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One of the contentious issues associated with the high-cycle fatigue of Nitinol, a nominally equiatomic alloy of nickel and titanium, is the claim that increasing the applied mean strain can increase, or at least have no negative impact, on the fatigue lifetime, in conflict with reported behavior for the vast majority of other metallic materials. To investigate this in further detail, cyclic fatigue tests in bending were carried out on electropolished medical grade Nitinol at 37 °C for lives of up to 400 million cycles of strain involving various levels of the mean strain. A constant life model was developed through statistical analysis of the fatigue data, with 90% reliability at a confidence level of 95% on the effective fatigue strain. Our results show that the constant life diagram, a plot of strain amplitude versus mean strain, is monotonic yet nonlinear for lives of 400 million cycles of fatigue loading. Specifically, we find that in contradiction to the aforementioned claim, the strain amplitude limit at zero mean strain is 0.55% to achieve a 400 million cycle lifetime, at 90% reliability with 95% confidence; however, to achieve the same lifetime, reliability and confidence level in the presence of a 3% or more mean strain, the required strain amplitude limit is decreased by over a factor of three to 0.16%. Moreover, for mean strains from 3% to 7%, the strain amplitude limit that allows a 400 million cycle lifetime, at 90% reliability with 95% confidence, is ~ 0.16%, and essentially independent of mean strain. We conclude that the debatable claim that an increase in the applied mean strain can increase the fatigue life of Nitinol components is not supported by the current data.

The most widely-used representation of the compressible, isotropic, neo-Hookean hyperelastic model is considered in this paper. The version under investigation is that which is implemented in the commercial finite element software ABAQUS, ANSYS and COMSOL. Transverse stretch solutions are obtained for the following homogeneous deformations: uniaxial loading, equibiaxial loading in plane stress, and uniaxial loading in plane strain. The ground-state Poisson’s ratio is used to parameterize the constitutive model, and stress solutions are computed numerically for the physically permitted range of its values. Despite its broad application to a number of engineering problems, the physical limitations of the model, particularly in the small to moderate stretch regimes, are not explored. In this work, we describe and analyze results and make some critical observations, underlining the model’s advantages and limitations. For example, a snap-back feature of the transverse stretch is identified in uniaxial compression, a physically undesirable behavior unless validated by experimental data. The domain of this non-unique solution is determined in terms of the ground-state Poisson’s ratio and the state of stretch and stress. The analyses we perform are essential to enable the understanding of the characteristics of the standard, compressible, isotropic, neo-Hookean model used in ABAQUS, ANSYS and COMSOL. In addition, our results provide a framework for the parameter-fitting procedure needed to characterize this standard, compressible, isotropic neo-Hookean model in terms of experimental data.

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.

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.

In a simple and interesting theory of ultratough peeling of an elastic tape from a viscoelastic substrate, Afferrante and Carbone find that there are conditions for which the load for steady state peeling could be arbitrarily large in steady state peeling, at low angles of peeling - what they call "ultratough" peeling (Afferrante, L., Carbone, G., 2016, The ultratough peeling of elastic tapes from viscoelastic substrates, Journal of the Mechanics and Physics of Solids, 96, pp.223-234). Surprisingly, this seems to lead to toughness enhancement higher than the limit value observed in a very large crack in an infinite viscoelastic body, possibly even considering a limit on the stress transmitted. The Afferrante-Carbone theory seems to be a quite approximate, qualitative theory and many aspects and features of this "ultratough" peeling (e.g. conformity with the Rivlin result at low peel angles) are obtained also through other mechanisms (Begley, M.R., Collino, R.R., Israelachvili, J.N., McMeeking, R.M., 2013, Peeling of a tape with large deformations and frictional sliding, Journal of the Mechanics and Physics of Solids, 61(5), pp. 1265-1279) although not at “critical velocities”. Experimental and/or numerical verification would be most useful.

The mechanics of detachment is analysed for 2 D flat-bottomed planar pillars and 3 D 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 σ ij is of the form σ ij = H 1 r λ1-1 f ij (λ 1 , θ)+H 2 r λ2−1 f ij (λ 2 , θ) , where f ij describe the angular dependence θ of σ ij , 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 3 D) or pillar width (in 2 D). 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.

The adhesion of micron-scale surfaces due to intermolecular interactions is a subject of intense interest spanning electronics, biomechanics and the application of soft materials to engineering devices. The degree of adhesion is sensitive to the diameter of micro-pillars in addition to the degree of elastic mismatch between pillar and substrate. Adhesion-strength-controlled detachment of an elastic circular cylinder from a dissimilar substrate is predicted using a Dugdale-type of analysis, with a cohesive zone of uniform tensile strength emanating from the interface corner. Detachment initiates when the opening of the cohesive zone attains a critical value, giving way to crack formation. When the cohesive zone size at crack initiation is small compared to the pillar diameter, the initiation of detachment can be expressed in terms of a critical value Hc of the corner stress intensity. The estimated pull-off force is somewhat sensitive to the choice of stick/slip boundary condition used on the cohesive zone, especially when the substrate material is much stiffer than the pillar material. The analysis can be used to predict the sensitivity of detachment force to the size of pillar and to the degree of elastic mismatch between pillar and substrate.

The adhesion of a punch to a linear elastic, confined layer is investigated. Numerical analysis is performed to determine the equivalent elastic modulus in terms of layer confinement. The size of the layer relative to the punch radius and its Poisson?s ratio are found to affect the layer stiffness. The results reveal that the equivalent modulus of a highly confined layer depends on its Poisson?s ratio, whereas, in contrast, an unconfined layer is only sensitive to the extent of the elastic film. The solutions of the equivalent modulus obtained from the simulations are fitted by an analytical function that, subsequently, is utilized to deduce the energy release rate for detachment of the punch via linear elastic fracture mechanics. The energy release rate strongly varies with layer confinement. Regimes for stable and unstable crack growth can be identified that, in turn, are correlated to interfacial stress distributions to distinguish between different detachment mechanisms.

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 optimisation of synthetic micropatterned adhesives.

Bio-inspired fibrillar surfaces with reversible adhesion to stiff substrates have been thoroughly investigated over the last decade. In this paper we propose a novel composite fibril consisting of a soft tip layer and stiffer stalk with differently shaped interfaces (flat vs. curved) between them. A tensile stress is applied remotely on the free end of the fibril whose other end adheres to a rigid substrate. The stress distributions and the resulting adhesion of such structures were numerically investigated under plane strain ( 2 D ) and axisymmetric ( 3 D ) conditions. The stress intensities were evaluated for different combinations of layer thickness and Young’s moduli. The adhesion strength values were found to increase for thinner layers and larger modulus ratio; these trends are also reflected in selected experimental results. The results of this paper provide a new strategy for optimizing adhesion strength of fibrillar surfaces.