روشهای عددی در مهندسی

روشهای عددی در مهندسی

شبیه‌سازی حرکت مرزدانه متاثر از کرنش با کوپل میدان‌فاز–کریستال‌پلاستیسیته: اثر اندازه المان حجمک نماینده

نوع مقاله : مقاله پژوهشی

نویسندگان
محمد شادپور 1
محمد جعفری 1
مصطفی جمشیدیان 2
1 دانشکده مهندسی مکانیک، دانشگاه یزد، یزد، ایران
2 دانشکده مهندسی، دانشگاه استرالیای غربی، کراولی، استرالیا
10.47176/jcme.45.1.1080
چکیده
مدل‌سازی چندمقیاسی1 رشد میکروساختار2 در فلزات چندبلوری3، معمولا بر پایه مفهوم المان حجمک نماینده4 صورت می‌گیرد. این مفهوم، رفتار یک نقطه مادی5 را در مقیاس ماکروسکوپی6 نمایش می‌دهد. در این پژوهش، با استفاده از روش کوپل‌شده7 میدان فاز8 و کریستال پلاستیسیته9 بر مبنای چگالی نابجایی10، تأثیر اندازه‌ی المان حجمک نماینده بر سینتیک حرکت مرزدانه ناشی از کرنش11 پلاستیک در فلز آلومینیوم بررسی می‌شود. مدل کریستال پلاستیسیته12 بر مبنای چگالی نابجایی برای محاسبه‌ی توزیع انرژی تغییرشکل ذخیره‌شده13 در هر دانه14 و مدل میدان فاز برای توصیف حرکت مرزدانه‌ها در طی فرآیند عملیات حرارتی15 به‌کار گرفته می‌شود. اندازه المان حجمک نماینده در محدوده 10 تا 60 میکرومتر تغییر می‌کند و میانگین قطر اولیه دانه‌ها برای همه المان‌های حجمک نماینده‌ سه میکرومتر و شرایط مرزی تکرار شونده درنظر گرفته می‌شود. برای تعیین اندازه بهینه المان حجمک نماینده، تحلیل همگرایی با رسم نمودار پارامترهای میکروساختار به صورت تابعی از زمان عملیات حرارتی برای اندازه‌های مختلف المان حجمک نماینده انجام می‌شود. نتایج نشان می‌دهد که از نظر آماری، اندازه المان حجمک نماینده 30 میکرومتر و بیشتر برای توصیف رفتار ماده در شرایط بارگذاری کششی مناسب است. این نتایج می‌تواند برای انتخاب ابعاد بهینه‌ی المان حجمک نماینده و طراحی فرآیندهای ترمومکانیکی16 در مهندسی مواد، مورد استفاده قرار گیرد.
کلیدواژه‌ها
حرکت مرزدانه متأثر از کرنش
کریستال پلاستیسیته
چگالی نابجایی
میدان فاز
اندازه المان حجمک نماینده
موضوعات

عنوان مقاله English

Simulation of Strain-Induced Grain Boundary Migration via Coupling Phase-Field and Crystal Plasticity Methods: Effect of Representative Volume Element Size

نویسندگان English

Mohammad Shadpour 1
Mohammad Jafari 1
Mostafa Jamshidian 2
1 Department of Mechanical Engineering, Yazd University, Yazd, Iran
2 School of Engineering, The University of Western Australia, Crawley, WA 6009, Australia
چکیده English

Multiscale modeling of microstructural evolution in polycrystalline metals is commonly conducted based on the concept of a representative volume element (RVE), which characterizes the response of a material point. In this study, a coupled phase field and dislocation density-based crystal plasticity framework is used to investigate the effect of RVE size on the kinetics of static strain-induced grain boundary migration. The finite element-based crystal plasticity model is employed to compute the stored deformation energy distribution within individual grains, while the phase field model describes the subsequent grain boundary migration during high-temperature annealing. The simulations of grain growth are performed for a polycrystalline aluminum with elastic cubic symmetry under plastic uniaxial loading. The RVE size is varied in the range from 10 to 60µm for simulations of static strain-induced grain boundary migration. The initial average grain diameter for all RVEs is 3 µm. The periodic boundary condition is applied to statistical RVEs with sufficient scale separation between the microstructure and macrostructure. To determine the optimum RVE size under a specific boundary condition, a convergence analysis is performed by plotting the grain growth component as a function of RVE size. The simulation results indicate that an RVE size of 30 µm statistically provides a representative response for tensile loading conditions. The outcomes of this work provide valuable insights for determining the optimum RVE size and for the design of thermomechanical processing strategies in metallic materials.

کلیدواژه‌ها English

Strain-induced grain boundary migration (SIBM)
Crystal plasticity
Dislocation density
Phase-field method
RVE size effect
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