PSI - Issue 8

L. Landi et al. / Procedia Structural Integrity 8 (2018) 3–13 L. Landi et al. / Structural Integrity Procedia 00 (2017) 000 – 000

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In order to locate a proper material modelling we need to define not only a constitutive equation but also a failure criterion. Hancock and Mackenzie (1976) demonstrate that ductile fracture is highly dependent on stress triaxiality ( ∗ ) . Johnson-Cook and equivalent plastic strain methods are widely used in other scientific publications. Johnson-Cook failure model is defined by: = ( 1 + 2 3 ∗ )(1 + 4 ln ̇ ∗ )(1 + 5 ∗ ) (5) As the constitutive model, Johnson-Cook failure criterion defines fracture strain using stress, strain rate hardening and temperature. Studies conducted by Bao and Wierzbicki (2004), and Teng (2005), have shown that the fracture cannot develop for stress triaxiality values lower or equal to -1/3. In order to consider this phenomenon, the Johnson-Crook model has been modified by Teng by inserting a threshold at fracture for σ ∗ = −1/3 . Figure 1 shows the comparison between Johnson-Cook and Teng failure models.

Fig. 1. Comparison between Johnson-Cook and Teng failure models, reprinted from Teng (2005).

In order to better represent this -1/3 fracture locus behaviour, the Johnson-Cook failure model has to be modified through new parameters D1-D5 to have a better approach to the physical limit: lim ∗→−1/3 = ∞ To achieve this result, the least square method was implemented, using the data arising from tensile tests and adding a point that creates an asymptote in correspondence of σ ∗ = −1/3 . Usually it can use ε f = 8 to have a realistic behaviour both positive and negative values of the fracture strain. We will refer to such failure criteria naming it Johnson-Cook Unipg (JCU). Another fracture criterion widely used in literature is the simple equivalent plastic strain failure. It defines the fracture with the simple the condition: = (6) For this criterion, fracture takes place when the equivalent strain reach a threshold level regardless whether the material is in a tension or compression condition. If this criterion is assumed, we state that there is no dependence of failure on ∗ . The equivalent element strain it is usually measured with formulation such as: