Supplementary Materials for

Transcription

1 Supplementary Materials for A fracture-resistant high-entropy alloy for cryogenic applications Bernd Gludovatz, Anton Hohenwarter, Dhiraj Catoor, Edwin H. Chang, Easo P. George,* Robert O. Ritchie* *Corresponding author. georgeep@ornl.gov (E.P.G.); roritchie@lbl.gov (R.O.R.) Published 5 September 2014, Science 345, 1153 (2014) DOI: /science This PDF file includes: Materials and Methods Supplementary Text Fig. S1 Table S1

2 Materials and Methods Materials Processing and Characterization The CrMnFeCoNi high-entropy alloys were prepared using high-purity elemental starting materials by arc melting and drop casting into rectangular cross-section copper molds measuring 25.4 mm 19.1 mm 127 mm. (The casting process is fully described in ref. (5)). The ingots were cut in half length wise and then cold forged and cross rolled at room temperature along the side that is 25.4 mm to a final thickness of ~10 mm (total reduction in thickness of ~60%). Each piece was subsequently annealed at 800 C for 1h in air leading to fully recrystallized, equiaxed grains of ~6 µm size. The alloy contained a distribution of either Cr-rich or Mn-rich particles (some of which contained oxygen), which were the source of the microvoid coalescence fracture mode. The particle size and spacing varied significantly; the average particle size was ~1.6 µm with an average spacing of ~49.6 µm. Mechanical Characterization Rectangular dog-bone shaped tensile specimen with a gauge length of 12.7 mm were machined from the recrystallized sheets by electrical discharge machining, EDM. Both sides of the specimen were ground using SiC paper resulting in a final thickness of 1.6 mm and a gauge section of 3.2 mm. The gauge length was marked with Vickers microhardness indents (300 g load) to enable strain measurements after fracture using a traveling microscope. Tensile tests were performed at an engineering strain rate of 10-3 s -1 in a screw-driven Instron 4204 testing rig. In total, eighteen (N = 18) samples were tested at three different temperatures; six at room temperature (293K), six in a mixture of dry ice and methanol (200K) and six at liquid nitrogen temperature (77K)). The elongation of each sample was measured after testing and engineering stressstrain curves were calculated from the load-displacement data. Yield strength, σ y, ultimate tensile strength, σ u, and elongation to failure, ε f, were analyzed from the uniaxial tensile stress-strain curves and are shown in Table S1 as mean ± standard deviation from five tests at 293K and six tests at both 200K and 77K. True stress-strain curves were calculated from the engineering stress-strain curves and strain hardening exponents, n, were calculated for each temperature based on the constitutive law σ = k ε n, where σ and ε are, respectively, the true stress and plastic strain, k is a scaling constant and n the strain-hardening exponent; n values are additionally listed in Table S1. Ten (N = 10) compact-tension C(T) specimen, of nominal width W = 18 mm and thickness B = 9 mm, were prepared in strict accordance with ASTM standard E1820 (10) using electrical discharge machining (EDM). Notches, 6.6 mm in length with notch root radii of ~100 µm, were cut using EDM; prior to pre-cracking the faces of all samples were gradually ground and polished to 1 µm surface finish to allow accurate crack-length measurements using optical microscopy. All samples were fatigue pre-cracked and tested using a servo hydraulic MTS 810 load frame (MTS Corporation, Eden Prairie, MN, USA) controlled by an Instron 8800 digital controller (Instron Corporation, Norwood, MA, USA). Fatigue pre-cracks were created under load control (tension-tension loading) at a stress intensity range of ΔK = K max K min of roughly MPa.m 1/2 and a constant 2

3 frequency of 10 Hz (sine wave) with a load ratio R = 0.1, where R is the ratio of minimum to maximum applied load, P min /P max. During pre-cracking, the crack length was optically checked from both sides of the sample to ensure a straight crack front with crack extension monitored using an Epsilon clip gauge of 3 mm (-1/+2.5 mm) gauge length (Epsilon Technology, Jackson, WY, USA) mounted at the load-line of the sample; final crack lengths, a were in the range of mm (a/w ~ ) thereby being well above the ASTM standard s minimum length requirement for a pre-crack of 1.3 mm. To improve the constraint conditions at the crack tip during testing, all samples were side-grooved using EDM to depths of ~1 mm, which resulted in a sample thickness of B N ~ 7 mm; this thickness reduction did not exceed 20 25%, as recommended by ASTM Standard E1820 (10). Nonlinear elastic fracture mechanics methodologies were used to incorporate both the elastic and the inelastic deformation in the evaluation of the fracture toughness; specifically, the change in crack resistance with crack extension, i.e., crack resistance curve (R-curve) behavior, was characterized in terms of the J-integral as a function of crack growth at three different temperatures (room temperature (293K), a mix of dry ice and methanol (200K) and liquid nitrogen temperature (77K)). Samples were tested under displacement control at a constant displacement rate of 2 mm/min. The onset of cracking as well as subsequent subcritical crack growth were determined by periodically unloading the sample (~20% of the peak-load) to record the elastic unloading compliance using an Epsilon clip gauge of 3 mm (-1/+7 mm) gauge length (Epsilon Technology, Jackson, WY, USA) mounted in the load-line of the sample. Crack lengths, a i were calculated from the compliance data obtained during the test using the compliance expression of a C(T) sample at the load-line (10): a i W = u u u u u 5, (1) where u = 1 B e EC c(i) ; (2) C c(i) is the rotation-corrected, elastic unloading compliance and B e the effective sample thickness of a side-grooved sample calculated as B e = B (B B N ) 2 /B. (Initial and final crack lengths were additionally verified by post-test optical measurements.) For each crack length data point, a i, the corresponding J i -integral was computed as the sum of elastic, J el (i), and plastic components, J pl (i), such that the J-integral can be written as follows: J i = K 2 i /E' + J pl (i), (3) where E' = E, the Young s modulus, in plane stress and E/(1-ν 2 ) in plane strain; ν is Poisson s ratio. K i, the linear elastic stress intensity corresponding to each data point on the load-displacement curve, was calculated for the C(T) geometry from: K i = P i (BB N W) 1 2 f(a i W), (4) 3

4 where P i is the applied load at each individual data point and f(a i /W) is a geometrydependent function of the ratio of crack length, a i, to width, W, as listed in the ASTM standard. The plastic component of J i can be calculated from the following equation: J pl (i) = J pl (i 1) + η pl (i 1) b (i 1) A pl (i) A pl (i 1) B N 1 γ (i 1) a (i) a (i 1), (5) b (i 1) where η pl (i-1) = b (i-1) /W and γ pl (i-1) = b (i-1) /W. A pl (i) A pl (i-1) is the increment of plastic area underneath the load-displacement curve, and b i is the uncracked ligament width (i.e., b i = W - a i ). Using this formulation, the value of J i can be determined at any point along the load-displacement curve and together with the corresponding crack lengths, the J- a resistance curve created. (Here, a is the difference of the individual crack lengths, a i, during testing and the initial crack length, a after pre-cracking.) The intersection of the resistance curve with the 0.2 mm offset/blunting line (J = 2 σ o a; where σ 0 is the flow stress) defines an provisional toughness J Q, which can be considered as a size-independent (valid) fracture toughness, J Ic, provided the validity requirements for J-field dominance and plane-strain conditions prevail, i.e., that B, b 0 > 10 J Q / σ 0, where b 0 is the initial ligament length. The fracture toughness expressed in terms of the stress intensity was then computed using the standard J-K equivalence (mode I) relationship K JIc = (E J Ic ) 1/2. Values for E and ν at the individual temperatures were determined using resonance ultrasound spectroscopy (13); at 293K, 200K and 77K, Young s moduli, E of 202 GPa, 209 GPa and GPa and Poisson s ratios, ν of 0.266, and were used, respectively. To discern the mechanisms underlying the measured fracture toughness values and investigate the microstructure in the vicinity of the crack tip and wake in the plane-strain region in the interior of the sample after testing, one sample of each of the two extreme temperatures (293K and 77K) was sliced in two, each with a thickness of ~B/2; one half was embedded at 180 C in a conductive resin and the other half at room temperature in non-conductive resin in order to exclude any structural changes from the embedding procedure at elevated temperatures. Both halves were progressively polished to a 0.05 µm surface finish followed by a final polishing step using colloidal silica. The microstructure was analyzed in a LEO (Zeiss) 1525 FE-SEM (Carl Zeiss, Oberkochen, Germany) operated at 20 kv in back-scattered electron mode as well as by electron backscatter diffraction, EBSD using a TEAM EDAX analysis system (Ametek EDAX, Mahwah, NJ, USA). The remaining ligament of all other samples was cycled to failure at a ΔK of ~30 MPa.m 1/2, a frequency of 100 Hz (sine wave) and a load ratio R = 0.5 so that both the initial and the final crack lengths could be optically determined with precision from the change in fracture mode. Additionally, the fracture surfaces of both halves of each sample were examined in the scanning electron microscopy (SEM) at an accelerating voltage at 20 kv in the secondary electron mode. Microvoid and particle sizes and spacing were recorded for samples tested at all three temperatures. Using an Energy Dispersive Spectroscopy (EDS) system from Oxford Instruments (Model 7426, Oxford, 4

5 England) EDS analyses were performed on various particles to determine their chemical composition. As noted, corresponding local estimates of the fracture toughness at crack initiation, determined at the physical onset of initial crack extension, were performed by quantifying the fracture surfaces using stereo-photogrammetry (21). Specifically, the initial crack-tip opening displacements, CTOD i, were determined from fracture surfaces of C(T) samples fractured at 293K and 77K. This was achieved by taking pairs of SEM images on both sides of the fracture surfaces at the same sample location, in particular at the transition between the fatigue pre-crack and the overload fracture; these images were taken at different angles (tilted by 5 ) so that a digital surface model could be created of each fracture surface using the software package MeX (Alicona, Graz, Austria). Identical crack paths were then identified on both fracture surfaces and the height profile of the two crack paths compared with each other to identify the point of the coalescence of the first void with the tip of the pre-crack; in this manner, the initial crack-tip opening displacement, CTOD i, could be established (22). Using these CTOD i values, corresponding J i values could then be estimated using the Shih relationship (50): J i = 1 d n σ o CTOD i, (6) where σ 0 is the corresponding flow stress and d n is a parameter that depends on the hardening exponent, n, the yield strain σ y /E, and whether plane strain or plane stress conditions prevail. Corresponding K i values can then be back-calculated using the standard J-K equivalence. Supplementary Text Micromechanical Modeling The basic micromechanical models for fracture ahead of a sharp crack, and hence of the fracture toughness of a material, relate to the attainment of a critical fracture stress or fracture strain over a microstructurally-significant (characteristic) distance ahead of the crack tip at the onset of crack initiation or instability, as shown schematically in Fig. S1 (24). For the fracture of the CrMnFeCoNi alloy in the present study, which occurs by microvoid coalescence, the relevant criterion is that of the stress-state modified critical strain-controlled model for ductile fracture (24,25) in Fig. S1-B. Taking the material to have a power-law hardening constitutive law of σ /σ o = (ε p/ε o ) n, where σ o and ε o are, respectively, the reference flow stress and strain and n is the strain hardening exponent, the nonlinear elastic HRR plastic strain field as a function of radial distance r ahead of a crack tip is given in terms of the J-integral by (28,29): ε ij ε o 1 J n+1 σ o ε o I n r ε ij (θ, n), as r 0, (7) where ε ij (θ, n) is a dimensionless function of n describing the variation of strain with respect to the angle θ to the crack plane, and I n is a dimensionless integration constant which is also a function of n. Using the nomenclature defined in Fig. S1-B, crack initiation can be considered to occur once the local plastic strain ε p ahead of the crack tip 5

6 exceeds the fracture strain, relevant to the stress-state at that location ε f( σ m ), over a σ characteristic distance l o which can be associated with the particle spacing d p, i.e., the global fracture criterion of K = K Ic (or J = J Ic ) is consistent with a local microscale criterion of ε p > ε f σ m σ at r = x ~ l o. Substituting J = J Ic, ε ij = ε p = ε f, and r ~ l o into Eq. (6) and noting that 1/(n + 1) unity, gives an expression for the ductile fracture toughness as: where I n ε ij (θ,n) J Ic = K Ic 2 I n. σ E o ε ij (θ,n) ε f l o, (8) is a dimensionless function of θ and n from the HRR solution, which for the CrMnFeCoNi material in plane strain has a value at θ ~ 0-45 on the order of 10. Consequently, for failure by ductile fracture, the fracture toughness can be related to the product of strength, ductility and a characteristic distance related to the particle spacing, i.e., J Ic ~ σ o ε f d p (24). References All reference numbers cited in these Supplementary Materials pertain to those listed in the main (published) paper. 6

7 Fig. S1. Micromechanical models for fracture (24). (A) Critical stress-controlled RKR model for brittle (transgranular cleavage) fracture, and (B) stress-state modified critical straincontrolled model for ductile (microvoid coalescence) fracture (24,25). Shown are the HRR solutions (28,29) at a particular crack-tip opening displacement δ for the local (A) tensile stress σ yy and (B) plastic strain ε p distributions at distance x directly ahead of the crack tip in a nonlinear elastic power-law hardening material. The RKR criterion for cleavage fracture requires the local tensile stress σ yy to exceed the fracture stress σ f * over a characteristically significant distance l o, which can be related to the grain size d g. The corresponding criterion for microvoid coalescence fracture, which is relevant to the failure of the CrMnFeCoNi, requires that the local plastic strain ε p exceeds a fracture strain ε f over a characteristic distance l o which now can be related to the particle spacing d p. The relevant fracture strain, however, is a strong function of the stress-state (defined as the ratio of the hydrostatic to equivalent stress, σ m /σ ) in the crack-tip region; it is roughly an order of magnitude smaller than the fracture strain (i.e., ductility ε f ) as measured in a uniaxial tensile test (25,26). 7

8 Table S1. Mechanical properties of the CrMnFeCoNi high-entropy alloy at room temperature and sub-zero temperatures. (Statistically significant data are shown as mean ± standard deviation using basic statistics. The strain hardening exponents, n and the work of fracture were estimated from the average stress-strain values and are therefore listed without standard deviations. The variations in the fracture toughness, K JIc results were statistically not significant and are hence not listed.) 293K 200K 77K Yield strength, σ y (MPa) 410 ± ± ± 67 Ultimate tensile strength, σ u (MPa) 763 ± ± ± 59 Strain to failure, ε f (-) 0.57 ± ± ± 0.09 Strain hardening exponent, n Young s modulus, E (GPa) Work of fracture (MJ/m 2 ) 2.3 ± ± ± 0.6 Fracture toughness, K JIc (MPa.m 1/2 ) CTOD i at crack initiation (µm) Initiation fracture toughness, K i (MPa.m 1/2 )* * estimated by stereo-photogrammetry 8