Microscopic Stress Distribution Research Articles

Digital Image-based Analysis of Morphology for Porous Materials

The porous material is one of the promising functional materials, and its macroscopic properties are strongly dependent on the microscopic morphology. To study the correlation between the microscopic heterogeneity and the macroscopic properties, a novel digital imagebased analysis methodology is proposed in this paper, which consists of high resolution X-ray CT, digital image-based modeling, multi-scale stress analysis and geometrical morphology analysis. The proposed morphology analysis enables us to predict the microscopic stress concentration for spherical porous ceramics considering the heterogeneous dispersion of spherical pores and the macroscopic loading condition. The heterogeneity can be analyzed geometrically for very huge data with approximately 58 million voxel elements quickly. The morphology analysis is helpful for the multi-scale modeling and microscopic stress evaluation. The microscopic stress distribution is also discussed in association with the random heterogeneity for ceramics with open pores and with high porosity ratios.

An enhanced asymptotic homogenization method of the static and dynamics of elastic composite laminates

The homogenization method has been used often in analyzing the composite materials but has had limited use with the laminated structures. This is due to a limitation of the homogenization theory, which assumes the unit cell should be periodically represented in any specific area. The main attraction of the homogenization method is its systematic capability to develop the homogenized macroscopic constitutive relation of composite materials and to compute the stresses in the microstructure of composites. In other words, both the macro- and micromechanics can be treated in the same context. In this paper, we will develop an enhanced asymptotic homogenization method (EHM); this method is developed from the partial asymptotic expansion and the condensed third-order shear deformation theory. This theory uses the reduced matrix method to consolidate all the stiffness matrices into four stiffness matrices (the extension; coupling; bending and transverse shear stiffness matrices) in the same manner as with the first-order shear deformation theory (FSDT). Two FORTRAN programs PRELAM and POSTLAM [Int. J. Comput. Struct. 76 (2000) 319; An enhanced asymptotic homogenization method of elastic composite laminates, Ph.D. Thesis, The University of Michigan, 1999] were also developed from the finite element implementation of the enhanced homogenization method. The pre-processor, PRELAM, reads the unit cell model and generates the homogeneous material stiffness matrix for a laminated structure. The post-processor, POSTLAM, calculates the local stress distribution based on the strains and curvatures obtained from the global structure analysis generated by the commercial finite element software, i.e., ABAQUS or MSC/NASTRAN. By the nature of homogenization method, these computational methods are capable of handling geometrically complicated microstructures and predicting the microscopic stress distributions. Since, the number of unknown variables for EHM and FSDT are the same, this implies that the results from EHM is easily utilized by ABAQUS in the global analysis. Therefore, one of the main benefits to EHM is that it is readily applied in commercial FEM packages, but not that it is as accurate as other methods. Numerical examples are also presented to validate these two programs.

Microstructure-based stress analysis and evaluation for porous ceramics by homogenization method with digital image-based modeling

Multi-scale analysis using the asymptotic homogenization method is becoming a matter of concern for microstructural design and analysis of advanced heterogeneous materials. One of the problems is the lack of the experimental verification of the multi-scale analysis. Hence, it is applied to the porous alumina with needle-like pores to compare the predicted homogenized properties with the experimental result. The complex and random microstructure was modeled three-dimensionally with the help of the digital image-based modeling technique. An appropriate size of the unit microstructure model was investigated. The predicted elastic properties agreed quite well with the measured values. Next, a four-point bending test was simulated and finally the microscopic stress distribution was predicted. However, it was very hard to evaluate the calculated microscopic stress quantitatively. Therefore, a numerical algorithm to help understanding the three-dimensional and complex stress distribution in the random porous microstructure is proposed. An original histogram display of the stress distribution is shown to be effective to evaluate the stress concentration in the porous materials.

Measurement of microscopic stress distribution of multilayered composite by X-ray stress analysis

In order to evaluate the effect of nano-sized dispersoid to microscopic stress distribution of multilayered composite, two kinds of multilayered composites, Al 2O 3/3 mol% Y 2O 3-stabilized ZrO 2 (3Y-TZP) and Al 2O 3/3Y-TZP(SiC), were fabricated. The latter composite contained nano-sized SiC dispersion within 3Y-TZP layers. The micro-residual stress measurement by X-ray diffraction (XRD) analysis for the monolithic 3Y-TZP and 3Y-TZP(SiC) nanocomposite layers within each composite revealed the existence of tensile and compressive stresses perpendicular and parallel directions to the layers, respectively. The tensile stress of approximately 200–300 MPa was observed to distribute across the zirconia layers in both composites. On the other hand, much higher compressive stress (i.e., 500–700 MPa) existed with a steep distribution across the layer especially for the monolithic Al 2O 3/3Y-TZP multilayered composite. However, both tensile and compressive stress distributions were found to be flattened when nano-sized SiC was incorporated into 3Y-TZP layer.

Multi-Scale Analysis and Microscopic Stress Evaluation for Ceramics Considering the Random Microstructures

A multi-scale computational method using the homogenization method is applied to the stress analysis of ceramics considering the random and complex microstructure three-dimensionally. The main purpose of this paper is to propose a numerical method to understand quantitatively the microscopic stress distribution in the random microstructure especially for porous ceramics. The voxel mesh is used to model the microstructure automatically with the help of the image-based modeling technique. In the analysis of porous alumina with needle-like random pores, the distance from the nearest pore is measured for all the voxel elements, which is plotted with the histogram of the microscopic stress distribution. This is of great help to study the relation between the stress concentration and the pore geometry and dispersion.

705 セラミックス多孔体のデジタルイメージベース・アナリシス

This paper proposes a digital image-based analysis of porous ceramics to study numerically the correlation between the heterogeneous microstructure and the macroscopic properties and behaviors. The homogenization method is the core technique of the multi-scale stress analysis with the help of the finite element method. The microstructure modeling is carried out practically by the digital image-based technique and the high resolution X-ray CT machine. The morphology analysis is very useful for the understanding of the heterogeneity and the microstructure modeling. The quantitative evaluation of the calculated microscopic stress distribution is very important, and therefore a practical post-processing tool "V-SEM" has been developed.

3D finite element analysis of particle-reinforced aluminum

Deformation in particle-reinforced aluminum has been simulated using three distinct types of finite element model: a three-dimensional repeating unit cell, a three-dimensional multi-particle model, and two-dimensional multi-particle models. The repeating unit cell model represents a fictitious periodic cubic array of particles. The 3D multi-particle (3D-MP) model represents randomly placed and oriented particles. The 2D generalized plane strain multi-particle models were obtained from planar sections through the 3D-MP model. These models were used to study the tensile macroscopic stress–strain response and the associated stress and strain distributions in an elastoplastic matrix. The results indicate that the 2D model having a particle area fraction equal to the particle volume fraction of the 3D models predicted the same macroscopic stress–strain response as the 3D models. However, there are fluctuations in the particle area fraction in a representative volume element. As expected, predictions from 2D models having different particle area fractions do not agree with predictions from 3D models. More importantly, it was found that the microscopic stress and strain distributions from the 2D models do not agree with those from the 3D-MP model. Specifically, the plastic strain distribution predicted by the 2D model is banded along lines inclined at 45° from the loading axis while the 3D model prediction is not. Additionally, the triaxial stress and maximum principal stress distributions predicted by 2D and 3D models do not agree. Thus, it appears necessary to use a multi-particle 3D model to accurately predict material responses that depend on local effects, such as strain-to-failure, fracture toughness, and fatigue life.

Multi-scale Analysis and Microscopic Stress Evaluation for Ceramics Considering the Random Microstructures.

A multi-scale computational method using the homogenization method is applied to the stress analysis of ceramics considering the random and complex microstructure three-dimensionally. The main purpose of this paper is to propose a numerical method to understand quantitatively the microscopic stress distribution in the random microstructure especially for porous ceramics. The voxel mesh is used to model the microstructure automatically with the help of the image-based modeling technique. In the analysis of porous alumina with needle-like random pores, the distance from the nearest pore is measured for all the voxel elements, which is plotted with the histogram of the microscopic stress distribution. This is of great help to study the relation between the stress concentration and the pore geometry and dispersion.

Raman Microprobe Evaluation of Bridging Stresses in Highly Anisotropic Silicon Nitride

The microscopic bridging stress distribution developed behind the crack tip of a highly anisotropic silicon nitride has been measured along the crack profile using Raman microprobe spectroscopy with a micrometer spatial resolution. The near‐tip rising R‐curve behavior and the crack‐opening displacement (COD) profile of the material were also determined and discussed in comparison with the Raman microstress data. A comparison with the fracture behavior of a previously investigated silicon nitride material with a three‐dimensional random microstructure is also proposed. According to this set of micro/macroscopic fracture characterizations, a self‐consistent view of toughening behavior in silicon nitride ceramics is obtained, and the role on toughness of anisotropically oriented acicular grains clarified. In agreement with previous studies, it is confirmed that crack‐face bridging is the most effective mechanism for toughening silicon nitride ceramics.

Mehanical Behavior of Metal Matrix Fiber Composities with Fiber-Matrix Interfacial Failure and Slide under Longitudinal Shear Loading.

Mechanical behavior of a metal matrix fiber composite under longitudinal shear loading is considered by means of a homogenization theory. The microstructure of the composite is assumed to be periodical array of fibers and associated hexagonal unit cells are placed in the composite. Displacement of the composite is described as two-scale asympotic expansion to observe the macroscopic and microscopic fields separately. On the basis of the homogenization theory, elasto-plastic analysis is made with the unit cell of the composite. The interface between fiber and matrix is modeled as a perfect bond before the interfacial failure and as a frictional contact with slide after the interfacial failure. This method is applied to a SCS6/Ti-6A1-4V metal matrix composite. The nonlinear constitutive behavior of the composite and microscopic stress distribution are shown with variation of the coefficient of the friction on the interface.

Microscopic Simulation Technique for Composite Meterials Using the Homogenization Method Based on Fixed Grid.

Recently, the homogenization method is becoming a matter of interest as a new analysis method of composite materials. This method aims at stricter modeling and more precise simulation for any kind of reinforcement. Discretization of complicated microstructures of such reinforcement, however, becomes the bottleneck in the analysis procedure. Therefore, a new simulation technique based on a fixed grid is proposed in this paper. Fundamental investigation of the accuracy of the homogenization method based on a fixed grid for unidirectional FRP is presented. The obtained elastic constants show good agreement with the solution of the Halpin-Tsai equation. Microscopic stress distribution has also been evaluated well compared with conventional smooth finite-element discretization.

SIMULATION OF DEBONDING ON THE INTERFACE AND SUBSEQUENT CREEP CRACK GROWTH IN THE MATRIX FOR METAL MATRIX COMPOSITE

Mode of debonding on the interface between Al matrix and SiC whisker aligned unidirectionally is simulated by using the finite element method, and the subsequent creep crack growth in the matrix at 300°C is treated in the framework of the continuum damage mechanics. In order to estimate damage and stress development in the vicinity of the whisker, a unit cell model which is based on a kind of periodical boundary condition is employed. Damage development associated with stress/strain for the unit cell model is calculated as the axisymmetric and also plane strain conditions, and the difference between both results are compared. The analyses of debonding and creep crack growth are carried out by using a local approach, and macroscopic creep deformation of MMC as well as microscopic damage and stress distribution is also evaluated, and the result is discussed in the comparison with the experimental data.

Stress distribution and dislocation dynamics in GaAs grown on Si by metalorganic chemical vapor deposition

We have investigated, by photoluminescence measurement, the microscopic stress distribution near the dislocation in GaAs grown on Si substrate and in planar homoepitaxial GaAs which was grown by metalorganic chemical vapor deposition (MOCVD). It was found that a compressive stress due to lattice deformation existed near the dislocation. Dislocation dynamics were observed by photoluminescence image while applying the external stress by a fine needle. Density and location of the dislocation could be artificially operated by some extent.

Finite element modelling of residual stresses and strength differential effect in discontinuously reinforced metal matrix composites

A finite element analysis is carried out on the development of residual stresses during the cooling process from the fabrication temperature in discontinuously reinforced metal matrix composites. The strength differential in subsequent compression and tension from the residual stress state is also analysed. The analysis employs three-dimensional models within the framework of unit cell assumptions with spherical, ellipsoidal and cylindrical SiC fibres in an Al matrix as test cases. The effect of morphology, aspect ratio, volume fraction and end-to-end spacing of the fibres on microscopic stress and strain distribution, plastic zone development at the matrix-particle interface and macroscopic mechanical properties of the composite is studied. The magnitude of the strength differential is shown to be highest for cylindrical fibre morphology and increases with fibre aspect ratio and volume fraction and to some extent with fibre end-to-end spacing. The results are compared with the available experimental data and an analytical model.

A micromechanical derivation of the differential equation of interfacial statics

A novel method is employed to derive the standard equation of interfacial statics from basic thermodynamic principles by employing the general ideas of matched asymptotic expansions. This entails describing the continuum thermodynamic properties of the system (such as pressure, species concentrations and chemical potentials) on two different length scales: (i) a “microscopic” length scale l, from which viewpoint the system is viewed as being continuous over its entire infinite extent. No interface, as such, exists at this level of description. Instead, however, there exists a distribution of short-range external forces (of intermolecular origin) acting on each of the chemical species i in a special direction over an effective length of O( l); (ii) a “macroscopic” or “bulk” length scale L( L ⪢ l). A “sharp” interface [of thickness O( l)] exists at this coarser level of description, separating the thermodynamic system into two continua. However, no external forces are observed at this level. Using singular perturbation theory, thermodynamic properties at the l and L scales are asymptotically matched so as to furnish the same macroscopic stress (i.e., pressure) distribution. The property of interfacial tension then arises naturally to reconcile the apparent difference between the exact l-scale microscopic stress distribution and the coarser L-scale macroscopic stress. In effect, the interfacial tension embodies the macroscopic manifestation of the l-scale intermolecular forces, which forces do not appear explicitly in the L-scale description of the phenomena because of their short-range [i.e., O( l)] nature. These forces do, however, appear implicitly in the L-scale description under the guise of an interfacial tension. The theory, which is rigorous, is shown to be formally equivalent to prior, ad hoc, hybrid, “microscopic” continuum theories which model interfacial phenomena by assuming a priori the existence of a transversely isotropic stress tensor in proximity to the interface. In contrast, the stress tensor is isotropic in our theory.

Magnetic Studies of Residual Stress in Iron and Steel Induced by Uniaxial Deformation

The nature of the residual stress in steel after uniaxial plastic deformation was investigated magnetically. The B-H curve measured in the residual stress state after elongation was similar to the one under compressive stress, and the induced magnetic anisotropy was uniaxial with the easy axis at right-angles to the previous direction of elongation. By employing a newly developed magnetic probe, which detects the sign and the magnitude of the induced uniaxial magnetic anisotropy under deformation, the magnetic yielding phenomenon was observed at the mechanical yield point. The probe output was highest at this point, compared with that observed during the subsequent cycles of loading. These results are interpreted semiquantitatively on the basis of the microscopic stress distribution and the anisotropy of the magnetostrictive strain.

The Changes in Misorientation during the Plastic Deformation of Polycrystalline Metals

In a series of studies on the influence of strain history on the plastic deformation of polycrystalline metals, the following experiments were performed in order to make clear the mechanism of plastic deformation of the material subjected to low-cycle tensile pulsating stresses. The measurement of misorientation was made by the use of back-reflection Laue X-ray method, employing the coarse-grained sheet specimens which were constructed with polycrystalline structure and monocrystalline structure respectively. From the viewpoint of crystal plasticity, it will be considered that the aggregate plastic deformation of the polycrystalline metals subjected to low-cycle tensile stressing is mainly interpreted upon the changes in the structure of the material and statistical inhomogeneity of microscopic stress and strain distributions in the material space. From the present experimental examinations, the following conclusions have been derived.(1) The measured values of misorientation in the polycrystalline structural grain under repeated tensile stressing have been found as larger than those in those in the monocrystalline structural grain. Moreover the farmer are dependent on the direction angle of principal strain in the grain.(2) Inhomogeneity in distribution of misorientation is more remarkable in the grains of polycrystalline structure than in those of monocrystalline structure.(3) The difference between the plastic deformation of polycrystalline structural sheet specimen under low-cycle tensile pulsating stresses and that of monocrystalline structural sheet specimen will be interpreted upon the model of mobility of lattice defects which is considered as the changes in structure of the material subjected to the repeated tensile stresses.