Populations Of Second Phase Particles Research Articles

A level set approach to simulate grain growth with an evolving population of second phase particles

In numerous polycrystalline materials, grain size is controlled by second phase particles (SPPs) that hinder the grain boundaries (GBs) by pinning mechanisms. The Smith–Zener pinning (SZP) model describes the physical interaction between SPPs and GBs. Both of them can evolve when applying a heat treatment to the material. As industrial forging processes involve hot deformation steps near the solvus temperature, it is thus of prime importance to characterize the evolution of the SPPs due to their impact on the final microstructure, notably on the grain size. The level set (LS) method is classically used to describe the influence of SPPs on grain growth (GG) by considering the simulated particles as inert and represented by static holes in the used finite element (FE) mesh. A new formalism to model GG mechanism under the influence of the SZP phenomenon, able to take into account evolving particles is proposed. It involves the representation of SPPs by a LS function and a particular numerical treatment around the grain interfaces encountering SPP, making possible the modelling of SPPs evolution without altering the undergoing pinning pressure. Validation and comparison of the new method regarding previous FE-LS formulation in 2D and 3D simulations and an application on GG under the influence of dissolving particles are described.

Influence of Solution and Aging Treatment Conditions on the Formation of Ultrafine-Grained Structure of CuFe2 Alloy Processed by Rolling with Cyclic Movement of Rolls

Abstract The effect of second phase particles on grain refinement in CuFe2 alloy has been investigated by using rolling with the cyclic movement of rolls (RCMR) method. Two different population of second phase particles of Fe: coherent, about 10 nm in diameter and about 100 nm in size were obtained by applying aging treatment followed at 500°C for 2 h and at 700°C for 24 h respectively. In addition, solution treated samples were deformed by RCMR method at the same parameters. The microstructures of the CuFe2 alloy were analyzed using light microscope (LM), electron backscattered diffraction (EBSD) microscope technique and scanning transmission electron microscope (STEM). The presence of high-density of coherent Fe particles in the matrix inhibits recovery process and in the result obtained grain/subgrain boundaries have diffused character and are weakly visible. The largest particles which are not coherent with the matrix act as an effective barrier against the boundary motion.

Prediction of Ductile Fracture Surface Roughness Scaling

Experimental observations have shown that the roughness of fracture surfaces exhibit certain characteristic scaling properties. Here, calculations are carried out to explore the extent to which a ductile damage/fracture constitutive relation can be used to model fracture surface roughness scaling. Ductile crack growth in a thin strip under mode I, overall plane strain, small scale yielding conditions is analyzed. Although overall plane strain loading conditions are prescribed, full 3D analyses are carried out to permit modeling of the three dimensional material microstructure and of the resulting three dimensional stress and deformation states that develop in the fracture process region. An elastic-viscoplastic constitutive relation for a progressively cavitating plastic solid is used to model the material. Two populations of second phase particles are represented: large inclusions with low strength, which result in large voids near the crack tip at an early stage, and small second phase particles, which require large strains before cavities nucleate. The larger inclusions are represented discretely and various three dimensional distributions of the larger particles are considered. The scaling properties of the predicted thickness average fracture surfaces are calculated and the results are discussed in light of experimental observations.

Three dimensional microstructural effects on plane strain ductile crack growth

Ductile crack growth under mode I, plane strain, small scale yielding conditions is analyzed. Overall plane strain loading is prescribed, but a full 3D analysis is carried out to model three dimensional microstructural effects. An elastic-viscoplastic constitutive relation for a porous plastic solid is used to model the material. Two populations of second-phase particles are represented, large inclusions with low strength, which result in large voids near the crack tip at an early stage, and small second-phase particles, which require large strains before cavities nucleate. The larger inclusions are represented discretely and the effects of different three dimensional distributions on the crack path and on the overall crack growth rate are analyzed. For comparison purposes, a two dimensional distribution of cylindrical inclusions is analyzed. Crack growth occurs off the initial crack plane in all 3D computations, whereas straight ahead crack growth occurs with the two dimensional cylindrical inclusions. As a consequence, the three dimensional distributions of spherical inclusions exhibit an increased crack growth resistance as compared to the two dimensional distribution of cylindrical inclusions.

Damage sensitivity in a commercial Al alloy processed by equal channel angular extrusion

A 5083 Al–Mg is processed by equal channel angular extrusion (ECAE) at 150 °C according to various routes. The resulting microstructures are characterised and tested in tensile conditions at high temperature. A particular attention is given to strain induced damage and to the effect of ECAE on the population of second phase particles initially present in the alloy. The relation between the second phase particles and the cavities are investigated by X-ray micro-tomography, which provides three-dimensional (3D) microstructural characterisations. It is shown that the mean size of the particles is progressively reduced by fragmentation when the number of extrusions is increased. Despite this reduction, the damage sensitivity of the alloy is not reduced since during ECAE, some cracks are generated and the average distance between the particles is decreased. Moreover, due to low temperature of deformation, superplastic properties of the ECAE processed microstructures are associated to relatively large stresses, which can promote cavity nucleation. Lastly, it is shown that despite small grain sizes (≈1 μm), the role of diffusion in the control of cavity growth is minor and that the extent of cavity coalescence before fracture remains limited.

Constraint effects on the ductile-brittle transition in small scale yielding

The effect of constraint on the ductile-brittle transition is investigated numerically under small scale yielding conditions in plane strain. An elastic-viscoplastic constitutive relation for a porous plastic solid is used to model ductile fracture by the nucleation and subsequent growth of voids to coalescence. Two populations of second phase particles are represented, large inclusions with low strength, which result in large voids near the crack tip at an early stage, and small second phase particles, which require large strains before cavities nucleate. Adiabatic heating due to plastic dissipation and the resulting thermal softening are accounted for in the analyses. Cleavage is modeled in terms of attaining a temperature and strain rate-independent critical value of the maximum principal stress over a specified material region. A characteristic length is associated with each failure mechanism; the large inclusion spacing for ductile failure and size of the cleavage region for brittle failure. The crack growth predictions are consequences of the constitutive characterization of the material, so that the present study is free from ad hoc assumptions regarding appropriate crack growth criteria. The numerical results show that the extent of cleavage fracture relative to ductile fracture is strongly controlled by temperature and constraint. Fracture resistance curves are obtained for a range of conditions.

Three dimensional analysis of dynamic ductile crack growth in a thin plate

A three dimensional analysis of dynamic ductile crack growth in an edge cracked plate is carried out, using a data parallel implementation in a transient three dimensional finite element program. An elastic-viscoplastic constitutive relation for a porous plastic solid is used to model ductile fracture by the nucleation and subsequent growth of voids to coalescence. Two populations of second phase particles are represented, large inclusions with low strength, which result in large voids near the crack tip at an early stage, and small second phase particles, which require large strains before cavities nucleate. Adiabatic heating owing to plastic dissipation and the resulting thermal softening are accounted for in the analyses. The crack speed and the crack path are based on the ductile failure predictions of the material model, so that the present study is free from ad hoc assumptions regarding appropriate dynamic crack growth criteria. A convected coordinate Lagrangian formulation is employed and the discretization is based on twenty-node brick elements with 2 × 2 × 2 Gauss points. The equations of motion are integrated numerically by an explicit integration procedure using a lumped mass matrix. Crack growth occurs by tunneling in the central part of the plate and shear lip formation at the free surface. The effect of various material parameters and of plate thickness on this process is studied. For comparison purposes, a calculation with overall plane strain boundary conditions is carried out.

A numerical investigation of ductile fracture initiation in a high-strength low-alloy steel

In this work, static and drop-weight impact experiments, which have been conducted using three-point bend fracture specimens of a high-strength low-alloy steel, are analysed by performing finite-element simulations. The Gurson constitutive model that accounts for the ductile failure mechanisms of microvoid nucleation, growth and coalescence is employed within the framework of a finite deformation plasticity theory. Two populations of second-phase particles are considered, including large inclusions which initiate voids at an early stage and small particles which require large strains to nucleate voids. The most important objective of the work is to assess quantitatively the effects of material inertia, strain rate sensitivity and local adiabatic temperature rise (due to conversion of plastic work into heat) on dynamic ductile crack initiation. This is accomplished by comparing the evolution histories of void volume fraction near the notch tip in the static analysis with the dynamic analyses. The results indicate that increased strain hardening caused by strain rate sensitivity, which becomes important under dynamic loading, plays a benign role in considerably slowing down the void growth rate near the notch tip. This is partially opposed by thermal softening caused by adiabatic heating near the notch tip.

Mesh effects in the analysis of dynamic ductile crack growth

For numerical studies of dynamic crack growth the mesh sensitivity of the crack growth predictions is investigated. The computed crack growth behavior is based on the ductile fracture predictions of an elastic-viscoplastic constitutive relation for a porous plastic solid, which models the nucleation and growth of voids to coalescence. Both initially sharp and initially blunt cracks are analyzed. Two populations of second-phase particles are represented: large inclusions with low strength, which result in large voids near the crack tip at an early stage, and small second-phase particles, which require large strains before cavities nucleate. For the larger voids the size and spacing are directly specified in the analyses, whereas no length scale is specified for the small-scale voids. Crack growth predictions in cases where the large-scale voids dominate show practically no mesh sensitivity, whereas cases dominated by the small-scale voids show a clear mesh sensitivity. For initially sharp cracks the initiation of crack growth is quite sensitive to the mesh. However, for initially blunt cracks the mesh sensitivity of the initiation time is removed.

Effect of crack meandering on dynamic, ductile fracture

Dynamic crack growth is analyzed numerically for a plane strain edge cracked specimen subject to impulsive tensile loading at one end. An elastic—viscoplastic constitutive relation for a porous plastic solid is used to model ductile fracture by the nucleation and subsequent growth of voids to coalescence. Two populations of second-phase particles are represented: large inclusions with low strength, which result in large voids near the crack tip at an early stage, and small second-phase particles, which require large strains before cavities nucleate. Adiabatic heating due to plastic dissipation and the resulting thermal softening are accounted for in the analyses. Various two-dimensional distributions of the larger inclusions in front of the crack tip are considered, while the small second-phase particles are taken to be uniformly distributed. It is found that in most cases cracks grow in a zig-zag manner, dependent on the distribution of larger inclusions. Predictions for the dynamic crack growth behavior and for the time variation of crack tip characterizing parameters are obtained for each case analyzed. The computed crack growth paths and speeds are entirely based on the ductile failure predictions of the material model, so that the present study is free from ad hoc assumptions regarding appropriate dynamic crack growth criteria.

An analysis of dynamic, ductile crack growth in a double edge cracked specimen

Dynamic crack growth is analysed numerically for a plane strain double edge cracked specimen subject to symmetric impulsive tensile loading at the two ends. The material behavior is described in terms of an elastic-viscoplastic constitutive model that accounts for ductile fracture by the nucleation and subsequent growth of voids to coalescence. Two populations of second phase particles are represented, including large inclusions or inclusion colonies with low strength, which result in large voids near the crack tip at an early stage, and small second phase particles, which require large strains before cavities nucleate. The crack growth velocities determined here are entirely based on the ductile failure predictions of the material model, and thus the present study is free from ad hoc assumptions regarding appropriate dynamic crack growth criteria. Adiabatic heating due to plastic dissipation and the resulting thermal softening are accounted for in the analyses. Different prescribed impact velocities, inclusion spacings and values of the inclusion nucleation stress are considered. Predictions for the dynamic crack growth behavior and for the time variation of crack tip characterizing parameters are obtained for each case analyzed.

A numerical study of void distribution effects on dynamic, ductile crack growth

Rapid crack propagation through a material containing two populations of second phase particles is analysed numerically. An elastic-viscoplastic model of a ductile porous material is used to represent small second phase particles that nucleate cavities at large strains as well as larger inclusions with low strength, which result in large voids near the crack tip at an early stage. Various random distributions of the larger inclusions in front of the crack tip are considered, while the small second phase particles are taken to be uniformly distributed. Analyses are carried out for a plane strain double edge cracked specimen under symmetric impulsive loading at the ends and adiabatic heating and the resulting thermal softening are accounted for. The predicted crack growth velocities are entirely based on the ductile failure criterion incorporated in the material model, and thus the present results give a direct estimate of the effect of various random inclusion distributions, compared to results for a uniform distribution. The resistance to crack growth increases and the average crack speed decays with increasing deviation from a uniform inclusion spacing. The dependence of the average crack speed on the root mean square particle spacing is found to be approximately linear over the range considered.