Investigation of size effects and heterogeneity in ductile failure

Vishal Vishwakarma

Research output: Book/ReportPh.D. thesis

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The research work reported here seeks to investigate the influence of void size-effect and heterogeneity in metallic alloys on ductile failure using the finite element method. The void size-effect owing to strain gradient strengthening is accounted for by utilizing the so-called gradient enriched Gurson-Tvergaard-Needleman (GTN) model, proposed by Niordson and Tvergaard (2019) and calibrated by Holte et al. (2019a). The model enriches the conventional Gurson model with a dissipative material length parameter dependent on the inter-void distance in the material. The current study aims to quantify the effect of gradient strengthening at different material length scales.

Firstly, the investigations are made at the micron-voids scale, where the material microstructure’s effective response is approximated using a periodic unit cell. Here, the focus is directed on the influence of secondary voids that co-exists with primary voids during the process of ductile failure. The unit cell comprises a discrete primary void surrounded by the matrix material with homogenized secondary voids, modeled by the gradient-enriched GTN model. The unit cell is subjected to a wide spectrum of stress triaxiality and Lode parameters. The results show that the presence of secondary voids accelerates the growth and coalescence of the primary void, thereby deteriorating the macroscopic ductility. This acceleration effect of secondary voids is drastically reduced in the presence of strain gradient strengthening. In fact, introducing sufficient gradient strengthening nullifies the effect of secondary voids.

The study is taken to the next level by investigating the effect of micron-scale strain gradient strengthening on the ductile tearing process in an engineering scale plate. A thin plate with a blunt pre-crack is subjected to mode I loading, and the material is defined by the gradient-enriched GTN model. The study aims to establish the void size effect on the crack initiation and transition from initiation to steady-state crack propagation by employing a full three-dimensional finite element model. The cohesive traction-separation law and the cohesive energy dissipated in the tearing process are revealed for different material length parameters incorporated into the constitutive law. It is shown that the gradient strengthening has a negligible effect on the onset of plate thinning ahead of the crack tip but delays the onset of shear localization, thereby increasing the total cohesive energy dissipation.

Finally, the study examines the heterogeneous second phase particles in metallic alloys to numerically investigate their effect on plate tearing at the engineering scale. The deformation sequences ahead of the crack tip are approximated using a 2D plane strain model. The particles are discretely modeled and randomly distributed in the plate. A novel micromechanics-based void nucleation model, capable of capturing the mechanisms of particle fracture and decohesion, is proposed by furnishing each particle with special attributes. It is shown that the proposed model accurately predicts the accepted trend of low-strength high ductility and high-strength low ductility response in a ductile plate.
Original languageEnglish
Place of PublicationKgs. Lyngby
PublisherTechnical University of Denmark
Number of pages112
ISBN (Electronic)978-87-7475-704-7
Publication statusPublished - 2022
SeriesDCAMM Special Report


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