M.K. Samal

A Mesh Independent GTN Damage Model and Its Application in Simulation of Ductile Fracture Behaviour

Ductile fracture process involves the typical stages of nucleation, growth and coalescence of voids in the micro-scale. In order to take the effects of these voids on the stress carrying capability of a mechanical continuum during simulation, damage mechanics models, such as those of Rousselier and Gurson-Tvergaard-Needleman (GTN) are widely used. These have been highly successful in simulating the fracture resistance behaviour of different specimens and components made of a wide spectrum of engineering steels. However, apart from the material parameters, a characteristic length parameter has to be used as a measure of the size of the discretisation in the zone of crack propagation. This inherent limitation of these local damage models prevents them from simulating the stress distribution near the sharp stress gradients satisfactorily, especially at transition temperature regime. There have been efforts in literature to overcome the effect of mesh-dependency by development of nonlocal and gradient damage models. A nonlocal measure (weighted average of a quantity over a characteristics volume) of damage is usually used in the material constitutive equation. In this paper, the authors have extended the GTN model to its nonlocal form using damage parameter ‘d’ as a degree of freedom in the finite element (FE) formulation. The evolution of the nonlocal damage is related to the actual void volume faction ‘f’ in ductile fracture using a diffusion type equation. The coupled mechanical equilibrium and damage diffusion equations have been discretised using FE method. In order to demonstrate the mesh independent nature of the new formulation, a standard fracture mechanics specimen (i.e., 1T compact tension) has been analysed using different mesh sizes near the crack tip and the results have been compared with those of experiment. The results of the nonlocal model have also been compared with those of the local model. The effect of different GTN parameters on the fracture resistance behaviour of this specimen has been studied for the nonlocal model and these results have been compared with those of experiment.Copyright

Edge cracks in nickel and aluminium single crystals: A molecular dynamics study

A molecular dynamics study of edge cracks in Ni and Al single crystals under mode-I loading conditions is presented. Simulations are performed using embedded-atom method potentials for Ni and Al at a temperature of 0.5K. The results reveal that Ni and Al show different fracture mechanisms. Overall failure behavior of Ni is brittle, while fracture in Al proceeds through void nucleation and coalescence with a zig-zag pattern of crack growth. The qualitative nature of results is discussed in the context of vacancy-formation energies and surface energies of the two FCC metals.

Stress Analysis for Integrity Assessment of High-Energy Hot Reheat Pipe Bends of 210 MW Coal-Fired Unit

The critical high-energy piping components of thermal power plant are predominantly subjected to damage mechanisms of creep, fatigue, and their interactions during their service. These pipings at high temperature and transient loadings under sustained loadings and thermal movements are designed as per the piping code. The creep damage mechanism causes irreversible thermal expansion in the piping inducing thermal stresses. The pipings under altered state of stresses due to thermal expansion are supported by suitable hangers and supports for ensuring stresses to be within the permissible design limits. The present paper discusses the layout of hot reheat piping of a coal-fired 210 MWe unit. The piping material as per specification ASTM A335 P22 with hot reheat steam temperature 540 °C and hot reheat steam pressure of 4.7 MPa pressure operates under creep domain. The piping under these pressure and temperature loadings is subjected to load ramps during the start-ups, shutdowns, and load fluctuations and the steady loading during the sustained load operations. The scope of the study includes hot reheat pressure and low-pressure bypass pipelines. The piping layout with respect to the designed stresses, stress ratios, support loads, element forces, and displacements at each node has been considered for the present ongoing assessment. The design of the piping layout is accomplished to ensure that the structural integrity of the piping doesn’t exert excessive load to the nozzles of the connecting equipment. The stress analysis of the piping and support system should be carried out to ensure that the stresses are within the allowable values as per the applicable design code during the service. The stress analysis data were utilized in modeling the pipe bend before control valve of the intermediate pressure turbine for online creep fatigue damage monitoring.

Investigation of failure behavior of thin-walled tubular components and development of a procedure for evaluation of their mechanical and fracture properties

Structural integrity evaluation of thin-walled tubes in various industries requires transverse mechanical properties, crack initiation toughness as well as ductile fracture resistance data of these components. In this work, the failure behavior, mechanical properties, and fracture resistance behavior of Zircaloy-4 fuel-clad tubes of Indian pressurized heavy-water reactor have been studied. As standard specimens cannot be machined from these components, ring-type segments of these components are directly tested in different types of loading setups. Both the specimen and the mandrel were modeled through 3D finite-element analysis and by comparing the results of analysis with experiment; the material stress-strain curve was evaluated using an inverse analysis procedure. For estimation of fracture resistance behavior, two types of loading mandrels, viz., conical mandrel and pair of semi-cylindrical split mandrels, have been used to open the axial crack in the tubular specimen and fracture resistance behavior in terms of J - R curve obtained from both the tests have been compared.

A nonlocal damage-mechanics-based approach suitable for failure assessment and remaining life estimation of critical industrial components

For structural integrity analysis of safety-critical industrial components, fracture resistance data are required in the upper-shelf as well as in the ductile-to-brittle transition (DBT) temperature regime in order to account for various types of postulated accidental loading conditions. Full-scale fracture tests on actual components are expensive and time-consuming. Unlike mechanical properties, the fracture resistance properties of ductile materials depend upon the state of stress at the crack-tip and hence, these are influenced by the specimen geometry, size, crack-depth, loading and boundary conditions, etc. In the DBT temperature regime, fracture toughness exhibits considerable scatter and dependency upon temperature. In this chapter, the effect of several geometric and loading parameters on the fracture toughness of a ferritic pressure vessel steel (base metal as well as dissimilar metal welded joint) has been studied. The results of numerical simulation have been verified against experimental data.

Numerical modeling of copper single crystal specimens subjected to mechanical loading at elevated strain rates

This paper describes the simulation methodology adopted to model the mechanical response of Copper single crystals subjected to dynamic loading in different crystallographic orientations. Crystal Plasticity Finite Element Simulations are performed to explain the observed plastic anisotropy in terms of stress-strain response and deformed shapes in [100] and [110] directions. The crystal plasticity model used is based on the thermally activated theory for plastic flow and an evolution equation for slip system deformation resistances incorporating self and latent hardening. The hardening parameters of the model are obtained by calibrating against the previous experiments. The computed stress-strain responses and the deformed shapes agree well with the experimental data.

Prediction of Fracture Resistance Behaviour Using Nonlocal Damage Model

Prevention of failure of pressurised and high-energy components and systems has been an important issue in design of all types of power and process plants. Each individual component of these systems must be dimensioned such that it can resist the forces or moments to which it will be subjected during normal service and upset conditions. Design by analysis is an important philosophy of modern design. The ability of now-a-days computers to numerically handle complex mathematical problems has inspired the use highly nonlinear material behaviour (including material softening) instead of classical linear constitutive theory for the materials. Under the influence of these developments, a fundamentally different type of modelling has emerged, in which fracture is considered as the ultimate consequence of a material degradation process. Crack initiation and growth then follow naturally from the standard continuum mechanics theory (called continuum damage mechanics). Numerical analyses based on these so-called local damage models, however, are often found to depend on the spatial discretisation (i.e., mesh size of the numerical method used). The growth of damage tends to localise in the smallest band that can be captured by the spatial discretisation. As a consequence, increasingly finer discretisation grids can lead to crack initiation earlier in the loading history and to faster crack growth. This non-physical behaviour is caused by the fact that the localisation of damage in a vanishing volume is no longer consistent with the concept of a continuous damage field, which forms the basis of the continuum damage mechanics approach. In this work, the Rousellier’s damage model has been extended to its nonlocal form using damage parameter ‘d’ as a degree of freedom. The finite element (FE) equations have been derived using the weak form of the governing equations for both mechanical force equilibrium and the damage equilibrium. As an example, a standard fracture mechanics specimen [SE(B)] made up of a German low alloy steel has been analysed in 2D plane strain condition using different mesh sizes near the crack tip. The results of the nonlocal model has been compared with experimental results as well as with those predicted by the local model. It was observed that the fracture resistance predicted by the local damage model goes on decreasing when the mesh size near the crack tip is refined whereas the nonlocal model predicts a converged fracture resistance behaviour which compares well with the experimentally determined behaviour.Copyright