The fracture energy of metal fibre reinforced ceramic composites (MFCs)

A model is presented for prediction of the fracture energy of ceramic-matrix composites containing dispersed metallic fibres. It is assumed that the work of fracture comes entirely from pull-out and/or plastic deformation of fibres bridging the crack plane. Comparisons are presented between these predictions and experimental measurements made on a commercially-available composite material of this type, containing stainless steel (304) fibres in a matrix predominantly comprising alumina and alumino-silicate phases. Good agreement is observed, and it's noted that there is scope for the fracture energy levels to be high (~20kJm-2). Higher toughness levels are both predicted and observed for coarser fibres, up to a practical limit for the fibre diameter of the order of 0.5mm. Other deductions are also made concerning strategies for optimisation of the toughness of this type of material. © 2010 Elsevier Ltd.

The ensemble statistics of the energy of a random system subjected to harmonic excitation

This paper is concerned with the ensemble statistics of the response to harmonic excitation of a single dynamic system such as a plate or an acoustic volume. Random point process theory is employed, and various statistical assumptions regarding the system natural frequencies are compared, namely: (i) Poisson natural frequency spacings, (ii) statistically independent Rayleigh natural frequency spacings, and (iii) natural frequency spacings conforming to the Gaussian orthogonal ensemble (GOE). The GOE is found to be the most realistic assumption, and simple formulae are derived for the variance of the energy of the system under either point loading or rain-on-the-roof excitation. The theoretical results are compared favourably with numerical simulations and experimental data for the case of a mass loaded plate. © 2003 Elsevier Ltd. All rights reserved.

Relation between Stabilization Energy, Crystal Field Coefficient and the Magnetic Exchange Interaction for Tb3+ Ion

Based on a single ion model, Hamiltonian of the simplest form about magnetocrystalline anisotropy for Tb3+ ion was solved by using the numerical method. The relation between the stabilization energy, crystal field coefficient B-2(0) and the magnetic exchange interaction was studied as temperature approaches to 0 K. The results show that the stabilization energy contributed by Tb3+ is linear with crystal field coefficient B-2(0) approximately, but it is insensitive to the change of magnetic exchange interaction for the strong magnetic substances such as TbCo5, Tb2Co17 and Tb2Fe14B compounds.

Energy Conversion in Shape Memory Alloy Heat Engine Part I: Theory

Shape Memory Alloy (SMA) can be easily deformed to a new shape by applying a small external load at low temperature, and then recovers its original configuration upon heating. This unique shape memory phenomenon has inspired many novel designs. SMA based heat engine is one among them. SMA heat engine is an environment-friendly alternative to extract mechanical energy from low-grade energies, for instance, warm wastewater, geothermal energy, solar thermal energy, etc. The aim of this paper is to present an applicable theoretical model for simulation of SMA-based heat engines. First, a micro-mechanical constitutive model is derived for SMAs. The volume fractions of austenite and martensite variants are chosen as internal variables to describe the evolution of microstructure in SMA upon phase transition. Subsequently, the energy equation is derived based on the first thermodynamic law and the previous SMA model. From Fourier’s law of heat conduction and Newton’s law of cooling, both differential and integral forms of energy conversion equation are obtained.

Damage Localization, Sensitivity of Energy Release and the Catastrophe Transition

Large earthquakes can be viewed as catastrophic ruptures in the earth’s crust. There are two common features prior to the catastrophe transition in heterogeneous media. One is damage localization and the other is critical sensitivity; both of which are related to a cascade of damage coalescence. In this paper, in an attempt to reveal the physics underlying the catastrophe transition, analytic analysis based on mean-field approximation of a heterogeneous medium as well as numerical simulations using a network model are presented. Both the emergence of damage localization and the sensitivity of energy release are examined to explore the inherent statistical precursors prior to the eventual catastrophic rupture. Emergence of damage localization, as predicted by the mean-field analysis, is consistent with observations of the evolution of damage patterns. It is confirmed that precursors can be extracted from the time-series of energy release according to its sensitivity to increasing crustal stress. As a major result, present research indicates that the catastrophe transition and the critical point hypothesis (CPH) of earthquakes are interrelated. The results suggest there may be two cross-checking precursors of large earthquakes: damage localization and critical sensitivity.

Investigation of Mn-Implanted n-Si by Low-Energy Ion Beam Deposition

Mn ions were implanted to n-type Si(0 0 1) single crystal by low-energy ion beam deposition technique with an energy of 1000 eV and a dose of 7.5 x 10^{17} cm^{-2}. The samples were held at room temperature and at 300degreesC during implantation. Auger electron spectroscopy depth profiles of samples indicate that the Mn ions reach deeper in the sample implanted at 300degreesC than in the sample implanted at room temperature. X-ray diffraction measurements show that the structure of the sample implanted at room temperature is amorphous while that of the sample implanted at 300degreesC is crystallized. There are no new phases found except silicon both in the two samples. Atomic force microscopy images of samples indicate that the sample implanted at 300degreesC has island-like humps that cover the sample surface while there is no such kind of characteristic in the sample implanted at room temperature. The magnetic properties of samples were investigated by alternating gradient magnetometer (AGM). The sample implanted at 300degreesC shows ferromagnetic behavior at room temperature.

Microdamage Evolution, Energy Dissipation and Their Trans-Scale Effects on Macroscopic Failure

The process of damage evolution concerns various scales, from micro- to macroscopic. How to characterize the trans-scale nature of the process is on the challenging frontiers of solid mechanics. In this paper, a closed trans-scale formulation of damage evolution based on statistical microdamage mechanics is presented. As a case study, the damage evolution in spallation is analyzed with the formulation. Scaling of the formulation reveals that the following dimensionless numbers: reduced Mach number M, damage number S, stress wave Fourier number P, intrinsic Deborah number D*, and the imposed Deborah number De*, govern the whole process of deformation and damage evolution. The evaluation of P and the estimation of temperature increase show that the energy equation can be ignored as the first approximation in the case of spallation. Hence, apart from the two conventional macroscopic parameters: the reduced Mach number M and damage number S, the damage evolution in spallation is mainly governed by two microdamage-relevant parameters: the Deborah numbers D* and De*. Higher nucleation and growth rates of microdamage accelerate damage evolution, and result in higher damage in the target plate. In addition, the mere variation in nucleation rate does not change the spatial distribution of damage or form localized rupture, while the increase of microdamage growth rate localizes the damage distribution in the target plate, which can be characterized by the imposed Deborah number De*.

Debonding and cracking energy release rate of the fiber/matrix interface

An investigation of fiber/matrix interfacial fracture energy is presented in this paper. Several existing theoretical expressions for the fracture energy of interfacial debonding are reviewed. For the single-fiber/matrix debonding and pull-out experimental model, a study is carried out on the effect of interfacial residual compressive stress and friction on interface cracking energy release rate.

(Ti,Al)N Film On Normalized T8 Carbon Tool Steel Prepared By Pulsed High Energy Density Plasma Technique

Under optimized operating parameters, a hard and wear resistant ( Ti,Al)N film is prepared on a normalized T8 carbon tool steel substrate by using pulsed high energy density plasma technique. Microstructure and composition of the film are analysed by x-ray diffraction, x-ray photoelectron spectroscopy, Auger electron spectroscopy and scanning electron microscopy. Hardness profile and tribological properties of the film are tested with nano-indenter and ring-on-ring wear tester, respectively. The tested results show that the microstructure of the film is dense and uniform and is mainly composed of ( Ti,Al)N and AlN hard phases. A wide transition interface exists between the film and the normalized T8 carbon tool steel substrate. Thickness of the film is about 1000 nm and mean hardness value of the film is about 26GPa. Under dry sliding wear test conditions, relative wear resistance of the ( Ti,Al)N film is approximately 9 times higher than that of the hardened T8 carbon tool steel reference sample. Meanwhile, the ( Ti,Al)N film has low and stable friction coefficient compared with the hardened T8 carbon tool steel reference sample.

Characteristics Of Energy Dissipation In Hyperconcentrated Flows

An equilibrium equation for the turbulence energy in sediment-laden flows was derived on the basis of solid-liquid two-phase flow theory. The equation was simplified for two-dimensional, uniform, steady and fully developed turbulent hyperconcentrated flows. An energy efficiency coefficient of suspended-load motion was obtained from the turbulence energy equation, which is defined as the ratio of the sediment suspension energy to the turbulence energy of the sediment-laden flows. Laboratory experiments were conducted to investigate the characteristics of energy dissipation in hyperconcentrated flows. A total of 115 experimental runs were carried out, comprising 70 runs with natural sediments and 45 runs with cinder powder. Effects of sediment concentration on sediment suspension energy and flow resistance were analyzed and the relation between the energy efficiency coefficient of suspended-load motion and sediment concentration was established on the basis of experimental data. Furthermore, the characteristics of energy dissipation in hyperconcentrated flows were identified and described. It was found that the high sediment concentration does not increase the energy dissipation; on the contrary, it decreases flow resistance.

An Improved Energy Method For Determining Young'S Modulus By Instrumented Indentation Using A Berkovich Tip

We previously proposed a method for estimating Young's modulus from instrumented nanoindentation data based on a model assuming that the indenter had a spherical-capped Berkovich geometry to take account of the bluntness effect. The method is now further improved by releasing the constraint on the tip shape, allowing it to have a much broader arbitrariness to range from a conical-tipped shape to a flat-ended shape, whereas the spherical-capped shape is just a special case in between. This method requires two parameters to specify a tip geometry, namely, a volume bluntness ratio V-r and a height bluntness ratio h(r). A set of functional relationships correlating nominal hardness/reduced elastic modulus ratio (H-n/E-r) and elastic work/total work ratio (W-e/W) were established based on dimensional analysis and finite element simulations, with each relationship specified by a set of V-r and h(r). Young's modulus of an indented material can be estimated from these relationships. The method was shown to be valid when applied to S45C carbon steel and 6061 aluminum alloy.

Energy Principle And Nonlinear Electric-Mechanical Behavior Of Ferroelectric Ceramics

Many experimental observations have shown that a single domain in a ferroelectric material switches by progressive movement of domain walls, driven by a combination of electric field and stress. The mechanism of the domain switch involves the following steps: initially, the domain has a uniform spontaneous polarization; new domains with the reverse polarization direction nucleate, mainly at the surface, and grow though the crystal thickness; the new domain expands sideways as a new domain continues to form; finally, the domain switch coalesces to complete the polarization reversal. According to this mechanism, the volume fraction of the domain switching is introduced in the constitutive law of the ferroelectric material and used to study the nonlinear constitutive behavior of a ferroelectric body in this paper. The principle of stationary total potential energy is put forward in which the basic unknown quantities are the displacement u(i), electric displacement D-i and volume fraction rho(I) of the domain switching for the variant I. The mechanical field equation and a new domain switching criterion are obtained from the principle of stationary total potential energy. The domain switching criterion proposed in this paper is an expansion and development of the energy criterion established by Hwang et al. [ 1]. Based on the domain switching criterion, a set of linear algebraic equations for determining the volume fraction rho(I) of domain switching is obtained, in which the coefficients of the linear algebraic equations only contain the unknown strain and electric fields. If the volume fraction rho(I) of domain switching for each domain is prescribed, the unknown displacement and electric potential can be obtained based on the conventional finite element procedure. It is assumed that a domain switches if the reduction in potential energy exceeds a critical energy barrier. According to the experimental results, the energy barrier will strengthen when the volume fraction of the domain switching increases. The external mechanical and electric loads are increased step by step. The volume fraction rho(I) of domain switching for each element obtained from the last loading step is used as input to the constitutive equations. Then the strain and electric fields are calculated based on the conventional finite element procedure. The finite element analysis is carried out on the specimens subjected to uniaxial coupling stress and electric field. Numerical results and available experimental data are compared and discussed. The present theoretic prediction agrees reasonably with the experimental results.

Energy Dissipation In Fracture Of Bulk Metallic Glasses Via Inherent Competition Between Local Softening And Quasi-Cleavage

Compression, tension and high-velocity plate impact experiments were performed on a typical tough Zr41.2Ti13.8Cu10Ni12.5Be22.5 (Vit 1) bulk metallic glass (BMG) over a wide range of strain rates from similar to 10(-4) to 10(6) s(-1). Surprisingly, fine dimples and periodic corrugations on a nanoscale were also observed on dynamic mode I fracture surfaces of this tough Vit 1. Taking a broad overview of the fracture patterning of specimens, we proposed a criterion to assess whether the fracture of BMGs is essentially brittle or plastic. If the curvature radius of the crack tip is greater than the critical wavelength of meniscus instability [F. Spaepen, Acta Metall. 23 615 (1975); A.S. Argon and M. Salama, Mater. Sci. Eng. 23 219 (1976)], microscale vein patterns and nanoscale dimples appear on crack surfaces. However, in the opposite case, the local quasi-cleavage/separation through local atomic clusters with local softening in the background ahead of the crack tip dominates, producing nanoscale periodic corrugations. At the atomic cluster level, energy dissipation in fracture of BMGs is, therefore, determined by two competing elementary processes, viz. conventional shear transformation zones (STZs) and envisioned tension transformation zones (TTZs) ahead of the crack tip. Finally, the mechanism for the formation of nanoscale periodic corrugation is quantitatively discussed by applying the present energy dissipation mechanism.