The hardening of crystals by non-deforming particles and fibres
TL;DR: In this paper, a theory was developed to explain the work hardening behaviors of crystals with non-deforming inclusions, which predicts that the rate of workhardening will be linear, and that this rate will be nearly proportional to the volume fraction of the inclusions.
About: This article is published in Acta Metallurgica.The article was published on 1970-08-01. It has received 272 citations till now. The article focuses on the topics: Strain hardening exponent & Work hardening.
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TL;DR: In this paper, a method of calculating the average internal stress in the matrix of a material containing inclusions with transformation strain is presented. But the authors do not consider the effects of the interaction among the inclusions and of the presence of the free boundary.
7,000 citations
TL;DR: The physical and mechanical properties that can be obtained with metal matrix composites (MMCs) have made them attractive candidate materials for aerospace, automotive and numerous other applications as discussed by the authors.
Abstract: The physical and mechanical properties that can be obtained with metal matrix composites (MMCs) have made them attractive candidate materials for aerospace, automotive and numerous other applications. More recently, particulate reinforced MMCs have attracted considerable attention as a result of their relatively low costs and characteristic isotropic properties. Reinforcement materials include carbides, nitrides and oxides. In an effort to optimize the structure and properties of particulate reinforced MMCs various processing techniques have evolved over the last 20 years. The processing methods utilized to manufacture particulate reinforced MMCs can be grouped depending on the temperature of the metallic matrix during processing. Accordingly, the processes can be classified into three categories: (a) liquid phase processes, (b) solid state processes, and (c) two phase (solid-liquid) processes. Regarding physical properties, strengthening in metal matrix composites has been related to dislocations of a very high density in the matrix originating from differential thermal contraction, geometrical constraints and plastic deformation during processing.
1,624 citations
TL;DR: A heterogeneous lamella structure in Ti produced by asymmetric rolling and partial recrystallization that can produce an unprecedented property combination: as strong as ultrafine-grained metal and at the same time as ductile as conventional coarse- grained metal.
Abstract: Grain refinement can make conventional metals several times stronger, but this comes at dramatic loss of ductility. Here we report a heterogeneous lamella structure in Ti produced by asymmetric rolling and partial recrystallization that can produce an unprecedented property combination: as strong as ultrafine-grained metal and at the same time as ductile as conventional coarse-grained metal. It also has higher strain hardening than coarse-grained Ti, which was hitherto believed impossible. The heterogeneous lamella structure is characterized with soft micrograined lamellae embedded in hard ultrafine-grained lamella matrix. The unusual high strength is obtained with the assistance of high back stress developed from heterogeneous yielding, whereas the high ductility is attributed to back-stress hardening and dislocation hardening. The process discovered here is amenable to large-scale industrial production at low cost, and might be applicable to other metal systems.
1,063 citations
Cites background from "The hardening of crystals by non-de..."
...First, it has been reported that the elongated inclusions produce higher strain hardening than spherical ones, especially when its long axis is aligned in the loading direction (32), which is the case in this study....
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TL;DR: In this article, a simple model for single-slip and multiple-slink deformation is proposed, in which the crystal is considered as a composite consisting of hard dislocation walls of high local dislocation density which are separated by soft regions of low local dislocations density.
1,001 citations
TL;DR: In this article, the deformation characteristics of ceramic whisker- and particulate-reinforced metal-matrix composites were studied experimentally and numerically with the objective of investigating the dependence of tensile properties on the matrix microstructure and on the size, shape, and distribution of the reinforcement phase.
721 citations
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TL;DR: In this article, a new theory of work hardening in dispersion-hardened single crystals is described, which is based on the fact that, if the particles do not deform plastically, and the interface between particle and matrix does not fracture, then secondary slip must occur locally round each particle when the crystal is deformed, even though the crystal may appear to deform by single slip.
Abstract: A new theory of work hardening in dispersion-hardened single crystals—by which we mean soft crystals containing hard non-deforming particles of a second phase—is described. It is based on the fact that, if the particles do not deform plastically, and the interface between particle and matrix does not fracture, then secondary slip must occur locally round each particle when the crystal is deformed, even though the crystal may appear to deform by ‘single slip’. The density of secondary dislocations rises steeply with strain, and acts as a forest impeding the movement of primary glide dislocations. The theory predicts a relation between stress and strain (eqn. (9)) which is in good agreement with experimental results. Fracture of the particle-matrix interface, and the importance of the strength of this interface, are discussed.
528 citations
TL;DR: In this paper, the dependence of the hardening effect of precipitate particles is computed in terms of a model in which the precipitate particle cause the dislocations from activated Frank-Read sources to form closed loops about the particles.
217 citations
TL;DR: In this paper, the effect of particles on the critical shear stress is described, and it is shown that solution hardening and particle hardening are additive at the critical stress.
Abstract: Pure copper single crystals of fixed orientation, containing dispersions of spherical particles of SiO2, were tested in tension. The crystals deform by single slip until the tensile axis reaches a symmetrical orientation, while the particles remain undeformed. The characteristic shear stresses, and rates of work hardening, of the crystals depend on particle size, spacing and volume fraction, on the temperature and strain rate of the test, and on the shear strength of the matrix material. The effect of particles on the critical shear stress is described, and it is shown that solution hardening and particle hardening are additive at the critical shear stress. The transition from the three stages of work-hardening characteristic of pure copper single crystals to the parabolic curve characteristic of dispersion hardened copper is described by analysing the effect of particles on each stage. Particles introduce a near-parabolic ‘stage α’ which occupies more and more of the stress-strain curve as the v...
189 citations
TL;DR: In this paper, a new theory for cavitation at the interface of a spherical inclusion in a plastically deformed matrix under uniaxial tensile stress is proposed, based on the energy calculation in and around the inclusion following Eshelby's transformation problem.
Abstract: A new theory for cavitation at the interface of a spherical inclusion in a plastically deformed matrix under uniaxial tensile stress is proposed. It is based on the energy calculation in and around the inclusion following Eshelby's transformation problem. It is shown that there is a size below which the fracture strain is inversely proportional to the square root of the particle size. There is also a size above which the applied stress causes cavitation without plastic strain.
182 citations
TL;DR: In this article, the authors made careful measurements of the stress-strain curves of tungsten wires of 10 μ and 20 μ diameter and of aligned composites of the same wires in copper at strains greater than the yield strain of the copper.
Abstract: Careful measurements have been made of the stress-strain curves of tungsten wires of 10 μ and 20 μ diameter and of aligned composites of the same wires in copper At strains greater than the yield strain of the copper the apparent stresses in the matrix, evaluated from the law of mixtures, are very high The effect appears to be due to the mutual constraint of the two phases caused by their different lateral contractions, since it disappears when the fibres yield and hence the transverse contractions become the same The experimental results are compared with those predicted for a completely plastic matrix and the stresses are found to be higher than calculated This is interpreted to mean that the yield of the copper is gradual, and that during stage II of the stress-strain curve of the composites an appreciable portion of the copper continues to deform elastically
111 citations