CHARACTERIZATION OF DUCTILE FRACTURE LOCI OF ISOTROPIC MATERIALS

Yıl 2020, , 65 - 73, 20.03.2020

FUZULI Akcay

https://doi.org/10.21923/jesd.542059

Öz

There is no generally accepted ductile fracture criterion by the fracture mechanics community. As a result of the comparison of various ductile fracture criteria proposed in the literature, Maximum Shear Stress (MSS) criterion has been observed to be the most advantageous criterion with respect to the number of calibrated parameters and the accuracy of the model. Nevertheless, recently developed Karr-Akçay Energy Balance (KAEB) criterion was not evaluated in these studies. Therefore, in this study, KAEB criterion and MSS criterion are compared, and the advantages and disadvantages of both criteria are discussed. One of the fundamental shortcomings of MSS criterion is that the criterion is based on Lode angle/parameter only. In contrast, KAEB criterion contains the stress triaxiality and Lode angle/parameter dependence inherently. Both criteria, however, require only one calibration parameter. In this study, KAEB criterion is observed to be more advantageous compared to MSS criterion with respect to the number of calibrated parameters and the accuracy of the model.

Anahtar Kelimeler

Fracture, Ductility, Plasticity, KAEB, MSS

İZOTROPİK MALZEMELERİN SÜNEK KIRILMA GEZENEKLERİNİN TAYİNİ

Öz

Kırılma mekaniği camiası tarafından genel kabul görmüş bir sünek kırılma kriteri henüz bulunmamaktadır. Literatürdeki çeşitli sünek kırılma kriterlerinin, kalibre edilen parametre sayısı ve modelin doğruluğu göz önünde bulundurularak karşılaştırılması sonucunda Maksimum Kayma Gerilmesi (MSS) kriterinin en avantajlı kriter olduğu gözlemlenmiştir. Buna karşın, bu karşılaştırma çalışmalarında yakın zamanda geliştirilmiş Karr-Akçay Enerji Dengesi (KAEB) kriteri göz önünde bulundurulmamıştır. Dolayısıyla, bu çalışmada, KAEB kriteri ile MSS kriteri deney sonuçları üzerinden karşılaştırılarak, her iki kriterin üstünlükleri ve eksiklikleri tartışılmıştır. MSS kriterinin yalnızca Lode açısına/parametresine bağlı bir kriter olması temel zayıflıklarından bir tanesidir. Buna karşın, KAEB kriteri gerilme üçeksenliliği ve Lode açısı/parametresi bağlılıklarını özünde içermektedir. Bununla birlikte, her iki kriter de yalnızca bir adet kalibrasyon parametresi hesabını gerektirir. Bu çalışmada, kalibre edilen parametre sayısı ve modelin doğruluğu göz önünde bulundurulduğunda, KAEB kriterinin MSS kriterine göre daha avantajlı bir kriter olduğu gözlemlenmiştir.

Anahtar Kelimeler

Kırılma, Süneklik, Plastisite, KAEB, MSS

Kaynakça

• Abedini, A., Butcher, C., Worswick, M. J., 2017. Fracture characterization of rolled sheet alloys in shear loading: Studies of specimen geometry, anisotropy, and rate sensitivity. Experimental Mechanics, 57, 75-88.
• Bai, Y., Wierzbicki, T., 2008. A new model of metal plasticity and fracture with pressure and Lode dependence. International Journal of Plasticity, 24, 1071-1096.
• Bai, Y., Wierzbicki, T., 2010. Application of extended Mohr–Coulomb criterion to ductile fracture. International Journal of Fracture, 161, 1-20.
• Bao, Y., Wierzbicki, T., 2004. On fracture locus in the equivalent strain and stress triaxiality space. International Journal of Mechanical Sciences, 46, 81-98.
• Barsoum, I., Faleskog, J., 2007. Rupture mechanisms in combined tension and shear—Experiments. International Journal of Solids and Structures, 44, 1768-1786.
• Charoensuk, K., Panich, S., Uthaisangsuk, V., 2017. Damage initiation and fracture loci for advanced high strength steel sheets taking into account anisotropic behaviour. Journal of Materials Processing Technology, 248, 218-235.
• Cockcroft, M. G., Latham, D. J., 1968. Ductility and the workability of metals. Journal of the Institute of Metals, 96, 33-39.
• Dunand, M., Mohr, D., 2011. Optimized butterfly specimen for the fracture testing of sheet materials under combined normal and shear loading. Engineering Fracture Mechanics, 78, 2919-2934.
• Eringen, A. C., 1980. Mechanics of continua. Robert E. Krieger Publishing Company: Melbourne.
• Fourmeau, M., Børvik, T., Benallal, A., Hopperstad, O. S., 2013. Anisotropic failure modes of high-strength aluminium alloy under various stress states. International Journal of Plasticity, 48, 34-53.
• Frodal, B. H., Pedersen, K. O., Børvik T., Hopperstad, O. S., 2017. Influence of pre-compression on the ductility of AA6xxx aluminium alloys. International Journal of Fracture, 206, 131-149.
• Griffith, A. A., 1921. The phenomena of rupture and flow in solids. Philosophical Transactions of the Royal Society of London, Series A, 221, 163–198.
• Gurson, A. L., 1977. Continuum theory of ductile rupture by void nucleation and growth: Part I—Yield criteria and flow rules for porous ductile media. Journal of Engineering Materials and Technology, 99, 2-15.
• Habibi, N., Ramazani, A., Sundararaghavan, V., Prahl, U., 2018. Failure predictions of DP600 steel sheets using various uncoupled fracture criteria. Engineering Fracture Mechanics, 190, 367-381.
• Hancock, J. W., Mackenzie, A. C., 1976. On the mechanisms of ductile failure in high-strength steels subjected to multi-axial stress-states. Journal of the Mechanics and Physics of Solids, 24, 147-160.
• Irwin, G. R., 1948. Fracture dynamics. Fracturing of metals: A seminar on the fracturing of metals held during the twenty-ninth national metal congress and exposition, içinde (s. 147-166). American Society for Metals: Cleveland.
• Irwin, G. R., 1957. Analysis of stresses and strains near the end of a crack traversing a plate. Journal of Applied Mechanics, 24, 361–364.
• Jia, Y., Bai, Y., 2016a. Experimental study on the mechanical properties of AZ31B-H24 magnesium alloy sheets under various loading conditions. International Journal of Fracture, 197, 25-48.
• Jia, Y., Bai, Y., 2016b. Ductile fracture prediction for metal sheets using all-strain-based anisotropic eMMC model. International Journal of Mechanical Sciences, 115, 516-531.
• Jia, Y., Ghazali, S., Bai, Y., 2017. Application of eMMC model to fracture of metal sheets. Proceedings of the Fracture, Fatigue, Failure and Damage Evolution, Cilt 8, içinde (s. 49-55). Springer International Publishing: Cham.
• Johnson, G. R., Cook, W. H., 1985. Fracture characteristics of three metals subjected to various strains, strain rates, temperatures and pressures. Engineering Fracture Mechanics, 21, 31-48.
• Karr, D.G., Akçay, F.A., 2016. A criterion for ductile fracture based on continuum modeling of energy release rates. International Journal of Fracture, 197, 201–212.
• Khan, A. S., Liu, H., 2012. A new approach for ductile fracture prediction on Al 2024-T351 alloy. International Journal of Plasticity, 35, 1-12.
• Kiran, R., Khandelwal, K., 2013a. A micromechanical model for ductile fracture prediction in ASTM A992 steels. Engineering Fracture Mechanics, 102, 101-117.
• Kiran, R., Khandelwal, K., 2013b. Experimental studies and models for ductile fracture in ASTM A992 steels at high triaxiality. Journal of Structural Engineering, 140, 04013044.
• Korkolis, Y. P., Kyriakides, S., 2008. Inflation and burst of anisotropic aluminum tubes for hydroforming applications. International Journal of Plasticity, 24, 509-543.
• Li, Y., Luo, M., Gerlach, J., Wierzbicki, T., 2010. Prediction of shear-induced fracture in sheet metal forming. Journal of Materials Processing Technology, 210, 1858-1869.
• Luo, M., Wierzbicki, T., 2010. Numerical failure analysis of a stretch-bending test on dual-phase steel sheets using a phenomenological fracture model. International Journal of Solids and Structures, 47, 3084-3102.
• Lou, Y., Huh, H., 2013. Extension of a shear-controlled ductile fracture model considering the stress triaxiality and the Lode parameter. International Journal of Solids and Structures, 50, 447-455.
• Lou, Y., Huh, H., 2013. Extension of a shear-controlled ductile fracture model considering the stress triaxiality and the Lode parameter. International Journal of Solids and Structures, 50, 447-455.
• Lou, Y., Yoon, J. W., Huh, H., 2014. Modeling of shear ductile fracture considering a changeable cut-off value for stress triaxiality. International Journal of Plasticity, 54, 56-80.
• Malcher, L., Pires, F. A., De Sá, J. C., 2014. An extended GTN model for ductile fracture under high and low stress triaxiality. International Journal of Plasticity, 54, 193-228.
• McClintock, F. A., 1968. A criterion for ductile fracture by the growth of holes. Journal of Applied Mechanics, 35, 363–371.
• Mohr, D., Marcadet, S. J., 2015. Micromechanically-motivated phenomenological Hosford–Coulomb model for predicting ductile fracture initiation at low stress triaxialities. International Journal of Solids and Structures, 67, 40-55.
• Nahshon, K., Hutchinson, J. W., 2008. Modification of the Gurson model for shear failure. European Journal of Mechanics-A/Solids, 27, 1–17.
• Needleman, A., Tvergaard, V., 1991. An analysis of dynamic, ductile crack growth in a double edge cracked specimen. International Journal of Fracture, 49, 41-67.
• Orowan, E., 1945. Notch brittleness and the strength of metals. Transactions of the Institution of Engineers and Shipbuilders in Scotland, 89, 165–215.
• Orowan, E., 1949. Fracture and strength of solids. Reports on Progress in Physics, 12, 185-232.
• Osovski, S., Srivastava, A., Ponson, L., Bouchaud, E., Tvergaard, V., Ravi-Chandar, K., Needleman, A., 2015. The effect of loading rate on ductile fracture toughness and fracture surface roughness. Journal of the Mechanics and Physics of Solids, 76, 20-46.
• Papasidero, J., Doquet, V., Mohr, D., 2014. Determination of the effect of stress state on the onset of ductile fracture through tension-torsion experiments. Experimental Mechanics, 54, 137-151.
• Papasidero, J., Doquet, V., Mohr, D., 2015. Ductile fracture of aluminum 2024-T351 under proportional and non-proportional multi-axial loading: Bao–Wierzbicki results revisited. International Journal of Solids and Structures, 69, 459-474.
• Park, N., Huh, H., Nam, J. B., Jung, C. G., 2015. Anisotropy effect on the fracture model of DP980 sheets considering the loading path. International Journal of Automotive Technology, 16, 73-81.
• Rice, J. R., 1968. A path independent integral and the approximate analysis of strain concentration by notches and cracks. Journal of Applied Mechanics, 35, 379–386.
• Rice, J. R., Tracey, D. M., 1969. On the ductile enlargement of voids in triaxial stress fields*. Journal of the Mechanics and Physics of Solids, 17(3), 201–217.
• Rodríguez-Millán, M., Vaz-Romero, Á., Arias, Á., 2015. Failure behavior of 2024-T3 aluminum under tension-torsion conditions. Journal of Mechanical Science and Technology, 29(11), 4657-4663.
• Sadighi, M., Alderliesten, R. C., Benedictus, R., 2012. Impact resistance of fiber-metal laminates: A review. International Journal of Impact Engineering, 49, 77-90.
• Shah, O. R., Tarfaoui, M., 2017. Determination of mode I & II strain energy release rates in composite foam core sandwiches. An experimental study of the composite foam core interfacial fracture resistance. Composites Part B: Engineering, 111, 134-142.
• Tvergaard, V., 1981. Influence of voids on shear band instabilities under plane strain conditions. International Journal of Fracture, 17, 389–407.
• Tvergaard, V., Needleman, A., 1984. Analysis of the cup-cone fracture in a round tensile bar. Acta Metallurgica, 32, 157-169.
• Valoppi, B., Bruschi, S., Ghiotti, A., Shivpuri, R., 2017. Johnson-Cook based criterion incorporating stress triaxiality and deviatoric effect for predicting elevated temperature ductility of titanium alloy sheets. International Journal of Mechanical Sciences, 123, 94-105.
• Wang, K., Luo, M., Wierzbicki, T., 2014. Experiments and modeling of edge fracture for an AHSS sheet. International Journal of Fracture, 187, 245-268.
• Wang, K., Wierzbicki, T., 2015. Experimental and numerical study on the plane-strain blanking process on an AHSS sheet. International Journal of Fracture, 194, 19-36.
• Wierzbicki, T., Bao, Y., Lee, Y. W., Bai, Y., 2005. Calibration and evaluation of seven fracture models. International Journal of Mechanical Sciences, 47, 719–743.
• Wierzbicki, T., Xue, L., 2005. On the effect of the third invariant of the stress deviator on ductile fracture. Impact and Crashworthiness Laboratory, Teknik Rapor 136.
• Xia, L., Shih, C. F., 1995. Ductile crack growth–I. A numerical study using computational cells with microstructurally-based length scales. Journal of the Mechanics and Physics of Solids, 43, 233–259.