Local Waviness Research Articles

Statistical modeling of 3D fiber geometry in pultruded GFRP composite: A multi-scale approach

The fiber geometry is a crucial determinant of the fiber reinforced polymer composites’ mechanical properties. Specifically, the manufacturing process of stretching and gradual curving in pultruded composites invariably results in complex 3D fiber geometries. Despite its significance, there is still lacking a statistical method to accurately describe these spatially curved fiber shapes. This paper presents a novel multi-scale mathematical approach for modeling the complex 3D fiber geometry in pultruded glass fiber reinforced polymer (GFRP) composites, which includes the analysis of fiber misalignment and waviness at two scales. At the mesoscopic level, a modified elliptical symmetry angular Gaussian (ESAG) model effectively characterizes the fiber misalignment. Simultaneously, at the micro scale, a cosine series representation is employed for capturing local fiber waviness. The approach is verified with XCT scanning results of pultruded GFRP specimens. The current statistical modeling method provides a multi-scale approach for geometry analysis and further simulation of pultruded composite materials.

Effect of AFP induced triangular gaps on manufacturing quality and stress distribution of composite panels

Automated fiber placement technology still faces some significant challenges in fiber path planning for composite laminates with unconventional geometries. Laying triangular gaps can inevitably result in material geometric discontinuities due to geometric constraints such as turning radius, tow angle deviation, and compaction requirements. How to effectively design the distribution of triangular gaps in the thickness direction to reduce the impact on composite parts has become a key issue. This study focuses on the through-thickness staggered distribution of triangular gaps during the path planning process for composite web panels of I-shaped spars. Through ultrasonic scanning analysis and microscopic observation of cross-sections, the effects of differently distributed triangular gaps on the thickness variation, defect distribution, and local waviness of web panels were thoroughly investigated. Afterwards, a finite element model containing gap defects was established to evaluate the effect of different staggered planning schemes of triangular gaps on the stress concentration of web panels by stress concentration factors. Results show that the trajectory planning scheme of layer-by-layer staggering distribution of triangular gaps has obvious advantages compared with the staggered approach with a specific number of layer intervals in terms of forming quality and stress concentration of composite panels.

Simulating performance of tow reinforced hybrid-molded composites

A critical milestone to the adoption of 3D tow reinforced hybrid-molded structures is the development of design guidelines and analysis techniques for accurate performance modelling. The cross-sectional dimensions of the tow bundle leads to fiber length discrepancies between the inner fibers and the outer fibers which manifest as tow spreading and local fiber waviness. The effects of simulating the resulting fiber orientations and effective elastic properties is investigated by modelling a representative beam in tension and bending load cases and comparing to previous experimental results. Accounting for fiber waviness in tension demonstrated greatly improved part stiffness predictions. Spread tow bundles improved predicted strength and stiffness over simulations where tow was constrained to a uniform cross section. Increased tow reinforcement increased bending stiffness, but failure behavior was significantly influenced by the overmolding material.

Modelling and evaluation of carbon fibre composite structures using high-frequency eddy current imaging

The mechanical performance of carbon fibre reinforced polymer (CFRP) composites is determined by the stacking sequence of specifically orientated ply lamina layers. In these multi-layer structures, global ply misalignment and local fibre waviness can occur during the manufacturing process, leading to reduced performance and structural failure during operation. High-frequency eddy-current testing (ECT) has previously demonstrated its capability for detecting orientation-related features, including fibre orientation and waviness. However, accurate sensor optimisation and inversion of orientation & material structure cannot be achieved without proper, validated modelling techniques to simulate CFRP features. The lack of suitable models is in part due to CFRP exhibiting highly-complex electromagnetic interactions between fibres, lamina and the ECT sensors, which are challenging to integrate. This work proposes a novel finite element modelling approach to simulate the ECT response to planar multi-layered CFRP components. The fibre tow structure of each unidirectional ply is modelled using orientation dependant 2D conductivity tensor waveforms, and virtual 2D ECT scans are simulated by shifting the waveforms within the model mesh. The results demonstrate that idealised electromagnetic characteristics of the CFRP structure can be successfully modelled compared with experimental data and that 2D ECT data of complex CFRP layers structures can be simulated with improved computational speeds, up to 5x faster compared to standard approaches. Automated data-analysis tools, including Radon transform (RT) and 2D FFT, are employed to validate the simulated 2D scan data through the characterisation of fibre orientations and simulated 2D scans used to evaluate the orientation inversion techniques. The results demonstrate that RT analysis detects fibre orientations with better accuracy, precision and consistency than equivalent 2D FFT analysis techniques. The simulation also demonstrates the reduced resistivity losses compared with isotropic materials caused by the different heterogeneous and multi-layer structures. It predicts high current densities at interfaces of plies with orthogonal orientations, resulting in an effective interface skin-depth.

The effect of local and random fiber waviness on the microbuckling of composite materials

A methodology which is capable of predicting the microbuckling of various types of composite materials containing several randomly located fiber waviness of spatially varying amplitudes is presented. This methodology forms a more realistic modeling over standard micromechanical analyses of composites based on the periodic microstructure assumption, implying that the waviness is necessarily periodic of the same amplitude. The proposed approach is based on the combined applications of a perturbation expansion on the nonlinear governing equations, the representative cell method and the high-fidelity generalized method of cell (HFGMC) micromechanics. The application of perturbation expansion on the nonlinear equations yields a zero-order linear problem, which is solved by the standard HFGMC analysis, and a first-order linear problem which is coupled to the former. In the framework of the representative cell method the composite is divided into numerous cells and the application of the discrete Fourier transform reduces the first-order problem to the problem of a single cell in the transform domain. The resulting governing equations, formulated in the transform domain, are solved by the extended HFGMC approach. The inversion of the transform yields, in particular, the waviness growth (which depends on the number of wavy fibers and their amplitude distribution) with the increase of externally applied compressive loading on the composite. The proposed analysis provides an estimate of the actual failure stress of the composite with respect to its ideal bifurcation buckling stress and the detailed stress distribution. The offered analysis is applied on bi-layered, continuous and short-fiber composites, as well as on two and three-dimensional lattice blocks.

Numerical study on the effect of out-of-phase wavy confining walls on the performance of Savonius rotor

Power generation using renewable energy, specifically from wind power is reliable, affordable and pollution-free energy. Turbine is the basic component in a wind energy conversion system. This research article, is on Savonius vertical axis wind turbine (VAWT) installed on building rooftops targeting power extraction from low wind speed. The novel idea proposed in this work is attachment of channel confinement with local waviness to increase drag on the advancing blade. The study has been carried out using ANSYS Fluent 2019 R3 software. The systematic study conducted on the effect of location of turbine in the wavy channel has been presented. The new configuration has improved the turbine output significantly. The maximum increase in power coefficient is 44.67% for waviness confinement channel than plain confinement channel.

3D topographical analysis for defect detection during loading of woven thermoplastic composites

The behaviour of the local weave architecture during large deformation influences the final composite properties, but this architecture is challenging to measure experimentally. In this work, a technique is proposed to examine the local out-of-plane topography of woven composites to improve defect and damage detection during deformation, using digital image correlation (DIC). Three load cases are presented to demonstrate the technique: tension–torsion in a universal testing machine, varied deformation mode testing, and thermo-forming, the latter two both using a hemispherical forming apparatus. Topographical results are found for all cases and show features that are not visible in the surface strain map, providing additional insight into weave response and defect progression. These topographical features include edge delamination, local fibre waviness under biaxial deformation, and undulating weave architecture under thermo-mechanical loading.

An experimental approach to reproduce in-plane fiber waviness in thermoplastic composites test coupons using a reverse forming method

In-plane fiber waviness is one of the defects that can occur from the stamp-forming process of thermoplastic composite (TPC) parts. The influence of this defect on the mechanical performance of multidirectional composites is not yet fully understood. The main challenge in determining the influence on mechanical properties lies in reproducing the waviness in test coupons that can subsequently be subjected to testing. This paper describes an experimental approach to reproduce representative in-plane waviness defects, specific for TPC, by reverse-forming of V-shape parts of various bend angles and inner radii. Characterization results show that this method enables the manufacturing of localized in-plane waviness in flat 24-ply quasi-isotropic C/PEEK composites with no voids. Furthermore, laminates having varying levels of maximum waviness angle ([Formula: see text]), between 14° to 64°, were successfully produced in this work. By comparing the [Formula: see text] value with the examples of industrial stamp-formed parts, it can be concluded that the developed coupon manufacturing method can reproduce waviness from TPC part production reasonably well. Finally, all of the produced laminates have defective region lengths smaller than 20 mm, localized within a predefined location which makes them well suited for standard compression test coupons.

Effect of in-plane fiber waviness defects on the compressive properties of quasi-isotropic thermoplastic composites

The influence of in-plane fiber waviness defects on the compressive properties of quasi-isotropic (QI) carbon polyether-ether-ketone (C/PEEK) composites was investigated experimentally. Specimens with localized waviness were manufactured using a stamp forming process resulting into laminates featuring multiple wavy plies, i.e. from one to three wavy 0° plies in a 24-ply QI composite and a range of maximum waviness angle between 23° to 60°. No significant influence of the waviness was found on the global laminate stiffness. Compression tests coupled with high-speed camera monitoring were performed to study the failure process. It was confirmed that the waviness defects act as a trigger for the initiation of damage, predominantly by the kinking mechanism, resulting into an early failure and significantly lower ultimate strength than the baseline when loading in 0° direction. Furthermore, it was found that all specimens with waviness and with the same layup have a similar strength, indicating that the maximum waviness angle within the range studied in this work did not significantly influence the ultimate compressive strength. However, the presence of waviness in multiple plies clearly affected the strength. It was found that the ultimate compressive strength decreased proportionally to the percentage of plies oriented in the loading direction that is wavy.

Modified 2D roughness parameters for rock joints at two different scales and their correlation with JRC

To overcome the drawbacks of the existing two-dimensional (2D) roughness parameters, this paper proposes two parameters to characterise the roughness of rock joints. One is used to represent the local features of the joint profiles, and the other is used to characterise the overall features. The proposed local 2D parameter θ2d can provide an alternative approach and facilitate the characterisation of the roughness of the joint rock surface when a three-dimensional measuring apparatus is unavailable. This parameter is calculated using 10 standard joint roughness coefficient (JRC) profiles, and the value of θ2d does not increase monotonically with an increase in the JRC. The results suggest that θ2d can reflect the local waviness but fails to describe the overall features of the profiles. Another parameter, h1, is introduced to consider the overall features of the profiles. A new equation for the JRC is derived by combining the small- and large-scale roughness parameters. Predictions based on the new equation are compared with the experimental data, and the results indicate the applicability of the new equation.

The Impact of Draping Effects on the Stiffness and Failure Behavior of Unidirectional Non-Crimp Fabric Fiber Reinforced Composites.

Unidirectional non-crimp fabrics (UD-NCF) are often used to exploit the lightweight potential of continuous fiber reinforced plastics (CoFRP). During the draping process, the UD-NCF fabric can undergo large deformations that alter the local fiber orientation, the local fiber volume content (FVC) and create local fiber waviness. Especially the FVC is affected and has a large impact on the mechanical properties. This impact, resulting from different deformation modes during draping, is in general not considered in composite design processes. To analyze the impact of different draping effects on the mechanical properties and the failure behavior of UD-NCF composites, experimental results of reference laminates are compared to the results of laminates with specifically induced draping effects, such as non-constant FVC and fiber waviness. Furthermore, an analytical model to predict the failure strengths of UD laminates with in-plane waviness is introduced. The resulting stiffness and strength values for different FVC or amplitude to wavelength configurations are presented and discussed. In addition, failure envelopes based on the PUCK failure criterion for each draping effect are derived, which show a clear specific impact on the mechanical properties. The findings suggest that each draping effect leads to a “new fabric” type. Additionally, analytical models are introduced and the experimental results are compared to the predictions. Results indicate that the models provide reliable predictions for each draping effect. Recommendations regarding necessary tests to consider each draping effect are presented. As a further prospect the resulting stiffness and strength values for each draping effect can be used for a more accurate prediction of the structural performance of CoFRP parts.

Improved Methods for Simultaneous Neutron and X-Ray Tomography of Operating Fuel Cells

Neutrons and X-rays provide complementary, non-destructive information on the operating conditions inside fuel cells. As previously reported, NIST has developed a fuel cell to facilitate simultaneous, multimodal tomography on the Neutron and X-ray Tomography (NeXT) system at the NIST Center for Neutron Research. The original cell design served as a developmental testbed but suffered several drawbacks such as CT artifacts caused by cell design and scan parameter choices and long, 18 hour tomography scans where the cell would need to operate at steady-state. Multiple improvements to the NeXT system and the tomography reconstruction workflow has resulted in a reduction of scan times down to as low as 4 hours with a reduction in CT artifacts. The improvements to reconstruction quality and the development of registration and segmentation tools that work on the multimodal datasets allows for the tracking of the gas diffusion layer – catalyst layer interfaces. This will improve the conversion of measured water thickness to saturation as local compression effects and MEA waviness can be accounted for. A new cell design to further reduce reconstruction artifacts and a new method for hybrid high resolution radiography and tomography will be discussed.

Experimental and computational analysis of failure mechanisms in unidirectional carbon fiber reinforced polymer laminates under longitudinal compression loading

This study investigates the failure mechanisms of notched unidirectional (UD) carbon fiber reinforced polymer (CFRP) laminates subjected to longitudinal compressive loading. A sequence of failure initiation and propagation is observed based on optical microscopy images of specimens during failure. The micrographs reveal that the main failure mechanism in UD laminates is fiber kinking failure. The influence of manufacturing defects and voids on fiber kinking mechanisms is also analyzed. The results show that the voids in the resin-rich area lead to kink-band splitting, while in some cases the voids cause the kink-band to deflect in a new direction depending on the location of the voids. The next focus of this study is to propose a computational micromechanics model considering local fiber waviness to study the fiber kinking failure mechanism. The computational results on kink-band formation and stress-strain response show good consistency with our experimental analysis. Finally, the failure envelopes of σ11-σ22 and σ11-τ12 subjected to combined loading conditions are obtained from the computational model, which provide essential inputs for future theoretical failure criteria.

Numerical study on the heat transfer characteristics between supercritical carbon dioxide and granite fracture wall

A two-dimensional numerical model was developed to investigate the flow and heat transfer characteristics of supercritical carbon dioxide (scCO2). The numerical results of flow and heat transfer characteristics of scCO2 through straight granite fracture were found to be in good agreement with the experimental results. Moreover, the heat transfer characteristics between scCO2 and rough granite fractures were also investigated by using the proposed model. The confining temperature outside the specimen was set at 200 °C and the pressure of scCO2 was 8 MPa. Four different case studies with the flow rates of 0.75, 0.51, 0.35, and 0.13 kg h−1 were, respectively, designed. The overall and the local heat transfer coefficients (OHTC, LHTC) were used to characterize the heat transfer properties of these cases. Furthermore, the effects of flow rate, fracture roughness, and phase state of CO2 on the heat transfer characteristics of CO2 were investigated. The results indicated that increased roughness or flow rate could improve the heat transfer performance of scCO2. Moreover, on the same area of the fracture, the temperature of the fracture wall was found to be always higher compared to that of scCO2; much similar to the water behavior and the OHTC of scCO2 increased with the increase in the injection flow rate. Surface morphology of the fracture significantly influenced the LHTC distribution of scCO2, and LHTC roughly exhibited a negative correlation with the local waviness of fracture. This was pronounced at the sunken positions of the fracture surface, which exhibited significantly larger LHTCs compared to the prominent positions. The heat transfer characteristics of CO2 were found to be closely related to its phase state. CO2 in the denser phase showed better heat transfer performance.

Effect of local waviness in confining walls and its amplitude on vortex shedding control of the flow past a circular cylinder

Numerical investigation of vortex shedding control and its suppression due to flow past a circular cylinder has been carried out starting from the Reynolds number 20 and upto the appearance of first instability in the wake. A technique “local waviness” is used in the confining walls for the effective control of shedding. The local waviness with crest near the cylinder wake eliminates vortex shedding with reduced drag (Deepakkumar et al., 2017). Effect of amplitude of local waviness on vortex shedding characteristics are systematically carried out and presented in this article. It is found that local waviness with amplitude A = 0.15D is an optimum value for effective vortex shedding suppression with reduced drag on the cylinder at Re = 200. As the amplitude of waviness increases, the wake size is reduced significantly as compared with plain wall confined cylinder. The presence of crest closer to the cylinder in the downstream generates a favorable pressure gradient and prevents flow separation at Reynolds number 20. The pressure drag is controlled significantly by the trough region in the waviness, whereas the crest region affects both pressure and frictional drag. Also, the appearance of first instability in the flow is identified for different amplitude of waviness.

Computational Study of Fluid Flow Characteristics past Circular Cylinder due to Confining Walls with Local Waviness

Flow past circular cylinder confined by walls with local waviness near the cylinder has been computed and the vortex shedding characteristics are studied at Reynolds number 200. The governing equations are solved using finite volume based CFD solver, ‘Ansys Fluent 15.0’. In the present study, flow fields have been computed with waviness placed at four different locations. The effect of the location of waviness on vortex formation and its shedding frequency has been closely captured and presented. The flow parameters such as drag, lift and Strouhal number are calculated using the field data obtained from computations. It has been observed that the vortex shedding is significantly controlled by changing the location of local waviness. Among the four different locations considered in the present study, the waviness located near the wake region effectively suppresses the shedding. Moreover, the inward projection of the waviness plays a vital role in vortex suppression. It is also observed this method of vortex suppression leads to increase in drag.

Distortion and its Control in Welding of Stainless Steel Structures - Case Studies

Distortion is a perennial problem faced by engineers engaged in welding fabrication. The shape change deformations and change in the dimensions that occur after welding is termed as distortion, leading to various undesirable consequences. So there exists a necessity to control distortion within limits. When distortion exceeds acceptable limits, correction of distortion after the complete fabrication results in major reworking operation that consumes both fabrication time and cost. Distortion control in complex structures has always been a challenge to fabrication engineers, dealing with stainless steels. To arrive at an appropriate control method, an in-depth analysis of the shape change deformation behavior of the component and adaptation of appropriate methods to control distortion are essential. In this study, two circular components made of stainless steel have been taken up for control of distortion. The first structure is the labyrinth used in hydro turbine assembly that consists of a ring type of flange made of martensitic stainless steel (ASTM grade A240 S41500) welded with a shell type web using grooved fillet welds. The size of the welded assembly is huge and the quantum of weld is very high leading to heavy distortion that often required to be corrected by way of weld build-up and subsequent machining. The second one is the vortex finder assembly which is a part of cyclone separator that is used to separate the fine particles of coal from coarse ones for use in the combustion chamber of typical Circulating Fluidised Bed Combustion (CFBC) boilers. This is again a cylindrical structure with three shells joined with three flanges and supported by stiffeners. The structure is made of special grade Austenitic stainless steel to withstand high temperature. In both the structures, most of joints are of Tee-joints with fillet welds. During fabrication of these assemblies, the angular tilt, local waviness and the diameter variation were the major issues. Correction after fabrication is not viable considering the configuration and shape of the component. This calls for control of distortion during fabrication itself. Towards this, a suitable welding procedure using an appropriate weld sequence was evolved after studying the weld details of the components. This weld sequence was implemented in-situ in actual components. During fabrication on-line monitoring was carried out and course corrections were provided. After implementation of the weld sequence, it was found that the distortion of the component could be reduced and contained well within the permissible limits. This made the extra rework redundant thus leading to a significant reduction in the cycle time of manufacture of the component. The details of the methodology adopted are described in this paper. Keywords: Labyrinth assembly, vortex finder assembly, stainless steel welding, distortion, T joint, grooved fillet weld, angular tilt, weld sequence.

Mid-spatial Frequency Error Identification of Precision Optical Surface Based on Empirical Mode Decomposition

Mid-spatial frequency surface error of optical lens is crucial to the performance of high-energy laser systems and high-resolution optical systems.Power spectrum density(PSD) is generally employed to evaluate mid-spatial frequency error of optical surface.PSD is based on Fourier transform which averages local characters to the whole space.And it gives a whole evaluation of mid-spatial frequency error of optical surface.It not only weakens characters but also loses location information of surface error.Abrasive processing,such as grinding and polishing,always introduces local waviness with time-varying frequency on optical lens surface,PSD fails for this situation.A new error separation method,which is based on empirical mode decomposition,is introduced in this paper in order to more accurately evaluate mid-spatial frequency error and guide compensation machining.Curve of optical surface is preliminary fitted and the difference between the origin data and the fitting curve is decomposed to a series of intrinsic mode functions(IMFs).Local waviness characters of optical lens surface and its frequency can be recognized from each IMF and the corresponding instantaneous frequency plot.All IMFs are divided into high-frequency group and mid-spatial frequency group by average of instantaneous frequency of each IMF considering with IMF characters.IMFs in the same group are added to acquire high-frequency error or mid-spatial frequency error of optical surface.The simulation and experimental results of optical surface with different machining methods are employed to validate the effectiveness and correctness of the method.

Effect of fiber waviness on the bending behavior of S-glass/epoxy composites

A study was conducted on the influence of localized ply waviness on the strength of uniaxial fiberglass composites subjected to three-point bending. A series of experimental three-point bending tests were performed to discover how wave geometry will affect the strength of these materials. It is shown that any waviness will decrease the strength, but this reduction is maximized by increased amplitude, deceased wavelength, and concave up waves as well as increased total specimen length. As much as 37% reduction in strength compared to a flat specimen is seen in the case of large concave up waves. The dominant failure mode for unidirectional wavy composites under bending was shown to be interlaminar shear, which in turn leads to microbuckling. Finally, a failure criterion is derived which can predict the load and location where failure will begin.

Effects of local fibre waviness on damage mechanisms and fatigue behaviour of biaxially loaded tube specimens

Damage development in and final failure process of glass fibre winding specimens during biaxial fatigue loading are investigated. The phenomena in nominally defect-free tubes and specimens exhibiting local fibre waviness in one layer are compared. A subset of wound tubes is analysed using non-destructive testing methods, i.e. air-coupled guided waves, thermography, optical fracture analysis by a high-speed camera, and discrete damage monitoring. Air-coupled guided waves are employed for detection of fibre waviness and for monitoring the failure progress initiated by this waviness. Stiffness degradation due to fatigue damage corresponds to a decline in guided wave velocity. Using infrared inspection, the fibre waviness can be detected in an early stage of fatigue life. Non-destructive evaluation reveals that initiation of final failure in the specimens is caused by local fibre waviness. Finally, the effect of local fibre waviness on the S–N curves of the specimens is illustrated.