Modelling and Simulation in Materials Science and Engineering

Ranjan, Devraj; Narayanan, Sankar; Kadau, Kai; Patra, Anirban

doi: 10.1088/1361-651X/abd621pmid: N/A

A crystal plasticity finite element (CPFE) framework is proposed for modeling the non-Schmid yield behavior of L12 type Ni3Al crystals and Ni-based superalloys. This framework relies on the estimation of the non-Schmid model parameters directly from the orientation- and temperature-dependent experimental yield stress data. The inelastic deformation model for Ni3Al crystals is extended to the precipitate (γ′) phase of Ni-based superalloys in a homogenized dislocation density based crystal plasticity framework. The framework is used to simulate the orientation- and temperature-dependent yield of Ni3Al crystals and single crystal Ni-based superalloy, CMSX-4, in the temperature range 260–1304 K. Model predictions of the yield stress are in general agreement with experiments. Model predictions are also made regarding the tension–compression asymmetry and the dominant slip mechanism at yield over the standard stereographic triangle at various temperatures for both these materials. These predictions provide valuable insights regarding the underlying (orientation- and temperature-dependent) slip mechanisms at yield. In this regard, the non-Schmid model may also serve as a standalone analytical model for predicting the yield stress, the tension–compression asymmetry and the underlying slip mechanism at yield as a function of orientation and temperature.

Moeini-Ardakani, S Sina; Taheri-Mousavi, S Mohadeseh; Li, Ju

doi: 10.1088/1361-651x/ac01b9pmid: N/A

Absorption of interstitial alloying elements like H, O, C, and N in metals and their continuous relocation and interactions with various microstructural features such as vacancies, dislocations, and grain boundaries have crucial influences on metals’ properties. However, besides limitations in experimental tools in capturing these mechanisms, the inefficiency of numerical tools also inhibits modeling efforts. Here, we present an efficient framework to perform hybrid grand canonical Monte Carlo and molecular dynamics simulations that allow for parallel insertion/deletion of Monte Carlo moves. A new methodology for calculation of the energy difference at trial moves that can be applied to many-body potentials as well as pair ones is a primary feature of our implementation. We study H diffusion in Fe (ferrite phase) and Ni polycrystalline samples to demonstrate the efficiency and scalability of the algorithm and its application. The computational cost of using our framework for half a million atoms is a factor of 250 less than the cost of using existing libraries.

Joudivand S, Mohammad Hasan; Demir, Eralp

doi: 10.1088/1361-651X/abffe3pmid: N/A

A dislocation density based model is developed to govern physics of complex mechanical behavior of bcc materials. Non-Schmid effects are incorporated into a novel dislocation density based model by using three-term projection operators. The model is used to explain dependence of mechanical response to crystal orientation, temperature, strain-rate and as well as tension–compression asymmetry. Simulations at different scales that include; a material point, a single finite element and a finite element model of exact test geometry are performed. The proposed model successfully captures crystal orientation, temperature, and strain-rate dependence of the experimentally observed stress–strain curves and also well explain the tension–compression asymmetry of experimental flow stresses of α-iron. The forest projection scheme that uses the slip plane normal, hardening interactions between slip systems for bcc materials, non-Schmid projections, and Peierls energy barrier for thermal activation of slip are important features of the model to imitate experimental mechanical behavior of bcc materials successfully at all scales with a better agreement though a finite element model considering exact tensile speciment geometry.

Yuan, Bin; Zeng, Fanlin; Peng, Chao; Wang, Youshan

doi: 10.1088/1361-651X/abfeaepmid: N/A

Coarse-grained (CG) cis-1,4-polyisoprene (PI) models with multiple silica nanoparticles (NPs) are built to study the effect of NPs and crosslinks in the uniaxial tensile simulation. The potential functions of the CG models are obtained mainly via the iterative Boltzmann inversion method. The tensile simulation results show that the grafted silica NPs and the crosslinked structure play reinforcing roles while the smooth silica NPs do the opposite, which have the similar trends with the experiment results. The differences of mechanical properties for these models are studied from different microscopic aspects, such as the network of NPs, the bond lengths, the free molecular chains, the entanglements, the stress and strain distribution and the microvoid evolution. As a result, the main reasons for the weakening of PI models with smooth silica NPs come from the weak interfacial interaction, the inhomogeneity of structural deformation and the reduction of the number of entanglements. However, if there are graft chains, the interfacial interaction can be enhanced by entangling with the matrix molecular chains. The graft chains can make it possible for the aggregated NPs to separate and can hinder the growth of microvoids at the interface. In addition, the inconsistency of the stress and strain distributions at the microscopic level is verified and the nucleation mechanism of microvoids is believed to be caused by the local violent movement of molecular chains.

Bäker, Martin; Rösler, Joachim

doi: 10.1088/1361-651X/abd043pmid: N/A

Alloy 718-type wrought nickel-based superalloys are the materials of choice for many high temperature applications. They are strengthened by the γ″-phase that forms small precipitates with a large lattice distortion. However, at temperatures above 650 °C, this phase may transform to the thermodynamically stable δ-phase. It is therefore important to understand the influence of alloying elements on the stability of these phases. In this paper, density functional theory calculations at 0 K are performed to determine the effect of aluminium and of the transition group elements on the stability and the lattice parameters of the γ″-phase. It is shown that the substitution energy is mainly determined by two parameters, the charge transfer and the change in the lattice constant. Solution energies are compared to those in the δ-phase and some conclusions for the design of 718-type alloys are drawn.

Zhang, Wenbing; Shen, Zhenzhong; Ren, Jie; Gan, Lei; Xu, Liqun; Sun, Yiqing

doi: 10.1088/1361-651x/ac03a4pmid: N/A

Recently, the use of the phase-field method (PFM) to simulate the fracture process of brittle materials has attracted increasing attention. The PFM describes the fracture process through a series of differential equations, thus avoiding tedious crack surface tracking and offering advantages in simulating crack initiation, propagation, and bifurcation. The essence of the PFM is a multifield coupling problem, so it is supposed that the COMSOL Multiphysics commercial finite element software, which is particularly suitable for solving multifield coupling problems, should be more efficient and simpler to implement for the PFM. In this paper, a crack propagation model for quasi-brittle materials based on PFM is implemented in COMSOL Multiphysics by means of the solid mechanics module and secondary development interfaces of the partial differential equation (PDE), domain ordinary differential equation (ODE) and differential algebraic equation (DAE). Combined with the collected tensile and shear numerical simulation data, validation studies are carried out both qualitatively and quantitatively. In addition, considering that the PFM involves many parameters would create a significant amount of work for model calibration.Therefore, multifactor sensitivity analysis based on the orthogonal test method is used to identify the parameter' sensitivity. The results show that the use of the solid mechanics module and interfaces of the PDE and domain ODE and DAE are effective for phase-field modelling, and the proposed method could reasonably characterize the whole fracture process of quasi-brittle materials. The sensitivity analysis results revealed that Young's modulus (E) and critical energy release rate (Gc) are the main factors affecting the output results of the model.

Zhang, Wenbing; Shen, Zhenzhong; Ren, Jie; Gan, Lei; Xu, Liqun; Sun, Yiqing

doi: 10.1088/1361-651X/ac03a4pmid: N/A

Recently, the use of the phase-field method (PFM) to simulate the fracture process of brittle materials has attracted increasing attention. The PFM describes the fracture process through a series of differential equations, thus avoiding tedious crack surface tracking and offering advantages in simulating crack initiation, propagation, and bifurcation. The essence of the PFM is a multifield coupling problem, so it is supposed that the COMSOL Multiphysics commercial finite element software, which is particularly suitable for solving multifield coupling problems, should be more efficient and simpler to implement for the PFM. In this paper, a crack propagation model for quasi-brittle materials based on PFM is implemented in COMSOL Multiphysics by means of the solid mechanics module and secondary development interfaces of the partial differential equation (PDE), domain ordinary differential equation (ODE) and differential algebraic equation (DAE). Combined with the collected tensile and shear numerical simulation data, validation studies are carried out both qualitatively and quantitatively. In addition, considering that the PFM involves many parameters would create a significant amount of work for model calibration.Therefore, multifactor sensitivity analysis based on the orthogonal test method is used to identify the parameter' sensitivity. The results show that the use of the solid mechanics module and interfaces of the PDE and domain ODE and DAE are effective for phase-field modelling, and the proposed method could reasonably characterize the whole fracture process of quasi-brittle materials. The sensitivity analysis results revealed that Young's modulus (E) and critical energy release rate (Gc) are the main factors affecting the output results of the model.

Shen, X J; Connétable, D; Andrieu, E; Tanguy, D

doi: 10.1088/1361-651x/abdc6apmid: N/A

The segregation of hydrogen and vacancies at the Σ5(210)[001] symmetric tilt grain boundary (GB) was studied by atomic scale simulations in Ni. First, the hydrogen segregation energies and hydrogen–hydrogen pair interaction energies were calculated on every interstitial site of the GB. The vacancy–hydrogen clusters’ formation energies were also determined on the most favorable site. All these calculations were done using the density functional theory. Second, based on these elementary energies, a free energy functional was built to determine the concentration of segregated hydrogen and of vacancy-hydrogen clusters, as a function of the bulk hydrogen concentration and the temperature. It was found that two configurations exits in typical conditions where embrittlement is observed experimentally: H segregation only, with up to 3 hydrogen atom per structural unit or 50% occupancy by VH5 clusters (1 cluster every two structural unit). The cohesive stress and ideal work of fracture were evaluated by fracturing the GB with different degrees of hydrogen and vacancy segregation. H segregation alone (no vacancy) decreased the work of fracture by 25%. A significantly larger decrease of cohesion was obtained when considering vacancy-hydrogen clusters. A maximum drop of the cohesive stress, of a magnitude of 40%, was obtained when every structural unit was hosting a VH4 cluster. Finally, these data were transformed into cohesive stress models. They were used to evaluate the degree of localization of the shear displacement at the crack tip. The conclusion is that, even if cohesion is very significantly decreased, shear localization is still effective, meaning that dislocation emission should occur at the expense of crack propagation. The comparison with other grain boundaries in the literature shows that the GB studied is almost an ideal sink and therefore is very favorable for the formation of equilibrium VHn. It represents more an upper bound of the effect. Therefore, extra ingredients should be considered to explain the embrittlement observed experimentally.

Han, Quan-Fu; Zhang, Ying; Yang, Kun Jie; Liu, Yue-Lin

doi: 10.1088/1361-651x/abfd1bpmid: N/A

We have studied the double effects of anisotropic strain and temperature on the dissolution behavior of hydrogen (H) in tungsten (W) by using first-principles calculation combined with thermodynamic model. The strain and temperature effects are reflected by uniaxial/biaxial strain loading and vibrational Helmholtz free energy, respectively. We calculated the dissolution energy of the H atom at four different interstitial sites of TIS(1), TIS(2), OIS(1) and OIS(2). For TIS(2), OIS(1) and OIS(2), the dissolution energy of H changes monotonically as the biaxial strain rises from −5% to 5%. However, the dissolution ability of H at TIS(1) can be promoted by employing either compressive or tensile biaxial strain. There are more interesting results, the temperature-dependent dissolution energy of H at TIS(1) shows a significant decrease with the compressive biaxial strain loading, but this phenomenon does not occur at other three positions, i.e., TIS(2), OIS(1) and OIS(2). Besides, with the same anisotropic strain loading, the dissolution energy of H for all four kinds of positions increase as the temperature rises from 300 to 1800 K, which is mainly originated from the contribution of the vibrational Helmholtz free energy. Our results indicate that H atoms are more easily to accumulate in the anisotropic strain enrichment region in W as the temperature rises, which will make it more easier to form H bubbles in W.

Vishnu, Karthik Guda; Reeve, Samuel Temple; Strachan, Alejandro

doi: 10.1088/1361-651x/abdb43pmid: N/A

We use density functional theory to investigate the possibility of polar and multiferroic states in free-standing, perovskite-based nanodots at the atomic limit of miniaturization: single unit cells with terminations which allow centro-symmetry. We consider both A-O and B-O2 terminations for three families of nanodots: (i) A = Ba with B = Ti, Zr, and Hf; (ii) A = Ca and Sr with B = Ti; and (iii) A = Na and K with B = Nb. We find all A–O terminated dots to be non-polar and to exhibit cubic symmetry (except for K8NbO6), regardless of the presence of ferroelectricity in the bulk. In contrast, all the B–O2 terminated nanodots considered relax to a non-cubic ground state. Rather surprisingly, all of these structures exhibit polar ground states (except NaNb8O12). We propose a new structural parameter, the cluster tolerance factor (CTF), to determine whether a particular chemistry will result in a polar ground state nanodot, analogous to the Goldschmidt factor for bulk ferroelectrics. In addition, we find that all A–O terminated (except Ca8TiO6) and all polar B–O2 terminated nanodots are magnetic, where none show magnetism in the bulk. As with bulk systems, multiferroicity in the B–O2 terminated dots originates from separation between spin density in peripheral B atoms and polarity primarily caused by the off-center central A atom. Our findings stress that surface termination plays a crucial role in determining whether ferroelectricity is completely suppressed in perovskite-based materials at their limit of miniaturization.