http://nanomechanics.mit.edu/sites/default/files/documents/Acta_2006_Cu_w_nanoTwins.pdf

Strength, strain-rate sensitivity and ductility of copper with nanoscale twins

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Computational homogenization for the multi-scale analysis of multi-phase materials

Following a review of the processing of functionally graded metals and metal-ceramic composites in Part 1; this Part 2 of the two part series focuses on the thermomechanical behaviour. The paper begins with an overview of the fundamentals of thermoelastic and thermoplastic deformation in metal-ceramic composites. Various approaches, including the rule of mixture approximations, mean field theories, crystal plasticity models, discrete dislocation models, and continuum finite element formulations of the constitutive phases of the composites, are discussed, and the significance and limitations of these approaches are highlighted. Issues specific to the thermomechanical analyses of graded materials are then addressed. It is reasoned that the introduction of a new length scale to the problem due to compositional gradients inevitably calls for detailed micromechanical analyses of the size, shape, continuity, and spatial dispersions of the constituent phases of graded metal-ceramic composites. Models for...

Functionally graded metals and metal-ceramic composites: Part 2 Thermomechanical behaviour

A356 Al–fly ash particle composites were fabricated using stir-cast technique and hot extrusion. Composites containing 6 and 12 vol.% fly ash particles were processed. Narrow size range (53–106 μm) and wide size range (0.5–400 μm) fly ash particles were used. Hardness, tensile strength, compressive strength and damping characteristics of the unreinforced alloy and composites have been measured. Bulk hardness, matrix microhardness, 0.2% proof stress of A356 Al–fly ash composites are higher compared to that of the unreinforced alloy. Additions of fly ash lead to increase in hardness, elastic modulus and 0.2% proof stress. Composites reinforced with narrow size range fly ash particle exhibit superior mechanical properties compared to composites with wide size range particles. A356 Al–fly ash MMCs were found to exhibit improved damping capacity when compared to unreinforced alloy at ambient temperature.

Synthesis of fly ash particle reinforced A356 Al composites and their characterization

Finite element implementation of a generalised non-local rate-dependent crystallographic formulation for finite strains

The mechanical behavior of particulate reinforced metal composites, in particular an SiC reinforced Al-3 wt% Cu model system, was analyzed numerically. The Computational micromechanics approach was taken, i.e. a detailed representation of microstructure in which the material was characterized by a finite deformation, thermo-elastic-viscoplastic crystallographic theory. Individual matrix grains and reinforcing particles were represented, in the context of two dimenssional repeating unit cell models. The performance of the microstructure under variation in microstructural parameters such as (1) reinforcement volume fraction, (2) morphology and (3) matrix strain hardening properties was investigated, as was the effect of change in loading state. In this, the first in a series of four articles, the isothermal microstructural deformation behavior is examined in detail. Localization of plastic deformation is seen to be a natural part of the deformation process and evolves according to patterns, which develop from the onset of yield and are determined for the most part by the positions of the reinforcing particles. This is in contrast to the microscale behavior of single phase polycrystals where deformation patterns only emerge at larger overall strains. Localization intensity depends strongly on reinforcement volume fraction and morphology and less significantly on matrix hardening properties. Results for tensile and compressive loading histories are compared showing differences that depend on particle position and finite geometry changes during deformation.

Computational modeling of metal matrix composite materials. I: Isothermal deformation patterns in ideal microstructures

The mechanical behavior of particulate reinforced metal matrix composites, in particular an SiC reinforced Al-3 wt% Cu model system, was analyzed numerically and analytically. In this, the third article in a series, the results of the computational micromechanics are compared with those of simpler and more approximate analytical/numerical models. The simplerapproaches considered use phenomenological theories of plasticity and power-law strain hardening. Models that predict overall composite behavior make use of a result, valid for incompressible materials in small strain, that both pure matrix material and composite harden with the same hardening exponent. Results of micromechanical simulations, with power-slip system hardening, show that in a very approximate sense over restricted strain regions, power-law slip hardening is preserved with the power-law exhonent tending to increase with volume fraction. The results of the computations presented in the previous article are compared with the predictions of one such analytical/numerical model, where the matrix hardening function is fitted to the unreinforced poyycrystal stress-strain response. This model employs the self-consistent method to quantify strengthening. There is good agreement between the computed and predicted results. Simulations are performed using existing reinforcement geometry but replacing the physically based crystal plasticity theory with the phenomenologically based J2 flow theory. The results are in good qualitative agreement with those of the original crystal plasticity simulations at both the microscale and the macroscale. Deformation patterns in the J2 flow theory composites are smoother and tend to be less localized than those in the crystal plasticity composites; however, these features depend strongly on volume fraction and morphology. The J2 flow theory composites display power-law exponents whose dependence on overall strain, volume fraction and morphology are much more easily characterized than in the crystal plasticity case.

Computational modeling of metal matrix composite materials—III. Comparisons with phenomenological models

The mechanical behavior of particulate reinforced metal matrix composites, in particular an SiC reinforced Al-3 wt% Cu model system, was analyzed numerically using the computational micromechanics approach. In this, the second in a series of four articles, the isothermal overall stress-strain behavior and its relation to microstructural deformation is examined in detail. The macroscopic strengthening effect of the reinforcement is quantified in terms of a hardness increment . As seen in the first article for microscale deformation, inhomogeneous and localized stress patterns develop in the microstructures. These are predominantly controlled by the positions of the reinforcing particles. Within the particles stress levels are high, indicating a load transfer from matrix to reinforcement. The higher straining that develops in the matrix grains, relative to the unreinforced polycrystal, causes matrix hardness advancement . Hydrostatic stress levels in the composite are enhanced by constraints on plastic flow imposed by the particles. Constrained plastic flow and matrix hardness advancement are seen as major composite strengthening mechanisms. The latter is sensitive to the strain hardening nature in the matrix alloy. To assess the effects of constraint more fully, simulations using external confining loads were performed. Both strengthening mechanisms depend strongly on reinforcement volume fraction and morphology. In addition, texture development and grain interaction influence the overall composite behavior. Failure mechanisms can be inferred from the microscale deformation and stress patterns. Intense strain localization and development of high stresses within particles and in the matrix close to the particle vertices indicate possible sites for fracture.

Computational modeling of metal matrix composite materials—II. Isothermal stress-strain behavior

The mechanical behavior of particulate reinforced metal matrix composites, in particular an SiC reinforced Al-3 wt% Cu model system, was analyzed numerically using the computational micromechanics approach. In this, the fourth and final article in a series, the microscale effects of thermo-mechanical processing is investigated in detail. Two ideal processes are considered. The first represents a simple quench and the second combines a high temperature compression, to simulate rolling or extrusion, with a quench. These processes, through applied deformation and thermal expansion mismatch, produce inhomogenous, and localized, stress and plastic strain fields in the composite microstructures. The structure of these residual fields can be related to reinforcement volume fraction and microstructural morphology. For the simple quench, volume average plastic strains are almost proportional to reinforcement volume fraction and there is a negligible morphological dependence. Large magnitude residual stress and strain fields, as well as large geometry changes, result from the second process. The effects of these processes on subsequent deformation behavior of composites for a selection of morphologies is investigated. Apart from almost doubling yield strains, the simple quench has relatively minor microscale and macroscale effects. The second process has a considerable effect on yield strength and introduces differences between tensile and compressive behavior on both the macroscale and microscale. Plastic constraint is an important mechanism. The physical relevance of these particular processing simulations, and the implications for modeling of microscale failure are discussed.

Computational modeling of metal matrix composite materials—IV. Thermal deformations

Computational mechanics has become increasingly concerned with the analysis of complex deformation processes and failure in material microstructures. In the work described in this article we use what, in light of this trend, we may call Computational micromechanics to study metal matrix composite materials, in particular materials with Al- 3 wt % Cu matrices reinforced with SiC particles. We focus on the evaluation of the performance of the microstructure, viz. deformation behavior, development of strenghtening mechanisms and failure mechanisms. We employ various methods to evaluate this performance, viz. variation of microstructural parameters such as 1) matrix properties, 2) volume fraction of reinforcement and 3) microstructural morphology; change in loading state; relation of macroscopic constitutive behavior to microscopic behavior using stress strain curves; introduction of the effects of processing, the residual stresses present due to working and temperature change. The modeling involves a detailed description of the material microstructure where individual matrix grains and reinforcing particles are represented and incorporates a physically based, rate dependent, crystallographic theory of plastic slip in the context of finite deformation kinematics. The theory is implemented using the finite element method.

R.J. Asaro

Papers

Computational modeling of metal matrix composite materials. I: Isothermal deformation patterns in ideal microstructures

Computational modeling of metal matrix composite materials—III. Comparisons with phenomenological models

Computational modeling of metal matrix composite materials—II. Isothermal stress-strain behavior

Computational modeling of metal matrix composite materials—IV. Thermal deformations

COMPUTATIONAL MODELING OF Al-Cu MATRIX, SiC REINFORCED COMPOSITE MATERIALS