PSI - Issue 2_B

M Muniz-Calvente et al. / Procedia Structural Integrity 2 (2016) 720–727 M.Muniz-Calvente/ Structural Integrity Procedia 00 (2016) 000 – 000

723

4

a

b

c

d

e

Figure 1. Representation of the experimental results obtained by Rathbun el al. (2006) for each sample

Homothetic samples, e.i samples with self-similar standard geometry, have equal constraint level because the (W a)/B ratio is constant, irrespective of the specimen size. Since the same crack ratio, is maintained throughout each specimen sample, a/W  0.5, this implies identical B/W ratio for the evaluation of those results. As a matter of fact, the same constraint conditions prevail by each of the samples so that the size effect can be analyzed unilaterally based only on statistical considerations. Accordingly, experimental results from the study of Rathbun el al. (2006) have been grouped in five distinct samples according to the constraint level acting on the specimens. Table 1 shows the number of test performed for each constraint level (B/W) and thickness. Fig 1 shows the experimental results evaluated. As can be seen, the mean fracture toughness increase inversely proportional to the thickness, as could be expected by the statistical size effect.  Normalized thickness (B/W) Thicknesses B [mm] 8 15.9 31.8 63.5 125 254 Total 1.25 8 8 8 7 - - 31 2.5 - 8 8 8 8 - 32 5 - - 8 7 8 6 29 10 - - - - 8 8 16 20 - - - - 8 8 16

Table 1. Overview of the test program by Rathbun el al. (2006) including the number of specimens tested by each sample.

3.2. Approach

The probability of failure associated to the test i is calculated using Eq. (2)



     i eq K

  

     



P

   1 exp

,

(2)

fail

i

where K eq is the equivalent stress intensity factor for the test i calculated according to the Equation: