PSI - Issue 2_B

S. Knitel et al. / Procedia Structural Integrity 2 (2016) 1684–1691 Author name / Structural Integrity Procedia 00 (2016) 000–000

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where r is the radial distance from the crack tip and  is the angle between the crack plane and the node. The above relations hold for plastic regions R p limited to a small fraction of the circular model radius R, typical R p < R/20. The SSY-mesh was employed to investigate the loading rate effect on the structure of near crack tip at much lower computational cost than the full 3D C(T) model. For Abaqus, the strain rate dependence of the flow stress was introduced by providing the flow stress – plastic strain data in tabular form per strain rate in an increasing manner. Tensile tests were conducted at nominal strain rates of 2.7 x 10 -5 , 2.7 x 10 -4 2.7 x 10 -3 s -1 on standard round shaped specimen with a 5 mm diameter and a 30 mm straight segment at -196 °C, -150 °C, -100 °C and -50 °C. Abaqus then interpolates the flow properties at the different strain rates from this table. Results of the FE simulations were post processed to obtain a so-called stressed volume V(  I ) representing the volume within which the maximum principal stress is greater than  I . To do so, a FORTRAN routine was written that checks if the maximum principal stress of every node of an element exceeds  I . The sum of the nodes that exceed the critical stress is divided by the total number of nodes of the element and used to weight the elemental volume. Finally the volume is calculated by summing up the weighted volume per element for the whole model. 4. Finite element simulation results and discussion The 3D FE simulation results of compact tension specimens are focused on the stress/strain fields at the crack tip, which exist at fracture on the lower shelf and lower part of the ductile to brittle transition region. The fracture toughness of Eurofer97 behavior in the transition region was characterized with a total of 186 data points obtained with pre-cracked (a/W  0.5) compact tension specimens of three different sizes, namely 0.18T, 0.36T and 0.88T, by Mueller et al. (2009). The analysis of this database revealed that the shape of the median fracture toughness temperature curve in the transition deviates somewhat from the ASTM-E1921 master-curve, which describes the fracture behavior of 1T-thick specimens of "ferritic" steels in the transition. The shape adjustment that needed to be done for Eurofer97 steel was essentially an adjustment of the athermal coefficient A in the master-curve (Eq. 4).       1 0 100 0 019 med , T K A A exp . T T     (4) While A= 30 MPam 1/2 is recommended in the ASTM-E1921 master-curve standard, the best description of the fracture toughness of Eurofer97 was obtained with a value of A equal to 12 MPam 1/2 . This clearly represents a significant decrease of the fracture toughness in the lower shelf. In order to gain insight into the critical condition of the stress/strain fields at fracture initiation on the lower shelf and lower transition, it is necessary to use a very fine mesh at the crack tip, and to use a very small initial root radius representative of the actual root radius at the end of the pre-cracking process. In steels, the fatigue crack tip has typically an initial opening  0 of the order of 0.1  m. Thus, a 3D mesh was developed with an initial root radius  0 to specimen width ratio  0 /W equal to 0.1/9000. Again, this mesh in real units corresponds to 0.18T C(T) specimen. With such  0 /W, it was found that the crack tip opening displacement  at failure of an 0.18T C(T) specimen even at -196 °C was such that  /  0 > 3. When  /  0 > 3, McMeeking et al. (1977) showed that the stress field calculated by FE corresponds to the self-similarity solution, or in other words that the calculated stress fields are independent of  0 . Only at T = -50 °C, the mesh with  0 = 1  m was used because the crack tip opening at failure is large enough to reach the condition  /  0 > 3. In Fig. 2, the fracture toughness data versus temperature are plotted along with the so-called lower bound determined for the 0.18T C(T) specimen size and defined as the 1% cumulative failure probability. We note that the 0.18T C(T) lower bound was calculated from that of the 1T C(T) specimen derived from the equation (26) of the ASTM E1921-15 standard, and additionally crack front length adjusted according the equation (17) of the standard. The orange stars highlighted in Fig. 2 on the lower bound curve indicate the fracture toughness values at which the stress/strain fields were analyzed and reported below.