مهندسی مکانیک مدرس

مهندسی مکانیک مدرس

مدل‌سازی شکست مواد شکل‌پذیر بر اساس مدل دراکر-پراگر و روش میدان فاز

نویسنده
مکانیک، دانشکده مهندسی، دانشگاه صنعتی خاتم الانبیاء، بهبهان، ایران
چکیده
در این مقاله با ترکیب مدل رفتار پلاستیک و روش میدان فاز مدلی جهت شبیه سازی شکست مواد شکل پذیر پیشنهاد شده است. مدل پلاستیسیته دراکر-پراگر که هم برای فلزات و هم برای پلیمرها، فوم‌ها، خاک، بتن و دیگر مواد وابسته به فشار قابل استفاده است، با روش میدان فاز ترکیب شده است. به عبارت دیگر مدل توانایی در نظر گرفتن اثرات فشار در فرآیند تسلیم و شکست مواد شکل‌پذیر را دارد. چگونگی استخراج معادلات حاکم از کمینه سازی انرژی کل، پیاده‌سازی اجزای محدود مدل، گسسته‌سازی و دیگر جزئیات حل تشریح شده است. الگوریتم‌های انتگرال‌گیری ارائه شده و چگونگی ترکیب رفتار ماده با متغیر میدان فاز جهت در نظر گرفتن اثرات ترک شرح داده شده است. جهت کنترل فرآیند شکست، متغیری جهت کنترل نیروی محرکه میدان فاز، معرفی شده است. در انتها با کمک شبیه‌سازی عددی، چگونگی تقریب ترک به روش میدان فاز بررسی شده و محدوده ثابت طول برای تقریب دقیق ترک به‌دست آمده است. نمونه‌هایی با هندسه و بارگذاری مختلفی انتخاب شده که صحت و دقت مدل و الگوریتم انتگرال‌گیری پیشنهادی با مقایسه با مقایسه آن‌ها با اطلاعات تجربی موجود تأیید شده است. در نهایت توانایی مدل در پیش‌بینی مسیر ترک در مدهای مختلف شکست با استفاده از نمونه آرکان نشان داده شده است.
کلیدواژه‌ها

عنوان مقاله English

Ductile fracture modelling based on the Drucker-Prager plasticity and phase field approach

نویسنده English

Hojjat Badnava
Department of Mechanical Engineering, Behbahan Khatam Alanbia University of Technology, Khuzestan, Iran
چکیده English

In this paper, a coupled plasticity-phase field model for ductile fracture is proposed. The Drucker-Prager plasticity model, which have been applied to metals, concrete, polymers, foams, and other pressure-dependent materials, is coupled with the phase field method. The governing equations are determined by a minimization principle that results in balance laws for the coupled displacement-fracture phase field problem. Furthermore, the finite element implementation, discretization and integration algorithms for the proposed model are presented for three-dimensional, plane strain and plane stress states. In addition, to control the influence of the plastic work and its effect on the crack propagation process, a threshold variable is introduced. Using a numerical example, it is demonstrated that a specific length scale and a certain minimum element size is necessary such that the regularized crack surface converges to the sharp crack. The accuracy of the proposed model and integration algorithm is verified by comparing the obtained results with existing experimental data. In addition, the Arcan sample, by means of a special test setup, allows to load a sample at different direction, and thus performing mixed mode fracture investigation using the model.

کلیدواژه‌ها English

Ductile fracture
Phase field method
Finite element
Drucker-Prager
Integration algorithm
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