Modelling and Simulation in Materials Science and Engineering

Bolmaro, R E; Fourty, A; Signorelli, J W; Brokmeier, H-G

doi: 10.1088/0965-0393/14/1/001pmid: N/A

The current paper presents a comparison of the influence over texture development of different heterogeneity levels of deformation. A viscoplastic self-consistent (VPSC) micromechanical model is coupled with a finite element method (FEM) to simulate wire drawing texture development in a two-phase CuFe material. VPSC models are capable of simulating grain-to-grain heterogeneity, and FEM models can accomplish the task of simulating the macroscopic variation of velocity gradient due to geometrical constraints during wire drawing. Intra-grain heterogeneities are empirically built in the VPSC model by enforcing a common spin between closest neighbour grains. The results are contrasted and validated by neutron diffraction experimental textures. Different levels of heterogeneity are simulated, and the results are assessed and compared against Taylor based simulations. The curling problem is also addressed by allowing the grains to interact through the co-spin model and the ellipsoid axes orientations to evolve independently.

Kleber, Xavier; Simonet, Laurence; Fouquet, Francis

doi: 10.1088/0965-0393/14/1/002pmid: N/A

In this paper, we report some numerical analysis results obtained in the study of the thermoelectric power (TEP) of 2D two phase materials. Based on the numerical resolution of transport equations, we compute the TEP of different composite structures. These were numerically simulated using a grain growth model. We show that the ratio of the electrical conductivity of the two phases is the relevant parameter for metallic material which is verified by the WiedemanFranz law. We observe that for a low ratio, the TEP of the composite follows a simple rule of mixture, whereas for a higher value, a S-shaped curve is obtained. Applied to the case of atoms precipitation in a metallic matrix, we show that for a low fraction of precipitates, their effect can be neglected when compared with the variation induced by the atoms precipitation. We found that an induced anisotropy in the shape of the grains leads to a strong deviation from the rule of mixture.

Gong, Changwei; Li, Yan; Wang, Yinong; Yang, Dazhi

doi: 10.1088/0965-0393/14/1/003pmid: N/A

We present ab initio calculations of the electronic and crystal structure for the R-phase of NiTi shape memory alloy. Our calculations have been performed using the density functional theory with plane-wave pseudopotentials. Based on two reported lattice symmetries, P3 and , for the R-phase, we carried out geometry optimization and compared the ground-state energies, total density of states (TDOS) and bond lengths between the two structures after geometry optimization. After geometry optimization, the P3 structure changes into a P31m structure, while the structure is unchanged. The P31m structure has lower energy and TDOS at the Fermi energy than that of the structure. Based on the low-energy P31m model, we suggest that the P31m structure is the correct crystalline ground state of the R-phase.

Chan, Philip K

doi: 10.1088/0965-0393/14/1/004pmid: N/A

This paper studied the thermal-induced phase separation (TIPS) phenomenon via spinodal decomposition (SD) in a polymer solution under a linear concentration gradient. The one-dimensional model consists of the CahnHilliard theory for SD and incorporates the FloryHuggins free energy equation, the slow mode mobility theory and Rouse model for polymer diffusion. The model is able to replicate frequently reported experimental observations reported in the literature, which includes the formation of anisotropic polymer membranes using the TIPS method. We show and explain that the anisotropic morphology is due to the polymer solution undergoing SD at different rates along the sample as a result of the initial concentration gradient.

Kawagai, Mitsuhiro; Sando, Atsushi; Takano, Naoki

doi: 10.1088/0965-0393/14/1/005pmid: N/A

This study is focused on the multi-scale modelling strategy for complex and heterogeneous microstructures of real materials by automatic image-based modelling and finite element mesh superposition method. The synergetic application of the conventional asymptotic homogenization method and the authors' mesh superposition method has been proposed to obtain the microscopic responses under high gradient of macroscopic fields at the macroscopic crack tip and/or interface, for instance. For complex and random microstructures, automatic image-based voxel meshing by means of x-ray CT is commonly required; however, it cannot always adapt to the mathematical theory of microscopic modelling in the mesh superposition method. Therefore, a modelling technique for mesh refinement is proposed in this paper using additional elements for insulation in consideration of the theoretical background of the mesh superposition method.In this paper, we provide the modelling procedure and its theoretical consideration of mesh refinement for flexible modelling of real materials. To demonstrate the technique, a numerical example of a porous ceramic component with random microstructure and macroscopic crack is illustrated.

Swaddiwudhipong, S; Hua, J; Tho, K K; Liu, Z S

doi: 10.1088/0965-0393/14/1/006pmid: N/A

The Berkovich indenter, which is one of the most commonly used indenter tips in instrumented indentation experiments, requires a tedious 3D finite element simulation. The indenter is widely idealized as a conical indenter of 70.3° half-angle to enable a substantially less demanding 2D axisymmetric modelling. Although the approach has been commonly adopted, limited studies have been performed to investigate possible deviations due to this simplification. The present study attempts to address the equivalency of the two indenters by performing extensively both 3D and 2D finite element analyses to simulate the load-displacement response of a wide range of elasto-plastic materials obeying power law strain-hardening during indentation for both Berkovich and conical indenters, respectively. It is demonstrated that the equivalency between these two indenters in terms of curvature of the loading curve is not valid across the range of material properties under study. However, it is established that if only the ratio of the remaining work done (WR) and the total work done (WT) of the load-indentation curve is of interest, this simplification can be adopted with satisfactory results.

Martorano, M A; Fortes, M A; Padilha, A F

doi: 10.1088/0965-0393/14/1/007pmid: N/A

This paper introduces a numerical method for curvature calculation, termed least square-normal and curvature (LSNC), for simulating the migration of two-dimensional boundaries. The method is based on the existing volume-of-fluid (VOF) method with new algorithms to calculate the normal and the curvature of a boundary. The LSNC method is applied to solve a number of simple problems pertaining to boundary migration driven by curvature and a uniform force associated with an energy density difference across the boundary. The accuracy of the LSNC method is assessed by comparing its results with exact solutions, when available. The method proved more accurate than the Ripple method, which is described in the literature as another variant of VOF methods.

Yang, H K; Wang, X

doi: 10.1088/0965-0393/14/1/008pmid: N/A

This paper investigates the bending stability of a multi-wall carbon nanotube (MWNT) embedded in an elastic medium, based on a multiple shell model. The effects of the surrounding elastic medium and the van der Waals forces between two adjacent tubes are taken into account. The critical bending moment and the corresponding buckling mode for three types of MWNTs with different layer numbers and ratios of radius to thickness are calculated. Results obtained show that the bending buckling mode corresponding to the critical bending moment is unique, which is obviously different from the purely axial compression buckling of an individual MWNT. On the other hand, a simplified method is applied to calculate the bending stability of MWNTs with larger layers, embedded in an elastic medium, by substitution of a multiple shell with fewer layers. The new features of the bending stability of MWNTs embedded in an elastic medium and some meaningful results in this paper are helpful for the application and the design of nanostructures in which MWNTs act as basic elements.