بررسی اثر اندازه در آزمون فشار به کمک مدل ترکیبی هیل- تیلور
محورهای موضوعی : شکل دهی فلزات
فراز رحیم زاده لطف آباد
1
(
دانشجوی کارشناسی ارشد، بخش مهندسی مواد- شکل‌دادن فلزات، دانشگاه شیراز، شیراز، ایران.
)
رامین ابراهیمی
2
(
استاد، بخش مهندسی مواد، دانشگاه شیراز، شیراز، ایران.
)
کلید واژه: اثر اندازه, ریز شکل‌دهی, مدل تیلور, پلاستیسته‌ی کریستال,
چکیده مقاله :
در این مقاله، ابتدا با ترکیب مفاهیم پلاستیسته‌ی کریستال ارائه شده توسط تیلور و فرم ریاضی معیار تسلیم هیل برای توصیف ناهمسانگردی، مدل نوینی جهت توصیف پاسخ مکانیکی دانه‌ها در نمونه برحسب جهت‌گیری آن‌ها توسعه داده شد. مزیت این روش نسبت به دیگر روش‌های المان محدود پلاستیسته‌ی کریستال در آن است که در کدهای مرسوم پلاستیسیته‌ی کریستال، عموماً تمام سیستم‌های لغزش فعال در نظر گرفته می‌شوند که این فرض معتبر نیست، اما در این روش، تغییر شکل با 5 سیستم لغزش مدنظر قرار می‌گیرد. با به‌کارگیری این مدل که مدل ترکیبی هیل-تیلور نامیده شد، آزمون فشار نمونه‌هایی متشکل از تعداد دانه‌ی مختلف با جهت‌گیری تصادفی شبیه‌سازی شد و حالت کرنش هر دانه و شرط رفع اثر اندازه در هندسه‌ی نهایی نمونه، مورد بررسی قرار گرفت. نتایج این پژوهش حاکی از آن است که حالت کرنش هر دانه در ماده وابسته به جهت‌گیری آن، منحصر به فرد بوده و حالت کرنش با عبور از مرز دانه‌ها به‌صورت ناگهانی تغییر می‌کند. همچنین مشاهده شد که با افزایش تعداد دانه‌ها، هندسه‌ی نهایی به هندسه‌ی ایده‌آلی که در آزمون فشار مورد انتظار است نزدیک می‌شود. میل کردن هندسه نهایی به هندسه ایده‌آل، از نقطه‌نظر آماری مورد بررسی قرار گرفت و مشخص شد با افزایش تعداد دانه‌ها در یک سطح مقطع ثابت با وجود حفظ پراکندگی حالت کرنش دانه‌ها، میانگین حالت کرنش در مسیرهای شعاعی مختلف به سمت حالت کرنش ایده‌آل میل می‌کند.
In this paper, first the crystal plasticity notions developed by Taylor are combined with the mathematical form of Hill’s yield criterion for the anisotropic materials and a novel model is developed for description of mechanical response of grains in a specimen, based on their orientation. The advantage of the proposed model compared to other crystal plasticity finite element techniques is that in the conventional crystal plasticity codes, the deformation taken to be consisted of slip on all slip systems which is not valid assumption, yet here, the deformation taken to be consisted of slip on 5 slip systems. Using the proposed model which is called combined Hill-Taylor model, compression test of specimens with different number of grains are simulated and the state of strain in each grain and the condition for elimination of size effect in the final geometry of specimen is studied. The results suggest that the state of strain in each grain is individual and depends on the orientation of that gain which changes abruptly by passing through the grain boundaries. It is also observed that as the number of grains increases, the final geometry approaches to the expected ideal geometry. This trend is studied in statistical point of view and it became clear that as the number of grains increases the average of the state of strain approaches the ideal condition while the scatter in the state of strain in grains continue to maintain.
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