# Crack growth

With crack growth or crack propagation of the process or operation will be described in the material of a component in which to grow one or more cracks. The crack growth occurs through material separation (breakage) and leads to failure of the component when the corresponding crack lengths are reached. The temporal and spatial progression of the crack propagation is therefore of particular interest in assessing the service life of components. The analysis and prediction of crack growth is the task of fracture mechanics .

## species

A crack in the material can spread in different ways depending on the available energy.

• Piece-wise crack growth with constant energy supply is referred to as subcritical or stable crack propagation and occurs mainly due to material fatigue. The crack is a hairline crack for most of the component life at this stage .
• However, if there is enough energy available, the crack will spread at an enormous speed. This is called supercritical or unstable crack propagation .

## Measurement and modeling

Crack growth curve for a macro crack under cyclic loading (crack growth speed da / dN as a function of the amplitude of the stress intensity factor ΔK)

The acceleration of the crack from the rest position can be seen as proverbial, as can be seen in the schematic representation of a fatigue experiment.

In this diagram, the crack propagation speed is plotted against the amplitude of the stress intensity factor for a metallic material in a double-logarithmic manner. This curve is in the load stepping determined procedure by a CT specimen ( C ompact T ension, the standard sample in fracture mechanics) stepwise with specifically incorporated of crack of a loading just below the critical stress intensity charged each with lower amplitude and the crack propagation rate is measured . ${\ displaystyle \ Delta K _ {\ mathrm {c}}}$

Below a threshold value (threshold) or no spread can be measured to an existing, long crack. Above this value, the crack speed increases steadily and the curve ends in a range with an exponential relationship between the crack propagation speed and the load amplitude (range 2). This area 2 marked in the figure can be described with the help of the Paris law. With a further increase in the amplitude of the stress intensity, the crack accelerates further until it moves through the specimen with the available energy within one load cycle, i.e. it spreads supercritically at the speed of sound. ${\ displaystyle \ Delta K _ {\ mathrm {0}}}$${\ displaystyle \ Delta K _ {\ mathrm {th}}}$

## literature

• H. Gudehus, H. Zenner: Guide for a fatigue strength calculation . Verlag Stahleisen mbH, Düsseldorf 1995
• S. Suresh: Fatigue of Materials . Cambridge University Press, Cambridge 1998
• PC Paris, MP Gomez, WE Anderson: A Rational Analytic Theory of Fatigue . The Trend in Engineering Vo.13 No.1 (1961), pp. 9-14
• PC Paris, F. Erdogan: A Critical Analysis of Crack Propagation Laws . Transactions of the ASME, Journal of Basic Engineering, 85 (1963), pp. 528-534
• Fracture Mechanics and Fatigue: A Historical Perspective . Fatigue and Fracture of Engineering Materials and Structures 21 (1998), pp. 535-540
• ASTM Standard E 647-95, Standard test method for measurement of fatigue crack growth rates , Annual Book of ASTM Standards, vol. 03.01, pp. 578-614, 1995