Abstract




 
   

IJE TRANSACTIONS B: Applications Vol. 27, No. 8 (August 2014) 1287-1296   

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  A NEW TECHNIQUE BASED ON STRAIN ENERGY FOR CORRECTION OF STRESS-STRAIN CURVE
 
G. H. Majzoobi and F. Fariba
 
( Received: November 18, 2013 – Accepted: March 06, 2014 )
 
 

Abstract    Tensile stress-strain curve is of high importance in mechanics of materials particularly in numerical simulations of material deformations. The curve is usually obtained by experiment but is limited by necking phenomenon. Engineering stress-strain curve is converted to true stress-strain curve through simple formulas. The conversion, however, is correct up the point of necking. From this point on, the curve should be corrected taking account of stress triaxiality. Over the past several decades, a number of methods such as Bridgeman correction technique have been proposed. In this investigation a new technique based on strain energy in introduced. Strain energy is assumed to be equal to the external work in tensile test. The energy method is compared with different approaches such as Bridgeman-Leroy, Bridgeman, Davidenkov, Siebel and optimization aided numerical simulation. The results indicate that the energy method prediction is very close to numerical simulation but at the same time it does not differ significantly too from the other approaches studied in this investigation.

 

Keywords    Stress-strain curve, Correction factor, Strain energy, External work, Numerical simulation

 

چکیده    منحنی های تنش-کرنش در مکانیک مواد و به ویژه در شبیه سازی تغییر شکل آن ها از اهمیت فراوانی برخوردار می باشند. این منحنی ها عموماً از طریق آزمایش کشش به دست می آیند که به خاطر پدیده گلوئی شدن محدود می باشند. منحنی تنش-کرنش مهندسی با استفاده از روابط بسیار ساده ای به منحنی تنش-کرنش حقیقی تبدیل می گردند. اما، این تبدیل تا نقطه آغاز گلوئی شدن معتبر است؛ زیرا از این نقطه به بعد باید سه بعدی شدن تنش را در این تبدیل مد نظر قرار داد. ظرف دهه های گذشته روش هائی مانند روش بریجمن برای تصحیح منحنی های تنش-کرنش پیشنهاد گردیده اند. در این تحقیق، یک روش جدید بر اساس انرژی کرنشی معرفی می شود. در این روش، فرض بر آن است که انرژی کرنش برابر کار خارجی انجام شده است که از آزمایش کشش به دست می آید. روش جدید با روش های ارائه شده قبلی مانند روش بریجمن-لئوری، بریجمن، دیویدنکو، سییبل و شبیه سازی به کمک بهینه سازی مورد مقایسه قرار می گیرد. نتایج به دست آمده حکایت از آن دارد که پیش بینی روش انرژی بسیار نزدیک به روش شبیه سازی به کمک بهینه سازی می باشد اما در عین حال، تفاوت قابل ملاحظه ای با دیگر روش های مورد مقایسه ندارد. این روش قابل کاربرد برای نمونه تخت و گرد هر دو می باشد.

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