Processing maps for hot-working of powder metallurgy 1100 Al-10 vol % SiC-particulate metal-matrix composite

The hot-working characteristics of the metal-matrix composite (MMC) Al-10 vol % SiC-particulate (SiCp) powder metallurgy compacts in as-sintered and in hot-extruded conditions were studied using hot compression testing. On the basis of the stress-strain data as a function of temperature and strain rate, processing maps depicting the variation in the efficiency of power dissipation, given by eegr = 2m/(m+1), where m is the strain rate sensitivity of flow stress, have been established and are interpreted on the basis of the dynamic materials model. The as-sintered MMC exhibited a domain of dynamic recrystallization (DRX) with a peak efficiency of about 30% at a temperature of about 500°C and a strain rate of 0.01 s�1. At temperatures below 350°C and in the strain rate range 0.001�0.01 s�1 the MMC exhibited dynamic recovery. The as-sintered MMC was extruded at 500°C using a ram speed of 3 mm s�1 and an extrusion ratio of 10ratio1. A processing map was established on the extruded product, and this map showed that the DRX domain had shifted to lower temperature (450°C) and higher strain rate (1 s�1). The optimum temperature and strain rate combination for powder metallurgy billet conditioning are 500°C and 0.01 s�1, and the secondary metal-working on the extruded product may be done at a higher strain rate of 1 s�1 and a lower temperature of 425°C.

Relationship Between The Impedance Matrix And The Transfer Matrix With Specific Reference To Symmetrical, Reciprocal And Conservative Systems

Impedance matrix and transfer matrix methods are often used in the analysis of linear dynamical systems. In this paper, general relationships between these matrices are derived. The properties of the impedance matrix and the transfer matrix of symmetrical systems, reciprocal systems and conservative systems are investigated. In the process, the following observations are made: (a) symmetrical systems are not a subset of reciprocal systems, as is often misunderstood; (b) the cascading of reciprocal systems again results in a reciprocal system, whereas cascading of symmetrical systems does not necessarily result in a symmetrical system; (c) the determinant of the transfer matrix, being ±1, is a property of both symmetrical systems and reciprocal systems, but this condition, however, is not sufficient to establish either the reciprocity or the symmetry of the system; (d) the impedance matrix of a conservative system is skew-Hermitian.

The superheating of Pb embedded in a Zn matrix the role of interface melting

Evidence of a shape-dependent superheating of entrained nanosized Pb particles in a Zn matrix has been presented. It is shown that size dependence and pressure effects cannot explain the observed differences in melting points. The importance of crystallography and morphology at the microlevel at the interphase interface in controlling interfacial melting has been emphasized in order to explain the melting of entrained particles.

Heterogeneous nucleation of pb particles embedded in a Zn matrix

Zinc-10 and 20 wt pct Pb alloys have been rapidly solidified by melt spinning to obtain a very fine scale dispersion of nanometer-sized Pb particles embedded in Zn matrix. The microstructure and crystallography of the Pb particles have been studied using transmission electron microscopy (TEM). Each embedded Pb particle is a single crystal, with a truncated hexagonal biprism shape with the 6/mmm Zn matrix point group symmetry surrounded by and { 0001 á },\text { \text10[`\text1] \text0 },\text and { \text10[`\text1] \text1 }0001 1010 and 1011 facets. The Pb particles solidify with a well-defined orientation relationship with the Zn matrix of ( 0001 )Zn ||(111)Pb\text and\text [ \text11[`\text2] \text0 ]Zn| ||[ 1[`1] 0 ]Pb 0001Zn(111)Pb and 1120Zn110Pb . The melting and solidification behavior of the Pb particle have been studied using differential scanning calorimetry (DSC). The Pb particles solidify with an undercooling of approximately 30 K, by heterogeneous nucleation on the {0001} facets of the surrounding Zn matrix, with an apparent contact angle of 23 deg.

Growing pseudo-eigenmodes and positive logarithmic norms in rotating shear flows

Rotating shear flows, when angular momentum increases and angular velocity decreases as functions of radiation coordinate, are hydrodynamically stable under linear perturbation. The Keplerian flow is an example of such a system, which appears in an astrophysical context. Although decaying eigenmodes exhibit large transient energy growth of perturbation which could govern nonlinearity in the system, the feedback of inherent instability to generate turbulence seems questionable. We show that such systems exhibiting growing pseudo-eigenmodes easily reach an upper bound of growth rate in terms of the logarithmic norm of the involved non-normal operators, thus exhibiting feedback of inherent instability. This supports the existence of turbulence of hydrodynamic origin in the Keplerian accretion disc in astrophysics. Hence, this answers the question of the mismatch between the linear theory and experimental/observed data and helps in resolving the outstanding question of the origin of turbulence therein.

Characteristics of superplasticity domain in the processing map for hot working of an Al alloy 2014---20vol.%Al2O3 metal matrix composite

The processing map for hot working of Al alloy 2014-20vol.%Al2O3 particulate-reinforced cast-plus-extruded composite material has been generated covering the temperature range 300-500 degrees C and the strain rate range 0.001-10 s(-1) based on the dynamic materials model. The efficiency eta of power dissipation given by 2m/(m + 1), where m is the strain rate sensitivity, is plotted as a function of temperature and strain rate to obtain a processing map. A domain of superplasticity has been identified, with a peak efficiency of 62% occurring at 500 degrees C and 0.001 s(-1). The characteristics of this domain have been studied with the help of microstructural evaluation and hot-ductility measurements. Microstructural instability is predicted at higher strain rates above (ls(-1)) and lower temperatures (less than 350 degrees C).

Concise row-pruning algorithm to invert a matrix

Presented here, in a vector formulation, is an O(mn2) direct concise algorithm that prunes/identifies the linearly dependent (ld) rows of an arbitrary m X n matrix A and computes its reflexive type minimum norm inverse A(mr)-, which will be the true inverse A-1 if A is nonsingular and the Moore-Penrose inverse A+ if A is full row-rank. The algorithm, without any additional computation, produces the projection operator P = (I - A(mr)- A) that provides a means to compute any of the solutions of the consistent linear equation Ax = b since the general solution may be expressed as x = A(mr)+b + Pz, where z is an arbitrary vector. The rank r of A will also be produced in the process. Some of the salient features of this algorithm are that (i) the algorithm is concise, (ii) the minimum norm least squares solution for consistent/inconsistent equations is readily computable when A is full row-rank (else, a minimum norm solution for consistent equations is obtainable), (iii) the algorithm identifies ld rows, if any, and reduces concerned computation and improves accuracy of the result, (iv) error-bounds for the inverse as well as the solution x for Ax = b are readily computable, (v) error-free computation of the inverse, solution vector, rank, and projection operator and its inherent parallel implementation are straightforward, (vi) it is suitable for vector (pipeline) machines, and (vii) the inverse produced by the algorithm can be used to solve under-/overdetermined linear systems.

Matrix method for eigenstructure assignment - The multi-input case with application

The eigenvalue and eigenstructure assignment procedure has found application in a wide variety of control problems. In this paper a method for assigning eigenstructure to a linear time invariant multi-input system is proposed. The algorithm determines a matrix that has eigenvalues and eigenvectors at the desired locations. It is obtained from the knowledge of the open-loop system and the desired eigenstructure. Solution of the matrix equation, involving unknown controller gams, open-loop system matrices, and desired eigenvalues and eigenvectors, results hi the state feedback controller. The proposed algorithm requires the closed-loop eigenvalues to be different from those of the open-loop case. This apparent constraint can easily be overcome by a negligible shift in the values. Application of the procedure is illustrated through the offset control of a satellite supported, from an orbiting platform, by a flexible tether.

Matrix method for eigenvalue assignment: The single input case

The eigenvalue assignment/pole placement procedure has found application in a wide variety of control problems. The associated literature is rather extensive with a number of techniques discussed to that end. In this paper a method for assigning eigenvalues to a Linear Time Invariant (LTI) single input system is proposed. The algorithm determines a matrix, which has eigenvalues at the desired locations. It is obtained from the knowledge of the open-loop system and the desired eigenvalues. Solution of the matrix equation, involving unknown controller gains, open-loop system matrices and desired eigenvalues, results in the state feedback controller. The proposed algorithm requires the closed-loop eigenvalues to be different from those of the open-loop case. This apparent constraint is easily overcome by a negligible shift in the values. Two examples are considered to verify the proposed algorithm. The first one pertains to the in-plane libration of a Tethered Satellite System (TSS) while the second is concerned with control of the short period dynamics of a flexible airplane. Finally, the method is extended to determine the Controllability Grammian, corresponding to the specified closed-loop eigenvalues, without computing the controller gains.

Influence of Bi 3+ ions in enhancing the magnitude of positive temperature coefficients of resistance in n-BaTiO3 ceramics

Bi3+ ions substituting at Ba-sites in a limited concentration range with another donor dopant occupying the Ti-sites in polycrystalline BaTiO3 enhanced the positive temperature coefficient of resistance (PTCR) by over seven orders of magnitude. These ceramics did not require normal post sinter annealing or a change to an oxygen atmosphere during annealing. These ceramics had low porosities coupled with better stabilities to large applied electric fields and chemically reducing atmospheres. Bi3+ ions limited the grain growth to less than 8 mum in size, they enhanced the concentration of acceptor-type trap centres at the grain-boundary-layer regions and maintained complete tetragonality at low grain sizes in BaTiO3 ceramics.

Matrix method for eigenstructure assignment - The multi-input case with application

The eigenvalue and eigenstructure assignment procedure has found application in a wide variety of control problems. In this paper a method for assigning eigenstructure to a Linear time invariant multi-input system is proposed. The algorithm determines a matrix that has eigenvalues and eigenvectors at the desired locations. It is obtained from the knowledge of the open-loop system and the desired eigenstructure. solution of the matrix equation, involving unknown controller gains, open-loop system matrices, and desired eigenvalues and eigenvectors, results in the state feedback controller. The proposed algorithm requires the closed-loop eigenvalues to be different from those of the open-loop case. This apparent constraint can easily be overcome by a negligible shift in the values. Application of the procedure is illustrated through the offset control of a satellite supported, from an orbiting platform, by a flexible tether,

Matrix method for eigenvalue assignment: The single input case

The eigenvalue assignment/pole placement procedure has found application in a wide variety of control problems. The associated literature is rather extensive with a number of techniques discussed to that end. In this paper a method for assigning eigenvalues to a Linear Time Invariant (LTI) single input system is proposed. The algorithm determines a matrix, which has eigenvalues at the desired locations. It is obtained from the knowledge of the open-loop system and the desired eigenvalues. Solution of the matrix equation, involving unknown controller gains, open-loop system matrices and desired eigenvalues, results in the state feedback controller. The proposed algorithm requires the closed-loop eigenvalues to be different from those of the open-loop case. This apparent constraint is easily overcome by a negligible shift in the values. Two examples are considered to verify the proposed algorithm. The first one pertains to the in-plane libration of a Tethered Satellite System (TSS) while the second is concerned with control of the short period dynamics of a flexible airplane. Finally, the method is extended to determine the Controllability Grammian, corresponding to the specified closed-loop eigenvalues, without computing the controller gains.

A study of microstructure and wear behaviour of TiB2/Al metal matrix composites

The present paper deals with the study of microstructure and wear characteristics of TiB2 reinforced aluminium metal matrix composites (MMCs). Matrix alloys with 5, 10 and 15% of TiB2 were made using stir casting technique. Effect of sliding velocity on the wear behaviour and tribo-chemistry of the worn surfaces of both matrix and composites sliding against a EN24 steel disc has been investigated under dry conditions. A pin-on-disc wear testing machine was used to find the wear rate, in which EN24 steel disc was used as the counter face, loads of 10-60N in steps of 10N and speeds of 100, 200, 300, 400 and 500 rpm were employed. The results showed that the wear rate was increased with an increase in load and sliding speed for both the materials. However, a lower wear rate was obtained for MMCs when compared to the matrix alloys. The wear transition from slight to severe was presented at the critical applied loads. The transition loads for the MMCs were much higher than that of the matrix alloy. The transition loads were increased with increase in TiB2 and the same was decreased with the increase of sliding speeds. The SEM and EDS analyses were undertaken to demonstrate the effect of TiB2 particles on the wear mechanism for each conditions.

Use of L matrix to obtain reliable ab initio force constants of polyatomic molecules: ethylene as a test system

Direct use of experimental eigenvalues of the vibrational secular equation on to the ab initio predicted eigenvector space is suggested as a means of obtaining a reliable set of intramolecular force constants. This method which we have termed RECOVES (recovery in the eigenvector space) is computationally simple and free from arbitrariness. The RECOVES force constants, by definition, reproduce the experimental vibrational frequencies of the parent molecule exactly. The ab initio calculations were carried out for ethylene as a test molecule and the force constants obtained by the present procedure also correctly predict the vibrational frequencies of the deuterated species. The RECOVES force constants for ethylene are compared with those obtained by using the SQM procedure.