The mechanical properties and deformation mechanisms of nano-polycrystalline (NPC) materials under tension are studied using molecular dynamics. The embedded atom method (EAM by Mishin et al. 1999) and the effective medium theory (EMT by Jacobsen et al. 1987) are adopted as the interatomic potentials of Al to investigate the influence of stacking fault energy (SFE) on the phenomena. The main difference between EAM and EMT potentials is that the latter underestimates the SFE of Al. Simulations using three different models are carried out to study the grain size dependence of the mechanical properties under different strain rate conditions. For all cases, the dependency of maximum stress on grain size can be expressed as an inverse Hall-Petch relation. This tendency is considered and may be directly explained by the volume effect of the grain boundary (GB). Both crystal slips and GB sliding are observed, but GB sliding is predominant in the small-grain model. Most of the crystal slips are caused by motion of perfect dislocation in EAM potential cases, but in EMT potential cases most of the crystal slips are caused by motion of Shockley's partial dislocation. Because the EMT potential underestimates the SFE, the core length of the extended dislocation is comparable to the grain size, and hence many stacking faults remain in grains. During the unique deformation process by partial dislocation movement, a strange rotation of grains is also observed. That is, the deformation mechanism of NPC materials is strongly influenced by the SFE. Another interesting deformation mechanism observed is the grain switching process. From the macroscopic viewpoint, this is quite similar to the switching mechanism proposed by Ashby and Verrall (1973). However, there is a significant difference: in the present study both the GB migration and sliding are predominant but in Ashby and Verrall's study, the mechanism of switching is based on diffusion.
Recent development of OIM (Orientation Imaging Microscope) makes the measurement of crystal orientation easy and advanced computer technology allows us to conduct a detailed stress analysis of component with microstructure. In this study, a high-cycle fatigue test was carried out for a copper polycrystal, where the shape and orientation of each grain is measured by the OIM. Thirteen PSBs are found along the grain boundaries, and the location and slip system are different from those expected by the Schmid factor. FEM analysis is conducted for the copper polycrystal with the same orientation and shape. It reveals that the increase of resolved shear stress, τrss, of specific slip system due to the constraint of deformation between grains causes the unique slip behavior near the grain boundary.
In order to investigate the criterion for the persistent slip band (PSB) formation near a Σ3(111) coherent twin boundary, where is a preferential site for formation of PSB, a high-cycle fatigue test is carried out at room temperature using a copper bicrystal specimen with the twin boundary. PSBs are observed near the boundary in the connection with the evolution of extrusion/intrusion on the specimen surface. The slip behavior is different from that predicted by the Schmid factor. A finite element method (FEM) analysis is conducted for the bicrystal, and it reveals that the increase of resolved shear stress on the specific slip system due to the constraint of deformation between the crystals is the main cause for promoting the nucleation of PSB near the twin boundary. By taking into account the interaction between the primary and the secondary slip systems, it is possible to specify the formation behavior of PSB near the twin boundary.
The stress concentration near the interface edge of a film/substrate, which dominates the delamination, is analyzed by molecular dynamics (MD) analysis. Here, the film thickness is on the nanoscale and the interatomic interaction is simulated by Morse-type model potentials. Three types of load are applied to the film/substrate to examine the effect of the stress-concentrated region on the delamination at the interface edge. At lower applied load, the stress distribution along the interface near the edge in the MD simulation coincides well with that obtained by linear elastic analysis (FEM: Finite Element Method). However, after the stress near the edge reaches the ideal strength of the interface, it deviates from the FEM result. The delamination crack is initiated from the free edge when the stress at y < 1nm (y: distance from the edge)reaches the ideal interface strength. This signifies the criterion of interface toughness that the delamination is governed by the stress in the region (process zone). This also suggests the limit of applicability of linear elastic fracture mechanics on the nanoscale components.
Materials or structures that contract in the transverse direction under uniaxial compression, or expand laterally when stretched are said to have negative Poisson's ratios. A theoretical approach to the prediction of negative Poisson's ratios of re-entrant honeycombs has been developed which is based on the large deflection model. The equations of the deflection curves of the inclined member of the re-entrant cell, strains and Poisson's ratios of re-entrant honeycombs in two orthogonal directions have been derived. The deformed shapes of the inclined members of the re-entrant cell are calculated. The negative Poisson's ratios of re-entrant honeycombs are no longer a constant at large deformation. They vary significantly with the strain. The effect of the geometric parameters of the cell on the Poisson's ratios is analyzed.
Mesoscale debonding initiation stress of a bundle of glass fibers and epoxy matrix under static loading is investigated. A special cylindrical bar specimen was designed for the experiment. The specimen contains a bundle of glass fibers in the center and the bundle diameters were 1 and 2mm. The fiber diameter is 7µm. A static tension test was performed under the displacement control. The applied load-displacement curve was recorded for each specimen and then the debonding initiation load was defined as the deviation point from the linear curve. In addition, the debonding length was measured directly from the tested specimen. Using the debonding load measured from experiment, an axisymmetric finite element analysis is performed and debonding parameters K1 and K2 were computed. The results show the debonding initiation is fully dominated by an opening mode rather than a sliding mode and the stress intensity factor K1 for the debonding initiation is 2.0E+05Pa√m. The mixed mode fracture takes place in the debonding propagation with constant mode mixity around 41.0 degree and the averaged stress intensity factors are 1.67E+05Pa√m and 1.41E+05Pa√m for the opening and the sliding mode, respectively.
Convergence of the solver and the regularization are two important issues concerning an ill-posed inverse problem. The intrinsic regularization of the conjugate gradient method along iteration makes the method superior for solving an ill-posed problem. The solutions along iteration converge fast to an optimal solution. If the termination criterion is not satisfied, the solution will diverge to a solution which dominated by the noise. Reformulation of an ill-posed problem as an eigenvalue formulation gives a very convenient formula since it is possible to estimate an optimal regularization parameter and an optimal solution at once. For very large problems, the fast Fourier transformation could be implemented in the circulant matrix-vector multiplication. The developed method is applied to some inverse problems of elasto-dynamic and the accurate estimation was achieved.
In this paper, a new numerical algorithm based on the discrete element method is presented for analyzing the dynamic problems under impact loading. Based on the basic principle of continuum mechanics, a connective model for orthotropic media is derived using disk elements. It is also extended to a bilinear hardening elastic-plastic model for calculating the plastic deformation in metals. Moreover, Mohr-Coulomb type failure criterion is used to judge the failure of concrete, and a contact discrete model is added in the algorithm. So the algorithm can calculate not only the impact problems of continuum and non-continuum, but also the transient process from continuum to non-continuum. The wave propagation in orthotropic planes under impact loading is numerically simulated. Through comparing the results with those computed by other numerical methods and examining the stability of the numerical solution, the accuracy and efficiency of the algorithm are discussed. In addition, the transient respondences of a steel warhead penetrating a concrete disc harrow is simulated, and three kinds of basic damage forms of concrete disc harrow under different penetration velocities of warhead are summarized.
The purpose of this work is to solve the governing differential equations of arbitrarily non-rectangular laminated anisotropic plates by using the Chebyshev collocation method. The four sides of the plate herein are not restricted to be straight lines, and they can be curves as well. Meanwhile, these four sides can be expressed in four mathematical functions. The transformation from non-rectangular boundary into rectangular type is the key point to the solution of this kind of problems. In general, the research on laminated anisotropic plates is almost focused on the case of rectangular plate. It is difficult to handle the laminated anisotropic plate problems with non-rectangular borders, any kind of stacking sequence and the variety of boundary conditions. However, through the merits of Chebyshev collocation method, such problems can be overcome as stated as follows. Two cases in EXAMPLES section are illustrated to highlight the displacements, stress resultants and moment resultants of our proposed work. The preciseness is also found in comparison with the numerical results by using finite element method incorporated with the software of NASTRAN.
The damping characteristics of an adhesively bonded beam in which two steel strips are joined by an adhesive are investigated. In particular, we focused on the effect of temperature on the damping characteristics. In the analysis, vibration modes of the bonded beam and strain energies distributed in each strip and the adhesive in motion are analyzed by the finite element method. Then the damping capacity of the bonded beam is estimated using the strain energies and damping ratios of the steel strips and the adhesive, which were obtained independently beforehand by experiments. The temperature dependence of Young's modulus, Poisson's ratio and the damping ratio of the adhesive are considered in the analysis. The estimated values of the damping capacity are in good agreement with the experimental results. Thus, the effects of temperature, vibration modes and the thickness of the adhesive layer on the damping capacity of a bonded beam are clarified.
A rate-type constitutive equation of compressible isotropic hyperelasticity and a finite element formulation based on the Updated Lagrangian approach are proposed. The constitutive equations of compressible hyperelasticity are simplified by introducing modified tensors in an intermediate configuration, which separates the volumetric deformation from the distortional deformation. Selective integration and a mixed pressure/displacement formulation have been adopted to avoid volumetric locking and the hourglass modes. The deformation of a simple rectangle block was simulated to show the effect of the choice of the finite elements and the integration methods on the stability and the accuracy of proposed method. Moreover, loading tests were carried out on a prototype specimen of a vibration control device made from circumferential rubber parts and reinforcing steel layers in order to evaluate applicability of the proposed formulation to such devices.
Using the Green's functions, the general solutions of a three-dimensional crack problem in piezoelectric materials under mechanical and electrical loads is derived by boundary element method. Then this crack problem is reduced to solve a set of hypersingular integral equations coupled with boundary integral equations. The unknown functions are the discontinuities of the elastic displacements and electrical potential of the crack surface. The singularity of the unknowns at the crack front is analyzed by the main-part analysis method of two-dimensional hypersingular integral equations, and the exact analytical solution of the singular stresses and electrical displacements near the crack front in a transversely isotropic piezoelectric solid is given.
This paper discusses an implementation of Hybrid Boundary Node Method (Hybrid BNM) to the heat conduction analysis within bodies containing thin-walled structures. As an application, the thermal analysis in carbon nanotubes (CNT) based composites is presented. CNTs are predicted to possess superior heat conductivity and may, even with a small amount embedded, substantially improve heat conducting behavior of polymers. In this paper the equivalent heat conductivities of CNT-based nanocomposites are evaluated using a 3-D nanoscale representative volume element (RVE) model and the hybrid boundary node method (Hybrid BNM). The temperature distribution and heat flux concentration are studied. The equivalent heat conductivity of the RVE as a function of the nanotube length is calculated and discussed, and, moreover, an approximate formula for its evaluation for an RVE containing single nanotube is proposed. Computations indicate that addition of about 7.2% to 17% (volume fraction) of CNT to the polymer matrix may result in the increase of heat conductivity of the composite varying from 49% to 334% both for short and long CNT.
The purpose of this paper is to present a method of material design for the weight reduction, the high thermal radiation and the relaxation of in-plane thermal stress and centrifugal stress in a rotating disk without hole composed of functionally graded material (FGM) with arbitrary thermal and mechanical nonhomogeneities in the radial direction. The disk is subjected to an intermittent heating in an annular region near the outer radius and has an arbitrary variation of heat-transfer coefficient along the radial position on the upper and lower surfaces. The transient temperature field is analyzed by modifying Vodicka's method for one-dimensional boundary value problems in composite regions, and the thermal stress and centrifugal stress are respectively obtained by solving approximately the equilibrium equations expressed in terms of the displacement component as Euler's differential equations. The material design is carried out for the rotating disks composed of Ti+6Al+4V and SUS410 FGM, and Ti+6Al+4V, PSZ and SUS410 FGM.
In this report, the new method of topology optimization technique that is able to deal with the three-dimensional structure with constant cross section is described. In actual design field, the structure with constant cross section is widely adopted because of manufacturing restrictions and efficient design and maintenance. A key technology is to form a longitudinal group by collecting finite elements along the sweeping curve, and the structure is constructed with these groups. Since the design variables are allocated to each group instead of to each finite element, the total number of design variables is drastically reduced. Illustrative examples are shown and the effectiveness of the proposed method is discussed.
This paper presents the results of an investigation carried out into the plastic collapse and deformation behaviour when a rotating pipe impacts on a stationary target pipe. To predict the plastic energy dissipation during the deformation of circular section pipes, a modified plastic collapse analysis adapting upper bound technique based on an existing deformation mechanism model was considered. The studies carried out show clearly that the failure mode in a pipe during impact with another pipe or with a solid rod does not only depend on relative local strength of these pipes but is due to a complex interaction of various parameters, e.g. impact velocity, span to diameter ratio of the target pipe and the supporting conditions of the target pipe and also of the impact position. The results throw good light and illustrate the influence of kinetic energy and its impact position on the energy absorption characteristics of the target pipe.
This paper presents the experimental and theoretical results of the effect between diameter-to-thickness ratio (D/t ratio) and curvature-rate on the response and collapse of circular tubes subjected to cyclic bending. In experimental tests, four different D/t ratios of circular tubes and three different controlled curvature-rates were used. It was observed from experimental data that if circular tubes with a certain D/t ratio were used to test by three different curvature-rates, three parallel straight lines can be seen from the relationship between the controlled curvature and the number of cycles to produce buckling in log-log scale. In addition, it was also found that the distances among three parallel straight lines for the tubes with a higher D/t ratio are wider than that with a lower D/t ratio. Finally, theoretical formulations proposed by Lee and Pan and Lee, et al. were combined and modified so that it can be used for simulating the relationship between the controlled curvature and the number of cycles to produce buckling for circular tubes with different D/t ratios subjected to cyclic bending with different curvature-rates. The theoretical simulation was compared with the experimental data. Good agreement between the experimental and theoretical results has been achieved.
In the present work, the formation of shear band under simple shear loading is investigated using the rate-independent elastic-plastic constitutive relations. A small initial perturbation representing material imperfection is introduced into the work piece to develop the post-localization behaviors. Since kinematic hardening rule assumed under a finite deformation regime, the stress rate is co-rotated with respect to the spin of substructure using the plastic spin concept. Moreover, the strain gradient terms are incorporated into the yield function to obtain a non-local plastic constitutive relation and its results are compared with a conventional plasticity model. It is noted that the shear band formation is accompanied by decrease in the magnitude of spatial increment within the regime of localization. Moreover, the strain gradient affects the shear localization behavior significantly such that the intensity of shear band increases as the strain gradient coefficient increases when the J2 flow theory is employed. The effect of strain gradient on the deformation localization is, however, almost negligible for a material deformed accord with the J2 deformation theory.