1,441 research outputs found
Crystal plasticity finite element simulations of cast α-uranium
α-uranium, the stable phase of uranium up to 670◦C, has a base-centred orthorombic crystal structure. This crystal structure gives rise to elastic and thermal anisotropy, meaning α-uranium exhibits complex deformation and fracture behaviour. Understanding the relationship between the microstructure and mechanical properties is important to prevent fracture during manufacture and usage of components. The lattice of α-uranium corresponds to a distorted close-packed-hexagonal crystal structure and it exhibits twins of both the 1st and 2nd kind. Therefore, detailed examination of the behaviour of α-uranium can also contribute to the general understanding of the interaction between plasticity, twinning and fracture in hcp crystals. Plastic deformation in α-uranium can be accommodated by 4 slip systems and 3 twin systems, previously identified by McCabe et al. These deformation modes are implemented into a crystal plasticity finite element (CPFE) material model. A temperature dependent, dislocation density based law is implemented to describe the critical resolved shear stress on the different slip/twin systems. The strong anisotropic thermal expansion behaviour is taken into account to simulate the development of internal residual stresses following casting of the material. During cooling, the internal stresses in α-uranium are sufficient to induce plasticity. This effect is quantified using polycrystal simulations, in which first the temperature is decreased, then plastic relaxation takes place, followed by application of a mechanical load. The asymmetry between mechanical properties in tension and compression, due to the presence of twins, is investigated. The model is calibrated using stress strain curves and the lattice strain found from published neutron diffraction experiments carried out on textured samples at ISIS. The strength of the slip systems is found to be lower than in fine grained material, while the strength of the twin system is similar to single crystals. The CPFE method allows the heterogeneity of the strain between neighbouring grains and its influence on the evolution of the internal stress state to be investigated
Mud peeling and horizontal crack formation in drying clays
Mud peeling is a common phenomenon whereby horizontal cracks propagate parallel to the surface of a drying clay. Differential stresses then cause the layer of clay above the crack to curl up to form a mud peel. By treating the clay as a poroelastic solid, we analyse the peeling phenomenon and show that it is caused by the gradient in tensile stress at the surface of the clay, analogously to the spalling of thermoelastic materials. For a constant water evaporation rate at the clay surface we derive equations for the depth of peeling and the time of peeling as functions of the evaporation rate. Our model predicts a simple relationship between the radius of curvature of a mud peel and the depth of peeling. The model predictions are in agreement with the available experimental data available
Ice-lens formation and connement-induced supercooling in soils and other colloidal materials
We present a new, physically-intuitive model of ice-lens formation and growth during the freezing of soils and other dense, particulate suspensions. Motivated by experimental evidence, we consider the growth of an ice-filled crack in a freezing soil. At low temperatures, ice in the crack exerts large pressures on the crack walls that will eventually cause the crack to split open. We show that the crack will then propagate across the soil to form a new lens. The process is controlled by two factors: the cohesion of the soil, and the confinement-induced supercooling of the water in the soil; a new concept introduced to measure the energy available to form a new ice lens. When the supercooling exceeds a critical amount (proportional to the cohesive strength of the soil) a new ice lens forms. This condition for ice-lens formation and growth does not appeal to any ad hoc, empirical assumptions, and explains how periodic ice lenses can form with or without the presence of a frozen fringe. The proposed mechanism is in good agreement with experiments, in particular explaining ice-lens pattern formation, and surges in heave rate associated with the growth of new lenses. Importantly for systems with no frozen fringe, ice-lens formation and frost heave can be predicted given only the unfrozen properties of the soil. We use our theory to estimate ice-lens growth temperatures obtaining quantitative agreement with experiments. The theory is generalizable to complex natural-soil scenarios, and should therefore be useful in the prediction of macroscopic frost heave rates
Coupling a discrete twin model with cohesive elements to understand twin-induced fracture
The interplay between twinning and fracture in metals under deformation is an open question. The plastic strain concentration created by twin bands can induce large stresses on the grain boundaries. We present simulations in which a continuum model describing discrete twins is coupled with a crystal plasticity finite element model and a cohesive zone model for intergranular fracture. The discrete twin model can predict twin nucleation, propagation, growth and the correct twin thickness. Therefore, the plastic strain concentration in the twin band can be modelled. The cohesive zone model is based on a bilinear traction-separation law in which the damage is caused by the normal stress on the grain boundary. An algorithm is developed to generate interface elements at the grain boundaries that satisfy the traction-separation law. The model is calibrated by comparing polycrystal simulations with the experimentally observed strain to failure and maximum stress. The dynamics of twin and crack nucleation have been investigated. First, twins nucleate and propagate in a grain, then, microcracks form near the intersection between twin tips and grain boundaries. Microcracks appear at multiple locations before merging. A propagating crack can nucleate additional twins starting from the grain boundary, a few micrometres away from the original crack nucleation site. This model can be used to understand which type of texture is more resistant against crack nucleation and propagation in cast metals in which twinning is a deformation mechanism. The code is available online at https://github.com/TarletonGroup/CrystalPlasticity
Simultaneous description of four positive and four negative parity bands
The extended coherent state model is further extended in order to describe
two dipole bands of different parities. The formalism provides a consistent
description of eight rotational bands. A unified description for spherical,
transitional and deformed nuclei is possible. Projecting out the angular
momentum and parity from a sole state, the band acquires a
magnetic character, while the electric properties prevail for the other band.
Signatures for a static octupole deformation in some states of the dipole bands
are pointed out. Some properties which distinguish between the dipole band
states and states of the same parity but belonging to other bands are
mentioned. Interesting features concerning the decay properties of the two
bands are found. Numerical applications are made for Gd, Yb,
Th, Ra, U and Pu, and the results are
compared with the available data.Comment: 36 pages, 13 figures, 12 table
Evaluation of local stress state due to grain-boundary sliding during creep within a crystal plasticity finite element multi-scale framework
Previous studies demonstrate that grain-boundary sliding could accelerate
creep rate and give rise to large internal stresses that can lead to damage
development, e.g. formation of wedge cracks. The present study provides more
insight into the effects of grain-boundary sliding (GBS) on the deformation
behaviour of realistic polycrystalline aggregates during creep, through the
development of a computational framework which combines: i) the use of
interface elements for sliding at grain boundaries, and ii) special triple
point (in 2D) or triple line (in 3D) elements to prevent artificial dilation at
these locations in the microstructure with iii) a physically-based crystal
plasticity constitutive model for time-dependent inelastic deformation of the
individual grains. Experimental data at various scales is used to calibrate the
framework and compare with model predictions. We pay particular consideration
to effects of grain boundary sliding during creep of Type 316 stainless steel,
which is used extensively in structural components of the UK fleet of Advanced
Gas Cooled Nuclear Reactors (AGRs). It is found that the anisotropic
deformation of the grains and the mismatch in crystallographic orientation
between neighbouring grains play a significant role in determining the extent
of sliding on a given boundary. Their effect on the development of stress
within the grains, particularly at triple grain junctions, and the increase in
axial stress along transverse boundaries are quantified. The article
demonstrates that the magnitude of the stress along the facets is
highly-dependent on the crystallographic orientations of the neighbouring
grains and the relative amount of sliding. Boundaries, transverse to the
applied load tend to carry higher normal stresses of the order of 100-180 MPa,
in cases where the neighbouring grains consist of plastically-harder
crystallographic orientations.Comment: Keywords: grain boundary sliding, creep, interface, polycrystalline,
triple grain junction, crystal plasticity. 21 Pages, 16 Figures, 2 Table
Fuelwood harvesting and selection in Valley Thicket, South Africa
The Thicket Biome is the second smallest biome in South Africa, and is renowned for its high biodiversity. Yet, less than 5% of the biome is in formal conservation areas. Much of the currently intact thicket outside protected areas is threatened by land transformation to commercial agriculture or heavy use by rural communities. There is limited understanding of the ecological structure and function of thicket communities and their response to these human pressures. This paper reports on a study to characterize the woody communities in Valley Thicket and Thornveld surrounding a rural village. We also examined the demand and selection for specific woody species. There was a marked selection for key species for different uses, including fuelwood, construction timber, and cultural stacks. There was also strong selection for specific size classes of stem, especially those between 16–45 cm circumference. The density, biomass and species richness of woody species was reduced close to the village, and increased with distance away from human settlement. A similar trend was found for the basal area of preferred species, but not for the basal area of all species. The strong selectivity for both species and size class means that the anthropogenic impacts are not uniform within the woody strata, leading to marked changes in community structure and floristics at a local scale
Characterisation of slip and twin activity using digital image correlation and crystal plasticity finite element simulation:Application to orthorhombic -uranium
Calibrating and verifying crystal plasticity material models is a significant
challenge, particularly for materials with a number of potential slip and twin
systems. Here we use digital image correlation on coarse-grained
-uranium during tensile testing in conjunction with crystal plasticity
finite element simulations. This approach allows us to determine the critical
resolved shear stress, and hardening rate of the different slip and twin
systems. The constitutive model is based on dislocation densities as state
variables and the simulated geometry is constructed from electron backscatter
diffraction images that provide shape, size and orientation of the grains,
allowing a direct comparison between virtual and real experiments. An
optimisation algorithm is used to find the model parameters that reproduce the
evolution of the average strain in each grain as the load is increased. A
tensile bar, containing four grains aligned with the load direction, is used to
calibrate the model with eight unknown parameters. The approach is then
independently validated by simulating the strain distribution in a second
tensile bar. Different mechanisms for the hardening of the twin systems are
evaluated. The latent hardening of the most active twin system turns out to be
determined by coplanar twins and slip. The hardening rate of the most active
slip system is lower than in fine-grained -uranium. The method
developed in the present research can be applied to identify the critical
resolved shear stress and hardening parameters of other coarse-grained
materials
"Beat" patterns for the odd-even staggering in octupole bands from a quadrupole-octupole Hamiltonian
We propose a collective Hamiltonian which incorporates the standard
quadrupole terms, octupole terms classified according to the irreducible
representations of the octahedron group, a quadrupole-octupole interaction, as
well as a term for the bandhead energy linear in K (the projection of angular
momentum on the body-fixed z-axis). The energy is subsequently minimized with
respect to K for each given value of the angular momentum I, resulting in K
values increasing with I within each band, even in the case in which K is
restricted to a set of microscopically plausible values. We demonstrate that
this Hamiltonian is able to reproduce a variety of ``beat'' patterns observed
recently for the odd-even staggering in octupole bands of light actinides.Comment: LaTeX, 20 pages plus 12 figures given in separate .ps file
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