[신간의 별자리x] 우리/미술, 그리고 ‘슬픔의 박물관’

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 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

Experiments were performed on spheroidized 1045 steel, Cu-06 pct Cr alloy, and maraging steel containing respectively Fe3C, Cu-Cr, and TiC particles of nearly equiaxed shape The local interfacial stresses for separation of these particles during plastic deformation were evaluated by the methods described in the two preceding papers The results show that the interfacial strengths for these particles in their respective matrices are 242, 144, and 264 ksi In the spheroidized steel the average diam of the separated particles is distinctly larger than the average diam of the whole population This is quantitatively explained by the enhanced interfacial stresses developed in regions of above average volume fraction of second phase which frequently occur in very dense populations of particles No such effect was observed in the other two systems which is consistent with their much lower volume fraction of second phase Some tension experiments have also been performed with the spheroidized 1045 steel at elevated temperature, giving results qualitatively similar to those at room temperature

Separation of second phase particles in spheroidized 1045 steel, Cu-0.6pct Cr alloy, and maraging steel in plastic straining

In 3-D interconnect structures, process-induced thermal stresses around through-silicon-vias (TSVs) raise serious reliability issues such as Si cracking and performance degradation of devices. In this study, the thermo-mechanical reliability of 3-D interconnect was investigated using finite element analysis (FEA) combined with analytical methods. FEA simulation demonstrated that the thermal stresses in silicon decrease as a function of distance from an isolated TSV and increase with the TSV diameter. Additional simulation suggested that hybrid TSV structures can significantly reduce the thermal stresses. An analytical stress solution was introduced to deduce the stress distribution around an isolated TSV, which was further developed to deduce the stress interaction in TSV arrays based on linear superposition of the analytical solution. We calculated the crack driving force in TSV lines under a thermal load. The effects of TSV diameter, pitch size, and the line configuration on crack driving force were investigated.

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Thermo-mechanical reliability of 3-D ICs containing through silicon vias

In this paper we investigated the interfacial delamination of through silicon via (TSV) structures under thermal cycling or processing. First finite element analysis (FEA) was used to evaluate the thermal stresses and the driving force of TSV delamaination. Then, the modeling results were validated by analytical solutions of the crack driving force deduced for a long crack at the steady state. Both results were found to be in good agreement at the steady state and together they suggested a fracture mechanism to account for the TSV delamination observed. The analytical solution further provided a basic framework for studying the impact of materials, process and structural design on reliability of the TSV structure. In particular, we found that reducing the TSV diameter yields a definite advantage in lowering the crack driving force. In addition, annular TSVs and an overlaying metal pad on a TSV can reduce the crack driving force for delamination during thermal cycling. Finally, the metallization effect was investigated for four TSV materials: copper, aluminum, nickel, and tungsten. Tungsten was found to have the smallest crack driving force due to the least thermal mismatch with the surrounding silicon. The reliability implication was discussed.

/pdf/thermal-stress-induced-delamination-of-through-silicon-vias-2e8srq6e7n.pdf

Thermal stress induced delamination of through silicon vias in 3-D interconnects

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.

Jay Im

Papers

Cavity formation from inclusions in ductile fracture

Separation of second phase particles in spheroidized 1045 steel, Cu-0.6pct Cr alloy, and maraging steel in plastic straining

Thermo-mechanical reliability of 3-D ICs containing through silicon vias

Thermal stress induced delamination of through silicon vias in 3-D interconnects

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