Young s Modulus Measurement Using a Simplified Transparent Indenter Measurement Technique

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1 Exerimental Mechanics (008) 48:9 5 DOI 0.007/s Young s Modulus Measurement Using a Simlified Transarent Indenter Measurement Technique C. Feng & B.S. Kang Received: October 006 /Acceted: 6 July 007 / Published online: 9 August 007 # Society for Exerimental Mechanics 007 Abstract In material nano- and micro-indentation research, it is well acceted to use the initial unloading stiffness of the load-deth curve to determine the material s Young s modulus. This aroach requires the use of high-recision dislacement sensors in order to calibrate the loading aaratus system comliance and thus obtain the loaddeth curve accurately. In this research, using a transarent sherical indenter couled with a multi-artial unloading technique, we resent a simler aroach to measure the material s Young s modulus. Exerimental results of several metallic alloys and related discussions are resented. Keywords Transarent indenter measurement (TIM). Sherical indentation. Young s modulus measurement. Load-deth curve. Multi-artial unloading Introduction In material nano- and micro-indentation research, among all the indentation arameters, load-deth relation and unloading characteristics have been studied extensively either exerimentally or numerically to elucidate the relevant mechanical behavior or roerties. For examle, it is well acceted to use the initial unloading stiffness of the loaddeth curve to determine the material s Young s modulus [ 4]. This aroach can be traced back to Sneddon s [] classical elastic indentation solutions which describe the general relationshi among the load, dislacement and C. Feng (*, SEM member) : B.S. Kang Mechanical and Aerosace Engineering Deartment, West Virginia University, Morgantown, WV 6506, USA chuanyufeng@yahoo.com contact area for any unch that can be treated as a solid of revolution of a smooth function. In the 970s, Bulychev et al. [] defined the initial unloading sloe and reduced modulus, thus roviding a theoretically sound methodology for determining the Young s modulus. This method is alicable to both sherical and yramidal indenters. Using instrumented indentations, Doerner and Nix [3] further investigated the unloading characteristics. In 99, Oliver and Pharr [4] showed that Bulychev s technique can be alied to any indenter that can be described as a body of revolution of a smooth function. In the indentation research for Young s modulus measurement, the contact area and initial unloading stiffness are the key arameters to be determined. However, in most cases, direct measurement of the contact area is not alicable or not ossible. Tyically, the unloading stiffness is used to estimate the contact area through some iterative algorithm [5, 6]. Furthermore, high-recision dislacement sensors are needed in order to accurately obtain load-deth curve and the unloading stiffness data [ 4]. As for the direct measurement of contact area, Kleesattel [7] designed a secial aaratus for direct measurement of the contact region through a sherical sahire indenter while conducting indentation tests, but the scanning method yields only one line of the contact region, and real-time access of the indented surface is not ossible. By alying a secial lighting technique, Frank [8] develoed a transyramidal indentation viewing system. It was also imlemented by Sakaia et al. [9] using a similar technique. Recently, we have develoed a Transarent Indenter Measurement (TIM) technique [5, 6]. By integrating a Twyman-Green tye interferometer with the sherical transarent indenter head, the TIM system can directly measure the indentation-induced out-of-lane deformation as well as the indented surface. It was found that by using the difference of out-of-lane

0 Ex Mech (008) 48:9 5 Fig. Simlified transarent indenter measurement technique with in-line imaging system deformation, Young s modulus can be evaluated without unloading stiffness measurement.

2 0 Ex Mech (008) 48:9 5 Fig. Simlified transarent indenter measurement technique with in-line imaging system deformation, Young s modulus can be evaluated without unloading stiffness measurement. Recently, a similar TIM aroach was also done by Miyajima and Sakia [0] using sahire sherical indenters on Aluminum and Zirconium oxide materials. In this aer, we resent a simlified TIM method for material s Young s modulus measurement. Comared with our revious work [5, 6], the simlified TIM method does not include interferometric otics and requires only a millimeter-size samle alloy for the indentation test, thus greatly simlifying the indentation test setu. Theory As shown in equation () [ 4], for material s Young s modulus measurement using deth-sensing indentation method, the initial unloading stiffness (/dh) of a loaddeth curve and the contact area (A) are the key arameters to be determined. Usually, the contact area, A, is estimated indirectly from the measured unloading stiffness couled with iterative scheme [5, 6] or determined afterwards using microscoic methods, such as otical microscoy, SEM, AFM, etc. dh ¼ ffiffiffi ffiffiffi E r A ðþ where P is the indentation load, h is the indentation deth, A is the indentation contact area, E r is the reduced modulus and E r ¼ v E þ v 0 E 0, where E is the Young s modulus, v is Poisson s ration of the secimen, and subscrit 0 denotes the indenter s mechanical roerties. Figure shows the simlified otical TIM method whereas the contact area, A, is measured directly through a transarent sherical indenter. As for the unloading stiffness (/dh) measurement, a closed-loo control PZT actuator is imlemented in the TIM aaratus as the loading device to conduct this measurement. The PZT actuator rovides high resolution dislacement control (± nm). However, the measured PZT ti dislacement, h PZT, includes both the loading system dislacement, h s, and the indention deth, h, i.e., h PZT =h s +h. In terms of comliance, it can be written as ¼ dh s þ dh ðþ Substitute equation () into equation (), ¼ dh ffiffiffi s þ ffiffiffi ð3þ A E r or ffiffiffi ¼ C s þ ffiffiffi ð4þ A E r where C s ¼ dh s is the system comliance, including the loading frame and all other comonents in the system. During a simlified TIM indentation test, the system comliance (C s ) is assumed to remain constant within a roer loading range. Under this assumtion, as shown in Fig. (a) and based on equation (4), for a simlified TIM indentation test with Fig. Schematic loaddislacement curve of a TIM indentation test. (a) With one additional artial unloading (b) With multi-artial unloadings during one indentation test Load (P) Load (P) (a) (b) Dislacement (h PZT ) Dislacement (h PZT )

3 Ex Mech (008) 48:9 5 two adjacent loading/artial unloading stes, the unloading comliances for both stes and can be written as: ffiffiffi j ¼ C s þ ffiffiffiffiffi ð5þ A E r j ¼ C s þ ffiffiffi ffiffiffiffiffi A E r Subtracting equation (5) from equation (6), the system comliance is cancelled out, and the difference of unloading comliance becomes, j dh ffiffiffi PZT j ¼ ffiffiffiffiffi ffiffiffiffiffi ð7þ E r A A Thus the reduced modulus can be calculated from equation (7): ffiffi ffiffiffiffi ffiffiffiffi A A E r ¼ j dh ð8þ PZT j Equation (8) shows that the reduced modulus can be obtained exerimentally from two artial unloading stes of a TIM indentation test. Young s modulus of the tested material can thus be determined from the reduced modulus E r, E ¼ v E r v 0 E 0 ð6þ ð9þ This rocedure can be further extended into multi-artial unloading stes, as shown in Fig. (b) with the corresonding in-line contact area measurement. Let s rewrite equation (4) as equation (0) such that both a (recirocal of reduced modulus) and b (system comliance) can be obtained through linear regression. ¼ ffiffiffi ffiffiffi þ C s ð0þ E r A or y ¼ ax þ b where y ¼, a ¼ E r, x ¼ ffiffi ffiffi, b ¼ C A s : Equation (0) rovides a convenient guideline to justify the validity of the roosed methodology, i.e., if the system comliance changes during the indentation loads, the linear relationshi as deicted in equation (0) can not be maintained. Further Discussion of System Comliance For mechanical roerty measurement using instrumented nano/micro indentation technique, the effect of the system comliance is always a concern and this is why in-situ high recision and sometimes sohisticated dislacement sensor is often used to remedy this roblem. In this aer, we roose a rather simle aroach to try to alleviate this roblem by making the assumtion that within a selected loading range (of an indentation test where data are collected for mechanical roerty evaluation) the system comliance is constant (i.e. load versus load-line system dislacement is linear within the loading range). We acknowledge that, exerimentally, it is difficult to conduct direct measurement of the system comliance and thus rove the validity of this assumtion. However, we noticed the investigation work of Oliver and Pharr [4] on system comliance measurement. Their aroach is similar to what described in this aer, the difference is that instead of calculating the Young s modulus as roosed in this aer, it was used for system comliance determination [4]. Secifically, equation (0) shows that if the system comliance, C s, is constant within the loading range, a lot of the measured comliance (y) versus ffiffi should be linear, A and the intercet is the system comliance C s. This rocedure was used by Oliver and Pharr [4] for system comliance determination. Exeriments Exerimental Setu As shown in Fig., a sahire half-sherical indenter (.5 mm diameter in this research) is attached to a hollow stainless steel suorting block, which is then attached to a load cell and PZT actuator. A mirror is mounted inside the hollow stainless steel suorting block. An exchangeable long working distance microscoe is attached to the indentation aaratus to cature the surface indentation images (i.e., the indented area, A). For the micro-indentation tests conducted in this aer, a 0 objective lens was used and through image analysis and calibration, the edge detection resolution of the indentation zone has an error of less than 0.5 μm. In order to run the indentation test and acquire related load-dislacement data and indented area images automatically, two LabVIEW rograms were develoed. One detects the initial contact between the indenter ti and secimen, and the other controls the indentation test as well as the data and image acquisition. Test Procedure A tyical TIM test involves two stes. The first ste is the initial adjustment. The secimen is first attached to the secimen holder and a dro of index matching fluid is oured to fill the ga between the indenter ti and the secimen. The initial contact between the indenter and the secimen surface is established by running an initial adjustment rogram,

4 Ex Mech (008) 48:9 5 Fig. 3 Results of Al 7075-T6 indentation test. (a) Load dislacement curve with multiartial unloadings. (b) Indented surface at unloading stes, 5, and 0, field of view: 395 μm 377 μm. (c) Comliance y ¼ dhpzt vs. variable x ¼ ffiffi π ffiffi A which automatically moves the indenter until it reaches the initial contact osition. For this research, the initial contact criterion is set to within a certain threshold load ( 0. N). When the alied load aroaches the threshold load, the indenter will sto moving, record and set the initial contact osition. If initial contact is to be avoided, the rogram can also retract the indenter to a certain distance after the initial contact has been found. After the initial contact is established, another LabVIEW rogram is used to define the indentation arameters (i.e., multi-artial unloading stes, data and image file names, velocity control, etc), and then conduct the indentation test automatically. For the results shown in this aer, all tests were conducted with ten loading/artial unloading stes, and each artial unloading dislacement was either 0.5 or μm, nominally. Table Measured Young s modulus of Al 7075-T6 Test Young s modulus (GPa) Error (%) # # # # #

5 Ex Mech (008) 48:9 5 3 Fig. 4 Results of Inconel 783 indentation test. (a) Load dislacement curve with multiartial unloadings. (b) Partial unloading/reloading at 5 μm. (c) Partial unloading/reloading at 30 μm. (d) Comliance y ¼ dhpzt vs. Variable x ¼ ffiffi π ffiffi A Test Materials Two alloys, Al 7075-T6 and Inconel 783 were selected for verification tests, and one research alloy Re-(6 30wt%)Cr was also investigated. The cast alloy Re-(6 30wt%)Cr was obtained from Oak Ridge National Laboratory (ORNL) as reorted in [3, 4]. The ublished Young s modulus values for Al 7075-T6 and Inconel 783 are 7.7 and 77.3 Ga, resectively [, ]. The Inconel 783 alloy had standard heat treatment (0 C/ h/ac+845 C/8 h/ac+ 70 C/8 h 50 C/h 60 C/8 h/ac). The Young s modulus of the sahire indenter is 340 Ga with Poisson s ratio equal to 0.9. Results Al 7075-T6 Figure 3(a) shows the indentation load and dislacement data. A detailed artial unloading ste was inserted into Fig. 3(a) to manifest the artial unloading. Prior to each

6 4 Ex Mech (008) 48:9 5 Table Measured Young s modulus of Inconel 783 Test Young s modulus (GPa) Error (%) # # # # # artial unloading, image of the indented contact zone was digitally catured in real time. Figure 3(b) shows the tyical indented surface images at unloading stes, 5 and 0. The frame dimension for each image is 395 μm by 377 μm. Those images were then rocessed to obtain the contact area at corresonding loading/unloading stes. Based on the unloading line data, comliances at each unloading ste were calculated. The rocessed data are shown in Fig. 3(c), which shows the existence of a linear relationshi within most of the alied indentation loading range. However, the data starts to deviate from the linear relationshi at higher indentation loads, indicating the breakdown of the constant system comliance assumtion, as discussed in the Theory and Further Discussion of System Comliance sections. Using the linear unloading line, Young s modulus was calculated by alying Equation 0 and assuming a Poisson ratio of 0.3. Table summarizes the results from five indentation tests. An average value of 68.7 Ga with a 4.4 Ga standard deviation was obtained. The exerimental data obtained are in good agreement with the book value of 7.7 Ga. Fig. 5 Results of cast Re-(6 30wt%)Cr indentation test. (a) Load dislacement curve with multi-artial unloadings. (b) Indented surface at unloading stes, 7, and 8, field of view: 395 μm 377 μm. (c) Comliance y ¼ dhpzt vs. Variable x ¼ ffiffi π ffiffi A

7 Ex Mech (008) 48:9 5 5 Inconel 783 Test results for Inconel 783 are shown in Fig. 4. Based on the linear unloading line data [e.g. Fig. 4(b,c)], comliances were calculated. The indented surface images were rocessed to obtain the contact area at corresonding loading/ unloading stes. Similar to the Al 7075-T6 test, a linear relationshi is observed within most of indentation loads [Fig. 4(d)] and the data starts to deviate at higher indentation loads. Again, using only the linear art in Fig. 4(d), and based on equation (0), Young s modulus values were calculated. Table summarizes the results for Inconel 783 from five indentation tests. An average value of 77.9 GPa with a 6. GPa standard deviation is obtained and agreed well with the book value of 77.3 GPa. Re-(6 30wt%)Cr An exloratory indentation test on a cast alloy Re-(6 30wt%) Cr [3, 4] is shown in Fig. 5. The load-deth curve shown in Fig. 5(a) clearly shows a sudden decrease of load between Stes 7 and 8. This was due to the onset of sli band formation near the surface high tensile stress region, as shown in Fig. 5(b). Due to the sudden change of the load, there is a noticeable comliance change in unloading ste 8, as shown in Fig. 5(c). Using indentation data before Ste 8, the Young s modulus was determined to be 34 GPa. Conclusions In this aer, without interferometric otics used in the original TIM technique [5, 6], a simlified TIM technique has been develoed. Couling with a multile artial unloading testing rocedure, material s Young s modulus can be determined using the simlified TIM method. Verification tests on Al 7075-T6 and Inconel 783 were conducted and the results agree well with the ublished values. An exloratory test of a new cast Re- (6 30wt%)Cr alloy was also conducted. Test results show the caability of the simlified TIM method to detect the sudden onset of sli bands. It should be noted that under large loads, the system comliance may change areciably and the roosed method to obtain the material Young s modulus may not be alicable. It is also ossible that the multi-artial unloadings can accumulate surface microstructural damage thus lowering the Young s modulus calculation using the unloading line aroach. Acknowledgement The work is sonsored by the Office of Fossil Energy, Advanced Research Materials (ARM) Program, U.S. Deartment of Energy, under contract DE-AC05-00OR75 managed by UT-Battelle, LLC. References. Sneddon IN (965) The relation between load and enetration in the axisymmetric Boussinesq roblem for a unch of arbitrary rofile. Int J Eng Sci 3: Bulychev SI, Alekhin VP, Shorshorov MKh, Ternovskii AP, Shnyrev GD (975) Determining Young s modulus from the indentor enetration diagram. Ind Lab 4(9):409 4 (Se). 3. Doerner MF, Nix WD (986) A method for interreting the data from deth-sensing indentation instruments. J Mater Res (4): (Jul/Aug). 4. Oliver WC, Pharr GM (99) An imroved technique for determining hardness and elastic modulus using load and dislacement sensing indentation exeriments. J Mater Res 7(6): (June). 5. Taljat B, Zacharia T (998) New analytical rocedure to determine stress strain curve from sherical indentation data. Int J Solids Struct 35(33): Haggag FM (989) Field indentation microrobe for structural integraity evaluation, U.S. atent no. 4,85,397, August. 7. Kleesattel C (98) Method and aaratus for the measurement of hardness testing indentations. U.S. atent no. 4,77,74, July Frank S (000) Transyramidal indentation viewing new ossibilities for mobile hardness testing. In: 5th world conference on non-destructive testing, Rome, October. 9. Sakaia M, Hakiri N, and Miyajima T (006) Instrumented indentation microscoe: A owerful tool for the mechanical characterization in microscales. J Mater Res (9): (Se). 0. Miyajima T, and Sakaia M (006) Otical indentation microscoy a new family of instrumented indentation testing. Philos Mag 86 (33 35): ( Nov Dec).. POC Comany. IN783 mechanical roerties. htt:// MatWeb. Al 7075-T6 mechanical roerties. htt:// 3. Brady MP, Anderson IM, Weaver ML, Meyer HM, Walker LR, Miller MK, Larson DJ, Wright IG, Sikka VK, Rar A, Pharr GM, Keiser JR, and Walls CA (003) Nitrogen imurity gettering in oxide disersion ductilized chromium. Mater Sci Eng A 358( ): Ma N, Cooer BR, and Kang BS (006) Tight-binding study of thermal exansions for Mo3Si. J Al Phys 99: Chuanyu F (005) Develoment of a transarent indenter measurement system and indentation analysis for material mechanical roerties evaluation. Dissertation, West Virginia University, Feng C, Kang BS (006) A transarent indenter measurement method for mechanical roerty evaluation. Ex Mech 46():9 03 (Feb).

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