Applied Strain Level Research Articles

Delamination at Thick Ply Drops in Carbon and Glass Fiber Laminates Under Fatigue Loading

Delamination at ply drops in composites with thickness tapering has been a concern in applications of carbon fibers. This study explored the resistance to delamination under fatigue loading of carbon and glass fiber prepreg laminates with the same resin system, containing various ply drop geometries, and using thicker plies typical of wind turbine blades. Applied stress and strain levels to produce significant delamination at ply drops have been determined, and the experimental results correlated through finite element and analytical models. Carbon fiber laminates with ply drops, while performing adequately under static loads, delaminated in fatigue at low maximum strain levels except for the thinnest ply drops. The lower elastic modulus of the glass fiber laminates resulted in much higher strains to produce delamination for equivalent ply drop geometries. The results indicate that ply drops for carbon fibers should be much thinner than those commonly used for glass fibers in wind turbine blades.

Visualization of bonding at an inclusion boundary using axial-shear strain elastography: a feasibility study

Ultrasound elastography produces strain images of compliant tissues under quasi-static compression. In axial-shear strain elastography, the local axial-shear strain resulting from application of quasi-static axial compression to an inhomogeneous material is imaged. The overall hypothesis of this work is that the pattern of axial-shear strain distribution around the inclusion/background interface is completely determined by the bonding at the interface after normalization for inclusion size and applied strain levels, and that it is feasible to extract certain features from the axial-shear strain elastograms to quantify this pattern. The mechanical model used in this study consisted of a single stiff circular inclusion embedded in a homogeneous softer background. First, we performed a parametric study using finite-element analysis (FEA) (no ultrasound involved) to identify possible features that quantify the pattern of axial-shear strain distribution around an inclusion/background interface. Next, the ability to extract these features from axial-shear strain elastograms, estimated from simulated pre- and post-compression noisy RF data, was investigated. Further, the feasibility of extracting these features from in vivo breast data of benign and malignant tumors was also investigated. It is shown using the FEA study that the pattern of axial-shear strain distribution is determined by the degree of bonding at the inclusion/background interface. The results suggest the feasibility of using normalized features that capture the region of positive and negative axial-shear strain area to quantify the pattern of the axial-shear strain distribution. The simulation results showed that it was feasible to extract the features, as identified in the FEA study, from axial-shear strain elastograms. However, an effort must be made to obtain axial-shear strain elastograms with the highest signal-to-noise ratio (SNRasse) possible, without compromising the resolution. The in vivo results demonstrated the feasibility of producing and extracting features from the axial-shear strain elastograms from breast data. Furthermore, the in vivo axial-shear strain elastograms suggest an additional feature not identified in the simulations that may potentially be used for distinguishing benign from malignant tumors—the proximity of the axial-shear strain regions to the inclusion/background interface identified in the sonogram.

Osteogenic Differentiation of Human Mesenchymal Stem Cells in Collagen Matrices: Effect of Uniaxial Cyclic Tensile Strain on Bone Morphogenetic Protein (BMP-2) mRNA Expression

Human mesenchymal stem cells (hMSCs) differentiate down an osteogenic pathway with appropriate mechanical and/or chemical stimuli. This study describes the successful culture of hMSCs in 3D collagen matrices under mechanical strain. Bone marrow-derived hMSCs were seeded in linear 3D type I collagen matrices and subjected to 0%, 10%, or 12% uniaxial cyclic tensile strain at 1 Hz for 4 h/day for 7 or 14 days. Cell viability studies indicated that hMSCs remained viable throughout the culture period irrespective of the applied strain level. Real-time RT-PCR studies indicated a significant increase in BMP-2 mRNA expression levels in hMSCs strained at 10% compared to the same day unstrained controls after both 7 and 14 days. An increase in BMP-2 was also observed in hMSCs subjected to 12% strain, but the increase was significant only in the 14-day sample. This is the first report of the culture of bone marrow-derived hMSCs in 3D collagen matrices under cyclic strain, and the first demonstration that strain alone can induce osteogenic differentiation without the addition of osteogenic supplements. Induction of bone differentiation in 3D culture is a critical step in the creation of bioengineered bone constructs.

Viscoelasticity and shear yielding onset in amorphous glassy polymers

In the present work, the effect of viscoelasticity on the yield behaviour of a polycarbonate, PC, was studied and the identification of a yield criterion which takes into account the effects of the mechanical history on the onset of plastic strain, was attempted. The attention was focused on the shear yielding plastic deformation process and different loading histories were performed under uniaxial compression: constant strain rate at different rates, stress relaxation at different applied strain levels, creep under different stress levels. Some tests were also carried out under shear loading, in which the hydrostatic stress component is equal to zero and its effect on the yield onset can be considered. For the definition of a yield criterion, different quantities, some already proposed in an analogous work on a styrene-acrylonitrile copolymer (SAN), were considered and determined at yield onset for each of the applied loading histories. The results obtained in this work show that the relative ratios of the viscoelastic strain over the overall strain and of viscoelastic energy over the deformation work are fairly constant irrespective of both loading history and stress state. The re-elaboration of the data previously obtained on SAN is consistent with these results. Discussing the experimental data, differences between the mechanical behaviour of the two glassy polymers were pointed out and a more difficult activation of the plastic deformation process of PC than SAN was generally observed.

Performance of integrated active fiber composites in fiber reinforced epoxy laminates

Active fiber composite (AFC) composed of lead zirconate titanate (PZT) fibers withinterdigitated electrodes (IDEs) has been integrated into orthotropic glass fiber reinforcedplastic (GFRP) laminates to characterize the performance of AFC as a smart materialcomponent in laminated materials. Monotonic cyclic tensile loading was performed onintegrated specimens at different strain levels. The AFC output was monitored todetermine the effect of applied strain level on the AFC performance. It was found that theAFC sensitivity degraded beyond strains of 0.20% and approached a minimum at 0.50%strain. The degradation in the AFC performance appears to be attributed tothe dominating effect of PZT fiber fragmentation during testing, as opposed todepolarization. Acoustic emission (AE) monitoring was used to detect damage inlaminates during testing and was correlated with crack evidence from microscopyobservations during testing to characterize damage evolution in response to strain levels.

Plasticity-Induced Martensitic Transformation in Austenitic Stainless Steels SUS 304 and SUS 316L at Room and Liquid Nitrogen Temperatures (Quantitative Measurement using X-ray Diffraction Method)

The present study investigates plasticity-induced martensitic transformation in two types of austenitic stainless steels SUS 304 and 316 L subjected to uniform tensile stresses at room and liquid nitrogen temperatures. The X-ray diffraction method was used in order to measure volume fractions of transformed α' and ε martensitic phases and to obtain the dependence of the volume fractions of these phases on the applied strain level ε. The difficulty in the measurement of the martensitic phases by the X-ray diffraction method caused by the preferred orientation which had been introduced during the rolling process and during the tensile tests was overcome by the help of Arnell's Method. Two types of target materials, i.e., Cu and Mo for the X-ray source were used to verify the accuracy and reproducibility of the present X-ray diffraction analyses. The results were also compared with those obtained by the saturation magnetization method using VSM, or vibrating-sample magnetometer reported elsewhere. It was revealed that α' was transformed in SUS 304 both at 297 and 77 K whereas in SUS 316L only at 77 K. Another type of martensitic phase, i. e., ε was transformed in the both steels only at 77 K. Almost the same values of the volume fractions of α' and ε phases were obtained by the two types of target materials. The plots of α' volume fraction obtained by the X-ray diffraction methods vs. that by VSM showed a good linear correlation.

Atomistic mechanisms of strain relaxation due to ductile void growth in ultrathin films of face-centered-cubic metals

A comprehensive computational analysis is reported of the atomistic mechanisms of strain relaxation and failure in free-standing Cu thin films under applied biaxial tensile strain for strain levels up to 6%. The analysis focuses on nanometer-scale-thick films with a preexisting void extending across the film thickness and the film plane oriented normal to the [111] crystallographic direction. Our computational study is based on isothermal-isostrain large-scale molecular-dynamics simulations within an embedded-atom-method parametrization for Cu. Our analysis has revealed various regimes in the film’s mechanical response as the applied strain level increases. Within the considered strain range, after an elastic response at a low strain (<2%), void growth is the major strain relaxation mechanism mediated by the emission of perfect screw dislocation pairs from the void surface and subsequent dislocation propagation; as a result, a plastic zone forms around the void. Plastic deformation is accompanied by the glide motion of the dislocations emitted from the void surface, void surface morphological transitions, formation of a step pattern on the film’s surfaces, dislocation jogging, vacancy generation due to gliding jogged dislocations, dislocation-vacancy interactions, vacancy pipe diffusion along dislocation cores, as well as dislocation–dislocation interactions. The increase in film surface roughness with increasing strain eventually leads to nucleation and propagation from the film surfaces of threading dislocation loops, which ultimately break up when they reach the opposite free surface of the thin film.

A Model for Nonlinear Viscoelastic Mechanical Responses of Collagenous Soft Tissues

AbstractExperimental observations of the time-dependent mechanical responses of collagenous tissues have demonstrated behavior that deviates from standard treatments of linear or quasi-linear viscoelasticity. In particular, time-dependent deformation can be strongly coupled to strain level, and strain-rate independence can be observed under monotonic loading, even for a tissue with dramatic stress relaxation. It was postulated that this nonlinearity is fundamentally associated with gradual recruitment of individual collagen fibrils during applied mechanical loading. Based on previously observed experimental results for the time-dependent response of collagenous soft tissues, a model is developed to describe the mechanical behavior of these tissues under uniaxial loading. Tissue stresses, under applied strain-controlled loading, are assumed to be a sum of elastic and viscoelastic stress contributions. The relative contributions of elastic and viscoelastic stresses is assumed to vary with strain level, leading to strain- and time-dependent mechanical behavior. The model formulation is examined under conditions of monotonic loading at varying constant strain rates and stress-relaxation at different applied strain levels. The model is compared with experimental data for a membranous biological soft tissue, the amniotic sac, and is found to agree well with experimental results. The limiting behavior of the novel model, at large strains relative to the collagen recruitment, is consistent with the quasi-linear viscoelastic approach.

Atomic-Scale Analysis of Strain Relaxation Mechanisms in Ultra-Thin Metallic Films

AbstractA comprehensive computational analysis is presented of the atomistic mechanisms of strain relaxation over a wide range of applied biaxial tensile strain in free-standing Cu thin films. The analysis is based on large-scale isothermal-isostrain MD simulations using slab supercells with cylindrical voids normal to the film plane and extending throughout the film thickness. Our analysis has revealed various regimes in the film's mechanical response as the applied strain level increases. Following an elastic response at low strain (≶ 2%), plastic deformation occurs accompanied by emission of screw dislocations from the void surface and threading dislocations from the film surfaces, in parallel with generation of vacancies due to slip of jogged dislocations. At the lower strain range following the elastic-to-plastic deformation transition (⋚ 6%), void growth is the major strain relaxation mechanism, while at higher levels of applied strain (≥ 8%), a subsequent transition leads to a new plastic deformation regime where void growth plays a negligible role in the film strain relaxation.

Strain-Recovery Kinetics in Rubber Toughened Polymethylmethacrylate

The viscoelastic nature of polymers influences the material’s behaviour not only during its deformation up to strains beyond yielding, but also during and after its unloading. In the present work the recovery of the strain after the removal of the applied stress was studied as a function of time and temperature on rubber toughened polymethylmethacrylates (RTPMMAs). Constant strain rate tests under uniaxial tensile loading were performed at room temperature on three RTPMMAs, differing in dispersed phase content. Identical samples were deformed up to the same strain level and then unloaded. The residual strain was measured as a function of time at different constant temperatures. By applying a time–temperature equivalence, a residual strain versus time master curve was obtained and the relevant shift factors were determined. Isothermal strain recovery on samples deformed up to the same strain was also measured at different temperatures, in the range between room temperature and the material’s glass transition temperature. The residual strain after a given time was plotted as a function of temperature, obtaining an isochronous strain-recovery curve. Using the appropriate shift factors, an isothermal strain-recovery curve was then determined. The latter and the strain-recovery master curve are similar in the range of time over which recovery takes place, although an effect of the applied strain level on the curves’ shape was observed. The effects of the applied strain level and of the rubber particles content on the strain-recovery kinetics were evaluated.

Room temperature creep–fatigue response of selected copper alloys for high heat flux applications

Two copper alloys, dispersion-strengthened CuAl25 and precipitation-hardened CuCrZr, were examined under fatigue and fatigue with hold time loading conditions. Tests were carried out at room temperature and hold times were imposed at maximum tensile and maximum compressive strains. It was found that hold times could be damaging even at room temperature, well below temperatures typically associated with creep. Hold times resulted in shorter fatigue lives in the high cycle fatigue, long life regime (i.e., at low strain amplitudes) than those of materials tested under the same conditions without hold times. The influence of hold times on fatigue life in the low cycle fatigue, short life regime (i.e., at high strain amplitudes) was minimal. When hold time effects were observed, fatigue lives were reduced with hold times as short as two seconds. Appreciable stress relaxation was observed during the hold period at all applied strain levels in both tension and compression. In all cases, stresses relaxed quickly within the first few seconds of the hold period and much more gradually thereafter. The CuAl25 alloy showed a larger effect of hold time on reduction of high cycle fatigue life than did the CuCrZr alloy.

Non-destructive detection of damage in an austenitic stainless steel SUS 304 by the use of martensitic transformation

The present study investigates a method for the non-destructive detection of damage in an austenitic stainless steel SUS 304 by the use of martensitic transformation. Volume fraction of � martensite transformed in uniformly stretched SUS304 plates was measured and expressed as a function of the applied strain level e. The distributions of � phase in the plastic wake regions produced around fatigue cracks were then electromagnetically measured in fatigued SUS 304 plate specimens. The results were compared with the distributions of magnetic flux density Bz above the fatigue cracks in the specimens magnetized by a strong magnetic field higher than 0.4 T. It was revealed that the Bz distributions reflected the α phase distributions in the wake regions: i.e., the distance between the points where Bz reached the minimum and the maximum had a high correlation with the fatigue crack length, and the minimum and the maximum values of Bz showed a linear relationship with the applied stress intensity factor range ∆K. These results imply that not only the crack length but also the fatigue damage can be detected effectively in an electromagnetic non-destructive way.

Elevated temperature bending stress rupture behavior AS4/APC-2 and comparison with AS4/PPS literature data

Abstract End-loaded bending stress rupture experiments were performed at elevated temperatures (70–150 °C) on unidirectional AS4/APC-2. A new fixture was developed enabling progressive and accurate loading. The composite showed times-to-rupture depending on applied strain level and temperature. Failure occurred mainly in the middle of the sample (high strain level) and, unlike AS4/PPS, did not show extensive microbuckling before failure. Surprisingly and despite large scatter in the results at 120 °C, it was found that the time-to-failure versus normalized strain levels for AS4/APC-2 tend to superimpose the literature data for AS4/PPS at given temperatures.

In situ analysis of delayed fibre failure within water-aged GFRP under static fatigue conditions

A stress corrosion model has been applied to the microscopic analysis of the delayed fibre failure processes occurring within a water-aged unidirectional glass/epoxy composite under static fatigue loading (i.e. relaxation). By means of in situ microscopic observations, the individual fibre failures within an elementary volume located on the tensile side of the flexural specimens have been quantified as a function of time under various applied strain levels. It was found that the time dependence of the in situ fibre failure processes obeyed a stress corrosion model. From the microscopic observations, it was possible to assess consistent values of the parameters characterising the in situ fibre strength distribution and the subcritical crack propagation law. A comparison with separate static fatigue experiments using unimpregnated fibre bundles demonstrated that the specific physico-chemical environment encountered by the glass fibres within the aged epoxy matrix can induce significant changes in the subcritical crack propagation rates, as compared to stress corrosion cracking data collected in humid air.

Phase-stress partition and residual stress in metal matrix composites

Finite element (FE) modeling based on axisymmetrical cells was performed for relating the phase-stress partition and residual phase stress in metal matrix composites (MMCs) to the reinforcement volume fraction and shape, matrix hardening behavior and applied strain levels. The phase stress is defined as mean effective stresses in the constituent phases. The elastic, plastic phase-stress partition behavior during loading, and the resultant residual stress in matrix followed unloading are delineated. A set of formulas is given for predicting the value of the phase stress in each phase, and residual stress in matrix from the inclusion volume fraction and aspect ratio, as well as matrix hardening exponent and applied strain level.

Influence of cyclic strain on life of a PVD TBC

A thermal mechanical fatigue (TMF) test has been developed to determine the effect of strain on the life of a thermal barrier coating. TMF tests were performed with different temperature–strain phasing and different applied strain levels to vary the imposed strain range on the coating and thus separate strain dependence of life from oxidation effects. Results for a single crystal superalloy coated with an EB–PVD yttria-stabilized zirconia layer showed that as the compression on the coating at minimum temperature was increased the cycles to spall decreased, following a power law dependence on total strain range.

Low cycle fatigue data evaluation for a high-strength spring steel

In the present investigation, low cycle fatigue (LCF) behavior is studied using the cylindrical smooth specimens under strain-controlled fully-reversed pull-push conditions for a high-strength spring steel heat-treated to different strength levels. During strain cycling the steel exhibits continuous softening independent of the applied strain levels and heat-treatments. Under the circumstances the saturation of the plastic strain energy density per cycle proves to be a valid criterion to determine the stable hysteresis loops for the cyclic stress-strain (CSS) curve formation. The strain-life curve calculated on the basis of the CSS relationship is in good agreement with the experimental counterpart, indicating a fine consistency between data from the CSS approach and from the strain-life approach. Then the LCF properties are discussed with regard to their dependence on the heat-treatments or strength levels of the steel.

Finite element modelling of interfacial failure in model carbon fibre-epoxy composites

Finite element analysis has been used to model a single unsized carbon fibre embedded in an epoxy matrix subjected to tensile loading. The predicted fibre strain distribution is compared with experimental data, obtained using the technique of laser Raman spectroscopy, for a number of incremental applied strain levels. Good correlation is obtained on the assumption that the prevailing mode of interfacial failure in the composite involves a conical matrix crack initiating at the fibre end. The geometry of the matrix crack is estimated on the assumption that the crack propagates in a self-similar manner.

Transverse Fatigue Response of a Metal Matrix Composite Under Strain-Controlled Mode at Elevated Temperature: Part I—Experiments

The transverse fatigue characteristics of a unidirectional titanium-based metal matrix composite (MMC) (SCS-6/Ti-15-3) were investigated under an isothermal condition. Fatigue tests were performed using a hybrid strain-controlled loading mode. In this hybrid control mode, the specimen was always in a tension-tension state of stress perpendicular to the fiber direction. This prevented any possible buckling effects. A systematic approach that involved fatigue tests, microscopic evaluation, and micromechanical analysis, was taken to characterize the fatigue response (that is, fatigue life, stress-strain response, and so forth) and identify the damage and deformation mechanisms. The analysis involved a unique method to model the fiber-matrix interfacial damage. It was found that the fatigue response was initially dominated by the amount of fiber-matrix interfacial damage that occurred during the first loading cycle. The subsequent response was dependent on the rate at which this interfacial damage progressed, the development and propagation of matrix cracks, and matrix inelastic deformation (plasticity and creep). The chronology and accumulation of these damage mechanisms were dependent on the applied strain level. Using the combined approach involving experiments, microscopy, and analysis, the correlation among applied strain levels, fatigue life, damage mechanisms, and macroscopic response (stress and stiffness) were established in this paper. In Part II, the details and results of the micromechanical analysis are presented.

Elasto-plastic finite element modelling of interfacial failure in model Kevlar 49 fibre—epoxy composites

Abstract Elasto-plastic finite element analysis has been used to model a single unsized Kevlar 49 fibre embedded in an epoxy matrix subjected to tensile loading. The predicted axial stress distribution along the fibre is compared with experimental data, obtained using the technique of laser Raman spectroscopy, for a number of incremental applied strain levels. The geometry of the fibre end has been modelled employing an analytical fibre end fibrillation model (FEFM). Furthermore, the influence of residual stresses in the system due to curing, has been analysed. Good correlation is obtained with the experimental data and it is shown that the mode of interfacial failure in the composite involves yielding at the fibre—matrix interface initiating at the fibre end.