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Modelling of environmentally assisted material degradation in the crack phase-field framework
(2019)
The simulation of crack propagation was conducted with a diffusive crack model in a variational framework. Moreover, the physically sound introduction of mass transport and coupling mechanisms due to environmentally assisted effects could be realised in this framework. The objective consists of the application of the phase-field Approach towards the simulation of environmentally assisted material degradation with the advantage of a non-required predefined crack path and a mesh-independent non-local formulation that facilitates the damage evolution with respect to material softening. The sharp crack is regularised by the introduction of a phase-field order parameter leading to a diffusive crack formulation.
Besides the equations originating from the linear momentum balance an additional evolution equation for the crack phase-field is introduced. Furthermore, mass transport is simulated by a Diffusion equation. The description delivered by the variational phase-field framework is able to simulate crack propagation according to published numerical test cases.
Additionally, the calculation of stress intensity factors is possible as well as crack resistance curves that describe stable crack propagation.
This study addressed a 7017 Al-alloy tailored for powder bed fusion – laser beam (PBF-LB) process. The alloy was prepared by mixing 3 wt% Zr and 0.5 wt% TiC powder to standard pre-alloyed 7017 grade aluminium powder. This made printing of the alloys possible avoiding solidification cracking in the bulk and achieving high relative density (99.8 %). Such advanced alloys have significantly higher Young’s modulus (>80 GPa) than conventional Al-alloys (70–75 GPa), thus making them attractive for applications requiring high stiffness. The resulting microstructure in as-printed condition was rich in particles originating from admixed powders and primary precipitates/inclusions originating from the PBF-LB process. After performing a T6-like heat treatment designed for the PBF-LB process, the microstructure changed: Zr-nanoparticles and Fe- or Mg/Zn- containing precipitates formed thus providing 75 % increase in yield strength (from 254 MPa to 444 MPa) at the cost of decreasing ductility (∼20 % to ∼9 %). In-situ tensile testing combined with SXCT, and ex-situ tensile testing combined with fracture analysis confirmed that the fracture initiation in both conditions is highly dependent on defects originated during printing. However, cracks are deflected from decohesion around Zr-containing inclusions/precipitates embedded in the Al-matrix. This deflection is seen to improve the ductility of the material.
The present paper provides a discussion on all these topics and it offers solutions for it. The authors present an analytical solution of a Delta J based crack driving force based on an R6 type approach but modified for cyclic loading. The gradual build-up of the crack closure effect is modelled by the so-called cyclic R curve which describes the crack size dependency of the fatigue crack propagation threshold in the short crack regime. It is explained how the cyclic R curve is experimentally determined and how it can be estimated by a modified Kitagawa-Takahashi approach.