Browsing by Author "Samal, Mahendra Kumar"

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Nonlocal damage models for structural integrity analysis
(2007) Samal, Mahendra Kumar; Roos, Eberhard (Prof. Dr.-Ing.)
The reliable safety assessment of steel components such as pressure vessels, pipe bends and shell-nozzle junctions etc. is of prime interest for the safe operation of plants. It is essential that the assessment be done in a realistic and not too conservative way in order not to impair the economic efficiency too much. In this context fracture mechanics plays an important role because the load bearing capacity of the components under given loading conditions can be assessed. However, the fracture mechanics parameters, determined from laboratory scale experiments are not directly transferable to components and hence additional considerations (like constraint effects etc.) need to be taken care of. Continuum damage mechanics is able to consider these effects inherently by incorporating the features of micro-structural damage evolution into the material models (also called local damage models). These types of models have been highly successful in simulating fracture resistance behaviour of specimens and components of varying geometries, loading and boundary conditions with the same set of material parameters and hence the question of transferability of parameters does not arise. This way, these parameters are truly micro-mechanical properties of the material. However, numerical analyses of ductile fracture process (for strain hardening metallic materials) based on local damage models are often found to depend on the mesh size used. Damage tends to localise in only one element layer. As a consequence, increasingly finer discretisation grids can lead to earlier crack initiation and faster crack growth. The reason behind this non-physical behaviour is the loss of ellipticity (non-uniqueness of the solution) of the set of partial differential equations, especially when the softening due to damage dominates over the plastic hardening. Discontinuities may then arise in the displacement solution, which results in a singular damage rate field. Displacement discontinuities and damage rate singularities can be avoided by adding a nonlocal damage term into the constitutive equation of the material model, which carries the material length scale information. With this enhanced continuum description, smooth damage fields are achieved, in which the localisation of damage is limited to a given length (i.e., characteristics length of the material). In this work, the Rousselier's damage model has been extended to its nonlocal form using nonlocal damage parameter as an additional degree of freedom in the finite element model. The evolution of nodal damage of a particular node is related to the nodal damage and the local ductile void volume fraction of the neighbouring nodes with the help of a diffusion type equation. This diffusion equation is coupled with the standard stress equilibrium equation of continuum mechanics. The model has been applied to simulate the load-displacement response and fracture resistance behaviour of different types of specimens in 2-D and 3-D domain made of the pressure vessel steel 22NiMoCr3-7. In the first part of this work, the deformation and failure behaviour of different types of specimens, such as, notched round tensile specimens, flat tensile specimens (with hole at the specimen center) of different sizes, standard 1T compact tension (CT) and single edge notched bend (SEB) specimens are simulated. The results obtained from the newly developed nonlocal model have been compared with those of the local model and the experiments (carried out at MPA Universität Stuttgart, Germany). In addition, the size and geometry effects have also predicted by the nonlocal model and the results have been compared with those of the experiments. All numerical results obtained with the nonlocal damage model developed in this work are in good agreement with the experimental results. A further key aspect of this work is prediction of the fracture resistance curve in the whole transition regime. Effects like purely cleavage fracture at the low end of the regime and ductile crack growth prior to cleavage fracture in the transition temperature region must be taken into account in order to simulate the fracture toughness transition curve accurately. In order to simulate the experimentally observed behaviour, numerous calculations in the temperature range from -120 deg. C to -20 deg. C have been carried out for specimens with different thickness values and different crack depths. At low temperatures, the stress gradient at the crack tip becomes high and hence a very fine mesh is required to simulate it accurately. However, in order to simulate the preceding stable crack (often very small in size) before cleavage fracture, the mesh independent form of the Rousselier’s damage model is necessary. For the simulation of fracture resistance behaviour of the different types of fracture mechanics specimens in the transition temperature region, the nonlocal mesh independent damage model developed in this work has been coupled with Beremin's model Calculations have been done using - Beremin's model along with elasto-plastic material model (in which prediction of stable crack growth is not possible) and - Beremin's model along with nonlocal Rousselier's model (in which prediction of stable crack growth is possible), assuming constant and temperature independent values for the Weibull parameters (two-parameter Weibull theory). It was observed that the model without damage is unable to predict the scatter in the fracture behaviour (observed experimentally) especially towards the higher temperature end of the transition region, whereas the combined model with nonlocal damage has been able to predict the scatter very accurately over the whole temperature range. The effects of specimen type, size and geometry on the fracture toughness transition curve have also been captured satisfactorily by the new model.