Modelling and Simulation in Materials Science and Engineering

Paul, Surajit Kumar

doi: 10.1088/0965-0393/21/5/055001pmid: N/A

The microstructure of dual-phase (DP) steels typically consists of a soft ferrite matrix with dispersed islands of hard martensite phase. Due to the composite effect of ferrite and martensite, DP steels exhibit a unique combination of strain hardening, strength and ductility. A microstructure-based micromechanical modeling approach is adopted in this work to capture the tensile and cyclic plastic deformation behavior of DP steel. During tensile straining, strain incompatibility between the softer ferrite matrix and the harder martensite phase arises due to a difference in the flow characteristics of these two phases. Microstructural-level inhomogeneity serves as the initial imperfection, triggering strain incompatibility, strain partitioning and finally shear band localization during tensile straining. The local deformation in the ferrite phase is constrained by adjacent martensite islands, which locally results in stress triaxiality development in the ferrite phase. As the martensite distribution varies within the microstructure, the stress triaxiality also varies in a band within the microstructure. Inhomogeneous stress and strain distribution within the softer ferrite phase arises even during small tensile straining because of material inhomogeneity. The magnitude of cyclic plastic deformation within the softer ferrite phase also varies according to the stress distribution in the first-quarter cycle tensile loading. Accumulation of tensile/compressive plastic strain with number of cycles is noted in different locations within the ferrite phase during both symmetric stress and strain controlled cycling. The basic mode of cyclic plastic deformation in an inhomogeneous material is cyclic strain accumulation, i.e. ratcheting. Microstructural inhomogeneity results in cyclic strain accumulation in the aggregate DP material even in symmetric stress cycling.

Gao, H; Otero-de-la-Roza, A; Aouadi, S M; Johnson, E R; Martini, A

doi: 10.1088/0965-0393/21/5/055002pmid: N/A

A set of parameters for the modified embedded atom method (MEAM) potential was developed to describe the perovskite silver tantalate (AgTaO3). First, MEAM parameters for AgO and TaO were determined based on the structural and elastic properties of the materials in a B1 reference structure predicted by density-functional theory (DFT). Then, using the fitted binary parameters, additional potential parameters were adjusted to enable the empirical potential to reproduce DFT-predicted lattice structure, elastic constants, cohesive energy and equation of state for the ternary AgTaO3. Finally, thermal expansion was predicted by a molecular dynamics (MD) simulation using the newly developed potential and compared directly to experimental values. The agreement with known experimental data for AgTaO3 is satisfactory, and confirms that the new empirical model is a good starting point for further MD studies.

Kuykendall, William P; Cai, Wei

doi: 10.1088/0965-0393/21/5/055003pmid: N/A

For two-dimensional dislocation dynamics simulations under periodic boundary conditions in both directions, the summation of the periodic image stress fields is found to be conditionally convergent. For example, different stress fields are obtained depending on whether the summation in the x-direction is performed before or after the summation in the y-direction. This problem arises because the stress field of a 1D periodic array of dislocations does not necessarily go to zero far away from the dislocation array. The spurious stress fields caused by conditional convergence in the 2D sum are shown to consist of only a linear term and a constant term with no higher order terms. Absolute convergence, and hence self-consistency, is restored by subtracting the spurious stress fields, whose expressions are derived in both isotropic and anisotropic elasticity.

Stenzel, O; Westhoff, D; Manke, I; Kasper, M; Kroese, D P; Schmidt, V

doi: 10.1088/0965-0393/21/5/055004pmid: N/A

A stochastic model is proposed for the efficient simulation of complex three-dimensional microstructures consisting of two different phases. The model is based on a hybrid approach, where in a first step a graph model is developed using ideas from stochastic geometry. Subsequently, the microstructure model is built by applying simulated annealing to the graph model. As an example of application, the model is fitted to a tomographic image describing the microstructure of electrodes in Li-ion batteries. The goodness of model fit is validated by comparing morphological characteristics of experimental and simulated data.

Xiang, Meizhen; Hu, Haibo; Chen, Jun; Long, Yao

doi: 10.1088/0965-0393/21/5/055005pmid: N/A

We present a molecular dynamics (MD) study of the micro-spallation of lead (Pb), which corresponds to damage and liquid fragment ejection following the reflection of a strong shock wave on the free surface of the target. First, the Hugoniot and melting curves of Pb are derived by equilibrium MD simulations, and the potential function is validated by comparing these curves with experimental results. Then nonequilibrium MD simulations are conducted to study the dynamical processes of micro-spallation. Damage and ejection processes are analyzed by a binning analysis and direct observations of atom configurations. Comparisons with classical spallation simulations or experiments are made where necessary. It is found that damages in classical spallation and micro-spallation are both dominated by cavitation, i.e. nucleation and the growth and coalescence of voids. The main difference in the cavitation process of classical and micro-spallation lies in the amount and spatial distribution of void nucleation sites. Different properties in dynamical stress evolutions between micro-spallation and classical spallation are also discussed. In addition, the properties of the surface micro-spall are found to be different from those of interior micro-spall particles in some shock intensity regimes. Factors that cause such differences are studied by analyzing in detail the thermodynamics paths of different parts of the shocked target.

Chaudhari, Mrunalkumar; Tiley, Jaimie; Banerjee, Rajarshi; Du, Jincheng

doi: 10.1088/0965-0393/21/5/055006pmid: N/A

Nickel-based superalloys are critical for aerospace and power applications due to excellent high-temperature properties. These high-temperature properties are attributed to the coherently precipitated gamma prime phase in the gamma matrix. The segregation of alloying elements between the matrix and the gamma prime phase drives precipitate misfit strains and impacts material strength. This study aims at understanding the site preference of Co and Cr within the ordered gamma prime phase. The study also calculates the interaction energy between alloying additions within the ternary systems Ni–Al–Cr and Ni–Al–Co, and the quaternary system Ni–Al–Cr–Co. It is found that Co has mixed substitution behavior between the Al and Ni sites in the gamma prime phase. The results from the Ni–Al–Cr ternary system show that two Cr atoms prefer being close to each other, with the most stable configuration of the first nearest neighbors of the Al–Al site. The interaction energies calculated from the Ni–Al–Co system show that the initial distance between two Co atoms will decide whether the two Co atoms prefer Ni–Ni or Ni–Al configuration. The study on the quaternary system Ni–Al–Cr–Co reveals that the initial configuration of Cr and Co atoms will affect the final most stable configuration. The results are found to be consistent with our previous findings.

Ghazisaeidi, M; Curtin, W A

doi: 10.1088/0965-0393/21/5/055007pmid: N/A

A mechanism for twin nucleation in Mg is studied in which edge 〈c〉 and mixed 〈c + a〉 lattice dislocations dissociate into a stable twin, having at least the minimum 6-layer thickness formed by three glissile twinning dislocations, plus a residual stair rod dislocation. Continuum dislocation theory is used to compute the energy of the initial and final states of the proposed dissociation process, using the twin boundary energy computed by density functional theory. For the 〈c〉 dislocation, the proposed dissociation is energetically favorable. An alternative dissociation path into partials on two -type pyramidal planes is possible, as seen in an atomistic analysis, and the continuum analysis predicts this alternative path to be more favorable than the twin process. For the 〈c + a〉 dislocation, the continuum model also predicts that dissociation into the twinned structure is energetically favorable for 6-layer and thicker twins. In both 〈c〉 and 〈c + a〉 cases, the equilibrium twin length is predicted to increase with increasing applied resolved shear stress and grow unstably beyond a critical stress. Atomistic simulations of these processes are then performed. For 〈c〉, a twinned structure is stable under zero loading but with higher energy than the alternative dissociation on two planes. Under a positive applied strain of 4%, resolved on the twin plane, the twinning structure grows while under a negative applied strain of −3%, it reverts back to the alternative low-energy dissociated configuration on the pyramidal planes. For the mixed 〈c + a〉 dislocation, the atomistic models predict that the dissociation into twinning dislocations does not occur spontaneously at zero applied strain but there is a stable twinned region at finite applied loads. These results demonstrate that dislocation-assisted mechanisms for twinning in Mg, initiating from lattice dislocations with large Burgers vectors, are physically feasible, and therefore twin nucleation from grain boundaries is not necessarily the dominant mechanism of twinning in Mg.

Xie, Hongxian; Yu, Tao; Tang, Chengchun

doi: 10.1088/0965-0393/21/5/055008pmid: N/A

The motion mechanism of the edge dislocation slipping in the cubic plane of Ni3Al under an applied shear stress at different temperatures is studied. At lower temperatures, the edge dislocation moves forward smoothly, and no dislocation lock is formed. At higher temperatures, the motion mechanism of the edge dislocation is controlled by the complex Lomer–Cottrell lock mechanism. Sometimes, the complex Lomer–Cottrell lock tends to transform into a full Lomer–Cottrell lock. The energy barriers of these transformation processes are calculated, and the underlying reason for these transformation processes can be understood in terms of the energy barriers and the applied shear stress. This work gives a good explanation of the in situ observation of the edge dislocation slipping in the cube planes of Ni3Al.

Bardella, Lorenzo; Segurado, Javier; Panteghini, Andrea; Llorca, Javier

doi: 10.1088/0965-0393/21/5/055009pmid: N/A

We aim at understanding the multislip behaviour of metals subject to irreversible deformations at small-scales. By focusing on the simple shear of a constrained single-crystal strip, we show that discrete Dislocation Dynamics (DD) simulations predict a strong latent hardening size effect, with smaller being stronger in the range [1.5 µm, 6 µm] for the strip height. We attempt to represent the DD pseudo-experimental results by developing a flow theory of Strain Gradient Crystal Plasticity (SGCP), involving both energetic and dissipative higher-order terms and, as a main novelty, a strain gradient extension of the conventional latent hardening. In order to discuss the capability of the SGCP theory proposed, we implement it into a Finite Element (FE) code and set its material parameters on the basis of the DD results. The SGCP FE code is specifically developed for the boundary value problem under study so that we can implement a fully implicit (Backward Euler) consistent algorithm. Special emphasis is placed on the discussion of the role of the material length scales involved in the SGCP model, from both the mechanical and numerical points of view.

Chandler, Mei Qiang; Peters, John F; Pelessone, Daniele

doi: 10.1088/0965-0393/21/5/055010pmid: N/A

The discrete element method (DEM) was used to model calcium-silicate-hydrate (C-S-H) at the nanoscale. The C-S-H nanoparticles were modeled as spherical particles with diameters of approximately 5 nm. Interparticle forces included traditional mechanical contact forces, van der Waals forces and ionic correlation forces due to negatively charged C-S-H nanoparticles and ion species in the nanopores. Previous work by the authors demonstrated the DEM method was feasible in studying the properties of the C-S-H nanostructures. In this work, the simulations were performed to look into the effects of nanoparticle packing, nanoparticle morphology, interparticle forces and nanoparticle properties on the deformation mechanisms and mechanical properties of the C-S-H matrix. This work will provide insights into possible ways to improve the properties of the C-S-H matrix.