Climb-Enabled Discrete Dislocation Plasticity Analysis of the Deformation of a Particle Reinforced Composite

2015 ◽  
Vol 82 (7) ◽  
Author(s):  
C. Ayas ◽  
L. C. P. Dautzenberg ◽  
M. G. D. Geers ◽  
V. S. Deshpande
Keyword(s):  
Particle Size ◽  
Size Effect ◽  
Strain Hardening ◽  
Volume Fraction ◽  
Dislocation Motion ◽  
Dislocation Climb ◽  
Discrete Dislocation ◽  
Dislocation Plasticity ◽  
Wall Structures ◽  
The Matrix

The shear deformation of a composite comprising elastic particles in a single crystal elastic–plastic matrix is analyzed using a discrete dislocation plasticity (DDP) framework wherein dislocation motion occurs via climb-assisted glide. The topology of the reinforcement is such that dislocations cannot continuously transverse the matrix by glide-only without encountering the particles that are impenetrable to dislocations. When dislocation motion is via glide-only, the shear stress versus strain response is strongly strain hardening with the hardening rate increasing with decreasing particle size for a fixed volume fraction of particles. This is due to the formation of dislocation pile-ups at the particle/matrix interfaces. The back stresses associated with these pile-ups result in a size effect and a strong Bauschinger effect. By contrast, when dislocation climb is permitted, the dislocation pile-ups break up by forming lower energy dislocation wall structures at the particle/matrix interfaces. This results in a significantly reduced size effect and reduced strain hardening. In fact, with increasing climb mobility an “inverse size” effect is also predicted where the strength decreases with decreasing particle size. Mass transport along the matrix/particle interface by dislocation climb causes this change in the response and also results in a reduction in the lattice rotations and density of geometrically necessary dislocations (GNDs) compared to the case where dislocation motion is by glide-only.

Formation of Cavities From Nondeformable Second-Phase Particles in Low Temperature Ductile Fracture

1976 ◽  
Vol 98 (1) ◽  
pp. 60-68 ◽  
Author(s):  
A. S. Argon
Keyword(s):  
Particle Size ◽  
Stress Concentration ◽  
Size Effect ◽  
Volume Fraction ◽  
Void Formation ◽  
Particle Size Effect ◽  
Interfacial Stress ◽  
Second Phase ◽  
Rigid Particles ◽  
The Matrix

Limiting solutions are discussed for elastic-plastic deformation around rigid particles of both equiaxed and greatly elongated shapes. It is shown that if the matrix can be characterized as a rigid nonhardening continuum the stress concentration at the particle interface and interior is less than two for either equiaxed or elongated particles. In a rapidly strain hardening matrix, however, while the interfacial stress concentration relative to the distant boundary traction remains at a factor of two for the equiaxed particles, it rises nearly linearly with aspect ratio for slender platelets and rods. Interaction between particles can occur when the local volume fraction of particles is high. Such interactions raise the interface tractions for a given state of shear of the matrix and hasten void formation, and are often discerned as a particle size effect. Another particle size effect based on flawed particles is also discussed.

scholarly journals Iron-chromium-carbon-vanadium white cast irons: Microstructure and properties

2014 ◽  
Vol 68 (4) ◽  
pp. 413-427 ◽  
Author(s):  
Mirjana Filipovic
Keyword(s):  
Fracture Toughness ◽  
Strain Hardening ◽  
Volume Fraction ◽  
Dynamic Fracture Toughness ◽  
M23c6 Carbide ◽  
Cast Irons ◽  
Repeated Impact ◽  
Secondary Carbides ◽  
The Matrix ◽  
Microstructure Parameters

The as-cast microstructure of Fe-Cr-C-V white irons consists of M7C3 and vanadium rich M6C5 carbides in austenitic matrix. Vanadium changed the microstructure parameters of phase present in the structure of these alloys, including volume fraction, size and morphology. The degree of martensitic transformation also depended on the content of vanadium in the alloy. The volume fraction of the carbide phase, carbide size and distribution has an important influence on the wear resistance of Fe-Cr-C-V white irons under low-stress abrasion conditions. However, the dynamic fracture toughness of Fe-Cr-C-V irons is determined mainly by the properties of the matrix. The austenite is more effective in this respect than martensite. Since the austenite in these alloys contained very fine M23C6 carbide particles, higher fracture toughness was attributed to a strengthening of the austenite during fracture. Besides, the secondary carbides which precipitate in the matrix regions also influence the abrasion behaviour. By increasing the matrix strength through a dispersion hardening effect, the fine secondary carbides can increase the mechanical support of the carbides. Deformation and appropriate strain hardening occur in the retained austenite of Fe-Cr-C-V alloys under repeated impact loading. The particles of precipitated M23C6 secondary carbides disturb dislocations movement and contribute to increase the effects of strain hardening in Fe-Cr-C-V white irons.

Ultrasonic Study of Elastic and Anelastic Properties of C/Mg-2wt.%Si Composite

2012 ◽  
Vol 184 ◽  
pp. 191-196
Author(s):  
S. Golyandin ◽  
K. Sapozhnikov ◽  
Sergey Kustov
Keyword(s):  
Carbon Fibers ◽  
Thermal Stresses ◽  
Volume Fraction ◽  
Dislocation Motion ◽  
Magnesium Matrix Composite ◽  
Magnesium Matrix ◽  
Alloy Matrix ◽  
Temperature Variations ◽  
The Matrix ◽  
Temperature Spectra

Microstructural changes induced in a carbon fiber – magnesium matrix composite during thermal cycling in the range of 100 - 360 K are detected by an ultrasonic technique. The composite was comprised of Mg-2wt.%Si alloy matrix reinforced with long unidirectional carbon fibers (volume fraction of about 30%). Temperature variations of the elastic modulus of the composite are largely determined by elasticity of the carbon fibers stressed by the thermally expanded/contracted matrix. Anelastic properties of the composite (internal friction and modulus defect) are caused by dislocation motion in the matrix. Temperature spectra of anelasticity of the composite are controlled by a competition between creation of fresh mobile dislocations under the action of thermal stresses and immobilization of the fresh dislocations by atmospheres of mobile point defects.

The strengthening of metals by dispersed particles

1964 ◽  
Vol 282 (1388) ◽  
pp. 63-79 ◽  
Keyword(s):  
Metal Matrix ◽  
Volume Fraction ◽  
Dislocation Motion ◽  
Model Systems ◽  
Dispersed Phase ◽  
Strong Phase ◽  
Large Volume Fraction ◽  
Density Of Dislocations ◽  
Dispersed Particles ◽  
The Matrix

A review is made of the yield strength attainable by dispersing particles in a metal matrix in order to hinder dislocation motion. The advantages and drawbacks of the various methods used to introduce the particles are considered. The greatest strengths are found in materials containing a large volume fraction of dispersed phase coupled with a high density of dislocations in the matrix. The greatest strengths should be achieved if the dispersed particles are very strong and are loaded to fracture. To load the particles they must be needle-shaped. Experiments on model systems of a metal containing wires to simulate the strong phase are described. These indicate some of the conditions necessary to obtain maximum strength and suggest how extreme brittleness can be avoided.

Investigations of the effects of particle properties on the wear resistance of the particle reinforced composites using a novel wear model

2016 ◽  
Vol 05 (02) ◽  
pp. 1650013 ◽  
Author(s):  
T. Ram Prabhu
Keyword(s):  
Particle Size ◽  
Wear Resistance ◽  
Volume Fraction ◽  
Two Dimensions ◽  
Reinforced Composites ◽  
Wear Model ◽  
Spring Force ◽  
Particle Reinforced Composites ◽  
The Matrix ◽  
Applied Forces

A wear model is developed based on the discrete lattice spring–mass approach to study the effects of particle volume fraction, size, and stiffness on the wear resistance of particle reinforced composites. To study these effects, we have considered three volume fractions (10%, 20% and 30%), two sizes ([Formula: see text] and [Formula: see text] sites), and two different stiffness of particles embedded in the matrix in a regular pattern. In this model, we have discretized the composite system ([Formula: see text] sites) into the lumped masses connected with interaction spring elements in two dimensions. The interaction elements are assumed as linear elastic and ideal plastic under applied forces. Each mass is connected to its first and second nearest neighbors by springs. The matrix and particles sites are differentiated by choosing the different stiffness values. The counter surface is simulated as a rigid body that moves on the composite material at a constant sliding speed along the horizontal direction. The governing equations are formed by equating the spring force between the pair of sites given by Hooke’s law plus external contact forces and the force due to the motion of the site given by the equation of motion. The equations are solved for the plastic strain accumulated in the springs using an explicit time stepping procedure based on a finite difference form of the above equations. If the total strain accumulated in the spring elements connected to a lump mass site exceeds the failure strain, the springs are considered to be broken, and the mass site is removed or worn away from the lattice and accounts as a wear loss. The model predicts that (i) increasing volume fraction, reducing particle size and increasing particle stiffness enhance the wear resistance of the particle reinforced composites, (ii) the particle stiffness is the most significant factor affecting the wear resistance of the composites, and (iii) the wear resistance reduced above the critical volume fraction ([Formula: see text]), and [Formula: see text] increases with increasing particle size. Finally, we have qualitatively compared the model results with our previously published experimental results to prove the effectiveness of the model to analysis the complex wear systems.

Analysis of Morphology Formation in Elastomer Blends

1977 ◽  
Vol 50 (2) ◽  
pp. 292-300 ◽  
Author(s):  
N. Tokita
Keyword(s):  
Particle Size ◽  
Interfacial Tension ◽  
Volume Fraction ◽  
Influential Factors ◽  
Theoretical Expression ◽  
Dispersed Phase ◽  
The Matrix ◽  
Breaking Energy ◽  
Internal Mixer ◽  
Future Work

Abstract Based on the assumption that an equilibrium particle size of dispersed phase will be reached when the breaking-down rate and the coalescence rate are balanced, a theoretical expression was obtained. The theory showed qualitatively that the equilibrium particle size becomes smaller when (1) the stress field is increased, (2) the interfacial tension between matrix and dispersed phase becomes smaller, and (3) the concentration of dispersed phase decreases. Qualitative verification of the theory was obtained by experimental examination of the NR-EPM blend system. In practice, in order to obtain a small particle size in a short time at above 20% volume fraction, the matching of rheological properties of the matrix and the dispersed phase is desirable. On changing from internal mixer to mill, the temperature became one of the most influential factors that control the particle size. Future work, such as the quantitative value of interfacial tension as a function of temperature, and macroscopic breaking energy measurement, etc., is necessary to confirm the theory quantitatively.

Modeling Interparticle Size Effect on Deformation Behavior of Metal Matrix Composites by a Gradient Enhanced Plasticity Model

2011 ◽  
Vol 133 (4) ◽  
Author(s):  
Rashid K. Abu Al-Rub ◽  
Mahmood Ettehad
Keyword(s):  
Particle Size ◽  
Plastic Strain ◽  
Size Effect ◽  
Metal Matrix ◽  
Mechanical Response ◽  
Volume Fraction ◽  
Experimental Tests ◽  
Interparticle Spacing ◽  
Precipitate Size ◽  
Aspect Ratios

Experimental tests show that particle (inclusion or precipitate) size and interparticle spacing, besides volume fraction, have a considerable effect on the macroscopic mechanical response of metal matrix microreinforced composites. Classical (local) plasticity models unlike nonlocal gradient enhanced plasticity models cannot capture this size dependency due to the absence of a material length scale. In this paper, one form of higher-order gradient plasticity enhanced model, which is derived based on principle of virtual power and laws of thermodynamic, is employed to investigate the size effect of elliptical inclusions with different aspect ratios based on unit cell simulations. It is shown that by decreasing the particle size or equivalently the interparticle spacing (i.e., the spacing between the centers of inclusions), while keeping the volume fraction constant, the average stress–strain response is stronger and more sensitive to the inclusion’s aspect ratio. However, unexpectedly, decreasing the free-path interparticle spacing (i.e., the spacing between the edges of inclusions perpendicular to the principal loading direction) does not necessarily lead to largest strengthening. This is completely dependent on the plastic strain gradient hardening due to distribution and evolution of geometrically necessary dislocations that depend on the particle size and shape. Gradient-hardening significantly alter the stress and plastic strain distributions near the particle-matrix interface.

Modeling of the Tensile Deformation Behavior of SiCp/Fe Composites

2012 ◽  
Vol 217-219 ◽  
pp. 79-85
Author(s):  
Yao Mian Wang ◽  
Huan Ping Yang ◽  
Cong Hui Zhang
Keyword(s):  
Particle Size ◽  
Deformation Behavior ◽  
Volume Fraction ◽  
Tensile Deformation ◽  
Equivalent Inclusion Method ◽  
Particle Cracking ◽  
Equivalent Inclusion ◽  
Tensile Deformation Behavior ◽  
The Matrix ◽  
Dislocation Strengthening

A combined model taking account of the dislocation strengthening effects and particle cracking during tensile straining based on Eshelby equivalent inclusion method is presented to model the deformation behavior of SiCp/Fe composites. Stress-strain curves of the composites were simulated and it is found that the curves vary obviously with the volume fraction and particle size. The yield stress is increased significantly by increasing the volume fraction and decreasing the particle size. Stress in particles is very high during straining and the fraction of cracked particles increased obviously with increasing the particle size. These results indicate that higher volume fraction and finer particles can give better mechanical properties of the composites attributed to the increased load sharing effect and dislocation strengthening effects of the matrix.

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