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This paper assesses the capabilities of scanning acoustic tomography (SAT) for the analysis of bonded silicon wafers. In order to quantitatively evaluate detectability and resolution, the authors acquired images from samples prepared with artificial voids. The samples consisted of two wafers, a cap wafer and a base wafer with dry-etched pits on a silicon-oxide layer. Cap wafers of different thicknesses were used along with transducers of appropriate focal length. The paper describes the experimental setup and test procedures in detail as well as the results.

Polycrystalline thin sheet metals under plane strain tension are modeled employing Asaro’s constitutive equation for plane strain deformation of single crystals, and finite element simulation is performed to investigate the growth of surface roughening and the localization of the deformation. The effects of intermediate annealing on surface roughening and related phenomena are discussed. Deformation behaviour and strain distribution of sheet metals with relatively fine crystals are not largely affected by the orientation of slip planes in annealed state. Intermediate annealing improves the formability of sheet metals, however, its effects are limited, and it is most efficient when the annealing is carried out just before the nonuniformity of sheet thickness starts to increase suddenly. In the case of very thin sheets, the formability depends upon the relative size of grains with respect to the sheet thickness.

This paper discusses the efforts to shrink the micro-bump pitch to $20\ \mu\mathrm{m}$ and then $10\ \mu\mathrm{m}$ with solder micro-bumps for silicon-on-silicon 3D assembly by leveraging alternate solder diffusion barrier metals and tuning the assembly process to realize both good yield and reliable interconnects. Specifically in this paper, the assembly process challenges are detailed and the impact of our barrier metal assessment and process optimization to resolve these technical challenges are discussed through the study of solder joint reliability results using internal $20 \mu \mathrm{m}$ pitch and $10\ \mu\mathrm{m}$ pitch solder micro-bump test-vehicles (TV).

We proposed constitutive equations for the strain rate and temperature-dependent behavior of rubber by employing the nonaffine molecular chain network theory and reptation theory. The finite element homogenization method along with the proposed constitutive equations have the capability of predicting the deformation behaviors of particle-filled rubber under changes in volume fractions, distribution patterns, and size heterogeneity of the particles without additional parameters. The only existing problem is the modest estimation of the stiffness of rubber immediately after the abrupt change in strain rate direction (ACSD) as can be seen in the cyclic deformation behavior. We restricted our attention to the generalization of our nonaffine molecular chain network theory to overcome the problems associated with ACSD. We consider the effect of the delay of deformation in surrounding chains on the elasticity modulus by introducing an amplification parameter dependent on the current chain stretch and direction of strain rate immediately after ACSD. The potential of the proposed constitutive equations is examined against the predictability of the experimentally obtained deformation exhibiting ACSD.

In this study, we fabricated carbon nanotube films for application to gas sensors. We assumed that the ratio of electrical conductance change was equal to the surface coverage, and our detection model verified this assumption. To prove this assumption, we simulated the sheet resistance of a film with numerous joints. Our Monte Carlo simulations proved that when the joint resistance increased owing to molecular adsorption, the sheet resistance increased in accordance with the surface coverage.

Application of carbon nanotube (CNT) film as a gas sensor is highly desired. Transient behavior of molecular adsorption provides adsorption and desorption constants; however, to date, few researchers have investigated it. Here, we focused on the transient behavior of electric conductance of the CNT film during adsorption. Adsorption of polar molecules showed predicable behavior, but non-polar molecules showed a sudden change of electric conductance that indicated excess adsorption. We analyzed the process based on Langmuir adsorption, and adsorption and desorption constants, which are considered to be physical properties; however, these parameters did not show good agreement for the same film.

In this contribution, a conformable 64×45 RGB light-emitting diode (LED) matrix is presented. A design concept of stretchable electronics is used: non-stretchable polymer islands host rigid LEDs and are interconnected by horseshoe shaped metallic conductors, which are able to deform together with an elastomeric substrate. Thin-film metallization is used to enable a pixel pitch of 1 mm, while polyimide is used to realize the non-stretchable islands, but also to support the meandering conductors. The design of the stretchable interconnections has been optimized with respect to their mechanical and electrical performance. Thermoplastic polyurethane is introduced at a final stage of the fabrication process to ensure its compatibility with conventional thin-film processing. A passive matrix addressing scheme is used to drive the LED matrix. At a supply voltage of 10 V, the brightness of the display reaches up to 700 cd/m2.

In the clinical application, the mechanical stimulation against the damaged brain tissue is adopted as the kinesitherapy for the nerve regeneration. Nevertheless, the fundamental mechanism to repair the damaged nerve cell has not been revealed yet. Recently, the cyclic stretch stimulation has been reported as the efficacious treatment method to enhance the axonal extension for regenerative therapy of injured nerve cell. Therefore, we try to develop a new cellular automaton (CA) finite element (FE) hybrid method to predict the axonal extension and nerve network generation, which can evaluate the effect of stretch stimulation on the cell body, axon and dendrites. In the FE results, the stress concentration occurred at the junction of the axon and cell body. The maximum stress value in the axon was 8.2 kPa which is about twice as large as that of the cell body. CA adopted to predict the morphological evolution of nerve cells under the mechanical stimulation. It was confirmed that the stress affects to accelerate the axonal extension as experimentally suggested. As a result, our CAFE can be employed to simulate the axonal extension and generation of nerve network system under the condition of extra cellular mechanical stimulation.

This paper reports the development of a new electromyography (EMG) sensor for the myoelectric prosthetic hand. The myoelectric prosthetic hand is controlled by EMG which is detected from the surface of human skin. Our study focuses on the dry type sensor with flexible adhesion material to fit to the skin surface instead of metal electrodes. The developed electrode consisted of silicone and conductive silicone blended with conductive carbon black. These electrodes were mounted on myoelectric prosthetic hands that were applied to perform the Pick and Place Tasks to test the total performance of the control system. The results showed that the developed material obtained a thinner sensor than the conventional ones, which enabled it to naturally trace to the subject’s forearm shape without burden on the skin.

We present a stretchable and foldable passive matrix driven display using 45 by 80 RGB LED’s mounted on a meandering printed circuitry embedded in a polyurethane film. The meander interconnections have been optimized with respect to their electrical and mechanical properties to provide a display with a 3 mm pitch between the pixels and a stretchability of up to 10%. At an operating supply voltage of 5 V, the brightness of the display exceeds 30 cd/m2.

To clarify the deformation induced crystal texture evolution of rolled and drawn magnesium alloy sheets with strong basal texture, we developed a multi-scale finite element (FE) analysis code based on the homogenization theory, which combines the microscopic poly-crystal structure and the macroscopic continuum. In our crystal plasticity constitutive equation of magnesium alloys, the plastic work induced temperature rise and twinning in the crystal slip systems was implemented into our multi-scale FE analysis code. To validate our numerical code to correctly predict macro and micro deformations including the crystal texture evolution, the tension and compression along normal direction (ND) and rolling direction (RD) at the room temperature 300K and the high temperature 673K were numerically investigated. It is confirmed that numerical results showed the similar tendency to experimentally obtained results including the strengthening the basal texuture in compression along ND, the twinning, the polarity of twinning and the temperature-dependency that twinning is hardly appear at high temperature. Finaly, we concluded that our numerical code can predict the plastic strain induced texture evolution of magnesium alloys.

Recently, the observation technology of micro structure has made great progress, and then collagen fiber orientation of meniscus can be measured accurately. This makes it possible to evaluate the stress in knee joint by considering the collagen fiber orientations at the micro scale. In this study, we developed visco-isotropic/anisotropic hyperelastic constitutive equations (Iso-VHE/Aniso-VHE) for menisci, which can reflect the initial collagen fiber orientations and their deformation induced rotations. Subsequently, we constructed a finite element (FE) model of normal human knee joint by using the magnetic resonance (MR) tomography images. The FE analysis with the proposed constitutive equations and FE model clarifies the reinforcement effect of collagen fibers on mechanical characteristics of knee joint. Our computational prediction clarified that the stress concentration occurred on the contact parts of articular cartilages of femur and tibia, which met the tendency of the experimental results. Furthermore, the maximum compressive stresses evaluated by Aniso-VHE always showed a lower value as compared with Iso-VHE. This suggested that the anisotropy of meniscal collagen fibers relieved the stress concentration and lowered the maximum value. Therefore, our proposed FE analysis was proved to have a potential to reveal the functions of meniscus and knee joint.

A new constitutive equation for rubber is derived by employing a nonaffine molecular chain network model for elastic deformation behavior and the reptation theory for viscoelastic deformation behavior. The effect of a silica coupling agent, whose condensation reaction heterogeneously creates a crosslinking agent that increases the number of entangled points, on the deformation behavior is evaluated through the nonaffine constitutive equation for rubber. Precise TEM observation suggests the generation of complex interfillers connecting gel phases in which the characteristics of rubber intricately changed depending on the volume fraction of the silica coupling agent. The deformation behaviors of 2D rubber unit cells containing silica fillers under monotonic and cyclic strainings are investigated by computational simulation based on the proposed constitutive equation and the homogenization method. The obtained results clarified the essential physical enhancement mechanisms of deformation resistance and hysteresis loss, i.e., the Mullins effect, for silica-filled rubber. The volume fraction of the silica coupling agent essentially affects the deformation behavior of silica-filled rubber, the finding suggests that the material characteristics of silica-filled rubber are much more controllable than those of carbon-black-filled rubber.

New finite element homogenization model with nonaffine constitutive equation of rubber is developed to study the deformation behavior of silica-filled rubber under monotonic and cyclic deformation. The obtained results clarified the effect of the volume fraction of the silica coupling agent and the networklike structure connecting the silica particles on essential physical enhancement mechanisms of deformation resistance and hysteresis loss for silica-filled rubber. The finding suggests that the material characteristics of silica-filled rubber are much more controllable than those of carbon-black-filled rubber.

Molecular adsorption on carbon nanotube (CNT) films follows the Langmuir adsorption isotherm even for polar molecules at low gas pressures. Therefore, this film can be applied to gas sensors. In order to clarify the effect of thickness on sensor response, we fabricated CNT films of different thicknesses and observed their behavior. Because the adsorption is expected to occur near the surface, we determined the effective penetration thickness for the gas molecules and identified an approximate thickness of 7 μm.

Dynamic recrystallization (DRX) occurs during the hot-working of a metallic material with low-to-medium stacking-fault energy. The macroscopic mechanical behavior during hot-working is largely affected by the microstructure evolution due to DRX. In this study, a novel multiscale hot-working model was developed by coupling the multi-phase-field dynamic recrystallization (MPF-DRX) model and large deformation elastic–plastic finite element (FE) method using J2 flow theory to evaluate the microstructure evolution and macroscopic mechanical behavior, respectively. We call this model the multi-phase-field and finite element dynamic recrystallization (MPFFE-DRX) model. Compression simulations with nonuniform deformation of a cylinder confirmed that the newly developed MPFFE-DRX model can be used to evaluate the macroscopic mechanical behavior during hot-working by considering the DRX microstructure evolution, which differs depending on the area. We also confirmed that the MPFFE-DRX model can be used to simulate macroscopic mechanical behavior depending on the initial microstructure by varying the initial grain size.

To clarify the essential deformation characteristics of silica-filled rubber, we construct the finite element homogenization models of silica-filled rubber with newly proposed nonaffine molecular chain network model of rubber. These models can reflect the generation of complicated inter-fillers connecting phases where the characteristics of rubber are intricately changed depending on the volume fraction of silica coupling agent and relative size of particles and their location. The results obtained clarified the essential physical enhancement mechanisms of deformation resistance and hysteresis loss for rubber filled with silica with different distribution patterns under diffrent rate of deformation. The volume fraction of coupling agent essentially affects the deformation behavior of silica filled rubber which suggests the high controlability of the material characteristics of silica filled rubber as compared with carbon black filled rubber.

The morphology and function of articular cartilage tissue is regenerated through the metabolic activity of cells stimulated by the mechanical loading. In this study, a biphasic multi-scale analyses scheme is adopted for stress evaluation occurred in the chondrocyte cell. The dynamic-explicit finite element (FE) method was employed for the solid phase and the smoothed particle hydrodynamics (SPH) method was used for the fluid phase. A macro-scale 3D human knee joint FE model was constructed based on magnetic resonance (MR) cross sectional images. Further, we derived the Representative volume element (RVE) based on the Multiphoton microscopy (MPM) observation to build a micro-scale FE model of cartilage tissue. We characterized three layers in the articular cartilage tissue. Parameters of the visco-anisotropic hyperelastic constitutive law and SPH models were determined using experimental results. Biphasic multi-scale FE and SPH analyses were carried out under the maximum loading condition in the normal walking motion. As a result, large flow velocity was observed around chondrocyte in the surface layer. The highest hydrostatic and shear stress occurred on chondrocyte in the surface layer. Numerical results shows a good agreement with experimental results.

In order to predict dynamic recrystallization (DRX) texture evolution during the forming processes of aluminum alloy, we propose a hypothesis to predict DRX evolution and develop a comprehensive computational tool for the thermal process metallurgy simulation. It consists of the two-scale finite element method based on the thermo-coupled elasto-crystalline plasticity analysis and the dynamic-explicit finite element procedure. It can predict the heat generation and diffusion, and plastic anisotropy at the macro-scale, and the crystal texture evolution including DRX due to the plastic deformation and heat generation at the micro-scale. The computationally evaluated texture evolution, which includes DRX texture, under the severe compression at high temperature is compared against the experimental results of pole figures and orientation distribution function (ODF) analyses. The results predict the evolution of the cube component which is observed in the experiments. Therefore, our proposed method is approved to have a potential predicting DRX texture evolution. Furthermore, we clarify the effect of DRX texture on the onset of such instabilities as necking, surface instability and shear bands which are closely related to the formability or failure of the materials.

Summary The articular cartilage of a knee joint has a variety of functions including dispersing stress and absorbing shock in the tissue, and lubricating the surface region of cartilage. The metabolic activity of chondrocytes under the cyclic mechanical stimulations regenerates the morphology and function of tissues. Hence, the stress evaluation of the chondrocyte is vital subject to assess the regeneration cycle in the normal walking condition, and predict the injury occurrence in the accidents. Further, the threshold determination of stress for the chondrocytes activation is valuable for development of regenerative bio-reactor of articular cartilage. In this study, in both macro- and micro-scale analyses, the dynamic-explicit finite element method was employed for the solid phase and the smoothed particle hydrodynamics (SPH) method was used for the fluid phase. In the homogenization procedure, the representative volume element (RVE) for the micro-scale finite element model was derived by using the Multi-Photon Microscope (MPM) measured 3D structure comprising three different layers: surface, middle, and deep layers. The layers had different anisotropic structural and rigidity characteristics because of the collagen fiber orientation. In both micro- and macro-scale FE analyses, the visco-anisotropic hyperelastic constitutive law was used. Material properties were identified by experimentally determined stress–strain relationships of three layers. With respect to the macro- and micro-scale SPH models for non-Newtonian viscous fluid, the previous observation results of interstitial fluid and proteoglycan were used to perform parameter identifications. Biphasic multi-scale FE and SPH analyses were conducted under normal walking conditions. Therefore, the hydrostatic and shear stresses occurring in the chondrocytes caused by the compressive load and shear viscous flow were evaluated. These stresses will be used to design an ex-vivo “bio-reactor” to regenerate the damaged articular cartilage, where chondrocytes are seeded in the culture chamber. To know the stress occurred on and in the chondrocytes is vitally important not only to understand the normal metabolic activity of the chondrocyte, but also to develop a bio-reactor of articular cartilage regeneration as the knee joint disease treatment.

This paper covers results from early pathfinding investigations of a wafer level package (WLP) technology that addresses future direct chip attach (DCA) needs. An overview of the WLP technology and pathfinding results covering key process flow evaluations and future challenges to apply the concept to DCA are presented. Proof-of-concept (POC) of 300mm wafer-level mold integrating with Cu bumps was demonstrated by investigating the mold thickness uniformity, wafer warpage, and solder joint reliability on the board. We conclude with a discussion of the key risk areas remaining challenges that includes the mold grinding thickness variance control, optimization of the material properties, and alternative low cost bumping technologies scalable less than 0.3mm pitch, and outline the next steps to continue data collection on the wafer warpage behavior, the die breakage strength, and the board level assembly process using a standard surface mount infrastructure in our pathfinding work.

Since semi-crystalline polymer has very complex hierarchical structure, it is essential to construct a suitable multiscale mechanical model for the prediction of its mechanical characteristics. For the establishment of the triple scale mechanical model of semi-crystalline polymer, which can reflect the non-uniform deformations in micro-, meso- and macroscopic scales, computationally efficient model to relate structures and deformations in micro- to mesoscopic scales is indispensable. In this paper, to solve the problems, tangent modulus method was introduced into the constitutive equations for crystalline and amorphous phases consisting of the microstructure of semi-crystalline polymer. Furthermore, we proposed a new laminar composite model connecting deformations in micro- to mesoscopic scales based on the equilibrium of stress acting on the interface between the phases and the compatibility of deformation along the interface. Appropriate time steps for stable simulation and validity of the proposed model were examined through the computational simulation of uniaxial tension of single lamellar and spherulite models of high density polyethylene. It has been clarified that the proposed model could predict an elasto-viscoplastic deformation behavior of semi-crystalline polymer in markedly less computational time and memory.

The rubbers containing various kinds of fillers exhibit fabulous mechanical characteristic and therefore, they are widely used in various production. Owing to the wide range of controllability in mechanical characteristics by adding the coupling agent, silica-filled rubber draws attention for extensive usage. Here, to clarify the mechanism of the marked increase in deformation resistance in silica-filled rubber in detail, we will construct the finite element homogenization models of silica-filled rubber. These models can reflect various experimental observations that include changes in microscopic structural characteristics such as distribution morphology of silica particles, the thickness of the interfacial phase between silica and rubber, and the networklike gel structures developed from the interfacial phase. The obtained results clarified the essential physical enhancement mechanisms of deformation resistance and hysteresis loss, i.e., the Mullins effect, for rubber filled with silica. The volume fraction of the silica coupling agent essentially affects the deformation behavior of silica-filled rubber suggesting the high controllability of the material characteristics of silica-filled rubber compared with carbon-black- filled rubber. Although, the present model underestimates the hysteresis loss as compared with the experimental results, it has a capability to evaluate the effect of adding coupling agents on the fundamental deformation behavior of silica filled rubber.

We performed deformation simulations of nanocrystalline structures under different temperature and grain-size conditions using the phase-field-crystal (PFC) method with an isovolumetric numerical scheme proposed by Hirouchi et al. [Development of numerical scheme for phase field crystal deformation simulation. Comput Mater Sci 2009;44:1192–7.], and we discussed the deformation behavior of bicrystalline and polycrystalline metallic materials during plastic deformation in detail. As a result, we were able to observe typical plastic deformation behavior such as the generation, annihilation and movement of dislocations as well as grain rotation and grain boundary (GB) migration depending on the grain size and temperature. It was concluded that the PFC method with the isovolumetric deformation scheme is a powerful tool for simulating polycrystalline metals, because the obtained behaviors were in qualitative agreement with the results obtained by molecular dynamics (MD) simulations and experiments.

We have developed a numerical model of recrystallization taking the inhomogeneities of the plastic deformation of a polycrystalline metal into account. Here, the plastic deformation of the polycrystalline metal is simulated by the finite element method based on crystal plasticity theory and the microstructure evolution during recrystallization is simulated by the multi-phase-field method. In primary recrystallization simulations, nucleation is the most difficult problem. In the present model, the deformation microstructure is predicted from the results of a crystal plasticity finite element simulation, and spontaneous nucleation is achieved through abnormal grain growth that is enabled by introducing the misorientation dependences of grain boundary energy and mobility. As a result of simulations under three different compression strains, it is confirmed that primary recrystallization simulations depending on the amount of deformation and taking the inhomogeneities of the plastic deformation of a polycrystalline metal into consideration can be successfully performed by employing the proposed model.

The martensitic transformation with plastic deformation in polycrystal is investigated by the elastoplastic phase-field model. The model can capture not only spatiotemporal change of martensitic microstructure, but also plastic deformation behavior to accommodate transformation-induced stress. In this paper, fcc → bcc martensitic transformation in Fe–Ni polycrystalline alloy is simulated in two-dimensions. The effects of self- and plastic accommodations on the transformation kinetics and morphology of microstructure are studied. The simulation results demonstrate that the martensite phase nucleates near crystal defects and grows into the parent phase. The morphology of the growing martensite phase presents a plate-like shape to minimize the elastic strain energy. The present simulation clearly shows that stress relaxation behavior is dominant factor which characterizes the morphology of martensite phase. The martensitic transformation only with the self-accommodation produces fine multivariant lamellar microstructure which accommodates internal stress-field. The high stress-field in the microstructure prevents completion of the transformation and causes formation of retained parent phase. In the martensitic transformation with the self- and the plastic accommodations, since the plastic deformation largely reduces the elastic strain energy, the self-accommodation driven by reduction of the elastic strain energy is suppressed. As a result, coarse multi-variant microstructure emerges in the grain where large amount of plastic strain is introduced. Furthermore, the parent phase can transform into the martensite phase completely.

A morphological evolution of the growth of Fe 2 B boride on steel substrate has been investigated using two dimensional (2D) multi-phase-field (MPF) simulations. In order to evaluate competitive growth between boride seeds during the coating process, variations on boride seed orientation have been implemented. In addition, in order to have anisotropy growth of boride, anisotropy of interfacial energy is considered on the evaluation of phase-field evolution. It was observed that boride seed with structure orientation of 90° shows a preferential growth as compared with the growth of boride seeds at other orientations. On the other hand, competitive growth between boride seeds at different crystal orientations can also be observed, where boride seeds approaching a preferential orientation angle grow faster and suppress the growth of boride seeds at the lower orientation angle. Both of these present observations agree with previous experimental observations that boride seeds tend to grow perpendicular to the substrate surface and the growth of boride seeds in this direction suppress growth in other directions. Additionally, it was observed that the preferential growth of boride is independent of the initial size of the boride seed.

The 2D extended homogenization model based on molecular chain network theory is employed to investigate the micro-to macroscopic mechanical behavior of polymer with randomly distributed voids under macroscopic compaction. A parametric study is performed to quantify the effect of the volume fraction of voids and the macroscopic stress triaxiality of loading conditions on the compaction behavior of porous polymer. The results suggest that the onset of localized shear band at the ligament between voids leads to the macroscopic yield of porous polymer. Furthermore, the microscopic localized shear deformation behavior is promoted in the polymer with high-volume fraction of voids under high macroscopic stress triaxiality loading condition, which results in the early appearance of the macroscopic yield. After the macroscopic yield, a remarkable strain hardening is shown in the macroscopic response of porous polymer under high macroscopic stress triaxiality loading condition, which is due to the onset and propagation of a large number of shear bands at the ligaments between voids. On the other hand, microscopic buckling develops at the narrowest ligament in the polymer with high-volume fraction of voids under high macroscopic stress triaxiality loading condition, which leads to the relative low macroscopic deformation resistance. Furthermore, to develop the macroscopic constitutive model of polymer with high-volume fraction of voids under high macroscopic stress triaxiality loading condition, a modified Gurson model is proposed which takes account of microscopic buckling and gives a good agreement with the unit cell computational results.

A dynamic recrystallization multi-phase-field (MPF-DRX) model that can approximately take into account grain deformation during dynamic recrystallization (DRX) has been developed, where the grain deformation was introduced by changing the size of a finite difference grid so as to keep the volume constant. The accuracy of the developed model was confirmed by simulating a single DRX grain growth. As a result of MPF-DRX simulations with grain deformation, it was clarified that, from microstructure evolutions, the appropriate deformation during DRX can be reproduced by the developed model. However, it was also concluded that the macroscopic stress–strain relationship and variations in grain size are not affected by the grain deformation introduced here. Furthermore, the DRX cycle was defined and the relationship between the DRX cycle fraction and the stress–strain curve was discussed. As a result, it was concluded that the stress–strain curve with multiple peaks is observed when the strain at the first valley of the stress–strain curve is smaller than that corresponding to the maximum first DRX cycle fraction.

In order to clarify the elasto-viscoplastic deformation behavior and strength of rubber blended semi-crystalline polymer, micro- to mesoscopic mechanical behavior was modeled by using large deformation finite element homogenization method. In this model, dimension of mesostructure is identified by the volume fraction of interface region around the rubber particles. The effects of strain rate and the size of rubber particles on the mesoscopic true stress—strain relation, strain rate distribution in mesoscopic area, and change in mesoscopic morphology with deformation are investigated by numerical simulation of uniaxial tensile deformation of semi-crystalline polymer with nonuniformly distributed rubber particles. A series of computational simulations clarified that mechanical behavior of blend polymer is strongly affected by the size of rubber particles. Mesoscopic true stress—strain relationship shows softening for blend polymer with large rubber particles, which is closely related to the distribution of strain rate on mesoscopic scale. When the rubber particles are large, local strain rate is highly concentrated in the ligament area between adjacent rubber particles, while it distributes in larger area of semi-crystalline polymer matrix in case of small rubber particles. The difference in these localized deformation leads to characteristic change in the size and shape of rubber particles with straining. Nonuniform deformation in mesoscopic area caused by heterogeneous rubber particle distribution is emphasized by high strain rate and large rubber particles. Furthermore, maximum mean stress generated in semi-crystalline polymer matrix is very high when the size of rubber particles is smaller than or ligament thickness is larger than a specific value. The specific thickness corresponds to the critical value for brittle-ductile transition of rubber blended semi-crystalline polymer obtained by impact test.

The phase field crystal (PFC) method is anticipated as a new multiscale method, because this method can reproduce physical phenomena depending on atomic structures in metallic materials on the diffusion time scale. Although the PFC method has been applied to some phenomena, there are few studies related to evaluations of mechanical behaviors of materials by appropriate PFC simulation. In a previous work using the PFC method, tensile deformation simulations have been performed under conditions where the volume increases during plastic deformation. In this study, we developed a new numerical technique for PFC deformation simulation that can maintain a constant volume during plastic deformation. To confirm that the PFC model with the proposed technique can reproduce appropriate elastic and plastic deformations, we performed a series of deformation simulations in one and two-dimensions. In one- and two-dimensional single-crystal simulations, linear elastic responses were confirmed in a wide strain rate range. In bicrystal simulations, we could observe typical plastic deformations due to the generation, annihilation and movement of dislocations, and the interaction between the grain boundary and dislocations. Moreover, the deformation behaviors of a nanopolycrystalline structure at high temperature were simulated and the intergranular deformations caused by grain rotation and grain boundary migration were reproduced.