Residual Strain Gradient Research Articles

Residual elastic strain and survivability of stabilized zirconia coated carbon-carbon (C/C) composite

Carbon-carbon (C/C) composites require protective coatings for prolonged use in elevated temperature, oxidizing environments. Ceramic coatings can provide oxidation protection; however, thermal expansion mismatch in conjunction with thermal events and interfacial constraint during coating deposition can result in residual stress, which can affect the lifetime and performance of the system. This work leveraged high energy synchrotron X-ray diffraction to determine the depth resolved residual elastic strain in two rare-earth oxide stabilized zirconia (12 mol% yttria and 6 mol% samaria) coatings, applied to a carbon-carbon composite substrate. The experimental characterization of the as-deposited coatings indicated a tension to compression residual elastic strain gradient, which was consistent with an energy-based model that illustrated the crystal structure dependence of the residual stress state. Via an oxyacetylene torch exposure, the ablation behavior and crack propagation were correlated to the measured residual elastic strain state and highlighted the influence of processing and exposure induced residual stress on coating performance. These experimental residual elastic strain measurements and relation to failure mechanisms support the survivability of these coating systems in applications that require thermal protection systems (TPS).

Interaction integral method for crack-tip intensity factor evaluations of magneto-electro-elastic materials with residual strain

Magneto-electro-elastic (MEE) materials generally consist of piezoelectric and piezomagnetic constituent phases so that the residual strain often occurs during the manufacturing process. The distributed residual strain and complex interfaces between constituents cause a great challenge to the fracture analysis of MEE materials. Considering the effect of the residual strain, this paper develops an interaction integral (I-integral) method for the extraction of the fracture parameters of an impermeable crack in nonhomogeneous MEE materials. The I-integral method has several merits: 1) it can decouple stress intensity factors (SIFs), electric displacement intensity factor (EDIF) and magnetic induction intensity factor (MIIF); 2) the I-integral is independent of the size of the integration domain, even when the integration domain contains nonhomogeneous and discontinuous material properties. Combined with the extended finite element method (XFEM), the I-integral is adopted to investigate several crack problems subjected to homogeneous, nonhomogeneous and discontinuous residual strains. The I-integral values calculated by different integration domains agree well with each other (relative deviation < 1%) for nonhomogeneous and discontinuous MEE properties. Then, single-crack and multi-crack problems are studied to show the influences of residual strain distributions on the intensity factors. Homogeneous residual strain affects the SIFs dramatically but has a slight influence on the EDIF and MIIF. By comparison, nonhomogeneous residual strains affect the SIFs, EDIF and MIIF significantly. In addition, the residual strain gradients affect the variations of intensity factors with crack location extremely.

Dark-field X-ray microscopy reveals mosaicity and strain gradients across sub-surface TiC and TiN particles in steel matrix composites

Residual strain gradients and crystallographic mosaicity across embedded ceramic particles within metal-matrix composites have remained experimentally inaccessible. In this work, we use synchrotron dark-field X-ray microscopy to characterize strain and orientation gradients across ~20 µm large TiC and TiN particles embedded in a steel matrix annealed at 480 and 600 °C. The results document gradual crystallographic orientation changes across the particles and the presence of sub-grains, in contrast to electron backscatter diffraction data. These gradients appear, however, not directly correlated with the observed strain gradients, which are attributed mainly to the different strain states within particles’ interiors and envelopes.

Mechanically Guided Assembly of Monolithic Three-Dimensional Structures from Elastomer Composites.

Mechanically guided assembly is considered a facile and scalable methodology for fabrication of three-dimensional (3D) structures. However, most of the previous methods require multistep processes for bonding bi- or multilayers and only result in non-freestanding 3D structures because of usage of a supporting elastomer substrate. Herein, we report a functional elastomer composite that can be transformed to a freestanding and monolithic 3D structure driven by the mechanically guided assembly. Photolithography can be used to selectively tune the mechanical properties of UV-exposed regions which exhibit enhanced ductility compared with the nonexposed regions. Thus, a gradient of the residual strain in the thickness direction makes the films assemble into 3D structures. These 3D structures are also predicted by our computational models using finite element simulations, which yields a reasonable agreement with the experiments. The systematically designed 2D structures with varied patterns can be transformed to various 3D structures with the control of the residual strain gradient, via key processing parameters including pre-strain, film thickness, and UV exposure time. By integrating different active electronic components on the fabricated 3D structures, potential applications of this 3D platform in electronics were demonstrated. This study offers a unique capability in constructing monolithic and freestanding 3D assembly, paving new routes to many applications such as wearable electronics, smart textiles, soft robotics, and structural health monitoring.

Characterization of the Microstructure, Local Macro-Texture and Residual Stress Field of Commercially Pure Titanium Grade 2 Prepared by CONFORM ECAP

The paper investigated the residual strain and stress distribution, microstructure, and macro-texture along the transverse direction of commercially pure titanium grade 2 samples prepared by the CONFORM ECAP technique. This method belongs to the severe plastic deformation methods; hence, it could be assumed that residual stress fields would be present in the work-pieces. Residual stresses cannot be directly measured; thus, neutron diffraction measurements, Electron back-scatter diffraction (EBSD) investigations, and local X-ray macro-texture measurements were performed in different regions of the sample to determine the data for the residual stress calculation. The calculation was based on the modified Kröner model. Neutron diffraction strain scans and residual stress calculations revealed that symmetrical residual strain and stress gradients with compression character were present in the axial and hoop direction after one and two passes. Asymmetric distribution of the residual strains and stresses remained after the third pass of the CONFORM ECAP. EBSD investigations showed that after the first pass, significant grain refinement occurred; however, further passes did not cause any dramatic grain refinement. X-ray texture measurements revealed that local macro-texture was dependent on the number of passes of the CONFORM ECAP and on the investigated area in the samples.

Precise Measurement of Steep Residual Strain Gradients Using Neutron Diffraction in Strongly Absorbing Materials with Chemical Compositional Gradients

Abstract A round robin benchmark weldment, denoted TG6, from the European Network on Neutron Techniques Standardization for Structural Integrity (NeT), offers the ability to test the technique of residual stress determination using neutron diffraction to an extreme. This test component comprises a 200 mm by 150 mm by 12 mm rectangular base plate made from Inconel 600 with three passes of Alloy 82 weld metal deposited in a slot of length 76 mm. This not only has large grain issues in the weld region but a large interplanar spacing variation caused by high strain gradients and a change in material composition. Because of the high absorption of neutrons in the Inconel 600 within the gauge volume, there is a large difference between the instrumental gauge volume IGV (which is the volume of space defined by the neutron beam paths through the defining apertures, taking into account properties of the beam) compared with the sampled gauge volume SGV (which is the intersection of the IGV with the sample that takes into account the absorption of the neutrons). The relative shift in position of the center of gravity of measurement (when the gauge volume is fully immersed in the sample) has been observed to be significant, for example, ∼0.3 mm, using 1 by 1 by 5 mm3 defining optics (where 5 mm is the gauge volume height) and increases approximately proportionally with larger gauge volumes dimensions in the horizontal plane. The magnitude of this shift depends upon many parameters. Measuring the sample and rotating 180° and measuring again, taking the average is another way one can eliminate this absorption effect. This novel approach is compared with three neutrons instruments on the same sample.

Evaluation of the physical properties of dental resin composites using optical fiber sensing technology

ObjectivesThe characterization of the physical properties of dental resin composites is fraught with difficulties relating to significant intra and inter test parameter variabilities and is relatively time consuming and expensive. The main aim of this study was to evaluate whether optical fiber Bragg grating (FBG) sensing system may become a viable tool to study dental material characteristics. Of particular focus was the potential for the system to demonstrate a multi parameter all-in-one feature. MethodsA miniature FBG was embedded in six different dental resin composites and employed as a sensor to evaluate linear polymerization shrinkage, thermal expansion and water sorption. Six commercially available dental composites with different filler types and volume are evaluated. The tests are repeated with three sets of samples. The curing characteristics and residual strain gradient exhibited by the cured dental composites were also observed and commented. ResultsAmong the studied samples, SDR shows lowest polymerization shrinkage, while Beautifil FO3 shows the highest. The results also show clear distinction between particle filler type and fiber reinforcement based composites in their polymerization shrinkage properties. The agreement of the results with existing literatures show that FBG based system provides accurate results. Polymerization shrinkage rate of the samples are also obtained. Thermal expansion of the composites are measured using the FBG sensing method for the first time and is correlated with resin type, volume, filler type and glass transition temperature. The water sorption characteristics of the dental composite are also successfully measured using the FBG sensing method. The high level of repeatability and the low standard deviations shown in the results indicate good reliability with the use of FBG sensors. SignificanceThis study demonstrates how optical fiber technology can provide simple and reliable methods of measuring the critical physical properties of dental composites. In addition due to the embedding and preservation of the sensor within the samples multiple parameters can be tested for with the same sample. These features are expected to greatly assist material science researchers in dentistry as well as other biomedical fields. Of some interest the phenomenon of stress relaxation of dental composite at higher temperature was observed.

Cross-sectional X-ray nano-diffraction and -reflectivity analysis of multilayered AlTiN–TiSiN thin films: Correlation between residual strain and bi-layer period

A multi-layered AlTiN–TiSiN thin film with a bi-layer period of ∼6nm is characterized by cross-sectional synchrotron X-ray nano-diffraction and -reflectivity using an X-ray beam size of 250×350nm2. The complementary approach allows for simultaneous determining gradients of residual strains and bi-layer thickness along the film depth and demonstrates a correlation between them. The observed dependency allows for a residual strain gradient design in multilayered thin films.

Functional properties of a spark plasma sintered ultrafine-grained 316L steel

A micrometric austenitic stainless steel 316L powder was densified by spark plasma sintering. The process parameters were varied over wide ranges and the impact of such variations on sintered materials was studied through the characterization of their microstructures, densities, hardness and corrosion resistance. For comparison with the properties of traditionally cast 316L, all these investigations were also systematically carried out on as cast samples. The sintered stainless steel produced this way was highly densified, with grains of a micrometric size and the forming process did not induce any residual strain gradients as shown by transmission electronic microscopy analysis. The investigation of the corresponding mechanical properties reveals an enhancement of hardness up to twice the value measured on one sample of as cast 316L. This result is in good agreement with the Hall–Petch formalism. Additionally, in the matter of corrosion behavior, fully dense samples display an enhanced passive state in chloride media compared to as cast material. Spark plasma sintering appears to be an interesting alternative elaboration way of ultrafine 316L stainless steel giving materials with high stress resistance, without strain gradients through the volume, and promising functional properties concerning corrosion behavior.

Silicon carbide MEMS-resonator-based oscillator

An oscillator employing a polycrystalline 3C silicon carbide (3C-SiC) folded-beam microelectromechanical resonator as a frequency-setting component with silicon discrete electronics has been designed and demonstrated. Due to the residual strain gradient in the 3C-SiC thin film, fabricated resonators exhibit a warped proof mass, thus causing vertical misalignment of the electrostatic comb-drive fingers. The folded-beam resonators, therefore, can generate three resonant modes, namely the lateral, rocking and vertical resonances, under electrostatic actuation. The lateral, rocking and vertical resonances exhibit a measured resonant frequency of 27.1 kHz, 30.3 kHz and 24.2 kHz; a phase shift of 0°, 0° and 180°; a quality factor (Q) of 13 550, 10 300 and 9480; and a small-signal motional resistance of 98 MΩ, 25 MΩ and 39 MΩ, respectively, under a 10 V dc bias and 1 mTorr pressure. The rocking resonant mode of the resonator is chosen for the prototype oscillator design due to its lower motional resistance than that of the other two modes and an adequate quality factor. With a MEMS resonator exhibiting closely spaced multiple resonances, sustaining electronics must be designed properly with an accurate small-signal loop gain and phase shift to ensure the excitation of the rocking mode as the single resonance in a closed-loop oscillator with a well-defined steady-state oscillation amplitude. Based on a proper design, the prototype oscillator outputs a desired sinusoidal waveform at 30.2 kHz with an output power of −17 dBm under 10 V dc bias and achieves a minimum phase noise of −78 dBc Hz−1 at a 12 Hz offset frequency from the carrier limited by the power developed in the resonator and noise floor from the interface electronics, which closely matches with the analytical result of −80 dBc Hz−1 defined by the signal-to-noise-floor ratio (SNfR). The oscillation frequency exhibits 16 ppm stability at room temperature under 1 mTorr pressure observed over a period of 100 h including all environment effects. The demonstrated oscillator design technique can be effectively applied to various MEMS resonators, particularly to the resonators exhibiting multiple resonant modes, for achieving a desired single-tone performance.

Residual stress characterization of polycrystalline 3C-SiC films on Si(100) deposited from methylsilane

Polycrystalline 3C-SiC thin films are deposited on 100 mm Si(100) wafers via low pressure chemical vapor deposition from the precursor methylsilane in the temperature range of 700–850 °C. Residual stress, strain, and strain gradient are characterized as functions of deposition pressure, temperature, and dichlorosilane as an additional silicon source. By optimizing the deposition parameters, the residual stress is found to decrease from 1377±10 to 196±19 MPa. The low stress film exhibits a strain of 3.4×10−4, corresponding to Young’s modulus of 455 GPa, and strain gradient of −8×10−4 μm−1. The analysis suggests that the change in stress values is due to a combination of effects, in particular, thermal mismatch, grain size effect, and chemical composition.

Local, submicron, strain gradients as the cause of Sn whisker growth

It has been shown experimentally that local in-plane residual strain gradients occur around the root of spontaneously growing Sn whiskers on the surface of Sn coatings deposited on Cu. The strain distribution has been determined with synchrotron white beam micro Laue diffraction measurements. The observed in-plane residual strain gradients in combination with recently revealed out-of-plane residual strain-depth gradients [M. Sobiech et al., Appl. Phys. Lett. 93, 011906 (2008)] provide the driving forces for whisker growth.

Effects of Annealing on Residual Stress and Strain Gradient of Doped Polycrystalline SiC Thin Films

We report the effects of annealing at 925 and 1050°C in argon ambient on the resistivity, average residual stress, and strain gradient of highly doped polycrystalline 3C-SiC films deposited at 800°C and 170 mTorr from 1,3-disilabutane, dichlorosilane, and ammonia. Residual stress shifts from -569 to 274 MPa, compressive strain gradient shifts from 4 X 10 -4 to -0.018 μm -1 , and resistivity shifts from -0.037 to 0.030 Ω cm. Characterization of the SiC films reveals that oxygen impurity diffusion from the ambient during annealing and a change in bonding of nitrogen dopant atoms are sources of the shifts in these properties.

Characterization of boron-doped micro- and nanocrystalline diamond films deposited by wafer-scale hot filament chemical vapor deposition for MEMS applications

Micro- and nanocrystalline diamond (MCD and NCD) films are deposited on 4-inch silicon substrates by a large-area multi-wafer-scale hot filament chemical vapor deposition (HFCVD) system. The films are in-situ doped by boron. The chemical and crystalline structures are studied by electron probe microanalysis (EPMA), Raman spectroscopy and X-ray diffraction (XRD). The microcrystalline films have a preferred (111) texture, while the nanocrystalline films exhibit (220) texture. Strain gauges and cantilever beam arrays are micro-fabricated by surface micro-machining techniques to characterize the residual strain and strain gradient of the diamond films. Both micro- and nanocrystalline films have small compressive strains of − 0.052% and − 0.040% respectively, with the strain gradient of about 10 − 5 μm − 1 . These values are low enough to enable the realization of many MEMS devices.

Characteristics of a commercially available silicon-on-insulator MEMS material

Design of microelectromechanical systems (MEMS) requires an understanding of the material characteristics inherent to the specific processing technologies. In this study, several design-critical characteristics of a silicon-on-insulator (SOI) MEMS fabrication technology (SOIMUMPs) have been examined and compared to a surface micromachined MEMS fabrication technology (polyMUMPs), both produced by MEMSCAP, Inc. Diagnostic structures were utilized to evaluate material characteristics including: minimum achievable feature size, deviation of feature size from nominal design dimensions, through-thickness residual strain gradient, in-plane residual strain, resistivity, surface roughness, and fracture strength. In general, most of the measured characteristics were similar for SOIMUMPs and polyMUMPs, in spite of their very different fundamental process constraints. For example, the characteristic fracture strength was 1.97 and 1.43 GPa, with associated Weibull moduli of 8.9 and 14.0, respectively. These values are similar given the very different sources of silicon: mechanically thinned single crystal silicon wafers versus low-pressure chemical vapor deposition for polycrystalline films. Fractography suggests that fracture strength for the both technologies is controlled by surface topography features: individual sidewall etching defects drive SOIMUMPs failures whereas top-surface grain boundary crevices drive polyMUMPs failures. Discussion focuses on the ramifications of the process-controlled material characteristics in SOIMUMPS and polyMUMPs to the design of MEMS components.

Mechanical Effects of Galvanic Corrosion on Structural Polysilicon

The mechanical properties of miniaturized materials depend strongly on their structure, which can be altered by wet chemistry methods common in microsystems postprocessing. In a comprehensive and systematic study, we examine the dissolution of silicon when immersed in various hydrofluoric acid (HF)-based chemistries. Specifically, the frequency of mechanical resonance fR of microcantilever beams is used as a vehicle to examine the corrosion of polycrystalline silicon (polySi). A decrease in fR that occurs as a function of immersion time in HF was measured for microcantilevers as well as comb drives in contact with a noble metal (gold). Time-dependent variation was also observed in the modulus and hardness measured during indentation testing, sometimes with pronounced difference for specimens contacted to gold. Secondary sources of influence, such as in-plane-oriented residual strain (which remained unchanged), through-thickness-oriented residual strain gradient (increased away from the substrate), and electrical resistance (greatly increased) are examined, but were found not to significantly contribute to the decrease in fR of the microcantilevers. Morphological characterization identified attack on the surface along with grain delineation for the polySi, with the formation of a nanoscale porous layer at the near surface. The damage to the microcantilevers can be modeled by approximating the beams as a laminated composite structure. Such analysis suggests that damage, induced as the result of galvanic corrosion, results from the decreased stiffness of the near surface porous silicon (PS) layer as well as a change in the effective thickness of the beams. Last, corrosion damage is compared between eight representative HF-based chemistries. The measurements here suggest that the fabrication and postprocessing of microsystems components are important, because they can greatly influence the material properties, design, performance, lifetime, tribology, manufacture, and required operating environment of microscale and nanoscale devices

Characterization of Polycrystalline Silicon-Germanium Film Deposition for Modularly Integrated MEMS Applications

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> The deposition of <emphasis emphasistype="bold"><emphasis>in situ</emphasis></emphasis> boron-doped polycrystalline silicon-germanium (poly-SiGe) films in a conventional low-pressure chemical-vapor deposition reactor has been characterized using the design of experiments method. The dependencies of deposition rate, resistivity, average residual stress, strain gradient, and wet etch rate in hydrogen peroxide solution are presented. Structural layer requirements for general microelectromechanical system applications can be met within the process temperature constraint imposed by complementary metal–oxide–semiconductor (CMOS) electronics. However, residual stress and strain gradient requirements for inertial sensor applications will be difficult to meet with a single homogeneous layer of poly-SiGe that is about 2 <formula formulatype="inline"><tex>$\mu{\hbox{m}}$</tex> </formula> thick. By correlating stress depth profile measurements with cross-sectional transmission electron microscopy images, we conclude that the large strain gradient is due to highly compressive stress in the lower (initially deposited) region of the film. For films deposited at very low temperature (near the range of amorphous film deposition), <emphasis emphasistype="bold"><emphasis>in situ</emphasis></emphasis> boron doping enhances film crystallinity and reduces the strain gradient.<papernumber>2006-0066</papernumber> </para>

Residual Deformation Measurement of Laser Weldment Using the Laser Interferometry

In this paper, the residual deformation induced in laser welding processing was studied by using the moiré interferometry and a novel high-temperature specimen grating technology. The experimental results indicate that the heat-affected zone of laser welding is a narrow strip. There exists great residual strain gradient in the heat-affected zone, especially great residual shear strain gradient. It implies that great residual stress and stress gradient exist near the welded seam. The relationship between the size of the heat-affected zone and the changes of the technology parameters were discussed in the experiments, which can supply some reliable experimental data for optimizing processing technology.

Stress control of polycrystalline 3C-SiC films in a large-scale LPCVD reactor using 1,3-disilabutane and dichlorosilane as precursors

Control of residual stress and strain gradient of polycrystalline SiC films deposited via low-pressure chemical vapor deposition on 100 mm Si wafers is achieved by varying dichlorosilane (DCS) and 1,3-disilabutane (DSB) fractions in the inlet gas mixture. For films deposited at 800 °C and 45 sccm DSB, stress decreases from 1.2 GPa tensile with no added DCS to 240 MPa tensile with 40 sccm DCS added to the inlet gas stream. The lowest magnitude strain gradient achieved is 3.1 × 10−5 µm−1 with 20 sccm DCS added. Electron probe microanalysis indicates that the films change from being slightly carbon-rich in the absence of DCS to successively more silicon-rich with the addition of DCS.

Correlating weld process conditions, residual strain and stress, microstructure and mechanical properties for high strength steel—the role of neutron diffraction strain scanning

This paper presents the results of neutron strain scanning for a series of welds in high strength steel. Residual strains transverse to the weld were measured at a series of points on planes perpendicular to the weld run, along lines either 1 mm below the plate surface or at the mid-depth. Welds were made using three types of filler metal (undermatched (UM), matched (M) and overmatched (OM) compared with parent plate tensile strength), two heat input values and two plate thicknesses. This work forms part of a programme whose objective of the work was to correlate residual strain and hardness gradients, and their position relative to the weld toe, with the process parameters and with fatigue performance in bending at lives of 10 5 cycles and 2 × 10 6 cycles. Fatigue performance was assessed via nominal applied stress, hot spot stress at the weld toe and hot spot strain. The overall aim is to better understand the underlying reasons for fatigue life variability often observed with high strength steels. This will enable development of better life prediction methodologies. Neutron diffraction results show that tensile stresses close to the proof strength of the parent material can occur in the weld and that tensile peaks in the strain profiles correlate with the weld zone width.