Large-Deflection Solution of the Coaxial-Ring-Circular-Glass-Plate Flexure Problem

Abstract

octahedral edge. In a disordered inverse spinel each octahedral cation has, on an average, 3 divalent and 3 trivalent neighbors. In a completely ordered inverse spinel, each divalent cation has 4 trivalent near neighbors and vice versa. Ordering within the octahedral sublattice would thus minimize the electrostatic repulsion of near neighbors of like charge relative to the average charge on the sublattice.Romeijn'l proposed that short range order within the octahedral sublattice exists in all inverse spinels. Assuming such short range order exists in Mg ferrite, the incomplete inversion of the structure requires that there always be Fe3+ ions on octahedral sites preferentially occupied by M e ions. If the octahedral sublattice were disordered, there would be no distinction between octahedral sites. In an incompletely inverse spinel, therefore, the greater the degree of order within the octahedral sublattice the greater would be the driving force for replacing the extra Fe" ions by Mg2+ ions from the tetrahedral sites. Simultaneously, the greater the degree of inversion the greater would be the driving force, once initiated, for octahedral sublattice ordering.Octahedral sublattice ordering and inversion would then occur cooperatively and result in the increasing rate of inversion with increasing degree of inversion, yielding the rapid emergence of the equilibrium phase in regions where random fluctuations first initiate ordering. Octahedral sublattice ordering, like the ordering in metallic systems, would require random fluctuations to initiate order regardless of the degree of inversion in the structure. The short range nature of the octahedral sublattice order would assure that some regions remained disordered (ultimately those comprising the antiphase domain walls). These would be the last regions to become inverted and would help account for the persistence of the high-temperature phase. V. Summary and ConclusionsThe transformation of MgFe,04 from the high-temperature random spinel structure to the "more inverse" lowtemperature structure does not occur uniformly throughout a ferrite body. Regions of the equilibrium structure appear to nucleate and grow from a matrix of constant disorder. (3) 102 [4] 857-60 (1956).

Effect of residual stress on the fracture of chemically strengthened thin aluminosilicate glass

“…Thus, large-deflection theory should be considered when analyzing the flexural strength of chemically strengthened thin aluminosilicate glass [7].…”

“…If the uncommon small-deflection theory is considered, then the strength value obtained would be significantly high because the membrane stress from the large deflection is neglected. Consequently, the rigorous large-deflection theory is required to convert failure load to failure stress (strength) of a glass substrate [7][8][9].…”

Fracture test of thin sheet electrolytes for solid oxide fuel cells

“…The critical deflection depends on the ratio of the loading to supporting ring and is ∼50% of the specimen thickness for a ratio of two. [11][12][13] At such large deflections the specimen stress has a localized maximum above the loading ring, contrary to the small deflection situation with a constant tensile stress within the specimen portion defined by the loading ring. Thus fracture of thin sheet electrolyte specimens will occur preferentially above the loading ring.…”

Improvement in the Specific Strength by Arranging Closed Pores in Fully Densified Zirconia Ceramics

“…Consequently, many nonlinear strengthening or toughening mechanisms have been proposed. [1][2][3][4][5][6] One of the most extreme examples is a SiC-SiC composite, [7][8][9][10][11] for which the strength or toughness is improved substantially, although the dispersoid is the same as the matrix (D ¼ M).…”