Description of loadings and screenings of cracks with the aid of universal weight functions

✍ Scribed by H. O. K. Kirchner

• Publisher: Springer Netherlands
• Year: 1986
• Tongue: English
• Weight: 520 KB
• Volume: 31
• Category: Article
• ISSN: 1573-2673
• DOI: 10.1007/bf00018926

✦ Synopsis

The stress intensity vector K i is defined as the limiting behaviour of the stress near the tip of a crack, the stress components being proportional to r-1/2 for any external loading. Internal stresses caused by dislocations show the same power dependence at the crack tip; the stress intensity associated with a loading can thus be screened (or amplified) by a plastic zone. Since for any particular specimen and crack geometry the stress intensity vector must be a functional of the loading and screening which are of vectorial character (lines of forces fi or dislocations with a Burgers vector bi) one can define two tensorial weight functions, one for screenings, Dsi(x, a), and one for forces, F~i(x, a), so that the stress intensity K s can be found by integration over the product of weight functions and dislocation or force density. In order to find the weight functions the displacement field and the Airy stress vector must be known for some, completely arbitrary, loading or screening.