A New Approach for Stress State - Dependent Flow Localization Failure Bounded Through Ductile Damage in Dynamically Loaded Sheets
محورهای موضوعی : Mechanical EngineeringF Hosseini Mansoub 1 , A Basti 2 , A Darvizeh 3 , A Zajkani 4
1 - Department of Mechanical Engineering, University Campus, University of Guilan, Rasht, Iran
2 - Department of Mechanical Engineering, University of Guilan, Rasht, Iran
3 - Department of Mechanical Engineering, University of Guilan, Rasht, Iran
4 - Department of Mechanical Engineering, Imam Khomeini International University, Qazvin, Iran
کلید واژه: Ductile damage, Stress State, Strain rate, Localized necking, Forming Limit,
چکیده مقاله :
In this paper, a new approach is proposed for stress state - dependent flow localization in bifurcation failure model bounded through ductile damage in dynamically loaded sheets. Onset of localized necking is considered in phenomenological way for different strain rates to draw the forming limit diagram (FLD). Using a strain metal hardening exponent in the Vertex theory related to the strain rate helps investigate rate- dependent metal forming limits. Besides, the paper utilizes the model of ductile damage as a function of strain condition, stress states (triaxiality and Lode parameters), and the symbols of stiffness strain to predict the onset of the necking. It is worth noting that updated level of elasticity modulus in the plastic deforming is attributed as an essential index for the ductile damage measuring. According to original formulations, a UMAT subroutine is developed in the finite element simulation by ABAQUS code to analyze and connect the related constitutive models. Results reveal that the FLD levels increase for St 13 material through enhancing the strain rate.
[1] Aboutalebi F.H., Farzin M., Poursina M., 2011, Numerical simulation and experimental validation of a ductile damage model for DIN 1623 St14 steel, The International Journal of Advanced Manufacturing Technology 53: 157-165.
[2] Ma X., Li F., Li J., 2015, Analysis of forming limits based on a new ductile damage criterion in St14 steel sheets, Materials & Design 68: 134-145.
[3] Hill R., 1952, On discontinuous plastic states, with special reference to localized necking in thin sheets, Journal of the Mechanics and Physics of Solids 1:19-30.
[4] Hill R., 1958, A general theory of uniqueness and stability in elastic-plastic solids, Journal of the Mechanics and Physics of Solids 6: 236-249.
[5] Borré G., Maier G., 1989, On linear versus nonlinear flow rules in strain localization analysis, Meccanica 24: 36-41.
[6] Thomas W.M., 1991, Friction stir butt welding, International Patent Application No PCT/GB92/0220.
[7] Chow C.L., Jie M., Wu X., 2005, Localized necking criterion for strain-softening materials, Journal of Engineering Materials and Technology 127: 273-278.
[8] Neilsen M.K., Schreyer H.L., 1993, Bifurcations in elastic-plastic materials, International Journal of Solids and Structures 30: 521-544.
[9] Chow C.L., Jie M., Wu X., 2007, A damage-coupled criterion of localized necking based on acoustic tensor, International Journal of Damage Mechanics 16: 265-281.
[10] Szabó L., 2000, Comments on loss of strong ellipticity in elastoplasticity, International Journal of Solids and Structures 37: 3775-3806.
[11] Bigoni D., Hueckel T., 1991, Uniqueness and localization—I. Associative and non-associative elastoplasticity, International Journal of Solids and Structures 28: 197-213.
[12] Rudnicki J.W., Rice J.R., 1975, Condition for the localization of deformation in pressure-sensitive dilatant materials, Journal of the Mechanics and Physics of Solids 23(6): 371-394.
[13] Xue L., Wierzbicki T., 2008, Ductile fracture initiation and propagation modeling using damage plasticity theory, Engineering Fracture Mechanics 75: 3276-3293.
[14] Marciniak Z., Kuczyński K., 1967, Limit strains in the processes of stretch-forming sheet metal, International Journal of Mechanical Sciences 9(9): 609-612.
[15] Marciniak Z., Kuczyński K., Pokora T., 1973, Influence of the plastic properties of a material on the forming limit diagram for sheet metal in tension, International Journal of Mechanical Sciences 15: 789-800.
[16] Mirfalah S.M., Basti A., Hashemi R., Darvizeh A., 2018, Effects of normal and through-thickness shear stresses on the forming limit curves of AA3104-H19 using advanced yield criteria, International Journal of Mechanical Sciences 137: 15-23.
[17] Erfanian M., Hashemi R., 2018, A comparative study of the extended forming limit diagrams considering strain path, through-thickness normal and shear stress, International Journal of Mechanical Sciences 148: 316-326.
[18] Zajkani A., Bandizaki A., 2017, An efficient model for diffuse to localized necking transition in rate-dependent bifurcation analysis of metallic sheets, International Journal of Mechanical Sciences 133: 794-803.
[19] Zajkani A., Bandizaki A., 2017, A path-dependent necking instability analysis of the thin substrate composite plates considering nonlinear reinforced layer effects, The International Journal of Advanced Manufacturing Technology 95: 759-774.
[20] Stören S., Rice J.R., 1975, Localized necking in thin sheets, Journal of the Mechanics and Physics of Solids 23: 421-441.
[21] Zajkani A., Bandizaki A., 2018, Stability and instability analysis of the substrate supported panels in the forming process based on perturbation growth and bifurcation threshold models, Journal of Manufacturing Processes 31: 703-711.
[22] Xue L., 2007, Ductile Fracture modeling-Theory, Experimental Investigation and Numerical Verification, Thesis Ph. D., Massachusetts Institute of Technology.
[23] 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.
[24] Simha C.H.M., Xu S., Tyson W.R., 2014, Non-local phenomenological damage-mechanics-based modeling of the Drop-Weight Tear Test, Engineering Fracture Mechanics 118: 66-82.
[25] Campos H.B., Butuc M.C., Grácio J.J., 2006, Theorical and experimental determination of the forming limit diagram for the AISI 304 stainless steel, Journal of Materials Processing Technology 179: 56-60.
[26] Kim S.B., Huh H., Bok H.H., Moon M.B., 2011, Forming limit diagram of auto-body steel sheets for high-speed sheet metal forming, Journal of Materials Processing Technology 211: 851-862.
[27] Mosavi F., Hashemi R., Madoliat R., 2018, Measurement of directional anisotropy coefficients for AA7020-T6 tubes and prediction of forming limit curve, International Journal of Advanced Manufacturing Technology 96: 1015-1023.
[28] Balasubramanian S., Anand L., 2002, Elasto-viscoplastic constitutive equations for polycrystalline fcc materials at low homologous temperatures, Journal of the Mechanics and Physics of Solids 50: 101-126.
[29] Brünig M., Gerke S., 2011, Simulation of damage evolution in ductile metals undergoing dynamic loading conditions, International Journal of Plasticity 27: 1598-1617.
[30] Shojaei A., Voyiadjis G.Z., Tan P.J., 2013, Viscoplastic constitutive theory for brittle to ductile damage in polycrystalline materials under dynamic loading, International Journal of Plasticity 48: 125-151.
[31] Huh J., Huh H., Lee C.S., 2013, Effect of strain rate on plastic anisotropy of advanced high strength steel sheets, International Journal of Plasticity 44: 23-46.
[32] Johnson G.R., Cook W.H., 1983, A constitutive model and data for metals subjected to large strains, high strain rates and high temperatures, 7th International Symposium on Ballistics, The Hague.
[33] Clausen A.H., Børvik T., Hopperstad O.S., Benallal A., 2004, Flow and fracture characteristics of aluminium alloy AA5083–H116 as function of strain rate, temperature and triaxiality, Materials Science and Engineering 364: 260-272.
[34] Erice B., Gálvez F., Cendón D.A., Sánchez-Gálvez V., 2012, Flow and fracture behaviour of FV535 steel at different triaxialities, strain rates and temperatures, Engineering Fracture Mechanics 79: 1-17.
[35] Kajberg J., Sundin K-G., 2013, Material characterisation using high-temperature Split Hopkinson pressure bar, Journal of Materials Processing Technology 213: 522-531.
[36] Smerd R., Winkler S., Salisbury C., 2005, High strain rate tensile testing of automotive aluminum alloy sheet, International Journal of Impact Engineering 32: 541-560.
[37] Verleysen P., Peirs J., Van Slycken J., 2011, Effect of strain rate on the forming behaviour of sheet metals, Journal of Materials Processing Technology 211:1457-1464.
[38] Mohr D., Dunand M., Kim K-H., 2010, Evaluation of associated and non-associated quadratic plasticity models for advanced high strength steel sheets under multi-axial loading, International Journal of Plasticity 26: 939-956.
[39] Kim J.H., Sung J.H., Piao K., Wagoner R.H., 2011, The shear fracture of dual-phase steel, International Journal of Plasticity 27: 1658-1676.
[40] 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.
[41] Sun X., Choi K.S., Liu W.N., Khaleel M.A., 2009, Predicting failure modes and ductility of dual phase steels using plastic strain localization, International Journal of Plasticity 25: 1888-1909.
[42] Gruben G., Fagerholt E., Hopperstad O.S., Børvik T., 2011, Fracture characteristics of a cold-rolled dual-phase steel, European Journal of Mechanics 30: 204-218.
[43] Chung K., Ma N., Park T., 2011, A modified damage model for advanced high strength steel sheets, International Journal of Plasticity 27: 1485-1511.
[44] Huh H., Kim S-B., Song J-H., Lim J-H., 2008, Dynamic tensile characteristics of TRIP-type and DP-type steel sheets for an auto-body, International Journal of Mechanical Sciences 50: 918-931.
[45] Curtze S., Kuokkala V-T., Hokka M., Peura P., 2009, Deformation behavior of TRIP and DP steels in tension at different temperatures over a wide range of strain rates, Materials Science and Engineering 507: 124-131.
[46] Roth C.C., Mohr D., 2014, Effect of strain rate on ductile fracture initiation in advanced high strength steel sheets: Experiments and modeling, International Journal of Plasticity 56: 19-44.
[47] Mirfalah S.M., Basti A., Hashemi R., 2016, Forming limit curves analysis of aluminum alloy considering the through-thickness normal stress, anisotropic yield functions and strain rate, International Journal of Mechanical Sciences 117: 93-101.
[48] Jie M., Cheng C.H., Chan L.C., Chow C.L., 2009, Forming limit diagrams of strain-rate-dependent sheet metals, International Journal of Mechanical Sciences 51: 269-275.
[49] Saradar M., Basti A., Zaeimi M., 2015, Numerical study of the effect of strain rate on damage prediction by dynamic forming limit diagram in high velocity sheet metal forming, Modares Mechanical Engineering 14: 212-222.
[50] Wu H-Y., Sun P-H., Chen H-W., Chiu C-H., 2012, Rate and orientation dependence of formability in fine-grained AZ31B-O Mg alloy thin sheet, Journal of Materials Engineering and Performance 21: 2124-2130.
[51] Kim D., Kim H., Kim J.H., 2015, Modeling of forming limit for multilayer sheets based on strain-rate potentials, International Journal of Plasticity 75: 63-99.
[52] Fakir O. El., Wang L., Balint D., 2014, Predicting effect of temperature, strain rate and strain path changes on forming limit of lightweight sheet metal alloys, Procedia Engineering 81: 736-741.