Ineffective Length Research Articles

Sensitive and rapid analysis of plasmid DNA topology isoforms by capillary gel electrophoresis with laser induced fluorescence in uncoated capillary.

The work describes the use of SYBR Gold to improve the detection sensitivity of plasmid DNA topoisomers by capillary gel electrophoresis with laser induced fluorescence in an uncoated capillary. The impact of different dyes, including ethidium bromide, SYBR Green and SYBR Gold, was compared based on detection and separation of DNA plasmid topoisomers. Use of SYBR Gold enabled improvement of detection sensitivity by 15-fold while maintaining good separation resolution of the different topoisomers. The baseline dropped with the use SYBR Gold but was overcome by the employment of a capillary with longer ineffective length (40 vs. 20cm). Separation resolution and reproducibility were impacted by the concentration of SYBR Gold and hydroxypropyl methylcellulose. With the use of a short capillary (10cm effective length and 50cm total length), fast separations of supercoiled, linear, open circular, and other isoforms were accomplished within 8min. Appropriate capillary cleaning with 0.1M sodium hydroxide/0.1M hydrochloric acid and capillary storage with 0.1M hydrochloric acid ensured good separation reproducibility of 217 runs during an extended period of use.

The effect of fibre misalignment in an impregnated fibre bundle on stress concentrations

This work investigates the stress redistribution around a broken fibre in a unidirectional impregnated fibre bundle accounting for misalignment of fibres. The study reveals, a statistically significant increase in stress concentration factor (SCF) within misaligned bundles. The effect of fibre misalignment is more pronounced for high fibre volume fraction (VF) and for the nearest neighbour fibres (NNFs) to the broken one. The peak of the SCF graphs shows a significant increase about 16 %, 33 %, and 55 % for VF30 %, VF50 %, and VF60 %, respectively. This implies that the influence of fibre misalignment is more localised, resulting in stronger SCF in the NNFs. Ineffective lengths at applied strain 2 % do not change in the case of fibre misalignment in comparison with the case of aligned fibres. This is linked to matrix yielding, as at applied strain 0.1 % the ineffective length increases for the misaligned case by 12–30 %, depending of fibre volume fraction.

Process-induced residual stress in a single carbon fiber semicrystalline polypropylene thin film

During the processing of semicrystalline thermoplastic composites, various models for the prediction of residual stress have been proposed but experimental validation is limited. In this study, a modeling framework is developed to predict the evolution of residual stress in a single carbon fiber embedded in a semicrystalline polypropylene thin film subjected to non-isothermal cooling. Validation is based on in-situ measurement of axial fiber strain after processing using micro-Raman Spectroscopy. A material model for polypropylene (50% equilibrium crystallinity) is presented that incorporates the effects of non-isothermal cooling on crystallinity-dependent resin shrinkage and crystallinity-dependent resin modulus from the amorphous polymer melt to room temperature. The evolution of residual stress is calculated using a finite element (FE) model with a user-developed subroutine incorporating the resin material models. Single-fiber polypropylene films are fabricated using a range of fiber pretension levels to prevent fiber waviness during cooling and to induce a wide range of axial strain levels in the fiber for model validation. The fiber axial strain was measured over the length of the fiber, from the free edge into the bulk, capturing the ineffective length region where strain builds up and plateaus. A good correlation has been obtained between the model results and the in-situ measurements of axial compression strain in the fiber. A key finding was the importance of including temperature-dependent resin modulus and that the contribution of crystallinity shrinkage to residual strain in the carbon fiber is relatively low. The model developed in this study is also compared to residual stress models in the literature which shows the importance of including the effects of crystallization and cooling rate on temperature and crystallinity-dependent modulus and resin shrinkage for accurate predictions.

Mapping complete eigensolution space for the analysis of stress transfer in and around the broken fiber: A variational principle based approach

One of the critical reasons for the failure of the Fiber Reinforced Composite (FRC) is fiber breakage. The stress transfer in and around this breakage has remained the topic of research for the last couple of decades. The two-phase composite model is generally considered standard to gain insight into the mechanics. Most of the literature simplifies the problem by considering the shear lag approximations or some other a-prior and/or ad hoc assumptions on various field variables. Moreover, the majority of the study in the literature considers both matrix and fiber to be isotropic. On the contrary, most of the fibers in FRC are transversely isotropic. In the present manuscript, an attempt has been made to provide a solution for this problem with an anisotropic fiber satisfying all the boundary conditions and continuity requirements in an exact sense. The solution strategy adopts the derivation of the solution for individual phases under axial traction and then imposes the boundary and the continuity conditions. The formulation of the problem for the individual phase is based on the variational principle and the solution is based on the method of separation of the variables and the Frobenius method. To validate the solution the numerical results for the various stresses have been compared against the results from the Finite Element Analysis (FEA). The comparison shows a good agreement between them. Further, the effect of the volume fraction and the fiber-matrix stiffness ratio on the Ineffective length, maximum shear stress at the interface, and the far-field stresses in the fiber has been studied.

Novel continuous fiber bending experiment to determine size- and spatial-distribution of surface defects in glass fibers

Tensile strength models for unidirectional composites require scaling of fiber strength distributions to small length scales in the range of the fiber radius to the ineffective length (5–200 μm). No test methods currently exist to measure and validate fiber strength at these length scales. In this paper, a novel continuous fiber bending test method is developed to measure the size and spatial distribution of defects in S-glass fibers. For this test method, a single glass fiber was placed between Kapton film and tape, and the sample is subjected to a sequence of controlled radii of curvatures ranging from 350 μm to 25 μm in a confocal microscope. From the bending tests, the number of defects and spacings between the defects over 780 mm length of fiber are obtained for each level of flexural stress. The Kapton film confines the fiber fragments and maintains fiber alignment allowing the same sample to be tested at lower radius of curvature (higher flexural strain/stress). The associated defect size is calculated using fracture mechanics. These results are used to map the size- and spatial-distribution of critical defects on the tension surface of a glass fiber. A methodology is presented to map additional defects around the circumference of the fiber, while maintaining the size and spatial distribution obtained from the bending tests. The results show that the lognormal distribution best fits the spatial distribution of defects along the fiber axis. The results also indicate that extrapolating the Weibull strength distribution (be it bimodal or unimodal) to gage lengths less than 200 μm leads to serious errors in fiber strength prediction.

Strength distributions of laminated FeNi-based metal amorphous nanocomposite ribbons

Metal Amorphous Nanocomposite (MANC) materials offer low losses at high magnetic switching frequency, enabling high power density motors with increased rotational speed. While MANCs have high strength, they are brittle. The use of motor components such as a rotor consisting of brittle material presents a reliability concern. Here, a promising MANC alloy is subjected to tensile tests and failure is observed with high-speed photography. A method is developed to prepare tensile specimens of laminated MANC and epoxy layers, simulating the stacking of an epoxy-impregnated tape-wound core. Tensile tests are conducted for single layer ribbon and for five- and ten-layer stacks of laminated material with thin layers of thermosetting epoxy. Failure distributions are shown to have increasing Weibull modulus with increasing layer count. The composite MANC material system is modeled using chain-of-bundles models. Using a k-failure model, we show that single ribbon strength distribution data can be used to predict well the failure distribution of laminated stacks. The agreement occurs when the assumed ineffective length, over which load is recovered in a failed layer, is comparable to the observed interlaminar separation length.

Experimental determination of bimodal strength distribution of S-glass fibers

Tensile strength distribution of S-Glass fibers at small gage lengths on the order of the ineffective length is required for both analytical and numerical models of composite unidirectional tensile strength. Historically unimodal Weibull strength distributions measured at large gage lengths are extrapolated to smaller length scales (5–200 μm). The accuracy of this approach is assessed by using 2 different experiments – the filament tensile test (gage lengths > 4 mm) and a continuously-monitored Single Fiber Fragmentation Test (SFFT, gage length = 544 μm). Extrapolation of the unimodal Weibull distribution to the 544 μm gage length leads to significant overprediction of fiber strengths (by ∼60%). The Weibull distribution obtained from SFFT also shows a significantly higher Weibull Modulus (12.9) as opposed to the tension dataset (4.5). This indicates that a different population of defects dominate at the shorter gage lengths. A bimodal Weibull equation has been fit to the combined data to account for the 2 different defect populations to provide accurate strength predictions over fiber lengths from ∼500 μm to 30 mm. An independent validation experiment was performed at 2 mm gage length to validate the Bimodal Equation.

Assessment of Intraoperative Spinal Angiography via the Popliteal Artery for Spinal Vascular Diseases

Intraoperative spinal angiography via the popliteal artery for patients in the prone position has been reported only twice in 4 patients. This study aimed to clarify the safety precautions to be taken with this technique in a larger patient cohort. Seven patients with spinal vascular disorders underwent intraoperative spinal angiography in the prone position via the popliteal artery. Ultrasound was used to evaluate the neurovascular anatomy in the popliteal fossa and guide the arterial puncture. Patient characteristics, features of angiography devices, puncture attempts, and angiography-related complications, such as hematoma formation and injury to the neurovascular bundle, were analyzed. The average number of arterial puncture attempts was 1.3 times (range: 1-2). Sheaths (4 and 4.5 Fr) with different ineffective lengths were used. In 1 case, a 4.5-Fr sheath was replaced with a 4-Fr sheath with a shorter noneffective length as the length of the catheter limited access to the target. Catheters with Type-JB2 tip shapes were used for craniocervical junction lesions, and those with Type-KAGAWA tip shapes were used for thoracic and lumbar spinal lesions. No puncture site complications were observed in any patient. Intraoperative spinal angiography via the popliteal artery was an effective tool in surgeries for spinal vascular diseases. The introduction of the ultrasound enabled atraumatic puncture of the popliteal artery. Spinal targets above T5 to T6 may be inaccessible from the popliteal fossa when using a 100-cm-long catheter.

Electromechanical-Mode Coupling Model and Failure Prediction of CFRP under Three-Point Bending

Carbon fiber reinforced polymer materials (CFRP) cause CFRP to bend or fail when subjected to external loads or impacts. In the case of static three-point bending, using the conductive properties of the carbon fiber inside the CFRP, the overall damage detection and failure prediction can be carried out by electromagnetic methods. The eddy current coil is used to realize real-time monitoring of damage, and the measured voltage value can be mapped to obtain the load of the sample. This paper conducts theoretical analysis and experimental verification, and obtains the relationship between CFRP stress damage and spatial conductivity change, and proposes a CFRP electromechanical coupling model under quasistatic three-point bending. Combined with the theory of electrically ineffective length, the CFRP three-point bending electromechanical coupling model was revised. Experimental results prove that the revised model can describe the load-conductivity change trend of three-dimensional braided CFRP more accurately, which provides a theoretical basis for monitoring the structural health of CFRP through electromagnetic methods.

A micromechanical model of carbon fiber-reinforced plastic and steel hybrid laminate composites

The fracture strain of carbon fiber-reinforced plastics (CFRPs) within CFRP/steel hybrid laminate composites is reportedly higher than that of CFRPs due to transverse compressive stress induced by the steel lamina. A micromechanical model was developed to explain this phenomenon and also to predict the mechanical behavior of CFRP/steel hybrid laminate composites. First, the shear lag theory was extended to calculate stress distributions on fibers and matrix material in a CFRP under multiaxial stress condition, considering three deformation states of matrix (elastic and plastic deformation and fracture) and the transverse compressive stress. Then, the deformation behavior of CFRP was predicted using average stress in the ineffective region and the Weibull distribution of carbon fibers. Finally, the mechanical properties of CFRP/steel hybrid laminate composites were predicted by considering the thermal residual stress generated during the manufacturing process. The micromechanical model revealed that increased transverse compressive stress decreases the ineffective lengths of partially broken fibers in the CFRP and results in increased fracture strain of the CFRP, demonstrating the validity of the current micromechanical model.

Characteristics of Compositions of Unidirectional Short Boron Fibers and Metal Matrices

Compositions of unidirectional short boron fibers and titanium, magnesium, and aluminum matrices are considered. The Rosen and Kelly parameters (the ineffective and critical lengths) characterizing the interaction of short fibers and the matrix are studied. These parameters as functions of material characteristics of components of the composites are established on rectangular (with a 2D reinforcement) or rectangular parallelepiped samples (with a 3D one) containing an inclusion in the form of a single short fiber. It is shown that the Rosen parameter is determined only by material characteristics of fibers and matrices, but the critical fiber length (Kelly parameter), in addition, also depends on the strain state of composition. In order to assess the interaction of a short reinforcing fiber with the matrix, a new parameter — the effective length — is introduced. This is the part of the short fiber whose stresses make up 100φ % (0.95 < φ < 1) of the stiffness of the same sample with a continuous fiber. A method for constructing the representative volumes of metal matrices statistically uniformly reinforced by unidirectional short boron fibers is proposed. It is shown that the ratio of the characteristic size of the representative volume of composite to the fiber length can reach two or more units. The elastic characteristics of unidirectionally reinforced short-fiber composites in relation to the fiber length are studied. On the basis of a numerical analysis of this dependence, the concept of the equivalent length of a short fiber is formulated. This length provides the stiffness of a short-fiber-reinforced sample equal to 100φ % (0.95 < φ < 1) of that in the case of a continuous reinforcing fiber. Results of the studies are illustrated by graphs and tables.

Effect of Environmental Conditions on the Resistance of Damaged Composite Materials

The present paper proposes a strength model for unidirectional composites with Lin/Epoxy. The model assumes that, a central core of broken fibers flanked by unbroken fibers which are subject to stress concentrations from the broken fibers. The approach of the model consists of using a modified shear lag model to calculate the ineffective lengths and stress concentrations around fiber breaks. In this paper, we attempt to incorporate in the proposed model the unidirectional composite property variation with temperature and moisture in order to predict even composite strength degradation. Strength degradation is often seen as a result of changes in ineffective lengths at fiber breaks. Subsequently, damage to the material can be estimated at the micromechanical scale under the effect of temperature and humidity.

Stress distribution around a broken carbon fibre and how it is affected by carbon nanotubes in the interface region

ABSTRACTWe performed a numerical study to evaluate the influence of carbon nanotubes (CNTs) on the stress build-up in and around a broken fibre in a single carbon fibre/epoxy composite loaded longitudinally. The CNTs were located in the interface region and mimicked one of the two deposition techniques: 1) direct growth on the fibre or 2) dispersion in the fibre sizing. These techniques are known to produce different alignment, orientation and concentration of CNTs in a composite, which affect stress redistribution upon the fibre failure. The study was performed using a two-scale finite element model based on the embedded regions technique. The most significant effect on the stress build-up was found for CNTs aligned in the fibre direction. In this case, the crack opening displacement and the ineffective length were reduced by 15% and 28%, respectively, thus making the stress recovery in the broken fibre faster. In addition, the shear stress at the fibre-matrix interface decreased by a factor of two. These results indicate that hybridization of microscopic fibres with nanotubes aligned in the fibre direction is a promising strategy to influence the process of fibre fragmentation in a composite.

Effects of local stress fields around broken fibres on the longitudinal failure of composite materials

An in-depth analysis of the stress fields that surround a broken fibre in fibre reinforced composites is performed and the effects of different material properties are analysed. The stress fields obtained using a spring element model with a random distribution are compared with analytical formulations present in the literature, within a progressive failure model framework. This analysis is then extended to clusters of broken fibres with different sizes and the evolution of the stress fields are analysed. Finally, material macro behaviour and cluster formation is analysed using the spring element model and the progressive failure model framework. The authors found that while for the spring element model the stress redistribution and material behaviour changes with the main material parameters, the same was not found to be true using the analytical formulations for stress concentration and ineffective length. Furthermore, it was found that the current definition for a cluster of broken fibres can lead to erroneous results, depending on the material system.

What is the shape of a bundle? An analysis of Rosen's fibrous composites experiments using the chain‐of‐bundles model

AbstractIn the 1960s, W. B. Rosen conducted some remarkable experiments on unidirectional fibrous composites that gave seminal insights into their failure under increasing tensile load. These insights led him to a grid system where the nodes in the grid were ineffective length fibers and to model the composite as something he called a chain‐of‐bundles model (i.e., a series system of parallel subsystems of horizontal nodes that he referred to as bundles), where the chain fails when one of the bundles fails. A load‐sharing rule was used to quantify how the load is borne among the nodes. Here, Rosen's experiments are analyzed to determine the shape of a bundle. The analysis suggests that the bundles are not horizontal collection of nodes but rather small rectangular grid systems of nodes where the load‐sharing between nodes is local in its form. In addition, a Gibbs measure representation for the joint distribution of binary random variables is given. This is used to show how the system reliability for a reliability structure can be obtained from the partition function for the Gibbs measure and to illustrate how to assess the risk of failure of a bundle in the chain‐of‐bundle model.

Axial load tests and numerical modeling of single-helix piles in cohesive and cohesionless soils

Small-diameter helical piles have been increasingly used in Western Canada, but there is a lack of research. The present research investigates the axial behavior of three types of small-diameter single-helix piles. Twenty-six helical piles were installed and loaded axially in a cohesive and a cohesionless soil sites. The limit state capacities are attained or extrapolated from the load versus displacement curves following Chin’s hyperbolic assumption. It is found that the hyperbolic assumption can closely predict the load versus displacement curves of the helical piles. The torque factor Kt was smaller for the larger pile shaft diameter in the homogeneous site, whereas in the heterogeneous site Kt is substantially affected by soil heterogeneity around the helix. To further understand the axial behavior of the tested piles, a beam-on-nonlinear-Winkler-foundation model is developed on the platform of the Open System for Earthquake Engineering Simulation, which is a finite element software framework for the computation of soil and structural systems. A parametric analysis is carried out to determine the best estimate of ineffective length, the equivalent shaft length where the shaft resistance is zero. It is shown that the numerical model with ineffective length of four helix diameters can properly simulate the axial load versus displacement behavior.

Numerical Study and Experimental Validation of Effect of Varying Fiber Crack Density on Stiffness Reduction in CFRP Composites

Representative volume element (RVE) has commonly been used to predict the stiffness of undamaged composite materials using finite element analysis (FEA). However, never has been an independently measured true microstructural damage quantity used in FEA to predict composite stiffness. Hence, in this work, measured fiber crack density in unidirectional fiber composite (generated using controlled fatigue loading) was used to predict reduction in stiffness using a RVE. It was found that the stiffness changes with change in depth of the volume element along the fiber direction and asymptotically reaches a constant value beyond a critical length called representative depth. It was argued that this representative depth should be more than the minimum of two characteristic length scales, twice of ineffective length and average length of broken fibers. Effective stiffness obtained from FEA of the optimum-sized RVE was in excellent agreement with the experimental results for given microstructural damage state.

A 3D Progressive Failure Model for predicting pseudo-ductility in hybrid unidirectional composite materials under fibre tensile loading

This paper presents a three-dimensional Progressive Failure Model based on the chain of bundles able to represent the stiffness loss in unidirectional composite materials loaded in the fibre direction. A representative volume element with a random distribution of fibres with their own radius is considered. Complete stress distributions around fibre breaks are obtained by associating a damage variable to the loss of stress transfer capability along the ineffective length and applying local stress concentrations. The model has been validated by comparing it against the literature results and exhibits good agreement with hybrids and non-hybrid composites. The aim of this model is to simulate the tensile response of unidirectional composite systems dominated by fibre fragmentation mechanisms using a very reduced computational effort, even for larger representative volume elements, compared to micro-mechanical finite element models.

Effect of Breakage & Ineffective Length of Fiber on Modulus of FRP

Effect of Breakage & Ineffective Length of Fiber on Modulus of FRP

Effect of the environmental conditions on the ultimate load of damaged unidirectional of natural hemp fiber/epoxy composite

Natural continuous natural fibres (hemp, flax, etc.) are gaining popularity in composite materials because they can advantageously replace glass fibers. It is found that intrinsic properties of unidirectional (UD) composites are almost equivalent to those of unidirectional glass fiber composites. Unfortunately it is difficult to get repeatable results because of the inherent variability in the properties of natural fibers compared to glass fibers. Their quality is largely affected by the weather conditions, the extraction location along the plant and the techniques used to extract them (retting, bleaching, etc.). The present paper proposes a strength reliability model for unidirectional composites with natural fibers in a hexagonal array. The model assumes that, a central core of broken fibers flanked by unbroken fibers which are subject to stress concentrations from the broken natural fibers. Thermal and hygroscopic residual stresses are neglected because they haven’t more effect when the composite was subjected to tensile than transverse loading. The approach of the model consists of using a modified shear lag model to calculate the ineffective lengths and stress concentrations around the broken fibers. In this paper, we attempt to incorporate in the proposed model the unidirectional composite property variation with temperature and moisture in order to predict even composite strength degradation. Strength degradation is often seen as a result of changes in ineffective lengths at natural fiber breaks and the corresponding stress concentrations in intact neighboring fibers.