PSI - Issue 28

B.W. Williams et al. / Procedia Structural Integrity 28 (2020) 1024–1038 Author name / Structural Integrity Procedia 00 (2019) 000–000

1030

7

D c is the critical damage at which to remove the element from the simulation and m is a material constant. The model has eight coefficients that need to be calibrated. Paredes et al. (2018) performed a number of mechanical tests on TC128 material removed from a section of a typical tank car which included tensile tests, tests on notched round bars, indentation tests, shear tests, tests on flat specimens with circular cut-outs, and biaxial specimens. The variety of mechanical test were required to produce a range of triaxiality and Lode angles for accurate model calibration. In additional to mechanical testing, several FEA simulations were carried out to calculate parameters such as stress triaxiality and Lode angle for the various specimen geometries. An optimization process was used to minimize the error between simulation and experiment during model calibration. The MMC-PW model coefficients for TC128 at room temperature and quasi-state strain-rate are given in Table 3.

Table 3: Quasi-static Damage Model Parameters for TC128 at Room Temperature [Paredes et al. (2018)]

� � ����� � � �

Strain Rate (s -1 )

A (MPa)

n

m

0.001

1105.7

0.20

0.165

620.5

0.969

1.0

1.8

0.1

3.3. Dynamic Ductile Fracture Model for TC128B: Multiple Temperatures The A and n coefficients in the MMC are given in Table 2 at 100 s -1 for each temperature. D 0 was always equal to unity. To determine the remaining five coefficients, C 1 , C 2 , C 3 , D c and m , at each temperature, several simulations were performed to obtain agreement with the load-displacement response from Charpy tests, as will be described in the next section. A goal was to keep the same trend of stress triaxiality and Lode angle of the room temperature MMC PW model. Although only Charpy simulations were used in the current effort, it would be expected that the model could be applied to other geometries to cover a wider range of loading conditions. The damage model detailed by Xue and Wierzbicki (2009), referred to as the XW model, was used by Simha et al. (2014) to predict crack propagation in the Drop-Weight-Tear-Test (DWTT) for X70 steel. This damage model has been shown to capture the transition from a flat, tunnelling crack undergoing ductile fracture to slanted shear fracture. The reason that the XW model was not adopted in the current work was that the MMC model coefficients were available for TC128 based on several mechanical test geometries. Simha et al. (2014) introduced a strain-rate dependency into the damage evolution law (Equation 3) according to � � � � � 1 � � ���� � � � � ⁄ � . This approach was not adopted in the current work but should be considered for strain-rate and temperature in the future to reduce the number of model coefficients. where m is the Weibull modulus and the normal stress,  1 , is integrated over a specified volume V 0 . The Weibull stress is often calculated for a 2D problem at a notch/crack tip as detailed by Lei et al. (1998). In the current work, the volume over which to calculate the Weibull stress for a 3-D problem was not certain. For instance, the plastic zone obtained in the 3D Charpy simulation is quite large and not limited to the vicinity of the crack. Consequently, a simple criterion was used in the current work based on the maximum principle stress of any element in the model. This is similar to the RKR criterion mentioned above. For the Charpy models, the maximum principle stress was always normal to the crack plane. Also, this criterion is dependant upon the element size on the crack plane (0.2 mm) such � � � 1 � � �� � � �⁄� (4) 3.4. Brittle Failure Criterion when Preceded by Ductile Fracture The Weibull stress is given by [Beremin (1983)],