Search for conditions of compressive fracture of hard brittle ceramics at impact loading

In this paper we discuss three different experimental configurations to diagnosing the modes of inelastic deformation and to evaluating the failure thresholds at shock compression of hard brittle solids. One of the manifestations of brittle material response is the failure wave phenomenon, which has been previously observed in shock-compressed glasses. However, based on the measurements from our “theory critical” experiments, both alumina and boron carbide did not exhibit this phenomenon. In experiments with free and pre-stressed ceramics, while the Hugoniot elastic limit (HEL) in high-density B₄C ceramic was found to be very sensitive to the transverse stress, it was found relatively less sensitive in Al₂O₃, implying brittle response of the boron carbide and ductile behavior of alumina. To further investigate the effects of stress states on the shock response of brittle materials, a “divergent flow or spherical shock wave” based plate impact experimental technique was employed to vary the ratio of longitudinal and transversal stresses and to probe conditions for compressive fracture thresholds. Two different experimental approaches were considered to generate both longitudinal and shear waves in the target through the impact of convex flyer plates. In the ceramic target plates, the shear wave separates a region of highly divergent flow behind the decaying spherical longitudinal shock wave and a region of low-divergent flow. Experiments with divergent shock loading of alumina and boron carbide ceramic plates coupled with computer simulations demonstrated the validity of these experimental approaches to develop a better understanding of fracture phenomena.     

Hyers-Ulam stability of an iterative equation for strictly increasing continuous functions

Aequationes mathematicae - The Hyers-Ulam stability of the iterative equation $$f^n=F$$ for continuous functions F was studied under the assumptions that F is a homeomorphism on its range, and the...     

Crystal Structure of Dimeric Cu(II) Complex {μ,μ'‐acetato O,O bis [N‐salicylidene‐2‐amino‐pyridine‐methanolato N,N,O]} : perchlorate

The crystal structure of the title complex has been solved using X‐ray diffraction data.The compound crystallizes from aqueous ethanol solvent in the triclinic system, space group P‐1, with unit cell parameters: a = 8.9532(1), b = 12.7423(3), c = 14.9012(3) Å, α = 73.767(1), β = 75.322(1), γ = 77.496(1)°, Z = 2, V = 1559.4(5) ų. The trial structure was determined by automated Patterson methods and subsequent difference Fourier techniques using DIRDIF98 and refined to a final R‐factor of 0.064. The copper ion Cu1 adopts a (4+1) square‐pyramidal geometry defined by the tridentate N‐salicylidimine dianions and the neutral monodentate pyridine ligand in the basal plane. The apical position is occupied by a solvent methanol molecule at a distance of 2.341(4) Å. The copper Cu2 adopts a square‐planar geometry.