Investigating the size effect in SENB specimens with a triaxiality and Lode angle based damage model

Investigating the size effect in SENB specimens with a triaxiality and Lode angle based damage model

Coppejans, Okko (TU Delft Civil Engineering & Geosciences; TU Delft Engineering Structures)

Sluys, Lambertus J. (mentor)
Kassapoglou, C. (graduation committee)
Popovich, V. (graduation committee)
Walters, C. L. (graduation committee)

Delft University of Technology

Civil Engineering | Structural Engineering | Structural Mechanics

2017-08-31

This master thesis is built up around two questions. First: Is it possible to calibrate a ductile failure model, where the strain at failure is a function of stress triaxiality and Lode angle, using only a single SENB specimen? The failure model that is referred to describes local failure in a finite element model to simulate ductile fracture. In this thesis, an orthotropic damage constitutive material model is constructed to accommodate the most realistic fictitious crack growth. Simple isotropic element erosion or deletion was found to have severe effects on the stress states of neighbouring elements due to a major loss of constraint. The damage model is based on the stress triaxiality and Lode angle, derived from the invariants of the stress tensor. For any combination of stress triaxiality and Lode angle, an equivalent plastic strain to failure is required in the form of a three-dimensional failure surface. Typically, multiple experiments with varying dominant stress states are needed to accurately calibrate such a failure surface or model. This research project shows that one can not only calibrate a failure surface from a single three-point bending specimen, but also obtains more calibration points than other approaches that are typically used for this purpose along the way. These calibration points are collected during a fully automated iterative procedure, where points are added every time the force in the simulation exceeds the force found in the experiment by more than 1%. As soon as enough calibration points with distinct stress states were found, the Hosford-Coulomb model was fitted using the least squares method. Finally, the obtained failure model was verified by using it to simulate the specimen on which it was calibrated. From these results, it can be concluded that it is possible to calibrate a failure model using only a single SENB specimen. In addition to this thesis, this procedure is outlined in a paper (Coppejans & Walters, 2017). The second part of the thesis revolves around whether a ductile failure model obtained from the procedure presented in this thesis can be successfully used to predict failure in different geometries. To verify this, the differences in stress states that occur in specimens with different dimensions and aspect ratios is researched both theoretically and numerically. From that study, it is found that indeed the geometry has an influence on the stress states that are present and where they are present. This influence is great enough that simple fracture mechanics approaches such as the J-Integral and CTOD are only transferable if strict requirements are met between SENB specimen from the same material but with different dimensions. Standards such as BS7448 and ASTM E1820 describe the validity of the experimentally obtained fracture toughness parameters with respect to the specimen size to deal with these requirements. Where the global approach (fracture mechanics) fails, the local approach (damage mechanics) finds a natural application due to its revolving around stress states. Application of the failure model obtained from the smallest specimen to the specimen with greater size and to the specimen with a different aspect ratio strengthens this claim. The failure model is able to predict the onset of element failure, used to simulate crack growth, within 2.5% deviation in experimental and simulated force at crack initiation. The force during crack propagation is simulated with 99% accuracy for crack mouth opening diameters (CMOD) at least twice and up to four times the CMOD due to plastic deformation. For greater amounts of CMOD, the reaction force is simulated with decreasing accuracy. The crack path on the free surface is verified by comparing the simulated crack path, visualised by removing all damaged elements from view, to a picture that was taken after the experiment. This reveals that while the extent of the crack is fairly accurately simulated, the width of the crack is both not accurately represented by simply removing all damaged elements from view, and the created damage model may require more development.

Continuum Damage Model
Fracture mechanics
Damage mechanics
SENB
Calibration
Crack growth
Ductile fracture
Steel
Plasticity
Lode angle
Stress triaxiality
orthotropic damage

http://resolver.tudelft.nl/uuid:db08aa87-eaa4-414f-8eca-5a2174356301

2017-08-31

Student theses

master thesis

© 2017 Okko Coppejans