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Fractal dimension is one of the parameters for characterizing the fracture surface of materials quantitatively, and is also the basis for analyzing the fracture mechanism of materials, so it is very important in mechanic of materials. In order to improve the efficiency of calculation on fractal dimension of fracture surface of materials by triangular prism surface area method (TPSAM), a program for TPSAM based on Matlab 7.1 was compiled and verified by using of two different samples. The results indicated that the program was easy to be read and operate, and the calculated fractal dimension of the samples was in a range from 2 to 3. Therefore, the program was accurate and could be used widely. 1.Introduction The mechanical properties of material are determined by its internal micro structure and experimental conditions, and the micro structure and the experimental conditions also affect the morphology of fracture surface of material. The researchers could study the relationship between the micro structure and the mechanical properties of the material by analyzing the characteristic of the fracture surface of the material. Therefore, how to characterize the morphology of the fracture surface of the material correctly and effectively was taken attention widely for a long time, and the researchers put forward many characteristic parameters. The parameters could be divided into three types. The first type is the qualitative characterization by the terms of the smoothness, flatness, coarseness, etc., thereby the fracture mechanism of material could be described as the brittleness, toughness and the combination with brittleness and toughness. The second type is statistic parameters including two dimensional parameters based on surface profile curve and the statistics and the three dimensional parameters based on the statistics [1]. The third type includes the roughness index including the roughness indexes of the profile curve of fracture surface and the ones of the fracture surface [2]. The parameters mentioned above had shortcomings of themselves. For example, the quantitative parameters can not evaluate the objective characteristics of the morphology of the fracture surface of the material, the number of the traditional statistic parameters and the roughness indexes of the fracture surface is too large and they are unstable [3]. The fractal theory was founded at the end of the 70s and early 80s in last century by Mandelbrot. The theory can be used to observe the fine structure hidden in the confused phenomena by using the similarity principle. So it is a new method for people to comprehend the world from the locality to the global. In 1984, Mandelbrot proposed firstly that the morphological characteristic of the fracture surface of the metal material could be described by the fractal theory [4]. With more than 30 years’ development, the fractal theory had been used to characterize the engineering surface, interface, and the the morphological characteristic of the fracture surface of the different material quantitatively [5~11], and at the same time, many methods used to measure the fractal dimension were proposed, which can be divided into two classes. The first one is indirect measurement method including the Secondary Electron Beam Scanning Method(SEBSM), the Vertical Section Method (VSM), and Silt Island Method (SIM), the second one is direct measurement method that includes the Pixel Covering Method (PCM) [12-13], The Projective Covering Method (PCM) [14] and Triangular Prism Surface Area Method (TPSAM) [15] etc..Among them, the TPSAM is earliest method and is widely used based on the grey image. Many researchers wrote the calculating procedures for the method to improve the calculating efficiency based on the C procedure language [16-17]. But, the International Conference on Automation, Mechanical Control and Computational Engineering (AMCCE 2015) © 2015. The authors Published by Atlantis Press 2242 source codes of the C procedure language is too long, always more than 300 procedure statements, and its operation efficiency is relative low [15].in this paper, the authors wrote the calculating procedures based on the Matlab 7.1 for shortening the procedure statements and improving the operation efficiency. 2.The basic principle of TPSAM The measuring principle was show in Figure 1(a) and Figure 1(b). The sign A and B in Fig. 1 represents the true fracture surface and projective network covering the true facture surface respectively. (a) (b) Fig.1 the TPSAM:(a) The projective network, (b) the projective grid If one chooses the grid abcd (a, b, c, d point is the vertex of the grid respectively) with size δ*δ to cover the facture surface at k time, and h(i,j+1),h(i+1,j+1),h(i+1,j) and h(i,j) are the height of the points a, b, c and d, respectively(as the Fig.1b shows). Four triangles S1, S2, S3, S4 are used to instead of the true coarse morphology of abcd. Then one can calculate the area Sij of the coarse surface enclosed by the projective grid of the abcd. If the number of the projective grids is N(δ) and to calculate the surface area of the zone δ*δ, one gets the total surface area[15] : ( )

Calculating the Fractal Dimension of the Material Fracture Surface Based on the Triangular Prism Surface Area Method