Small-scale mechanical behavior of intermetallics and their composites

Materials Science and Engineering A 483–484 (2008) 218–222

Small-scale mechanical behavior of intermetallics and their composites H. Bei a,b , E.P. George a,b,∗ , G.M. Pharr a,b a b

Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA Department of Materials Science and Engineering, The University of Tennessee, Knoxville, TN 37996, USA Received 6 June 2006; received in revised form 10 October 2006; accepted 15 December 2006

Abstract To model and predict the mechanical behavior of composite materials, knowledge of the properties of their constituent phases as well as how they interact with each other is required. Although these mechanical properties can sometimes be deduced from measurements on bulk specimens, it is not always possible due to difficulties in producing bulk materials with compositions and structures similar to those of the individual phases in the composite. In such cases, in situ measurements of mechanical properties are needed. We review here our recent work on the application of nanoindentation and neutron diffraction to investigate the in situ mechanical responses of Cr-Cr3 Si and NiAl-Mo, two model eutectic composites that were chosen because they can be processed by directional solidification to yield well-aligned lamellar and fibrous microstructures. Phasespecific mechanical properties were measured and correlated with bulk behavior. We will discuss recently developed techniques that improve the accuracy of mechanical property measurements at small microstructural length scales. © 2007 Elsevier B.V. All rights reserved. Keywords: Intermetallics; Composite; Mechanical behavior; Nanoindentation; Neutron diffraction

1. Introduction Most structural materials are multi-phase alloys because it is difficult to obtain a good balance of properties (e.g. strength and ductility/toughness) in a monolithic material. Composite materials with well-controlled microstructures and sub-micron length scales have the potential for unique combinations of mechanical properties, such as strength and fracture toughness. In order to understand and model the thermo-mechanical response of such a composite, and determine how its properties change with microstructural length scale, it is important to be able to measure the properties of the constituent phases [1,2]. For example, the coefficient of thermal expansion (CTE) of a composite determines its overall length change upon heating or cooling, whereas the CTEs of its constituent phases determine how much thermally induced internal stresses are generated. Likewise, a stiffness mismatch between the constituent phases may result in mechanically induced internal stresses during loading. In order to use conventional “bulk” techniques to characterize the mechanical behavior of the constituent phases in a composite, it is necessary to synthesize bulk specimens having the same

∗

Corresponding author. Tel.: +1 865 574 5085; fax: +1 865 576 6298. E-mail address: [email protected] (E.P. George).

0921-5093/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2006.12.185

composition and structure as the phases of interest. This is not always possible and in situ techniques have to be employed in those cases where the properties of the individual phases must be measured while they are still embedded in the composite. Examples of in situ techniques include nanoindentation, which is a useful technique for measuring the mechanical properties (hardness and modulus) of small volumes of materials [3,4], and neutron diffraction, which can be used to measure phasespecific CTEs [5,6] as well as the response of the constituent phases to mechanical loading [7,8], that is, the elastic-plastic behavior of the individual phases and load sharing between the phases. We review here recent results on two model eutectic composites, Cr-Cr3 Si [9–11] and NiAl-Mo [12–16], which can be processed by directional solidification to yield geometrically simple morphologies of the constituent phases.

2. Microstructures Well-aligned, self-similar microstructures can be produced in NiAl-Mo and Cr-Cr3 Si eutectic alloys by directional solidification in an optical floating zone furnace. Their microstructures represent two important composite geometries, fibrous (NiAlMo) and lamellar (Cr-Cr3 Si), as shown in Figs. 1 and 2,

H. Bei et al. / Materials Science and Engineering A 483–484 (2008) 218–222

219

Fig. 1. Scanning electron micrograph of a transverse section through the wellaligned rod-like (fibrous) microstructure of a directionally solidified NiAl-Mo eutectic alloy.

respectively [9,13]. The details of their microstructures, including orientation relationships and the effects of solidification conditions on microstructure, have been discussed previously [9,13]. Under carefully controlled solidification conditions, the lamellar spacing and fiber size can be systematically varied without changing the morphology of microstructures. For example, the size of the Mo fibers in NiAl-Mo can be varied from 250 nm to 1 ␮m [13], and the lamellar spacing in Cr-Cr3 Si varied from 1 to 5 ␮m [9]. 3. Nanoindentation Fig. 3 illustrates the use of nanoindentation to measure the mechanical properties of the individual phases in a Cr-Cr3 Si lamellar composite. As shown in Fig. 3a [4], several of the indents were located entirely within one of the two phases. Fig. 3(b and c) are load (P) versus displacement (h) curves obtained by indenting the Cr3 Si and Cr phases, respectively.

Fig. 3. Nanoindentation results for the lamellar Cr-Cr3 Si eutectic alloy: (a) optical micrograph showing the locations of the indents, [4] (b) typical load–displacement curve obtained in the Cr3 Si phase, showing pop-in behavior during loading, and (c) typical load–displacement curve obtained in the Cr phase.

The modulus (E) and hardness (H) of the individual phases can be determined using the Oliver–Pharr method [3] as follows: H=

P , A

(1)

where P is the load and A is the projected contact area at that load, and √ π S √ , (2) Er = 2β A where Er is the so-called reduced elastic modulus and β is a constant that depends on the geometry of the indenter taken in this work to be β = 1.034 [3]. The modulus of the specimen, Es , is calculated from Er using the following relationship: 1 − υi2 1 1 − υs2 = + Er Es Ei

(3)

where Es and υs are the modulus and Poisson’s ratio of the specimen, and Ei and υi are elastic modulus and Poisson’s ratio of the indenter. For the diamond indenters used in our studies, the relevant elastic constants are: Ei = 1141 GPa and υi = 0.07 [3]. The contact stiffness (S) in Eq. (2) is obtained by analytically differentiating the P–h curve during unloading and evaluating the result at the maximum depth of penetration, h = hmax , that is:   dP S= . (4) dh h=hmax

Fig. 2. Optical micrograph of a longitudinal section through the well-aligned lamellar microstructure of a directionally solidified Cr-Cr3 Si eutectic alloy.

The projected contact area (A) is derived from an area function rather than from the image of the residual indent, as is done in conventional hardness tests, such as the Vickers hardness test. The area function relates the cross-sectional area of the indenter

220

H. Bei et al. / Materials Science and Engineering A 483–484 (2008) 218–222

Table 1 Experimentally measured modulus and hardness of the constituent phases in a Cr-Cr3 Si lamellar eutectic (assuming υ = 0.2) Cr3 Si

Modulus (GPa) Hardness (GPa)

Cr-rich solid solution

In lamellar microstructure

Single phase

In lamellar microstructure

Single phase

370 ± 16 21.6

381 ± 17 22.5

269 ± 13 5.2

273 ± 11 4.6

For comparison, the constituent phases were prepared in bulk form (with the same composition and structure) and their mechanical properties measured.

(A) to contact depth (hc ). An experimental procedure for determining the area function is discussed in detail by Oliver and Pharr [3], and can be expressed as: A = f (hc )

(5)

Once the area function and contact stiffness are known, the hardness and elastic modulus can be calculated from Eqs. (1) and (2). The modulus and hardness of the Cr3 Si and Cr phases so determined are listed in Table 1, assuming a Poisson’s ratio of 0.2 for both phases. The modulus and hardness of Cr3 Si were found to be 370 GPa and 22 GPa and that of the Cr solid solution phase 269 and 5.2 GPa, which are in good agreement with their corresponding values measured on bulk, single phase, samples [4]. A special point of interest is the sudden displacement excursion (pop-in) in the loading curve of the Cr3 Si phase (Fig. 3b). Before the pop-in event the deformation is fully elastic, whereas after pop-in it changes from elastic to plastic [17]. A lack of mobile dislocations in the vicinity of the indenter tip is likely responsible for the initial elastic deformation. With increasing load the material eventually yields (dislocations multiply), resulting in a sudden displacement excursion in the loading curve. In contrast, pop-in events were not observed in the Cr phase, possibly because dislocations were introduced into this (softer) phase during sample preparation, causing plasticity to occur essentially from the start of loading. Nanoindentation can also be performed on the NiAl-Mo fibrous composite. However, because of the smaller scale of the Mo fibers (<1 ␮m) compared to the lamellar spacing in Cr-Cr3 Si, the hardness and modulus computed using Eq. (1) and (2) can result in big errors. Therefore, the continuous stiffness mode (CSM) [18] was used to probe the hardness and modulus as a function of indentation depth. Fig. 4 shows examples of indentation impressions located entirely within the NiAl and Mo phases. For indentations, such as these, Fig. 5 shows the depth dependence of the modulus and hardness of the individual NiAl and Mo phases measured using the CSM method. The modulus and hardness of the NiAl (matrix) remain roughly constant and independent of depth. However, since the size of the Mo (fiber) is comparable to the size of the indents (Fig. 4b), its modulus and hardness may be affected by the surrounding softer NiAl. Therefore, to minimize interference from the surrounding matrix, the CSM method needs to be used at shallow depths (<75 nm), where the hardness and modulus of the Mo phase are constant and independent of depth. Using this method, the modulus and hardness of the Mo phase were deter-

mined to be about 270 and 5.0 GPa, and those of the NiAl phase 182 and 2.9 GPa, respectively. As discussed above, small indents are needed to determine the mechanical properties of fine-scale microstructures. Therefore, it is important to know the tip geometry of the indenters used in nanoindentation as accurately as possible. Pyramidal indenters, such as the Berkovich are typically used in nanoindentation. Real Berkovich indenters are not perfectly sharp but are blunt to varying degrees. The most common approximation that has been used to describe a blunt Berkovich indenter is that it is spherical near the tip. However, the radius of such a spherical tip is not well known. Some investigators have used tip radii quoted by manufacturers (e.g. [19]), but these are subject to great uncertainty since they are usually no better than order-ofmagnitude estimates, in addition to which the actual radius may

Fig. 4. Scanning electron micrographs showing the locations of nanoindents in (a) the NiAl matrix and (b) Mo fiber in a directionally solidified NiAl-Mo fibrous composite [13].

H. Bei et al. / Materials Science and Engineering A 483–484 (2008) 218–222

221

Fig. 6. Stress vs. phase-specific lattice strain for the NiAl-Mo composite at 800 ◦ C showing that elastic strains are produced only in the Mo phase [6]. The NiAl phase flows freely at this temperature and transfers all the load to the Mo fibers.

Fig. 5. Nanoindentation results for the directionally solidified NiAl-Mo fibrous composite obtained in the CSM mode: (a) hardness and (b) modulus as a function of indentation depth.

change during use due to wear. We have recently developed a method [17] to describe the Berkovich tip shape using the experimentally determined area function of the indenter at small depths (0–100 nm). Our analysis shows that the tip geometry resembles a cone at large depths and a sphere at small depths but that, in the depth range of interest for most nanoindentation measurements, neither shape dominates and the indenter is best described as a linear combination of these two shapes. As a validation of our method it was used to accurately predict the elastic load–displacement curve and determine the theoretical strength of a material from pop-in data [17]. 4. Neutron diffraction The mechanisms of stress/strain transfer across phase boundaries in composites can be investigated by in situ time-of-flight neutron diffraction [20]. We have used this technique to deter-

mine the response of the constituent phases in a NiAl-Mo fibrous composite to mechanical loading at different temperatures [6]. Fig. 6 shows the phase-specific {0 0 2} elastic-strain response of the NiAl and Mo phases as a function of applied tensile stress along the axial and transverse directions at 800 ◦ C, which is above the ductile-to-brittle transition temperature (∼650 ◦ C) of the NiAl-Mo composite [13]. At this temperature, there is no elastic strain in the NiAl phase at even the lowest stress levels and the Mo phase supports essentially the entire applied load. The slope of the longitudinal stress-strain data for Mo, when normalized with its effective area in the composite (14.1%), yields a modulus of 214 GPa for the Mo fibers. Additionally, the slope of the transverse stress-strain data indicates a Poisson’s ratio of 0.38. For comparison, the {0 0 2} elastic strains in single crystal NiAl having the same orientation and composition as the matrix NiAl in the composite are shown in Fig. 7. The elastic strains increase linearly with increasing applied stress up to ∼140 MPa with a modulus of ∼67 GPa. Clearly, the elastic-plastic response of NiAl, when it is the matrix phase in a composite, is different from its monolithic response. Residual stress resulting from CTE mismatch may be the cause of this difference; because the CTE of NiAl is larger than that of Mo [6], there will likely be a residual tensile stress in the NiAl matrix upon solidification. The magnitude of this residual stress along the fiber direction (σ m ) can be estimated using the analysis of Deve and Maloney [21]: σm =

λ2 Ef Em Vf αT , λ1 Ec (1 − υm )

(6)

where E and υ represent modulus and Poisson’s ratio and the subscripts f, m, and c stand for fiber, matrix and composite, respectively. The other symbols in Eq. (6) are: Vf , volume fraction of fibers; α, CTE difference between matrix and fiber; and T, temperature change. The constants λ1 and λ2 can be

222

H. Bei et al. / Materials Science and Engineering A 483–484 (2008) 218–222

plastic transitions [17,22] and interface debonding [23]. Recent developments that allow for accurate determinations of nanoindenter tip shapes make it possible to better characterize the mechanical properties of fine-scale microstructures. In situ neutron diffraction performed during heating or loading of a composite material helps us to understand the various deformation mechanisms of a composite, including elastic to plastic transition in a given phase, and load sharing/transfer between the phases (e.g. [6,24]). Acknowledgments

Fig. 7. Stress vs. phase-specific lattice strain at 800 ◦ C for a [1 0 0]-oriented single crystal of NiAl having the same composition and orientation as the matrix phase in the NiAl-Mo fibrous composite.

calculated from the elastic constants if it is assumed that the composite, fiber, and matrix all have the same Poisson’s ratio [21]:   Ec (1 − 2υc ) λ1 = 1 − , (7) 1− 2(1 − υc ) Ef   1 Ec λ2 = . (8) 1+ 2 Ef The moduli of the fiber and matrix obtained by neutron diffraction are Ef = 214 GPa and Em = 67 GPa. The CTE difference between the matrix and fibers is 10.2 × 10−6 K−1 [8], and the temperature difference between the melting point of the NiAl-Mo composite (1600 ◦ C) and the test temperature (800 ◦ C) is 800 ◦ C. Parallel to the fiber direction the modulus of the composite (Ec ) can be estimated by the rule of mixtures: Ec = Ef Vf + Em Vm = 88 GPa. If the Poisson’s ratios of the fiber, matrix, and the composite are all assumed to be 0.35, the CTE mismatch stress along the fiber direction is calculated to be 236 MPa, which is greater than the yield strength of [1 0 0]oriented NiAl single crystal at 800 ◦ C. Therefore, the residual stress is sufficient to cause yielding of the NiAl matrix, which explains why all the applied stress is carried by the Mo fibers (Fig. 6). 5. Summary Nanoindentation and neutron diffraction are useful techniques to investigate the phase-specific mechanical properties of composites, which cannot be obtained by conventional compression and tensile tests. If suitable care is taken, the hardness and modulus of the individual phases in a composite can be obtained by nanoindentation. In addition, analysis of the load–displacement curve may provide information on elastic-

This research was sponsored by the Division of Materials Sciences and Engineering, Office of Basic Energy Sciences, U.S. Department of Energy, and the SHaRE Collaborative Research Center at Oak Ridge National Laboratory, under contract DEAC05-00OR22725 with UT-Battelle, LLC. The authors wish to thank S. Kabra (The University of Tennessee) and D. W. Brown (Los Alamos National Laboratory) for useful discussions. References [1] M. Taya, R.J. Arsenault, Metal Matrix Composites: Thermomechanical Behavior, Pergamon Press, New York, 1989. [2] N. Chawla, K.K. Chawla, Metal Matrix Composites, Springer, New York, 2006. [3] W.C. Oliver, G.M. Pharr, J. Mater. Res. 7 (1992) 1564–1583. [4] H. Bei, E.P. George, G.M. Pharr, Scr. Mater. 51 (2004) 875–879. [5] R.S. Krishnan, R. Srinivasan, S. Devanarayanan, Thermal Expansion of Crystals, Pergamon Press, New York, 1979. [6] H. Bei, E.P. George, D.W. Brown, G.M. Pharr, H. Choo, W.D. Porter, M.A. Bourke, J. Appl. Phys. 97 (2005) 123503. [7] J.C. Hanan, E. Ustundag, B. Clausen, M. Sivasambu, I.J. Beyerlein, D.W. Brown, M.A.M. Bourke, Mater. Sci. Forum 404-4 (2002) 907– 911. [8] P. Rangaswamy, M.B. Prime, M. Daymond, M.A.M. Bourke, B. Clausen, H. Choo, N. Jayaraman, Mater. Sci. Eng. A 259 (1999) 209–219. [9] H. Bei, E.P. George, E.A. Kenik, G.M. Pharr, Acta Mater. 51 (2003) 6241–6252. [10] H. Bei, E.P. George, G.M. Pharr, Intermetallics 11 (2003) 283–289. [11] B.P. Bewlay, H.A. Lipsitt, M.R. Jackson, W.J. Reeder, J.A. Sutliff, Mater. Sci. Eng. A 192/193 (1995) 534–543. [12] A. Misra, Z.L. Wu, M.T. Kush, R. Gibala, Philos. Mag. A 78 (1998) 533–550. [13] H. Bei, E.P. George, Acta Mater. 53 (2005) 69–77. [14] D.R. Johnson, X.F. Chen, B.F. Oliver, R.D. Noebe, J.D. Whittenberger, Intermetallics 3 (1995) 99–113. [15] J.L. Walter, H.E. Cline, Metall. Trans. 4 (1973) 33–38. [16] P.R. Subramanian, M.G. Mendiratta, D.B. Miracle, Metall. Mater. Trans. A 25 (1994) 2769–2781. [17] H. Bei, E.P. George, J.Y. Hay, G.M. Pharr, Phys. Rev. Lett. 95 (2005) 045501. [18] W.C. Oliver, G.M. Pharr, J. Mater. Res. 19 (2004) 3–20. [19] W. Wang, C.B. Jiang, K. Lu, Acta Mater. 51 (2003) 6169–6180. [20] M.A.M. Bourke, D.C. Dunand, E. Ustundag, Appl. Phys. A 74 (2002) s1707–s1709. [21] H.E. Deve, M.J. Maloney, Acta Metall. Mater. 39 (1991) 2275–2284. [22] H. Bei, Z.P. Lu, E.P. George, Phys. Rev. Lett. 93 (2004) 125504. [23] H.F. Wang, J.C. Nelson, W.W. Gerberich, H.E. Deve, Acta Metall. Mater. 42 (1994) 695–700. [24] B. Clausen, M.A.M. Bourke, D.W. Brown, E. Ustundag, Mater. Sci. Eng. A 421 (2006) 9–14.