A. Juhász

Holomorphic discs and sutured manifolds

In this paper we construct a Floer-homology invariant for a natural and wide class of sutured manifolds that we call balanced. This generalizes the Heegaard Floer hat theory of closed three-manifolds and links. Our invariant is unchanged under product decompositions and is zero for nontaut sutured manifolds. As an application, an invariant of Seifert surfaces is given and is computed in a few interesting cases.

Investigation of the superplasticity of tin―lead eutectic by impression creep tests

The superplasticity of the Pb-Sn eutectic was investigated in the temperature range of 283 to 340 K. The strain-rate sensitivity, the activation energy and the activation volume were determined by impression creep measurements at various strain rates and temperatures. The results obtained are in good agreement with the results of conventional unidirectional tensile tests, which show that the simple and economic impression creep test can lead to equivalent results with the conventional creep test.

Indentation creep in a short fibre-reinforced metal matrix composite

Abstract Creep properties of an unreinforced M124 (AlSi12CuMgNi) base alloy and an Al 2 0 3 (Saffil) fibre reinforced M124+s metal matrix composite (MMC) were investigated by indentation tests performed between 250 and 350°C. It has been found that the creep curve of the base alloy consists of two stages (transient and steady state), whereas the curve of the composite material contains a decelerating third stage as well. This creep behavior is correlated with the changes of the microstructure below the indenter during the deformation process. In the region of steady state creep the stress exponent and the activation energy was determined for both materials.

A new method for hardness determination from depth sensing indentation tests

A new semiempirical formula is developed for the hardness determination of the materials from depth sensing indentation tests. The indentation works measured both during loading and unloading periods are used in the evaluation. The values of the Meyer hardness calculated in this way agree well with those obtained by conventional optical observation, where this latter is possible. While the new hardness formula characterizes well the behavior of the conventional hardness number even for the ideally elastic material, the mean contact pressure generally used in hardness determination differs significantly from the conventional hardness number when the ideally elastic limiting case is being approached.

Cobordisms of sutured manifolds and the functoriality of link Floer homology

Abstract It has been a central open problem in Heegaard Floer theory whether cobordisms of links induce homomorphisms on the associated link Floer homology groups. We provide an affirmative answer by introducing a natural notion of cobordism between sutured manifolds, and showing that such a cobordism induces a map on sutured Floer homology. This map is a common generalization of the hat version of the closed 3-manifold cobordism map in Heegaard Floer theory, and the contact gluing map defined by Honda, Kazez, and Matic. We show that sutured Floer homology, together with the above cobordism maps, forms a type of TQFT in the sense of Atiyah. Applied to the sutured manifold cobordism complementary to a decorated link cobordism, our theory gives rise to the desired map on link Floer homology. Hence, link Floer homology is a categorification of the multi-variable Alexander polynomial. We outline an alternative definition of the contact gluing map using only the contact element and handle maps. Finally, we show that a Weinstein sutured manifold cobordism preserves the contact element.

Occurrence of plastic instabilities in dynamic microhardness testing

Plastic instabilities were observed to appear during dynamic ultramicrohardness testing of a solid solution Al–3.3 wt.% Mg alloy. The tests were carried out at room temperature with a Vickers hardness indenter in a computer-controlled dynamic ultramicrohardness testing machine. During the tests the applied load was increased from 0 to 2000 mN at constant loading rate. The instabilities appear as characteristic steps in the continuously recorded load-indentation depth curves. The physical basis for the occurrence of the instabilities is the interaction between moving dislocations and solute atoms, a phenomenon termed in the literature as serrated yielding, jerky flow, or Portevin-Le Châtelier effect. The instabilities start at a critical load, F c , in the depth-load curve. Varying the loading rate, μ, by two orders of magnitude F c was found to increase linearly with the loading rate.

The decategorification of sutured Floer homology

We define a torsion invariant T for every balanced sutured manifold (M, γ), and show that it agrees with the Euler characteristic of sutured Floer homology (SFH). The invariant T is easily computed using Fox calculus. With the help of T, we prove that if (M, γ) is complementary to a Seifert surface of an alternating knot, then SFH(M, γ) is either 0 or ℤ in every Spin c structure. The torsion invariant T can also be used to show that a sutured manifold is not disc decomposable, and to distinguish between Seifert surfaces.The support of SFH gives rise to a norm z on H 2 (M, ∂ M; ℝ). The invariant T gives a lower bound on the norm z, which in turn is at most the sutured Thurston norm x s . For closed 3-manifolds, it is well known that Floer homology determines the Thurston norm, but we show that z<x s can happen in general. Finally, we compute T for several wide classes of sutured manifolds.

Determination of the hardness and elastic modulus from continuous Vickers indentation testing

Continuous Vickers (Hv) indentation tests were performed on different materials (ion crystals, metals, ceramics, silica glass and plastic). Load-indentation depth curves were taken during the loading as well as during the unloading period by a computer controlled hydraulic mechanical testing machine (MTS 810). The indentation work measured both the loading and the unloading periods, and these were used for the evaluation of parameters characterizing the materials. It was found empirically that there were linear connections between the maximum load to the power 3/2 and the indentation work. These connections were used to relate the conventional hardness number, Hv, and Youngs modulus, E, with the work performed during loading and unloading. This work can be determined with great accuracy from the measurements. The values of the Youngs modulus and the Vickers hardness determined this way agree well with those obtained by conventional methods. On the basis of continuous indentation tests, materials can be easily classified into the isomechanical groups introduced by Ashby. For this classification the Hv/E ratio is generally used. As a substitute for Hv/E another parameter is recommended which can be determined easily from a single measurement.

Indentation test for the investigation of high-temperature plasticity of materials

High-temperature behaviour of materials has been investigated by indentation creep methods. Materials investigated belong to three typical groups of materials: glasses, pure metals and alloys. Indentation tests were performed with flat-ended cylindrical and hemispherical punches. It is shown that the hemispherical punch is also proper for the determination of the high-temperature creep characteristics of the materials investigated. It is also proved that there is a unique correspondence between the results obtained by the two indentation methods.

Indentation tests for the investigation of the plasticity of glasses

Various types of indentation tests are used to investigate the plasticity of glassy materials. It is shown that indentation creep tests performed with both flat ended cylindrical and hemispherical indenters are suitable for viscosity measurements in the viscosity range of 108–1011Pa·s. It is also shown that the activation energy of the flow process can be evaluated from the results of indentation measurements.