Locking-Free Finite Elements for Unilateral Crack Problems in Elasticity

We consider mixed and hybrid variational formulations to the linearized elasticity system in domains with cracks. Inequality type conditions are prescribed at the crack faces which results in unilateral contact problems. The variational formulations are extended to the whole domain including the cracks which yields, for each problem, a smooth domain formulation. Mixed finite element methods such as PEERS or BDM methods are designed to avoid locking for nearly incompressible materials in plane elasticity. We study and implement discretizations based on such mixed finite element methods for the smooth domain formulations to the unilateral crack problems. We obtain convergence rates and optimal error estimates and we present some numerical experiments in agreement with the theoretical results

Electrochemical and Raman studies of beta-type nickel hydroxides Ni1-xCox(OH)2 electrode materials

A large variety of pure β-Ni(OH)2 and cobalt-substituted nickel hydroxides Ni1-xCox(OH)2 of well-controlled chemical composition, particle size, and morphology have been prepared and characterized by x-ray, transmission electron microscopy, electrochemical, and Raman spectrometry studies. The hydroxide particle size and its Co-substituted content were found to govern the Ni-electrode capacity. Once these parameters were controlled, β-nickel hydroxide specimens able to reversibly exchange more than one electron per metal atom (Ni + Co) were routinely prepared. β-Ni1-xCox(OH)2 Raman spectra consists of five lines. The intensities of the ones located at 3605 and 515 cm-1, were found to change as a function of the particle size and the Co content. Indeed, the line at 3605 cm-1, ascribed to adsorbed water, appears and grows when the particle size decreases (e.g., when the surface/volume ratio increases), while the line located at 515 cm-1 is enhanced by the presence of coprecipitated cobalt. A direct correlation between the intensity of the 515 cm-1 Raman line and the electrochemical capacity of the nickel hydroxide sample is found. Raman spectroscopy can then be used as a powerful nondestructive tool to differentiate "high capacity" from low capacity nickel hydroxide samples

Evidence for direct γ-NiOOH ↔ β-Ni(OH)2 transitions during electrochemical cycling of the nickel hydroxide electrode

We report on a detailed study of the γ-NiOOH → β-Ni(OH)2 phase transformation previously proposed as the origin of the second low voltage plateau, occasionally observed during the discharge of Ni-based alkaline batteries. This was done by means of intermittent galvanostatic as well as low rate potentiodynamic techniques coupled with X-ray diffraction (XRD) and transmission electron microscopy (TEM) measurements. X-ray data confirmed that the second plateau originates from the direct reduction of γ(III) into β(II). Although this phase transformation always occurred, independently of the discharge rate, near 0.8 V with an overvoltage of 400 mV, electrochemical measurements showed that its equilibrium voltage is 1.25 V. TEM measurements gave direct evidence of a textural memory effect during the γ-NiOOH ⇄ β-Ni(OH)2 phase transformation, so that a phase, called βexγ and retaining some of the layers buckling of the γ-phase, was isolated for the first time. Upon oxidation, the βexγ-phase was found to directly reconvert to the γ(III)-phase

Self-discharge of the nickel electrode in the presence of hydrogen. I. Textural study

To investigate the self-discharge mechanism in Ni/H2 cells, the interactions of hydrogen with the β-NiOOH and γ-NiOOH nickel oxyhydroxide phases were simulated in a water-loaded autoclave as functions of both temperature and pressure. Under such conditions, X-ray diffraction measurements coupled with transmission electron microscopy showed that both γ(III) and β(III) phases are reduced to a β(II) phase, thus providing direct evidence of hydrogen-nickel oxyhydroxide chemical interaction in charged Ni/H2 cells. The kinetics for such a reaction were found to be mainly controlled by temperature rather than hydrogen pressure. Partial dissolution of solid β-NiOOH and γ-NiOOH phases, followed by dissolved hydrogen reduction concomitant with an oriented nucleation growth of the reduced phase on the intact NiOOH, is proposed to account for the self-discharge mechanism observed in the autoclave

On the origin of the second low-voltage plateau in secondary alkaline batteries with nickel hydroxide positive electrodes

The nickel oxyhydroxide electrode (NOE) that acts as the positive electrode in Ni-based rechargeable alkaline batteries was studied. A survey of the influence of crystal-chemistry factors (nature and ratio of the various nickel hydroxide phases), cycling parameters (charge/discharge rates, charge/discharge cutoff voltages, and percentage of overcharge), and technological parameters (nature of the current collector, active material morphology, and type of additives) on the appearance of the second voltage plateau was performed. Direct experimental evidence shows that the appearance of the second plateau is directly linked to the amount of the γ-phase present in the nickel oxyhydroxide electrode prior to its discharge. The occasional appearance of this phase in the electrode results from a poor active material/current collector interface related to the electrode-forming technology, or to secondary reactions that can lead to a physical disconnection of the active material upon cycling. Based on these findings, the presence of this γ-phase accounts for the ohmic drop that has led to previous speculation of a barrier layer as the origin of the second plateau. Finally, tentative recommendations to eliminate or mitigate the appearance of the second plateau phenomena are given

Competition between the two reduction reactions of the γ(111) phase in the ni-based batteries

We show that the γ(III)/β(II) phase transition is at the origin of the second plateau at 0.8V in the Ni-based batteries by means of transmission electron microscopy (TEM) and X-ray diffraction (XRD) studies and intermittent galvanostatic measurements (GITT). This study shows that the equilibrium voltage of this transition is 1.25V vs Cd-Cd(OH) 2, thus implying an overvoltage of 400 mV. Direct evidence for a textural memory effect trough the γ(III)/β(II) phase transition is given by TEM studies. The reoxidation of the β(II) phase to γ(III) phase occurs without going trough the β(III) phase. © 1998 OPA (Overseas Publishers Association) Amsterdam B.V. Published under license under the Gordon and Breach Science Publishers imprint