We present the results of repeated relaxation tests using nanoindentation to derive the activation volume of the dislocation velocity and the ratios of the dislocation density and dislocation velocity. An experimental technique, based on classical uniaxial relaxation experiments, was developed to establish a constant strain during repeated load relaxation transients and then to calculate the stiffness of unloading, and therefore the hardness, across the transients with acceptable results. We found that the activation volume of the dislocation velocity from our nanoindentation methodology was in good agreement when compared to the same reported for uniaxial experiments. © 2014 AIP Publishing LLC

Crawford, B.

Elmustafa, A, A.

Mamun, M. A.

Stegall, D. E.

English

Old Dominion University

Old Dominion UniversityODU Digital CommonsMechanical & Aerospace Engineering FacultyPublications Mechanical & Aerospace Engineering2014Repeated Load Relaxation Testing of PurePolycrystalline Nickel at Room Temperature UsingNanoindentationD. E. StegallOld Dominion UniversityM. A. MamunOld Dominion UniversityB. CrawfordA, A. ElmustafaOld Dominion University, aelmusta@odu.eduFollow this and additional works at: https://digitalcommons.odu.edu/mae_fac_pubsPart of the Engineering Physics Commons, and the Materials Science and EngineeringCommonsThis Article is brought to you for free and open access by the Mechanical & Aerospace Engineering at ODU Digital Commons. It has been accepted forinclusion in Mechanical & Aerospace Engineering Faculty Publications by an authorized administrator of ODU Digital Commons. For moreinformation, please contact digitalcommons@odu.edu.Repository CitationStegall, D. E.; Mamun, M. A.; Crawford, B.; and Elmustafa, A, A., "Repeated Load Relaxation Testing of Pure Polycrystalline Nickel atRoom Temperature Using Nanoindentation" (2014). Mechanical & Aerospace Engineering Faculty Publications. 22.https://digitalcommons.odu.edu/mae_fac_pubs/22Original Publication CitationStegall, D. E., Mamun, M. A., Crawford, B., & Elmustafa, A. A. (2014). Repeated load relaxation testing of pure polycrystalline nickelat room temperature using nanoindentation. Applied Physics Letters, 104(4), 041902. doi:10.1063/1.4862799Repeated load relaxation testing of pure polycrystalline nickel at roomtemperature using nanoindentationD. E. Stegall,1,2 M. A. Mamun,1,2 B. Crawford,3 and A. A. Elmustafa1,2,a)1Department of Mechanical and Aerospace Engineering, Old Dominion University, Norfolk, Virginia 23529,USA2Applied Research Center, Newport News, Virginia 23606, USA3Nanomechanics, Inc., Oak Ridge, Tennessee 37830, USA(Received 28 October 2013; accepted 8 January 2014; published online 27 January 2014)We present the results of repeated relaxation tests using nanoindentation to derive the activationvolume of the dislocation velocity and the ratios of the dislocation density and dislocationvelocity. An experimental technique, based on classical uniaxial relaxation experiments, wasdeveloped to establish a constant strain during repeated load relaxation transients and then tocalculate the stiffness of unloading, and therefore the hardness, across the transients withacceptable results. We found that the activation volume of the dislocation velocity from ournanoindentation methodology was in good agreement when compared to the same reported foruniaxial experiments.VC 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4862799]A plastically deforming crystalline solid is subject tovarious competing atomistic processes that contribute to theflow stress and the ability for the material to work harden. Inthe case of metals, these processes are primarily governed bythe mechanisms that influence the movement of dislocationsand their direct dependence on stress and temperature. Theuse of single transient tests (either constant load or constantstrain) to study the deformation mechanisms in plasticallydeforming crystalline materials has been examined exten-sively using techniques primarily developed for monotonicuniaxial test machines.1,2 These tests have provided the capa-bility for the measurement of two key quantities, the strainrate sensitivity of the stress (m) and the activation volume(V*), which are used to characterize the kinetic aspects ofplastic deformation.3–7 These two quantities are importantfor determining the macroscopic deformation mechanismsthat are operating but provide little information on the spe-cific microscopic processes that can be contributing to theflow stress. To address this, repeated transient tests (eitherrepeated stress relaxations or creep) were developed to studythe contribution of specific dislocation mobility mechanismson the flow stress and in particular the relative influence ofthe thermally activated and athermal components.8–10In recent years, the use of instrumented indentation test-ing (nanoindentation) to conduct similar transient tests (con-stant load or constant strain) and develop meaningfulrelationships with those performed in a uniaxial machinehas been well documented in literature.11–13 Caijun et al.11explained that the precaution when using these methods is inthe interpretation of the data given the complex stress statethat exists in indentation that is not present in traditional uni-axial tests. However, they provide a detailed analysis of dif-ferent transient tests in indentation and conclude thatmeaningful power law creep parameters can be measuredand are comparable to those measured in a uniaxial test. Inaddition, there have been multiple researchers who haveused single transient methods to determine m and V* for avariety of materials and have reported general agreementwith those measured in uniaxial tests.14–17 While examiningthe relationship between the indentation size effect (ISE) andm and V*, Stegall and Elmustafa18 concluded that using acti-vation volume analysis from nanoindentation based on singletransient creep tests V* decreased with increasing hardness(or stress) while the strain rate sensitivity of the hardnesswas relatively constant regardless of load for a variety ofFCC metals and alloys. These results were similar to theones reported in the literature in prior uniaxial tests.19–21 Inthis work, we present a methodology developed to performrepeated load (stress) relaxation tests using nanoindentationto obtain information about the relative mobility and densityof dislocations. The measurement of dislocation densitiesand their interaction at varying load levels are keys to betterunderstand the mechanisms that control the so called ISE.The material chosen for this research was 99.95% purepolycrystalline Nickel. Two samples were cut to sizes suita-ble for indentation testing and annealed at 750 C and fol-lowed by air cooling resulting in an average grain size of100 lm.A Nanoindenter XP (Agilent Technologies, Inc., SantaClara, CA) equipped with a three-sided diamond Berkovichprobe was used to conduct the repeated load (stress) relaxa-tion tests. The Berkovich indenter was specifically fabricatedto have a useful shape to about 30 lm for higher load (deeperdepth) experiments. The test protocol was designed to initi-ate repeated loading cycles, each of which was followed byrelaxation hold period of 30 s. During the relaxation holdsegment the load was adjusted continuously to maintain theindentation depth constant and equal to the maximum valueattained at the end of the preceding load segment. The dis-placement tolerance and the small incremental step load sizefor the dynamic calculation of the load during relaxation seg-ment were adopted to achieve a constant indentation depthduring relaxation period. Great care was taken to capture thefinal displacement upon termination of the loading cycle;this final displacement was used as the set-point for controla)Author to whom correspondence should be addressed. Electronic mail:aelmusta@odu.edu. Tel.: þ1-757-269-60670003-6951/2014/104(4)/041902/4/$30.00 VC 2014 AIP Publishing LLC104, 041902-1APPLIED PHYSICS LETTERS 104, 041902 (2014)during the relaxation hold segment. The tolerance and incre-ment step size were varied for the different repeated loadingcycles of the tests to minimize the noise during the relaxationphase. The load limit was varied from 50mN to 500mN. Inthis paper we only report on the 50mN and 500mN. Thetime to load for the first loading cycle was set at 20 s and thesame loading rate was followed for subsequent cyclic load-ings. Only the final relaxation segment is followed by theunloading cycle and the unloading rate was set equivalent tothe loading rate. Figure 1 shows a typical set of repeatedrelaxations for tests at two different maximum loads, 50mNand 500mN.The stiffness of contact was determined by the slope ofthe load and displacement curves during the unloading seg-ment of the test and the data were used to determine the me-chanical properties by the Oliver–Pharr analysis.22 Thenanoindenter continuously records displacement, load, andtime throughout the plunge. The hardness is calculatedbased on contact depth at the point of unloading followingthe end of the hold segment for a standard load control test.To accomplish this, the contact depth was extrapolatedthrough the hold segment using the as calculated valuesprovided by the test protocol at the end of the hold time atthe point of unloading. The contact depth was determinedby establishing the stiffness through the hold segmentaccording toS ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi4Pp  ðHErÞs; (1)where S is the stiffness, P is the load, H is the hardness, andEr is the reduced modulus.Based on Eq. (1), we were able to back out the stiffnessvalues at different load levels. Next, the contact depth wascalculated using Eq. (2) and subsequently the contact area byEq. (3). The hardness is determined from the load and thecontact areahc ¼ h e PS ; (2)where hc is the contact depth, h is the displacement, e is 0.75for a Berkovich tip, P is the load, and S is the stiffnessAc ¼ f hcð Þ: (3)Figure 2(a) shows the indentation load versus the dis-placement for a 50mN load control experiment with fiveincremental loading steps identified as A through E. Theload displacement curve is represented by the solid line andthe dotted line shows the extrapolated contact depth. To con-firm that the extrapolated values in Figure 2(b) were derivedcorrectly, the hardness values were calculated using the loadcorresponding to the intermediate increments A through D ofFigure 2(a) since the hardness value at E is automaticallyretained by the machine. It was found that the hardness val-ues correlate well with the load control method and theresults are indicated in Table I.The purpose of this work was to develop a technique ca-pable of examining the coupled relationship between V* andFIG. 1. Incremental load relaxations versus time for maximum loads of500mN and 50mN.FIG. 2. (a) Load versus displacement curve using the load control test proto-col with 5 incremental unloading segments. The dotted line shows the calcu-lated contact depth while the hardness calculated at each unloading arerepresented by A through E and are given in Table I. (b) Load versus dis-placement curve using the load control test protocol modified for repeatedload relaxations. The dotted line shows the calculated contact depth whilethe hardness calculated at each unloading are represented by A through Eand are given in Table I.041902-2 Stegall et al. Appl. Phys. Lett. 104, 041902 (2014)the components controlling the dislocation mobility usingnanoindentation. Some researchers have argued that attempt-ing to perform repeated relaxation testing in indentation isproblematic to obtain valuable results due to the complexstate of strain ahead of the indenter.23 We demonstrated thata repeated relaxation indention experiment can be imple-mented to equivocally generate results similar to thoseobtained using traditional uniaxial experiments.8,10,23Further, we have shown that the hardness (stress) can bedetermined with confidence at various load levels by extrap-olation of the contact stiffness using the Oliver and Pharranalysis allowing for the precise monitoring during the relax-ation hold segments. Therefore, we believe using repeatedrelaxation indentation experiments can be used to examinedislocation mechanisms that may be influencing the ISE.Based on this perspective, we are specifically interested inestablishing relationships between dislocation density andvelocity in the presence of an ISE.In dislocation plasticity, the activation volume repre-sents the volume in which dislocations are mobile duringthermal activation. In terms of the measured hardness, theapparent activation volume is generally defined by Eq. (4)and linked to the strain rate sensitivity of the hardness by Eq.(5).14 In these equations kB is Boltzmann’s constant, T is theabsolute temperature (K), H is the hardness, _e is the strainrate, and 9 is a factor that represents the Taylor factor andthe ratio of hardness to yield strength. It can be seen that theactivation volume is a rate dependent quantityV ¼ 9kbT @ln_e@lnH ; (4)m ¼ @lnH@ln_e : (5)The Orowan equation is represented by Eq. (6) and showsthat the strain rate is a function of the density of a movingdislocation qm with an average velocity v_e ¼ bqmv: (6)Caillard and Martin showed that when Eqs. (4) and (6)are combined, V* is examined based on the relative contribu-tions of the qm and v, but it is not possible to discern whichis dominating the stress.8 We modified their relationship totake into account the ratio of the flow stress to hardness andthe corresponding result is given byV ¼ 9kbT @lnqm@Hþ @lnv@H : (7)The activation volume V* is classically determined based onEq. (4) from a single transient creep or load relaxation test.13However, in order to examine the contribution of the rate ofthe dislocation density to the hardness and the rate of the dis-location velocity to the hardness as given by Eq. (7), we needto define Vr, a phenomenological activation volume and V,activation volume of the dislocation velocity which are bothneeded for the stress relaxation analysis according to Caillardand Martin.8 The first of these is Vr which is experimentallydetermined in conjunction with a time constant Cr to charac-terize the logarithmic nature of the relation. The second valueV is a measure of the dislocation density moving between thebeginning and end of successive relaxations. Therefore Vr, Cr,and V can be defined by the relations given in Caillard andMartin8 and modified here to account for hardness asDH ¼ 9KbTVr ln1þ tCr ; (8)V ¼ 9KbTDHln_ei2_ef1 : (9)In order to investigate the ISE from an activation vol-ume of the dislocation velocity perspective, V, a parameter Xwhich represents the ratio Vr to V needs to be defined todraw the relationship between qm and vX ¼ 1þ bð Þ 1þ KrM ; (10)where the value of Kr is the work hardening coefficient andM is the combined modulus of the machine and the speci-men.8 The value of Cr is used to determine the ratio ofqm/qmo that describes the change in the mobile dislocationdensity over the transient to the initial mobile dislocationdensity. This ratio is given by8qmqmo ¼ CrCr þ t  b1þb: (11)TABLE I. Comparison of the hardness results from load control and the ex-trapolated load relaxation experiments.Hardness (GPa)Measured ExtrapolatedInterval LC SRA 2.60 2.58B 2.22 2.19C 1.93 1.93D 1.67 1.71E 1.46 1.46FIG. 3. Hardness (stress) relaxations versus time compared with the ratio ofv/vo and q/qo for the 50 mN maximum load.041902-3 Stegall et al. Appl. Phys. Lett. 104, 041902 (2014)Finally, according to Caillard and Martin8 the ratio ofthe dislocation velocity v can be determined using the rela-tionship given inqmqmo ¼ vvo b: (12)Figures 3 and 4 show the change in hardness with theratios for the mobile dislocation density and velocity versustime for the repeated transients of a 50mN and 500mN maxi-mum loads, respectively. The data in these figures show thatthe dislocation velocity increases as the dislocation densitydecreases over each successive transient. The magnitude ofthe activation volume of the dislocation velocity, V, was foundto be on the order of 30b3 at 50mN and 70b3 at 500mNfor the first relaxation segments. The value of V at 500mN of70b3 is comparable to the value of 100b3 reported byWang et al. for bulk polycrystalline Ni obtained in a uniaxialrelaxation test .23 Further, they reported that in general thevalue of V tended to be a factor of two smaller than Vr fortheir experiments.23 We found a similar trend in our datawhere the ratio of Vr/V (X) according to Eq. (10), was on theorder of 2 for the first relaxation, but in our case the ratio tendsto increase with successive relaxations. We associate thisincrease in X to be influenced by the ISE and will explore thisissue in depth in forthcoming research.The purpose of this work is to develop an experimentaltechnique for indentation, beyond that of single transientcreep, capable of generating data to examine the coupledrelationship between V, q, and v for metals that exhibit anISE. We have presented a method for performing repeatedhardness (stress) relaxation tests using nanoindentation andhave demonstrated that this experimental technique can gen-erate results similar to those obtained using traditional uniax-ial experiments. Specifically, we derived the activationvolume of the dislocation density V, the phenomenologicalactivation volume Vr, which reasonably compare to previ-ously published values for polycrystalline nickel in tensionutilizing established closed form solutions. We found thatthe ratio of the initial to the final dislocation densitydecreases with increasing depth of indentation while the dis-location velocity increases. This finding would seem to indi-cate that as the depth of indentation decreases; the velocityof mobile dislocations is directly inhibited by the increase inthe dislocation density and is at a minimum consistent withthe accepted theory that the ISE is governed by a dislocationmechanism. A complete examination of the possible rela-tionship between these results and the ISE along with addi-tional pure metals will be covered in forthcoming research.1H. Mecking, U. F. Kocks, and H. Fischer, in Proceedings of the FourthInternational Conference on the Strength of Metals and Alloys, France,1976, p. 334.2R. W. Rohde and T. V. Nordstrom, Scr. Metall. 7(3), 317 (1973).3F. H. Dalla Torre, E. V. Pereloma, and C. H. J. Davies, Scr. Mater. 51(5),367 (2004).4C. Duhamel, Y. Brechet, and Y. Champion, Int. J. Plast. 26(5), 747 (2010).5K. Tanoue, Acta Metall. Mater. 40(8), 1945 (1992).6Y. M. Wang, A. V. Hamza, and E. Ma, Acta Mater. 54(10), 2715 (2006).7X. X. Wu, X. Y. San, Y. L. Gong, L. P. Chen, C. J. Li, and X. K. Zhu,Mater. Des. 47, 295 (2013).8D. Caillard and J. L. Martin, Thermally Activated Mechanisms in CrystalPlasticity, 1st ed. (Pergamon, Oxford, 2003), pp. 13–53.9B. Lo Piccolo, P. Spatig, T. Kruml, J. L. Martin, and J. Bonneville, Mater.Sci. Eng. A 309–310, 251 (2001).10J. L. Martin, B. Lo Piccolo, T. Kruml, and J. Bonneville, Mater. Sci. Eng.A 322(1-2), 118 (2002).11S. Caijun, E. G. Herbert, S. Sangjoon, J. A. LaManna, W. C. Oliver, andG. M. Pharr, J. Mech. Phys. Solids 61(2), 517 (2013).12Y. Liu, C. Huang, H. Bei, X. He, and W. Hu, Mater. Lett. 70(0), 26(2012).13D. S. Stone, T. Plookphol, and R. F. Cooper, J. Geophys. Res. B: SolidEarth 109(12), 1978 (2004).14A. A. Elmustafa and D. S. Stone, Mater. Lett. 57(5-6), 1072 (2003).15J. K. Mason, A. C. Lund, and C. A. Schuh, Phys. Rev. B: Condens. MatterMater. Phys. 73(5), 54102 (2006).16D. Pan and M. W. Chen, J. Mater. Res. 24(4), 1466 (2009).17B. Xu, Z. Yue, and X. Chen, J. Phys. D: Appl. Phys. 43(24), 245401(2010).18D. Stegall and A. A. Elmustafa, in Supplemental Proceedings: Volume 2:Materials Properties, Characterization, and Modeling, TMS (TheMinerals, Metals & Materials Society), Orlando, FL, USA, 11–15 March2012, pp. 747–752.19W. Bochniak, Acta Metall. Mater. 43(1), 225 (1995).20M. Z. Butt and P. Feltham, Metal Sci. 18(3), 123 (1984).21M. Z. Butt, P. Feltham, and S. M. Raza, Phys. Status Solidi A 84(2), K125(1984).22W. C. Oliver and G. M. Pharr, J. Mater. Res. 19(1), 3 (2004).23Y. M. Wang, A. V. Hamza, and E. Ma, Appl. Phys. Lett. 86(24), 241917(2005).FIG. 4. Hardness (stress) relaxations versus time compared with the ratio ofv/vo and q/qo for the 500 mN maximum load.041902-4 Stegall et al. Appl. Phys. Lett. 104, 041902 (2014)

Repeated Load Relaxation Testing of Pure Polycrystalline Nickel at Room Temperature Using Nanoindentation

D. E. Stegall

M. A. Mamun

B. Crawford

A. A. Elmustafa

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Applied Physics Letters

Repeated load relaxation testing of pure polycrystalline nickel at room temperature using nanoindentation

https://digitalcommons.odu.edu/cgi/viewcontent.cgi?article=1025&amp;context=mae_fac_pubs

Repeated Load Relaxation Testing of Pure Polycrystalline Nickel at Room Temperature Using Nanoindentation

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