A nonlocal method for modeling interfaces: Numerical simulation of decohesion and sliding at grain boundaries

摘要

Understanding and modeling the interface behavior is an important task for predicting materials response in various applications. To formulate the behavior of an arbitrary interface, one needs to construct the relation between acting tractions and displacement jumps at the interface. In addition to capturing the correct physics of the interface, the so-called traction-separation relation must also be thermodynamically consistent and satisfy the basic balance laws. Apart from many attempts in the literature to address these issues, a new and simple method to capture the complex mechanical behavior at an arbitrary interface is proposed. The new formulation is based on introducing a new quantity called "traction density". As a result, the traction-separation relation for any arbitrary interface is automatically computed by integrating the traction density over the interface. The traction density can be formulated based on understandings and observations from lower scales. As will be shown, the mathematical representation of the traction density is relatively simple and therefore its consistency can be verified easily. When it comes to the grain boundary (GB) behavior, the proposed methodology is able to represent not only intergranular fracture but also grain boundary sliding. For calibration and verification of the model, molecular dynamics (MD) simulations for aluminum Sigma 5 GB are utilized. Interestingly, the calculations from current MD simulations show size-dependent behavior for the GB. By introducing a healing parameter in the new interface model, it is now possible to explain and predict possible GB size-dependent behavior. (C) 2020 Elsevier B.V. All rights reserved.