the effects of prolonged thermal

13
The Effects of Prolonged Thermal Exposure on the Fracture and Fatigue Behavior of Aluminum-Lithium Alloy 8090 K.T. VENKATESWARA RAO, J.C. McNULTY, and R.O. RITCHIE Aluminum-lithium alloys are currently being considered for applications at moderately elevated temperatures; accordingly, a study has been made on the effects of prolonged (100 and 1000 hours overaging) thermal exposure at 149 ~ and 260 ~ on the mechanical properties of a peak- aged AI-Li-Cu-Mg-Zr alloy 8090-T8771. In the as-received T8771 temper, the alloy exhibits an excellent combination of strength (-500 MPa) and toughness (35 MPaV~) with moderate tensile elongation (4 pct). Overaging at 149 ~ results in a -50 pct reduction in ductility and toughness, primarily associated with the growth of equilibrium phases along grain/subgrain boundaries, resulting in formation of solute-depleted precipitate-free zones and coarsening of matrix 6' and S precipitates; strength levels and fatigue-crack growth rates, however, remain largely unchanged. Thermal exposures at 260 ~ conversely, lead to dramatic reductions in strength (by ~50 to 80 pct), toughness (by -30 pct) and fatigue-crack propagation resistance; crack-growth rates at all AK levels above -5 MPa~/-m are 2 to 3 orders of magnitude faster. Microstructurally, this was associated with complete dissolution of 6', severe coarsening of S and 7'2 precipitates in the matrix, and formation of equilibrium Cu- and Mg-rich intermetallic phases in the matrix and along grain boundaries. The resulting lack of planar-slip deformation and low yield strength of 8090 following overaging exposures at 260 ~ increase the cumulative crack-tip damage per cycle and reduce the tendency for crack-path deflection, thereby accel- erating fatigue-crack growth rates. Despite this degradation in properties, the 8090-T8771 alloy has better strength retention and generally superior fatigue-crack growth properties compared to similarly overaged A1-Li-Cu-Zr 2090 and A1-Cu-Zn-Mg 7150 alloys. I. INTRODUCTION THE unique mechanical property characteristics of aluminum-lithium alloys at ambient and cryogenic tem- peratures are well documented in the literature. 11-7]More recently, however, there have been some efforts to uti- lize these alloys at moderately elevated temperatures ap- proaching 300 ~ Potential applications include wing skins and other structural airframe parts of supersonic and subsonic aircraft, including advanced aerospace ve- hicles such as the Advanced Tactical Fighter, the F-20A, and High-Speed Civil Transport aircraft. At cruising speeds approaching Mach-3, specific components of these supersonic aircraft will periodically be exposed to skin temperatures between 150 ~ and 300 ~ (-300 ~ and 600 ~ under spectrum fatigue loading conditions.rS~ Although competitive materials, such as titanium alloys, have superior mechanical properties in this temperature range, they are far more expensive; moreover, with a density nearly half that of titanium, aluminum-based al- loys like AI-Fe-Ce, A1-Fe-Co, A1-Fe-V-Si, and 2219, in general, and A1-Li, in particular, offer significantly greater weight savings at comparable specific strength and stiffness. The use of A1-Li alloys in these applications, how- ever, can only be justified if their microstructural sta- bility and mechanical properties at, and following, prolonged exposure at these temperatures is adequate. Since A1-Li alloys are primarily strengthened through precipitation hardening, there is concern that strength levels may diminish due to rapid coarsening of precip- itates at elevated temperatures. Unfortunately, only lim- ited studies to date have examined the behavior of A1-Li alloys at elevated temperatures; specifically, only the tensile, fracture, and fatigue properties of A1-Li alloy 2090 at various temperatures following thermal expo- sure t9,~~ and the creep crack-growth behavior in AI-Li- Cu-Mg-Zr alloys t~] have been reported. It is therefore the objective of the present study to examine the effect of long-term high-temperature exposure (overaging) in air on the strength, ductility, fracture toughness, and fatigue-crack propagation behavior of a peak-aged AI- Li-Cu-Mg-Zr alloy, 8090-T8771. Results are compared with equivalent behavior in an A1-Li-Cu-Zr alloy 2090 (vintage I) and in traditional high-strength aluminum alloys. K.T. VENKATESWARA RAO, Research Engineer, and R.O. RITCHIE, Professor, are with the Department of Materials Science and Mineral Engineering and the Center for Advanced Materials, Materials Sciences Division, Lawrence Berkeley Laboratory, University of California, Berkeley, CA 94720. J.C. McNULTY, Graduate Student, formerly with the University of California, Berkeley, is with the Materials Department, College of Engineering, University of California, Santa Barbara, CA 93106. Manuscript submitted December 14, 1992. II. EXPERIMENTAL PROCEDURES Aluminum-lithium alloy 8090, with nominal compo- sition (wt pct) of AI-2.5Li-I.3Cu-0.7Mg-0.12Zr, was supplied by ALCAN as ingot-cast 100-mm-thick rolled plate in the commercially peak-aged condition, desig- nated as T8771; this refers to proprietary thermo- mechanical processing involving solution treatment at METALLURGICAL TRANSACTIONS A U.S. GOVERNMENT WORK VOLUME 24A, OCTOBER 1993--2233 NOT PROTECTED BY U.S. COPYRIGHT

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The Effects of Prolonged Thermal Exposure on the Fracture and Fatigue Behavior of Aluminum-Lithium Alloy 8090

K.T. VENKATESWARA RAO, J.C. McNULTY, and R.O. RITCHIE

Aluminum-lithium alloys are currently being considered for applications at moderately elevated temperatures; accordingly, a study has been made on the effects of prolonged (100 and 1000 hours overaging) thermal exposure at 149 ~ and 260 ~ on the mechanical properties of a peak- aged AI-Li-Cu-Mg-Zr alloy 8090-T8771. In the as-received T8771 temper, the alloy exhibits an excellent combination of strength ( -500 MPa) and toughness (35 MPaV~) with moderate tensile elongation (4 pct). Overaging at 149 ~ results in a - 5 0 pct reduction in ductility and toughness, primarily associated with the growth of equilibrium phases along grain/subgrain boundaries, resulting in formation of solute-depleted precipitate-free zones and coarsening of matrix 6' and S precipitates; strength levels and fatigue-crack growth rates, however, remain largely unchanged. Thermal exposures at 260 ~ conversely, lead to dramatic reductions in strength (by ~50 to 80 pct), toughness (by - 3 0 pct) and fatigue-crack propagation resistance; crack-growth rates at all AK levels above - 5 MPa~/-m are 2 to 3 orders of magnitude faster. Microstructurally, this was associated with complete dissolution of 6', severe coarsening of S and 7'2 precipitates in the matrix, and formation of equilibrium Cu- and Mg-rich intermetallic phases in the matrix and along grain boundaries. The resulting lack of planar-slip deformation and low yield strength of 8090 following overaging exposures at 260 ~ increase the cumulative crack-tip damage per cycle and reduce the tendency for crack-path deflection, thereby accel- erating fatigue-crack growth rates. Despite this degradation in properties, the 8090-T8771 alloy has better strength retention and generally superior fatigue-crack growth properties compared to similarly overaged A1-Li-Cu-Zr 2090 and A1-Cu-Zn-Mg 7150 alloys.

I. INTRODUCTION

THE unique mechanical property characteristics of aluminum-lithium alloys at ambient and cryogenic tem- peratures are well documented in the literature. 11-7] More recently, however, there have been some efforts to uti- lize these alloys at moderately elevated temperatures ap- proaching 300 ~ Potential applications include wing skins and other structural airframe parts of supersonic and subsonic aircraft, including advanced aerospace ve- hicles such as the Advanced Tactical Fighter, the F-20A, and High-Speed Civil Transport aircraft. At cruising speeds approaching Mach-3, specific components of these supersonic aircraft will periodically be exposed to skin temperatures between 150 ~ and 300 ~ ( -300 ~ and 600 ~ under spectrum fatigue loading conditions.rS~ Although competitive materials, such as titanium alloys, have superior mechanical properties in this temperature range, they are far more expensive; moreover, with a density nearly half that of titanium, aluminum-based al- loys like AI-Fe-Ce, A1-Fe-Co, A1-Fe-V-Si, and 2219, in general, and A1-Li, in particular, offer significantly greater weight savings at comparable specific strength and stiffness.

The use of A1-Li alloys in these applications, how- ever, can only be justified if their microstructural sta- bility and mechanical properties at, and following, prolonged exposure at these temperatures is adequate. Since A1-Li alloys are primarily strengthened through precipitation hardening, there is concern that strength levels may diminish due to rapid coarsening of precip- itates at elevated temperatures. Unfortunately, only lim- ited studies to date have examined the behavior of A1-Li alloys at elevated temperatures; specifically, only the tensile, fracture, and fatigue properties of A1-Li alloy 2090 at various temperatures following thermal expo- sure t9,~~ and the creep crack-growth behavior in AI-Li- Cu-Mg-Zr alloys t~] have been reported. It is therefore the objective of the present study to examine the effect of long-term high-temperature exposure (overaging) in air on the strength, ductility, fracture toughness, and fatigue-crack propagation behavior of a peak-aged AI- Li-Cu-Mg-Zr alloy, 8090-T8771. Results are compared with equivalent behavior in an A1-Li-Cu-Zr alloy 2090 (vintage I) and in traditional high-strength aluminum alloys.

K.T. VENKATESWARA RAO, Research Engineer, and R.O. RITCHIE, Professor, are with the Department of Materials Science and Mineral Engineering and the Center for Advanced Materials, Materials Sciences Division, Lawrence Berkeley Laboratory, University of California, Berkeley, CA 94720. J.C. McNULTY, Graduate Student, formerly with the University of California, Berkeley, is with the Materials Department, College of Engineering, University of California, Santa Barbara, CA 93106.

Manuscript submitted December 14, 1992.

II. EXPERIMENTAL PROCEDURES

Aluminum-lithium alloy 8090, with nominal compo- sition (wt pct) of AI-2.5Li-I.3Cu-0.7Mg-0.12Zr, was supplied by ALCAN as ingot-cast 100-mm-thick rolled plate in the commercially peak-aged condition, desig- nated as T8771; this refers to proprietary thermo- mechanical processing involving solution treatment at

METALLURGICAL TRANSACTIONS A U.S. GOVERNMENT WORK VOLUME 24A, OCTOBER 1993--2233 NOT PROTECTED BY U.S. COPYRIGHT

530 ~ water quenching, 1.5 to 3 pct permanent stretch- ing, and artificial aging for 32 hours at 170 ~ Sub- sequently, the as-received 8090-T8771 alloy plate was thermally exposed (overaged) in air for periods of 100 and 1000 hours at two different temperatures: (a) at 149 ~ (300 ~ which represents an anticipated service temperature and (b) at 260 ~ (500 ~ which represents a limiting (upper bound) temperature for use.

Plane-strain fracture toughness (KI~) and fatigue-crack propagation tests were performed in ambient tempera- ture air (22 ~ 45 pct relative humidity) in accordance with ASTM standards E399-90 and E647-91, respec- tively, using 50-mm wide and 10-ram thick compact ten- sion (C(T)) specimens, machined from midthickness (t/2) plate locations in the long-transverse (L-T) orien- tation. Fatigue-crack growth rates were determined over the range ~10 -t~ to 10 -5 m/cycle using automated electro-servohydraulic testing machines operating under stress-intensity (K) control at a frequency of 50 Hz (sine wave) and a load ratio R (of minimum to maximum load) of 0.1; crack lengths were continuously monitored using direct-current electrical-potential techniques. Fatigue thresholds, AKrH, operationally defined as the applied stress-intensity range, AK, where the maximum crack- growth rate was less than 10 -~2 m/cycle, were ap- proached using exponential load-shedding 1 schemes with a normalized K gradient of -0.1 mm- ; behavior at higher AK levels was characterized using similar schemes with a positive K gradient of 0.1 mm-~. *

*Despite the low strength levels in overaged structures, plastic zones remained small compared to specimen dimensions such that no net section yielding occurred during fatigue-crack growth.

Crack-closure levels were monitored using back-face strain compliance methods; the closure stress intensity, K,.t, defined at first contact between the fracture surfaces during unloading, was determined from the load corre- sponding to first deviation in linearity on the unloading compliance curve. Following fatigue testing, cracked samples were monotonically loaded to failure to char- acterize the fracture toughness properties. Correspond- ing uniaxial tensile properties were measured using 6.5-ram-diameter specimens with a 25-ram gage length.

Fracture surfaces were examined using scanning elec- tron microscopy (SEM). In addition, fatigue-crack paths were observed optically from metallographically pol- ished and etched (Keller's reagent) sections taken per- pendicular to the crack surface, both in the specimen plane and across the specimen thickness. Microstructural features were also imaged using transmission electron microscopy (TEM); samples were prepared by diamond saw cutting -1-mm-thin slices from plate (in the rolling plane), mechanically grinding them to a thickness of -0.1 mm, and punching 3-ram-diameter disks. The disks were then electrolytically thinned using a twin-jet polishing apparatus maintained at a voltage of 20 V in a solution of 20 pct nitric acid and 80 pct methanol cooled to -37 ~

III. RESULTS AND DISCUSSION

A. Microstructure

Akin to many thermomechanically processed micro- structures in wrought aluminum alloys, the grain mor- phology in the 8090-T8771 alloy is nonuniform,

displaying a disklike appearance (Figure l(a)). The grains are essentially equiaxed, roughly 200-/xm long and 200-~m wide in the rolling plane and -50-/zm thick across the plate thickness (short-tranverse direction). However, compared to early vintages of commercial AI-Li alloys, such as 2090, 8090, and 8091, t6'121 the morphology is relatively isotropic; equivalent grains in

~ i ~ i i i i~ "�84

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t.-J'-.s

Fig. 1--Three-dimensional optical micrographs of grain structures in wrought AI-Li-Cu-Mg-Zr alloy 8090 plate (a) in the as-received (peak-aged) T8771 condition and following 1000 h exposures at (b) 149 ~ (300 ~ and (c) 260 ~ (500 ~

2234--VOLUME 24A, OCTOBER 1993 METALLURGICAL TRANSACTIONS A

a 13-ram-thick rolled plate of 2090-T81 (vintage I), for example, are far more elongated, i.e., some 2 to 3 mm in length, in the longitudinal direction. 16"9~

Strengthening in the peak-aged T8771 condition is provided principally by the homogeneous precipitation of ordered 6' (A13Li) spheres and S(AI2CuMg) laths,*

*There is some question as to whether two different S-type precip- itates, S' (precursor to S) and S, exist. ~t3'~5~ In this article, no distinc- tion is made between S and S'.

with additional minor contributions from/3' (AI3Zr) dis- persoids and small amounts of T~ (A12CuLi) plates (Figure 2). I~2-~61 The distribution of S precipitates in the matrix was found to be relatively uniform, possibly due to additional heterogeneous nucleation along residual dislocations generated during plastic stretching prior to aging. The presence of ordered 6' particles in the micro- structure, of ~13-nm diameter** (Figures 2(a), (c)), is

**Estimates of precipitate dimensions were based on direct measurements of typically 50 or so particle from TEM micrographs. However, these estimates should be considered to be approximate due to small errors from residual strain contrast from dislocations and co- herency strains.

also indicated by the superlattice reflection spots at 1/2(200) positions on the selected area diffraction (SAD) patterns imaged along the [001 ] zone axis (Figure 2(d)). In addition, ~' was found to precipitate around the/3' dispersoids that nucleate first during cooling fol- lowing the homogenizing treatment. The S laths were ~45-nm long and 10-nm thick (Figure 2(b)); T~ plates

were ~6-nm thick and - 3 7 nm in size. Despite the preaging deformation, heterogeneous precipitation of solute-rich equilibrium phases, /'2 (A16CuLi3) or R(AlsCuLi3), t14,161 along grain boundaries was apparent (Figure 2(c)). This was possibly due to the slower quench rates typically experienced in thick-section prod- uct forms, including the 100-mm-thick 8090 plate, that are unable to maintain a high degree of supersaturation in solid solution and suppress these grain-boundary ef- fects. Concurrently, this resulted in the formation of ~50-nm-wide 6' precipitate-free zones (PFZs) along high-angle grain boundaries from local solute depletion around grain-boundary phases; no PFZs were seen at the low-angle grain boundaries (Figure 2(a)).

Overaging at 149 ~ for 100 and 1000 hours had little or no effect on grain growth, which is typical of Zr- bearing wrought aluminum alloys. However, TEM ob- servations indicated that the subgrain structure was more developed in the 1000 h exposed condition because of subgrain-boundary precipitation. As shown in Figure 3(a), the subgrain boundaries are marked by equi- librium precipitates embedded in narrow ~50- to 60-nm- wide ~' PFZs. Concurrently, coarsening of matrix 6' particles (to ~30 nm), S laths (to ~36 by 7 nm), and grain-boundary particles was seen after 1000 hours of exposure at 149 ~ with a corresponding increase in PFZ width to approximately 100 nm along high-angle grain boundaries.

Similarly, thermal exposures for 100 and 1000 h at 260 ~ had no effect on grain size but did cause exten- sive development of the subgrain structure. In fact, as

:~ '~i~ . . . .

Fig. 2 - - T E M micrographs of the predominant microstructural features of 8090 in the as-received 8090-T8771 condition showing (a) 6' and/3' coated with 6' particles (the latter marked by arrows), (b) S laths, (c) grain-boundary precipitates and resultant PFZ, and (d) SAD pattern of (a) showing 8' superlattice reflections (highlighted by squares) along the [001] zone axis. Also note the subgrain boundary precipitates in (a) are without a significant PFZ.

METALLURGICAL TRANSACTIONS A VOLUME 24A, OCTOBER 1993--2235

Fig. 3 - - T E M micrographs of the principal microstructural features in 8090-T8771 alloy following (a) 1000 h exposure at 149 ~ (b) 100 h and (c) 1000 h exposure at 260 ~ and (d) SAD pattern of (b) after 100 h exposure at 260 ~ ([001] zone axis). Note the subgrain boundary precipitation with a tS'-PFZ in (a) and the absence of 6' particles in (b) and (c) which is also evidenced by the absence of superlattice reflections at 1/2(200) sites in (d).

shown in Figure l(c) grain/subgrain boundaries are not clearly apparent, as the etchant severely attacks the boundaries which are richly decorated with large grain- boundary precipitates (Figures 3(b) and (c)), i.e., pre- sumably, T2 I141 and other Li-containing intermetallics of A1, Cu, and Mg. More importantly, however, no evi- dence could be found for the presence of 8' precipitates in either microstructure after 100 or 1000 hour exposures (e.g., compare Figure 2 with Figures 3(b) and (c)), most probably because 260 ~ is above the 8'-solvus temper- ature for the present A1-Li-Cu-Mg alloy. Although meta- stable 8' particles are observed in binary A1-Li alloys (with >5 at. pct Li) artificially aged at temperatures up to about 300 ~ 8' precipitation is considerably reduced in ternary AI-Li-Cu and quarternary A1-Li-Cu-Mg sys- tems for aging temperatures above 200 ~ The ab- sence of 8' is also confirmed by the missing 1/2(200) superlattice spots on the SAD pattern taken along the [001] zone axis (Figure 3(d)). The matrix S phase, which is the major source for precipitation strengthening in 260 ~ exposed microstructures, and grain-boundary particles were seen to coarsen significantly; S and T2 were found to be roughly 400 • 150 nm in size (an order of magnitude coarser than in the peak-aged T8771 con- dition). In addition, intermetallic phases rich in Cu, Mg, Fe, and possibly Li were also observed within the grains (Figures 3(b) and (d)).

B. Strength and Fracture Toughness

Ambient-temperature mechanical properties for 8090- T8771 alloy, before and after various thermal exposures,

are compared in Table I with corresponding data for a peak-aged A1-2Li-3Cu-0.1Zr alloy 2090-T81 (12.7-mm- thick rolled plate, vintage I) and a high-temperature A1-6 wt pct Cu alloy (2219-T851). In the peak-aged T8771 temper, alloy 8090 exhibits a good combination of yield strength (o-z__= 483 MPa) and fracture toughness (Kit = 35 MPaX/m), with moderate tensile ductility ( - 4 pct), mainly due to the uniform distribution of ma- trix 8' and S precipitates and reduced grain-boundary precipitation from plastic stretching prior to aging. Al- though strength levels are - 1 0 pct lower than in A1-Li alloy 2090, the 8090 alloy has a far more isotropic grain structure.

1. Overaging at 149 ~ Overaging the 8090-T8711 alloy at 149 ~ for 100 or

1000 hours has essentially no effect on the yield and ulti- mate strengths compared to properties in the as-received temper, although ductility and toughness are decreased by over 50 pct. By comparison, 2090-T81 showed a ~10 pct decrease in yield, a - 1 5 pct decrease in tough- ness, and a marginal increase in ductility; t9~ the A1-Cu alloy 2219-T851, with - 3 0 pct lower yield and ~ 12 pct lower tensile strength, however, retains its properties following similar overaging treatments, tl~

Corresponding failures observed on fracture toughness and tensile specimens in the as-received T8771 (peak-aged) and 149 ~ microstructures were predominantly intergranular (Figures 4(a) and (c)). At higher magnifications, the intergranular facets reveal fine dimples indicative of failure by microvoid nucle- ation and void growth around grain-boundary particles

2236--VOLUME 24A, OCTOBER 1993 METALLURGICAL TRANSACTIONS A

(Figures 4(b) and (d)). The mechanism is referred to as intergranular or grain-boundary ductile fracture and is commonly reported in precipitation-hardened A1- and Ni-based alloys. ~ With increased exposure at 149 ~ intergranular ductile failure becomes more predominant with an observed increase in density of voids; no clear dependence of void size on aging time was found.

Based on these observations, the reduction in ductility and resultant loss in fracture toughness of 8090-T8771 after prolonged thermal exposure at 149 ~ can be at- tributed primarily to localized plastic deformation (strain localization) effects near grain boundaries and surround- ing PFZs. tlS-21j Intergranular ductile failure by void nu- cleation, growth, and linkage is facilitated by the presence of heterogeneously nucleated solute (Mg, Cu, and possibly Li)-rich equilibrium particles embedded in the soft, solute-depleted zones along grain boundaries.

Extensive aging at 149 ~ accentuates this failure mode, compared to the T8771 condition, due to increased grain-boundary precipitation; this takes the form of a larger area fraction of particles along grain and subgrain boundaries and the coarsening of these phases, both fac- tors which expedite void coalescence and can lead to premature intergranular failure. In addition, the presence of PFZs near grain-boundary particles can reduce the strains required for microvoid initiation, although in- creased PFZ width has been observed to slightly increase tensile ductility, t22,231 Yield and ultimate strengths, however, are relatively unchanged, as 8' and S precip- itate distributions, which principally contribute to hard- ening, coarsen uniformly in the matrix; this is similar to other precipitation-hardened A1 alloys that show strength levels which are relatively independent of the PFZ width or the grain-boundary precipitate distribution, t2~

Fig. 4 - - S E M micrographs of monotonic fracture surfaces at K = Kic in 8090 alloy tested in the (a) and (b) T8771 condition, (c) and (d) following 1000 h exposure at 149 ~ and (e) and ( f ) after 1000 h exposure at 260 ~ at (a), (c), and (e) low and (b), (d), and (f) high magnifications. The horizontal arrow represents the crack-growth direction.

METALLURGICAL TRANSACTIONS A VOLUME 24A, OCTOBER 1993--2237

2. Overaging at 260 ~ In contrast to behavior at 149 ~ prolonged thermal

exposure at 260 ~ causes a dramatic loss in strength of 8090, with yield and ultimate strengths reduced by --50 and 80 pct, respectively. Concurrent with this softening, the fracture toughness and ductility are found to be higher than in the 149 ~ microstructures, yet Kit values are - 3 0 pct lower compared to the as- received T8771 temper and there is an almost a threefold increase in tensile elongation. In comparison, whereas A1-Li-Cu-Zr alloy 2090-T81 experiences similar losses in strength and a - 6 0 pct reduction in ductility following thermal exposure at 260 ~ the 2219-T851 alloy shows a - 2 0 to 30 pct decrease in strength with an - 1 6 pct increase in ductility, t9'l~

As with 149 ~ microstructures, fracture surfaces for the 260 ~ microstructures exhib- ited features resembling failure via microvoid nucleation and coalescence (Figures 4(e) and (f)). However, in ad- dition to ductile, intergranular failure surrounding grain- boundary particles, transgranular linkup between microvoids, initiated around coarse S precipitates in the matrix, was also observed. Microvoids along grain and subgrain boundaries were correspondingly larger than those in the matrix, consistent with TEM micrographs that illustrate rapid coarsening of grain-boundary phases.

Although ductility is increased, the marked reduction in strength and resultant loss in toughness of 260 ~ overaged microstructures, compared to the as-received T8771 temper, can be related to the considerably low volume fraction of strengthening precipitates and the heterogeneity of their distribution. Contributions to the matrix strength from both 6' and S phase distributions, which are the principal hardening phases in 8090-type AI-Li alloys, become severely limited as (1) 6' dissolves during aging and (2) S particles in the matrix rapidly coarsen and alter the deformation mechanism. In contrast to localized planar-slip deformation in the T877 l-tempered condition and in 149 ~ structures from shearing of the coherent 6' particles by paired dis- location motion, the S phase homogenizes slip in the ma- trix by inducing moving dislocations to bypass or loop the large second-phase matrix particles. The presence of the S phase also enhances void nucleation and growth at the matrix/S interface, as well as at the T2 and R phases that are distributed along grain and subgrain boundaries. In effect, the influence of plastic strain lo- calization, which was previously limited to PFZs along grain boundaries for the as-received T8771 and 149 ~ overaged microstructures, is experienced throughout the matrix. Microvoid nucleation is promoted at lower stress levels due to the relatively unimpeded movement of dislocations in the solid-solution matrix, thus contribut- ing to the decrease in toughness of 260 ~ microstructures; the increase in ductility is presumably associated with a concurrent increase in work-hardening capacity of the material.

The fracture toughness behavior of various micro- structures after long-term exposure at elevated temper- atures is essentially a function of two prime factors, namely, strength and ductility. Overaging at 149 ~ causes a loss in ductility at equivalent strength levels (Table I) which, in turn, results in a significant loss of

toughness (Figure 5(a)); exposures at 260 0(3, on the other hand, lead to smaller reductions in toughness due to loss in strength and a concomitant increase in ductil- ity. Such trends are consistent with simple models for ductile fracture, which are based on the concept of a stress-state modified critical strain criteria; i.e., crack extension occurs when the local equivalent plastic strain, ep, exceeds a critical fracture strain or ductility, e) ~, across a significant microstructural dimension, r*, char- acteristic of the specific fracture mechanism, r24'25'26~ Such models suggest that the toughness should scale with the elastic modulus E, strength, and ductility as

K,c oc (E' tr o e~ r*) 1/2 [11

where o- 0 is the flow stress (taken as the mean of try and O'u) and E' is the Young's modulus in plane strain (= E / ( I - v 2) - 90 GPa for the 8090 AI-Li alloy, where v is Poisson's ratio).* For the present mechanism of

*It should be noted that although Eq. [ll is a generic expression for ductile fracture, 1271 it is explicitly derived assuming that the crack- tip strain field is dominated by the HRR singularitff s'29~ over the di- mensions where the characteristic fracture events occur. 125"26! As such, the constant of proportionality in Eq. [1] becomes [I./e~ (0, n)] m, where 1. and ep (0, n), are, respectively, the integration constant and angular factor (derived for the equivalent strain) from the HRR so- lution ~3~ and n is small such that 1/(n + 1) ~ 1. However, since in the present case the characteristic fracture events occur within the fi- nite strain field close to the tip, i.e., r* < 26, where 6, is the crack- tip opening displacement, the appropriate crack-tip strain distribution is given by the blunting solutions of Rice and Johnson ~3tl and McMeeking. 1321

grain-boundary ductile failure, r* is likely to be some multiple of the mean spacing between particles contrib- uting to the nucleation and coalescence of microvoids; based on TEM images of the microstructures and SEM fractography, values of the particle spacing varied from - 3 2 0 nm in the T8771 condition to -121 nm in the 1000 h-149 ~ overaged conditions. Values of the frac- ture strain, e)~, must reflect the highly triaxial conditions local to the crack tip; assuming plane-strain conditions, e~' values should thus be approximately one-third of the uniaxial tensile ductility values listed in Table I . t24'251

Using these values, a good correlation is seen between the function (E' tro e~ r*) 1/2 and measured fracture toughness values (Figure 5(b)), confirming that strain- controlled ductile fracture processes are the dominant mechanism controlling toughness in 8090 microstructures.

C. Fatigue-Crack Propagation Behavior

1. Overaging at 149 ~ Fatigue-crack propagation rates (da/dN) at R = 0.1

in the as-received and 149 ~ 8090 micro- structures (L-T orientation) are plotted as a function of the applied stress-intensity range, AK, in Figure 6(a); corresponding crack-closure values, K~ normalized with respect to the maximum stress intensity, are shown in Figure 6(b). In general, it is apparent that there is little change in the fatigue-crack growth and crack-closure re- sponse of 8090-T8771 alloy following prolonged ther- mal exposure at 149 ~ although crack-growth rates above AK = 10 MPa~/-m are observed to slightly in- crease and fatigue threshold values to marginally de- crease with increasing aging time.

2238--VOLUME 24A, OCTOBER 1993 METALLURGICAL TRANSACTIONS A

Table I. Room-Temperature Mechanical Properties of 8090-T8771 Following Thermal Exposures Compared to 2090-T81 and 2219-T851 in the Longitudinal (L-T) Orientation

Condition

Pct Elongation Yield Strength Ultimate Strength (on 25-mm Strain-Hardening

try (MPa) tr, (MPa) Gage) Coefficient (n) Fracture Toughness

Klc (MPaV'-~)

8090-T8771 483 518 4.3 0.08 35 +100 h at 149 ~ 484 514 2.5 0.07 19 + 1000 h at 149 ~ 497 520 2 0.06 16 +100 h at 260 ~ 148 280 10.2 0.25 29 +1000 h at 260 ~ 118 250 12.1 0.26 23 2090-T81" 552 589 9.3 0.06 24** + 100 h at 149 ~ 558 593 8 - - - - + 1000 h at 149 ~ 503 552 9 - - 20** +100 h at 260 ~ 186 296 10 - - - - +1000 h at 260 ~ 110 206 14 - - - - 2219-T851" 352 455 12 - - - - +100 h at 149 ~ 352 455 12 - - - - +1000 h at 149 ~ 331 448 12 - - - - + 100 h at 260 ~ 248 372 14 - - - - + 1000 h at 260 ~ 241 365 14 - - - -

*Taken from Refs. 9 and 10. **T-L orientation.

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35

30

25

15 �9

5

0 i i i

0,0 0.1 0,2 0.3

(E'oo ~; ,.;)r~ (b) (a)

Fig . 5 - - V a r i a t i o n o f f rac tu re t o u g h n e s s in 8 0 9 0 as a func t ion o f (a) y ie ld s t r eng th a n d (b) (E" fro {j* ro*) ~/2, s h o w i n g g o o d cor re l a t ion b e t w e e n the c o m b i n e d in f luence o f s t r eng th , duc t i l i ty , and m i c r o s t r u c t u r e o n m e a s u r e d t o u g h n e s s .

Consis tent with the small variat ion in fa t igue-crack growth behavior for AK levels be low - 10 MPa%/-~, fa- t igue fracture-surface morphologies remain re la t ively unchanged with aging t ime. As shown in Figures 7(a) and (b) for the as- received T8771 t emper o f 8090, the surfaces for all three microstructural condi t ions in the intermediate AK range be tween 5 to 10 M P a V ~ are un- usual ly rough and are covered with t ransgranular -shear facets , character is t ic of c rys ta l lographic crack advance along {111} sl ip bands , c o m m o n l y repor ted in A1-Li al- loys. 16'71 Simi lar ly , fat igue crack paths in the loading plane are tortuous (Figures 8(a) and 8(b)), and crack fronts across the spec imen thickness are unusual ly non- uniform (Figures 9(a) through 9(d)) in the peak-aged

T8771 (as-received) microstructure and fo l lowing ex- posures at 149 ~ Texture studies t331 have identif ied the crys ta l lographic facets in Figures 9(b) and (d), which show an included angle o f - 6 0 deg, to be the traces o f an intersect ing set of c lose -packed {111} planes. In con- trast, c rack morpholog ies are less def lected at near- threshold s tress- intensi ty levels be low - 5 MPaV/-m (Figures 9(a) and (c)), compared to behavior at inter- media te to high AK levels (Figures 9(b) and (d)). The latter is thought to result f rom hydrogen embr i t t lement effects in a mois t ambient air envi ronment which pro- mote flat t ransgranular fat igue cracking along low index {100} or {110} planes , t6,34,351

As d iscussed prev ious ly , t6,7] such nonl inear cracking

METALLURGICAL TRANSACTIONS A VOLUME 24A, OCTOBER 1 9 9 3 - - 2 2 3 9

"~ 10""

~ 10" ~

Z ~ 10-'

u3 ,~ 10-' CE

~ 10-'

o ~0-.

,~ 10 -~~

10-"

10" 'a

&K (ksi~n) 2 5 10 i i i I r i i 1 I

ALCAN 8090

= T8771 ' o = 1 0 0 hr at 149"C 100 hr o = 1000 hr at 149'~C lO0~hr /.n~na

~ ~ ! 7 71

1 IIItlice

I~1 & per cycle

g n t=

'~b STRESS-INTENSITY RANGE, AK (MPa~m)

(a)

1.0

10.;'

~ 10"

10"

10''

�9 10" ~ ~

10"

10'

10"~

K m O.B E

0 .6 u3 g

q 0 . 4 -

(_1 0 .2 -

0.0

1000 hr /

~ 1 7 6 o ~o o o~1 ~, ~ ~ ~ 1 7 6 o O O o ~ l O O h r

�9 " ' 4 ~ ' ~ o OOoo

"~B~, o ~

- %

ALCAN 8090 /~% a = T8771 T8771

o = 100 hr at 149"C ~ = 1000 hr at 149"C

STRESS-INTENSITY RANGE. &K (MPa~/m)

(b)

Fig. 6 - - ( a ) Fatigue-crack propagation and (b) crack-closure behavior in 8090 AI-Li alloy following 100 and 1000 h exposures at 149 ~ (300 ~ compared to properties in the peak-aged T8771 temper (L-T orientation R = 0.1, 50 Hz).

profiles reduce the effective mode I stress intensity lo- cally at the crack tip, increase the length of the crack path, and most importantly, because of the associated shear displacements at the crack tip, induce premature closing of the crack due to wedging between fracture- surface asperities (termed roughness-induced crack clo- sure). Moreover, whereas such cracking morphologies are seen in most aluminum alloys close to M~rH, it is the prevalence of this mode at higher stress-intensity ranges that is primarily responsible for the superior fatigue-crack propagation resistance of AI-Li alloysfi Microstructurally, planar-slip deformation due to shear- ing of coherent 6' precipitates and coarse, textured grains in wrought A1-Li alloys are the principal factors that promote such meandering crack growth. In the pres- ent case, since the mechanism of fatigue-crack advance remains unchanged by thermal exposures at 149 ~ there is only a minimal effect on crack-growth rates and crack-closure levels following such exposures.

However, small regions of intergranular fracture, sim- ilar to features noted in Figure 4 for behavior under

Fig. 7 - - S E M micrographs of fatigue fracture surfaces in 8090 alloy tested in the (a) through (d) as-received T8771 temper and following (e) 100 h and (f) 1000 h exposures at 149 ~ at various magnifica- tions and ~ levels. The horizontal arrow indicates the general direc- tion of crack growth.

monotonic loading, are seen at high zSJf levels above - 1 0 MPaVm, the onset and extent of which are de- pendent on exposure time. In the as-received T8771 temper, whereas no intergranular failure is seen below z~; --14 MPaVm (Figures 7(c) and (d)), in micro- structures exposed to 100 and 100 hour periods at 149 ~ intergranular facets are observed at 2tK levels as low as 10 and 7 M P a V m , respectively (Figures 7(e) and (f)); moreover, their incidence is found to increase with stress-intensity range. Accordingly, growth rates rapidly increase with z~K level (Figure 6(a)), influenced by the onset of these monotonic or "static" fracture modes typ- ical of fatigue-crack growth in the stage 111 (or high-AfrO regime where Kmax values approach the fracture tough- ness of the material, Kh.. 1361 As overaging at 149 ~ tends to degrade K+,., this concurrently results in an accelera- tion in fatigue-crack growth rates in the high-z~" regime, i.e., above 10 MPaVm. With increasing exposure time at 149 ~ the acceleration is enhanced due to the pro- gressively earlier onset of the static fracture modes dur- ing fatigue-crack propagation at lower Kma, values.

2. Overaging at 260 ~ Prolonged thermal exposure at 260 ~ results in a

more significant degradation in fatigue-crack growth properties (Figure 10). Although fatigue-threshold val- ues remain essentially unchanged, crack-propagation rates are accelerated for all 2tK levels above - 5 MPa~/-m and continue to increase with overaging; in fact, after 1000 hour exposures, crack velocities are

2240--VOLUME 24A, OCTOBER 1993 METALLURGICAL TRANSACTIONS A

T8771

2~m

Fig. 8 - -Op t i ca l micrographs of in-plane fatigue-crack path mor- phologies in 8090 A1-Li alloy tested (a) in the peak-aged T8771 tem- per, (b) after 1000 h exposure at 149 ~ and (c) after 1000 h exposure at 260 ~ The arrow represents the general direction of crack growth.

nearly two orders of magnitude faster than those mea- sured for the as-received T8771 material. Surprisingly, similar to behavior after overaging at 149 ~ crack- closure levels appear to be relatively unaffected by prior exposure at 260 ~

Fatigue fracture surfaces following both 100 and 1000 hour exposures were completely transgranular for all 2tK levels examined (Figure 11). Unlike features seen in the as-received T8771 temper, the surfaces were relatively fiat without any macroscopic evidence of crystallo- graphic slip band cracking. Fracture surfaces, however, were covered with corrosion deposits resulting from en- vironmental reactions between the precipitates and mois- ture in air. It is likely that the lithium-containing equilibrium phases were primarily the source of such de- bris, as they are known to be reactive in moist air; ~81 in fact, due to such environmental effects, fracture surfaces of 8090 samples exposed at 260 ~ were generally dull in luster compared to the as-received T8771 or 149 ~ exposed microstructures. At higher 2d~ levels, the fatigue fracture surfaces clearly showed evidence of ductile striations indicative of fatigue-crack advance via alternating blunting and shear processes (Figures 1 l(c) and (d)). Compared to other microstructures, corre- sponding crack-path profiles were also more or less lin- ear (Figure 8c) and through-thickness crack fronts were comparatively planar at all stress-intensity ranges (Figures 9(e) and (f)); no evidence of crystallographic crack extension was apparent.

Microstructural effects on fatigue-crack growth in A1-Li alloys are primarily associated with variations in

5 0 # m

Fig. 9 - -Op t i ca l micrographs of through-thickness fatigue crack front morphologies in 8090 AI-Li alloy tested (a) and (b) in the T8771 temper, (c) and (d) after 1000 h exposure at 149 ~ and (e) and ( f ) after 1000 h exposure at 260 ~ at (a), (c), and (e) near-threshold (AK - 5 MPa~/m) and (b), (d), and (f) intermediate to high AK levels (z~df --7 to 12 MPa~/-m). The crack-growth direction is represented by the outward normal to the plane of the paper.

METALLURGICAL TRANSACTIONS A VOLUME 24A, OCTOBER 1993--2241

~ 1 6 " g Z

t~

~ l f f '

O 1~'; 1G,o!

8

1.O-

&K (ksiv~n) 2 5 10 I i i i I I i t [

ALCAN 8090 ,~ ='1"8771 1OO hr

1 0 0 0 h r

�9 ==100hr ~ T~87

at 260~ �9 ~d ' �9 at 260"C aP ~; = 1000 hr

71

1 lattice spscmg per cycle

==

5 10 STRESS-INTENSITY RANGE, AK IMPa~/m)

(a)

�9 1G =

1G'

1G' A

I G = i c

1 6 '

I U =

1 0 '

1~ '~

in slip planarity from complete dissolution of ordered ~' particles at 260 ~ The change in deformation mode from localized and heterogeneous slip by dislocation shearing to a homogeneous Orowan looping of particles causes crack advance along a number of low-angle slip systems, [37[ thus resulting in a more planar fatigue frac- ture surface. The absence of 3' and planar slip can also reduce the degree of slip reversibility at the crack tip, which may result in more irreversible crack-tip damage per cycle and, hence, in faster growth rates. Moreover, reductions in yield strength with increased exposure ac- centuate the damage per cycle due to increased crack-tip opening displacements; environmental effects also ap- pear to play a role. Finally, in light of the planar crack paths and flat fracture surfaces in the 260 ~ microstructures, the high measured crack-closure levels may be associated with mechanisms other than asperity wedging; specifically, effects of oxide wedging 138J and cyclic plasticity t391 in the crack wake may contribute to the extent of closure.

N �9 O.B- E

*.s 0.6

l~ 0.4- 0

~ 0.2-

O.O

,=~. . -1000 hr

�9 eR . . . . t l | ~ �9 .

100 hr

ALCAN 8090

= T8771 �9 = 100 hr at 260~ �9 = 1000 hr at 260~

. . . . Ib STRESS-INTENSITY RANGE, &K (MPa~/m)

T8771

(b)

Fig. 1 0 - - ( a ) Fatigue-crack propagation and (b) crack-closure behav- ior in 8090 alloy following 100 and 1000 h exposures at 260 ~ (500 ~ compared to properties in the as-received (peak-aged) T8771 temper (L-T orientation R = O. 1, 50 Hz).

the extent to which crack closure (principally from as- perity wedging) is promoted or restricted in the different temper conditions. [6,7,9~ Under- and peak-aged micro- structures generally show better fatigue resistance con- current with nonlinear crack paths and high closure levels; conversely, overaged structures generally exhibit faster growth rates due to more linear crack profiles and correspondingly lower closure levels. 16,71 In the present study, fatigue-crack growth behavior for microstructures exposed at 260 ~ is characterized by reduced crack-path meandering and fracture-surface roughness and, hence, by accelerated propagation rates, although measured crack-closure levels do not differ markedly from those measured in the T8771 condition.

These results and the fractography in Figure 11 sug- gest that the faster crack-growth rates seen following 100 and 1000 hour exposures at 260 ~ are associated with intrinsic changes in the fatigue-crack growth mechanism rather than from extrinsic differences in the crack- closure levels. Such changes could result from the loss

D. Comparison with Other Alloys

The strength properties of 8090-T8771 after 1000 hours exposure at various temperatures are compared with equivalent properties for a conventional A1-Cu alloy 2219, A1-Li-Cu-Zr alloy 2090, and competing high-temperature A1-Fe-V-Si and A1-Fe-Ce alloys in Figure 12(a). ta~ Although the advantage of using dispersion-hardened A1-Fe-V-Si and A1-Fe-Ce alloys vs precipitation-hardened 8090 and 2090 is clearly evident at temperatures above 149 ~ (300 ~ both 8090 and 2090 A1-Li alloys are clearly attractive for applications at or below 149 ~ due to their high strength and low density (i.e., high specific stiffness). "~ Furthermore, as shown in Figure 12(b), fatigue-crack growth rates in the 8090-T8771 A1-Li alloy are relatively unaffected by prior exposure at 149 ~ are comparable to behavior in underaged 2124, and are far superior to behavior in 7150-T651 and the newly developed A1 alloys contain- ing Fe, V, Si, and Ce. Moreover, peak-aged 8090- T8771 also ranks better than 2090-T81 A1-Li alloy after identical 1000 hour exposures at 149 ~ Exposures at 260 ~ (500 ~ however, severely degrade the strength and fatigue resistance of the 8090-T8771 alloy; never- theless, the fatigue properties after 1000 hours overaging at 260 ~ are still comparable and, in certain cases, slightly superior (for da/dN below -10 -8 m/cycle) to unexposed 7150-T651, AI-7Fe-6Ce, and AI-8Fe- 1V-2Si alloys. In summary, A1-Li alloy 8090 is an excellent candidate material for design-durable and damage- tolerant aerospace structures for moderately high- temperature applications up to 149 ~

IV. CONCLUSIONS

Based on a study of the ambient-temperature mechan- ical properties of A1-Li-Cu-Mg-Zr alloy 8090-T8771 following prolonged (100 and 1000 hours) high- temperature exposures (overaging) at 149 ~ or 260 ~ the following conclusions can be made.

2242-- VOLUME 24A, OCTOBER 1993 METALLURGICAL TRANSACTIONS A

AK = 6 = M P ~ hr ~t 260'C, AK = 6 MPa~m

Fig. l l - - 5 E M micrographs of fatigue fracture surfaces in 8090-T8771 alloy after (a) through (d) 1000 h and (e) and ( f ) 100 h exposures at 260 ~ at various magnifications and AK levels. The horizontal arrow indicates the getterat direction of crack growth.

1. Overaging for 100 or 1000 hours at 149 ~ led to ~50 pct reductions in fracture toughness and ductility compared to the as-received T8771 condition; cor- responding strength levels remained unchanged. Microstructurally, such behavior was associated with coarsening of 6' and S matrix precipitates, the growth of Cu-, Li-, and Mg-rich grain and subgrain- boundary particles, and the resulting formation of solute-depleted PFZs near the boundaries.

2. Similar 100 or 1000 hour exposures at 260 ~ conversely, led to dramatic (~50 to 80 pct) re- ductions in strength and a threefold improvement in ductility compared to the T8771 condition; fracture toughness values were -30 pct lower than in the as-received T8771 temper and higher than those measured after 149 ~ exposures. Microstructurally, this was associated with the complete dissolution of matrix 8' precipitates and the severe coars- ening of matrix and particularly grain-boundary precipitates,

3. Fatigue-crack propagation behavior was largely un- changed by prior thermal exposures at 149 ~ al- though growth rates above AK - 10 MPaX/'m progressively increased with aging time. The lower resistance to fatigue-crack growth at high AK levels was associated with the reduced toughness of the overaged microstructures, which resulted in the ear- lier onset of static fracture modes during fatigue- crack growth,

4. Similar exposures at 260 ~ led to increased fatigue-crack growth rates at ali AK leve~s above - 5 MPaV'-m, although fatigue thresholds remained unchanged, The accelerated growth-rate behavior was attributed primarily to loss in slip planarity from the dissolution of coherent 6' precipitates and resul- tant effects of slip reversibility at the crack tip; the lower yield strength and increased susceptibility to environmental effects in these microstructures were also reasoned to play a role.

METALLURGICAL TRANSACTIONS A VOLUME 24A, OCTOBER [993--2243

TEMPERATURE, *F

100 200 300 400 500 700 I I I I I

�9 8090-T8771 600 o 2~0-T81

~" 500 i ~

400 AI-Fe-Co (CZ42)

q o 100 B

0 I I I I I 0 50 100 150 200 250

THERMAL EXPOSURE TEMPERATURE

(a)

100

80

60

40

20

0

300

2,

~ tkmlv~ ,o-', , , , 5, .... p 20

o QOgO-TIr/71 '* ~ 1 10" ~ 1 0 ' �9 8090+1000 h Q 149"C / . ~ , -

�9 80G0+1000 h Q 2gO'C y..'"

............. = - , / [,o-.

. . . . . . ~ . 1 ~ h a 149"C vjIv f,-* ~ ./ 10" �9 8 . * o ...-"

-----2124-T~1 ".~, ,Li,r ~ 7" l~ 10"* - - - - - 7150-'1"(151 " . . ~r,.a .i . .~..~" Ld "G

AUeF~-W-2S~ .,f~

I IllUCI '~ ~' /I �9 ,p*clno "]~ 10"'

pit cycle " o r

,o-,,

10-" i ~[I~I!~,AKT," , , , , I ~10''~ 5 10 :20 30

STRESS INTENSITY RANGE, *K (MPa~/m)

(b)

Fig. 12--Compar ison of (a) strength-retention capability and (b) fatigue-crack propagation resistance of 8090-T871 1 alloy prior to and fol lowing 1000 h exposures at 149 ~ and 260 ~ with similarly overaged A1-Li-Cu-Zr 2090-T81, AI-Cu 2124-T351, AI-Zn-Cu-Mg 7150-T651 plate alloys 19J~ and high-temperature A1-8Fe-4Ce and AI- 8Fe-IV-2Si (in wt pct) sheet alloys. Data for A1-8Fe-4Ce and AI-8Fe- IV-2Si were taken from Ref. 40.

5. Despite the loss in toughness and strength following 100 to 1000 hour exposures at 149 ~ and 260 ~ the 8090-T8771 alloy retains a competitive advantage over similarly overaged A1-Li-Cu-Zr 2090 and AI- Cu-Zn-Mg 7150 alloys at room temperature; in fact, the fatigue behavior of overaged 8090 is even com- parable to that of (unexposed) A1-Fe-Ce and AI-Fe- V-Si high-temperature alloys.

A C K N O W L E D G M E N T S

This work was supported by the Director, Office of Energy Research, Office of Basic Energy Sciences, Materials Sciences Division of the United States Department of Energy, under Contract No. DE-AC03- 76SF00098, with additional support (for the mechanical testing) from the Aircraft Division of Northrop Corporation, Hawthorne, CA, through Contract No. 831466. One of the authors (KTVR) thanks Alcoa for the Alcoa Foundation Science Support grant for assis- tance with specific equipment. Thanks are also due to Dr. Michael T. Hahn of Northrop Corporation for help- ful discussions and to D. Kovar for experimental assistance.

R E F E R E N C E S

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Trans. A, 1979, vol. 10A, pp. 1557-70.

2244--VOLUME 24A, OCTOBER 1993 METALLURGICAL TRANSACTIONS A

27. G.T. Hahn and A.R. Rosenfield: Metall. Trans. A, 1975, vol. 6A, pp. 653-68.

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36. R.O. Ritchie: Int. Met. Rev., 1979, vol. 24, pp. 205-30. 37. R.D. Carter, E.W. Lee, E.A. Starke, Jr., and C.J. Beevers:

Metall. Trans. A, 1984, vol. 15A, pp. 555-63. 38. S. Suresh, G.F. Zamiski, and R.O. Ritchie: Metall. Trans. A,

1981, vol. 12A, pp. 1435-43. 39. W. Elber: Eng. Fract. Mech., 1971, vol. 2, pp. 37-45. 40. R.A. Rainen and J.C. Ekvall: J. Met., 1988, vol. 40 (5),

pp. 16-18.

METALLURGICAL TRANSACTIONS A VOLUME 24A, OCTOBER 1993--2245