مدل آسیب میکرومکانیکی برای پلاستیسیته‌ مواد به‌منظور پیش‌بینی شکست تحت بارهای برشی

نوع مقاله : مقاله پژوهشی

نویسندگان

1 دانشگاه صنعتی امیرکبیر، دانشکده مهندسی مکانیک، تهران، ایران

2 صنعتی امیرکبیر*مهندسی مکانیک

3 Imperial College-مهندسی مکانیک

چکیده

در این مقاله به مدل مکانیک آسیب مبتنی بر میکرومکانیک جی‌تی ان جهت اضافه کردن قابلیت پیش‌بینی و محاسبه آسیب تحت بارهای برشی پرداخته‌شده؛ تا از آن به‌منظور مدل‌سازی آسیب و شکست در شرایطی که بارهای برشی و آسیب برشی غالب است استفاده گردد. در توسعه‌ مدل جی‌تی ان، نظر به اینکه آسیب‌های مختلف مفاهیم فیزیکی و اثرات تضعیف متفاوتی دارند لذا یک پارامتر آسیب برشی مستقل و مجزا به‌عنوان تابعی از کرنش پلاستیک معادل ماتریس ارائه گردید. مدل آسیب جی‌تی ان‏ اصلاح‌شده با توسعه‌ کد در محیط نرم‌افزار آباکوس پیاده‌سازی شد. جهت آنالیز آسیب با مدل جدید، 16 پارامتر ورودی مدل برای ماده تعیین گردید. پس از توسعه‌ مدل، توسعه‌ کد و تعیین پارامترهای ورودی، ابتدا مدل اصلاح‌شده‌ بر روی تک المان آزمایش شد. بررسی نتایج نشان داد که جواب‌های مدل توسعه داده‌شده مطابقت کاملی با نتایج مدل جی‌تی ان‏‏ پایه و روابط تحلیلی به ترتیب تحت بارگذاری‌های کششی و برشی دارد. درنهایت مدل توسعه داده‌شده در بارگذاری برشی و روی نمونه‌ برشی مورد آزمایش قرار گرفت. مشاهده گردید مدل اصلاح‌شده تحت بارگذاری برشی ضعف مدل جی‌تی ان ‏پایه را رفع کرده و به‌خوبی بروز آسیب و تضعیف خواص مکانیکی ماده را تحت شرایط برشی حاکم پیش‌بینی می‌کند.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Micromechanical Damage Model for Plasticity of ‎Metals to Predict Failure under Shear Loads

نویسندگان [English]

  • Hamed Ghoolipour 1
  • FaridReza Biglari 2
  • Kamran Nikbin 3
1 Amirkanir University of Technology, Mechanical Engineering Department, Tehran, Iran
3 Imperial College-مهندسی مکانیک
چکیده [English]

The present work deals with the Gurson-Tvergaard-Needleman micromechanics based damage model to add ‎the ability to predict damage under shear loads and use it in modeling damage and failure under shear dominated ‎loading conditions. In the development of the Gurson-Tvergaard-Needleman model, since different damages have ‎different physical concepts and attenuation effects, so an independent shear damage parameter was presented as a ‎function of an equivalent plastic strain of the matrix. The modified Gurson-Tvergaard-Needleman damage model ‎was implemented by developing a code in the Abaqus software. To use the modified Gurson-Tvergaard-‎Needleman model, 16 input parameters of the model were determined for the material under study. After ‎modifying the model, developing the code, and determining the input parameters, it was first tested on a single ‎element. The results of the developed model showed complete agreement with the results of the basic Gurson-‎Tvergaard-Needleman model and analytical solutions under tensile and shear loads, respectively. Finally, the ‎developed model was tested in shear loading on the shear specimen. It was observed that the modified model ‎eliminates the weakness of the base Gurson-Tvergaard-Needleman model and well predicts the occurrence of ‎damage and weakening of the mechanical properties of the material under the prevailing shear conditions.‎

کلیدواژه‌ها [English]

  • Damage mechanics
  • Gurson-Tvergaard-Needleman model
  • Yield function
  • Shear damage
  • Shear loading
[1] J. Lemaitre, A continuous damage mechanics model for ductile fracture, Journal of engineering materials and technology, 107(1) (1985) 83-89.
[2] A.L. Gurson, 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(1) (1977) 2-15.
[3] C. Chu, A. Needleman, Void nucleation effects in biaxially stretched sheets, Journal of Engineering Materials and Technology, 102(3) (1980) 249-256.
[4] V. Tvergaard, Influence of voids on shear band instabilities under plane strain conditions, International Journal of Fracture, 17(4) (1981) 389-407.
[5] V. Tvergaard, Influence of void nucleation on ductile shear fracture at a free surface, Journal of the Mechanics and Physics of Solids, 30(6) (1982) 399-425.
[6] A. Needleman, V. Tvergaard, An analysis of ductile rupture in notched bars, Journal of the Mechanics and Physics of Solids, 32(6) (1984) 461-490.
[7] Q.-Y. Song, A. Heidarpour, X.-L. Zhao, L.-H. Han, Experimental and numerical investigation of ductile fracture of carbon steel structural components, Journal of Constructional Steel Research, 145 (2018) 425-437.
[8] C. Ruggieri, Numerical investigation of constraint effects on ductile fracture in tensile specimens, Journal of the Brazilian Society of Mechanical Sciences and Engineering, 26(2) (2004) 190-199.
[9] B. Qiang, X. Wang, Ductile crack growth behaviors at different locations of a weld joint for an X80 pipeline steel: A numerical investigation using GTN models, Engineering Fracture Mechanics, 213 (2019) 264-279.
[10] P. Zhao, Z. Chen, C. Dong, Failure analysis based on microvoids damage model for DP600 steel on in-situ tensile tests, Engineering Fracture Mechanics, 154 (2016) 152-168.
[11] T.-S. Cao, E. Maire, C. Verdu, C. Bobadilla, P. Lasne, P. Montmitonnet, P.-O. Bouchard, Characterization of ductile damage for a high carbon steel using 3D X-ray micro-tomography and mechanical tests–Application to the identification of a shear modified GTN model, Computational Materials Science, 84 (2014) 175-187.
[12] K. Nahshon, J. Hutchinson, Modification of the Gurson model for shear failure, European Journal of Mechanics-A/Solids, 27(1) (2008) 1-17.
[13] L. Xue, Constitutive modeling of void shearing effect in ductile fracture of porous materials, Engineering Fracture Mechanics, 75(11) (2008) 3343-3366.
[14] K.L. Nielsen, V. Tvergaard, Ductile shear failure or plug failure of spot welds modelled by modified Gurson model, Engineering Fracture Mechanics, 77(7) (2010) 1031-1047.
[15] M. Achouri, G. Germain, P. Dal Santo, D. Saidane, Numerical integration of an advanced Gurson model for shear loading: Application to the blanking process, Computational Materials Science, 72 (2013) 62-67.
[16] Z. Xue, J. Faleskog, J.W. Hutchinson, Tension–torsion fracture experiments–Part II: Simulations with the extended Gurson model and a ductile fracture criterion based on plastic strain, International Journal of Solids and Structures, 50(25) (2013) 4258-4269.
[17] L. Malcher, F.A. Pires, J.C. De Sá, An extended GTN model for ductile fracture under high and low stress triaxiality, International Journal of Plasticity, 54 (2014) 193-228.
[18] J. Zhou, X. Gao, J.C. Sobotka, B.A. Webler, B.V. Cockeram, On the extension of the Gurson-type porous plasticity models for prediction of ductile fracture under shear-dominated conditions, International Journal of Solids and Structures, 51(18) (2014) 3273-3291.
[19] W. Jiang, Y. Li, J. Su, Modified GTN model for a broad range of stress states and application to ductile fracture, European Journal of Mechanics-A/Solids, 57 (2016) 132-148.
[20] J. Lemaitre, H. Lippmann, A course on damage mechanics, vol. 2Springer, in, Berlin, 1996.
[21] V. Tvergaard, A. Needleman, Analysis of the cup-cone fracture in a round tensile bar, Acta metallurgica, 32(1) (1984) 157-169.
[22] W. Lode, Versuche über den Einfluss der mittleren Hauptspannung auf die Fliessgrenze, ZAMM, 5 (1925) 215-220.
[23] S.M. Graham, T. Zhang, X. Gao, M. Hayden, Development of a combined tension–torsion experiment for calibration of ductile fracture models under conditions of low triaxiality, International Journal of Mechanical Sciences, 54(1) (2012) 172-181.
[24] J. Lemaitre, Coupled elasto-plasticity and damage constitutive equations, Computer Methods in Applied Mechanics and Engineering, 51(1-3) (1985) 31-49.
[25] J. Zhou, X. Gao, M. Hayden, J.A. Joyce, Modeling the ductile fracture behavior of an aluminum alloy 5083-H116 including the residual stress effect, Engineering Fracture Mechanics, 85 (2012) 103-116.
[26] L. Xue, Damage accumulation and fracture initiation in uncracked ductile solids subject to triaxial loading, International Journal of Solids and Structures, 44(16) (2007) 5163-5181.
[27] X. Gao, G. Zhang, C. Roe, A study on the effect of the stress state on ductile fracture, International Journal of Damage Mechanics, 19(1) (2010) 75-94.
[28] H. Gholipour, F. Biglari, K. Nikbin, Experimental and numerical investigation of ductile fracture using GTN damage model on in-situ tensile tests, International Journal of Mechanical Sciences, 164 (2019) 105170.
[29] H. Gholipour, F. Biglari, Experimental Study and Numerical Simulation of Ductile Fracture on In-Situ Tensile Specimens Using GTN Micromechanical Damage Model, Modares Mechanical Engineering, 20(8) (2020) 2087-2099.
[30] Q. Yin, B. Zillmann, S. Suttner, G. Gerstein, M. Biasutti, A.E. Tekkaya, M.F.-X. Wagner, M. Merklein, M. Schaper, T. Halle, An experimental and numerical investigation of different shear test configurations for sheet metal characterization, International Journal of Solids and Structures, 51(5) (2014) 1066-1074.
[31] Q. Yin, C. Soyarslan, K. Isik, A. Tekkaya, A grooved in-plane torsion test for the investigation of shear fracture in sheet materials, International Journal of Solids and Structures, 66 (2015) 121-132.
[32] S. Gatea, H. Ou, B. Lu, G. McCartney, Modelling of ductile fracture in single point incremental forming using a modified GTN model, Engineering Fracture Mechanics, 186 (2017) 59-79.
[33] C.C. Roth, D. Mohr, Determining the strain to fracture for simple shear for a wide range of sheet metals, International Journal of Mechanical Sciences, 149 (2018) 224-240.
[34] S. Baltic, J. Magnien, H.-P. Gänser, T. Antretter, R. Hammer, Coupled damage variable based on fracture locus: Modelling and calibration, International Journal of Plasticity, 126 (2020) 102623.
[35] N. Aravas, On the numerical integration of a class of pressure‐dependent plasticity models, International Journal for numerical methods in engineering, 24(7) (1987) 1395-1416.
[36] Z. Zhang, On the accuracies of numerical integration algorithms for Gurson-based pressure-dependent elastoplastic constitutive models, Computer methods in applied mechanics and engineering, 121(1-4) (1995) 15-28.
[37] Z. Zhang, Explicit consistent tangent moduli with a return mapping algorithm for pressure-dependent elastoplasticity models, Computer Methods in Applied Mechanics and Engineering, 121(1-4) (1995) 29-44.
[38] B.C. Simonsen, S. Li, Mesh‐free simulation of ductile fracture, International Journal for Numerical Methods in Engineering, 60(8) (2004) 1425-1450.
[39] M.B. Bettaieb, X. Lemoine, L. Duchêne, A.M. Habraken, On the numerical integration of an advanced Gurson model, International journal for numerical methods in engineering, 85(8) (2011) 1049-1072.
[40] K. Nahshon, Z.J.E.f.m. Xue, A modified Gurson model and its application to punch-out experiments, 76(8) (2009) 997-1009.
[41] J. Dong, S. Wang, J. Zhou, C. Ma, S. Wang, B. Yang, Experimental and numerical investigation on the shearing process of stainless steel thin-walled tubes in the spent fuel reprocessing, Thin-Walled Structures, 145 (2019) 106407.
[42] A. Standard, B831-14, Standard Test Method for Shear Testing of Thin Aluminum Alloy Products, ASTM International, West Conshohocken, PA,  (2005).
[43] A. Mendelson, Plasticity; theory and application, Macmillan, 1968.
[44] M. Achouri, G. Germain, P. Dal Santo, D. Saidane, Experimental characterization and numerical modeling of micromechanical damage under different stress states, Materials & Design, 50 (2013) 207-222.