PSI - Issue 13

Johannes Tlatlik et al. / Procedia Structural Integrity 13 (2018) 243–248 Johannes Tlatlik, Dieter Siegele / Structural Integrity Procedia 00 (2018) 000 – 000

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crack tip loading rate. Figure 2 a) shows the result of the fracture assessment of the original model (dotted lines) for selected dynamic testing conditions. It is apparent that the model is not able to adequately describe the fracture behavior for a wide range of dynamic testing conditions. Considering an increase in testing temperature at a constant crack tip loading rate of ̇ ≈ 10 5 MPa√m/s , the model shortcomings are rather small at -20 °C, and become significantly larger with a rise in testing temperature. Conclusively, conditions that lead to higher fracture toughness values result in a stronger discrepancy between experimental results and model prediction. This tendency, but also its magnitude, is very similar when compared to a macroscopic assessment by the Master Curve concept (i.e. Reichert and Tlatlik (2017a) or Reichert et al. (2017b)), despite considering adiabatic effects in the simulations.

Figure 2: a) Comparison of original model (dotted) and modified model (solid); b) illustration of initiation and failure probability P ini and P f

6. Model modification

In order to improve local cleavage fracture models for utilization under dynamic loading, a micromechanical modification is proposed to incorporate local crack arrest. According to Tlatlik (2017b) it can be assumed that the actual physical conditions for cleavage fracture initiation do not change at elevated loading rates. Moreover, the model discrepancies show a clear correlation with the observed local crack arrest. The basic concept of the proposed arrest term is a comparison of local crack energy γ crack ( σ I , Δ a ) of a potentially propagating crack, and the local matrix resistance γ mat ( T ). If local material resistance exceeds crack energy, then arrest will occur. While γ crack ( σ I , Δ a ) can be calculated from numerical data, the material resistance γ mat ( T ) is interpreted as an unknown material parameter which inherently conceives all microstructural properties relevant for local crack arrest. It is assumed to increase with temperature, and therefore varies within the cleavage fracture process zone due to the heterogeneous temperature distributions upon dynamic loading. The physical justification for the temperature dependency is found in the increased plastic deformation at the grain boundaries, as indicated by the red highlighted areas Figure 1 a). In terms of the modified model, global failure is not only determined by the individual local initiation probabilities for cleavage fracture any more, but now influenced by a deterministic arrest behavior. If local arrest is determined for a finite element at a specific time during loading, then it is no longer considered for the calculation of global failure. For reasons of simplification, local crack arrest condition is always verified for a crack length of Δ a = 0.031 µm (cleavage fracture island diameter of 0.062 µm), which represents the observed average crack propagation distance before local arrest. It is notable that during loading the local calculated values for σ I and T are considered. Details of the extended study are described in Tlatlik et al. (2018). The model parameters are once again adjusted in the described manner with the exception of the new additional parameter γ mat ( T ) which shows a progressive increase similar to the macroscopic arrest toughness curve. Due to the formulation of the modified model, cleavage initiation is now assumed at lower loads. The results of the modified model (solid lines) can be seen in Figure 2 a) compared to the original version. A much better agreement with the experimental results for different testing temperatures and crack tip loading rates is now obtained, and the over conservatism of the method is greatly reduced. Figure 2 b) shows the resulting probability for initiation P ini and global failure P f according to the modified model, and how global failure is postponed by the arrest condition. The impact of the arrest condition increases with