Tham khảo tài liệu 'modeling and simulation for material selection and mechanical design part 10', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Figure 42 Continued Copyright 2004 by Marcel Dekker Inc. All Rights Reserved. The estimation of the rate of growth of such microcracks can be achieved mainly by two methods a the determination of the statistical distribution of the microcrack length and its variation with the creep time and b finite-element simulation of the creep behavior regarding the material as a composite consisting of grains separated by thin grain boundary layer with different properties. 1. Statistical Model The fundamental concept of the statistical model is that a small fraction of short cracks and a high fraction of long cracks are expected when the growth rate is high and vice versa 95-98 . In order to achieve reliable results using statistics a great number of cracks have to be classified. Over a period of several years about 50 000 cracks were classified in the steel X6 CrNi18-11 and more than 60 000 cracks in the steel X8CrNiMoNb16-16 for different temperatures and stresses. Based on the results of metallographic investigations the following assumptions are introduced a A crack grows quickly along the grain boundary from one triple point to the next where it rests for a longer time before it grows again to the next triple point b The crack length is always an integral multiple n of grain boundary facets and c every crack is initiated in the length class n 1 and grows step by step to next higher length classes. Let Z be the total number of cracks per unit area and Yn the number of cracks having a length n. In a time unit Vn n 1 cracks grow out of the length class n into the next higher length class n 1 . In the same time Vn - 1 n cracks grow from the lower length class n 1 into the considered class n. The mean rate of growth is given by dn dt Vnn 1 Yn and the rate of change of dYn dt Vn n 1 Vn-Ijn. As all cracks initiate with the length n 1 the rate V0 1 represents the rate of crack initiation and must be equal to rate dZ dt of the increase of the total crack number. Therefore .
