Cavity formation from inclusions in ductile fracture

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 100? 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. This work has been presented in part orally at the Third International Conference on Fracture in Munich, Germany April 1973.     

Thermal cavity nucleation at intergranular inclusions in high temperature creep

The role of intergranular inclusions at the thermal cavity nucleation in high temperature creep is analysed in detail. The theoretical treatment is generalized for cavities the free surface curvature radius of which is comparable with the inclusion size and for cavities forming with inclusions the equilibrium systems. Special attention is devoted to the influence of the interface energies, the inclusions volume and the internal stress concentrations to the cavity nucleation kinetics. Each kinetics of cavity nucleation observed is qualitatively explained on the basis of the thermally activated heterogeneous cavity nucleation at intergranular inclusions.     

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

Experiments were performed on spheroidized 1045 steel, Cu-0.6 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.     

Effect of hydrostatic pressure on cavitation in superplastic aluminium alloys

Cavitation during superplastic flow has been examined in 3 aluminium alloys (Supral 220, Al-7475E and AlCuLi alloy) strained in uni-axial and bi-axial tension with varying superimposed hydrostatic pressures. Measurements of volume fractions, population densities and size distributions of cavities have been made using precision density and/or quantitative metallographic procedures. It has been found that the rate of increase of the volume fraction of cavities with strain can be decreased by increasing the superimposed pressure. The experimental observation that cavity growth is controlled primarily by plastic flow and that cavitation should be greatly reduced by pressures equal to approximately half of the effective flow stress of the material is in broad agreement with theoretical predictions. The difference between the magnitude of the experimentally determined cavity growth rate factors and the smaller predicted values is believed to arise from the combined effects of non-equilibrium cavity growth, coalescence and the decrease in strain rate sensitivity with strain. It is envisaged that superimposed pressures substantially greater than the flow stress of the material would be required to eliminate cavitation completely.     

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

Experiments were performed on spheroidized 1045 steel, Cu-0.6 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. This work has been presented in part orally at the Third International Conference on Fracture in Munich, Germany, April 1973.     

The interaction between deformation,fracture initiation and fracture propagation in two phase Co-CoAl alloys

Fracture initiation and propagation in two phase alloys containing fairly large volume fractions of nonplastically deforming inclusions have been analyzed. The Argon, Im and Safoglu treatment of fracture initiation of elastic inclusions as a result of back stresses resulting from strain accommodation of the phases has been extended to relatively large volume fractions of second phase. This allows calculation of the distribution of fractured particles as a function of alloy strain provided the fracture stress of the elastically deforming phase is known. The analysis has been applied to the Co-CoAl two phase alloy for volume fractions of CoAl ranging from about two to twenty-five pct. Quantitative metallographic analysis of fractured specimens indicates very good agreement between the measured fraction of fractured particles and those predicted from the theory without recourse to any adjustable parameters. Critical crack propagation in alloys of this type can also be analyzed on the basis of a fracture mechanics approach of Rice which was modified to consider that the crack spacing decreases with increasing strain due to cumulative hard phase cracking. The tensile strengths of the alloys can then be predicted with recourse to one adjustable parameter which varies with hard phase volume fraction. The deduced variation of this parameter with hard phase volume fraction, however, is as expected. Formerly graduate student, Michigan Technological University, Houghton, MI. Formerly Postdoctoral Research Associate, Michigan Technological University.     

Deformation consolidation of metal powders containing steel inclusions

Uniaxial consolidation experiments have been conducted at room temperature for two deformable metal powders (1100 Al and Pb5%Sb) containing various amounts of spherical steel inclusions. The experiments illustrate that the inclusion phase offers little constraint to matrix deformation at volume fractions <0.20, but produces a rapidly increasing constraint at larger volume fractions. Two constraining mechanisms have been identified through microstructural observations: (1) the matrix must be deformed more within the composite because of the excluded volume associated with the packing of particles and inclusions of different sizes, and (2) the inclusions form a continuous touching network (predicted with site percolation theory and direct observations of deformation flats on the steel spheres) which supports a portion of the applied stress and thus, partially “shields” the deformable phase from the total applied consolidation pressure. An analysis is presented to separate the contributions of each mechanism and shows that both mechanisms contribute comparable amounts to the constraint of matrix consolidation. It is suggested that because the inclusion network supports a significant portion of the applied pressure and releases its elastic strain in a non-linear manner (as described by Hertzian theory), the matrix is placed in tension when the applied pressure is released after consolidation.     

The effect of transformation stresses on the devitrification kinetics of a minory phase in liquid phase sintered ceramics

The crystallization of minory amorphous constituents in liquid phase sintered ceramics, for example in Si₃N₄, is usually accompanied by a volume change. The resulting mismatch between crystallizing second phase inclusions and the surrounding matrix of the primary phase leads to the formation of transformation stresses. The strain energy stored in the stress field reduces the thermodynamic driving force of crystallization. The coupling of crystallization, stress formation and relaxation is modelled. The extended duration of the crystallization process due to an intermediate stress induced decrease of the crystallization rate is assessed. The properties of amorphous grain boundary films are discussed with respect to stress relaxation and creep resistance at high temperatures.     

Microstructural observations of superplastic cavitation in fine grained 7475-Ai

Intergranular cavitation is an important consideration in the successful development of a commercially viable superplastic forming process for the high strength aluminum alloy, 7475. This work examined the microstructural features involved in the initiation stages of cavity formation. The observations suggest that, with the optimum superplastic deformation conditions, cavity nucleation is generally the rate determining step in the overall development of cavitation with strain. Cavities do not generally form at even the largest of the common single phase inclusion particles unless forming conditions are such that the flow stress significantly increases. It appears that, as well as local stress concentrations, additional effects are required, such as temperature induced particle decohesion and internal gas evolution, in order that cavities may grow to stable sizes. Such conditions may exist at certain two phase inclusion particles in the 7475 Al alloy. Suitable modifications to the standard alloy processing may therefore be devised which result in even lower rates of cavitation at the optimum superplastic forming conditions. C.C. BAMPTON, formerly at the Rockwell International Science Center J.W. EDINGTON, formerly at the University of Delaware     

Cavitation at grain and phase boundaries during superplastic flow of an aluminum bronze

Cavities have been observed to form at grain and phase boundaries under certain strain rate conditions during superplastic tensile deformation of a Cu-9.5 pct Al-4 pct Fe aluminum-bronze. The cavities form preferentially at α-β interfaces or triple junctions involving both phases. The process of cavitation is associated with grain boundary sliding and cavity nucleation probably occurs at points of stress concentration in the sliding interfaces. The ductility is not markedly impaired by the cavities because the high strain-rate sensitivity of the material inhibits the interlinkage of cavities at high strains. A range of strains and strain rates for superplastic forming processes has been determined at which the volume fraction of cavities present was tolerable.     

Crack and cavity nucleation at interfaces during creep

Athermal nucleation of microcracks and thermal nucleation of cavities during creep deformation are reviewed with an emphasis on effects of solute segregation to grain boundaries and cavity surfaces. The magnitude and the duration of stress concentration at a triple grain junction or at a grain boundary inclusion are estimated for transient Coble creep and steady state power-law creep conditions. Stable configurations of wedge-type microcracks are predicted by a Griffith-like crack model. The rate for thermal nucleation of cavities is obtained by the Fokker-Planck equation for vacancy clusters. Cracks and cavities are interdependent, and cavity nucleation occurs continuously throughout the three creep stages. The local stress concentration enhances microcrack and cavity nucleation. The cavity nucleation rate is generally increased as a result of solute segregation to the surfaces and interfaces and/or gas precipitation into cavity volume. This enhanced nucleation is more effective in a system with mobile solutes than with immobile solutes. Immobile solute or trace elements may affect the nucleation rate also by changing the grain boundary diffusivity. Experimental techniques for quantitative analyses of cavity nucleation processes are discussed. This paper is based on a presentation made at the symposium “The Role of Trace Elements and Interfaces in Creep Failure” held at the annual meeting of The Metallurgical Society of AIME, Dallas, Texas, February 14-18, 1982, under the sponsorship of The Mechanical Metallurgy Committee of TMS-AIME.     

Influence of inclusion content on fatigue crack

Fatigue crack growth rates were measured at room temperature in dry air for three 7075-T6 aluminum alloys with different inclusion content. Volume fractions of inclusions were determined for each alloy by the point count method with two different automated systems. Plots of the fatigue crack growth rate (da/dN) vs the stress-intensity-factor range (ΔK) show a well defined change of slope at the transition between plane strain and plane stress fracture. This transition is associated with a marked increase in the amount of fracture by void growth around inclusions. The volume fraction and mean spacing of voids within the cyclic plastic zone have been determined as a function of ΔK by quantitative fractography. Fracture by voids is important when the mean spacing of such voids is approximately equal to the width of the cyclic plastic zone in the plane of the crack. It is concluded that the inclusion content increases the fatigue-crack growth rates only within the plane stress range, that is for values of the stress-intensity-factor range ΔK \s> 20 kpsi√in.     

Multiparticle interfacial drag in equiaxed solidification

A physical model is proposed for the solid/liquid interfacial drag in both globular and dendritic equiaxed solidification. By accounting for the presence of multiple particles and the nonsphericity and porosity of the individual equiaxed crystals, a drag correlation is developed, which is valid over the full range of solid volume fractions. It is shown that neither the solid liquid interfacial area concentration nor the grain size alone is adequate to characterize the interfacial drag for equiaxed dendritic crystals in both the free particle and packed bed regimes; thus, the present model is based on a multiple length scale approach. The model predictions are compared to previous analytical and numerical results as well as to experimental data available in the literature, and favorable agreement is achieved. Formerly Graduate Research Assistant, Department of Mechanical Engineering, University of Iowa     

Elastic state and orientation of plate-shaped inclusions

The inclusion problem of linear elasticity is applied to predict the crystallography of misfitted plate-shaped inclusions with isotropic and anisotropic elastic constants. Habit-plane orientations are considered to be determined so as to minimize the elastic strain energy. When plastic accommodation occurs in the inclusion, the strain energy reduces and the habit-plane orientation changes. Similarities and differences between the present energy consideration and previous purely geometrical analyses are elucidated. The implication and significance of “incoherent” inclusions are discussed within the framework of micromechanics.     

Local and Global Stress–Strain Behaviors of Transformation-Induced Plasticity Steel Using the Combined Nanoindentation and Finite Element Analysis Method

Transformation-induced plasticity (TRIP) steels have excellent strain hardening exponents and resistibility against tensile necking using the strain-induced martensite formation that occurs as a result of the plastic deformation and strain on the retained austenite phase. Detailed studies on the microstructures and local mechanical properties, as well as global mechanical properties, are necessary in order to thoroughly understand the properties of TRIP steels with multiple phases of ferrite, bainite, retained austenite, and martensite. However, methods for investigating the local properties of the various phases of the TRIP steel are limited due to the very complicated and fine microstructures present in TRIP steel. In this study, the experimental and numerical methods, i.e., the experimental nanoindenting results and the theoretical finite element analyses, were combined in order to extract the local stress–strain curves of each phase. The local stress–strain curves were in good agreement with the values presented in the literature. In particular, the global plastic stress–strain behavior of the TRIP steel was predicted using the multiple phase unit cell finite element analysis, and this demonstrated the validity of the obtained properties of each local phase. The method of extracting the local stress–strain curves from the nanoindenting curves and predicting the global stress–strain behavior assists in clarifying the smart design of multi-phase steels.     

Cavity nucleation at high temperatures involving pile-ups of grain boundary dislocations

The current concept of sliding-induced cavitation is first reviewed, with due consideration to the respective role of the remote and internal stresses. The results show that the transient stresses produced by sliding play only a secondary role in cavity nucleation and that at high temperatures, the effect of sliding is eliminated in less than 1 millisecond. It is thus concluded that sliding cannot be the cause for cavity nucleation. Next, a model involving pile-ups of grain boundary dislocations (GBDs) is proposed. Unlike the sliding mechanism, the high strain energy ahead of the pile-up is a steady state phenomenon during secondary creep. It helps to compensate the large capillarity forces in the formation of sub-micron sized cavities, thereby rendering cavity nucleation barrierless. However, a threshold stress exists below which the cavities cannot grow to effect fracture. The present model suggests that cavity nucleation is feasible in single phase metals and alloys at the intersections of cell and grain boundaries. Predominant cavity formation after the onset of steady state creep and an intermediate temperature ductility trough during hot tensile tests are also features of the model. Good agreements are found between the model's predictions and the experiments.     

Calculation of the Critical Radius of an Inclusion for Fracture from a Porous Matrix under the Conditions of Plastic Deformation

This work is concerned with the theoretical determination of the critical radius of a rigid inclusion at the moment of its decohesion from the material of a porous matrix. The criterion of V. V. Skorokhod served as the basis for analysis of the limiting state. Change of the porosity and accumulated strain of the solid phase in the process of plastic deformation were taken into account in the calculations. It is shown that the values of investigated properties depend on the concentration of inclusions and the porosity of the ductile layer. The dependence of accumulated strain in the solid phase on porosity was obtained.     

Theoretical calculation of the stress-strain behavior of dual-phase metals with randomly oriented spheroidal inclusions

A simple model is developed to determine the overall response of dual-phase metals with an inclusion/matrix microgeometry. The inclusions are taken to be spheroidal in shape and are randomly oriented and homogeneously dispersed in the matrix. No restriction is placed on whether the inclusions are harder or softer (in the sense of flow stress) than the matrix, and as with most dual-phase metals, both phases are capable of undergoing plastic flow. The yielding process of the inclusions is now orientation dependent and sequential, and the overall elastoplastic response of the two-phase system is found to be strongly dependent upon the inclusion shape and concentration, even more so than on the corresponding elastic behavior. Disc-shaped inclusions generally give a superior reinforcing effect when the matrix is the softer phase, whereas spherical inclusions are more effective when the matrix is the harder one. As compared to the condition when the inclusions are strictly elastic, the plasticity of inclusions is found to translate into noticeable reduction in the flow stress of the composite. Comparison of the theoretical prediction with the experimental data for a ferrite/austenite system further shows a reasonable agreement.     

自蔓延-离心不锈钢内衬钢管应力及裂纹研究

通过热应力计算及不锈钢层组织分析，研究了SHS－离心法制备的不锈钢内衬复合钢管不锈钢层中裂纹产生的原因以及消除裂纹的措施，研究表明，内衬层开裂是钢中的夹杂使钢变脆以及冷却过程中热应力共同作用的结果，通过加速相分离过程、减少内衬层中的夹杂、提高塑性以及提高钢中奥氏体含量等措施，可消除不锈钢层中的裂纹。