J Mater Sci (2012) 47:2088–2094 DOI 10.1007/s10853-011-6007-5
Surface form memory in NiTi shape memory alloys by laser shock indentation Xueling Fei • David S. Grummon • Chang Ye Gary J. Cheng • Yang-Tse Cheng
•
Received: 6 July 2011 / Accepted: 28 September 2011 / Published online: 15 October 2011 Ó Springer Science+Business Media, LLC 2011
Abstract An indentation-planarization method for NiTi shape memory alloys has been developed that produces a robust surface topographical memory effect that we call ‘‘surface form memory’’, or SFM. Surface form memory entails reversible transitions between one surface form (flat) and another (say, wavy) that occur on changing temperature. These transitions are cyclically stable and exhibit very high mechanical energy density. Our previous study has demonstrated SFM transitions in NiTi alloys derived from quasistatic (i.e., low strain rate) spherical indents, as well as other geometries. Here, we report on experiments using confined laser ablation to indent a similar martensitic NiTi substrate, but in the dynamical regime (very high strain rate). As in the quasistatic case, subsurface plastic strain gradients are created via martensite twinning reactions, and later by dislocation-mediated slip. The resulting defects and stress fields support the two-way shape memory effect underlying SFM. In the dynamical case however, relative cyclic two-way displacements are found to be significantly larger, when normalized to the initial indent depth, than is the case with quasistatic indentation. This confers certain processing and boundary condition advantages. Analysis of the shock
X. Fei D. S. Grummon (&) Department of Chemical Engineering and Materials Science, Michigan State University, East Lansing, MI 48824, USA e-mail:
[email protected] C. Ye G. J. Cheng School of Industrial Engineering, Purdue University, West Lafayette, IN 47906, USA
dynamics is found to be consistent with the observed surface displacements.
Background NiTi shape memory alloys (SMAs) are of technical interest because of the very large energy density ([10 MJ/m3) associated with both the shape memory effect and transformational superelasticity. Normally, spontaneous shape change in SMAs occurs only during heating, but thermomechanical processing can be used to induce a two-way shape memory effect (TWSME) [1–3]. In this case both cool and warm shapes are remembered, so that a shape change occurs reversibly (and therefore cyclically) on both heating and cooling. Whether by over-straining the martensite, or by stress/strain/temperature cycling, it is believed that a remnant dislocation substructure supports preferential selection of thermodynamically favored martensite variants when cooling from the austenitic condition. This bias in the habit plane variant selection mechanism produces a shape change during martensitization [4–7]. We have previously used single Hertzian contact loading conditions with hard spherical indenters to induce TWSME in NiTi SMAs [8, 9], at low strain rate (de/ dt \ 0.05, i.e., in the ‘‘quasistatic’’ regime). We found that deep1 (a/r [ 0.25) spherical indents become shallower when transforming to the austenite, and again become deeper when cooled to form the martensite. This is a twoway indent depth change that may be cycled many times. 1
Y.-T. Cheng Department of Chemical and Materials Engineering, University of Kentucky, Lexington, KY 40506, USA
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The normalized size of the indent is commonly quantified by a/r, the ratio of the in-plane indent radius, a, to the radius r of the indenter itself, such that a ball pressed into its equator gives an a/r ratio of unity.
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Surface form memory (SFM), however, involves a radical change in the macroscopic kind of topography, differentiating between, say, flat and bumpy surface forms, at a scale much longer than that of the intrinsic surface roughness. To achieve SFM, we must add an additional step: following indentation the specimen is cycled a few times between Mf and Af (the martensite and austenite finish temperatures, respectively), after which the martensitic surface is mechanically ground away, but only enough to just remove all visible topographical traces of the original indent. Following this step, heating the substrate will lead to the formation of a bump (which we call an ‘exdent’) that will disappear when the specimen is subsequently cooled (see Fig. 1). Emergence and retreat of the bump is subsequently cyclically reversible, and the bump amplitude is on the order of the original two-way indent depth change. The amplitude of this two-way response is related to the size of a subsurface deformation zone—a region in which indentation has caused plastic strain beyond that which can be accomplished by martensite detwinning reactions [8, 9]. In previous study careful experimental measurements showed that, for quasistatic spherical indentation, the
Fig. 1 Surface form memory in NiTi that has been indented with tungsten rods, thermally cycled, and planarized by mechanical grinding. The emergence and recession of the ‘‘exdents’’ is repeatable indefinitely
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depth, D*, of the active subsurface zone was equal to about 2.4% of the cyclic exdent amplitude. In the present study, Laser Shock Peening (LSP) has been used to introduce a similar deformation zone by making indents with shock waves generated by laser ablation of a metal foil on the surface of the NiTi specimen. As in the quasistatic case described above, both two-way indent depth changes, and exdent-to-flat transitions after planarization (SFM), were observed. LSP produces extremely high shock pressures (as high as 4–5 GPa) and ultrahigh strain rates ([106/s) [10], and affords precise control for localized treatment. It can introduce a strong workhardened layer and compressive residual stresses that have been used to improve fatigue performance, corrosion resistance, wear resistance and service life in various materials [11]. Lavender, for example, reported using a LSP technique to induce compressive residual stresses in the failure-prone zone of Pilger dies made of A2 steel, leading to increase service life [12]. The salient difference between mechanical indentation using hardened spheres, and indentation using laser shocks, thus involves the very high strain rate associated with the latter method. Differences in response between the two approaches will therefore depend to a large degree on the strain rate sensitivity of monoclinic NiTi. There are few reports on the effect of ultra-high strain rates on deformation of NiTi-based SMAs, especially for the case of behavior of the martensite. Nasser reported that there exists a critical strain rate above which plastic slip dominates deformation mechanisms for loading of the austenite, and below which stress-induced martensite formation occurs in superelastic SMAs [13]. Millett [14] reported that the strain rate sensitivity of austenitic NiTi increases the yield strength of NiTi from 500 to 794 MPa when deformation is caused by a shock wave instead of quasistatically (in this study shock pressures as high as 10 GPa were recorded). It must be stressed however, that in the present case it is the deformation only of the martensite that is at issue, and complications of transformational plasticity, with attendant heat transfer effects, do not arise. This having been said, martensite deformation can proceed either by deformation twinning reactions, or by dislocation multiplication and slip. Both are of crucial significance in the case of two-way shape memory, but rather little is known about either of these mechanisms at ultra-high strain rates. Adharapurapu [15] studied deformation of a superelastic NiTi composition (SE508) at temperatures in the martensitic regime (-50 °C) which showed a mild strain rate sensitivity for the martensite phase, and Liu, et al., [16] demonstrated a similar effect. An important observation in the latter study is that no transformation from martensite to austenite was observed under high strain rate adiabatic loading conditions that may have caused a transient temperature rise to above the Af temperature.
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Methods and materials For our experiments using LSP indentation, a 3 mm thick 50.26 at.% Ni wrought NiTi alloy sheet was acquired from Special Metals Corporation. The transformation temperatures were determined by differential scanning calorimetry to be Mf = 295 K, Ms = 331 K, As = 343 K, and Af = 383 K. Specimens were first electro-discharge cut into 12.7 mm diameter disks and manually ground with 2000 grit SiC paper. They were then machine polished at room temperature with 0.05 lm colloidal silica. Before LSP the specimens were chilled to approximately 250 K to insure a fully martensitic condition, and then pulsed after warming the specimen back to room temperature. A 65 lm thick self-adhesive aluminum foil tape from 3 M, used as an ablative overlay to absorb the laser energy and protect the sample from thermal effects, was attached to the surface of the NiTi disk. A confining medium of BK7 glass (a borosilicate glass purchased from McMaster Carr) was used to constrain the plasma generated by laser beam impingement on the foil. The confining medium, the ablative overlay, and the sample were firmly pressed together during the experiment. The laser beam was generated by a Continuum Surelite III Q-Switched Nd-YAG laser with a wavelength of 1064 nm and full width half maximum pulse duration of 5 ns. The beam sizes used were 0.5 and 1 mm, respectively. The laser intensities were varied from 1 to 3.5 GW/cm2 to generate different indent depths. The pressure pulse generated by the plasma propagated into the base NiTi substrate to make the indent. Figure 2 shows an optical image of a typical shock peened specimen. The NiTi specimen on the left has indents made with beam size of 0.5 mm with indent spacing of 2 mm. The specimen on the right has indents made with beam size of 1 mm and a similar spacing. Below, we report
Fig. 2 Optical image of laser shock peened NiTi disks. The left has indents made with beam size of 0.5 mm and the right with beam size of 1 mm
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preliminary results on experiments using the 0.5 mm beam at 2.5 GW/cm2. Three dimensional surface profiles of the as-indented surfaces were acquired with a WYKO NT 1000 optical profilometer. The indents were then heated to 413 K (30 K above Af) using a thermoelectric cooler (TE Technologies VT-127-1.4-1.15-71) placed directly under the specimen in the profilometer. After heating and measurement of the warm profile the specimen was cooled to 243 K (52 K below Mf) using liquid Freon, to insure a fully martensitic state. The profiles of the indents were then recorded at 293 K (2 K below Mf and 50 K below As). Temperatures were measured by thermocouples spot-welded on either side of the indent.
Results and discussion Figure 3 shows measured profiles of an indent made with a 5 ns laser pulse at an intensity of 2.5 GW/cm2 and a beam size of 0.5 mm. In Fig. 3a, a trace is shown of the as-peened surface (dashed line), and the same indent at a temperature above Af (red), and after subsequent cooling back below Mf (blue). The initial indent is somewhat
Fig. 3 Schematic illustration of a initial indent depth-recovery, and b exdent-to-flat surface transition during heating and cooling after planarization of the LSP indent
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narrower than the nominal beam diameter, and is 5.7 lm deep. Upon heating to above Af, the indent became much shallower, reaching a depth of 0.6 lm by the shape memory mechanism. This 4.9 lm depth change represents a shape memory driven recovery of 85.9% of the initial indent depth. Upon cooling again to below Mf, the indent deepened to 2 lm. This cycle could be repeated indefinitely with the indent 0.6 lm deep at T [ Af and 2 lm deep at T \ Mf. Thus, the reversible depth change for the LSP indent was 1.4 lm, or 24.6% of the initial indent depth. The visible presence of the indent was then removed by mechanical grinding (planarization), after which the specimens were heated and cooled again over the same temperature range, and the thermally-reversible surface distortion recorded. Figure 3b shows profilometer traces of a thermally reversible flat-to-exdent transition, with the indent profile just before planarization included for reference (dashed line). An exdent with amplitude of 1.2 lm was observed—slightly less than the previously recorded two-way indent recovery displacement of 1.4 lm, but still 17.5% of the initial indent depth. The inset in Fig. 3b shows typical 3-D profiles for the thermally reversible and cyclically repeatable exdent-flat-exdent (austenitemartensite-austenite) transitions. Having shown that LSP is capable of inducing reversible SFM, it is of interest to compare high strain rate LSP and conventional quasistatic indentation methods with regard to various geometrical and deformation parameters. Figure 4 shows the initial profile (in half-space) of an indent made by the LSP process using a laser intensity of 2.5 GW/cm2 and a beam size of 0.5 mm, compared to a quasistatic indent that would be predicted to simultaneously produce both (a) the same reversible indent depth change and (b) the same initial in-plane indent diameter, based on previous observations and analysis. That is, the spherical indenter radius indicated in Fig. 4 was chosen to give a similar reversible depth change (1.4 lm) when pressed into the material to a depth that would produce an indent diameter equal to that of the LSP indent (500 lm in this case). In previous study [8], we found empirically that the reversible indent depth change, d, for quasistatic indents depends on both the indenter radius rqs, and the inplane diameter 2a of the spherical indent made with it, according to d = 0.06a - 0.0155rqs. Therefore, the radius of a quasistatic indenter expected to give a 1.4 lm depth change when the in-plane indent radius is 250 lm is rqs = (.06a-d)/.0155 = 877 lm. This corresponds to an a/rqs ratio of 0.285 for the quasistatic case. On the other hand, assuming the LSP indent is spherical in shape, its equivalent ‘‘indenter radius’’, rlsp, can be calculated as rlsp = (a2 ? h2)/2 h, where a is the in-plane indent radius (250 lm), and h is the initial indent depth (5.7 lm), so rlsp = 5.5 mm. The a/rlsp ratio for the LSP indent is thus
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Fig. 4 Comparisons of initial indent depth and two-way recovery between the spherical indent and the LSP indent. Vertical scales are identical for each impression, but the lower extreme of the quasistatic indent is well off the scale
calculated to be only 0.05—very much lower than that for an equivalent quasistatic spherical indent. In fact, an a/rqs ratio of 0.05 would be expected to cause no observable TWSME, and therefore no SFM effect, if the indent had been made quasistatically [17]. Indent and recovery parameters for both indent types are summarized in Table 1 below. It is therefore concluded that when using LSP, reversible indent displacements can be generated from a much shallower indent than is required in the quasistatic case, by a factor of approximately 6.5. Furthermore, these displacements occur at an a/r ratio that would produce no detectable two-way distortion from a quasistatic indent. This is significant, since it may reduce the overall SMA substrate thickness required for expression of robust SFM in NiTi, and would also reduce the amount of material removal required in the planarization process. It is of interest then to estimate the peak pressures, to determine the plastified depth likely produced by the LSP approach, and to compare these estimates to our previous experimental observations of the plastic zone produced by quasistatic spherical indents. The peak pressure of the shock produced using laser ablation is given by [10] P ¼ 0:01½Z Io d=ð2d þ 3Þ1=2
ð1Þ
where Io is the incident laser power density in GW/cm2, P is the pressure in GPa, and Z = 2/(1/Zt ? 1/Zcf) is the reduced acoustic impedance between a target with
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Table 1 Comparison of quasistatic and LSP SFM parameters a/r Ratio
Quasistatica
LSPb
0.285
0.05
lm
lm
%Change
LSP/QS (%)
%Change
Indenter Radius
877
5500
Initial indent depth
36.5
5.7
Initial recovery Reversible depth change
31.9 1.4
87.5 3.8
5.1 1.4
89.5 24.6
6.5
Reversible exdent height
1.4
3.8
1.2
17.5
4.6
a
Quasistatic parameters are interpolations based on previous experiments
b
LSP a/r ratio estimated assuming a spherical indent profile
impedance Zt and a confining medium with impedance Zcf. Taking the acoustic impedance of glass to be 1.3 9 106 and the acoustic impedance of NiTi to be 1.34 9 106 gives Z = 1.32 9 106 g/cm2-s. The efficiency of the plasmamaterial interaction, d, is 0.1 in the present experiment [18]. Therefore, a laser intensity of 2.5 GW/cm2 should produce a peak pressure of 3.2 GPa. In the confined plasma regime this pressure is constant during the duration of the laser pulse and declines to half the maximum value after a time equal to 1.8 times the pulse duration [19]. Momentum thus continues to be added to the shocked material after the end of the pulse. However, the peak pressure calculated in this way occurs at the surface and decays rapidly with depth and can therefore only be regarded as an upper bound in the present setting. As the shock wave propagates into the NiTi substrate, plastic deformation occurs to a depth at which the peak pressure drops below the Hugoniot elastic limit (HEL). The HEL is related to the dynamic yield strength, ry,dyn, according to HEL ¼ ry;dyn ð1 mÞ=ð1 2mÞ
ð2Þ
where m is Poisson’s ratio [20]. The literature contains one experimental estimate of the HEL for NiTi [14], but only for austenitic, rather than martensitic NiTi. The measured quasistatic compressive stress strain behavior of the NiTi material used in the present study is shown in Fig. 5 for data collected at a strain rate of 1 9 10-2/s and at room temperature. Two yield features can be discerned. The first is unambiguously associated with the onset of plastic strain by martensite variant detwinning and occurs at 93 MPa, whereas the second, which can be associated with the onset of dislocation activity after dewtinning mechanisms have been exhausted, is found at 315 MPa. For two-way shape memory to occur, both detwinning and slip must occur, and must do so in that temporal order. This is because memory of a cool shape in the martensite requires that dislocations be created in the martensite after it has been largely detwinned. Only in this way can such dislocations stabilize
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Fig. 5 Compressive stress strain behavior for the martensitic NiTi used in the study
the variant distribution of the deformed martensite. We therefore proceed on the assumption that the shock interacts with the martensitic structure on the basis of one HEL value for martensite detwinning, and another (higher) HEL applicable to slip deformation. An estimate for the value of the dynamic (high strain rate) yield stress for the martensitic material in the present study can be obtained based on results presented in [15] and [16], both of which measured yield stresses for the martensite phase at different strain rates, in both the quasistatic and dynamic regimes. We first develop a logarithmic curve fit to low and high strain rate data for martensite deformation in these two studies, and use this regression to extrapolate the results to a strain rate of 106/s (assumed to apply to deformation under LSP conditions), and additionally to interpolate them for a strain rate of 10-2/s—the rate used to obtain the data shown in Fig. 5. Table 2 summarizes the data values used for this estimate, where regression parameters m and b are used to
J Mater Sci (2012) 47:2088–2094 Table 2 Data and regression coefficients used in estimating the dynamic yield stress for slip deformation in the martensite for the present study
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Ref.
Strain rate de/dt
Compressive yield stress (MPa)
[15]
1 9 10-3
1,290
1.2 9 103
1,720
1 9 10-2, interp.
1,360
1 9 106, extrap.
1,927
3 9 10-4
1,250
[16]
3 9 10
Present work, slip Present work, detwinning
3
1.293
1 9 10-2, meas.
315
1.355
1 9 106, est.
427
1 9 10-2, meas. 1 9 10 , est.
ð3Þ
From this we extract the ratio, R ¼ r106 =r102 , for each study, take the average of the two values, and finally estimate r106 for the present material as equal to R times the measured quasistatic slip-yield strength of 315 MPa. This procedure, while obviously quite approximate, predicts that the dynamic yield stress for slip is 427 MPa. Assuming a Poisson ratio of 0.3, this value yields an HEL of 747 MPa for slip deformation. The shock pressure of 3.2 GPa is therefore about four times the HEL and will clearly cause extensive plastic deformation. Applying the same procedure to the yield stress for detwinning gives an HEL estimate for the dynamic case of 133 MPa. The plastified depth depends on the HEL, the pressure, P, and the pressure duration, sp, and may be estimated according to [20] as Dp ¼ Cel Cpl sp ½ðP HELÞ=2HELÞ= Cel Cpl : ð4Þ The latter two parameters are the elastic and plastic wave propagation speeds: Cel = [(k ? 2l)/q]1/2 and Cpl = [(k ? 2l/3)/q]1/2, respectively [21], where k is Lame’s constant (16.2 GPa in this case), l is the shear modulus of the martensite, taken to be 10.77 GPa, and q is density of NiTi which is 6.45 g/cm3.The Cel and Cpl are therefore about 2420 and 1900 m/s, respectively. The pressure pulse duration, sp, is longer than the laser pulse duration by a factor of 1.8 [19] and is taken to be 9 ns in the present case. These parameters give an estimate for the depth, DS,P, of 131 lm. This is the depth to which slip deformation takes place. The strain in this zone saturates at P = 2.5 HEL at a magnitude
Regression parameter b
30.719
1502.2
21.094
1421.1
1,590 1,324 1,713
6
Regression parameter m
1.416
1 9 10-2, interp. 1 9 106, extrap.
extrapolate rdyn at de/dt = 106 and 10-2, for each of the two studies, according to rðde=dtÞ ¼ ½m lnðde=dtÞ þ b:
Yield stress ratio R, de/dt :106/10-2
93 133
eP ¼ 2HELðP=HEL 1Þ=ð3k þ 2lÞ
ð5Þ
giving eS = 3.2% in compression (for P = 2.5 HEL) for the present experiment. The saturation depth, DS,2.5, by Eq. 4 is 60.2 lm. Similar calculations for the detwinning HEL of 133 MPa give a saturation strain, eT, of 1% at the same saturation depth (DT,2.5 = 60.2 lm) However, for the case of the detwinning yield, the depth at the HEL, DT,P = 512 lm, is much greater than that for slip deformation. It is useful to assess the above estimates in terms of the observed initial LSP indent depth of 5.7 lm and the initial recovered depth of 0.6 lm. The former should be consistent with the sum of strain contributions from detwinning and slip. Here, it is assumed that the strain decays from the saturation value at the saturation depth (DS,2.5 and DT,2.5) to zero at the HEL. The total indent depth should therefore be DTot ¼ 1=2eS DS;P þ DS;2:5 þ 1=2eT DT;P þ DT;2:5 ð6Þ which is 6 lm if the above estimates are used, in reasonable agreement with the observed depth of 5.7 lm. The residual indent depth after heating should reflect only the slip component of the deformation, giving DResid = 1/2eS (DS,P ? DS,2.5) which is 3.1 lm—substantially greater than the 0.6 lm residual depth observed. In addition to highlighting the necessarily approximate nature of the forgoing analysis, this suggests that we have overestimated the plastic strain attributable to slip, or that the effect of surface relief waves has reversed some of the slip deformation. For example, it has been reported [20] that when the peak load is above 2.5 HEL, surface release waves focus and amplify from the edge of the impact. The peak load 3.2 GPa is considerably higher than 2.5 HEL for slip (1.87 GPa), which may additionally explain the observed 0.5 lm pile up effect observed in Fig. 4.
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For quasistatic spherical indents, we have previously made extensive experimental measurements of the depth of the subsurface active zone that participates in the reversible surface displacements [8, 22]. In every case so far observed we have found this depth, D*, to be approximately 40 times the height of the stable cyclic exdent amplitude. Conversely, the stable exdent amplitude is consistently found to be about 2.4% of the active zone depth. If LSP indents respond in the same way, an estimate of the active zone depth in the present experiment would 1.2/.024 = 58 lm, which is in good agreement with the 60 lm depth estimated above. Given the approximate nature of the analysis presented here it may be concluded that our observations are not obviously inconsistent with known laser shock dynamics, but never the less some of these close correlations may be fortuitous. Transient austenitization, while not indicated by literature reports, cannot be entirely ruled out as resulting from thermal effects, nor can the possibility that some degree of amorphization may have occurred in a near surface zone. A hardened zone formed in this way would also be expected to stabilize the observed two-way effects.
Conclusions We conclude that the Laser Shock Indentation of martensitic NiTi is an effective means of producing two-way shape memory that can be harnessed to achieve robust surface form memory (SFM). Compared to quasistatic indentation using spherical indenters, laser shock indentation produces SFM amplitudes that are about five times greater. Conversely, SFM of a given amplitude derived from laser shock indents needs a much shallower initial indent depth, requiring less material removal during the planarization process. Considering the versatility, speed, and the precision of the laser shock technique, these results indicate that laser shock indentation may be a useful approach to harnessing SFM for MEMS actuation, lithography, tribology, or novel adaptive optics, and metamaterials.
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J Mater Sci (2012) 47:2088–2094 Acknowledgement The authors gratefully acknowledge funding from the National Science Foundation under grants CMS0336810 and CMS0510294, NSF grant CMMI 0900327, and from General Motors Corporation.
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