Constitutive Equations of Power-Law Composites and Failure of Materials Having Multiple Cracks

1994 ◽  
Vol 116 (3) ◽  
pp. 359-366 ◽  
Author(s):  
S. C. Lin ◽  
Y. Hirose ◽  
T. Mura
Keyword(s):  
Power Law ◽  
Constitutive Equations ◽  
Fracture Criterion ◽  
Volume Fraction ◽  
Piecewise Linear ◽  
Pure Shear ◽  
Failure Criteria ◽  
Multiple Cracks ◽  
Critical Volume Fraction ◽  
The Matrix

Based upon the Mori-Tanaka method, the constitutive equations of power-law materials and the failure criteria of multiple cracks materials are investigated. The piecewise linear incremental approach is also employed to analyze the effective stress and strain of the power-law materials. Results are presented for the case of pure shear where the matrix is a power-law material with rigid or void inhomogeneities. For the multiple cracked materials, the Griffith fracture criterion is applied to determine the critical volume fraction which causes the catastrophic failure of a material. The failure criteria of penny shaped, flat ellipsoidal, and slit-like cracked materials are examined and it is found that the volume fraction of cracks and critical applied stress are in linear relation.

Numerical Analysis of the GF/UHMWPEF Interply Hybrid NOL Ring Critical Volume Fraction

2012 ◽  
Vol 457-458 ◽  
pp. 449-452
Author(s):  
Ming Lin Xu ◽  
Xiao Qing Wu ◽  
Ming Kang An
Keyword(s):  
Finite Element ◽  
Volume Fraction ◽  
Critical Volume ◽  
Tooth Contact Analysis ◽  
Breaking Strain ◽  
Finite Element Software ◽  
Critical Volume Fraction ◽  
The Matrix ◽  
The Relationship ◽  
Strain Model

The tensile test of NOL ring composites with different interply hybrid ratio is simulated by finite element software. The relationship between the stress of Naval Ordnance Laboratory(NOL) ring and the volume fraction of UHMWPEF is linear when the matrix suffering from the equal loading, but tower suddenly appears at the point of 56.25% which is about the critical volume fraction. The critical volume fraction of hybrid NOL ring is figured out on the basis of the constant strain model. By contrast, the results of the Finite Element Method (FEM) and constant strain model have subtle differences. Tooth contact analysis can exactly predict the stress of the interply hybrid NOL ring and the critical volume fraction of GF in interply hybrid NOL ring which has lower breaking strain than UHMWPEF does.

scholarly journals The AC and DC Conductivity of Nanocomposites

2007 ◽  
Vol 2007 ◽  
pp. 1-9 ◽  
Author(s):  
David S. McLachlan ◽  
Godfrey Sauti
Keyword(s):  
Electrical Properties ◽  
Volume Fraction ◽  
Matrix Material ◽  
Dc Conductivity ◽  
Critical Volume ◽  
Matrix Structure ◽  
Electrical Measurements ◽  
Conducting Component ◽  
Critical Volume Fraction ◽  
The Matrix

The microstructures of binary (conductor-insulator) composites, containing nanoparticles, will usually have one of two basic structures. The first is the matrix structure where the nanoparticles (granules) are embedded in and always coated by the matrix material and there are no particle-particle contacts. The AC and DC conductivity of this microstructure is usually described by the Maxwell-Wagner/Hashin-Shtrikman or Bricklayer model. The second is a percolation structure, which can be thought to be made up by randomly packing the two types of granules (not necessarily the same size) together. In percolation systems, there exits a critical volume fraction below which the electrical properties are dominated by the insulating component and above which the conducting component dominates. Such percolation systems are best analyzed using the two-exponent phenomenological percolation equation (TEPPE). This paper discusses all of the above and addresses the problem of how to distinguish among the microstructures using electrical measurements.

Effect of Mo microstructure on the critical volume fraction for conduction in Mo-alumina cermets

1997 ◽  
Vol 12 (3) ◽  
pp. 738-744 ◽  
Author(s):  
J. F. Kelso ◽  
R. R. Higgins ◽  
F. J. Krivda
Keyword(s):  
Volume Fraction ◽  
Critical Volume ◽  
Glass Content ◽  
Alumina Powder ◽  
Particle Sizes ◽  
Initial Particle ◽  
Electrical Percolation ◽  
Metal Contents ◽  
Critical Volume Fraction ◽  
The Matrix

The microstructure of Mo in an alumina/frit matrix was found to be dependent on the initial particle sizes of the alumina and Mo powders, the glass content in the matrix ceramic, and the amount of moisture in the firing atmosphere. The Mo microstructure had a significant influence on the critical volume fraction for conductivity in these cermets. Coarser alumina powder, finer Mo powder, and higher glass content promoted coalescence of Mo into conductive networks at lower metal contents. Drier firing atmospheres produced a more coarsened Mo microstructure with a slight decrease in the amount of network contiguity, causing an increase in the amount required for electrical percolation.

Toughening of cement and other brittle solids with fibres

1983 ◽  
Vol 310 (1511) ◽  
pp. 175-190 ◽  
Keyword(s):  
Unit Volume ◽  
Volume Fraction ◽  
Interfacial Area ◽  
Theoretical Models ◽  
Brittle Solids ◽  
Final Failure ◽  
Critical Volume Fraction ◽  
The Matrix ◽  
Critical Flaw ◽  
Work Done

In common with other brittle solids, cements are toughened much more by the incorporation of fibres than by inclusions of other geometries. The largest energies required to break a specimen are found when multiple fracture of the specimen occurs before final failure. Theoretical models of a crack moving normal to a set of parallel fibres will be considered, to show that the crack spacing and first cracking strain should depend on the area of fibre-matrix interface per unit volume of composite. The first cracking strain is shown to increase for all fibre volumes provided that the fibre spacing is less than the critical flaw size according to the Griffith’s equation. The theoretical models are compared with experiment and the practical difficulties of defining first cracking strain and interfacial area mentioned. The best practical means of assessing the resistance to failure of the composite is the work done per unit volume of the specimen in separating it into two distinct pieces. The maximum values of toughness attainable - some 10 6 J m -3 - can decrease with time under external weathering, owing to continuing hydration of the matrix and consequent increase in the critical volume fraction of fibres.

Formation of Persistent Slip Band in Fatigued Copper Single Crystals

1982 ◽  
Vol 40 ◽  
pp. 470-471
Author(s):  
N. Y. Jin
Keyword(s):  
Volume Fraction ◽  
Fatigue Cracks ◽  
Wall Structure ◽  
Matrix Structure ◽  
Dislocation Dipole ◽  
Slip Bands ◽  
Persistent Slip Bands ◽  
The Matrix ◽  
Hard Shell ◽  
Copper Single Crystals

Localised plastic deformation in Persistent Slip Bands(PSBs) is a characteristic feature of fatigue in many materials. The dislocation structure in the PSBs contains regularly spaced dislocation dipole walls occupying a volume fraction of around 10%. The remainder of the specimen, the inactive "matrix", contains dislocation veins at a volume fraction of 50% or more. Walls and veins are both separated by regions in which the dislocation density is lower by some orders of magnitude. Since the PSBs offer favorable sites for the initiation of fatigue cracks, the formation of the PSB wall structure is of great interest. Winter has proposed that PSBs form as the result of a transformation of the matrix structure to a regular wall structure, and that the instability occurs among the broad dipoles near the center of a vein rather than in the hard shell surounding the vein as argued by Kulmann-Wilsdorf.

Preparation of Electron Transparent Metal-Matrix Composites

1968 ◽  
Vol 26 ◽  
pp. 334-335 ◽  
Author(s):  
M. R. Pinnel ◽  
A. Lawley
Keyword(s):  
Stainless Steel ◽  
Load Transfer ◽  
Volume Fraction ◽  
Steel Wire ◽  
Initial Step ◽  
Interfacial Region ◽  
Matrix Composites ◽  
Specific Test ◽  
The Matrix ◽  
The One

Numerous phenomenological descriptions of the mechanical behavior of composite materials have been developed. There is now an urgent need to study and interpret deformation behavior, load transfer, and strain distribution, in terms of micromechanisms at the atomic level. One approach is to characterize dislocation substructure resulting from specific test conditions by the various techniques of transmission electron microscopy. The present paper describes a technique for the preparation of electron transparent composites of aluminum-stainless steel, such that examination of the matrix-fiber (wire), or interfacial region is possible. Dislocation substructures are currently under examination following tensile, compressive, and creep loading. The technique complements and extends the one other study in this area by Hancock.The composite examined was hot-pressed (argon atmosphere) 99.99% aluminum reinforced with 15% volume fraction stainless steel wire (0.006″ dia.).Foils were prepared so that the stainless steel wires run longitudinally in the plane of the specimen i.e. the electron beam is perpendicular to the axes of the wires. The initial step involves cutting slices ∼0.040″ in thickness on a diamond slitting wheel.

scholarly journals Jet Impingement Heat Transfer of Confined Single and Double Jets with Non-Newtonian Power Law Nanofluid under the Inclined Magnetic Field Effects for a Partly Curved Heated Wall

2021 ◽  
Vol 13 (9) ◽  
pp. 5086
Author(s):  
Fatih Selimefendigil ◽  
Hakan F. Oztop ◽  
Ali J. Chamkha
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Particle Size ◽  
Aspect Ratio ◽  
Power Law ◽  
Volume Fraction ◽  
Inclined Magnetic Field ◽  
Magnetic Field Effects ◽  
Power Law Nanofluid ◽  
Power Law Index

Single and double impinging jets heat transfer of non-Newtonian power law nanofluid on a partly curved surface under the inclined magnetic field effects is analyzed with finite element method. The numerical work is performed for various values of Reynolds number (Re, between 100 and 300), Hartmann number (Ha, between 0 and 10), magnetic field inclination (γ, between 0 and 90), curved wall aspect ratio (AR, between 01. and 1.2), power law index (n, between 0.8 and 1.2), nanoparticle volume fraction (ϕ, between 0 and 0.04) and particle size in nm (dp, between 20 and 80). The amount of rise in average Nusselt (Nu) number with Re number depends upon the power law index while the discrepancy between the Newtonian fluid case becomes higher with higher values of power law indices. As compared to case with n = 1, discrepancy in the average Nu number are obtained as −38% and 71.5% for cases with n = 0.8 and n = 1.2. The magnetic field strength and inclination can be used to control the size and number or vortices. As magnetic field is imposed at the higher strength, the average Nu reduces by about 26.6% and 7.5% for single and double jets with n greater than 1 while it increases by about 4.78% and 12.58% with n less than 1. The inclination of magnetic field also plays an important role on the amount of enhancement in the average Nu number for different n values. The aspect ratio of the curved wall affects the flow field slightly while the average Nu variation becomes 5%. Average Nu number increases with higher solid particle volume fraction and with smaller particle size. At the highest particle size, it is increased by about 14%. There is 7% variation in the average Nu number when cases with lowest and highest particle size are compared. Finally, convective heat transfer performance modeling with four inputs and one output is successfully obtained by using Adaptive Neuro-Fuzzy Interface System (ANFIS) which provides fast and accurate prediction results.

scholarly journals Continuous Cooling Transformation Behaviour and Bainite Transformation Kinetics of 23CrNi3Mo Carburised Steel

Metals ◽  
2020 ◽  
Vol 11 (1) ◽  
pp. 48
Author(s):  
Wenjun Song ◽  
Min Lei ◽  
Mingpan Wan ◽  
Chaowen Huang
Keyword(s):  
Phase Transformation ◽  
Volume Fraction ◽  
Austenite Formation ◽  
Steel Matrix ◽  
Transformation Kinetics ◽  
Bainite Transformation ◽  
Continuous Cooling ◽  
The Matrix ◽  
Dimensional Growth ◽  
Kinetics Of

In this study, the phase transformation behaviour of the carburised layer and the matrix of 23CrNi3Mo steel was comparatively investigated by constructing continuous cooling transformation (CCT) diagram, determining the volume fraction of retained austenite (RA) and plotting dilatometric curves. The results indicated that Austenite formation start temperature (Ac1) and Austenite formation finish temperature (Ac3) of the carburised layer decreased compared to the matrix, and the critical cooling rate (0.05 °C/s) of martensite transformation is significantly lower than that (0.8 °C/s) of the matrix. The main products of phase transformation in both the carburised layer and the matrix were martensite and bainite microstructures. Moreover, an increase in carbon content resulted in the formation of lamellar martensite in the carburised layer, whereas the martensite in the matrix was still lath. Furthermore, the volume fraction of RA in the carburised layer was higher than that in the matrix. Moreover, the bainite transformation kinetics of the 23CrNi3Mo steel matrix during the continuous cooling process indicated that the mian mechanism of bainite transformation of the 23CrNi3Mo steel matrix is two-dimensional growth and one-dimensional growth.

scholarly journals Predictive Computational Model for Damage Behavior of Metal-Matrix Composites Emphasizing the Effect of Particle Size and Volume Fraction

Materials ◽  
2021 ◽  
Vol 14 (9) ◽  
pp. 2143
Author(s):  
Shaimaa I. Gad ◽  
Mohamed A. Attia ◽  
Mohamed A. Hassan ◽  
Ahmed G. El-Shafei
Keyword(s):  
Finite Element ◽  
Metal Matrix Composites ◽  
Metal Matrix ◽  
Volume Fraction ◽  
Particulate Composites ◽  
Aluminum Matrix Composites ◽  
Matrix Composites ◽  
Zone Method ◽  
Stress Strain ◽  
The Matrix

In this paper, an integrated numerical model is proposed to investigate the effects of particulate size and volume fraction on the deformation, damage, and failure behaviors of particulate-reinforced metal matrix composites (PRMMCs). In the framework of a random microstructure-based finite element modelling, the plastic deformation and ductile cracking of the matrix are, respectively, modelled using Johnson–Cook constitutive relation and Johnson–Cook ductile fracture model. The matrix-particle interface decohesion is simulated by employing the surface-based-cohesive zone method, while the particulate fracture is manipulated by the elastic–brittle cracking model, in which the damage evolution criterion depends on the fracture energy cracking criterion. A 2D nonlinear finite element model was developed using ABAQUS/Explicit commercial program for modelling and analyzing damage mechanisms of silicon carbide reinforced aluminum matrix composites. The predicted results have shown a good agreement with the experimental data in the forms of true stress–strain curves and failure shape. Unlike the existing models, the influence of the volume fraction and size of SiC particles on the deformation, damage mechanism, failure consequences, and stress–strain curve of A359/SiC particulate composites is investigated accounting for the different possible modes of failure simultaneously.

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