Self-affine fracture surface parameters and their relationship with microstructure in a cast aluminum alloy
- PDF / 709,656 Bytes
- 7 Pages / 612 x 792 pts (letter) Page_size
- 11 Downloads / 194 Views
le role of microstructural features in determining the self-affinity of the fracture surface of a cast aluminum alloy is explored in this work. Fracture surfaces generated both in tension and impact tests were topometrically analyzed by atomic force microscopy, scanning electron microscopy, and stylus profilometry. The roughness exponent exhibited the “universal” value ≈ 0.78, and the correlation length was of the order of the grain size. The brittle intermetallic compounds known to be important in crack initiation did not show any correlation with the self-affine parameters of the resulting fracture surfaces in this particular case.
I. INTRODUCTION
One of the first applications of fractal concepts in materials science was the seminal study of fracture surfaces of metals by Mandelbrot et al.1 Since then, the quest for useful relationships between “fractal” or self-affine parameters and macroscopical properties has resulted in a renewed understanding of the fracture process. However, no clear relationship appears to exist between mechanical properties and the self-affine parameters. The current scenario2,3 can be summarized as follows: fracture surfaces are natural fractals4 manifesting statistical invariance through an affine transformation: (x, y, z) → (bx, by, bz)
,
(1)
where z is the height and x and y are the coordinates associated to the plane perpendicular to z. The Hurst or roughness exponent quantifies the roughness of the surface and is related to the fractal dimension D through the relation D⳱3− .
(2)
A flat Euclidean surface will have D ⳱ 2 and ⳱ 1 while a rough surface will have < 1; the rougher the surface the smaller the value of . The Hurst exponent can be evaluated knowing that for a self-affine surface the typical height h(r) at point r ⳱ (x2 + y2)1/2 satisfies the following power law: ≅ r . h(r) ⳱ 〈[z(r0 + r) − z(r0)]2〉r1/2 0
(3)
Fracture surfaces are self-affine up to a characteristic length called the correlation length , beyond which the surface can be regarded as a flat Euclidean object. 1276
http://journals.cambridge.org
J. Mater. Res., Vol. 17, No. 6, Jun 2002 Downloaded: 02 Apr 2015
In the region of validity of Eq. (3), a self-affine surface can exhibit more than one roughness exponent. In the case of fracture surfaces, it appears that for threedimensional crack propagation two regimes govern the self-affine character of the resulting fracture surface. A now vast quantity of experimental evidence involving many materials, such as metals, ceramics, and polymers, indicates that two regimes exist.2 For rapid crack propagation it has been postulated that a somehow “universal” value of the roughness exponent ≈ 0.78 exists regardless of the material, microstructure, or load conditions.5 For slow crack propagation, such as that resulting from fatigue tests, and particularly when the analysis is performed at small enough length scales, the fracture surface roughness exponent appears to have another universal value of 0.5.6 This state of affairs unfortunately implies that
Data Loading...
