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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3. Local Cleavage Fracture Model

The calculation of fracture probability P f was performed with the model developed by Hohe et al. (2010). It describes the increase in fracture probability dP f for a finite element i due to the relation ( ) = ( , ℎ) ∙ ( ) ( ) (1) with a combined probability for defect nucleation f nucl and defect instability f inst , as well as the element volume dV . Defect instability is governed by maximum principal stress σ I leading to the expression ( ) = −( ) 2 − −( ℎ ) 2 (2) considering an exponential distribution for the brittle particles within the microstructure. Model parameters are σ u and σ th . Defect nucleation is described by the expression ( , ℎ) = 2 − 1 ℎ (3) with the accumulated plastic equivalent strain ε e pl , the local stress triaxiality coefficient h , as well as the relevant model parameters C 2 and c 1 . Using the weakest-link assumption, the probability of failure of the entire structure can be expressed as = 1 − − ∫ ( ) (4) 4. Fractographic Investigation of Local Crack Arrest Crack arrest is only rarely witnessed under quasi-static loading for this type of material, so in other words, a successfully initiated cleavage fracture will lead to the failure of the entire structure. Hence, it is neglected in local cleavage fracture models. Upon dynamic loading, however, it was observed in this study that the material can very well stop a cleavage crack after several micrometers of propagation, so global failure is postponed to higher crack tip loads. The previously arrested fresh crack tip is blunted and experiences ductile crack growth. These local crack arrest incidences, or cleavage fracture islands, are mostly found in the vicinity of the ductile crack growth, Figure 1 a).

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Figure 1: a) Typical example of a cleavage fracture island (red: pastic deformation at grain boundaries); b) cleavage fracture islands per individual specimen for selected testing conditions Figure 1 b) shows the amount of these cleavage fracture islands found on the fracture surface. Strikingly, even testing conditions at = −20 ° and ̇ ≈ 10 5 MPa√m/s (very brittle) can cause occasional local arrest incidents.