Strain gradient plasticity: energetic or dissipative?

It has been established by computation, and confirmed by analysis, for an infinite slab of strain-gradient sensitive material subjected to plane-strain tensile loading, that passivation of the lateral boundaries at some stage of loading inhibits plastic deformation upon further loading. This result is not surprising in itself except that, remarkably, if the gradient terms contribute to the dissipation, the plastic deformation is switched off completely, and only resumes at a clearly-defined higher load, corresponding to a total strain ε_c say. The analysis presented in this paper confirms the delay of plastic deformation following passivation and determines the exact manner in which the plastic flow resumes. The plastic strain-rate is continuous at the exact point ε_c of resumption of plastic flow and, for the first small increment Δε = ε − ε_c in the imposed total strain, the corresponding increment in plastic strain, Δε^p, is proportional to (Δε)^2. The constant A in the relation Δε^p(0) = A(Δε)^2, where Δε^p(0) denotes the plastic strain increment at the centre of the slab, has been determined explicitly; it depends on the hardening modulus of the material. The presence of energetic gradient terms has no effect on the value of ε_c unless the dissipative terms are absent, in which case passivation reduces the rate of plastic deformation but introduces no delay. This qualitative effect of dissipative gradient terms opens the possibility of experimental discrimination of their presence or absence. The analysis employs an incremental variational formulation that is likely to find use in other problems.This is the author accepted manuscript. The final version is available from Springer via http://dx.doi.org/10.1007/s10409-015-0468-

The effective non-linear properties of a composite coating and a composite sandwich layer

Hashin-Shtrikman based bounds and estimates are obtained for the linear and non-linear effective properties of composites in the form of a thin coating or sandwich layer. It is assumed that the thickness of the layer is of the same order of magnitude as the correlation length between phases, and size effects thereby result. Boundary layers exist within the coating adjacent to the substrate and to the free surface (in the case of a coating). Attention is focused on two-dimensional problems by considering anti-plane shear of an isotropic 2-phase composite on a single-phase substrate, with microstructure prismatic along the direction of anti-plane shear.NAF is grateful for financial support in the form of an ERC MULTILAT grant 669764, and to the US ONR (N62909-14-1-N232, project manager, Dr. Dave Shifler).This is the author accepted manuscript. The final version is available from Elsevier via http://dx.doi.org/10.1016/j.euromechsol.2016.02.00

Compressive behavior and failure mechanisms of freestanding and composite 3D graphitic foams

Open-cell graphitic foams were fabricated by chemical vapor deposition using nickel templates and their compressive responses were measured over a range of relative densities. The mechanical response required an interpretation in terms of a hierarchical micromechanical model, spanning 3 distinct length scales. The power law scaling of elastic modulus and yield strength versus relative density suggests that the cell walls of the graphitic foam deform by bending. The length scale of the unit cell of the foam is set by the length of the struts comprising the cell wall, and is termed level I. The cell walls comprise hollow triangular tubes, and bending of these strut-like tubes involves axial stretching of the tube walls. This length scale is termed level II. In turn, the tube walls form a wavy stack of graphitic layers, and this waviness induces interlayer shear of the graphitic layers when the tube walls are subjected to axial stretch. The thickness of the tube wall defines the third length scale, termed level III. We show that the addition of a thin, flexible ceramic Al2O3 scaffold stiffens and strengthens the foam, yet preserves the power law scaling. The hierarchical model gives fresh insight into the mechanical properties of foams with cell walls made from emergent 2D layered solids.We acknowledge funding from EPSRC (Grant No. EP/K016636/1, GRAPHTED) and the ERC (Grant No. 279342, InsituNANO; Grant No. 669764, MULTILAT). A.I.A. acknowledges the 2014 Green Talents Research Stay program from The German Federal Ministry of Education and Research (BMBF) and the EU Marie Sklodowska-Curie (Grant No. 645725, FRIENDS2). K.N. acknowledges funding from the EPSRC Cambridge NanoDTC (Grant No. EP/G037221/1)

Crack growth resistance in metallic alloys: The role of isotropic versus kinematic hardening

The sensitivity of crack growth resistance to the choice of isotropic or kinematic hardening is investigated. Monotonic mode I crack advance under small scale yielding conditions is modelled via a cohesive zone formulation endowed with a traction-separation law. R-curves are computed for materials that exhibit linear or power law hardening. Kinematic hardening leads to an enhanced crack growth resistance relative to isotropic hardening. Moreover, kinematic hardening requires greater crack extension to achieve the steady state. These differences are traced to the non-proportional loading of material elements near the crack tip as the crack advances. The sensitivity of the R-curve to the cohesive zone properties and to the level of material strain hardening is explored for both isotropic and kinematic hardening

Mode I crack tip fields: Strain gradient plasticity theory versus J2 flow theory

The mode I crack tip asymptotic response of a solid characterised by strain gradient plasticity is investigated. It is found that elastic strains dominate plastic strains near the crack tip, and thus the Cauchy stress and the strain state are given asymptotically by the elastic K-field. This crack tip elastic zone is embedded within an annular elasto-plastic zone. This feature is predicted by both a crack tip asymptotic analysis and a finite element computation. When small scale yielding applies, three distinct regimes exist: an outer elastic K field, an intermediate elasto-plastic field, and an inner elastic K field. The inner elastic core significantly influences the crack opening profile. Crack tip plasticity is suppressed when the material length scale $\ell$ of the gradient theory is on the order of the plastic zone size estimation, as dictated by the remote stress intensity factor. A generalized J-integral for strain gradient plasticity is stated and used to characterise the asymptotic response ahead of a short crack. Finite element analysis of a cracked three point bend specimen reveals that the crack tip elastic zone persists in the presence of bulk plasticity and an outer J-field

Failure mechanisms of a notched CFRP laminate under multi-axial loading

A quasi-isotropic CFRP laminate, containing a notch or circular hole, is subjected to combined tension and shear, or compression. The measured failure strengths of the specimens are used to construct failure envelopes in stress space. Three competing failure mechanisms are observed, and for each mechanism splitting within the critical ply reduces the stress concentration from the hole or notch: (i) a tension-dominated mode, with laminate failure dictated by tensile failure of the 0° plies, (ii) a shear-dominated mode entailing microbuckling of the -45° plies, and (iii) microbuckling of the 0° plies under remote compression. The net section strength (for all stress states investigated) is greater for specimens with a notch than a circular hole, and this is associated with greater split development in the load-bearing plies. The paper contributes to the literature by reporting sub-critical damage modes and failure envelopes under multi-axial loading for two types of stress raiser.Financial support from Mitsubishi Heavy Industries (MHI) and the US Office of Naval Research are gratefully acknowledged.This is the author accepted manuscript. The final version is available from Elsevier via http://dx.doi.org/10.1016/j.compositesa.2015.06.00

Convective Assembly of a Particle Monolayer.

Recently, the steady-state process of convective assembly has emerged as a viable production route for colloidal monolayers. The present study models the regions of particle assembly: Region I comprises convective concentration of a particle suspension in a liquid below a meniscus, Region II comprises permeation of fluid through the dense particle monolayer, and Region III comprises capillary densification. For each region, the dominant physics and nondimensional groups are identified, and quantitative models are derived to describe the evolution of microstructure in terms of the main process parameters. The concentration profile within the assembly zone of Region I is predicted, including the role of a concentration-dependent diffusion constant and the shape of the meniscus. The fluid flow through the assembled monolayer is treated in Region II, along with a stability calculation to reveal that isolated particle clusters do not survive on top of the monolayer. The physics of capillary crystallization is addressed in Region III, with an emphasis on the density of cracks that emerge. The Peclet number and Capillary number both play important roles but in different regions of the assembly process.Part of this work was performed during Norman Fleck’s stay at INM that was supported by the Alexander von Humboldt Foundation. The authors acknowledge Eduard Arzt’s continuing support of this project.This is the author accepted manuscript. The final version is available from ACS via http://dx.doi.org/10.1021/acs.langmuir.5b0363

Water rise in a cellulose foam: By capillary or diffusional flow?

Critical experiments and predictive models reveal that water rise through a cellulose foam is initially by capillary rise, followed by non-linear diffusion in the presence of trapping sites. Classical ideas on capillary rise are supported by observations that the Washburn law is obeyed up to the Jurin height. However, water rise continues beyond the Jurin height, and this subsequent phase is diffusion-controlled according to the following evidence: the nature of the quantitative dependence of water rise upon time, the insensitivity of water rise to the direction of gravity, and the fact that the water front continues to rise in the foam after the water reservoir has been removed. Water diffusion occurs through the cellulose fibre network, along with trapping/de-trapping at molecular sites. The diffusion equations are solved numerically, and, upon comparing the predictions with the observed response, values are obtained for the diffusion constant and for the ratio of trap density to lattice density. The diffusion model explains why the drying of a damp foam is a slow process: the emptying of filled traps requires diffusion through an adjacent lattice of low water content.ERC H2020 GA-66976

Analysis of thermal desorption of hydrogen in metallic alloys

The degree of embrittlement of metallic alloys is sensitive to the concentration of absorbed hydrogen, with hydrogen traps (particularly at grain boundaries) playing an important role. Thermal desorption spectrometry (TDS) is widely used to measure the detrapping and diffusion behaviour of hydrogen in metallic alloys. However, it is problematic to obtain a consistent interpretation of TDS data from the literature, due to the large number of material parameters that influence the measurement, and this results in a wide range of quoted values for trapping parameters such as the number of trap types, trap binding energies and trap densities. In this paper, the governing partial differential equation for hydrogen diffusion with sink and source terms for a single trap is formulated in non-dimensional form, assuming local equilibrium between the hydrogen atoms at the lattice sites and the trap sites. An asymptotic analysis reveals two distinct regimes of diffusion behaviour in TDS tests. Kissinger-type behaviour is expected in a TDS test for low heating rates on an alloy with a low lattice activation energy. Contour maps of maximum hydrogen flux and the corresponding temperature are plotted using axes of trap density and trap binding energy by making use of the full numerical solution (and asymptotic solutions). These maps serve as a useful tool for an accurate and simple determination of the trap binding energy as well as the trap density.ERC H2020 GA66976

On the geometric stability of an inorganic nanowire and an organic ligand shell

The break-up of a nanowire with an organic ligand shell into discrete droplets is analysed in terms of the Rayleigh-Plateau instability. Explicit account is taken of the effect of the organic ligand shell upon the energetics and kinetics of surface diffusion in the wire. Both an initial perturbation analysis and a full numerical analysis of the evolution in wire morphology are conducted, and the governing non-dimensional groups are identified. The perturbation analysis is remarkably accurate in obtaining the main features of the instability, including the pinch-off time and the resulting diameter of the droplets. It is conjectured that the surface energy of the wire and surrounding organic shell depends upon both the mean and deviatoric invariants of the curvature tensor. Such a behaviour allows for the possibility of a stable nanowire such that the Rayleigh-Plateau instability is not energetically favourable. A stability map illustrates this. Maps are also constructed for the final droplet size and pinch-off time as a function of two non-dimensional groups that characterise the energetics and kinetics of diffusion in the presence of the organic shell. These maps can guide future experimental activity on the stabilisation of nanowires by organic ligand shells