Tow Failure Research Articles

Estimating the survival function Maximum Likelihood and Cramér-Von Mises Method use of amixture distribution weibull and ailamujia with apractical application

Tow failure distributions were mixed ,weibull distribution and ailamujia distribution it's called weibull –ailamujia distribution which consists of four features, the two distributions were mixed by adding a mixing parameter ,the mixture of two distributions would be more efficient ,and representative of the data than the single distributions. A group of statistical properties of the mixture distribution were studied , such as the probability function ,the survival function and the failure rate function .classical estimation method were used to estimate the parameters of the mixture distribution, which are maximum likelihood of method ,the cramer –von mises method ,The method were compared using monte carlo simulations real data were taken regarding drug –resistant tuberculosis (TB) Multi Drug Resistance(MDR) methods were compared using the MSE statistical criterion ,and the result should a preference for the method cramer-von mises for having the lowest MSE

Subcritical crack growth models for SiC fiber in air and steam: Low temperature data and possible effects of residual stress

Failure times (tf) and brittle creep strain rates (ἑ) for static fatigue of Hi-Nicalon™-S fiber tows were measured at 500 and 600 °C. These measurements added to those done previously at 700–1100 °C. Subcritical crack growth (SCG) based models developed to predict tf and ἑ from the 700–1100 °C data were modified to include the additional data. Parameters for two SCG laws were determined for air and Si(OH)4 saturated steam environments, and an additional parameter for effective room-temperature residual stress (σRo) along the crack path was introduced. Tow failure was modelled as sequential filament failure by SCG from weakest to strongest in a Weibull distribution. The increase in stress on intact filaments as they oxidized and as other filaments failed caused brittle creep strain. SCG-based models for both surface and interior cracks were considered. Orthogonal direction regression (ODR) was used to find the best parameter fits to data. Faster numerical methods to find the global parameter-space minima and avoid local minima were developed. New model parameters were determined using the entire 500–1100 °C tf and ἑ data set, done at initial applied stresses from 260 to 1526 MPa. In air, measured tf and ἑ at 500 and 600 °C follow the trends previously observed for higher temperatures. However, beneath 700 °C in steam, tf are longer and ἑ are much slower than expected. They are similar to values measured for air, suggesting an SCG mechanism change between 700° and 600 °C in steam. An atomistic SCG law-based model with activation energy (Q) of 310 kJ/mol and σRo of ∼200 MPa compression is suggested to be appropriate for static fatigue in air. An atomistic SCG law-based model with Q of 360 kJ/mol and σRo of ∼0 MPa best fit data measured in steam. However, differences in data fit quality between models were small, so firm conclusions about the correct model, residual stress effects, and associated crack paths could not be made. As stress approaches zero, the model converges to tow failure times that are the times for complete fiber oxidation. As failure times approach zero and temperatures decrease, the model converges to tow strengths predicted by fiber bundle theory at room temperature. The sources of error in data fit, the merit of different SCG models, and the possible roles of residual stress in SCG for Hi-Nicalon™-S fibers are discussed.

Failure by slow crack growth of SiC fibers: Comparing the lifetime scatter for single filaments and multifilament tows

AbstractSiC‐based fibers are subjected to slow crack growth, a crack growth mechanism activated by stresses and the chemical environment, as identified by static fatigue testing. Such tests can be performed on filaments or bundles. Although both types of specimens show a similar lifetime variation, testing of bundles is often preferred. This work compares the scatter of lifetimes predicted for filaments and for tows using a dedicated Monte Carlo simulation tool relying on the following hypotheses: The stress applied to a single filament can be defined, whereas the size of its most critical flaw cannot; on a bundle, neither the applied stress nor the strength of the critical filament (which triggers the cascade failure and the tow failure) can be defined. Depending on the parallelism of fibers inside the bundle and their strength dispersion, the lifetime scatter can be narrower for filaments compared to tows or vice versa.

A 2D image-based multiphysics model for lifetime evaluation and failure scenario analysis of self-healing ceramic-matrix mini-composites under a tensile load

We propose a multi-physics numerical model for a self-healing ceramic matrix mini-composite under tensile load. Crack averaged PDEs are proposed for the transport of oxygen and of all the chemical species involved in the healing process and studied in the dimensionless form to perform the most appropriate discretization choices concerning time integration, and boundary conditions. Concerning the fibres’ degradation, a slow crack growth model explicitly dependent on the environmental parameters is calibrated using a particular exact solution and integrated numerically in the general case. The tow failure results from the statistical distribution of the fibres’ initial strength, the slow crack growth kinetics, and the load transfer following fibres breakage. The lifetime prediction capabilities of the model, as well as the effect of temperature, spatial variation of the statistical distribution of fibres strength, and applied load, are investigated highlighting the influence of the diffusion/reaction processes (healing) on the fibre breakage scenarios.

Subcritical crack growth models for static fatigue of Hi‐NicalonTM‐S SiC fiber in air and steam

AbstractThree subcritical crack growth (SCG) laws were used to model strain‐rates and failure times for static fatigue of Hi‐NicalonTM‐S SiC fiber tows in air and Si(OH)4(g)‐saturated steam. Models were fit to tow failure times (tf) and steady‐state strain rates (ἑ) for brittle creep measured at 700 to 1100°C under initial applied stresses (σA) of 260 to 1260 MPa. A power law, a reaction‐rate law, and a bond‐energy law were used to describe SCG that caused sequential filament failure, and ultimately tow failure. Two versions of each model were developed. One allowed access of chemisorbed species to flaws throughout the fiber (mode 1) and another only allowed access to flaws at the SiC‐SiO2 interface (mode 2). The stress increase on intact filaments as others fractured and as filaments oxidized, and the increase in stress intensity geometric factors (Y) as crack size increased were incorporated in the models. The fits to data were compared for the different models by using both simple regression analysis and orthogonal distance regression (ODR) analysis. Faster convergence and more consistent results were achieved using ODR analysis. Regression analyses found parameters for all models with similar error in data fits, so validity of a model could not be distinguished by regression analysis alone. For all models, the stress dependence of SCG rates was much stronger in steam than in air, and for most models activation energies were between 300 and 420 kJ/mol, regardless of environment. For the steam environment, the bond‐length parameter (δ) for the bond‐energy model was very close to the lattice parameter of β‐SiC (.436 nm), but in air it was significantly lower at 0.25‐0.26 nm, but still larger than the Si‐C bond length of 0.189 nm. Other factors suggest that either a bond‐energy based law or a modified version of a reaction‐rate law are the best choices for a SCG law. Filament strength distributions initially described by Weibull distributions could not be described by such distributions after application of the models. SCG mechanisms are discussed.

Static Fatigue of SiC Multifilament Tows at Temperatures up to 1200 °C in Air

SiC-based fibers are sensitive to delayed failure under constant load at high temperatures in air. Static fatigue at intermediate temperatures < 800 °C was attributed to slow crack growth from flaws located at the surface of fibers, driven by the oxidation of free carbon at grain boundaries. The present paper examines the static fatigue behavior of SiC-based Hi-Nicalon fibers at high temperatures up to 1200 °C and Hi Nicalon S fibers at intermediate temperatures (500–800 °C). The degradation of stress- rupture time relation of multifilament tows with increasing temperature was investigated. Predictions of tow lifetime based on critical filament-based model of tow failure were compared to experimental stress-rupture time diagrams. Critical filaments are characterized by strength–probability relation. The critical filament-based model was found to describe satisfactorily the static fatigue behavior of fiber tows at these temperatures. The influence of various factors on lifetime as well as the origins of variability is analyzed.

Progressive damage modelling and experimental investigation of three-dimensional orthogonal woven composites with tilted binder

This paper investigates the tensile properties of 3D orthogonal woven carbon fiber composites with tilted binder by experiment and simulation. The tensile failure strain and fracture mode of this composite show distinguished discrepancy with idealized 3D orthogonal woven composites experimentally. In order to explain this specific failure mechanism, a unit cell finite element model incorporated with damage models of constituents is established to reproduce the damage initiation and propagation of 3D orthogonal woven composites with tilted binder during tensile test. A three-dimensional failure criterion based on Hashin's criterion and Pinho's criterion is utilized to describe the progressive damage of yarns, while the non-linear behavior of the matrix is predicted by Drucker-Prager yield criterion. Besides, a traction-separation law is applied to predict the damage of yarn-matrix interface. The proposed unit cell model is correlated and validated by global stress–strain curves, DIC full-field strain distributions and modulus history curve. The damage evolution process of 3D orthogonal woven carbon fiber composites with tilted binder, including fiber tow failure, matrix cracking, and interfacial debonding, is recorded and investigated by the modulus history curve from simulation.

Joining of carbon fiber and aluminum using ultrasonic additive manufacturing (UAM)

Various methods have been reported to join carbon fiber reinforced polymer (CFRP) composites with aluminum alloy (AA), with strengths ranging from 13 MPa to 112 MPa. This paper presents a new method for joining carbon fiber reinforced composites and metals using ultrasonic additive manufacturing (UAM). Although UAM is a metal 3D printing process, it is applied here to produce continuous CF-AA transition joints that can have uniform thickness across the CF and AA constituents. Joint strength is achieved by mechanical interlocking of CF loops within the AA matrix; tensile tests demonstrate that UAM CFRP-AA joints reach strengths of 129.5 MPa. The dry CF fabric extending from these joints can be laid up and cured into a CFRP part, whereas the AA can be welded to metal structures using traditional metal welding techniques – hence their designation as “transition joints.” This approach enables the incorporation of CFRP parts into vehicle structures without requiring modifications to existing metal welding infrastructure. Two failure modes, CF tow failure and AA failure, have been identified. It is shown that the joint failure mode can be designed for maximum strength or maximum energy dissipation by adjusting the ratio of embedded CF to AA matrix.

Failure Theory/Failure Criteria for Fiber Composite Laminates

Failure criteria are derived for the case of a quasi-isotropic laminate and for the more general case of orthotropic laminates. The former requires two calibrating failure properties obtained directly from laminate testing and the latter requires five standard experimental measurements for its calibration. Then the quasi-isotropic failure theory is taken much further, also admitting full calibration by only the two composites tow failure properties, the associated unidirectional tensile, and compressive strengths. The theoretically predicted failure envelope for the quasi-isotropic laminate is favorably compared with some comprehensive testing data. As a related matter, the general failure criteria for unidirectional fiber composites are also reviewed.

Electromechanical, self-sensing and viscoelastic behavior of carbon fiber tows

The electromechanical, electrical-resistance-based self-sensing and viscoelastic stress-relaxation phenomena of unsized binderless pitch-based carbon fiber tows have been observed for the first time, using the elastica loop test innovatively modified with four-probe tow electrical resistance measurement. The resistance increases upon fiber breakage and decreases upon stress-relaxation-related fiber rearrangement. With a fixed tensile strain applied, the resistance decreases with time, levelling off after ∼40 s, due to the relative movement of the fibers causing more fiber-fiber contact as the tow relaxes, and indicating viscoelastic stress-relaxation behavior. Minor fiber fracture and inelastic behavior occur more upon loading than unloading. Strain-controlled fatigue loading results in cycle-by-cycle monotonically increasing fraction of fibers broken. Loop major-to-minor axis ratio increase accompanies fiber fracture, which promotes the inelastic behavior. The increase of the fraction of fibers broken upon strain cycling becomes more abrupt when this fraction exceeds 40% and the ratio exceeds 1.4. This fraction increases monotonically with progressively increasing strain amplitude, being gradual at fraction <4% and significant at fraction >4%, with tow failure occurring upon loading from an effectively unloaded state with fraction 22%. For fatigue loading at a relatively high strain amplitude, tow failure occurs upon loading from an effectively unloaded state with fraction 81%.

Predicting dynamic in-plane compressive properties of multi-axial multi-layer warp-knitted composites with a meso-model

Proper prediction of material microstructure from known processing conditions and constituent material properties is a critical step to determine the bulk properties of the composite. This paper reports a meso-structure model of multi-axial multi-layer warp-knitted (MMWK) composites from an elastic–plastic material model considering the strain rate effect for the components of the MMWK composite. The representative unit cell (RUC) of fiber tow is created to obtain the elastic–plastic parameters of the fiber tow. The 3D meso-structure model of the MMWK composite is based on an idealized geometrical model according to the preform structure of the MMWK fabric. The model is used to investigate the effect of the volume fraction of the knitting yarn on the dynamic in-plane compressive properties. The results show that the fiber tow failure at large extent is mainly caused by the micro cracking of the matrix, and the effects of the knitting yarn on the mechanical properties of MMWK composite are very limited. Particularly, MMWK composites could be considered as laminates when the volume fraction of the knitting yarn is low, such as below 1.5%. Experiments were also conducted to validate the results from the simplified meso-structure model of the MMWK composite. The material is found to be strain rate sensitive, and the experimental and predicted results agree well with respect to the compressive strength and modulus of the composite. This confirms that the meso-structure MMWK composite model proposed is capable of capturing the essential features for the response of the composite under different strain rate conditions at the meso-level.

Prediction of stress–strain and fracture behaviour of an 8-Harness satin weave ceramic matrix composite

A computationally economic finite-element-based approach has been developed to predict the stress–strain and fracture behaviour of an 8-Harness satin woven ceramic matrix composite with strain-induced damage. The finite element analysis utilises a solid element to model the behaviour of the homogenised orthotropic uni-directional tow and its matrix. The underpinning models of the tow and matrix, (Tang et al., 2009) capture the physics of the interactions between fibres and matrix; and, in this way, permit modelling that bridges the length scales of the fibres and full-scale components. The non-linear multi-axial stress–strain behaviour of the composite has been discretised by multi-linear elastic curves; and the latter has been used as input to a user defined subroutine, UMAT, in the commercial finite element package, ABAQUS. A partial unit cell model has been constructed of the 8-Harness satin weave composite of carbon fibres embedded in an amorphous carbon matrix, HITCO C/C. Predictions of the global stress–strain curve, which include the effects of fibre waviness, have been made for two failure modes: the first by deformation localisation, and the second by dynamic tow failure on fibre fracture, triggered by instantaneous pull-out deactivation. Comparisons have been made between the predictions and experimental data that exhibit two classes of fracture behaviour: brittle and quasi-ductile. The predicted results, both with and without tow waviness, compare well with the experimental data; however, the predictions for waviness are slightly better. The two extremes of experimental behaviour have been found to correspond with the two tow fracture criteria modelled.

Mechanical assessment and deformation mechanisms of aluminum foam filled stainless steel braided tubes subjected to transverse loading

An experimental study investigating the mechanical response of both empty and aluminum foam filled braided stainless steel tubes subjected to transverse loading is presented in this manuscript. Tube specimens were loaded using a custom built testing machine which operated at a constant velocity of 18.8mm/s. The braided tubular specimens utilized in this study were round AISI 301 stainless steel tubes with a nominal wire diameter of 0.51mm, external nominal diameter of 64.5mm, and length of 330mm. Four different foam core configurations were tested, with densities ranging from 248kg/m3 to 493kg/m3. Additionally, two different core geometries were considered, namely cylindrical and rectangular prism configurations. Both core geometries were constructed from circular and rectangular flat panel sections of larger metallic foam panels. Structural adhesive was used to bond the smaller sections of the foam panels together to generate the cylindrical and rectangular prism cores. Deformation mechanisms of these structures were identified through use of a high speed, high resolution camera. The applied transverse load resulted in significant tensile loads within the braided tube and further resulted in braid diameter reduction as well as crushing and pulverization of the metallic foam core. Failure of the circular foam filled braided tubes was observed to be a combination of foam core separation, foam pulverization, as well as braid tow failure resulting from tensile forces and to a lesser extent bending. Failure of rectangular foam filled braided tubes was generally consistent with the mechanisms associated with the cylindrical cores, with the exception of the foam core separation. Force/displacement behavior was dependent on foam core density prior to tow lockup. Energy absorption levels ranged from 2.37kJ to 9.13kJ for the core densities and geometries are considered within this investigation.

3D damage characterisation and the role of voids in the fatigue of wind turbine blade materials

The fatigue mechanisms of Glass Fibre Reinforced Polymer (GFRP) used in wind turbine blades were examined using computed tomography (CT). Prior to mechanical testing, as-manufactured [+45/−45/0] 3,s glass/epoxy specimens were CT scanned to provide 3-dimensional images of their internal microstructure, including voids. Voids were segmented and extracted, and individual characteristics and volumetric distributions were quantified. The coupons were then fatigue tested in uniaxial loading at R = −1% to 40% of the nominal tensile failure stress. Some tests were conducted to failure for correlation with the initial void analysis and to establish failure modes. Other tests were stopped at various life fractions and examined using CT to identify key damage mechanisms. These scans revealed transverse matrix cracking in the surface layer, occurring predominantly at free edges. These free-edge cracks then appeared to facilitate edge delamination at the 45/−45° interface. Propagation from sub-critical, surface ply damage to critical, inner ply damage was identified with either a −45/0° delamination, or a 0° fibre tow failure allowing a crack to propagate into the specimen bulk. Final failure occurred in compression and was characterised by total delamination between all the 45/−45° plies. A quantitative void analysis, taken from the pre-test CT scans, was also performed and compared against the specimens’ fatigue lives. This analysis, to the authors’ knowledge the first of its kind, measured and plotted approximately 10,000 voids within the gauge length of each specimen. The global void measurement parameters and distributions showed no correlation with fatigue life. A local ply-level investigation revealed a significant correlation between the largest void and fatigue life in the region of the laminate associated with the crack propagation from sub-critical to critical damage.

Shock response of 3D woven composites: An experimental investigation

A modified shock tube was used to determine the effect of shock wave loading on 3D woven composite panels . The shock wave, which produces a short duration steeply rising pressure pulse when impacting the panel, was used to load the panels. The out of plane deformation response was measured using a full field Digital Image Correlation (DIC) technique. The results allow for measurements of full field displacements and strains in the samples. Three distinct textile composite architectures, corresponding to different amounts of Z-fiber (fiber tows that bind the different textile layers together) were investigated. Two separate shock intensities were used. Matrix micro-cracking was observed to be the mechanism by which failure is initiated, and this micro-cracking was found to occur closest to the center of the panel where the outer-surface straining is highest. Fiber tow failure was absent in the shock strengths studied in the present work. The results suggest that the 6% Z-fiber architecture provided the largest panel stiffness and the least amount of damage. This result suggests that this may be the optimal architecture and density for orthogonally woven Z-fiber reinforced composites, however due to the complex nature of the problem the same architecture with a different tow (and fiber) volume fraction may yield different results.

Influence of Interface Characteristics on the Mechanical Properties of Hi‐Nicalon type‐S or Tyranno‐SA3 Fiber‐Reinforced SiC/SiC Minicomposites

The tensile behavior of CVI SiC/SiC composites with Hi‐Nicalon type‐S (Hi‐NicalonS) or Tyranno‐SA3 (SA3) fibers was investigated using minicomposite test specimens. Minicomposites contain a single tow. The mechanical behavior was correlated with microstructural features including tow failure strength and interface characteristics. The Hi‐NicalonS fiber‐reinforced minicomposites exhibited a conventional damage‐tolerant response, comparable to that observed on composites reinforced by untreated Nicalon or Hi‐Nicalon fibers and possessing weak fiber/matrix interfaces. The SA3 fiber‐reinforced minicomposites exhibited larger interfacial shear stresses and erratic behavior depending on the fiber PyC coating thickness. Differences in the mechanical behavior were related to differences in the fiber surface roughness.

Influence of uniaxial and biaxial tension on meso-scale geometry and strain fields in a woven composite

Representative volume element (RVE) of a woven composite is often idealised to have identical geometry in the warp and weft directions. While this may be true in the case of consolidating a completely relaxed preform with equal warp and weft densities, majority of woven composites have non-ideal RVE geometry. The present paper investigates the influence of membrane stresses – applied during the moulding process – on the mechanical properties of the finished composite. Crimp interchange due to uniaxial stress and tow flattening due to biaxial stress have been computed by a fabric compliance model developed by the authors. Compliance model is based on the principle of stationary potential energy by taking into consideration tow bending, compression and extensional energies, and the external work done by the tensile forces. It has been shown that a uniaxial tensile stress applied to the preform results in an increase in tensile modulus and a corresponding reduction in the transverse modulus, as a result of reduced crimp in the loading direction with a corresponding increase in the transverse direction. Tensile strength and stiffness increase in the loading direction, and the mode of failure initiation changes from ‘knee phenomena’ to tow failure. A biaxial stress applied during the forming stage results in crimp reduction in both axial and transverse directions; this leads to an improved tensile modulus and strength of a composite laminate. RVE of the deformed geometry has been modelled using ABAQUS CAE pre-processor. The elastic moduli were computed using the concept of equivalent strain energy proposed by Zhang and Harding. The resulting strain fields were compared for various cases of uniaxial and biaxial extension.

A physically-based model for the notched strength of woven quasi-isotropic CFRP laminates

Damage growth and fracture at circular holes in quasi-isotropic CFRP laminates loaded in tension has been studied. The laminates were based on two weave types and of three different thicknesses. A notch edge damage analysis was performed on a layer by layer basis after decomposition of the matrix. It was shown that near the notch edge, damage in the form of fibre tow failure occurred in the tows orientated at 0°, whilst the tows oriented at 45° within the damage area remained intact to loads just below the maximum load. The well known semi-empirical point and average stress criteria resulted in accurate notched strength predictions with the average stress criterion being better than the point stress criterion. A recently developed critical damage growth model, requiring as input parameters the unnotched strength and fracture toughness of the laminate which were measured from independent experiments, yielded accurate notched strength predictions, while being easy to implement. The resilience of the critical damage growth model was investigated and it was found that a variation in both the input parameters of the model by 10% result, even in the worst case, in a 10% variation in the notched strength predicted by the model.

A Binary Model of textile composites: III high failure strain and work of fracture in 3D weaves

Prior experiments have revealed exceptionally high values of the work of fracture (0.4– 1.1 MJm −2 ) in carbon/epoxy 3D interlock woven composites. Detailed destructive examination of specimens suggested that much of the work of fracture arose when the specimens were strained well beyond the failure of individual tows yet still carried loads ∼1 GPa . A mechanism of lockup amongst broken tows sliding across the final tensile fracture surface was suggested as the means by which high loads could still be transferred after tow failure. In this paper, the roles of weave architecture and the distribution of flaws in the mechanics of tow lockup are investigated by Monte Carlo simulations using the so-called Binary Model. The Binary Model was introduced previously as a finite element formulation specialised to the problem of simulating relatively large, three-dimensional segments of textile composites, without any assumption of periodicity or other symmetry, while preserving the architecture and topology of the tow arrangement. The simulations succeed in reproducing all qualitative aspects of measured stress–strain curves. They reveal that lockup can indeed account for high loads being sustained beyond tow failure, provided flaws in tows have certain spatial distributions. The importance of the interlock architecture in enhancing friction by holding asperities on sliding fibre tows into firm contact is highlighted.

Failure of anchored sheet pile walls : BROMS, BB ROYAL INST. TECH., STOCKHOLM, S STILLE, H CITY ROADS BD. VICTORIA, AUS 13F, 5T, 6R. J. GEOTECH. ENGNG DIV. ASCE, V102, GT3, MARCH, 1976, P235–251

This discussion of the above paper attempts to demonstrate the influence of the axial force on the magnitude and distribution of the lateral pressure on the stability of the anchored sheet pile walls. Attention is focused on one type of failure, tow failure, and several fundamental facts are stressed. It is noted that the bulkhead is stable if the depth of penetration of the sheet piles is sufficient, and the free earth support and the fixed earth support are discussed. Experiments have shown that the rigidity of real bulkheads is relatively so great with regard to the density of soils into which they are normally driven, that their elasticity line always corresponds to the scheme of the vertical beam with free earth support. As a consequence, sheet piles should be computed on the assumption of free earth support. The use of a shape of passive earth pressure diagram and a method of introducing the safety factor with respect to failure of lateral earth support is recommended. Further comments are made on the assumed magnitude of the angle of internal friction, and the introduction into the analyses of the vertical component caused by sloping anchor rods.