&Al

c

b

2000 % 1

1000

0

I

0

-1

2

1

3

Displacement (mm)

0.2 -

a

e

0

c

b w=

O.l-

?? 0

0

:

??

0

0

A

A A

u I

0.0 0.0

0.1

-

I

0.2

-

I

.

0.3

I

0.4

-

I

0.5

-

0.6

x2 (mm> Fig. 7. Deformation field revealed by metallic grids: (a) loading history; (b) illustration of the grids on the surface of the specimen; (c) the grid at point a unloaded from A; (d) the grid at point a unloaded from F; and (e) the strain measured from the distortion of the grids.

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XU and SCHULSON:

NOTCH SENSITIVITY OF INTERMETALLIC

N&Al

stress across the notched section at fracture and for the greater reduction in area. At the notch tip 5 and 0, again reached levels similar to those of the smooth bar at fracture. This apparent reproducibility suggests that one of these parameters may define the fracture criterion (more below). Returning to the triaxiality Tof the stress state, this was defined by the relationship: T=l-

(a)

(b)

Fig. 8. Plastic zones calculated for plane stress deformation (note the boundaries of the zones correspond to 7% strain).

keeping with the observation of a more distributed notch-tip deformation field. The lower gradients account for the higher average value of the axial 0.4

fr 01 +a,+a,’

(3)

where cr2 and Q~ are the second and third principal stresses, respectively. (Note that T = 0 for smooth bars uniaxially loaded and T = 1 when the principal stresses are equal to each other. Although T = 0.5for balanced biaxial tension, where no triaxiality exists, “triaxiality” is retained in this discussion to convey that aspect of the stress state important to intergranular fracture.) Again, the calculations were made (for xj = 0) for both the sharply notched and the bluntly notched bars at fracture. Figure 9(d) shows that for the more sharply notched bars of different thickness, T increased slightly ahead of the notch tip and that it increased also with increasing thickness. At about two notch radii from the tip (x2 = 0.08 mm), for instance, T increased from around 0.35 for the thinnest bar (t = 0.2 mm) to around 0.65 for the thickest bar (t = 2 mm), reaching about 0.6 at the thickness that marked the transition to about 50% intergranular fracture. For the more bluntly notched bar T was significantly lower and ranged from about 0.2 to 0.4, Fig. 10(d). When coupled with the greater 3ooo

i

0.3 -

‘a B 2

0.2 -

d .s *

O.l-

-

w

t=1.5mm t=1mIn t = 0.5 mm t=0.2 mm

-I

o.o! 0.0

0.1

0.2

0.3

0.4

0.5

OI 0.0

x2 c-1

0.1

0.3

0.2

0.4

x2 bd

(‘4

m-

0.75 -

lGQO-

01

0.0

0.1

0.2

0.3

0.4

0.5

x2 (-)

Fig. 9. Distribution of: (a) the equivalent plastic strain; (b) the maximum principal stress; (c) the equivalent stress; and (d) the triaxiality in the sharply notched specimens having different thickness.

0.5

XU and SCHULSON:

NOTCH SENSITIVITY OF INTERMETALLIC

1611

Ni,Al

0.4

1-_

~i:~

<

0.1

0 0.0

0.1

0.2

0.3

0.4

0.5

0.0

0.1

0.2

x2 em

0.3

I 0.4

0.5

x2 Cm)

W

B

II

c

9

3 6

E

L ‘6

looo

.ii 2

(if

1:: 0

-

0.0 0.0

0.1

0.2

0.3

0.4

0.5

x2 (-)

0.0

0.1

0.2

0.3

0.4

I 0.5

x2 md

Fig. 10. Distribution of: (a) the equivalent plastic strain; (b) the maximum principal stress; (c) the equivalent stress; and (d) the triaxiality in the bluntly notched specimen. amount of transgranular fracture in this case, the calculations suggest that the intergranular mode is activated once T reaches about 0.4 and that the 50/50 mixture sets in when T reaches about 0.6.

5.DISCUSSION The following picture thus emerges: as a notched bar sufficiently thick to support a large throughthickness tensile stress is loaded in tension, a triaxial tensile state of stress develops behind the notch (Fig. 3).As the stress rises, plastic flow initiates at the notch tip, but remains confined to the surface region. As the stress increases further, the surface region strains and hardens; also, the plastic zone begins to spread, more extensively in less acutely notched bars owing to the lower degree of triaxiality. As the stress increases still further, the surface region deforms and hardens still more until a crack initiates there. Mode-I propagation ensues and the bar fractures. Given that the effective plastic strain at the notch tip at fracture seems to be independent of the notch geometry and that it is similar to the true fracture strain of the smooth bar, while the average notch-section stress at fracture increases as the notch acuity decreases, it appears that fracture is controlled by the initiation of a crack. The crack path seems to reflect the degree of triaxiality of the stress state at the onset of crack propagation. Transgranular fracture dominates under low degrees of triaxiality, while a mixture of transgranular and intergranular fracture develops once the triaxiality exceeds a critical level. Possibly,

intergranular fracture dominates at higher levels of triaxiality than explored here. For thick, sharply notched bars the critical condition is met early, once the crack grows through the plane stress region near the notch tip. Fracture is then preceded by little plastic flow and by little strain hardening across the reduced section. Consequently, the ductility and the fracture stress are significantly lower than for the smooth bar. For thick, bluntly notched bars, on the other hand, the critical level of triaxiality appears not to be met until the crack has lengthened, probably to the point that its own stress field dominates that of the notch. At this point the crack has already propagated about two-thirds of the way across reduced sections of the shape and size examined here, through material which had undergone significant plastic deformation and work hardening prior to crack propagation. As a result, the ductility and the fracture stress of the more bluntly notched bar are closer to those of the smooth bar. The reason intergranular fracture becomes abundant once the degree of triaxiality reaches around 0.6 is not known. Such behavior is not a characteristic of all ductile metals, for silver [18] still fractures transgranularly under even higher degrees of triaxiality than applied here. The critical value thus seems to be specific to Ni,Al(B) and possibly to the composition and microstructure of the alloy examined and to the deformation conditions. How the notch re-activates intergranular fracture is not clear. In fact, the origin of intergranular fracture in the unalloyed material is still an issue. One expla-

1612

XU and SCHULSON:

NOTCH SENSITIVITY OF INTERMETALLIC

nation stems from the slip transmission model [19] of the boron-induced brittle-to-ductile transition. Presumably, grain boundaries crack when the combination of the far-field stress and the local tensile stress acting on them reaches a critical level. The far-field component arises from the applied stress, while the local component arises from microstructural features such as dislocation pile-ups [20] and elastic anisotropy. If, as argued elsewhere [19], boron eases the transmission of slip across boundaries, then it probably lowers the local stress component. Also, if boron prevents the ingress of hydrogen along grain boundaries, as argued by George et al. [12-141, then it probably has the additional effect of restoring the cohesive strength to the boundaries. The two effects together could then allow the boundaries to support a greater far-field stress before they crack. Global yielding and significant plastic flow could then follow before strain hardening raises the stress on the boundaries to the level required for cracking. A sharp notch, in raising the axial stress for plastic flow, increases significantly the far-field component, and so the combined stresses may once again be sufficient to nucleate intergranular cracks after little global plastic how. Why notches activate a brittle fracture mode in N&Al(B), but not in ductile metals like silver, is part of the general problem of crack intolerance that characterizes all strongly ordered intermetallics. The issue, it seems, reduces to a competition between dislocation emission and atomic bond decohesion. Of the several factors that have been considered [21] the only one that appears to be common to all the intermetallics, whether strong or weak, is the workhardening rate. It is more than twice that of ductile metals and alloys [21]. One wonders, therefore, whether in hardening so rapidly material near the tips of sharp notches and cracks reaches its cohesive strength earlier than it does in less rapidly hardening materials. Speculative though this is, the possibility that work hardening may be important is consistent with the suppression of notch sensitivity in Zr,Al by neutron irradiation [5], which partially disorders the alloy and lowers its work hardening rate [22], and by warming the material to the temperature where its work hardening rate begins to fall [5]. The possibility is also consistent with increasing the notch strength ratio of N&Al(B) upon raising the temperature (3). 6. CONCLUSIONS From experiments is concluded that:

and finite element calculations

it

N&Al

(i) the notch sensitivity of N&Al(B) is caused by plastic constraint induced by the triaxial tensile state of stress produced by the notch; (ii) cracks initiate at the tip of the notch where plastic strain and stress are concentrated; (iii) cracks propagate in a brittle manner when the degree of triaxiality exceeds a critical value, T, which, for the material studied here and for triaxiality as defined in the text, is around 0.6; and (iv) the tensile strength is controlled by crack initiation. Acknowledgements-This

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