Fractal characterization of fractured surfaces

Pande, C. S.; Richards, L.E.; Louat, N.; Dempsey, B.D.; Schwoeble, A. J.

doi:10.1016/0001-6160(87)90110-6

Cited by 184 publications

(29 citation statements)

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“…The results noted above are consistent with the behavior of brittle materials reported by Mecholsky [25,34] (Figure 1), comparable with the study of Underwood and Banerji [36] who also report an increase in fractal dimension with increasing toughness (temper embrittled steel) and generally in harmony with the observations of Pande et al [28] in ductile titanium alloys who show a roughly decreasing fractal dimension with increasing dynamic tear energy (a measure of toughness).…”

Section: Previous Work In Fractal Dimension Measurement In Metalssupporting

confidence: 91%

“…Many researchers have long suspected a toughness-fracture topography relationship in metals [5,[26][27][28][29][30][31]. Mandelbrot, Passoja, et al [26] used impact toughness specimens of type 300-grade maraging steel and the perimeter-area version of the slit-island method.…”

Section: Previous Work In Fractal Dimension Measurement In Metalsmentioning

confidence: 99%

“…Most studies [28,32,33,35] with metals have explored the fractal qualities of fracture surfaces but have failed to offer mathematical relationships between these quantities or explanations for why this behavior exists.…”

Section: Suggested Modelmentioning

confidence: 99%

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Relationship between Fracture Toughness and Fracture Surface Fractal Dimension in AISI 4340 Steel

Carney¹,

Mecholsky²

2013

MSA

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This study analyzes the relationship between fracture toughness and the fracture surface fractal dimension for a set of twenty-four CT-type AISI 4340 steel specimens heat treated to a variety of tensile strengths. Specimens were tested in accordance with ASTM E 399. Their respective fracture surfaces were plated, polished, photographed under an SEM in BSE mode and measured according to the Richardson method to obtain fractal dimensions. For brittle materials the limited results are consistent with previous literature: increasing fractal dimension with increasing toughness. For partially or fully ductile materials the results indicate a decrease in fractal dimension with an increase in fracture toughness. The data are modeled using a variation of the function applied to ceramics. Fracture in a ductile mode is characterized by the formation of dimples which exhibit fractal characteristics. The results are discussed in terms of the micromechanisms of fracture.

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Section: Previous Work In Fractal Dimension Measurement In Metalssupporting

confidence: 91%

Section: Previous Work In Fractal Dimension Measurement In Metalsmentioning

confidence: 99%

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Relationship between Fracture Toughness and Fracture Surface Fractal Dimension in AISI 4340 Steel

Carney¹,

Mecholsky²

2013

MSA

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“…The experimental results show that a general conclusion cannot easily be drawn [9]: some studies report a positive variation of fracture toughness along with the fractal dimension [6,[10][11][12][13], and others a negative one [14][15][16][17]. To other researchers, there is either no correlation [18][19][20] or the fractal dimension of the fractured surfaces is a universal constant [21].…”

Section: Introductionmentioning

confidence: 98%

Statistical artefacts in the determination of the fractal dimension by the slit island method

Bigerelle

Iost

2004

Engineering Fracture Mechanics

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is an open access repository that collects the work of Arts et Métiers ParisTech researchers and makes it freely available over the web where possible. AbstractThis paper comments upon some statistical aspects of the slit island method which is widely used to calculate the fractal dimension of fractured surfaces or of materialsÕ features like grain geometry. If a noise is introduced when measuring areas and perimeters of the islands (experimental errors), it is shown that errors are made in the calculation of the fractal dimension and more than a false analytical relation between a physical process parameter and the fractal dimension can be found. Moreover, positive or negative correlation with the same physical process parameter can be obtained whether the regression is performed by plotting the variation of the noisy area versus the noisy perimeter of the considered islands or vice versa. Monte-Carlo simulations confirm the analytical relations obtained under statistical considerations.

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“…Por outro lado, as superfícies de uma fi ssura podem possuir certas características aproximadamente fractais (apenas). Esse entendimento decorre da inexistência clara de fractalidade na geração dessas superfícies (UNDERWOOD e BANERJI,1986;PANDE et al, 1987;LUNG e MU, 1988e HUANG et al, 1990apud CONSTANTIN e IORDACHE, 2012.…”

Section: Introductionunclassified

Características Fractais Dos Contornos De Bacias Hidrográficas E Dos Perímetros a Eles Associados: Uma Análise Inversa Relativa Às Implicações Dimensionais Sobre Os Descritores Morfométricos De Compacidade

Ferreira

Ferreira²

2015

Rev. Bras. Geomorfol.

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Resumo:Neste artigo, uma análise dos mecanismos de obtenção dos descritores morfométricos é inicialmente procedida. Posteriormente, considerações relativas às características fractais dos contornos das bacias e dos perímetros a eles associados, são levadas a efeito. Por incorporarem grandezas geométricas em suas defi nições, fi ca evidenciada a necessidade de uma reavaliação relativa, tanto à qualidade, como à efetividade dos descritores morfométricos, tendo em vista que os mesmos são habitualmente computados por meio de ferramentas da geometria euclidiana. Para tanto, a técnica denominada Técnica da Caminhada sobre o Contorno, é adotada para a determinação das dimensões fractais, Df, dos contornos das bacias hidrográfi cas. Subsequentemente, essa técnica é explorada de maneira a obterem-se as dimensões fractais dos contornos de treze bacias e seis sub-bacias hidrográfi cas de diferentes características. Finalmente, dentro de procedimentos de análise inversa, as informações assim obtidas são utilizadas com vistas à determinação de contornos regularizados para essas bacias hidrográfi cas e de valores dos perímetros a eles associados, objetivando a reavaliação dos descritores de compacidade. Ao fi nal, conclui-se que o modelo adotado conduz a reduções drásticas no número de pontos que constituem os novos contornos, com modifi cações insignifi cantes nas magnitudes das áreas ou descaracterizações das formas primitivas. Verifi caram-se, ainda, reduções signifi cativas nos Índices

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Fractal characterization of fractured surfaces

Cited by 184 publications

References 2 publications

Relationship between Fracture Toughness and Fracture Surface Fractal Dimension in AISI 4340 Steel

Relationship between Fracture Toughness and Fracture Surface Fractal Dimension in AISI 4340 Steel

Statistical artefacts in the determination of the fractal dimension by the slit island method

Características Fractais Dos Contornos De Bacias Hidrográficas E Dos Perímetros a Eles Associados: Uma Análise Inversa Relativa Às Implicações Dimensionais Sobre Os Descritores Morfométricos De Compacidade

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