| dc.description.abstract | Numerical models and simulations are valuable tools to aid engineers in the design of products and structures and can help reduce the number of costly and time-consuming experiments needed. The modelling of ductile material failure is sometimes vital in simulations of applications where large plastic deformation may occur due to unsought incidents such as mass impact, vehicle crash or high pressure loads from explosions. To develop accurate models for material damage and failure, understanding and quantitative description of the ductile damage processes occurring at the lower scale are necessary. Furthermore, these models must be extensively validated in different case studies to disclose their performance and limitations before they may be adopted in more practical applications by engineers. Numerical simulation may also aid the understanding of the fracture mechanisms observed in experiments. As such, this PhD thesis investigates ductile failure of aluminium through experimental campaigns and numerical simulations.
Part 1 of the thesis aims to disclose the effects small secondary voids growing between larger voids have on material plasticity and failure. The secondary voids are assumed nucleated on secondary particles, such as dispersoids, while the larger voids are assumed nucleated on the primary particles. To reach this objective, finite element-based unit cell simulations on the growth of a primary void are carried out where the material matrix response is described by a Gurson-type model with void size effects to account for the growth of smaller secondary voids. Material data from the aluminium alloy 6110 in temper T6 is used as a basis for the numerical models. The analyses demonstrate that smaller secondary voids only contribute to the strength and ductility of the material when their size is large compared to some intrinsic material length scale. They will not influence the initial growth of the primary void but promote strain softening of the unit cell by weakening the inter-void ligament material. By comparing the spacing between primary voids to pictures of the fracture surface from physical experiments, it becomes apparent that the contribution from dispersoids on ductile failure is probably only limited for this considered model material.
In Part 2 and Part 3 of the thesis, experimental campaigns are carried out on specimens extracted from 1.5 mm thick plates of the aluminium alloy 6016 in the three tempers T4 (naturally aged), T6 (artificially peak-aged), and T7 (artificially over-aged). The different heat treatments result in materials with different yield stress, work hardening, ductility and fracture mechanism, while micro-structural features such as size, shape and distribution of constituent particles and the shape and size of the grains remain unchanged. The campaign includes quasi-static tension tests on smooth and notched specimens, quasi-static tearing tests on single edge notch tension (SENT) and double edge notch tension (DENT) specimens, and dynamic low-velocity impact tests and quasi-static push-through tests on intact and pre-cracked plates. Two and three-dimensional digital image correlation is used to measure the displacements and strains during testing. The force is continuously monitored using load cells. Depending on the temper, the main fracture mechanism in the plate tearing tests changes from grain boundary failure for temper T6 to the coalescence of voids nucleated at the constituent particles for temper T7. The experiments demonstrate that material with a high ductility is preferred in applications where ductile tearing can occur as crack growth is more restrained. Since strength and ductility are generally mutually exclusive properties, one should carefully select the correct material based on the application. Another important observation is that the resistance force is significantly reduced in the quasi-static push-through tests on pre-cracked plates compared to the dynamic low-velocity impact tests, but only for plates in temper T6 and T7. By a numerical examination, there are clear indications that some rate dependence in the fracture resistance of the plate must be taken into consideration for these two tempers.
The experiments are complemented by numerical analyses where different approaches to predict ductile failure are investigated. In Part 2, the simple phenomenological Cockcroft-Latham fracture model is used to model material failure. The fracture model can accurately describe ductile tearing in the SENT test, to which the fracture model is calibrated. However, the Cockcroft-Latham fracture model can not accurately predict failure in applications where the material is exposed to entirely different loading conditions (i.e. the notch tension tests) as it only accounts for the stress triaxiality and Lode parameter in an implicit manner. Moreover, the Cockcroft-Latham model is less accurate in predicting the correct response for the dynamic problems in tempers T6 and T7, possibly due to the lack of representing material rate dependence.
The numerical investigation of ductile failure and tearing of thin plates continues in Part 3. Here, an enriched Gurson-Tvergaard-Needleman (GTN) model is used to describe the material response where the onset of accelerated void growth, and thus material failure, is initiated in-situ either by incipient material softening or by the occurrence of strain localization. It is found that the model where failure is initiated by strain localization performs well over a wide range of stress states. The approach where failure is initiated by material softening is less versatile as the occurrence of material softening does not portray strong dependence on the Lode parameter. Furthermore, it is found that strain localization takes place when a critical porosity is reached where the critical porosity depends solely on the current stress triaxiality and Lode parameter. While the failure strain depends on the path taken by the stress, the critical porosity appears to be path-independent. Consequently, a critical porosity surface can also be used as a substitute for in-situ strain localization analysis.
Part 4 takes on the problem of pathological mesh dependence observed in finite element simulation of strain-softening materials. The formulation and implementation of a gradient-based non-local GTN model for explicit finite element analysis are investigated for different plane strain problems. To include non-local effects, a non-local porosity is defined using an implicit gradient modelling approach. The simulations are based on material data and experimental observation from the previous parts of this thesis. The gradient-based GTN model is implemented in A!”#$%/Explicit by utilizing the coupled thermal-mechanical solver, which proves to be both a simple and computationally efficient approach. It is demonstrated by considering a uniform refinement of the mesh that the non-local GTN model can resolve the problem of pathological mesh dependence.
Moreover, the solution becomes independent of the mesh orientation. The non-local GTN model can also preserve the fracture mode (slant versus cup-cup fracture mode) observed in plane-strain tension specimens when the mesh is refined. In contrast, the fracture mode predicted by the original (local) GTN model depends on the mesh refinement. However, one should be aware that the non-local averaging can sometimes over-smooth the fields and exclude slant fracture from occurring if the intrinsic material length that determines the intensity of the averaging is too large. | en_US |
