مطالعه‌ای بر پاسخ پلاستیک ورق‌های دایره‌ای تحت بار دینامیکی با توزیع یکنواخت و محلی

نوع مقاله: مقاله مستقل

نویسندگان

1 استادیار، دانشکده مهندسی مکانیک، دانشگاه ایوان‌کی، ایوان‌کی، ایران

2 مربی، دانشکده مهندسی مکانیک، دانشگاه ایوان‌کی، ایوان‌کی، ایران

3 دانشیار، دانشکده مهندسی مکانیک، دانشگاه گیلان، رشت، ایران

10.22044/jsfm.2020.9264.3091

چکیده

در این مقاله، از یک روش تحلیل بی‌بعد جهت ارائه سه رابطه تجربی بر اساس اعداد بی‌بعد به‌منظور پیش‌بینی نسبت بیشترین خیز دائمی ورق‌های تک‌لایه دایره‌ای به ضخامت آن تحت بارگذاری دینامیکی با توزیع یکنواخت و محلی استفاده شده است. در اعداد بی‌بعد پیشنهادی، اثر هندسه ورق، شدت بار اعمالی، خواص مکانیکی ورق، حساسیت ماده به نرخ کرنش، شعاع بارگذاری و فاصله استقرار در نظر گرفته شده است. جهت صحت سنجی مدل‌های تجربی از چهارده سری آزمایش و 562 داده موجود در ادبیات تحقیق در طول چهل سال گذشته استفاده شده است. نتایج حاصل از مدل‌سازی نشان داد که تطابق خوبی بین نتایج پیش‌بینی مدل و مقادیر تجربی وجود دارد به‌طوری‌که درمجموع 338 داده تجربی برای بارگذاری یکنواخت، به ترتیب 75% (255 داده) و 94% (318 داده) از کل نقاط تجربی در محدوده خطای کمتر از 10% و 20% قرار دارند. همچنین، درمجموع 108 داده تجربی موجود برای بارگذاری محلی بدون استفاده از فاصله استقرار، به ترتیب 59% (64 داده) و 92% (99 داده) از کل نقاط تجربی در این دو محدوده قرار گرفتند. در بارگذاری محلی با استفاده از فاصله استقرار خرج، به ترتیب 68% (79 داده از 116) و 85% (99 داده از 116) در محدوده خطای کمتر از 10% و 20% قرار دارند.

کلیدواژه‌ها


[1] Hudson GE (1951) A theory of the dynamic plastic deformation of a thin diaphragm. J Appl Phys 22(1): 1-11.

[2] Duffey TA (1967) Large deflection dynamic response of clamped circular plates subjected to explosive loading. Sandia Corp., Albuquerque, N. Mex.

[3] Jones N (1971) A theoretical study of the dynamic plastic behavior of beams and plates with finite-deflections. Int J Solids Struct 7(8): 1007-1029.

[4] Wierzbicki T, Florence AL (1970) A theoretical and experimental investigation of impulsively loaded clamped circular viscoplastic plates. Int J Solids Struct 6(5): 553-568.

 [5] Lippmann H (1974) Kinetics of the axisymmetric rigid-plastic membrane subject to initial impact. Int J Mech Sci 16(5): 297-303.

[6] Symonds PS, Wierzbicki T (1979) Membrane mode solutions for impulsively loaded circular plates. J Appl Mech 46(1): 58-64.

[7] Soares CG (1981) A mode solution for the finite deflections of a circular plate loaded impulsively. Rozprawy Inzynierskie 29(1):99-114.

[8] Perrone N, Bhadra P (1984) Simplified large deflection mode solutions for impulsively loaded, viscoplastic, circular membranes. J Appl Mech 51(3): 505-509.

[9] Nurick GN, Pearce HT, Martin JB (1987) Predictions of transverse deflections and in-plane strains in impulsively loaded thin plates. Int J Mech Sci 29(6):435-442.

[10] Nurick GN, Martin JB (1989) Deformation of thin plates subjected to impulsive loading—a review part II: experimental studies. Int J Impact Eng 8(2): 171-186.

[11] Nurick GN, Martin JB (1989) Deformation of thin plates subjected to impulsive loading—a review: Part I: Theoretical considerations. Int J Impact Eng 8(2): 159-170.

[12] Jacob N, Nurick GN, Langdon GS (2007) The effect of stand-off distance on the failure of fully clamped circular mild steel plates subjected to blast loads. Eng Struct 29(10): 2723-2736.

[13] Gharababaei H, Nariman-Zadeh N, Darvizeh A (2010) A simple modelling method for deflection of circular plates under impulsive loading using dimensionless analysis and singular value decomposition. J Mech 26(03): 355-361.

[14] Gharababaei H, Darvizeh A, Darvizeh M (2010) Analytical and experimental studies for deformation of circular plates subjected to blast loading. J Mech Sci Tech 24(9): 1855-1864.

[15] Babaei H,  Darvizeh A (2011) Investigation into the response of fully clamped circular steel, copper, and aluminum plates subjected to shock loading. Mech Based Des Struct 39(4): 507-526.

[16] Babaei H, Darvizeh A (2012) Analytical study of plastic deformation of clamped circular plates subjected to impulsive loading. J Mech Mater Struct 7(4): 309-322.

[17] Cloete T, Nurick G (2014) On the influence of radial displacements and bending strains on the large deflections of impulsively loaded circular plates. Int J Mech Sci 82: 140-148.

[18] Yuen SC, Nurick GN, Langdon GS, Iyer Y (2017) Deformation of thin plates subjected to impulsive load: Part III–an update 25 years on. Int J Impact Eng 107: 108-117.

[19] Johnson, W (1972) Impact strength of materials. Edward Arnold London.

[20] Zhao YP (1998) Suggestion of a new dimensionless number for dynamic plastic response of beams and plates. Arch Appl Mech 68(7-8): 524-538.

[21] Jones N (2012) Structural impact. Cambridge university press.

[22] Jones N (1967) Influence of strain-hardening and strain-rate sensitivity on the permanent deformation of impulsively loaded rigid-plastic beams. Int J Mech Sci 9(12): 777-796.

[23] Rezasefat M, Mostofi TM, Ozbakkaloglu T (2019) Repeated localized impulsive loading on monolithic and multi-layered metallic plates. Thin Wall Struc 144: 106332.

[24] Wierzbicki T, Florence AL (1970) A theoretical and experimental investigation of impulsively loaded clamped circular viscoplastic plates. Int J Solids Struct 6(5): 553-568.

[25] Bodner SR, Symonds PS (1979) Experiments on viscoplastic response of circular plates to impulsive loading. J Mech Phys Solids 27(2): 91-113.

[26] Teeling-Smith RG, Nurick GN (1991) The deformation and tearing of thin circular plates subjected to impulsive loads. Int J Impact Eng 11(1): 77-91.

[27] Nurick GN, Teeling-Smith RG (1994) Predicting the onset of necking and hence rupture of thin plates loaded impulsively—an experimental view. Struct Under Shock Impact 11: 431-445.

[28] Thomas B, Nurick GN (1995) The effect of boundary conditions on thin plates subjected to impulsive loads. In: Plasticity 95—The 5th international symposium on plasticity and its current application 85-88.

[29] Nurick GN, Gelman ME, Marshall NS (1996) Tearing of blast loaded plates with clamped boundary conditions. Int J Impact Eng 18: 803-827.

[30] Nurick GN, Lumpp DM (1996) Deflection and tearing of clamped stiffened circular plates subjected to uniform impulsive loads. In: Jones N, Brebbia CA and Watson AJ (eds) Structures under shock and impact. Southampton, UK: Computational Mechanics Publications 393-402.

[31] Nurick GN, Radford AM (1997) Deformation and tearing of clamped circular plates subjected to ocalized central blast loads. In: Recent developments in computational and applied mechanics: A volume in honour of John B. Martin. Barcelona, Spain: International Centre for Numerical Methods in Engineering 276–-301.

[32] Chung Kim Yuen S, Nurick GN (2000) The significance of the thickness of a plate when subjected to localized blast load. In: 16th international symposium on military aspects of blast and shock, MABS 16, Oxford, UK 491-499.

[33] Mostofi TM, Babaei H, Alitavoli M (2017) The influence of gas mixture detonation loads on large plastic deformation of thin quadrangular plates: Experimental investigation and empirical modelling. Thin Walled Struct 118: 1-11.

[34] Mostofi TM, Babaei H, Alitavoli M, Lu G, Ruan D (2019) Large transverse deformation of double-layered rectangular plates subjected to gas mixture detonation load. Int J Impact Eng 125: 93-106.

[35] Symonds PS (1973) Approximation techniques for impulsively loaded structures of rate sensitive plastic behavior. SIAM Journal Appl Math 25(3): 462-473.

[36] Hu YQ (2000) Application of response number for dynamic plastic response of plates subjected to impulsive loading. Int Journal Pres Ves Pip 2000 77(12): 711-714.

[37] Babaei H, Mostofi T.M, Alitavoli M, Darvizeh A (2016) Empirical Modelling for Prediction of Large Deformation of Clamped Circular Plates in Gas Detonation Forming Process. Exp Tech 40(6): 1485-1494.

[38] Mostofi TM, Babaei H, Alitavoli M, Hosseinzadeh S (2017) On dimensionless numbers for predicting large ductile transverse deformation of monolithic and multi-layered metallic square targets struck normally by rigid spherical projectile. Thin Wall Struc 112: 118-124.

[39] Babaei H, Mostofi TM, Alitavoli M (2017) Experimental and analytical investigation into large ductile transverse deformation of monolithic and multi-layered metallic square targets struck normally by rigid spherical projectile. Thin Wall Struc 107: 257-265.

 [40] Mirzababaie Mostofi T, Babaei H, Alitavoli M (2017) Experimental and theoretical study on large ductile transverse deformations of rectangular plates subjected to shock load due to gas mixture detonation. Strain 53(4): e12235.

[41] Babaei H, Mostofi TM, Namdari-Khalilabad M, Alitavoli M, Mohammadi K (2017) Gas mixture detonation method, a novel processing technique for metal powder compaction: Experimental investigation and empirical modeling. Powder Tech 315: 171-81.

[42] Babaei H, Mirzababaie Mostofi T, Armoudli E (2017) On dimensionless numbers for the dynamic plastic response of quadrangular mild steel plates subjected to localized and uniform impulsive loading. Proc Inst Mech Eng-Part E J Process MechEng 231(5): 939-950.

[43] Babaei H, Mirzababaie Mostofi T (2016) New dimensionless numbers for deformation of circular mild steel plates with large strains as a result of localized and uniform impulsive loading. Proc Inst Mech Eng-Part L J Mater Des Appl 1464420716654195.

[44] Babaei H, Mostofi TM, Alitavoli M, Saeidinejad A (2017) Experimental investigation and dimensionless analysis of forming of rectangular plates subjected to hydrodynamic loading. J Appl Mech Tech Phys 58(1):139-47.

[45] Babaei H, Mirzababaie Mostofi T (2016) Modeling and prediction of fatigue life in composite materials by using singular value decomposition method. Proc Inst Mech Eng-Part L J Mater Des Appl 1464420716660875.

[46] Rezasefat M, Mirzababaie Mostofi T, Babaei H, Ziya-Shamami M, Alitavoli M (2019) Dynamic plastic response of double-layered circular metallic plates due to localized impulsive loading. Proc Inst Mech Eng-Part L J Mater Des Appl 233(7):1449-1471.

[47] Babaei H, Mostofi TM, Sadraei SH (2015) Effect of gas detonation on response of circular plate-experimental and theoretical. Struct Eng Mech 56(4): 535-548.

[48] Babaei H, Mostofi TM, Alitavoli M (2015) Experimental investigation and analytical modelling for forming of circular-clamped plates by using gases mixture detonation. Proc Inst Mech Eng-Part C J Mech Eng Sci 0954406215614336.

[49] Mostofi TM, Babaei H, Alitavoli M (2016) Theoretical analysis on the effect of uniform and localized impulsive loading on the dynamic plastic behavior of fully clamped thin quadrangular plates. Thin-Walled Struct 109: 367-376.

[50] Mostofi TM, Golbaf A, Mahmoudi A, Alitavoli M, Babaei H (2018) Closed-form analytical analysis on the effect of coupled membrane and bending strains on the dynamic plastic behaviour of fully clamped thin quadrangular plates due to uniform and localized impulsive loading. Thin Wall Struc 123: 48-56.

[51] Babaei H, Mirzababaie Mostofi T, Alitavoli M (2015) Experimental study and analytical modeling for inelastic response of rectangular plates under hydrodynamic loads. Journal of Modares Mechanical Engineering 15(4): 361-368. (In Persian)

[52] Babaei H, Mirzababaie Mostofi T, Alitavoli M (2017) Experimental and theoretical study of large deformation of rectangular plates subjected to water hammer shock loading. Proc Inst Mech Eng-Part E: J Process Mech Eng 231(3): 490-496.

[53] Babaei H, Mirzababaie Mostofi T, Alitavoli M
(2015) Study on the response of circular thin plate under low velocity impact. Geomech Eng 9(2): 207-218.

[54] Mostofi TM, Badkhor MS, Ghasemi E (2019) Experimental investigation and optimal analysis of the high-velocity forming process of bilayer plates. Journal of Solid and Fluid Mechanics 9(3): 65-80.

[55] Mostofi TM, Babaei H (2019) Plastic deformation of polymeric-coated aluminum plates subjected to gas mixture detonation loading: Part I: Experimental studies. Journal of Solid and Fluid Mechanics 9(1): 71-83.

[56] Mostofi TM, Babaei H (2019) Plastic deformation of polymeric-coated aluminum plates subjected to gas mixture detonation loading: Part II: Analytical and empirical modelling. Journal of Solid and Fluid Mechanics 9(2): 15-2.