Issue 11

D. Taylor, Frattura ed Integrità Strutturale, 11 (2009) 3-9; DOI: 10.3221/IGF-ESIS.11.01 6 most papers are confined to studies of tensile test specimens containing either circular holes or very sharp edge notches. The limited range of test specimens studied is, in my view, the source of some misconceptions about the use of the TCD. This contrasts with work in the parallel field of metal fatigue, where different types of notches have been investigated, especially with regard to the effects of notch root radius, along with different types of loading. D OES L VARY WITH NOTCH SIZE ? he large amount of data collected by Awerbuch and Madhukar allowed various correlations to be studied. One trend which emerged was that in some cases the value of L which best predicted the results tended to vary, increasing with the size of the hole or notch. These effects seemed quite significant, for example these workers show a case in which changing the length of a sharp notch from about 1mm to 20mm caused the best-fit value of L to approximately double in size. Further work was done by other researcher, to investigate this phenomenon, especially for the case of circular holes. As a result, two equations were developed which are now in common use. The first is that of Karlak [11], which relates L to the hole diameter ( a ) using a constant C 1 , as follows: L = C 1 a 1/2 (2) The second equation is that proposed by Pipes et al [12] w ho developed a more general relationship including another constant m: L = C 2 a m (3) This second equation covers a wide range of possible conditions: two interesting cases are m=0, for which L becomes a material constant and m=1 which leads to a situation in which the size of the hole has no effect on the fracture strength, since L scales in direct proportion to a . In the example mentioned above, from Awerbuch and Madhukar, the value of m was 0.235. In fact, even the original data in Whitney and Nuismer shows something of this effect: for example in Fig.2 prediction lines were drawn using different values of the critical distance and one can see that the data tend to move from the smallest to the largest value with increasing hole size. Investigating the data and the methods of analysis in some detail, I have come to the conclusion that there are four separate reasons for this effect, as follows. Stress Analysis Errors In calculating the stresses in the vicinity of the notch, for use in the Point Method or Line Method, Whitney and Nuismer used the following approximate method. They started from the equation for a notch in an infinite body: for example for a circular hole they used the well-known Airy equation for the stress  (r) as a function of distance r :                         4 2 2 3 2 1 1 )( r a a r a a r   (4) They then modified this equation to take account of the finite width of the plate, W, multiplying it by the following factor Y: ) 1(3 ) 1( 2 3 W a W a Y    (5) The same approach has been followed by many subsequent researchers in this field. Unfortunately, this approach is not precise, and leads to significant errors. Fig. 4 c ompares the stress/distance curve predicted by these equations to an accurate result obtained using finite element analysis, for the case of a hole with a /W = 0.375. The two curves begin to deviate significantly around r/ a = 1. Unfortunately, many test specimens use a /W values equal to or greater than this, and in many cases the relevant values of r are quite large, given that L typically takes a value of several millimetres in these materials. One can appreciate that this error will lead to a situation in which L appears to increase with notch size, because if notch size increases (at constant W) then the estimated stress at the point L/2 will deviate more and more from the actual stress, T