تعیین مدول الاستیک با استفاده از نتایج آزمون نفوذ ساچمه کروی، برینل

نوع مقاله : مقاله پژوهشی

نویسنده

گروه مهندسی مکانیک، دانشکده مهندسی، دانشگاه صنعتی کرمانشاه، کرمانشاه، ایران

چکیده

رفتار تنش-کرنش مواد معمولاً در آزمون کشش یا فشار تک محوری بررسی می‌شود. با این حال، این روش‌ها به طور کلی برای مقادیر کوچک مواد و یا به‌طور موضعی قابل استفاده نیستند. آزمون سختی‌سنجی با استفاده از نفوذکننده کروی، پتانسیل پر کردن این شکاف را با امکان تخمین دقیق خواص مکانیکی را دارد. در این مقاله تکنیکی مبتنی بر اصول آزمون سختی‌سنجی برینل، برای تخمین مقدار مدول الاستیک ارائه شده‌است. مدول الاستیک نمونه مورد آزمایش با استفاده از تکنیک ارائه‌شده محاسبه و سپس نتایج به‌دست آمده با استفاده از نتایج آزمون کشش ساده صحت‌سنجی شده‌اند. بر اساس نتایج، مقادیر تخمین زده‌شده تابع نیروی نفوذ هستند و برای نیروی مشخصی بهترین دقت حاصل می‌شود و مقادیر کمتر و بیشتر نیرو باعث کاهش قابل توجه دقت خواهد شد؛ نیروی‌نفوذ با تاثیر بر مقدار برآمدن یا فرورفتن مواد در اطراف ناحیه نفوذ دقت عمق‌نفوذ اندازه‌گیری شده را تحت تاثیر قرار می‌دهد و بر دقت مقادیر تخمین‌زده شده تاثیر می‌گذارد. در این پژوهش مقدار مدول الاستیک با خطای کمتر از ۵ درصد محاسبه شده‌است. مقدار مناسب نیروی نفوذ تابع جنس است و باید پیش از استفاده از این تکنیک تعیین شود. نتایج تایید می‌کنند که این روش می‌تواند با دقت مناسب برای تخمین مقدار مدول الاستیک قطعات و تجهیزات، بویژه برای مواد محدود و یا خواص موضعی، حین بهره‌برداری و طی یک آزمون غیرمخرب استفاده شود.

کلیدواژه‌ها

موضوعات

عنوان مقاله [English]

Determination of Elastic Modulus Using Spherical Ball Indentation, Brinell Test Results

نویسنده [English]

  • Sajad Rasaee
Department of Mechanical Engineering, Kermanshah University of Technology, Kermanshah, Iran
چکیده [English]

The stress–strain behavior of materials is traditionally characterized using uniaxial tensile or compression tests. However, these conventional methods are often impractical when dealing with small material volumes or when localized mechanical property evaluation is required. As a non-destructive, simple, and widely applicable alternative, the spherical indentation hardness test presents a promising approach for estimating mechanical properties such as the elastic modulus. In this study, a methodology based on the Brinell hardness testing principle is introduced to estimate the elastic modulus of materials. The obtained results are validated against data derived from standard uniaxial tensile tests. The findings reveal that the estimated elastic modulus values are significantly influenced by the applied indentation load, with optimal accuracy achieved at a specific load level. Deviations from this optimal load, whether higher or lower, result in diminished estimation accuracy, primarily due to variations in material pile-up or sink-in phenomena surrounding the indentation zone. These effects alter the penetration depth measurement and, consequently, the calculated mechanical properties. The proposed method demonstrated an estimation error of less than 5% for the elastic modulus. Moreover, the optimal indentation load is found to be material-dependent and should be determined prior to application. Overall, the results confirm that this method provides a reliable, non-destructive means of estimating the elastic modulus, particularly in situations where material availability is constrained or localized evaluation is required under in-service conditions.

کلیدواژه‌ها [English]

  • Hardness Testing
  • Elastic Modulus
  • Mechanical Properties
  • Penetration Test
  • Penetration Load
  • Meyer Parameter

مراجع

[1] D. Tabor, A simple theory of static and dynamic hardness, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 192(1029) (1948) 247-274.
[2] I.N. Sneddon, Boussinesq's problem for a rigid cone, in:  Mathematical Proceedings of the Cambridge Philosophical Society, Cambridge University Press, 1948, pp. 492-507.
[3] W.C. Oliver, G.M. Pharr, An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments, Journal of Materials Research, 7(6) (1992) 1564-1583.
[4] G. Pharr, W.C. Oliver, F.J.J.o.m.r. Brotzen, On the generality of the relationship among contact stiffness, contact area, and elastic modulus during indentation, 7 (1992) 613-617.
[5] H.A. Francis, Phenomenological Analysis of Plastic Spherical Indentation, Journal of Engineering Materials and Technology, 98(3) (1976) 272-281.
[6] N.A. Stilwell, D. Tabor, Elastic Recovery of Conical Indentations, Proceedings of the Physical Society, 78(2) (1961) 169.
[7] S. Bulychev, V. Alekhin, M. Shorshorov, A. Ternovskii, G. Shnyrev, Determining Young's modulus from the indentor penetration diagram, Ind. Lab., 41(9) (1975) 1409-1412.
[8] B. Taljat, T. Zacharia, F.M. Haggag, Analysis of ball-indentation load-depth data: Part I. Determining elastic modulus, Journal of Materials Research, 12(4) (1997) 965-974.
[9] G. Das, S. Ghosh, S. Sahay, V. Ranganath, K. Vaze, Influence of pre-straining on mechanical properties of HSLA steel by using ball indentation technique, International Journal of Materials Research, 95(12) (2022) 1120-1127.
[10] B. Zou, Z. Wei, K. Guan, Fature toughness valuation of seel by continuous ball indentation test, Journal of Materials Science and Engineering, 34(4) (2016) 577-580.
[11] R. Pamnani, V. Karthik, T. Jayakumar, M. Vasudevan, T. Sakthivel, Evaluation of mechanical properties across micro alloyed HSLA steel weld joints using Automated Ball Indentation, Materials Science and Engineering: A, 651 (2016) 214-223.
[12] H. Xue, J. He, J. Zhang, Y. Xue, Approach for Obtaining Material Mechanical Properties in Local Region of Structure Based on Accurate Analysis of Micro-indentation Test, Chinese Journal of Mechanical Engineering, 34(1) (2021) 130.
[13] T.-H. Pham, J.J. Kim, S.-E. Kim, Estimating constitutive equation of structural steel using indentation, International Journal of Mechanical Sciences, 90 (2015) 151-161.
[14] M. Miyabe, M. Iyota, S. Okano, M. Mochizuki, Semi-destructive Method for Evaluation of Local Mechanical Properties in the Notch-Tip Region using an Indentation Technique, Quarterly Journal of the Japan Welding Society, 31(4) (2013) 114s-118s.
[15] J.-H. Ahn, D. Kwon, Derivation of plastic stress–strain relationship from ball indentations: Examination of strain definition and pileup effect, Journal of Materials Research, 16(11) (2001) 3170-3178.
[16] S. Suresh, A.E. Giannakopoulos, A new method for estimating residual stresses by instrumented sharp indentation, Acta Materialia, 46(16) (1998) 5755-5767.
[17] H. Peng, Y. Xia, Z. Zhou, Y. Jiang, Q. Yu, Residual stress evaluation by spherical indentation: Analysis of the asymmetry of load–depth curves, International Journal of Solids and Structures, 249 (2022) 111772.
[18] S.S. Ghanbari, A.-H. Mahmoudi, Application of a portable indentation rig with Rockwell indenter to determine mechanical properties and residual stresses on an aluminum plate, The Journal of Strain Analysis for Engineering Design, 55(7-8) (2020) 246-257.
[19] F. Barati, R. Moharrami, Accurate Estimating of Mechanical Properties of Austenitic Stainless Steels with Residual Stresses Using Indentation Technique, AUT Journal of Mechanical Engineering, 6(4) (2022) 511-524.
[20] G. Yao, Z. Liu, H.J.A.S. Ma, A novel method for predicting residual stress in GH4169 machined surfaces through micro-hardness measurement, 13(24) (2023) 13257.
[21] J.S. Field, M.V. Swain, Determining the mechanical properties of small volumes of material from submicrometer spherical indentations, Journal of Materials Research, 10(1) (1995) 101-112.
[22] M.F. Doerner, W.D. Nix, A method for interpreting the data from depth-sensing indentation instruments, Journal of Materials Research, 1(4) (1986) 601-609.
[23] A. Norbury, T. Samuel, The recovery and sinking-in or piling-up of material in the Brinell test, and the effects of these factors on the correlation of the Brinell with certain other hardness tests, J. Iron Steel Inst, 117 (1928) 673-687.
[24] J.R. Matthews, Indentation hardness and hot pressing, Acta Metallurgica, 28(3) (1980) 311-318.
[25] R. Hill, On a class of constitutive relations for nonlinear infinitesimal elasticity, Journal of the Mechanics and Physics of Solids, 35(5) (1987) 565-576.
[26] E. Meyer, Z.J.Z.D.V.D.I. Ver, Contribution to the knowledge of hardness and hardness testing, 52 (1908) 740-835.
[27] H.J.P.o.t.I.o.M.E. O'Neill, The significance of tensile and other mechanical test properties of metals, 151(1) (1944) 116-146.
[28] K.L. Johnson, Contact Mechanics, Cambridge University Press, Cambridge, 1985.
نشریه مهندسی مکانیک امیرکبیر
دوره 57، شماره 3
خرداد 1404
صفحه 267-282

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