Galvanizli düşük karbonlu EREGLI 1312 çeliğinin akış gerilmesi ve kırılma gerinmesi davranışı

Yıl 2025, Cilt: 31 Sayı: 5, 721 - 733, 19.10.2025

Ahmet Çetkin

Öz

Gerilme, deformasyon hızı ve sıcaklığın, akış gerilmesi ve oluşabilecek hasar üzerindeki birleşik etkileri altında malzemelerin davranışının modellenmesi, özellikle metal şekillendirme, patlama, talaş kaldırma vb. simülasyonlardaki gereklilikleri nedeni ile son derece önemlidir. Analizde istenilen malzemenin kullanılabilmesi için ihtiyaç duyulacak model parametrelerinin önceden var olması gerekir. Her malzemeye ait parametreler olmadığı gibi, elde edilmesi de maliyetli ve uzun süreli çabaları gerektirir. Bu modeller içinde simülasyon programlarında en çok tercih edilenlerden biri Johnson Cook (JC) akış gerilmesi ve hasar modellerine ait parametrelerdir. Bu çalışmanın amacı, düşük karbonlu EREGLI 1312 çeliğinin, basit çekme testleri ve düşük gerilme oranı referansında mekanik davranışını tanımlayan JC parametrelerini, testlerin simülasyonları yardımıyla daha ekonomik olarak elde etmektir. Malzememizin akış gerilmesi ve hasar davranışını tahmin etmek için JC tarafından önerilen hasar modeli kullanılmış, model parametrelerini belirlemek için plakalardan kesilen düz ve çentikli altı farklı tipte numunelere, oda sıcaklığında ve değişik hızlar altında çekme testi uygulanmıştır. Eğri uydurma ve regresyon işlemleri, bu amaçla yazılan programla otomatik olarak uygulanmış, simüle edilen testler ile çekme testleri eşleştirilerek parametrelerin hesabı için gereken veriler kolaylıkla elde edilmiştir. Elde edilen parametrelerin tüm deformasyon hızları için oda sıcaklıktaki malzeme davranışını oldukça yakın tahmin edebildiği hesaplanmıştır. Test sonuçlarına oranla, kopma gerçekleşene kadar olan gerilme-gerinme değişimi sürecini ortalama %3.63 oranında küçük bir hatayla simüle edebilmektedir. Bu araştırmada EREGLI 1312 çeliği için tahmin edilen JC akış gerilmesi ve hasar modeli parametrelerinin, metal bükme, sıvama benzeri simülasyonlarında güvenle kullanılabilir olduğu görülmüştür

Anahtar Kelimeler

JC modeli , Akış gerilmesi parametreleri , Düşük karbonlu çelik , Hasar gerinmesi , Eğri uydurma , Gerilme üç-eksenliliği

Flow stress and fracture strain behavior of galvanized low carbon EREGLI 1312 steel

Öz

Modeling the behavior of materials under the combined effects of stress, deformation rate and temperature on the flow stress and damage that may occur is extremely important, especially because of the requirements in simulations such as metal forming, blast, chip removal, etc. In order to use the desired material in the analysis, the model parameters that will be needed must exist in advance. Not every material does not have parameters, and obtaining them requires costly and long-term efforts. Among these models, one of the most preferred ones in simulation programs are the parameters of Johnson Cook (JC) flow stress and damage models. The aim of this study is to economically obtain the JC parameters describing the mechanical behavior of low carbon EREGLI 1312 steel in simple tensile tests and low stress ratio reference with the help of simulations of the tests. The damage model proposed by JC was used to predict the flow stress and damage behavior of our material. In order to determine the model parameters, tensile tests were applied to six different types of notched and unnotched specimens cut from plates at room temperature and under different speeds. Curve fitting and regression procedures were performed automatically with the program written for this purpose, and the data required for the calculation of the parameters were easily obtained by matching the simulated tests with the tensile tests. It was calculated that the parameters obtained can predict the material behavior at room temperature very closely for all strain rates. Compared to the test results, it can simulate the process of stress-strain variation until rupture with a small error of 3.63% on average. In this research, the JC flow stress and damage model parameters estimated for EREGLI 1312 steel were found to be safely used in simulations such as metal bending and deep drawing.

Anahtar Kelimeler

JC model , Flow stress parameters , Low carbon steel , Failure strain , Curve fitting , Stress triaxiality

Kaynakça

• [1] Johnson GR, Cook WH. “A constitutive model and data for metals subjected to large strains high strain rates and high temperatures”. Proceedings of the 7th International Symposium on Ballistics, The Hague, Netherlands, 19-21 April, 1983.
• [2] Johnson GR, Cook WH. “Fracture characteristics of three metals subjected to various strains, strain rates, temperatures and pressures”. Engineering Fracture Mechanics, 21, 31-48, 1985.
• [3] Nemat‐Nasser S. “Introduction to high strain rate testing”. Asm Handbook, 8, 427-428, 2000.
• [4] Murugesan M, Lee S, Kim D, Kang YH, Kim N. “A comparative study of ductile damage models approaches for joint strength prediction in hot shear joining process”. Procedia Engineering, 207, 1689-1694, 2017.
• [5] Wang Y, Xing J, Zhou Y, Kong C, Yu H. “Tensile properties and a modified s-Johnson-Cook model for constitutive relationship of AA7075 sheets at cryogenic temperatures”. Journal of Alloys and Compounds, 942, 169044, 2023.
• [6] Nalla MM. “Evaluation of Johnson-Cook constitutive material model parameters for additively manufactured AlSi10Mg alloy test specimens”. Materials Today: Proceedings, 72(4), 2044-2048, 2023.
• [7] Priest J, Ghadbeigi H, Ayvar-Soberanis S, Liljerehn A, Way M. “A modified Johnson-Cook constitutive model for improved thermal softening prediction of machining simulations in C45 steel”. Procedia CIRP, 108, 106-111, 2022.
• [8] Deb S, Muraleedharan A, Immanuel RJ, Panigrahi SK, Racineux G, Marya S. “Establishing flow stress behaviour of Ti-6Al-4V alloy and development of constitutive models using Johnson-Cook method and artificial neural network for quasi-static and dynamic loading”. Theoretical and Applied Fracture Mechanics, 119, 103338, 2022.
• [9] Mohan N, Veerabhadrappa K, Basavaraja JS, Suhas BG, Kumar RS. “Thermal analysis on Ti-6AL-4V tool architecture using Johnson-Cook material model”. Global Transitions Proceedings, 3(2), 432-437, 2022.
• [10] O’Toole L, Haridas R S, Mishra R S, Fang F. “Determination of Johnson-Cook plasticity model parameters for CoCrMo alloy”. Materials Today Communications, 34, 105128, 2023.
• [11] Chao ZL, Jiang LT, Chen GQ, Zhang Q, Zhang NB, Zhao QQ, Pang BJ, Wu GH. “A modified Johnson-Cook model with damage degradation for B4Cp/Al composites”. Composite Structures, 282, 115029, 2022.
• [12] Wang Y, Zeng X, Chen H, Yang X, Wang F, Zeng L. “Modified Johnson-Cook constitutive model of metallic materials under a wide range of temperatures and strain rates”. Results in Physics, 27, 104498, 2021.
• [13] Shrot A, Bäker M. “Determination of Johnson-Cook parameters from machining simulations”. Computational Materials Science, 52, 298-304, 2012.
• [14] Gambirasio L, Rizzi E. “An enhanced Johnson-Cook strength model for splitting strain rate and temperature effects on lower yield stress and plastic flow”. Computational Materials Science, 113, 231-265, 2016.
• [15] Bobbili R, Ramakrishna B, Madhu V, Gogia AK. “Prediction of flow stress of 7017 aluminium alloy under high strain rate compression at elevated temperatures”. Defence Technology, 11, 93-98, 2015.
• [16] Majzoobia GH, Dehgolan FR. “Determination of the constants of damage models”. Procedia Engineering, 10, 764-773, 2011.
• [17] Banerjee A, Dhar S, Acharyya S, Datta D, Nayak N. “Determination of Johnson cook material and failure model constants and numerical modelling of Charpy impact test of armour steel”. Computational Materials Science, A 640, 200-209, 2015.
• [18] Chen X, Peng Y, Peng S, Yao S, Chen C, Xu P. “Flow and fracture behavior of aluminum alloy 6082-T6 at different tensile strain rates and triaxialities”. Plos One, 12(7), 1-28, 2017.
• [19] Murugesan M, Jung DW. “Johnson Cook material and failure model parameters estimation of AISI-1045 medium carbon steel for metal forming applications”. Materials, 12(4), 609, 2019.
• [20] Buchely M, Ganguly S, Aken D, O'Malley R, Lekakh S, Chandrashekhara K. “Experimental development of Johnson-Cook strength model for different carbon steel grades and application for single pass hot rolling”. Steel Research International, 91(7), 1900670, 2020.
• [21] Vedantam K, Bajaj D, Brar NS, Hill, S. “Johnson ‐ Cook strength models for mild and DP 590 steels”. AIP Conference Proceedings, 845(1), 775-778, 2006.
• [22] Md Shahanur H, Dennis De P, Richard C, Cheng Y. “Johnson-Cook model parameters determination for 11% and 14% Mn-Steel”. Materials Science and Engineering: B, 283(2), 115788, 2022.
• [23] Sandeep Y, Sorabh S, Yogeshwar J, Ravindra KS. “Determination of Johnson-Cook material model for weldment of mild steel”. Materials Today: Proceedings, 28(3), 1801-1808, 2020.
• [24] Gopinath, K, Narayanamurthy V, Khaderi SN. “Determination of parameters for Johnson-Cook dynamic constitutive and damage models for E250 structural steel and experimental validations”. Journal of Material Engineering and Perform, 33, 10940-10960, 2024.
• [25] Akbari Z, Mirzadeh H, Cabrera J. “A simple constitutive model for predicting flow stress of medium carbon microalloyed steel during hot deformation”. Materials and Design, 77, 126-131, 2015.
• [26] Zejian X, Fenglei H. “Plastic behavior and constitutive modeling of armor steel over wide temperature and strain rate ranges”. Acta Mechanica Solida Sinica, 25(6), 598-608, 2012.
• [27] Banerjee B. “An Evaluation of Plastic Flow Stress Models for the Simulation of High-Temperature and High-Strain-Rate Deformation of Metal”. Department of Mechanical Engineering, University of Utah, USA, Technical Report, 2019.
• [28] Kachanov LM. “Time of the rupture process under creep conditions”. Izvestiia Akademii Nauk SSSR, Otdelenie Teckhnicheskikh Nauk, 8, 26-31, 1958.
• [29] Rabotnov YN. Creep Problems of Structural Members. 7th ed. Amsterdam, Holland, North-Holland Publising Company, 1969.
• [30] Lemaitre J. “Evaluation of dissipation and damage in metals submitted to dynamic loading”. In Proceedings ICM, Kyoto, Japan, 15-20 August, 1971.
• [31] Lemaitre J. “A continuous damage mechanics model for ductile fracture”. Journal of Engineering Materials and Technology, 107, 83-89, 1985.
• [32] Bao Y. Prediction of Ductile Crack Formation in Uncracked Bodies. PhD Thesis, Impact and Crashworthiness Lab, Department of Ocean Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts, USA, 2003.
• [33] Fischer F, Kolednik D0, Shan GX, Rammerstorfer FG. “A note on calibration of ductile failure damage indicators”. International Journal of Fracture, 73, 345-357, 1995.
• [34] Abbasi-Bani A, Zarei-Hanzaki A, Pishbin MH, Haghdadi N. “A comparative study on the capability of Johnson-Cook and Arrhenius-type constitutive equations to describe the flow behavior of Mg-6Al-1Zn alloy”. Mechanical Materials, 71, 52-61, 2014.
• [35] He A, Xie G, Zhang H, Wang X. “A comparative study on Johnson-Cook, modified Johnson-Cook and Arrhenius-type constitutive models to predict the high temperature flow stress in 20CrMo alloy steel”. Material Design, 52, 677-685, 2013.
• [36] Maheshwari AK. “Prediction of flow stress for hot deformation processing”. Compututer Materials Science, 69, 350-358, 2013.
• [37] Zhan H, Wang G, Kent D, Dargusch M. “Constitutive modelling of the flow behaviour of a beta titanium alloy at high strain rates and elevated temperatures using the Johnson-Cook and modified Zerilli-Armstrong models”. Materials Science and Engineering, A, 612, 71-79, 2014.
• [38] Samantaray D, Mandal S, Bhaduri AK. “A comparative study on Johnson Cook, modified Zerilli-Armstrong and Arrhenius-type constitutive models to predict elevated temperature flow behaviour in modified 9Cr-1Mo steel”. Computer Materials Science, 47, 568-576, 2009.
• [39] Cao Y, Di HS, Misra RDK, Zhang J. “Hot deformation behavior of alloy 800 H at intermediate temperatures: Constitutive models and microstructure analysis”. Journal of Material Engineering and Performance, 23, 4298-4308, 2014.
• [40] Huh H, Kang WJ. “Crash-worthiness assessment of thin-walled structures with the high-strength steel sheet”. International Journal of Vehicle Design, 30(1/2), 1-21, 2002.
• [41] Allen DJ, Rule WK, Jones SE. “Optimizing material strength constants numerically extracted from taylor impact data”. Experimental Mechanics, 37, 333-337, 1997.
• [42] Cowper GR, Symonds PS. “Strain hardening and strain rate effects in the impact loading of cantilever beams”. Brown University, Providence, Rhode Island, USA, Applied Mathematics Report, TR-C11-28, 1958.
• [43] Buzyurkina AE, Gladkyb IL, Krausa EI. “Determination and verification of Johnson-Cook model parameters at high-speed deformation of titanium alloys”. Aerospace Science and Technology, 45, 121-127, 2015.
• [44] Bao Y. “Dependence of ductile crack formation in tensile tests on stress triaxiality, stress and strain ratios”. Engineering Fracture Mechanics, 72, 505-522, 2005.
• [45] Bai Y, Wierzbicki T. “A new model of metal plasticity and fracture with pressure and Lode dependence”. International Journal of Plasticity, 24, 1071-1096, 2008.
• [46] Mirone G, Corallo D. “A local viewpoint for evaluating the influence of stress triaxiality and Lode angle on ductile failure and hardening”. International Journal of Plasticity, 26, 348-371, 2010.
• [47] Brunig M, Chyra O, Albrecht D, Driemeier L, Alves M. “A ductile damage criterion at various stress triaxialities”. International Journal of Plasticity, 24, 1731-1755, 2008.
• [48] Cao TS, Gachet JM, Montmitonnet P, Bouchard PO. “A Lode-dependent enhanced Lemaitre model for ductile fracture prediction at low stress triaxiality”. Engineering Fracture Mechanics, 124-125, 80-96, 2014.
• [49] Çetkin A. "Estimate of the flow stress and damage model parameter coefficients from tensile test with the help of code". Journal of Materials and Mechatronics: A 2, 99-111, 2021.
• [50] Ereğli Demir ve Çelik Fabrikaları TAŞ. “Erdemir Ürün Kataloğu”.https://www.erdemir.com.tr/Sites/1/upload/files/Urun_Katalogu-2017-1269.pdf (12.02.2023).