Peridynamic Modeling of Granular Fracture in Polycrystalline Materials

Abstract

A new peridynamic formulation is developed for cubic polycrystalline materials. The new approach can be a good alternative to traditional techniques such as finite element method and boundary element method. The formulation is validated by considering a polycrystal subjected to tension loading condition and comparing the displacement field obtained from both peridynamics and finite element method. Both static and dynamic loading conditions for initially damaged and undamaged structures are considered and the results of plane stress and plane strain configurations are compared. Finally, the effect of grain boundary strength, grain size, fracture toughness and grain orientation on time-to-failure, crack speed, fracture behaviour and fracture morphology are investigated and the expected transgranular and intergranular failure modes are successfully captured. To the best of the authors' knowledge, this is the first time that a peridynamic material model for cubic crystals is given in detail.

Wave reflection and cut‐off frequencies in coupled FE‐peridynamic grids

“…where m = m FE + m PD , m FE , and m PD are the mass contributions from the FE and PD model, respectively, and F FE and F PD are the total forces applied from the FE and the PD model, respectively. Combining Equations (4), (11), (19), and (20), the final system of equations for coupling case 1 is derived. If the linearized formulation of PD is used in PD , it is possible to formulate the stiffness matrix of the PD bonds and write the bar response in the form MÜ + KU = 0.…”

“…Combining these time equations (4), (11), (24), and (25), the final system of equations for the second coupling case is formed. Again, using the linearized PD formulation, it is possible to construct the stiffness matrix of the system.…”

“…This terminology is also adopted here. Using such a coupling approach, it is envisaged to combine the computational efficiency of FE with the ability of PD to accommodate discontinuous fields and microstructural characteristics within the solution domain …”

“…Using such a coupling approach, it is envisaged to combine the computational efficiency of FE with the ability of PD to accommodate discontinuous fields and microstructural characteristics within the solution domain. 11 The advantages of coupling a computational efficient local theory with the capabilities that are offered in finer-scale descriptions (eg, molecular dynamics) have already been identified within multiscale applications. 12 One of the challenges in the coupling methodologies arises when dynamic problems are considered.…”

Modelling of Granular Fracture in Polycrystalline Materials Using Ordinary State-Based Peridynamics

“…Peridynamics has been used for the fracture analysis of many different types of materials and material behaviours [12,13,14,15,16,17,18,19]. It has also been applied for the analysis of polycrystalline materials [20,21,22]. However, these studies used either original bond-based formulation (BB) [11] or non-ordinary state-based (NOSB) [23] formulations.…”