Non-uniform Strain Distribution Research Articles

Microstructural Characterization of Ti-6Al-4V Metal Chips by Focused Ion Beam and Transmission Electron Microscopy

During machining, the cutting surface of a metal is subjected to high strain rates and temperatures. Due to the small mass of the formed chip, the metal is rapidly quenched, preserving the as-machined microstructure. These extreme conditions are reported to be favorable to form nanograin or ultrafine-grain microstructures. However, detailed investigation of this region is problematic due to the size of the chips and the difficulty in preserving the cutting surface microstructure during traditional transmission electron microscopy (TEM) preparation. This study investigates the use of focused ion beam (FIB) specimen preparation to preserve and TEM to image the microstructure of the secondary deformation zone (SDZ) at the cutting surface in chips of Ti-6Al-4V formed during machining. Use of the FIB allowed precise extraction of a side or transverse view specimen, which preserved the cutting surface to reveal an inhomogeneous microstructure resulting from the nonuniform distribution of strain, strain rate, and temperature. Initial imaging of a conventional TEM foil prepared from the plan view of the cutting surface revealed microstructures ranging from heavily textured to regions of fine grains. Using FIB preparation of a transverse foil, a layered microstructure was observed revealing a variation of fine grains near the cutting surface, which transitioned to coarse grains toward the free surface. At the cutting surface, a 10-nm-thick recrystallized layer was observed capping a 20-nm-thick amorphous layer.

Non-uniform distribution of strain during stretch of relaxed skeletal muscle fibers from rat soleus muscle.

Tension and regional average sarcomere length (L(s)) behavior were examined during repeated stretches of single, permeabilized, relaxed muscle fibers isolated from the soleus muscles of rats. We tested the hypothesis that during stretches of single permeabilized fibers, the global fiber strain is distributed non-uniformly along the length of a relaxed fiber in a repeatable pattern. Each fiber was subjected to eight constant-velocity stretch and release cycles with a strain of 32% and strain rate of 54% s(-1). Stretch-release cycles were separated by a 4.5 min interval. Throughout each stretch-release cycle, sarcomere lengths were measured using a laser diffraction technique in which 20 contiguous sectors along the entire length of a fiber segment were scanned within 2 ms. The results revealed that: (1) the imposed length change was not distributed uniformly along the fiber, (2) the first stretch-release cycle differed from subsequent cycles in passive tension and in the distribution of global fiber strain, and (3) a characteristic "signature" for the L(s) response emerged after cycle 3. The findings support the conclusions that longitudinal heterogeneity exists in the passive stiffness of individual muscle fibers and that preconditioning of fibers with stretch-release cycles produces a stable pattern of sarcomere strains.

Strain-induced magnetization change in patterned ferromagnetic nickel nanostructures

We report strain-induced coercive field changes in patterned 300 × 100 × 35 nm3 Ni nanostructures deposited on Si/SiO2 substrate using the magnetoelastic effect. The coercive field values change as a function of the applied anisotropy strain (∼1000 ppm) between 390 and 500 Oe, demonstrating that it is possible to gradually change the coercive field elastically. While the measured changes in coercive field cannot be accurately predicted with simple analytical predictions, fairly good agreement is obtained by using a micromagnetic simulation taking into account the influence of nonuniform strain distribution in the Ni nanostructures. The micromagnetic simulation includes a position dependant strain-induced magnetic anisotropy term that is computed from a finite element mechanical analysis. Therefore, this study experimentally corroborates the requirement to incorporate mechanical analysis into micromagnetic simulation for accurately predicting magnetoelastic effects in patterned ferromagnetic nanostructures.

A micromechanical analysis of elastoplastic behavior of porous materials

In this paper, we present a micromechanical analysis of elastoplastic behavior of porous materials. The non-uniform transformation field analysis (NTFA) is used and the non-uniform distribution of local plastic strain in the solid matrix is taken into account. Comparisons with the classical Gurson's model and standard FEM solution are presented.

Indentation behavior of functionally graded Al–SiC metal matrix composites with random particle dispersion

This study addresses the effects of number of layers, compositional gradient exponent (material composition) and random particle dispersion on the indentation behavior of a functionally graded metal matrix composite. The ceramic particles in a certain volume fraction were randomly distributed within each layer depending on the compositional gradient exponent in order to have a similar structure to an actual microstructure as possible. Increasing the number of layers caused an evident increase in indentation depths for all compositional gradient exponents. The compositional gradient exponent had an important effect on the indentation depth. The random particle dispersion also played an important role on the central indentation depth ( n < 3) as well as on the deformed surface profiles for both high layer numbers ( N = 75 and 150 layers) and the material compositions approaching to a metal-rich structure resulted in some fluctuations in the deformed surface profiles. Increasing the number of layers at a certain compositional gradient exponent resulted in larger mean residual stresses and plastic deformations. Increasing the compositional gradient exponent at a certain layer number decreased mean residual stresses and strains since the ceramic volume fraction is increased. The random particle dispersion also resulted in non-uniform residual stress and strain levels and distributions.

Study on the spectral response of fiber Bragg grating sensor under non-uniform strain distribution in structural health monitoring

Many theoretical studies have been developed to study the spectral response of a fiber Bragg grating (FBG) under nonuniform strain distribution along the length of FBG in recent years. However, almost no experiments were designed to obtain the evolution of the spectrum when a FBG is subjected to non-uniform strain. In this paper, the spectral responses of a FBG under non-uniform strain distributions are given and a numerical simulation based on the Runge-Kutta method is introduced to investigate the responses of the FBG under some typical non-uniform transverse strain fields, including both linear strain gradient and quadratic strain field. Experiment is carried out by using loads applied at different locations near the FBG. Good agreements between experimental results and numerical simulations are obtained.

A New Axial Upsetting Process for Large Ingots with Large Ratio of Height to Diameter

To remove casting porosity and obtain smaller crystal grains, many large forgings need ingots to be upset axially with large ratio of height to diameter (H/D) greater than 3. But the ingots with large H/D are prone to buckling during upsetting process, and have non-uniform internal stress and strain distribution, cracks at barreling and other defects. A new axial upsetting process was proposed to handle these problems. Firstly, the research described deformation inhomogeneity and cracking tendency, and analyzed the causes of defects in the flat anvil upsetting process. Secondly, three two-stage upsetting processes were tried to improve the uneven deformation in the flat anvil upsetting, which applied symmetrical spherical convex die, conical convex die and multi-line sweeping concave die respectively in the first stage, and used flat anvils in the second stage. The effect of the die surfaces on constraining those defects was analyzed. Finally, three three-stage upsetting processes were suggested to take advantages of different die surfaces to stabilize the process. It was observed that the upsetting had better result from using conical convex die and multi-line sweeping concave die in the first stage, conical convex die and flat anvil in the second stage, two flat anvils in the third stage. The new axial upsetting process could improve the quality of the large forgings with more uniform deformation and less barreling.

Formation and growth of tin whiskers on aluminum–tin alloys

In order to clarify the mechanism of formation and growth of nodules and whiskers on the leads used in aluminum electrolytic capacitors, aluminum–tin binary alloys were subjected to the investigation as the model alloys for the joints in the leads. The concentration of tin in the binary alloys was 1, 5 or 10 at%. The alloy of 10 at% tin showed the largest number of nodules or whiskers on its polished surface after keeping under ambient conditions for 7.8 Ms. Many whiskers whose length were more than several tens of micrometers were observed in the case of the alloy of 5 at% tin. The alloy of 1 at% tin showed few nodules or whiskers. Growth of nodules and whiskers is caused by difusion of tin atoms from the strained or unstable areas into the stable ones or the root grains. Then, the extrusion toward the surface at the root grains develops nodules and whiskers. As a prevention measure of whiskers, selective etching of the aluminum phase using a solution of sodium hydroxide was confirmed to be successful. Thus the aluminum phase was thought to form a non-uniform distribution of strain in the tin phase. This acts as the driving force in difusion of tin atoms.

Equivalent strain, microstructure and hardness of H62 brass deformed by constrained groove pressing

Constrained groove pressing (CGP) has been developed to refine grain sizes, and in most cases is conducted under partially constrained conditions. Here we report the first investigation of the Von Mises equivalent strain and its distribution in samples subject to CGP under partially constrained conditions. Using finite element modeling, we show that the value of the equivalent strain and its distribution depend strongly on the constraint condition of CGP. Experiments using an annealed H62 brass confirm the simulation and reveal that the non-uniform strain distribution results in the corresponding non-uniform profile of the grain size and hardness. These findings are of great importance since many CGP are conducted under partially constrained conditions which generate lower equivalent strains than the counterpart under fully constrained conditions.

Simulation of Multi-Pass ECAP by 3D Finite Element Method

Multi-pass ECAP process of pure Al for square samples (Φ＝90º, Ψ＝37º, pressing speed of 1mm/s), was simulated by using 3D finite element method (FEM).The distribution of equivalent strain for two and four passes was compared. The results showed that route A leads to non-uniform distribution of equivalent strain during multi-pass ECAP. The distribution of equivalent strain is uniform in BC route, but the value of equivalent strain is larger in C route. The simulation results were compared with the experimental ones with previous work in the literature. The simulation also shows that equivalent strain and load increase with pass increasing.

Study on forming defects in the rolling process of large aluminum alloy ring via adaptive controlled simulation

According to the distribution characteristics of equivalent plastic strain (PEEQ) in radial–axial ring rolling, the plastic deformation zones in cross section were established. A 3D rigid-viscoplastic finite element model (FEM) which was controlled adaptively was applied to investigate defects that occurred during ring rolling under ABAQUS software. PEEQ, stress, and temperature distributions in different deformation zones have been analyzed in this study. Strain peaks were found in the cross-section corners. Moreover, it was investigated that non-uniform strain, stress, and temperature distributions in the ring tend to cause non-uniform microstructure and properties. Therefore, forming defects and microstructure damage would appear in cross-section corners due to the high-strain deformation. Based on the new developed FEM of the radial–axial ring-rolling process and comprehensive numerical simulations, the size effects of feed rate and lubrication conditions on strain and temperature distributions and their uniformity were investigated by 3D coupled thermomechanical FE simulation. The results have good agreement with experiment. The achievements of this study can provide basis for quality control and technical guidance.

Non-Uniform Deformation Characteristic of in 690 Superalloy Tube in Glass Lubricated Hot Extrusion

A two-dimensional axi-symmetric finite element model for the tube hot extrusion process was developed based on Deform-2D software by consideration of the billet transfer, glass lubrication and the constitutive characteristics of IN 690 superalloy. An enhanced technique for adaptive mesh refinement (AR) is used to solve the large deformation problem. This model was then used to study the effect of boundary conditions and process parameters in tube hot extrusion. The Non-uniform deformation index as the representative parameter, which denotes the non-uniform deformation during the steady state of tube hot extrusion, is presented accordance to the feature of metal flow at deformation zone. The bigger of Non-uniform deformation index, the worse of non-uniform strain distribution. When the non-uniform deformation index getting smaller, the equivalent strain distribution along the length and cross section become more uniform and better product quality could be obtained. An increase in the billet and die preheating temperature could reduce the non-uniform deformation index individually. But the billet and die preheating temperature should not be too high. The increase of friction coefficient, the non-uniform deformation index also increased, which indicate appreciable results of metal flow. With the ram speed increase, the non-uniform deformation index decreases, but too fast speed is inadmissibility.

A weighted osteon morphotype score outperforms regional osteon percent prevalence calculations for interpreting cortical bone adaptation

Using circularly polarized light microscopy,we described a weighted-scoring method for quantifying regional distributions of six secondary osteon morphotypes(Skedros et al.: Bone 44 (2009) 392-403). This osteon morphotype score (MTS) strongly correlated with "tension" and "compression" cortices produced by habitual bending. In the present study, we hypothesized that the osteon MTS is superior to a relatively simpler method based on the percent prevalence (PP) of these osteon morphotypes. This was tested in proximal femoral diaphyses of adult chimpanzees and habitually bent bones: calcanei from sheep, deer, and horses, radii from sheep and horses, and third metacarpals (MC3s) from horses. Sheep tibiae were examined because their comparatively greater torsion/shear would not require regional variations in osteon morphotypes. Predominant collagen fiber orientation (CFO), a predictor of regionally prevalent/predominant strain mode, was quantified as image gray levels (birefringence). Ten PP calculations were conducted. Although PP calculations were similar to the osteon MTS in corroborating CFO differences between "tension" and "compression" cortices of the chimpanzee femora and most of the habitually bent bones, PP calculations failed to show a compression/tension difference in equine MC3s and sheep radii. With the exception of the prevalence of the "distributed" osteon morphotype, correlations of PP calculations with CFO were weak and/or negative. By contrast, the osteon MTS consistently showed positive correlations with predominant CFO. Compared with the osteon MTS and predominant CFO, regional variations in PP of osteon morpho types are not stronger predictors of nonuniform strain distributions produced by bending.

Deformation induced martensite in AISI 316 stainless steel

The forming process leads to a considerable differentiation of the strain field within the billet, and finally causes the non-uniform distribution of the total strain, microstrusture and properties of the material over the product cross-section. This paper focus on the influence of stress states on the deformation-induced a’ martensitic transformation in AISI Type 316 austenitic stainless steel. The formation of deformation-induced martensite is related to the austenite (g) instability at temperatures close or below room temperature. The structural transformation susceptibility is correlated to the stacking fault energy (SFE), which is a function not only of the chemical composition, but also of the testing temperature. Austenitic stainless steels possess high plasticity and can be easily cold formed. However, during cold processing the hardening phenomena always occurs. Nevertheless, the deformation-induced martensite transformation may enhance the rate of work-hardening and it may or may not be in favour of further material processing. Due to their high corrosion resistance and versatile mechanical properties the austenitic stainless steels are used in pressing of heat exchanger plates. However, this corrosion resistance is influenced by the amount of martensite formed during processing. In order to establish the links between total plastic strain, and martensitic transformation, the experimental tests were followed by numerical simulation.

Stochastic laminate analogy for simulating the variability in modulus of discontinuous composite materials

Abstract Recent composite technology research and development efforts have focused on discontinuous carbon fiber/epoxy molding systems derived from chopped aerospace-grade unidirectional tape prepreg. Although the average elastic modulus of this material has been shown to be as high as that of the continuous tape quasi-isotropic benchmark, experimental measurement by means of strain gage or extensometer has shown variation as high as 20%. Digital Image Correlation can be used successfully to obtain a full-field strain measurement, and it shows that a highly non-uniform strain distribution exists on the surface of the specimen, with distinct peaks and valleys. This pattern of alternating regions of high and low strain gradients, and which exhibit a characteristic shape and size, can be described in terms of Random Representative Volume Element (RRVE). The RRVE proposed here exhibits random elastic properties, which are assigned based on stochastic distributions. This approach leads to the analysis method proposed here, which is designed to compensate for the fact that traditional methods cannot capture the experimentally observed variation in modulus within a specimen and among different specimens. The method utilizes a randomization process to generate statistical distributions of fractions and orientations of chips within the RRVE, and then applies Classical Laminated Plate Theory to an equivalent quasi-isotropic tape laminate to calculate its average elastic properties. Validation of this method is shown as it applies to a finite element model that discretizes the structure in multiple RRVEs, whose properties are generated independently of the neighboring ones, and then are solved simultaneously. The approach generates accurate predictions of the strain distribution on the surface of the specimen.

Investigation on packages of fiber Bragg grating for use as embeddable strain sensor in concrete structure

The paper covers detailed investigation on encapsulation and packaging of fiber Bragg grating (FBG) for strain sensing of concrete structures in embeddable form. Non-uniform strain distribution due to imperfect curing of the epoxy and its effect on the FBG spectrum has been studied experimentally and correlated with theoretical simulation. For a specific package, an optimal curing condition has been found and shown to have good repeatability. The successfully packaged sensor has been embedded in a concrete structure and the response has been found to be linear. Response of the sensor under static loading condition is compared with surface mountable electrical resistance strain gauge (ERSG) and embeddable type EFPI (extrinsic Fabry Perot interferometer) fiber optic sensor. The sensor has also been tested under dynamic loading of the structure.

Polycrystalline behavior analysis of pure magnesium by the homogenization method

In this study, mechanical behaviors of pure magnesium polycrystals are numerically investigated. The homogenization method, which combines the crystal and macroscopic scales, is introduced to include the effect of crystalline scale behaviors. The polycrystal plasticity model modified for pure magnesium, in which twinning is considered as asymmetric slip-like deformation, is utilized as a constitutive equation. Within this framework, numerical convergence analyses are conducted, and a representative volume element to present realistic deformation of pure magnesium is investigated. Second, polycrystalline behaviors of pure magnesium are investigated. The present approach is shown to reproduce the typical phenomena induced by crystalline scale structure in pure magnesium: nonuniform strain distribution, asymmetric crystal lattice orientation, strength differential effect, and strongly anisotropic initial and subsequent yield surfaces.

The Response of Embedded NIR (830 nm) Fiber Bragg Grating Sensors in Glass Fiber Composites under Fatigue Loading

The fabrication and use of fiber Bragg grating (FBG) sensors, which operates in near infrared region (Bragg wavelength λB = 830 nm) to monitor the damage accumulation in composite is reported. The spectra ∼830 nm of the embedded FBG sensor in 0°/90° woven cloth/vinyl ester composite were distorted and broadened due to fatigue loading, as expected. These distortions in FBG spectra indicate asymmetric and nonuniform strain distributions along the grating length of the FBG sensors due to the accumulation of damage during fatigue loading regimes. This information is useful for formulating a fundamental relationship between FBG spectral changes and the damage accumulation of composite structures. The results demonstrate that the sensitivity and durability of the embedded FBG sensors fabricated by conventional writing techniques at 830 nm range and monitored using inexpensive Si-based source and arrays were excellent for health monitoring of composite structures.

Barely visible impact damage detection for composite sandwich structures byoptical-fiber-based distributed strain measurement

The authors developed an impact damage-detection system for large-scale compositesandwich structures using an optical fiber network running throughout the structure. ABrillouin-based sensing system with high spatial resolution (pre-pump pulse Brillouinoptical time-domain analysis (PPP-BOTDA)) was utilized for distributed strainmeasurement. The PPP-BOTDA sensing system can measure axial strain along theoptical fiber by employing stimulated Brillouin scattering. The system realizes aspatial resolution of 10 cm, a sampling interval of 5 cm, and a sensing range ofmore than 1 km. Our previous study revealed that a non-uniform axial strainwithin centimeter spatial resolution broadens the width of the Brillouin gainspectrum, which is the output of the PPP-BOTDA. The specific response of thePPP-BOTDA was employed to detect non-uniform strain distribution along a residualfacesheet dent in a damaged area. First, the response of the optical fiber sensornetwork, formed in the adhesive layer, was simulated to clarify the effectivenessand limitations of the proposed damage-detection technique. The system wasthen validated by an experiment. As the damage became larger, the width of theBrillouin gain spectra became broader. Consequently, the location and size ofbarely visible damage could be estimated. The system developed is quite usefulfor a first inspection of large-scale sandwich structures in aerospace and marineapplications.

Assessment of cure-residual strains through the thickness of carbon–epoxy laminates using FBGs Part II: Technological specimen

This paper is a continuation of our previous study [Mulle M, Collombet F, Olivier P, Grunevald Y-H. Assessment of cure residual strains through the thickness of carbon–epoxy laminates using FBGs, part I: elementary specimen. Compos Part A 2008. doi:10.1016/j.compositesa. 2008.10.008] pertaining to the assessment of autoclave cure-induced strains through the thickness of carbon–epoxy laminates. In this first part, postulates and measurement procedures were established for cure of elementary specimens. Based on these, this study undertakes investigation on what are called technological specimens. These specimens are of the beam type and contain geometrical specificities which represent typical structural issues. In-plane process-induced strains were studied through the thickness of a thick reinforced zone using several optical fibre Bragg gratings (FBGs) sensors embedded at different levels of the ply stack. A non-uniform distribution of residual strains was detected. Once cured, the technological specimen was subjected to a heating test whose cycle was comparable to the cure cycle. Thermally induced strains were measured with the embedded FBGs. The values recorded were compared with those of cure-induced residual strains and FEM simulation. Discrepancies were observed that strongly suggest the possible influence of environmental effects and the need for the calculation to take into account the through-the-thickness variability of thermal properties.