Akiyuki Takahashi

Computer-simulated bone architecture in a simple bone-remodeling model based on a reaction-diffusion system

Bone is a complex system with functions including those of adaptation and repair. To understand how bone cells can create a structure adapted to the mechanical environment, we propose a simple bone remodeling model based on a reaction-diffusion system influenced by mechanical stress. Two-dimensional bone models were created and subjected to mechanical loads. The conventional finite element method (FEM) was used to calculate stress distribution. A stress-reactive reaction-diffusion model was constructed and used to simulate bone remodeling under mechanical loads. When an external mechanical stress was applied, stimulated bone formation and subsequent activation of bone resorption produced an efficient adaptation of the internal shape of the model bone to a given stress, and demonstrated major structures of trabecular bone seen in the human femoral neck. The degree of adaptation could be controlled by modulating the diffusion constants of hypothetical local factors. We also tried to demonstrate the deformation of bone structure during osteoporosis by the modulation of a parameter affecting the balance between formation and resorption. This simple model gives us an insight into how bone cells can create an architecture adapted to environmental stress, and will serve as a useful tool to understand both physiological and pathological states of bone based on structural information.

γ-precipitate strengthening in nickel-based superalloys

We describe here a computational method to study γ-precipitate strengthening in nickel-based superalloys, and to specifically investigate the relative importance of stacking-fault energy and coherency strains. The method is a combination of the Parametric Dislocation Dynamics (PDD), an analytical solution to the spherical inclusion problem and the generalized Peierls–Nabarro (P-N) model. Earlier analytical solutions to stacking-fault strengthening predict a lower critical resolved shear stress (CRSS) in comparison with the results of the present model. This is attributed to shape changes of super-dislocations during their interaction with γ-precipitates. However, existing analytical solutions to coherency strengthening provide considerably larger values of the CRSS compared with the results of present simulations. The dislocation core is found to spread widely as it interacts with γ-precipitates, and is thus much softer than what has been considered in previous analytical solutions. This remarkable effect is a direct result of the core structure of dislocations interacting with precipitates. When this effect is accounted for, a new analytical solution is shown to give excellent agreement with present simulation results. We finally discuss the combined effects of the two strengthening mechanisms, when they operate simultaneously.

Numerical simulation of molding-defect formation during resin transfer molding

The present study investigated a numerical simulation of molding-defect formation during resin transfer molding using boundary element method and line dynamics. The proposed method enables to simulate small molding defects by increasing the node for required position during time evolution; thereby, the method computes high-resolution flow front without being affected by the initial mesh geometry. The method was applied to the radial injection RTM with single inlet, and it was confirmed by comparison with theoretical value based on Darcy’s law that the flow advancement was computed with high accuracy. In addition, the method was also applied to the flow advancement for inclusion problem with cylinder, and four-point injection problem. The simulated flow behavior, void formation, and shrinkage agreed with the results in references. Finally, the method was compared with experiments using two-point injection problem. The computed configuration of the flow front and weld line agreed well with the experimental results.

Kinetic Monte Carlo Simulation of Helium-Bubble Evolution in ODS Steels

Oxide dispersion strengthened (ODS) ferritic/martensitic steels are being developed for high temperature applications for fission reactors and future fusion devices. ODS-Eurofer97 (Fe–9CrWVTa–0.3Y2O3) and ODS-MA957 (Fe–14CrTiMo–0.25Y2O3) have shown promising high temperature mechanical properties, such as tensile strength, toughness, fatigue, and creep rupture. Recent neutron irradiation experiments with simultaneous helium implantation indicate that helium transport is favorably impacted by the nanometer-sized oxide particles, small grain sizes, and high dislocation densities of ODS steels. Simulating helium transport in ODS steels requires a three-dimensional spatially resolved model, which takes into account discrete geometric and microstructural features of the steel. We have developed such a helium transport simulation model using an event kinetic Monte Carlo (EKMC) approach called M onte C arlo simulation of he lium-bubble evolution and r es o lution s (McHEROS). First, a spatially resolved kinetic rate theory is used to establish helium-vacancy cluster and stable helium-bubble nuclei concentrations. The maximum helium-bubble density is then used as an initial condition for randomly distributed matrix bubbles for the EKMC simulation. Migration, coalescence, and trapping of helium bubbles by oxide particles are simulated. Matrix helium bubbles that come into contact with each other are assumed to undergo instantaneous coalescence, which leads to bubble growth. However, migrating bubbles that are intercepted by oxide particles are assumed trapped but can grow through coalescing with newly arriving bubbles. The oxide particles effectively reduce the growth rate of matrix bubbles. Helium-bubble size and spatial distributions of the EKMC simulation are compared with recent experimental measurements. As part of this study, the effectiveness of the ODS microstructure on reducing helium-bubble growth rates is presented by comparing EKMC simulations of steels with and without ODS particles. This first application of the McHEROS code has demonstrated the viability of the code as a tool in describing the behavior of helium-bubble transport in ODS alloys.

Large scale water entry simulation with smoothed particle hydrodynamics on single- and multi-GPU systems

Abstract In this paper, a Weakly Compressible Smoothed Particle Hydrodynamics (WCSPH) framework is presented utilizing the parallel architecture of single- and multi-GPU (Graphic Processing Unit) platforms. The program is developed for water entry simulations where an efficient potential based contact force is introduced to tackle the interaction between fluid and solid particles. The single-GPU SPH scheme is implemented with a series of optimization to achieve high performance. To go beyond the memory limitation of single GPU, the scheme is further extended to multi-GPU platform basing on an improved 3D domain decomposition and inter-node data communication strategy. A typical benchmark test of wedge entry is investigated in varied dimensions and scales to validate the accuracy and efficiency of the program. The results of 2D and 3D benchmark tests manifest great consistency with the experiment and better accuracy than other numerical models. The performance of the single-GPU code is assessed by comparing with serial and parallel CPU codes. The improvement of the domain decomposition strategy is verified, and a study on the scalability and efficiency of the multi-GPU code is carried out as well by simulating tests with varied scales in different amount of GPUs. Lastly, the single- and multi-GPU codes are further compared with existing state-of-the-art SPH parallel frameworks for a comprehensive assessment.

Molecular Dynamics Simulation of Dislocation-γ-Precipitate Interactions in γ’-Precipitates

There are clear experimental evidences of the formation of either spherical or platelet γ-precipitates inside cubic γ’-precipitates in nickel-based superalloys, which strengthen the mechanical property of the alloy. In this work, molecular statics (MS) and dynamics (MD) simulations of the interaction between a super edge dislocation and a γ-precipitate in γ’-precipitates were performed. The strengthening mechanism was then investigated by comparing the simulation results with the theoretical prediction. As the result, it could be found that the critical resolved shear stress (CRSS) of the interaction has a strong dependence on the shape of the γ-precipitate, and could be well predicted by the theory of precipitation strengthening. Especially, the stacking-fault, chemical, coherency and interface strengthening play a major role in determining the CRSS. Finally, the interaction under a finite temperature was simulated using the MD simulations. It was found that the influence of temperature on the interaction is negligibly small.

Fracture mechanics of propagating 3-D fatigue cracks with parametric dislocations

Abstract Propagation of 3-D fatigue cracks is analyzed using a discrete dislocation representation of the crack opening displacement. Three dimensional cracks are represented with Volterra dislocation loops in equilibrium with the applied external load. The stress intensity factor (SIF) is calculated using the Peach–Koehler (PK) force acting on the crack tip dislocation loop. Loading mode decomposition of the SIF is achieved by selection of Burgers vector components to correspond to each fracture mode in the PK force calculations. The interaction between 3-D cracks and free surfaces is taken into account through application of the superposition principle. A boundary integral solution of an elasticity problem in a finite domain is superposed onto the elastic field solution of the discrete dislocation method in an infinite medium. The numerical accuracy of the SIF is ascertained by comparison with known analytical solution of a 3-D crack problem in pure mode I, and for mixed-mode loading. Finally, fatigue crack growth simulations are performed with the Paris law, showing that 3-D cracks do not propagate in a self-similar shape, but they re-configure as a result of their interaction with external boundaries. A specific numerical example of fatigue crack growth is presented to demonstrate the utility of the developed method for studies of 3-D crack growth during fatigue.

Ductile Fracture Simulation of a Pipe of Steam Generator in PWR

Ductile fracture of steam generator pipes may occur due to inner pressure. The final fracture process by inner pressure occurs as a burst of a pipe, and ductile high speed crack growth occurs with large deformation of the structure. For the simulation of such fracture process, Gurson’s yield function is used as a constitutive equation, and large deformation theory is employed. As the simulation is conducted by load control condition, it is difficult to simulate burst phenomenon. Final fracture condition is discussed and finally crack opening displacement is chosen as burst fracture criterion. Fracture simulations of a pipe with multiple through cracks are conducted by changing distances between two crack tips. Burst loads are evaluated, and they are compared with estimated values by Maintenance rules. Surface crack problems are also simulated. Burst loads are also compared with results by limit load analysis method. Conservativeness of conventional evaluation methods are studied and discussed.Copyright

Numerical Simulation of Dislocation-Precipitate Interactions Using Dislocation Dynamics Combined with Voxel-Based Finite Elements

This paper provides a computational method for dislocation-precipitate interaction problems. The computational method is a combination of the parametric dislocation dynamics and the voxel-based finite element method, and has a potential to enable the simulation of interaction between dislocations and multiple precipitates. To reduce the computational time, a multi-level voxel element model is employed. The convergence behavior of numerical accuracy and the computational time of the proposed method are examined by solving a dislocation-precipitate interaction problem. The results show that the proposed method has a good convergence behavior, and the computational time can be drastically reduced by the use of the multi-level voxel element model. Finally, the interaction between dislocations and multiple precipitates is solved to demonstrate a potential of the proposed method with various average diameters and constant volume fraction of precipitate. As the result, the proposed method successfully captured the dependence of the critical resolved shear stress on the average precipitate diameter.

Phase Field Simulation of Rafting Behavior of γ`Phase in Nickel Base Superalloy

This paper describes phase field simulations of the rafting behavior of γ’ phase with a simple interfacial dislocation network model. The interfacial dislocation network model accounts for the effect of the network on the lattice misfit between γ and γ’ phases and the subsequent rafting behavior. The model is implemented into the phase field simulation to see the dependence of the rafting behavior of γ’ phases on the interfacial dislocation network. Without the dislocation network model, the amount of the rafting was negligibly small. On the other hand, with the dislocation network model, the γ’ phases shows a large amount of rafting, which is in good agreement with the results of the experimental observations. Therefore, the combination of the phase field method and the simple interfacial dislocation network model developed in this work is appropriate for the simulation of the rafting of γ’ phases.