Dov Sherman

Low-speed fracture instabilities in a brittle crystal

When a brittle material is loaded to the limit of its strength, it fails by the nucleation and propagation of a crack. The conditions for crack propagation are created by stress concentration in the region of the crack tip and depend on macroscopic parameters such as the geometry and dimensions of the specimen. The way the crack propagates, however, is entirely determined by atomic-scale phenomena, because brittle crack tips are atomically sharp and propagate by breaking the variously oriented interatomic bonds, one at a time, at each point of the moving crack front. The physical interplay of multiple length scales makes brittle fracture a complex ‘multi-scale’ phenomenon. Several intermediate scales may arise in more complex situations, for example in the presence of microdefects or grain boundaries. The occurrence of various instabilities in crack propagation at very high speeds is well known, and significant advances have been made recently in understanding their origin. Here we investigate low-speed propagation instabilities in silicon using quantum-mechanical hybrid, multi-scale modelling and single-crystal fracture experiments. Our simulations predict a crack-tip reconstruction that makes low-speed crack propagation unstable on the (111) cleavage plane, which is conventionally thought of as the most stable cleavage plane. We perform experiments in which this instability is observed at a range of low speeds, using an experimental technique designed for the investigation of fracture under low tensile loads. Further simulations explain why, conversely, at moderately high speeds crack propagation on the (110) cleavage plane becomes unstable and deflects onto (111) planes, as previously observed experimentally.

The ballistic failure mechanisms and sequence in semi-infinite. supported alumina tiles

The basic ballistic failure mechanisms and their sequence occurring in dense alumina tiles during projectile penetration were investigated. The alumina tiles were supported by semi-infinite support blocks made of three different materials. Initially, a drop-weight test (DWT) was used to gain an insight into the damage mechanisms and sequence during quasi-static impact conditions. The quasi-static damage mechanisms were compared with the damage obtained in 0.3 cal. armor-piercing tests (APT). The DWTs results suggested the following sequence of quasi-static failure mechanisms: Radial tensile cracks, associated with the low tensile strength of the ceramic formed initially, as a result of the bending induced by local deformation at the opposing surface. Subsequently, a shear-dominated cone crack propagated from the edge of the contact zone. If sufficient energy was available, crushing of the material beneath the contact zone developed during the final stages of failure. It is shown that these so-called “quasi-static” damage mechanisms, identified from the DWTs, also corresponded to the damage mechanisms and sequence during APTs.

On the lower limiting velocity of a dynamic crack in brittle solids

The existence of forbidden velocity gap in dynamic crack propagation in brittle crystals has been proposed previously, based on analytical calculations and numerical simulations. These suggested that the minimal velocity of a dynamically propagating crack is a significant portion of the Rayleigh wave speed. On the other hand, theoretical analysis based on continuum mechanics does not identify any lower limit to the crack velocity. In this work, we studied experimentally the crack velocity in glass and single-crystal silicon, in a geometry that constrains the crack profile to a nearly quarter elliptical shape, such that at a certain part of the crack it is forced to move appreciably slowly. Direct measurements show that the crack velocity along this profile decreases to less than 1% of the Rayleigh wave speed, both at room temperature and at 77 K, which is notably below the expected velocity gap.

A solvent free process for the generation of strong, conducting carbon spheres by the thermal degradation of waste polyethylene terephthalate

An efficient, solvent-free, catalyst-free approach is reported for the synthesis of strong, paramagnetic, conducting carbon microspheres from used polyethylene terephthalate (PET). The thermal decomposition of used PET polymer at 700 °C for 3 h in a closed reactor under autogenic [self generating] pressure yielded exceptionally hard spherical (2 to 10 μm diameters) solid carbon bodies, with the average tensile strength for a single [∼6 μm diameter] carbon sphere calculated to be 8.30 ± 0.69 GPa.

Shape and energies of a dynamically propagating crack under bending

We report on the exact shape of a propagating crack in a plate with a high width/thickness ratio and subjected to bending deformation. Fracture tests were carried out with brittle solids-single crystal, polycrystalline, and amorphous. The shape of the propagating crack was determined from direct temporal crack length measurements and from the surface perturbations generated during rapid crack propagation. The shape of the crack profile was shown to be quarter-elliptical with a straight, long tail; the governing parameter of the ellipse axes is the specimens thickness at most length of crack propagation. Universality of the crack front shape is demonstrated. The continuum mechanics approach applicable to two-dimensional problems was used in this three-dimensional problem to calculate the quasistatic strain energy release rate of the propagating crack using the formulations of the dynamic energy release rate along the crack loci. Knowledge of the crack front shape in the current geometry and loading configuration is important for practical and scientific aspects.

Mechanical properties of hard materials and their relation to microstructure

The design of components for applications requiring high stiffness, hardness and wear resistance under extreme conditions of load and temperature leaves little choice for materials selection outside the realm of hard materials. But a combination of advances in materials and process development has led to a significant reduction in the uncertainties and risks associated with the estimation of mechanical failure probabilities and component for brittle materials in service.

Macroscopic scattering of cracks initiated at single impurity atoms

Brittle crystals, such as coloured gems, have long been known to cleave with atomically smooth fracture surfaces, despite being impurity laden, suggesting that isolated atomic impurities do not generally cause cracks to deflect. Whether cracks can ever deviate when hitting an atomic defect, and if so how they can go straight in real brittle crystals, which always contain many such defects, is still an open question. Here we carry out multiscale molecular dynamics simulations and high-resolution experiments on boron-doped silicon, revealing that cracks can be deflected by individual boron atoms. The process, however, requires a characteristic minimum time, which must be less than the time spent by the crack front at the impurity site. Deflection therefore occurs at low crack speeds, leading to surface ridges which intensify when the boron-dopage level is increased, whereas fast-moving cracks are dynamically steered away from being deflected, yielding smooth cleavage surfaces.

Fracture mechanisms of sapphire under bending

The fracture mechanisms of a rapidly advancing crack in a single crystal are under investigation. Thin sapphire plates parallel to the basal plane were used as a model material for this purpose. Tests in three point bending (3PB) were carried out with smooth and with notched thin strip-shaped specimens having three different orientations with respect to the (10―10) plane. The effect of the orientation on the fracture mechanisms is discussed and explained. Unique behavior was observed in the 3PB loading configuration, resulted from the typical state of stress in bending, i.e., tension in the lower, and compression in the upper region of the beam, which affected the fracture mechanisms. The continual changes of the crack direction and energy revealed a large spectrum of fracture phenomena. The major phenomena are explained. The effect of the mechanical energy on fracture mechanisms and topology is discussed.

Decay of elastic waves in alumina

The dynamic response of alumina under shock compression was studied using planar impact experiments with different tile thicknesses. Stress-time measurements were made with manganin gauges backed by different backing materials in order to optimize gauge response. The results show an apparent decay in the Hugoniot elastic limit with propagation distance. However, further analysis reveals that this phenomenon is probably a measurement artifact, resulting from the relatively slow response times of manganin gauges.

The mechanical behavior of layered brazed metal/ceramic composites

Brazing as a method of joining thin metal and ceramic plates to form a layered composite for structural applications is examined. The constituents are Ti-6Al-4V alloy sheets and alumina thin plates and the brazing alloy is 63 wt% Ag, 1.75 Ti and bal. Cu active braze alloy. The interfacial shear strength of the joint is relatively high, which makes it attractive for structural applications. A model Ti alloy/alumina bilayer and laminate joined by active brazing was evaluated for its basic mechanical behavior. The bilayer structure tested under bending exhibited improved properties when the alumina layer was under compression during loading. In that case, a combination of the high compressive strength of ceramics, the high toughness of metals and the high shear strength of the interface are causes of the improved mechanical properties when compared with those of the monolithic metal. Using composite beam theory, the properties of bilayers were evaluated for design purposes and, in particular, the interfacial shear strength. The laminated structure tested under bending showed reduced strength but improved undamaged stiffness when compared with the metal constituent.