Pritam Chakraborty

Wavelet decomposed dual-time scale crystal plasticity FE model for analyzing cyclic deformation induced crack nucleation in polycrystals

A microstructure sensitive criterion for dwell fatigue crack initiation in polycrystalline alloys is proposed in this paper. Local stress peaks due to load shedding from time dependent plastic deformation fields in neighboring grains are responsible for crack initiation in dwell fatigue. A calibrated and experimentally validated crystal plasticity finite element model (CFEM) is employed for predicting slip system level stresses and strains. Vital microstructural features related to the grain morphology and crystallographic orientations are accounted for in the FEM by construction of microstructures that are statistically equivalent to those observed in OIM scans. The output of the FEM is used to evaluate the crack initiation condition in the post processing stage. The functional form of the criterion is motivated from the similarities in the stress fields and crack evolution criteria ahead of a crack tip and dislocation pile-up. A specific model is developed for estimating the pile-up length necessary for the nucleation criterion using the notion of geometrically necessary dislocations. The crack nucleation criterion is calibrated and validated by using experimental data obtained from ultrasonic crack monitoring techniques. In order to be able to model a large number of cycles to failure initiation, a dual-time scaling algorithm is proposed using wavelet induced decomposition. The algorithm decouples the governing equations into two sets of problems corresponding to two different time scales. One is a long time scale (low frequency) problem characterizing a cycle-averaged solution, while the other is a short time scale (high frequency) problem for a remaining oscillatory portion. The method significantly reduces the computational time till crack initiation.

Modeling Fatigue Crack Nucleation Using Crystal Plasticity Finite Element Simulations and Multi-time Scaling

This chapter addresses two important aspects of predicting fatigue crack nucleation in polycrystalline alloys under dwell cyclic loading. The first is a microstructure sensitive criterion for dwell fatigue crack initiation in polycrystalline titanium alloys. Local stress peaks due to load shedding from time-dependent plastic deformation fields in neighboring grains are responsible for crack initiation. Crystal plasticity finite element simulation results are post-processed to provide inputs to the fatigue crack nucleation model. The second part of this chapter discusses a wavelet transformation based multi-time scaling (WATMUS) algorithm for accelerated crystal plasticity finite element simulations. The WATMUS algorithm does not require any scale-separation and naturally transforms the coarse time scale response into a “monotonic cycle scale” without the requirement of subcycle resolution. The method significantly enhances the computational efficiency in comparison with conventional single timescale integration methods. Adaptivity conditions are also developed for this algorithm to improve accuracy and efficiency.

Microstructure Sensitive Fatigue Crack Nucleation in Titanium Alloys Using Accelerated Crystal Plasticity FE Simulations

This chapter investigates microstructure and load sensitive fatigue behavior of Ti-6242 using cyclic crystal plasticity finite element (CPFE) simulations of statistically equivalent image-based microstructures. A wavelet transformation induced multi-time scaling (WATMUS) method (Joseph et al., Comput Methods Appl Mech Eng 199:2177–2194, 2010; Chakraborty et al., Finite Elem Anal Des 47:610–618, 2011; Chakraborty and Ghosh, Int J Numer Methods Eng 93:1425–1454, 2013; Ghosh and Chakraborty, Int J Fatigue 48:231–246, 2013) is used to perform accelerated cyclic CPFE simulations till crack nucleation, otherwise infeasible using conventional time integration schemes. A physically motivated crack nucleation model in terms of crystal plasticity variables (Anahid et al., J Mech Phys Solids 59(10):2157–2176, 2011) is extended in this work to predict nucleation. The dependence of yield strength on the underlying grain orientations and sizes is developed through the introduction of an effective microstructural parameter Plastic Flow Index or PFI. To determine the effects of the microstructure on crack nucleation, a local microstructural variable is defined in terms of the surface area fraction of soft grains surrounding each hard grain or SAFSSG. Simulations with different cyclic load patterns suggest that fatigue crack nucleation in Ti-6242 strongly depends on the dwell cycle hold time at maximum stress.

Modeling and Simulation of Used Nuclear Fuel During Transportation with Consideration of Hydride Effects and Cyclic Fatigue

The objective of this work is to understand the integrity of Used Nuclear Fuel (UNF) during transportation. Previous analysis work has been performed to look at the integrity of UNF during transportation but these analyses have neglected to analyze the effect of hydrides and flaws (fracture mechanics models to capture radial cracking in the cladding). In this study, the clad regions of interest are near the pellet-pellet interfaces. These regions can experience more complex stress-states than the rest of the clad during cooling and have a greater possibility to develop radially reoriented hydrides during vacuum drying.

Characterization of Load Sensitive Fatigue Crack Initiation in Ti-Alloys Using Crystal Plasticity Based FE Simulations

Fatigue life in near \(\alpha \) Ti-alloys shows large variation with characteristics of applied load and is due to the microstructurally dependent deformation behavior in these alloys. In the present work, the load sensitive fatigue crack nucleation behavior is investigated using a physically motivated crack initiation law and cyclic crystal plasticity based finite element (CPFE) simulations of statistically equivalent image based microstructures. Since cyclic CPFE simulation for large number of cycles using conventional time integration schemes is computationally prohibitive, a wavelet transformation based multi-time scale (WATMUS) method developed in [1, 2] is used in the present work to perform accelerated simulations. To predict cycles to nucleation, a physically motivated crack nucleation model based on crystal plasticity variables developed in [3] has been used in this work. The nucleation model is calibrated and validated with experiments. The sensitivity of crack nucleation to the characteristics of the applied load is studied by performing WATMUS method based CPFE simulations for different cyclic load profiles on a statistically equivalent microstructure.

Modeling the Ductile Brittle Fracture Transition in Reactor Pressure Vessel Steels Using a Cohesive Zone Model Based Approach

Fracture properties of Reactor Pressure Vessel (RPV) steels show large variations with changes in temperature and irradiation levels. Brittle behavior is observed at lower temperatures and/or higher irradiation levels whereas ductile mode of failure is predominant at higher temperatures and/or lower irradiation levels. In addition to such temperature and radiation dependent fracture behavior, significant scatter in fracture toughness has also been observed. As a consequence of such variability in fracture behavior, accurate estimates of fracture properties of RPV steels are of utmost importance for safe and reliable operation of reactor pressure vessels.A cohesive zone based approach is being pursued in the present study where an attempt is made to obtain a unified law capturing both stable crack growth (ductile fracture) and unstable failure (cleavage fracture). The parameters of the constitutive model are dependent on both temperature and failure probability. The effect of irradiation has not been considered in the present study. The use of such a cohesive zone based approach would allow the modeling of explicit crack growth at both stable and unstable regimes of fracture. Also it would provide the possibility to incorporate more physical lower length scale models to predict DBT. Such a multi-scale approach would significantly improve the predictive capabilities of the model, which is still largely empirical.Copyright

Multi-scale modeling of inter-granular fracture in UO2

A hierarchical multi-scale approach is pursued in this work to investigate the influence of porosity, pore and grain size on the intergranular brittle fracture in UO2. In this approach, molecular dynamics simulations are performed to obtain the fracture properties for different grain boundary types. A phase-field model is then utilized to perform intergranular fracture simulations of representative microstructures with different porosities, pore and grain sizes. In these simulations the grain boundary fracture properties obtained from molecular dynamics simulations are used. The responses from the phase-field fracture simulations are then fitted with a stress-based brittle fracture model usable at the engineering scale. This approach encapsulates three different length and time scales, and allows the development of microstructurally informed engineering scale model from properties evaluated at the atomistic scale.

Modeling of Late Blooming Phases and Precipitation Kinetics in Aging Reactor Pressure Vessel (RPV) Steels

The principle work at the atomic scale is to develop a predictive quantitative model for the microstructure evolution of RPV steels under thermal aging and neutron radiation. We have developed an AKMC method for the precipitation kinetics in bcc-Fe, with Cu, Ni, Mn and Si being the alloying elements. In addition, we used MD simulations to provide input parameters (if not available in literature). MMC simulations were also carried out to explore the possible segregation/precipitation morphologies at the lattice defects. First we briefly describe each of the simulation algorithms, then will present our results.

Light Water Reactor Sustainability Program Grizzly Year-End Progress Report

The Grizzly software application is being developed under the Light Water Reactor Sustainability (LWRS) program to address aging and material degradation issues that could potentially become an obstacle to life extension of nuclear power plants beyond 60 years of operation. Grizzly is based on INL’s MOOSE multiphysics simulation environment, and can simultaneously solve a variety of tightly coupled physics equations, and is thus a very powerful and flexible tool with a wide range of potential applications. Grizzly, the development of which was begun during fiscal year (FY) 2012, is intended to address degradation in a variety of critical structures. The reactor pressure vessel (RPV) was chosen for an initial application of this software. Because it fulfills the critical roles of housing the reactor core and providing a barrier to the release of coolant, the RPV is clearly one of the most safety-critical components of a nuclear power plant. In addition, because of its cost, size and location in the plant, replacement of this component would be prohibitively expensive, so failure of the RPV to meet acceptance criteria would likely result in the shutting down of a nuclear power plant. The current practice used to perform engineering evaluations of the susceptibility of RPVs to fracture is to use the ASME Master Fracture Toughness Curve (ASME Code Case N-631 Section III). This is used in conjunction with empirically based models that describe the evolution of this curve due to embrittlement in terms of a transition temperature shift. These models are based on an extensive database of surveillance coupons that have been irradiated in operating nuclear power plants, but this data is limited to the lifetime of the current reactor fleet. This is an important limitation when considering life extension beyond 60 years. The currently available data cannot be extrapolated with confidence further out in time because there is a potential for additional damage mechanisms (i.e. late blooming phases) to become active later in life beyond the current operational experience. To develop a tool that can eventually serve a role in decision-making, it is clear that research and development must be perfomed at multiple scales. At the engineering scale, a multiphysics analysis code that can capture the thermomechanical response of the RPV under accident conditions, including detailed fracture mechanics evaluations of flaws with arbitrary geometry and orientation, is needed to assess whether the fracture toughness, as defined by the master curve, including the effects of embrittlement, is exceeded. At the atomistic scale, the fundamental mechanisms of degradation need to be understood, including the effects of that degradation on the relevant material properties. In addition, there is a need to better understand the mechanisms leading to the transition from ductile to brittle fracture through improved continuum mechanics modeling at the fracture coupon scale. Work is currently being conducted at all of these levels with the goal of creating a usable engineering tool informed by lower length-scale modeling. This report summarizes progress made in these efforts during FY 2013.