Materials characterization and classification on the basis of materials pile-up surrounding the indentation

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Materials Science and Engineering A 408 (2005) 158 164 Materials characterization and classification on the basis of materials pile-up surrounding the indentation G.

Ghosh Material Science and Technology Division, National Metallurgical Laboratory (CSIR), Jamshedpur 831 007, India Received in revised form 19 July 2005; accepted 19 July 2005 Abstract The ball

1 Materials Science and Engineering A 408 (2005) Materials characterization and classification on the basis of materials pile-up surrounding the indentation G. Das, Sabita Ghosh, Sukomal Ghosh, R.N. Ghosh Material Science and Technology Division, National Metallurgical Laboratory (CSIR), Jamshedpur , India Received in revised form 19 July 2005; accepted 19 July 2005 Abstract The ball indentation technique (BIT) has been used to classify various engineering materials on the basis of observed pile-up/sink-in in materials, surrounding the indentation. In respect of revealed pile-up, viz., prominent, moderate and negligible, the materials could be classified into three respective groups. The dependence of the pile-up on the yield ratio and the strain-hardening exponent of materials have also been established as a novel concept. The actual indentation diameters (both plastic and total) differ from the diameters calculated from the depth of indentation measured by linear variable transducers (LVDT). This difference is due to the accumulation of materials (pile-up) surrounding the indentation. The methodology to determine the correction factor, to be incorporated in the measurement of actual diameter, has been highlighted and is compared with the reported approach Elsevier B.V. All rights reserved. Keywords: Ball indentation technique; Pile-up; Mechanical properties; Yield ratio; Materials classification 1. Introduction The conventional methods to evaluate mechanical properties of materials are well established. Yet, evaluation of the same through tests conducted in situ or by using small amount of test materials, are in great demand for estimation of remaining lives of service-exposed components [1 13]. The ball indentation test requires a small amount of material. During indentation, underneath the indenter, the material undergoes plastic deformation. An elastic zone surrounds this plastic deformation. Therefore, the plastic zone is always in a state of confinement. The indentation impression grows with increase in load resulting in extension of the plastic zone. At the surroundings of the indentation, a material pile-up/sink-in are observed due to the forced flow of material caused by the multiaxial stresses acting at this region. The extension and the height of accumulation of materials was found to be independent of the size of impression [14], yet, dependent on the work hardening Corresponding author. Tel.: ; fax: address: gd@nmlindia.org (G. Das). characteristic of the material [15]. The formation of this pile-up/sink-in in materials has a significant influence on the accuracy of measurement of indentation diameter. The actual diameter of indentation differs from that calculated from the depth of indentation, measured by linear variable transducers (LVDT), often, the difference is too large to be ignored. Some of the present authors [16 20] did extensive work on the influence of pile-up in materials in measurement of indentation diameter using a hard spherical ball. They observed that the accumulation of materials surrounding the indentation was not only dependent on the work hardening characteristic of the material but also on the initial prestraining of the test sample. It was shown [19] that the Lüders band appearing during conventional test on pre-strained samples had correlation with the formation of pile-up/sink-in. To determine the indentation diameter from the LVDT measured depth of indentation, they [16 21] did consider the pile-up phenomenon. Meyers and Chawla [22] worked on pile-up/sink-in behaviour of materials using a conical indenter. They divided the metallic materials into three categories according to the nature and extent of deformation surrounding the indentation. Those were (a) non-work hardening, (b) work hardening and /$ see front matter 2005 Elsevier B.V. All rights reserved. doi: /j.msea

G. Das et al. / Materials Science and Engineering A 408 (2005) 158 164 159 (c) work softening metals.

2 G. Das et al. / Materials Science and Engineering A 408 (2005) (c) work softening metals. The elastic stresses underneath the indenter were not easily accommodated in the metal that exhibited high work hardening rate. Thus, a large plastic zone existed beneath the indenter. On the other hand, due to least resistance to plastic deformation, localized plastic zone was observed in non-work hardening metals. The latter exhibited more extension and height of bulging (pile-up) compared to the former. The extent of plastic zone, along the surface, often observed to be six times the diameter of the indenter [22]. The bulging, surroundings the indentation, affects the dimension of the indented area and consequently the values of true-stress and true-strain of the material. Therefore, in any attempt to determine the mechanical properties, due consideration of pile-up/sink-in is of utmost importance. In determination of mechanical properties of materials from indentation diameter obtained from depth of indentation, one Korean group [23] had due consideration of the effect of pileup/sink-in. A practical parameter has been contemplated in this work to classify the materials. This is termed as yield ratio (YR) and is defined as the ratio of yield strength (YS) to ultimate tensile strength (UTS). As a specification of materials, both YS and UTS are usually known. The present work attempts to explore a relationship amongst the pile-up/sink-in, strain-hardening exponent and yield ratio parameter of some engineering materials. The work also aims to establish a suitable correction factor to determine the actual indentation diameter having due consideration of pile-up/sink-in in materials. 2. Experimental procedure A laboratory scale set-up, developed in-house [16,19], has been used for the conduction of the ball indentation tests. Conventional tests also have been carried out on test specimens as per ASTM standards, to validate BI test results by comparison. The conventional tensile test has been carried out by using an INSTRON 8529 mechanical testing machine. Fig. 1. Cross-sectional view of the indentation profiles for CP Cu (a and b), HSLA 100 steel (c and d) and HSLA 80 steel (e and f), showing prominent pile-up surrounding the indentation.

160 G. Das et al. / Materials Science and Engineering A 408 (2005) 158 164 2.1. Test specimen for BIT The dimensions of the test samples vary from 5 mm 5mm 2mmto10mm 10 mm 6 mm.

3 160 G. Das et al. / Materials Science and Engineering A 408 (2005) Test specimen for BIT The dimensions of the test samples vary from 5 mm 5mm 2mmto10mm 10 mm 6 mm. These samples are ground using an electrical grinding machine for proper surface preparation. The surfaces are further polished with emery paper up to 1000 grade. Care has been taken to ensure the uniform thickness of the test specimens (noting average of measurement using a digital Vernier caliper) BI test The details of experimentation, using ball indentation technique (BIT) have been published elsewhere [16 21]. The tests have been carried out at room temperature. In the experimentation, the prepared samples are placed on the test bed. The test head is properly aligned so that the load is perpendicular to the surface. With the help of software [16 21], the initial load is set at zero and the indenter tip is allowed to proceed gradually towards polished surface with pre-set indenter velocity of mm/min, depending on the nature (strain rate sensible) of the material under test. A particular experiment, when terminated, shows the total indentation depth measured by LVDT is less than the radius of the indenting ball. Records of applied load and corresponding depth are stored in a PC, attached with the BI set-up. Several load cycles (typically six or more) are performed at the same indentation location to determine the true-stress/true plasticstrain curve (data from each load cycle yield a point on this curve). From the plotted true-stress/true plastic-strain curve, the strain-hardening exponent (n) is determined [16]. The BI tests are repeated for several times for each of the material under the same test condition and similar test parameters. Multiple load depth curves constitute raw data in these experiments. For each cycle, the total (h t ) as well as plastic indentation depth (h p ) and corresponding maximum applied load are obtained from the load deflection curve generated from digitally stored load deflection data. Typically, for each successive cycle, the load increases. For each loading cycle, the total depth (h t ) of indentation is obtained at a sustained load and the plastic indentation depth (h p ) is obtained after complete unloading. The unloading curve is fairly linear. Fig. 2. Cross-sectional view of the indentation profiles for CP Al (a and b), SA 333 steel (c and d) and En 24 steel (e and f), showing moderate pile-up surrounding the indentation.

4 G. Das et al. / Materials Science and Engineering A 408 (2005) The computer program calculates the slope of each unloading curve and the intersection of the extrapolated unloading line with the zero load line (abscissa or X-axis) indicates the value of h p. The raw data are analyzed to obtain flow curve and flow properties. In specific cases, the analytically determined plastic diameter is compared with the plastic diameter of the indentation profile, measured by optical microscope, to effect validation. For the studies of pile-up/sink-in in materials, the indented specimens have been coated by electroless nickel deposition. The nickel-coated samples are sectioned transversely at a distance slightly away from the indentation profile using a precession diamond cutter. The specimens are mounted, fine ground and polished till the total diameter of the indentation profile is revealed. The specimens are polished and examined under optical and scanning electron microscope Materials for experimentation The investigations have been conducted on different engineering materials. These are, SA333, SS316L, En-24 (designated as A, B, C and D based on varying microstructure), HSLA steel (GRV 100 and GPQ 80), mild steel, Cr Mo steel (16 Cr Mo 44 and 9 Cr Mo), ASTM A517 Gr.F, brass (60% Cu, 40% Zn), commercial pure copper (CP Cu), commercial pure aluminum (CP Al), and nickel base super alloy (Udimet 700). 3. Results and discussion To evaluate the mechanical properties of materials by BIT, the indentation diameters are determined from the depth of indentation, measured by LVDT. The contact area determined from LVDT measured depth, however, differs from the actual contact area of the indented surface. This difference is due to the pile-up in materials formed during indentation. The incorporation of correction factor is necessary to determine the actual contact area between the indenter and the specimen, in conjunction with the measured depth of indentation by LVDT. The work of Das et al. [19,20] corroborates this fact. According to them, the pile-up in materials and subsequent correction factor vary as per work-hardening characteristic of the materials and these, also depend on prior mechanical working of the materials. The light microscopy and SEM studies on the morphology of pile-up/sink-in reveal that extent of pile-up/sink-in is material dependent and differs from one material to another. The forms of pile-up/sink-in in different materials are shown in Figs These are designated in category of prominent, moderate and negligible. Fig. 1 shows the cross-sectional view (a, c and e) as well as magnified view (b, d and f) of CP Cu and HSLA (GRV and GPQ) steels. A considerable amount of accumulation of material, termed as prominent pile-up, surround the indentation. Comparatively, a moderate pile-up has been observed Fig. 3. Cross-sectional view of the indentation profiles for Ni base super alloy (a and b) and brass (c), showing negligible pile-up surrounding the indentation.

5 162 G. Das et al. / Materials Science and Engineering A 408 (2005) in CP Al, SA333 and En-24 steel, as shown in Fig. 2(a, c and e) with corresponding magnified views (b, d and f). The nickel base super alloy and brass exhibit negligible pile-up (Fig. 3). In this category of materials, it is expected that, actual indentation diameter and diameters determined from the depth of indentation measured by LVDT are almost similar. The materials, those show negligible pile-up may not require incorporation of correction factor. Mathew et al. [2] suggested that indentation diameter, d p, can be determined from h p, if there is no accumulation of test material around the indentation. This supposition is based on their studies on the effect of ageing on mechanical properties of alloy 625. According to the Jang et al. [23], a suitable correction factor can be determined from the load depth curve. A schematic of a single cycle, loading unloading (P δ) curve is shown in Fig. 4. The linear part of P δ plot, during unloading, is extrapolated to find the value of h i, the intercept indentation depth. From the h max, depth at the maximum indentation load, the contact depth (h c ) has been evaluated by analyzing the unloading curve considering the indenter geometry and elastic deflection in accordance with the mentioned relation [23] h c = h max w(h max h i ) (1) where, w is the indenter shape parameter and of value 0.75 for the spherical indenter [23]. The material pile-up around the indentation produces the actual contact radius larger than the apparent one. The following empirical relation [23] determines the extent of this pile-up, expressed in a ratio. C 2 = a2 5(2 n) = (2) a 2 2(4 + n) where, C is a constant, n is the work hardening exponent of the material, a is the actual contact radius and a * is the apparent radius (without pile-up). Using the mentioned geometrical relationship of the spherical indenter, the actual contact radius is expressed in terms of h c and indenter radius Fig. 4. Schematic diagram of a single cycled load depth curve with the slope of the unloading line. Table 1 Comparison of the indentation diameters determined through the approach of Jang et al. and proposed approach in the present case Deviation in dp (mm) dp determined using Eq. (3) (mm) C by using Eq. (2) n from conventional test dp after implying correction factor (mm) Correction factor as per proposed approach (mm) dp from LVDT (mm) Investigated materials Indentation load (N) CPCu HSLA steel (GRV) HSLA steel (GPQ) ASME A517 Gr.F Cr 44 Mo steel Cr Mo steel En-24(A) a En-24(B) a En-24(C) a Mild steel SA SS316L CPA Brass Udimet a With various microstructure.

6 G. Das et al. / Materials Science and Engineering A 408 (2005) R as[23] a 2 = C 2 (2Rh c h 2 c ) (3) As listed in Table 1, the values of d p for all the experimental materials have been determined at a specific load by using a, obtained from Eq. (3). The constant C ineq.(2), isa function of work hardening exponent n, which is material parameter and need to be separately determined during each experiment. In the present work, to introduce simplicity, an attempt has been made where only the established parameter (Young s modulus) is considered for determination of d p, through the regression analysis of the following Hertzian [15] equation (Eq. (4)). The value of n has been determined by using the values of d p, whereas in the reported approach the conventionally obtained n values were used for determining the values of a and hence d p. Also conventional determination of n has been done in the present case for the purpose of validation (Tables 1 and 2). ( d p = P + 1 ) { h 2 p D + } 0.25d2 p E 1 E 2 h 2 p d2 p h pd p (4) where, E 1 and E 2 are respectively the Young s modulus of the indenter and the test specimen. The plastic depth of indentation, h p, is measured through LVDT attached to the BI set-up. The indented diameters (plastic), at various loads, are also measured through optical microscope. Thus obtained both the diameters (against each load) are separately fitted in second-degree polynomial equation and plotted in a load diameter curve (Fig. 5). At a particular load, the difference between the values of two diameters ascertains the required correction factor. With increase in load, the extent of pile-up is expected to increase (depending on the nature Fig. 5. Plastic indentation diameter obtained from optically measured and LVDT determined plastic indentation depths vs. indentation load plots for CP Cu. of material), so is in the absolute value of the correction factor. The d p values of various materials at a particular load have been determined following the approach of Jang et al. [23] and also through pursuance of mentioned present approach. Table 1 depicts the convergence of d p values obtained from both the approaches. In BI test, the strain-hardening exponent (n) has been determined from correction incorporated actual indentation diameter [16]. The obtained values, when compared with the values determined from conventional test, are found to be in close approximation (Table 2). The bulging behaviour of various materials is correlated with the yield ratio (YR) and work hardening characteristic (n) of the materials and a classification of materials are made accordingly (Table 2). The YR values are separately determined by using UTS and YS values obtained both from BIT and conventional tests. The YR values obtained through BI test are mentioned in bracket in Table 2. The investigated materials could be classified on the basis of Table 2 Classification of material based on pile-up/sink-in and yield ratio (YR) parameter of the investigated materials Investigated materials n values [conventional and BIT (in the bracket) obtained] YR = (YS/UTS) 100 [Conventional and BIT (in the bracket) obtained] in % Extent of pile-up CPCu (0.04) 98.5 (99.6) HSLA steel (GRV) 0.08 (0.081) 95 (88) ASMEA517 (welded zone) 0.09 (0.08) 92 (94) Prominent HSLA steel (GPQ) (0.11) 88 (90) 16Cr 44Mo steel (0.13) 75 (73) 9Cr Mo steel (0.166) 75.7 (76) En-24(A) a 0.17 (0.1698) 62.5 (64) En-24(B) a (62) Moderate En-24(C) a 0.12 (0.122) 77 (70) Mild steel 0.28 (0.23) 62.4 (61.68) SA (0.267) 72 (68) SS316L 0.3 (0.31) 47.8 (48.8) CPA (0.196) (45.3) Brass 0.34 (0.349) (35.58) Negligible Ni base super alloy (Udimet) 0.43 (0.41) 65 (63.55) a With various microstructure.

7 164 G. Das et al. / Materials Science and Engineering A 408 (2005) yield ratio and strain hardening exponent. In reference to Table 2, it is observed that the materials having lower n values (less than 0.12) show a prominent pile-up, also, these can be grouped in the category of materials showing yield ratio ranging between 88% and close to 100%. The inference is, the materials with high yield ratio and having low strain hardening exponent (<0.12), exhibit prominent pileup. The affiliations of these materials are to a group, which show low work hardening rate. In this case, the required correction factor, to determine the actual indentation diameter is higher for highest allowable load (i.e. the maximum load on the load deflection curve). The maximum additive correction factor at the highest load level is in the range of 0.1 mm. The materials with YR parameter in the range of 50 75% and with intermediate strain hardening exponent (0.12 < n < 0.3) show moderate pile-up. This group of materials posses medium work hardening rate, and the correction factor, for this group of materials is about mm. The least or almost negligible pile-up is observed in the materials of low YR values (<40%) and high strain hardening exponent values (>0.3). The only exception is for Udimet 700. The work hardening rate of materials under this category is comparatively higher. Incorporation of correction factor may not be required to determine the actual indentation diameter for this group of materials. 4. Conclusions Based on the experimentation and obtained results, following conclusions are drawn. 1. The yield ratio (YR), a novel material parameter, could be introduced as an index of material pile-up and subsequent classification of metallic materials. 2. The materials have been classified into three distinct categories, based on the formed pile-up, which has correlation with yield ratio and strain hardening exponent. 3. The strain hardening exponents, determined from correction incorporated actual diameter are in good agreement with the values determined by conventional tests. 4. Though direct measurement of indentation diameter through optical microscope does not require incorporation of correction factor, yet, incorporation of correction factor is necessary for determination of actual diameter from indentation depth measured by LVDT. 5. The correction factors determined through present approach and those obtained by pursuance of reported approach are analogous. 6. The correction factors are similar for the materials belonging to the same classified group. 7. The investigation postulates that similar correction factor can likely be introduced for other materials on the basis of yield ratio. Acknowledgements The authors would like to thank their colleagues Dr. S. Tarafder, Shri S.K. Das and Shri P.K. De for their extended help and participation in stimulating discussion. The authors are also grateful to Prof. S.P. Mehrotra, Director, National Metallurgical Laboratory (NML), for received encouragement and his permission to publish this work. One of the authors conveys thank to the Council of Scientific and Industrial Research (CSIR), India, for granting her fellowship to carryout this work. References [1] F.M. Haggag, G.E. Lucas, Metall. Trans. A 14 (1983) [2] M.D. Mathew, K.L. Murty, K.B.S. Rao, S.L. Mannan, Mater. Sci. Eng. A 264 (1999) 159. [3] K.L. Murty, F.M. Haggag, Miner. Metals Mater. Soc. (1996) 37. [4] K.L. Murty, M.D. Mathew, Y. Wang, V.N. Shah, F.M. Haggag, Int. J. Pres. Ves. Piping 75 (1998) 831. [5] F.M. Haggag, T.S. Byun, J.H. Hong, P.Q. Miraglia, K.L. Murty, Scripta Mater. 38 (1998) 645. [6] F.M. Haggag, ASME 429 (2001) 99. [7] Y. Choi, W.Y. Choo, D. Kwon, Scripta Mater. 45 (2001) [8] G.E. Lucas, Metall. Trans. A 21 (1990) [9] G.E. Lucas, A. Okada, M. Kiritani, J. Nucl. Mater (1986) 532. [10] J.H. Bulloch, Int. J. Pres. Ves. Piping 75 (1998) 791. [11] K.L. Murty, M.D. Mathew, Trans. SMiRT 16 (2001) 1. [12] E.G. Herbert, G.M. Pharr, W.C. Oliver, B.N. Lucas, J.L. Hay, Thin Solid Films (2001) 331. [13] J.S. Field, M.V. Swain, J. Mater. Res. 10 (1) (1994) 101. [14] A.L. Norbury, T. Samuel, J. Iron Steel Inst. 117 (1928) 673. [15] D. Tabor, The Hardness of Metals, Clarendon Press, Oxford, 1951, p. 15. [16] G. Das, S. Ghosh, S.K. Sahay, V.R. Ranganath, K.K. Vaze, Trans. IIM 56 (5) (2003) 465. [17] S. Ghosh, S.K. Sahay, G. Das, Trans. IIM 57 (1) (2004) 51. [18] S. Ghosh, S.K. Sahay, G. Das, J. Metall. Mater. Sci. 46 (2) (2004) 95. [19] G. Das, S. Ghosh, V.R. Ranganath, K.K. Vaze, Int. J. Mater. Res. Adv. Tech., Metall. 95 (2004) [20] G. Das, S. Ghosh, S.K. Sahay, Mater. Lett. 59 (2005) [21] V.R. Ranganath, G. Das, S. Tarafder, S.K. Das, Eng. Failure Anal. 11 (2004) 599. [22] M.A. Meyers, K.K. Chawla, Mechanical Metallurgy Principle and Applications, Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1984, p [23] J.-I. Jang, Y. Choi, Y.-H. Lee, D. Kwon, D.-J. Kim, J.-T. Kim, J. Mater. Sci. Lett. 22 (2003) 499.

EFFECT OF PILE-UP ON THE MECHANICAL CHARACTERISTICS OF STEEL WITH DIFFERENT STRAIN HISTORY BY DEPTH SENSING INDENTATION

EFFECT OF PILE-UP ON THE MECHANICAL CHARACTERISTICS OF STEEL WITH DIFFERENT STRAIN HISTORY BY DEPTH SENSING INDENTATION Peter BURIK 1,a, Ladislav PEŠEK 2,b, Lukáš VOLESKÝ 1,c 1 Technical University of