PSI - Issue 28

L.D. Jones et al. / Procedia Structural Integrity 28 (2020) 1856–1874 Author name / Structural Integrity Procedia 00 (2019) 000–000

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Weibull critical strain was modified according to the edge length (in material points) of the specimen, doubled to account for the two free surfaces of the model. In the second, the Weibull critical strain was modified according to the total number of material points in the model, as an analogue for the volume of the specimen. Examples of the models produced using these scaling methods can be seen in Fig. 2, and the distributions can be seen in Fig. 3.

Fig. 2 Failure maps based on using surface scaling (a) and volume scaling (b). Based on a 200 x 40 material point mesh, and an intended distribution of β = 6 and ε 0 = 8.3x10 -4 .

If it is assumed that fracture will occur at the surface (a reasonable assumption in many applications) the effect on fracture behaviour of the strength inside the bulk of the 2D model should ideally be negligible. This was achieved by applying the Weibull distribution only to the bonds at or near the surface and using a single value failure criterion for the remaining bulk. The value chosen for the bulk failure criterion was somewhat arbitrary. It is necessary that the bulk bond strength was high enough that fracture initiation does not occur in the bulk, but low enough that should failure occur in the Weibull region, the progress of a crack is not hindered by encountering too strong bonds in the bulk. The value chosen for this work was the strain equivalent to 99.9% probability of failure, based on the Weibull distribution for the entire part (i.e. not the distribution for the material points).

Fig. 3 The distributions used to generate bond strengths for surface and volume scaled bonds, relative to the intended distribution. Based on a 200 x 40 material point mesh, and an intended distribution of β = 6 and ε 0 = 8.3 x 10 -4 3. Peridynamics in Abaqus This work was completed in Abaqus, a commercial software designed for FE simulations, rather than a peridynamics-