A novel computational treatment of dense, stiff, coupled reaction rate equations is introduced to study the nucleation, growth, and possible coalescence of cavities during neutron irradiation of metals. Radiation damage is modeled by the creation of Frenkel pair defects and helium impurity atoms. A multi-dimensional cluster size distribution function allows independent evolution of the vacancy and helium content of cavities, distinguishing voids and bubbles. A model with sessile cavities and no cluster-cluster coalescence can result in a bimodal final cavity size distribution with coexistence of small, high-pressure bubbles and large, low-pressure voids. A model that includes unhindered cavity diffusion and coalescence ultimately removes the small helium bubbles from the system, leaving only large voids. The terminal void density is also reduced and the incubation period and terminal swelling rate can be greatly altered by cavity coalescence. Temperature-dependent trapping of voids/bubbles by precipitates and alterations in void surface diffusion from adsorbed impurities and internal gas pressure may give rise to intermediate swelling behavior through their effects on cavity mobility and coalescence.
Molecular dynamics simulations in three-dimensional copper have been performed to quantify the void coalescence process leading to fracture. The correlated growth of the voids during their linking is investigated both in terms of the onset of coalescence and the ensuing dynamical interactions through the rate of reduction of the distance between the voids and the directional growth of the voids. The critical inter-void ligament distance marking the onset of coalescence is shown to be approximately one void radius in both measures.
Coalescence of voids by internal necking is in most cases the last microscopic event related to ductile fracture and corresponds to a localized plastic flow between adjacent voids. Macroscopic load associated to the onset of coalescence is classically estimated based on limit analysis. However, a rigorous upper-bound mathematical expression for the limitload required for flat voids coalescence that remains finite for penny-shaped voids/cracks is still unavailable. Therefore, based on limit analysis, theoretical upper-bound estimates - both integral expression and closed-form formula - are obta…
Void coalescence and interaction in dynamic fracture of ductile metals have been investigated using three-dimensional strain-controlled multi-million atom molecular dynamics simulations of copper. The correlated growth of two voids during the coalescence process leading to fracture is investigated, both in terms of its onset and the ensuing dynamical interactions. Void interactions are quantified through the rate of reduction of the distance between the voids, through the correlated directional growth of the voids, and through correlated shape evolution of the voids. The critical inter-void li…
A decrease of fracture toughness of irradiated materials is usually observed, as reported for austenitic stainless steels in Light Water Reactors (LWRs) or copper alloys for fusion applications. For a wide range of applications (e.g. structural steels irradiated at low homologous temperature), void growth and coalescence fracture mechanism has been shown to be still predominant. As a consequence, a comprehensive study of the effects of irradiation-induced hardening mechanisms on void growth and coalescence in irradiated materials is required. The effects of irradiation on ductile fracture mech…
Voids can be observed at various scales in ductile materials, frequently of sizes lower than the grain size, leading to porous single crystals materials. Two local deformation modes of porous ductile (single crystals) materials have been identified and referred to as void growth and void coalescence, the latter being characterized by strong interactions between neighboring voids. A simple semi-analytical coalescence criterion for porous single crystals with periodic arrangement of voids is proposed using effective isotropic yield stresses associated with a criterion derived for isotropic mater…
Ductile fracture through void growth and coalescence depends significantly on the plastic anisotropy of the material and on void size, as shown by experiments and/or numerical simulations through several studies. Macroscopic (homogenized) yield criteria aiming at modeling nanoporous materials have been proposed only for the growth regime, i.e. non-interacting voids. The aim of this study is thus to provide a yield criterion for nanoporous materials relevant for the coalescence regime, i.e. when plastic flow is localized between voids. Through homogenization and limit analysis, and accounting f…
Ductile fracture has been extensively studied in metals with weak mechanical anisotropy such as copper and aluminum. The fracture of more anisotropic metals, especially those with a hexagonal crystal structure (e.g. titanium), remains far less understood. This paper investigates the ductile fracture process in commercially pure titanium (CP-Ti) with particular emphasis on the influence of grain orientation and local state of strain on void growth. An experimental approach was developed to directly relate the growth of a void in three dimensions to its underlying grain orientation. Grain orient…
Understanding how properties of materials change due to nuclear transmutations is a major challenge for the design of structural components for a fusion power plant. In this study, by combining a first-principles matrix Hamiltonian approach with thermodynamic integration we investigate quasi-steady state configurations of multi-component alloys, containing defects, over a broad range of temperature and composition. The model enables simulating transmutation-induced segregation effects in materials, including tungsten where the phenomenon is strongly pronounced. Finite-temperature analysis show…
The effect of hydrogen on the fracture behaviour of austenitic stainless steel has been investigated in the past [1][2]. It has been reported that fracture initiates by void formation at inclusions and regions of enhanced strain localisation [3]. There is experimental evidence that supports the fact that hydrogen influences void nucleation, growth and coalescence during material fracture [4]. This work investigates the effect of hydrogen on void growth and coalescence in austenitic stainless steel. The effect of hydrogen on void growth and coalescence for different stress triaxialities has bee…
The ductile fracture process in porous metals due to growth and coalescence of micron scale voids is not only affected by the imposed stress state but also by the distribution of the voids and the material size effect. The objective of this work is to understand the interaction of the inter-void spacing (or ligaments) and the resultant gradient induced material size effect on void coalescence for a range of imposed stress states. To this end, three dimensional finite element calculations of unit cell models with a discrete void embedded in a strain gradient enhanced material matrix are perform…
Turing (or double-diffusive) instabilities describe pattern formation in reaction-diffusion systems, and were proposed in 1952 as a potential mechanism behind pattern formation in nature, such as leopard spots and zebra stripes. Because the mechanism requires the reacting species to have significantly different diffusion rates, only a few liquid phase chemical reaction systems exhibiting the phenomenon have been discovered. In solids the situation is markedly different, since species such as impurities or other defects typically have diffusivities $\propto\!\exp\left( -E/k_{\rm B} T\right)$, w…
A cluster dynamics (CD) model has been developed to investigate the nucleation and growth of point defect clusters, i.e., interstitial prismatic loops and nanoscale and sub-nanoscale voids, in ThO2 during irradiation by energetic particles. The model considers cluster off-stoichiometry due to the asymmetry of point defect generation on the O and Th sublattices under irradiation, as well as the point defect diffusivities and the defect binding energies to clusters. The energies were established using detailed molecular dynamics simulations considering the statistical variability of cluster conf…
The mechanical response of isotropic elastoplastic materials containing random distributions of initially spherical voids is investigated computationally based on Fast Fourier Transform simulations. Numerical limit-analysis simulations at constant stress triaxiality allow to determine the yield surfaces, leading in particular to the determination of a Representative Volume Element size for the onset of coalescence / inhomogeneous yielding. Moreover, two different coalescence regimes are observed that differ by the presence of shearing. The yield surfaces are found to be consistent with the com…
Ductile metals undergo a considerable amount of plastic deformation before failure. Void nucleation, growth and coalescence is the mechanism of failure in such metals. α/β titanium alloys are ductile in nature and are widely used for their unique set of properties like specific strength, fracture toughness, corrosion resistance and resistance to fatigue failures. Voids in these alloys were reported to nucleate on the phase boundaries between α and β phase. Based on the findings of crystal plasticity finite element method (CPFEM) based investigation of the void growth at the interface of α and …
Modeling dynamics fracture in materials involves usage of hydrodynamic codes which solve basic conservation laws of mass, energy and momentum in space and time. This requires appropriate models to handle elastic-plastic deformation, equation of state, material strength, and fracture. Nucleation and Growth (NAG) damage model is a micro-physical model which computes amount of damage in the material by accounting for phenomena like nucleation, growth and coalescence of voids or cracks. The NAG model involves several material model parameters, such as nucleation threshold, growth threshold, etc. T…
We have presented the kinetic study of the very initial growth stages of an ultra thin film (40 $Å$- 150$Å$) of Ag sputter-deposited on Si(001) substrate containing native oxide using grazing incidence x-ray reflectivity (GIXR) technique and Atomic Force Microscopy (AFM). We observe that the film consists of mounds with the presence of voids. The thickness `d_{xray}' and the packing fraction `η' of the film as a function of time `t' follow a simple power law, d_{xray} $\thicksim t^{m} and η\thicksim $t^{n}$ with the exponent m = 0.58 and n = 0.37 respectively. We have quantitatively determined…
Object kinetic Monte Carlo simulations were performed to study the impact of varying dose rate and grain size up to a dose of 1.0 dpa in pure, polycrystalline tungsten, subjected to a neutron irradiation having a PKA spectrum corresponding to the High Flux Isotope Reactor. The present study models defect cluster accumulation in tungsten, but does not consider the impact of transmutation or pre-existing defects beyond the grain boundary sinks, with varying grain size. With increasing dose rate, the vacancy cluster density increases, while the number density of vacancies decreases. Accordingly, …
