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Quantitative fractography

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Abstract

In many disciplines, such as biology, botany, geology, materials science and medicine, quantitative image analysis is being used to an increasing extent. In materials science this technique makes it possible to relate the microsctructure to the mechanical properties. In this review we shall show that image analysis can be applied in a fractographic study to characterize quantitatively the morphology of fracture. Such an analysis provides information which, together with that obtained by mechanical tests, enables an explanation of the mechanism of rupture to be made.

The different problems encountered in quantitative fractography — analysis of fracture paths or of fractured surfaces — are presented, and the concept of mean plane of fracture is introduced. Whatever the type of analysis used, a small number of parameters exist which can be used to determine the size and proportion present of the different fracture morphologies. Then the stereometric relationships, first established for plane sections, are modified as a function of the morphology of the fracture surface. Methods based on the notion of linear roughness and on fractal object allow a quantitative description of the morphology of the fracture paths. A criticism is also made of the different types of analysis — manual, semi-automatic and automatic — used in quantitative fractography. Finally, some examples are given to show what kinds of investigations are possible using quantitative fractography.

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Abbreviations

A :

area (plane)

A′:

projected area

D(i):

diameter of equivalent sphere of classi

d(i):

diameter of equivalent circle of classi

H :

distance between two planes, tangent to a given object

L :

length

L′:

projected length

L 2 :

mean chord in space R2

L 3 :

mean chord in space R3

L P :

perimeter

k :

curvature

a :

major axis of ellipsoid of revolution

b :

small axis of ellipsoid of revolution

ε :

eccentricity of ellipsoid of revolution

t :

thickness of the thin film analysed

P P :

fraction of points

P′P :

fraction of projected points

V V :

volume fraction

N V :

number of objects per unit volume

L V :

length per unit volume

S V :

(curved) surface per unit volume

P A :

number of points per unit area

N A :

number of objects per unit area

N′A :

number of projected object per unit area

A A :

areal fraction

A′A :

fraction of projected surface

L A :

length per unit area

L′A :

projected length per unit area

N L :

number of objects per unit length

N′L :

number of objects per unit projected length

L L :

fraction of length

L′L :

fraction of projected length

L S :

length per unit of curved surface

N S :

number of objects per unit curved surface

S S :

fraction of curved surface

K :

fraction of fracture nominally flat

E :

thickness of plastic zone

R L :

linear roughness index, according to Pickens and Gurland

P S :

waveiness or linear index, according to Chermant, Coster and Osterstock

Δ:

discrepancy parameter at rupture

ρ :

ratio of value measured on fracture surface to those measured on a polished surface

D c :

critical diameter

L (j) :

Saltykov coefficient

X :

geometrical set to be analysed

x :

position of the structuring element

h :

measurement step size

r :

size of the structuring element

h′:

projection of step of sizeh

B :

structuring element

γ(h):

variogram function

E :

mathematical probability

D :

fractal dimension

σ rf :

rupture stress in bending

\(\bar L_{Co}\) :

mean free path in the cobalt phase

\(\bar D_{WC}\) :

mean diameter of tungsten carbide crystals

K IC :

critical stress intensity factor

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Authors and Affiliations

  1. Laboratoire de Cristallographie et Chimie du Solide, L. A. No. 251, Equipe Matériaux-Microstructure, ISMRA-Université de Caen, 14032, Caen Cedex, France

    J. L. Chermant & M. Coster

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  1. J. L. Chermant
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  2. M. Coster
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Chermant, J.L., Coster, M. Quantitative fractography. J Mater Sci 14, 509–534 (1979). https://doi.org/10.1007/BF00772710

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