Analysis of the cup-cone fracture in a round tensile bar

Particle reinforced metal matrix composites are now being produced commerically, and in this paper the current status of these materials is reviewed. The different types of reinforcement being used, together with the alternative processing methods, are discussed. Depending on the initial processing method, different factors have to be taken into consideration to produce a high quality billet. With powder metallurgy processing, the composition of the matrix and the type of reinforcement are independent of one another. However, in molten metal processing they are intimately linked in terms of the different reactivities which occur between reinforcement and matrix in the molten state. The factors controlling the distribution of reinforcement are also dependent on the initial processing method. Secondary fabrication methods, such as extrusion and rolling, are essential in processing composites produced by powder metallurgy, since they are required to consolidate the composite fully. Other methods, suc...

Particle reinforced aluminium and magnesium matrix composites

A cohesive zone model, taking full account of finite geometry changes, is used to provide a unified framework for describing the process of void nucleation from in­itial debonding through complete decohesion. A boundary value problem simulating a periodic array of rigid spherical inclusions in an isotropically hardening elastic-viscoplastic matrix is analyzed. Dimensional considerations introduce a characteristic length into the formulation and, depending on the ratio of this characteristic length to the inclusion radius, decohesion occurs either in a "ductile" or "brittle" manner. The effect of the triaxiality of the imposed stress state on nucleation is studied and the numerical results are related to the description of void nucleation within a phenomenological constitutive framework for progressively cavitating solids. 1 Introduction The nucleation of voids from inclusions and second phase particles plays a key role in limiting the ductility and toughness of plastically deforming solids, including structural metals and composites. The voids initiate either by inclusion cracking or by decohesion of the interface, but here attention is confined to consideration of void nucleation by interfacial decohesion. Theoretical descriptions of void nucleation from second phase particles have been developed based on both continuum and dislocation concepts, e.g., Brown and Stobbs (1971), Argon et al. (1975), Chang and Asaro (1978), Goods and Brown (1979), and Fisher and Gurland (1981). These models have focussed on critical conditions for separation and have not explicitly treated propagation of the debonded zone along the interface. Interface debonding problems have been treated within the context of continuum linear elasticity theory; for example, the problem of separation of a circular cylindrical in­clusion from a matrix has been solved for an interface that supports neither shearing nor tensile normal tractions (Keer et al., 1973). The growth of a void at a rigid inclusion has been analyzed by Taya and Patterson (1982), for a nonlinear viscous solid subject to overall uniaxial straining and with the strength of the interface neglected. The model introduced in this investigation is aimed at describing the evolution from initial debonding through com­plete separation and subsequent void growth within a unified framework. The formulation is a purely continuum one using a cohesive zone (Barenblatt, 1962; Dugdale, 1960) type model for the interface but with full account taken of finite geometry

A Continuum Model for Void Nucleation by Inclusion Debonding

A continuum model for void nucleation by inclusion debonding

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.

Particulate reinforced metal matrix composites — a review

The previously proposed conditions for cavity formation from equiaxed inclusions in ductile fracture have been examined. Critical local elastic energy conditions are found to be necessary but not sufficient for cavity formation. The interfacial strength must also be reached on part of the boundary. For inclusions larger than about 100A the energy condition is always satisfied when the interfacial strength is reached and cavities form by a critical interfacial stress condition. For smaller cavities the stored elastic energy is insufficient to open up interfacial cavities spontaneously. Approximate continuum analyses for extreme idealizations of matrix behavior furnish relatively close limits for the interfacial stress concentration for strain hardening matrices flowing around rigid non-yielding equiaxed inclusions. Such analyses give that in pure shear loading the maximum interfacial stress is very nearly equal to the equivalent flow stress in tension for the given state of plastic strain. Previously proposed models based on a local dissipation of deformation incompatibilities by the punching of dislocation loops lead to rather similar results for interfacial stress concentration when local plastic relaxation is allowed inside the loops. At very small volume fractions of second phase the inclusions do not interact for very substantial amounts of plastic strain. In this regime the interfacial stress is independent of inclusion size. At larger volume fractions of second phase, inclusions begin to interact after moderate amounts of plastic strain, and the interfacial stress concentration becomes dependent on second phase volume fraction. Some of the many reported instances of inclusion size effect in cavity formation can thus be satisfactorily explained by variations of volume fraction of second phase from point to point.

Cavity formation from inclusions in ductile fracture

The distributions of plastic strain and negative pressure (hydrostatic tensile stress) have been computed both by an approximate method based on an extension of the Bridgman development and by a finite element analysis in inhomogeneously deforming bars after necking. The computations have been made for both initially smooth bars as well as bars having machined initial natural neck profiles, for two types of stress-strain behavior, modelling a spheroidized 1045 steel and a fully aged Cu-0.5 pct Cr alloy. The results of the finite element analysis show that the approximate method based on an extension of the Bridgman development is good only for slightly necked bars. In more acutely necked bars the Bridgman development is good only near the center of the neck. Some experimental results on strain distribution and on neck profiles are also presented.

A. S. Argon

Papers

Cavity formation from inclusions in ductile fracture

Distribution of plastic strain and negative pressure in necked steel and copper bars