Microscopic Strain Distribution Research Articles

Fully-Modeled Unit Cell Analysis for Macro/Micro Elastic-Viscoplastic Behavior of Quasi-Isotropic CFRP Laminates

A fully-modeled unit cell analysis is performed to investigate the macroscopic and microscopic elastic-viscoplastic behaviors of a quasi-isotropic carbon fiber-reinforced plastic (CFRP) laminate. To this end, a quasi-isotropic CFRP laminate and its microstructure composed of carbon fibers and a matrix material are considered three-dimensionally. Then, a hexagonal prism-shaped unit cell fully modeled with fibers and a matrix including interlaminar areas is defined. For this quasi-isotropic laminate, a homogenization theory for nonlinear time-dependent composites with point-symmetric internal structures is applied, enabling us to analyze both the macroscopic and microscopic elastic-viscoplastic behaviors of the laminate. The substructure method is introduced into the theory to reduce computational costs. The present method is then applied to the elastic-viscoplastic analysis of a quasi-isotropic carbon fiber/epoxy laminate subjected to an in-plane uniaxial tensile load, to investigate the macroscopic elastic-viscoplastic behavior of the laminate and the microscopic stress and strain distributions in them.

Mapping of Microscopic Strain Distributions in an Alloy 600 C-Ring After Application of Hoop Stresses and Stress Corrosion Cracking

Laue diffraction measurements made using polychromatic synchrotron x-radiation have revealed significant changes to the microscopic strain distributions in an Alloy 600 (UNS N06600) tube following ...

Strain localization behavior in low-carbon martensitic steel during tensile deformation

The microscopic strain distribution of lath martensitic steel during tensile deformation up to a strain of 10% has been measured in situ. Strain localization, which indicates grain interaction, is clearly observed in the vicinity of subblock boundaries, and it affects the inhomogeneous crystal rotation behavior within the block (or subblock), and hence the resultant rapid grain subdivision of the lath martensitic steel during elongation.

Imaging stress and strain in the fracture of drying colloidal films

Drying-induced fracture limits the applications of thin films based on colloidal materials. To better understand the mechanics of drying, we directly measure the microscopic distribution of strain and stress of a colloidal silica film during the course of drying and cracking. We observe the build-up and release of internal stresses inside the film before and after the opening of individual cracks, and extract a critical stress for fracture of approximately 1 MPa. We also find an inherent time scale for stress relaxation within the film of 25 minutes, likely due to the competition between elastic deformation of and solvent flow through the porous particle network. By correlating the stress and strain, we estimate the plane strain Young's modulus of our colloidal film of the order of 100 MPa.

Plastic and elastic strains in short and long cracks in Alloy 600 studied by polychromatic X-ray microdiffraction and electron backscatter diffraction

The microscopic strain distributions were studied for stress corrosion cracks produced electrochemically in C-rings of Alloy 600 (0.65 Ni, 0.16 Cr, 0.08 Fe). The strain data were obtained using polychromatic X-ray microdiffraction (PXM) and (in part) by electron back-scatter diffraction (EBSD). PXM was used to measure plastic and elastic strain distributions around the tip of a short crack, along with the changes to the direction and shape of the diffraction spots (ellipticity). For a sample with a short (30μm) crack, the misorientation map showed a well-defined region of plastic deformation along the grain boundary in advance of the crack tip, extending to the next triple point. For the large crack sample, plastic and elastic stains as well as crystalline order could be measured in high detail with respect to the crack path. However, no correlation between these could be obtained, except for a notable degradation of crystalline order near the crack mouth. A comparable EBSD misorientation map shows strong correlation between misorientation and the crack edges; this may in part reflect the role of sharp edges in the more surface-sensitive approach.

Strain localization and damage development during bending of Al–Mg alloy sheets

► The grain scale strain distribution during bending was studied in AA5754 CC sheets. ► DIC based strain mapping from SEM images of in situ bent samples was applied. ► Tendency for strain localization due to the presence of particle stringers was found. ► Facilitated matrix shearing and decreased local fracture strength were observed. ► Maximum Mises strain of 2.0 was calculated within dominant shear bands. The mechanism triggering failure during deformation in Al–Mg alloys often includes localization of the plastic flow into narrow and intense transgranular shear bands propagating through the microstructure with little evidence of damage prior to the final fracture event. The cracks initiate in the sheared zones and propagate by conventional ductile mechanism of fracture, including nucleation of voids at second-phase particles, followed by their growth and ultimate coalescence. In an attempt to fully understand the mechanism of damage in continuous cast (CC) AA5754 aluminium alloy sheet, a methodology for characterization of the microscopic fracture strain distribution during bending was adopted in this work. A batch of digital images representing the deformation history of the samples bent during in situ V-bending tests performed in a scanning electron microscope (SEM) was recorded and later used as an input to a digital image correlation system (DIC) for strain calculations. Local strain maps of the tensile through-thickness cross-section of the bent sheets were built. The results clearly reveal development of spatial inhomogeneity of the strain at microscopic level. The strain concentration inside the formed intensive shear bands, which were the predecessors of the subsequent crack propagation, was found to be considerably larger than the macro-strains typically suggested by the forming limit diagrams for aluminium sheet materials. The presented results are consistent with previously published results on the general forming characteristics of continuous cast AA5754 aluminium alloy sheet materials.

8D46 生体軟組織内微細構造と局所ひずみ分布の関連 : 解析方法の確立と大動脈壁への応用(OS07 軟組織およびその構成要素のバイオメカニクス2)

8D46 生体軟組織内微細構造と局所ひずみ分布の関連 : 解析方法の確立と大動脈壁への応用(OS07 軟組織およびその構成要素のバイオメカニクス2)

A numerical investigation of porous titanium as orthopedic implant material

Porous titanium is being developed as an alternative orthopedic implant material to alleviate the inherent problems of bulk metallic implants by reducing the stiffness to be comparable to bone stiffness and allowing complete bone ingrowth. However, a porous microstructure is susceptible to local permanent plastic strain and residual stress under cyclic loading which reduces damage tolerance and therefore limits their application as orthopedic implants. The mechanical properties of porous titanium are governed by the microstructural configurations such as pore morphology, porosity, and bone ingrowth. To understand the influence of these features on performance, the macroscopic and microscopic responses of porous Ti are studied using three-dimensional finite element models. The models are generated based on simulated microstructures of experimental materials at porosities of 15%, 32% and 50%. The results show the effect of porosity and bone ingrowth on Young’s modulus, yield stress, and microscopic stress and strain distribution. Importantly, simulations predict that the bone ingrowth reduces the stress and strain localization under cyclic loading so significantly that it counteracts the concentration condition caused by the increased porosity of the structure.

Measurement of Cortical Bone Strain Distribution by Image Correlation Techniques and from Fracture Toughness

Bone fracture toughness has been well studied, however, it is also important to investigate the effect of preservative treatment on the mechanical properties of bones. It is necessary to evaluate crack initiation and propagation after fracture because this process may be different in the case of injured bone tissues. In this study, we attempted to analyze the strain distribution on bone tissue surface by using image correlation techniques in order to elucidate the relationship between microscopic bone damage and strain distribution. Bovine femoral cortical bone was employed as the bone specimen and the three-point bend test method was used to determine the fracture toughness, in accordance with the ASTM E399 guidelines. An Instron type machine was used in the fracture toughness test and the loading rate was set to 1 mm/min. Black and white spray paint was applied in a random pattern to the surface of the specimens, and the specimens were loaded until they were ruptured. Bone surface strain analysis was performed using image correlation techniques and the changes were recorded in a digital image. In order to evaluate the effects of preservative treatment on the mechanical properties of bone, we categorized the specimens into 4 groups: the control group included the specimens that were submitted for testing immediately after machining and the preservation group comprised specimens that were analyzed after preservative treatment with different method (formalin, ethanol and physiological saline solution). A strain analysis performed using image correlation techniques allowed the visualization of the increased strain at the forward end of the slit of the specimens. The strain value at the forward end of the slit (the longitudinal direction of specimens) measured at the time of rupture in the control group was approximately 4 times larger than that in the formalin preservation group, thereby suggesting the embrittlement of bone organic constituents due to preservative treatment. [doi:10.2320/matertrans.M2010426]

画像相関法を用いた皮質骨のひずみ分布測定と破壊じん性

Bone fracture toughness has been well studied, however, it is also important to investigate the effect of preservative treatment on the mechanical properties of bones. It is necessary to evaluate crack initiation and propagation after fracture because this process may be different in the case of injured bone tissues. In this study, we attempted to analyze the strain distribution on bone tissue surface by using image correlation techniques in order to elucidate the relationship between microscopic bone damage and strain distribution. Bovine femoral cortical bone was employed as the bone specimen and the three-point bend test method was used to determine the fracture toughness, in accordance with the ASTM E399 guidelines. An Instron type machine was used in the fracture toughness test and the loading rate was set to 1 mm/min. Black and white spray paint was applied in a random pattern to the surface of the specimens, and the specimens were loaded until they were ruptured. Bone surface strain analysis was performed using image correlation techniques and the changes were recorded in a digital image. In order to evaluate the effects of preservative treatment on the mechanical properties of bone, we categorized the specimens into 4 groups: the control group included the specimens that were submitted for testing immediately after machining and the preservation group comprised specimens that were analyzed after preservative treatment with different method (formalin, ethanol and physiological saline solution). A strain analysis performed using image correlation techniques allowed the visualization of the increased strain at the forward end of the slit of the specimens. The strain value at the forward end of the slit (the longitudinal direction of specimens) measured at the time of rupture in the control group was approximately 4 times larger than that in the formalin preservation group, thereby suggesting the embrittlement of bone organic constituents due to preservative treatment.

Spatially resolved x-ray diffraction study of GaSb layers grown laterally on SiO2-masked GaAs substrates

In this work spatially resolved x-ray diffraction (SRXRD) is used to analyze strain in GaSb layers grown by epitaxial lateral overgrowth (ELO) on SiO2-masked (001) GaAs substrates. We show that this heteroepitaxial structure contains local mosaicity in the wing area that cannot be detected by selective etching. While the standard x-ray diffraction measurements only suggest the presence of grain structure of the ELO layer, SRXRD allows examining the microscopic strain distribution in the sample. In particular, size of microblocks and their relative misorientation are determined.

Digital image correlation studies for microscopic strain distribution and damage in dual phase steels

We have measured the microscopic strain distribution of a dual phase steel at the grain scale, using digital image correlation based on scanning electron microscopy topography images at large strains. The results show how strain is partitioned between the ferritic and martensitic regions. We find that tempering changes the microscopic strain distribution considerably and that this correlates directly with the tensile properties, including the rate of damage accumulation and the consequent ductility of the material.

Multiscale modeling of materials by a multifield approach: Microscopic stress and strain distribution in fiber–matrix composites

A recently developed multiscale, multifield model is used to study the elastic response of a fiber-reinforced polymer composite material under different loading conditions. The multifield model is based on the theory of microstructured continua, and allows the introduction of microstructural variables (in this case the local microfiber orientation) within a standard continuum model. The numerical solution is implemented in a finite element approach. By simulated loading tests on a model system, we show that the multifield model goes well beyond the conventional anisotropic Cauchy solution, and can effectively incorporate the dependence of the elastic response on (i) an internal length scale, representing the actual fiber length, and (ii) the local fiber orientation.

Theoretical analysis of microscopic strain distribution and phase stability of Zn chalcogenide alloys using valence force field model

Microscopic strain distribution in II–VI–O alloy systems is theoretically analyzed using the valence force field model. ZnSeO and ZnSO alloys have a maximum strain energy at O composition of 50% due to a large lattice mismatch between constituting materials. Zn–Se bond length decreases with increasing O composition and Zn–O bond increases with decreasing O composition. Se atoms rather than O are easier to move in order to reduce strain energy because of the small elastic constant of ZnSe compared with ZnO. The lattice deformation occurs mainly at tetrahedra containing O–Zn–Se bonds with Zn atom in the center.

Effects of fiber distribution on elastic–viscoplastic behavior of long fiber-reinforced laminates

In this paper, effects of transverse fiber distribution on the elastic–viscoplastic behavior of long fiber-reinforced laminates subjected to in-plane tensile loading are studied using a homogenization theory. To this end, a unit cell with random fiber distribution is arranged point-symmetrically with respect to cell facet centers and also Y-periodically. By discussing these two fiber arrangements in terms of standard deviations and a radial distribution function, it is demonstrated that the point-symmetric cell arrangement can enhance the randomness of fiber distribution in comparison with the Y-periodic arrangement. Then, on the assumption that the random fiber distribution generated by the point-symmetric cell arrangement prevails on the transverse section in each lamina, the in-plane elastic–viscoplastic deformation of carbon fiber/epoxy laminates is analyzed using a homogenization theory of nonlinear time-dependent composites. The analysis based on the perfectly periodic hexagonal fiber distribution in laminae is additionally performed for comparison. It is thus shown that the transverse randomness of fiber distribution in laminae has negligible influence on the macroscopic elastic–viscoplastic behavior of laminates, though it markedly affects the microscopic distribution of stress and strain. It is also shown that the analysis predicts very well the macroscopic behavior observed in the corresponding experiments.

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.

524 位相シフトモアレ干渉法による電子パッケージの熱ひずみ計測

Phase shifting moire interferometry was developed by using wedged glass plate. This technique was employed to measurement of thermal deformation of electronic package, Stacked-MCP (Multi Chip Package). A thermal loading was applied by heating the devices from room temperature 25℃ to an elevated temperature 100℃. The experimental results showed that large shearing and bending deformations were yielded. The microscopic strain distributions around the chips and resin were quantitatively determined.

Local Strain Measurements in Hexagonal Systems

Abstract It is challenging to access the microscopic distribution of strain in subsurface systems with a lateral resolution better than 1 nm and an accuracy of about 10-3 because such measurements require the detection of displacements by 1 pm at near atomic resolution. Nevertheless, such measurements are commonly desirable, in particular, for the investigations of thin heteroepitaxial films. A particular method developed in the past extracted geometrical information from unit cells in lattice images to perform this task in thin layers of cubic quantum well structures. Strain relaxation in thin TEM samples may falsify such measurements and needs to be controlled. It is the purpose of this paper to describe a quantitative method to measure strain with the required accuracy and resolution in the more complex hexagonal systems. A AxGa1-xN/GaN heterostructure grown on a sapphire substrate was investigated. Local strain comes from compositional variations which alter the size of the unit cells that are shown in Figure 1.

Direct Evaluation of Strain and Strain Distribution Using Grid Method during Shear Deformation of Metal Matrix Composites.

A grid method is applied to measure the specimen's strain during dynamic deformation in the split-Hopkinson torsional bar(SHTB) experiments. A streak camera is used to record the motion of an inclined grid pattern(5 lines/mm)previously formed on the outer surface of the specimen. The average shear strain of the metal matrix composites(MMC) is successfully obtained in a large strain range by analyzing frequency of the streak image. The nominal shear strain evaluated by the conventional SHTB method agrees well with the directly measured strain for these materials. Microscopic strain distribution in MMC is also measured by observing a diffraction grating(600 lines/mm)on the specimen's surface in quasi-static testings. Localization of the shear strain becomes strong with increasing volume fraction of the reinforcement, and would reduce ductility of the composite materials.

Raman microprobe analysis of strained polysilicon deposited layers

Microscopic strain distributions in varying thicknesses of polysilicon layers deposited as bridges over silicon substrates were determined by high resolution micro-Raman spectroscopy. In particular, we mapped the dependence of the first order Raman spectrum as a function of the position across polysilicon bridges (approximately 550 × 230 μm2), over tunnels etched in the silicon substrate. Shifts in Raman band frequencies as a function of position on the bridge structures were observed to be dependent upon the thickness of the membrane layer (between 1 and 3 μm) as well as the annealing conditions. Assuming a simplified uni-axial stress parallel to the surface, the effective tensile stress at the center of the bridge of thickness 2.5 μm is reduced by annealing from 2.5 GPa to 0.18 GPa.