Modelling and Simulation in Materials Science and Engineering

Hayhurst, D R

doi: 10.1088/0965-0393/2/3A/001pmid: N/A

It is shown how mechanisms-based constitutive equations may be formulated which are based on single-state damage variables for ferritic steels undergoing high-temperature creep and damage. In addition, it is shown how this description may be used to express the constitutive equations for weld and heat-affected-zone (HAZ) materials in terms of the same description of parent material behaviour and of simple property ratios. Computed predictions of damage, and failure lifetimes, of a welded pressurized steam pipe are presented and shown to compare well with experimental results. A computational study is then reported that considers controlled variations of weld and HAZ materials achievable using present technology, and which leads to the selection of a set of weld and HAZ materials to maximize the lifetime of the same steam pipe. In this way it is shown how a 30% increase of lifetime can be achieved. The paper is illustrated with computer colour field plots of creep damage and failure within the pipe weldment. It is discussed how these techniques have been used in real time to convey how the interactions between stress, strain and damage evolve.

Becker, R; Richmond, O

doi: 10.1088/0965-0393/2/3A/002pmid: N/A

Detailed numerical simulations of the deformation of measured microstructures are reviewed, analysing grain interactions in a polycrystal, flow localization between holes in a sheet and particle cracking in a reinforced material. The analyses employ two-dimensional models, but the results demonstrate the necessity of considering the three-dimensional microstructural geometry in accurate predictions of crystallographic orientation evolution, strain localization and fracture. Several methods of characterizing the three-dimensional microstructures from planar sections of the material are described. The importance of the size and distribution of the microstructural features is discussed in relation to the size of the volume elements utilized in numerical simulations, and the impact of this relative size on the formulation of constitutive relations by homogenization techniques is explored.

Alber, E S; Bassani, J L; Vitek, V; Wang, G J

doi: 10.1088/0965-0393/2/3A/003pmid: N/A

The lattice dynamics (phonons) of bicrystals with stable grain-boundary structures are computed and the results of these calculations are linked with continuum elasticity solutions of interface waves. Through comparisons of the lattice-dynamics calculations for ideal crystals with those for the corresponding bicrystals, the low-frequency acoustic branches of the dispersion curves associated with the interface vibrations are identified. These vibrational modes, in the limit of long wave length and low frequency, are the ones for which we seek to establish connections with continuum solutions for localized interface waves that decay exponentially with distance from the interface. We find that the perfect-bonding assumption over-restricts the nature of these latter waves, that is, these solutions do not reproduce the atomistic results for continuum-like waves. The reason lies in the fact that these localized waves are significantly influenced by the local properties of the interfacial region associated with its distinct structure.

Aoki, S; Ishii, N

doi: 10.1088/0965-0393/2/3A/004pmid: N/A

An elastic-plastic finite-element calculation based on finite-strain theory is carried out to estimate the fracture toughness of a ductile bimaterial with an interface crack under mixed-mode loading. A semi-infinite crack lying on an interface between an elastic-plastic material and a rigid substratum is considered, and the small-scale yielding condition and the plane-strain condition are assumed. The crack is modelled as a sharp notch. The modified Gurson constitutive equation for porous plastic materials is used to take into account the nucleation and growth of microvoids near a crack tip, and the element-vanish technique introduced by Tvergaard et al is employed to simulate the initiation of ductile fracture. It is found from the computational results that ductile fracture in a bimaterial initiates always at the crossing point of the blunted crack tip and the interface for any mixed-mode ratio, while for a crack in a homogeneous material ductile fracture initiates at a different point on the blunted crack tip depending on the mixed-mode ratio. It is also found that the values of the fracture toughness (i.e., the critical values of the J-integral) of a bimaterial are not only much lower than those of a homogeneous material, but also depend strongly on the mixed-mode ratio and take the minimum value at a certain critical ratio.

Aravas, N

doi: 10.1088/0965-0393/2/3A/005pmid: N/A

A detailed analysis of the kinematics of anisotropic elastoplastic solids under finite isothermal deformations is presented. The formulation is based on a multiplicative decomposition of the deformation gradient tenser into elastic and plastic parts. Emphasis is placed on the proper definition and the physical meaning of the so-called 'plastic spin', which is the spin of the continuum relative to the material substructure. Constitutive equations for the plastic spin are derived for three different material systems: (i) a fibre-reinforced metal-matrix composite, in which the local axis of transverse isotropy is defined by the local orientation of the fibres, (ii) polymeric materials, in which the anisotropy is deformation induced, and (iii) an elastoplastic material which yields according to a yield condition of the kinematic hardening type. The numerical implementation of the elastoplastic equations in a finite element programme, as well as an algorithm for their numerical integration, are briefly discussed. The choice of the intermediate unstressed configuration and the proper definition of the plastic spin in 'non-isoclinic' configurations are also discussed.

Baskes, M I; Angelo, J E; Bisson, C L

doi: 10.1088/0965-0393/2/3A/006pmid: N/A

The modified embedded atom method (MEAM), an empirical extension of the embedded atom method (EAM) that includes angular forces, has been used to examine the interface between a silicon substrate and a thin overlayer of nickel. A brief review of the MEAM is given and parameters are determined for the Si-Ni system. As verification of the reliability of the model, the geometry, energy and elastic constants of a number of ideal Si-Ni compounds are calculated and are found to agree reasonably well with experiment and first-principles calculations. Planar defect energies are also presented. Calculations of the relaxed energy and geometry of a coherent 10 AA overlayer of Ni on Si(001) yield two similar structures, both of which were typified by a slightly rippled Ni structure relative to perfect FCC Ni. The lower-energy interface also contained rows of slightly shifted Ni atoms. It is found that significant differences occur between the energetics of a rigid or relaxed separation of the overlayer. Separation of the overlayer with a monolayer of Si atoms attached to the Ni yields a significantly lower-energy structure than separation exactly at the interface. The relaxed brittle fracture energy of this interface is found to be 1.5 J m-2, which is significantly lower than the unrelaxed fracture energy of 4.8 J m-2.

Belytschko, T; Gu, L; Lu, Y Y

doi: 10.1088/0965-0393/2/3A/007pmid: N/A

Element free Galerkin (EFG) methods are methods for solving partial differential equations that require only nodal data and a description of the geometry; no element connectivity data are needed. This makes the method very attractive for the modeling of the propagation of cracks, as the number of data changes required is small and easily developed. The method is based on the use of moving least-squares interpolants with a Galerkin method, and it provides highly accurate solutions for elliptic problems. The implementation of the EFG method for problems of fracture and static crack growth is described. Numerical examples show that accurate stress intensity factors can be obtained Without any enrichment of the displacement field by a near-crack-tip singularity and that crack growth can be easily modeled since it requires hardly any remeshing.

Benson, D J

doi: 10.1088/0965-0393/2/3A/008pmid: N/A

Shock processing consolidates powders at high dynamic pressures over a very short time span. In contrast to conventional sintering, the temperature distribution in the particles is not uniform. The temperature increase at a material point is caused by the mechanical work associated with the compression and plastic flow of the material. A numerical study of the effects of the particle morphology on the plastic flow, and, hence, the final temperature distribution in a powder, is presented. The accuracy of the numerical calculations is validated by comparing the calculated shock velocity-particle velocity relationship to a least-squares fit of experimental data.

Clapp, P C; Becquart, C S; Shao, Y; Zhao, Y; Rifkin, J

doi: 10.1088/0965-0393/2/3A/009pmid: N/A

The microscopic mechanism of 'transformation toughening' is thought to be the stress reduction at a crack tip resulting from a displacive phase transformation induced by the stress field of a crack under external loading. Whether transformation toughening or 'transformation embrittlement' is the result depends on many different characteristics of the displacive transformation, as well as the geometry of the stress field of the crack. Since both crack and displacive transformation dynamics are sufficiently rapid to be suitably simulated in a molecular dynamics scheme we have explored this approach with the ordered intermetallic NiAl, employing embedded atom method (EAM) potentials. These potentials, in turn, have allowed the construction of a Ginzburg-Landau strain free energy functional (with all the material dependent parameters determined from molecular dynamics simulations), which may then be used to carry out Monte Carlo simulations of the crack-transformation zone interaction on a substantially larger spatial scale. These various types of simulation will be described and the results analysed.

Devincre, B; Kubin, L P

doi: 10.1088/0965-0393/2/3A/010pmid: N/A

The strain hardening properties of FCC single crystals are examined with the help of a three-dimensional simulation of dislocation dynamics and interactions at mesoscale. The basic properties discussed are the line tension of the dislocations, the conditions at which sessile junctions are formed at the intersection of two slip systems and the stability of these locks. The relation between the flow stress and the square root of the intersecting dislocation density is examined in areal glide and in multislip conditions. A validation of the model is performed by comparison with experimental results on copper single crystals. At the small strains reached by the simulation and in multislip conditions, strain hardening is found to originate from the continuous increase of forest density rather than from the formation of immobile loops around clusters of forest obstacles. It is suggested that at larger strains a stabilizing mechanism, possibly cross-slip, should enhance the dislocation storage processes and initiate the formation of dislocation cells.