کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
7961443 1513930 2013 10 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Scaling function in conductivity of planar random checkerboards
ترجمه فارسی عنوان
تابع مقیاس بندی در هدایت الگوریتم های تصادفی مسطح
موضوعات مرتبط
مهندسی و علوم پایه سایر رشته های مهندسی مکانیک محاسباتی
چکیده انگلیسی
Under investigation is the finite-size scaling of the Fourier thermal conductivity in two-phase planar random checkerboard microstructures at 50% nominal volume fraction. Examples considered include Aluminum-Copper, Constantan-Lead, Stainless Steel-Gold, Inconel X-750-Aluminum, Titanium Dioxide-Gold, Carbon Steel-Diamond, Lead-Diamond, Boron-Diamond, Molybdenum-Test, Constantan-Diamond. Mesoscale bounds are obtained using an approach consistent with the Hill-Mandel homogenization condition. Extensive numerical simulations are conducted on 10 types of microstructures with the contrast (k) ranging from 1.54 to 100. The effects of mesoscale (δ) and phases' contrast are evaluated and generic scaling laws are established quantitatively. This is accomplished using a non-dimensional scaling function derived by contracting the mesoscale conductivity and resistivity tensors. The scaling function very closely fits all the material combinations and is given by g(δ,k)=12(k-1/k)2exp[-0.53(δ-1)0.69]. As a verification of our procedure, it is observed that, with increasing domain size, the mesoscale conductivity tends to the exact theoretical result for macroscopic conductivity of random checkerboards: being the geometric mean of two phases. By choosing an appropriate functional form of the scaling function, a material scaling diagram is constructed with which one can rapidly estimate the size of representative volume element for a given contrast within acceptable accuracy.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Computational Materials Science - Volume 79, November 2013, Pages 252-261
نویسندگان
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