Due to the strain-induced martensitic transformation during plastic deformation, a transformation-induced plasticity (TRIP) steel possesses favorable mechanical properties such as high strength, ductility and toughness. Since its favorable mechanical properties are realized under restricted circumstances, the prediction and control of deformation processes are indispensable to determine the expected mechanical properties of TRIP steel. However, it is very difficult to obtain TRIP steel that only has the martensitic structure before deformation, and the stress-strain relationship of each phase at various temperatures cannot be measured experimentally. Therefore, the identification of the parameters in the constitutive equations for TRIP steel is necessary. Here, a method employing finite-element simulation and the nonlinear least-squares method under constraint conditions was proposed to identify the constitutive parameters of TRIP steel from the true stress-plastic strain and the volume fraction of martensite-plastic strain relations obtained by the uniaxial tensile test and computational simulations. Then, the application of this procedure employing virtual data of an ideal TRIP steel that possesses highly favorable mechanical properties is discussed to investigate the improvement of the mechanical properties of TRIP steel.
A computer simulation for fatigue crack growth is described. The simulation is based upon the crack-tip opening process which is induced by the emission and movement of dislocations from the crack-tip. The behavior of the dislocations is determined using the dislocation dynamics method. The basic analysis for the elastic interaction between a Mode I crack and discrete edge dislocations shows that the existence of dislocations in the vicinity of the crack-tip suppresses the emission of new dislocations. This result predicts that the shielding effect which results from the residual dislocations around a fatigue crack is an important factor affecting crack propagation rate. Further, the results of the simulation show that the temporary variation in crack propagation rate with the sharp increase or decrease in the stress intensity factor range can be caused by the change in the shielding effect of the residual dislocations which are left behind the moving crack front.
This paper utilizes the potential function method to analyze the problem of circular uniform or linear variation of pressure and electric displacement on the surface of piezoelectric half space. The half space is taken as transversely isotropic piezoelectric, where the planes of isotropy are parallel to the free surface. Considering the variation of the boundary conditions, the solutions presented here actually comprise six different boundary value problems. The Green’s functions for a point normal force and charge are first used to obtain the potential functions in the form of double integrals. Using the Hankel transform, these integrals are eveluated by converting them into single infinite integrals containing product of the Bessel functions. It is shown that the integrals appearing in the potential functions have been previously evaluated in terms of complete elliptic integrals. Hence the potential functions and the electroelastic fields are presently written in terms of these integrals. Numerical results are presented to illustrate both qualitative and quantitative behavior of the induced electroelastic fields.
In this paper, we analyze the elastic field caused by an arbitrary polygonal inclusion (with uniform eigenstrain prescribed) in an infinite elastic solid. Closed-form solutions are obtained using Green’s function technique. Numerical calculations are performed for the strain and stress distributions in and around a regular polygonal inclusion. It is shown that logarithmic-type stress singularity at each corner of the inclusion may vanish only for a square inclusion of a specific orientation. Unique properties of the Eshelby tensor of a regular polygonal inclusion found by Nozaki and Taya [ASME J. Appl. Mech., Vol. 64, 1997, pp. 495-502] are also investigated in detail and the terms that cause the properties are specified.
A method is proposed for calculating the large deflection of a rectangular plate on an elastic foundation by the boundary integral equation method. The elastic foundation is assumed to be of the Pasternak type. The large deflection is formulated based on the nonlinear Berger equation. In the analysis, the governing nonlinear partial differential equation for a plate is transformed into an ordinary nonlinear differential equation using the Kantrovich method. The resultant fourth-order nonlinear differential equation was analyzed by the boundary element method. The nonlinear boundary integral equation is solved by using an iteration scheme. A fundamental solution required in the formulation is derived by solving the singular differential equation. It is found that the numerical results obtained by the present method agree well with the analytical solutions. To show the usefulness of the method, serveral numerical results based on the present formulation are given for various types of boundary and loading conditions.
The present study shows a mechanism of fractal branches of stacking sequences of laminated composites and proposes a novel approach for stacking sequence optimizations named the fractal branch and bound method. Applications of the method are limited to the stacking sequence optimizations that can be computed only by out-of-planes lamination parameters. First, values of the objective function are approximated by response surfaces as a function of the out-of-plane lamination parameters using design of experiments and the least-square-error method, and an optimal set of lamination parameters is obtained. Next, a set of candidates of optimal stacking sequences is collected using a branch-and-bound method near the optimal point of the set of lamination parameters. All of the candidates are examined thoroughly and the actual optimal stacking sequence is obtained. The fractal branch and bound method is applied to the stacking sequence optimization problems for a maximization of buckling load of a simply supported rectangular plate, and the method obtained the exact optimal stacking sequence with very low computational cost.
Changes in the three-dimensional (3D) shapes of roughened surfaces and the inhomogeneous deformation behaviors of individual grains during uniaxial tension of polycrystalline iron are experimentally investigated. The principal strains of each grain are evaluated by obtaining the approximated ellipse of the strain distribution of the grain, and then the relationship between the change in surface roughening and grain deformation is discussed. It is found that the mountains and the valleys of the roughened surface elongate in the axial direction with increasing amplitude during uniaxial tension. The grains continue to deform with the applied strain, though the rate of increase of the maximum principal strain differs among grains. From the comparison between the roughening phenomenon and the deformation of grains, it is found that surface roughening is closely related to the mutual rotation of grains. Thus, roughness increases due to the different deformation behaviors of individual grains.
A two-layer plasma sprayed thermal barrier coating on Ni base superalloy substrate was characterized. The coating was comprised of an inner layer of MCrAlY bond coating and an outer layer of 8 wt% yttria stabilized zirconia (YSZ) thermal barrier coating (TBC). After aging, the thermally grown oxide (TGO) layer at interface between YSZ and MCrAlY was observed. The TGO layer had two different contrast layers in the SEM images. The black one was closer to MCrAlY and the gray one was closer to YSZ. The thickness of both layers increased with aging. Countless porosities at the gray layer and microcrack at YSZ were also observed. Most of the macrocrack grew through the porosities. From this point of view one may say that the mechanism of macrocrack formation is a deterioration of adhesion accompanied by an increase of number of the porosities or the microcrack.
Partial penetration butt welded joints are widely used because they require relatively less weld metal for fabrication. However, incomplete penetration acts as a crack-like flaw. When the size of flaw in a material is known, the tensile strength of the material can be evaluated using fracture mechanics. This paper deals with a practical method of estimating the size of flaw (the incomplete penetration of a partial penetration butt welded joint) by ultrasonic testing (UT). The refraction angle of the probe and the method of UT are discussed. In addition, tensile strengths of welded joints are evaluated using fracture mechanics, and are found to be in good agreement with experimental results.
The effects of various basic factors of combustion gas flow conditions on the degradation behavior of silicon carbide (SiC) have been experimentally clarified. The degradation of SiC in combustion gas flow was expressed in terms of weight loss. The weight loss depended markedly on the water vapor partial pressure, becoming larger with increasing water vapor partial pressure. The effect of oxygen partial pressure on weight loss was small, and the weight loss decreased with increasing oxygen partial pressure. By considering the effects of the partial pressures of water vapor and oxygen, the gas temperature, the pressure and the gas flow velocity did not have such a significant effect on the weight loss in the given range of test conditions. Based on experimental results, it was clarified that water vapor partial pressure is the major factor causing the degradation of SiC.
A new thermographic NDT technique was proposed, in which singular electrothermal field near crack tips under the application of periodically modulated electric current was measured using an infrared thermography combined with lock-in data processing technique. Experimental investigations were made on the resolution and the applicability in the identification of through-thickness artificial cracks and fatigue cracks embedded in steel and aluminum alloy plate samples. Modulated electric current was applied to the cracked sample by an induction coli. Lock-in thermal images synchronized to the reference current modulation signal were taken by the lock-in thermography. Significant singular electrothermal field was observed at the crack tip in the lock-in thermal image. The fatigue cracks as well as artificial cracks were found to be sensitively identified by the proposed technique in good resolution compared with the singular method using a conventional thermographic temperature measurement.
Mechanical shear characteristics of hybrid composites with non-woven carbon tissue (NWCT) are investigated under uni-axial static tensile loadings. In-plane characteristics were studied on [±45]3S angle-ply CFRP laminates and [+45/−45/+45/−45/+45/−45]S angle-ply hybrid laminates. Here, the symbol “/” means that the NWCT is located at an interface between CFRP layers. A new estimation method was proposed for the stiffness of hybrid composites. Chord shear modulus and 0.2%-offset shear strength of hybrid laminates were compared with those of CFRP laminates. Results estimated with the new method were compared with results of experiments and an ordinary rule of mixtures, and then the validity was confirmed. The hybrid angle-ply laminate seems to be effective to improve the shear characteristics. The damage and failure mechanisms of the hybrid composites were discussed through observation results with an optical microscope.
This paper deals with the two-dimensional thermoelastic contact problem of a rolling rigid roller of specified shape, which induced of friction and heat generation in the contact region, moving with constant velocity in an elastic half-space containing a couple of subsurface cracks. In the present temperature analysis, the speed of the moving heat source is assumed to be much greater than the ratio of the thermal diffusivity and the half contact length. The problem is solved using complex-variable techniques and is reduced to singular integral equations which are solved numerically. Numerical results of stress intensity factors are obtained for the case of two short cracks which are located parallel to the surface. The variance in interference effects on the stress intensity factors with the distance between two cracks, and the effects of the frictional coefficient, the sliding/rolling ratio and the depth of the crack location on the results are considered.
In this study, the singular stress field around the edge point of a bonded strip subjected to thermal loading is analyzed by the body force method. The intensity of the singular stress field is defined by a parameter called the stress intensity factor. Based on the numerical results, the effects of the strip geometry and material combination on the stress intensity factors are investigated. It is found that the singular stress σθ on the interface caused by heating or cooling may be positive or negative, depending on the material combination. Also, a unique relationship between the stress intensity factor K and the eigenvalue λ does not exist.
Theoretical analysis of the singular field near an interface edge of bonded axisymmetric transversely isotropic piezoelectric materials has been carried out. The eigenequation determining the singular order, and the stress and electric displacement fields are deduced in details. The results show that the singular order depends on the geometry shape of the interface edge and the material combination. It is found that the piezoelectric and dielectric constants have no effect on the singularity under the torsion loading condition, but have a complicated effect under axisymmetric deformation condition. It is of interest that the electric displacement also behaves as singular, and its magnitude can be described by the same parameter as the intensity coefficient of the stress field. The analysis of bonded axisymmetric piezo/isotropic materials has also been carried out.
Fatigue life estimation of solder bumps is one of the most critical technologies for the development of ball grid array packages. In this study, mechanical fatigue tests were carried out using Sn63-Pb37 solder bump specimens. The cracks were initiated along the entire circumference in the vicinity of the interface. The fatigue life estimation of the solder bumps was performed based on the elastic-creep finite element method (FEM) analysis. It was clear that the strain concentration region coincides with the crack initiation site. The estimation result for the crack initiation was in good agreement with the experimental results. The results reconfirmed that it was desirable to employ the equivalent creep strain range occurring at a distance of 50 μm from the singularity point. The life ratio, which provides the quantitative correlation between the crack initiation and the ultimate fracture, was determined from the experimental results. The number of cycles to the fatal failure can be roughly estimated by multiplying the analytical estimation results for the crack initiation by this life ratio. This simple estimation of fatal failure may well be of practical use in actual ball grid array (BGA) design for thermal load conditions.
Effects of fiber/matrix interface and matrix microstructure on the mode I interlaminar fracture toughness of C/C composite materials were investigated by coating bismaleimide-triazine co-polymer (BT-resin) on the surface of carbon fiber and changing the heat-treatment temperature (HTT). For the case of laminates with HTT of 1600°C (carbonized C/C composites), the initial fracture toughness, GIC, was insensitive to BT-resin coating. Moreover, the fracture toughness during crack propagation, GIR, increased by coating BT-resin. On the other hand, both GIC and GIR decreased with BT-resin coating for the laminates with HTT of 2500°C. While both GIC and GIR are insensitive to HTT for laminates without BT-resin coating, they both decreased by increasing HTT for laminates with BT-resin coating. The difference of the effects of interface control and HTT was discussed on the basis of microscopic mechanism consideration. Comparison between in-plane and interlaminar strength indicated the possibility to optimize the interface control.
This paper presents a method of parallel computation particularized for the two-scale analysis of elastic-plastic heterogeneous media with periodic microstructures. Due to the mathematical structure inherent to the multi-scale modeling by the homogenization theory, the numerical algorithm is successfully incorporated with a clustered-type parallel computer. A simple numerical example is presented to illustrate the essential idea of parallelized, nonlinear two-scale analysis method and the algorithmic difficulty associated with computational load for each CPU. To overcome such difficulty, we present the modified parallel algorithm, in which the computational loads of CPU’s are almost equalized according to the nonlinear response of each microstructure. A proposed method is applied to simulate the tensile test for a steel specimen.
CAE tools have been applied for the crash safety design of vehicles, though they haven’t satisfied the optimum design of vehicles. The authors have proposed a Statistical Design Support System (SDSS), and have found that the SDSS is one of available optimization approaches for the nonlinear and dynamic phenomena. This system is a synthetic design method which is based on the response surface methodology and the design of experiments. In this study, a multilevel optimization approach using the SDSS is presented. This approach is well-suited to large-scale multilevel and multidisciplinary optimization problems, and optimum design of vehicle frontal structure and occupant restraint system for crashworthiness is solved. It is shown that successfully and effectively collaborative optimization for frontal structure and occupant restraint system can be conducted by this new approach.
The finite element mesh superposition method is applied to the two-dimensional crack problem of composite materials. The microscopic heterogeneity involved in the composite materials is modeled by the fixed grid model. On this global mesh, a local mesh that considers the local crack is superimposed without taking care of the matching of nodes and elements of both meshes. The use of the fixed grid model for the global mesh can reduce the time and efforts for the mesh generation to express the complex heterogeneous microstructures. Also it makes the computation and the implementation of the finite element mesh superposition method very easy. The accuracy was verified by comparing with the theory and the calculation by the conventional fine mesh.
A modified wavelet Galerkin method for the analysis of Mindlin plates is proposed. The analysis of Mindlin plates often suffers from ‘shear locking’, which is the phenomena that the overstiff response is estimated under the Kirchhoff constraint condition in the very thin plate. In order to overcome shear locking, in the proposed formulation of wavelet Galerkin method, the B-spline scaling function is adopted for the approximation of transverse displacement field, while the direct derivative of B-spline function is utilized for rotational field, which is consistent with the definition of the transverse shear strain. Various kinds of plate analyses are conducted under several conditions. As results, the completely locking free responses are always obtained if the direct derivative scaling function is used for the approximation of rotational field and the validity of the proposed wavelet Galerkin method is clarified.
The paper deals with homologous topology optimization of structures undergoing large deformations. The objective function is defined so that the load-displacement curve follows the prescribed trajectry, which shows a typical snap-through buckling. The geometrically non-linear behavior of the structures is modeled using the total-Lagrangian finite element formulation and the equilibrium is found using a Newton-Raphson iterative scheme. In order to escape from the singularity at critical points, the displacement control is utilized. The sensitivities of the objective functions are found with the adjoint method and the optimization problem is solved using the sequential linear programming method. Two algorithms are proposed to obtain homologous deformation. Several numerical examples are demonstrated to validate the present optimization method.
With development of CAD/CAE technology and computer hardware, more design engineers are using the CAE software. However, the CAE software is not an easy tool to use because of its versatility and amount of expertise required to understand and evaluate simulation results. An autonomous interface agent that supports Finite Element analysis was proposed and implemented in CAE software. The agent’s four major functions include giving overview of analysis procedure, planning capability, error support and proactive help that considers user’s situation and past experiences. The system was usability-tested by two groups of student testers of two different majors. Results showed agent support was indispensable for novice users. It also showed that first two functions were effective, that great care must be paid in concluding that a user is lost before activating the fourth function and that the way an error case instance is presented to the user should be refined.
This paper presents large-scale eigenvalue analysis of structures on parallel computer using component mode synthesis (CMS). The algorithm of the CMS used in this paper was previously developed by the authors especially for large-scale eigenvalue analysis on parallel environment. It was implemented on a parallel computer Hitachi SR2201 and the performance of the analysis system was examined. Taking full advantage of the independence of the tasks in the CMS, ideal speed up was achieved by increasing the number of CPUs. The computation time for the analysis of 8 million DOFs model with simple configuration was about 116 minutes using 64 CPUs, whereas the computation time for the analysis of 1 million DOFs model with general configuration was about 92 minutes using 241 CPUs.