A new CTOD calculation method considering the variation of crack tip blunting due to strain hardening has recently been developed. New calculation formula was proposed that was applicable to standard crack depth to width ratio conditions, a0/W=0.45-0.55 based on a number of 3-dimensional finite element outcomes, which were efficient in the parametric study for the establishment of a computational formula for crack tip opening displacement. The modification from the current formula would be the introduction of a coefficient ‘f’. This describes the blunting configuration established by the strain-hardening exponent.
In their recent report, the authors clarified deformation behavior for a wide range of crack depth to width ratio conditions. They obtained a number of important pieces, namely, clear rotational deformation in the ligament observed under all conditions, coordination of the rotational center as a function of crack depth to width ratio only, and the plastic exponent of the crack tip opening displacement computed by the plastic hinge relationship between plastic component of crack mouth opening displacement and rotational factor.
In the current study, Tomoya Kawabata and co-workers at The University of Tokyo modified and developed the calculation formula based on that knowledge to enable the application to an extended range of crack depth to width ratio conditions. They also investigated the possibility of simple application of the suggested formula to the BxB type specimen. They validated the finite element analysis for both Bx2B and BxB type specimen by silicone rubber replica approach. Their work is published in Engineering Fracture Mechanics.
A previous study analyzing the plastic deformation behavior over a wide range of crack depth to width ratio conditions indicated that there was a slight deviation from complete formation of a plastic hinge model in the computation of plastic component of crack tip opening displacement even when the blunting behavior was corrected implementing the strain hardening exponent. Under normal conditions i.e. a0/W =0.5, correction was not needed. The amount of deviation of a0/W of 0.3-0.7 could be linearly arranged with a0/W.
However, in the shallower zone of 0.1, the deviation was larger than the linear extrapolation from the other crack depth to width ratio conditions. This could be related to the unique characteristics observed under shallower conditions than 0.2. When a correction coefficient for this deviation was introduced in the formula covering various crack depth to width ratio conditions, the authors supposed that the coefficient could be separated into two terms.
This report reveals that the plastic hinge model can be implemented to crack depth to width ratio conditions other than the 0.45-0.55 range dictated by an observation of plastic deformation for wider crack depth to width ratio conditions. Coordination of the rotational center was steady irrespective of the load level and strain-hardening exponent.
Based on the knowledge of the plastic deformation behavior analyzed in the previous report, the authors were able to come up with a new crack tip opening displacement calculation formula covering a range of crack depth to width ratio conditions. They introduced a new coefficient optimized by B=25mm, Bx2B and several crack depth to width ratio conditions into the formula. This new formula has high accuracy with wide range of thickness and with the BxB type specimen without modification of the formula.
Tomoya Kawabata, Tetsuya Tagawa, Yoichi Kayamori, Mitsuru Ohata, Yoichi Yamashita, Masao Kinefuchi, Hitoshi Yoshinari, Shuji Aihara, Fumiyoshi Minami, Hiroshi Mimura, Yukito Hagihara. Applicability of new CTOD calculation formula to various a0/W conditions and BxB configuration. Engineering Fracture Mechanics, volume 179 (2017), pages 375–390.Go To Engineering Fracture Mechanics