applied fracture mechanics

Foundations of Measurement Fractal Theory for the Fracture Mechanics 39scale transformation (self-similarity or self-affinity). This means that some facts concerningthe fracture have the same character independently of the magnification scale, i.e. thephenomenology that give rise to these structures is the same in different observation scales.The Euclidean scaling of physical quantities is a common occurrence in many physicaltheories, but when it comes to fractality appears the possibility to describe irregularstructures. The fracture for each type of material has a behavior that depends on theirphysical, chemical, structural, etc. properties. Looking at the topography and the differentstructures and geometrical patterns formed on the fracture surfaces of various materials, it isimpossible to find a single pattern that can describe all these surfaces (Figure 11), since thefractal behavior of the fracture depends on the type of material [52]. However, the fracturesurfaces obtained under the same mechanical testing conditions and for the same type ofmaterial, retains geometric aspects similar of its relief [53] (see Figure 12).This similarity demonstrates that exist similar conditions in the fracture process for the samematerial, although also exist statistically changinga from piece to piece, constructed of thesame material and under the same conditions [54; 55]. Based on this observation was bornthe idea to relate the surface roughness of the fracture with the mechanical properties ofmaterials [50].Figure 11. Various aspects of the fracture surface for different materials: (a) Metallic B2CT2 sample, (b)Polymeric, sample PU1.0, with details of the microvoids formation during stable crack propagation, (c)Ceramic [56].4.1.2. Fractal theory applied to description of the relief of a fracture surfaceLet us now identify the fractal aspects of fracture surfaces of materials in general, to beobtained an experimental basis for the fractal modeling of a generic fracture surface. Thedescription of irregular patterns and structures, is not a trivial task. Every description isrelated to the identification of facts, aspects and features that may be included in a class ofphenomena or structure previously established. Likewise, the mathematical description ofthe fracture surface must also have criteria for identifying the geometric aspects, in order toidentify the irregular patterns and structures which may be subject to classification. Thecriteria, used until recently were provided by the fractográfico study through statistical