Journal of Minerals & Materials Characterization & Engineering, Vol. 10, No.7,.661-669, 011 jmmce.org Printed in the USA. All rights reserved Alication of Automated Ball Indentation for Proerty Measurement of Degraded Zr.5Nb Kamal Sharma*, P.K. Singh, Vivek Bhasin and K.K. Vaze RSD, BARC, Trombay, Mumbai, 400085 India *Corrsonding Author: hello_kamal@yahoo.com ABSTRACT In this work, Automated Ball Indentation (ABI) technique is based on load controlled multile indentations (at a single enetration location) of a olished surface by a sherical indenter (0.7 to 1.46 mm) and indentation deth is rogressively increased to a maximum user secified limit with intermediate artial unloading. This technique ermits measurement of yield strength, stress-strain curve, strength coefficient and strain hardening exonent. ABI Testing was carried out on samles of Zr-Nb.5 (Pressure Tube Material) with different heat treatment conditions in which temerature was varying (550 degree to 900 degree and retention time was varying 0.5 to 6 hour and furnace cooled. For all these test material and conditions, the ABI derived results were in very good agreement with those from conventional standard test methods. Keywords: Automated Ball Indentation, Irradiated Nuclear Material, Miniature Secimen Testing, Zr-.5 Nb 1. INTRODUCTION The integrity of safety-related comonents in a nuclear reactor (such as the ressure retaining comonents viz. reactor ressure vessels (RPVs), ressure tubes) is crucial for continued safe oeration of the reactor. Material roerty measurement is an element in this safety assessment. The mechanical roerty changes for materials suscetible to neutron radiation embrittlement, which in turn limits service life. Conventional testing (Chary imact, tensile test, and fracture toughness) of surveillance secimens (if available) oses the roblem of exosure to significant amount of radiation. 661
66 Kamal Sharma, P.K. Singh, Vivek Bhasin and K.K. Vaze Vol.10, No.7 So determination of mechanical roerties of materials by using non-conventional techniques has been an active area of research for a long time. Among some nondestructive methods for determining mechanical roerties of materials, a semi-destructive tye of testing, called Automated Ball Indentation (ABI) has been develoed. The Automated Ball Indentation technique is caable of extracting degraded mechanical behavior and roerties of thermally aged or irradiated materials from very small secimens. The significance of this technology is obvious to the nuclear industry where neutron irradiation sace is limited and irradiation cost scales u with secimen volume. For this evaluation the secimen undergoes multile indentations by a sherical ball indenter. Furthermore, this method can be used to characterize weldments and associated Heat Affected Zone (HAZ), it also avoids the need to fabricate test secimen, and it is relatively raid.. REVIEW OF EARLIER WORK A few research grous have ublished a series of investigations on ball indentation technique to evaluate mechanical roerties. It was Mayer [1] who first develoed a relationshi between the mean ressure and indentation diameter to evaluate the yield strength of materials. Tabor [] gave an emirical relationshi to find the reresentative strain of materials while indentation is done through a hard sherical ball. However, Tabor s relation holds very close to the test observation when the indentation rocess becomes fully lastic. Haggag et.al. [3] did extensive work and develoed an automated ball indentation test set u for determining flow roerties directly from the test around a small volume of material. The location deendence of the mechanical roerties was successfully measured by Murthy et.al. [4]. Gradients in mechanical and fracture roerties of SA 533B steel welds were studied using ball indentation technique. The local stress-strain behaviors of different microstructure zones of the weld were observed at different temeratures. Haggag and Nansted [5] also described a simle technique for estimating the fracture toughness by couling the measured flow roerties with a modified but emirically correlated critical fracture strain model. Mathew et.al. [6] studied the effects of low temerature aging (673K) u to 18 months on the mechanical and fracture roerties of cast CF-8 stainless steel in the range of 173-43K. A theoretical model is roosed to estimate fracture toughness of ferritic steel in the transition region from ball indentation test data by Byun, Kin, Hang [7]. The key concet of the model is that the indentation energy to a critical load is related to fracture energy of material. Using this set-u many research grous [8-11] studied flow roerties of different materials through the thickness variation/gradient in mechanical and fracture roerties and found good agreement with the conventional test results. Non-linear finite element and artificial neural network was used by Sharma et al. [1].
Vol.10, No.7 Alication of Automated Ball Indentation 663 3. METHODOLOGY AND CALCULATION FOR ABI BI is based on multile indentations by a sherical indenter at the same test location on metal surface. The indentation deth and diameter is shown in Figure 1. Here a sherical ball with a secific rate of loading indents the test materials/comonents and multile indentations in a single osition is made through loading-unloading-holding-reloading sequence. A tyical load indentation deth is shown in Figure. It is seen that the load increases aroximately linearly with the enetration deth. Figure 1. Automatic Ball Indentation Process Figure. Tyical load indentation deth
664 Kamal Sharma, P.K. Singh, Vivek Bhasin and K.K. Vaze Vol.10, No.7 Here two non-linear but oosing rocesses occur simultaneously, i.e. the non-linear decrease in the alied load with indentation deth due to the sherical geometry of the indenter and nonlinear increase of load with indentation deth due to the work hardening of the test ieces. During each subsequent loading the amount of materials exeriencing lastic deformation increases, so continuous yielding and strain hardening occurs simultaneously. In-contrast, for the case of a uni-axial tensile test the lastic deformation is confined only to the limited volume of test samle of gauge section. 3.1 True Strain In Figure a schematic ball indentation rofile in the loaded and unloaded condition is shown. Here h, h t are the lastic and total indentation deth and d, d t are the lastic and total indentation diameter. Beneath the indenter a comlex deformation zone exists. The lastic zone and the indentation imression will exand as the indentation load increases. As the indenter is sherical in shae (having non-linear geometry) multile stress-strain data oints can be obtained. The strain field roduced beneath the indenter is regarded as reresentative strain as the total true strain (ε f ) by Tabor. ε f can be exressed as a function of d and D. ε f = f (d/d) (1) Where, D = indenter diameter and d = indentation diameter. After analyzing emirical data he found that ε f varies linearly with the ratio of d/d and found the linearity coefficient is equivalent to 0.. Later on Haggag and his grou calculated the true lastic strain (ε ) as Where, d = lastic indentation diameter. 3.. True Stress ε = 0. (d / D) () An advancing sherical indenter generates multi-axial comressive stresses just beneath the indenter and due to these stresses an increasing volume of test material is forced to flow. The region of contact is a hemishere of radius a. The mean ressure ( m ) over the region of contact is roortional to P 1/3 (alied load). Beside normal ressure, a shear stress also acts and the maximum shear stress acts along the axis of the indenter. Using the maximum shear stress theory as yielding criterion the uni-axial flow stress (σ) can be exressed by σ = m / δ (3) Where δ is a constraint factor, which increases as the lastic zone increases and reaches a maximum until whole of the material around the indentation is in a state of full lasticity.
Vol.10, No.7 Alication of Automated Ball Indentation 665 3.3 Evaluation of Tensile Strength (s uts ) The following exression was used for evaluating the engineering value of suts: suts = K (n/e) n (4) Where, suts = The engineering vale of UTS K = strength coefficient and n = strain hardening exonent The K and n values can be determined through the regression analysis of the following ower law equation for different values of s and e from equations () and (3). The flow curve may be exressed as: s = K. e n (5) Where, s = true stress e=true lastic strain and these values can be obtained by fitting various data oints of load (P) and indentation lastic diameter (d ) in the following exressions. e = K1 (d / D) (6) s = 4.P /.d. d (7) Where, P = alied load d= lastic indented diameter and d=constrained factor deending on alied load and materials tested. The lastic diameter of the indentation can be calculated through the regression analysis of the following Hertzian equation: d = 3 1.735P( E 1 + 1 ) D{ E h h + 0.5d } + 0.5d h d (8) Where, E 1 and E are the Young s Modulus of the indenter and the secimen tested, h is lastic deth of the indentation.
666 Kamal Sharma, P.K. Singh, Vivek Bhasin and K.K. Vaze Vol.10, No.7 d can be exressed as d = 1.1 + t ln f (9) Where, f is a function of a arameter t, and its value is deendent on the flow stress and lastic strain of the test iece. An iteration method has been utilized to determine d values by using BI software develoed by us. Again, t is a function of a m that is deendent on strain rate sensitivity and work hardening characteristic of the test materials. 3.4 Evaluation of Yield Strength (YS) Here the total enetration deth (h t ) is measured while the load is alied and the deth is converted to a total indentation diameter (d t ) using following equation: dt=(ht.d-ht )0.5 (10) Where, dt = total indentation diameter D = diameter of the indenting ball and ht = total enetration deth The data oints from all loading cycles are fit by linear regression analysis to the following relationshi of Meyer relation: P/dt =A (dt / D )m- (11) Where, m = Meyer s coefficient P = alied load and A = material arameter sy= bm. A (1) Where bm = Material constant and can be calculated with a known value of sy. Then this bm will be same for a secific class of materials irresective of heat-treatment and mechanical working. The value of bm is determined for each class or tye of materials from the various known YS values by using BI analysis software. 4. CONDITION OF MATERIAL The heat treatment condition of the test is shown in Table 1.
Vol.10, No.7 Alication of Automated Ball Indentation 667 Table 1: Descrition of heat treatment condition of Zr-.5 Nb secimen Secimen ID Heat treatment Conditions A As received Zr-.5 Nb ressure tube material (AR) B AR+550 o C for 6 hour and furnace cooled C AR+700 o C for hour and furnace cooled D AR+800 o C for 0.5 hour and furnace cooled E AR+850 o C for 0.5 hour and furnace cooled F AR+900 o C for 0.5 hour and furnace cooled 5. NUMERICAL RESULTS Load (N) 000 1600 100 800 A B C D E F RSD 400 0 0.00 0.04 0.08 0.1 0.16 Indentation Deth (mm) Figure 3. Load vs Indentation deth for different heat treated condition True Stress (MPa) 1300 100 1100 1000 900 800 RSD A B C D E F 700 0.0 0.04 0.06 0.08 0.10 0.1 True Strain (mm/mm) Figure 4. True Stress vs True Starin Curvefor different heat treated condition
668 Kamal Sharma, P.K. Singh, Vivek Bhasin and K.K. Vaze Vol.10, No.7 Table : Comarsion of ABI Testing and Conventional Testing Results Samle No ABI Results (MPa) Conventional (MPa) % Error YS UTS YS UTS YS UTS A 658 86 606 811 8.58 6.9 B 580 830 551 780 5.6 6.41 C 518 656 49 64 5.8.18 D 486 604 456 594 6.58 1.68 E 445 561 40 540 5.95 3.89 F 40 53 386 501 4.15 4.39 6. CONCLUSIONS 1. Plot of the load and indentation deth for different heat treatment conditions shows that ABI technique is sensitive to the change in tensile roerties due to the heat treatment conditions.. Yield strength and UTS of the material decreases with increase in heat treatment temerature corresonding reduction in hold time. This observation is consistent with that of conventional test results. 3. Change in YS and UTS of the heat-treated material with resect to as received condition of the material are also consistent with that of conventional tests. 4. True stress strain curve also reflects the effect heat treatment on the tensile roerties of the material, thereby indicating that ABI technique is sensitive to detection of variation in mechanical roerties. 5. Although conventional tests show that there is increase in ercentage elongation of 100 % with resect to the as received condition of the material. Holman s equation used for evaluation of strain hardening exonent may not be suitable for this material. 6. Finally it can be inferred that ABI can be used in-situ for evaluation of change in mechanical roerties of the ageing comonent, which will hel in residual life estimation and extension of the comonents if mechanical roerties for virgin material is known. REFERENCES 1.) E. Meyer and Z. Ver, Dtsch. Ing. 5 (1908)..) D. Tabor The Hardness of Metals; 1951 3.) F. M. Haggag, American Society for Testing and Materials, Philadelhia, 7-44, 1993. 4.) K. L. Murthy, P.Q. Mirgania, and M. D. Mathew, International journal of Pressure Vessel and Piing, 76 (1999) 361. 5.) F M Haggag and R K Nanstad, PVP, 170 (1989).
Vol.10, No.7 Alication of Automated Ball Indentation 669 6.) M D Mathew, K L Murthy, L M Lietzan and V N Shah, A69 (1999) 186. 7.) T. S. Byan, J. W. Kim, J. H. Hong, Journal of Nuclear Materials, 5 (1998) 187. 8.) Y H Lee, W J Ji and D Kwon, Exerimental Mechanics, 44 (004). 9.) Ghosh Sabita et. al. Mater. Lett, 6 (008) 619. 10.) Hyungyil Lee et.al., J Mech. Phy of Solids, 53 (005) 037. 11.) G. Das et.al. J. Mat. Res. Adv. Tech., Metallkunde, 95 (004) 110. 1.) K. Sharma, V. Bhasin & A K Ghosh, JJMIE, 4 (010).