It is well known that the fracture toughness Jc in the ductile-to-brittle transition temperature region depends highly on the specimen thickness (hereafter, TST). The TST effect on Jc, which Wallin [1] described as Jc (∝ KJc2) ∝ B(-1/2) (Jc was calculated from the equations outlined in ASTM E1820 [2], KJc was derived from Jc as KJc = (Jc·E′)1/2; E′ = E/(1−ν2), B: TST), has been reproduced by Anderson et al. [3] based on the weakest link model. However, as Anderson et al. [3] themselves admit, Jc does not decrease indefinitely with B. On the other hand, Meshii et al. [4–6] tried to explain this TST effect on Jc as a mechanical issue. They obtained the same relationship, Jc ∝ B(-1/2) from the fracture toughness test for a non-standard CT and 3PB specimen (non-standard on the point that planar configuration was identical and thickness to width ratio B/W was varied from 0.25 to 0.5) and the stress intensity factor (SIF) corresponding to fracture load Pc denoted as Kc (Kc was calculated from the equations outlined in ASTM E399 [7]), was almost constant for TST. They also reproduced the experimental tendency by large strain FEA under the assumption based on their experimental observation that Kc was independent of TST. In addition, they expressed the TST effect on Jc by correlating Jc with the out-of-plane elastic T-stress T33.
We thought that if TST effect on Jc is a mechanical issue, the lower bound Jc for TST could be predicted by FEA under some assumption such as Kc = constant for TST, and the TST corresponding to the lower bound Jc could be predicted by T33. However, before proceeding to this prediction, we thought we have to understand the candidate assumption for prediction more deeply, i.e, understand why Kc was constant for TST.
Thus in this work, we attempted to explain the reason why Kc was constant for TST. Our idea was to apply the well-known “planar” failure criterion to our out-of-plane TST issue. After demonstrating our idea was valid, the lower bound Jc of carbon S55C for non-standard 3PB specimen was predicted based on this planar failure criterion and the large strain elastic-plastic FEA. The results showed that Jc showed a lower bound for specimen of B/W ≥ 1.5. In addition, it was shown that this threshold B/W could be estimated by the elastic out-of-plane T33.
A failure criterion to explain the test specimen thickness effect on fracture toughness in the transition temperature region
