Numerical investigation of phase-field models for fracture on the micro- and nanoscale

• Numerische Untersuchung von Phasenfeld-Modellen für Bruchmechanik auf der Mikro- und Nanoskala

Jansen, Carlos; Markert, Bernd (Thesis advisor); Kurfess, Thomas (Thesis advisor); Barrales Mora, Luis Antonio (Thesis advisor)

Aachen : Rheinisch-Westfälische Technische Hochschule Aachen (2020, 2021)
Book, Dissertation / PhD Thesis

In: Report. IAM, Institute of General Mechanics 07
Page(s)/Article-Nr.: 1 Online-Ressource : Illustrationen, Diagramme

Dissertation, Rheinisch-Westfälische Technische Hochschule Aachen, 2020

Abstract

The presented work combines the widely spread theory of phase-field modelling and more physically-rigorous and state-of-the-art simulation techniques in order to help establish a bridge between the nano- and mesoscales, towards the modelling of fracture of solids. In this way, this work looks after contributing to describe this phenomenon under a holistic perspective. Accordingly, different examples on how to complement and couple phase-field models for ductile and brittle fracture with molecular dynamics and crystal plasticity are presented. On the one hand, a careful coupling of crystal plasticity theories is implemented into a modified phase-field model for brittle fracture. Hereby, a novel method to account for plastic damage and ductile fracture, under a hybrid phase-field-crystal-plasticity framework is proposed. On the other hand, the estimation of several parameters on the nanoscale, by means of molecular dynamics is conducted and then sequentially scaled into the phase field continuum-framework. This confirms the versatility of the phase-fields to describe any kind of phase-transition problem, despite the length scale, and the possibility of using all-atom simulations in order to estimate crucial parameters, that so far are only estimated either experimentally or obtained through curve-fitting procedures. To this end, initial boundary value problems are mathematically modelled and numerically simulated by means of the Finite Element Method, considering quasi-static conditions and small-strains. The standard tensile tests on different homogeneous, pre-cracked materials are performed to validate both, the brittle fracture and ductile fracture phase-field models. Moreover, an extension to 3D of the brittle fracture model is also presented. Further validations under consideration of fracture under shear (mode II) loads and the application of the model to a bio-inspired, two-phase material are delivered as well. Consequently, the outcome of this work does not only propose a way to ease a physical enrichment of phase-field models for crack propagation and growth, but in the outlook it proposes a way to ease the theoretical intertwining between damage and fracture characteristics at the nano-, the micro- and the mesoscale.