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-

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

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

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

Perforation of aluminium alloy-CFRP bilayer plates under quasi-static and impact loading

The ability of a metallic surface layer to protect CFRP cross-ply plates against perforation is explored. Aluminium alloy plates (either AA1050A or AA6082-T6) were placed in front of a CFRP layer, and the bilayer was subjected to either quasi-static indentation or to ballistic impact by a spherical projectile, with rigid back support or an edge-clamped boundary condition. The observed perforation mechanism of the CFRP layer is neither influenced by the presence of the metallic layer nor by the choice of loading rate (i.e. quasi-static versus ballistic). In the back-supported condition, the CFRP layers fail by an indirect tension mode that consists of tensile failure of plies in the material directly beneath the indenter or projectile. Alternatively, in the edge-clamped condition, the CFRP layers fail by a shear plugging mechanism. Although the presence of metallic layers does not suppress the shear plugging of the underlying CFRP layer, the loaded area in the CFRP layer increases by the addition of the protective metallic layer, thereby increasing the perforation resistance of the CFRP layer.he research work was sponsored by the Office of Naval Research (ONR), U.S. (Prime Award No. N62909-14-1-N232). The raw composite materials and the autoclave manufacturing process were generously provided by Hexcel Ltd. Finally, the doctoral study of one of the authors (B. Yu) was sponsored by the Croucher Foundation and the Cambridge Commonwealth, European & International Trust