Crack Stress Concentration Factor

Good day,

There are some good references in Roarks (Sec. 17). However, I'm not a real an expert in this but there are somethings i'd like to discuss further.

1. Can a fine V-notch in plane plating be considered are crack tip?
2. Stress is a function of force and area. Then how could SCF be different for different materials. I know its in the range of 2.5 to

1. YouGoFirst, what is causing the crack? Is it a shearing or bending crack?

Open for discussion! Thanks.

- Yugabalan Koothayan

Thanks for replying. So far I have found that the stress concentration factor for a crack is typically a large value. The problem is that I don't know what good value to use is.

The crack that I am analyzing is caused by fatigue.

Hello again,

Fatigue induced cracks are typically caused by cyclic loadings. Now these cycles of load can be unique (could be in tension, bending or even shearing). Typically, tension based fatigue cracks occur in the perpendicular direction of the max principal stress direction (most likeliest location). So I'm not really sure what's causing your crack, although you've said its fatigue.

I have another suggestion for you. You can determine your SCF using simplified FE analysis. Input the relavent material model and include the crack in your model. The stress peak will be highest at the valley of the crack (based on your load). If you make a ratio of peak stress to nominal stress, thats the SCF. However, this could be complicated as its uncertain how the 'crack' is going to look like. If you have similar crack patterns from your previous project, then you may use some engineering judgement to validate the new crack.

Hope this helps!!

Yugabalan Koothayan

At the tip of a 'mathematically' sharp crack, the stresses are theoretically unbounded (infinite). This singular behaviour of the stresses and strains is described by the "stress intensity factor", K. This can be calculated and there are handbooks of 'K solutions' (e.g. the handbook edited by Y. Murakami).

The units of SIF are stress times square root of distance: typically MPa root(metre).

For example, the SIF of a straight through crack in a very large plate is given by

K = Y sigma root(pi a)

where 'Y' is a geometrical parameter, equal to 1 for a through crack in a very large plate, 'sigma' is the uniform nominal stress acting across the plane of the crack (i.e. the uncracked stress), 'a' is half the crack length. Simplistically the handbooks give you the values of 'Y' for different cracked geometries.

The resistance of the material is the "fracture toughness", KIc.

Simplistically, the crack grows when the applied SIF exceeds the material toughness:

K > K1c

Values of fracture toughness depend on the material, processing temperature, etc. The *initiation* fracture toughness of a typical Al 2024-T351 is about 30 MPa root(m). I don't know about your cast material.

There are test standards for measuring fracture toughness, e.g. BS 7448 and ASTM E1820-05.

A fatigue-sharpened crack in a structure must be treated in this way (fracture mechanics) and is not amenable to conventional analysis using scfs.

I hope this helps to send you in the right direction.

You are looking for a Stress Intensity factor. This factor does not depend on the material. The material's response (crack growth) does however.

Try looking in a Fracture Mechanics book. Or try some internet searches for crack growth software/information.