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Detachment of an adhered micropillar from a dissimilar substrate
Abstract The mechanics of detachment is analysed for 2D flat-bottomed planar pillars and 3D cylindrical pillars from a dissimilar elastic substrate. Application of an axial stress to the free end of the pillar results in a singularity in stress at the corner with the substrate. An eigenvalue analysis reveals that the stress field near the corner is dominated by two singular eigenfields having eigenvalues ( λ 1 , λ 2 ) with corresponding intensities ( H 1 , H 2 ) . The asymptotic stress field σij is of the form σ ij = H 1 r λ 1 − 1 f ij ( λ 1 , θ ) + H 2 r λ 2 − 1 f ij ( λ 2 , θ ) , where fij describe the angular dependence θ of σij, and r is the radial distance from the corner. The stress intensities ( H 1 , H 2 ) are calculated numerically, using a domain integral approach, as a function of the elastic mismatch between the pillar and substrate. The singular zone extends across approximately 10 of the pillar diameter (in 3D) or pillar width (in 2D). Interfacial failure is predicted for an assumed crack emanating from the corner of pillar and substrate. For the case of an interfacial crack that resides within the domain of corner singularity, a boundary layer analysis is performed to calculate the dependence of the interfacial stress intensity factor K upon ( H 1 , H 2 ) . When the crack extends beyond the domain of corner singularity, it is necessary to consider the full geometry in order to obtain K. A case study explores the sensitivity of the pull-off stress to the flaw size and to the degree of material mismatch. The study has implications for the optimum design of adhesive surface micropatterns, for bonding to either stiffer or more compliant substrates.
Vacancy diffusion and its consequences for void growth at the interface of a stripping metal electrode and solid electrolyte
It is commonly observed that voids can nucleate and grow in the lithium anode of a solid state Li-ion battery at a location adjacent to the solid electrolyte during the stripping (discharge) phase of the battery; a similar phenomenon is observed in sodium-based batteries. It is hypothesised in the current literature that the formation of these voids is due to the coalescence of vacancies that have been generated at the electrode/electrolyte interface when metal atoms are oxidized and transported into the electrolyte: the slow diffusion of the vacancies away from the electrolyte interface into the adjacent electrode results in their coalescence and the consequent growth of voids. These hypotheses are challenged in the current study by using the Onsager formalism to generate a variational principle for vacancy diffusion. Our analysis reveals that no driving force exists for the diffusion of vacancies into a homogeneous metal electrode that thins by stripping. This finding is contrary to models in the literature which have mistakenly assumed that the vanishing flux at the current collector prevents rigid body motion (drift) of the electrode which in turn prevents thinning of the electrode during stripping. Based on our analysis, we conclude that vacancy diffusion within a homogeneous electrode is not responsible for the nucleation and growth of voids at the interface between a stripping metal electrode and a solid electrolyte.
Cracking and associated volumetric expansion of NMC811 secondary particles
Secondary particles comprising a large number of nickel-rich single crystal primary particles are extensively used as storage particles in cathodes of lithium-ion batteries. It is well-established that crack formation in secondary particles is an important degradation mode that contributes to decline in battery performance. Recent X-ray tomographic observations suggest that, at very low C-rates, concentration gradients of lithium within an NMC811 secondary particle are negligible yet cracking still occurs. Additionally, during delithiation the primary particles shrink yet a volumetric expansion of the secondary particle occurs. These observations are explained by a numerical model of distributed cracking due to the extreme anisotropy of lithiation strain of primary particles. The incompatible deformation from grain to grain induces large self-stresses even in the absence of spatial gradients in the lithium concentration. The stress state is sufficient to drive a dynamic catastrophic fracture event, and the associated kinetic energy acquired by the primary particles moves them apart (akin to an explosive event) with the carbon and binder domain surrounding each secondary particle restricting the outward motion of the primary particles. It is predicted that a volume expansion of the secondary particles on the order of 20 % accompanies cracking, in agreement with recently reported observations.
Numerical simulation of the edge stress singularity and the adhesion strength for compliant mushroom fibrils adhered to rigid substrates
Bio-inspired adhesion of micropatterned surfaces due to intermolecular interactions has attracted much research interest over the last decade. Experiments show that the best adhesion is achieved with compliant “mushroom”-shaped fibrils. This paper analyses numerically the effects of different mushroom shapes on adhesion to a rigid substrate. When a remote stress is applied on the free end of a fibril perfectly bonded to a rigid substrate, the resultant stress distribution along the fibril is found to change dramatically between the straight punch and mushroom fibrils. A singular stress field is present at the edge of the fibril where it contacts the substrate and, in this work, the amplitude of the singularity is evaluated for fibrils perfectly bonded to a flat substrate so that sliding cannot occur there. This exercise is carried out for fibril geometries involving combinations of different diameters and thicknesses of the mushroom cap. By assuming a pre-existing detachment length at the corner where the stress singularity lies, we predict the adhesive strength for various mushroom cap shapes. Our study shows that a smaller stalk diameter and a thinner mushroom cap lead to higher adhesive strengths. A limited number of results are also given for other shapes, including those having a fillet radius connecting the stalk to the cap. The results support the rational optimization of synthetic micropatterned adhesives.