Initial Waviness Research Articles

Failure analysis of unidirectional CFRP composites with the coupled effects of initial fibre waviness and voids under longitudinal compression

This research delves into the failure mechanisms exhibited by unidirectional Carbon Fiber Reinforced Polymer (CFRP) composites under longitudinal compression, while considering the interplay of three types of manufacturing-induced defects: initial waviness of fibres, void volume fraction, and void size. The study employs 3D high-fidelity intact representative volume element (RVE) models, incorporating the initial waviness of fibres and voids based on Micro-CT imaging. A novel algorithm is proposed to generate more accurate 3D void shapes, departing from conventional circular or triangular approximations. The results highlight the substantial influence of the initial waviness angle on the reduction of predicted compressive stiffness and strength. The volume and size of voids play a significant role in determining damage initiation within the composites. The failure mechanisms of the composite under the coupled effects of initial waviness of fibres and voids are discussed, exhibiting reasonable agreement with experimental observations.

Longitudinal elastic nonlinearity of composite material

It is known that the initial waviness of the fiber affects the stiffness characteristics and strength of the polymer composite material. The article presents a continuum model taking into account the nonlinearity of the longitudinal stiffness of the unidirectional composite. In this study, a finite element experiment was conducted to investigate the variations in the longitudinal stiffness of the composite material subjected to uniaxial compression. The experiment considered a range of different degree of fiber’s waviness to comprehensively examine the impact on the material's stiffness. Obtained results explain the difference in stiffness observed in fiber composites in the longitudinal direction under uniaxial tension and compression. Special constitutive relations proposed to model compressive stiffness reduction in longitudinal direction.

Waviness Affects Friction and Abrasive Wear

Abrasive wear can have a detrimental effect on machinery, especially in the mining and construction industries. To prolong machinery lifetime and cut down energy consumption, a thorough understanding of abrasive wear is essential: surface topography measurement and interpretation (including form, waviness, and roughness) are vitally important. However, the potentially crucial influence of surface topography intricacies on tribological behavior has been obscured since roughness and waviness are considered simple scalar quantities in most cases (e.g., roughness Ra and waviness Wt). In this work, the complete waviness profile of the sliding track was used to shed light on the influence of surface topography on abrasive wear. Bearing steel (100Cr6, AISI 52100) pins and disks were tribologically tested in a flat-on-flat contact with Al2O3-based slurries as interfacial medium. Using slurries with two different particle sizes, 5 and 13 μm, we found that friction fluctuates only with small abrasive particles (5-µm slurry) and relatively low waviness disks. It was found that even small surface deviations (albeit minimized and controlled for) can significantly increase the friction coefficient—up to 91%. Remarkably, not only are frictional fluctuations strongly correlated with the disk’s initial waviness profile, but these small fluctuations correlate with unevenly distributed high wear. These findings enhance our understanding of the friction wear structure and provide the basis for exploring how surfaces can be optimized for better tribological performance.Graphical

Development of a new in-situ rotating magnetorheological honing technique for fine finishing the inner cylindric surfaces

A new in-situ rotary magnetorheological honing (RMRH) approach has been developed in this study to fine-finish the machined inner surface of cylindric workpieces with increased productivity and dimensional accuracy. A single in-situ honing tool is used for performing both traditional as well as magnetorheological (MR) honing. The tool is fabricated based on the designed tool through magnetostatic analysis. In this work, the final MR finished surface is achieved up to 60 nm from the original machined surface roughness of 510 nm with the expense of 40 min of traditional honing and 60 min of MR finishing. Also, the great improvement in surface waviness is confirmed through the final surface waviness is achieved as 50 nm from the initial surface waviness of 1460 nm. The improvement in circularity is confirmed through the circularity test performed in this work. The improvement in surface texture has been analyzed through the scanning electron microscope images. As a result of the finishing capability of the currently designed in-situ tool, it is useful in a variety of industrial applications such as oil pipes, bearings, hydraulic cylinders, cylindrical molds, cylindrical barrels of injection molding machines, compressor bodies, valve bodies, etc.

A Novel Laser-Aided Machining and Polishing Process for Additive Manufacturing Materials with Multiple Endmill Emulating Scan Patterns

In additive manufacturing (AM), the surface roughness of the deposited parts remains significantly higher than the admissible range for most applications. Additionally, the surface topography of AM parts exhibits waviness profiles between tracks and layers. Therefore, post-processing is indispensable to improve surface quality. Laser-aided machining and polishing can be effective surface improvement processes that can be used due to their availability as the primary energy sources in many metal AM processes. While the initial roughness and waviness of the surface of most AM parts are very high, to achieve dimensional accuracy and minimize roughness, a high input energy density is required during machining and polishing processes although such high energy density may induce process defects and escalate the phenomenon of wavelength asperities. In this paper, we propose a systematic approach to eliminate waviness and reduce surface roughness with the combination of laser-aided machining, macro-polishing, and micro-polishing processes. While machining reduces the initial waviness, low energy density during polishing can minimize this further. The average roughness (Ra=1.11μm) achieved in this study with optimized process parameters for both machining and polishing demonstrates a greater than 97% reduction in roughness when compared to the as-built part.

Machinability of wire and arc additive manufactured components

Wire and Arc Additive Manufacturing (WAAM) aims to be a cost-effective and material-efficient process to produce medium and large-scale metal parts. Nevertheless, post-processing is still required due to the low quality of the as-deposited surface. With the objective to divulge the complex interaction between the welding and machining phenomena, which determines the final surface quality, this paper focuses on the machinability of WAAM parts through a comprehensive investigation on the key parameters of both additive and subtractive processes. The effect of the WAAM parameters on the as-deposited part characteristics (i.e., hardness, flatness deviation, wall thickness, and initial surface waviness) and machining process has been analyzed. Consequently, the first of its kind, a non-linear function that can predict the effect of welding and milling parameters on the final surface roughness, is presented. The complex interaction between the local (e.g., surface irregularities and hardness) and global (e.g., wall thickness) effects of welding heat input and the resulting impact on the machining stability is analyzed. For example, slow welding speed results in a soft and irregular surface that is not easy to machine. Still, at the same time, the slow speed increases the wall width that provides the essential damping to reduce the chatter during machining. The obtained results help understand the interactions between the WAAM and milling processes and further determine the optimal machining allowances and optimal process conditions.

Improvement strategy for edge waviness in roll bending process of corrugated sheet metals

This paper focuses on the corrugated thin-walled sheet metal in the roll bending process. The main defect that appears in corrugated panels subjected to high amounts of bending deformation is a wavy edge. Edge defects are caused by excessive longitudinal stress and strain near the edge of the plate, and local edge buckling may occur when some critical value of the bending radius is exceeded. This paper proposes two different approaches to avoid a wavy edge for a formed panel: excessive stress on the edge region is restrained by controlling the length of the cross-sectional end of the corrugated panel while considering the stress distribution, and the bending radius in each forming step is determined by considering the strain limit at which the initial edge waviness occurs to avoid excessive compression at particular steps. The experimental and numerical results indicated that the two proposed design strategies can minimize wavy edges in the formed shape.

Experimental Study on the Compressive Strengths of Woven Glass-Epoxy Composites

Reliable experimental data on compressive strength of composite material are important, especially for designing structures having dominant compressive stresses, such as bolted joints. Composite materials usually have lower compressive strengths compared to tensile strengths. Woven composites added more complications. Initial waviness in woven composites makes the compressive strengths even much lower. Therefore, in this paper, experimental study on the compressive strengths of woven composites will be presented. The experiments used standard ASTM D3410M-03. Woven glass-epoxy will be tested extensively. The specimens were produced using standard hand layup techniques. Several layup configurations were tested, namely (0/90)s, (0/90/±45)s and (±45)s. The results showed that woven glass-epoxy generated failure modes specifically found in compressive tests of composites, such as: fiber micro-buckling, fiber crushing and shear band-formation. It was also found that unlike in the case of tensile tests, the layup configurations did not affect the compressive strength values. It seems that the fiber orientation will not affect significantly the compressive strengths. The epoxy matrix played more dominant role on the compressive behavior of woven glass-epoxy composites.

Nonlinear viscous behavior of the tendon's fascicles from the homogenization of viscoelastic collagen fibers

The level of the fascicle including collagen fibers, membranes and interstitial fluid is quite representative of the structure of tendons. We presently investigate the effect of the rheology of the components of the tendon fascicles in a multiscale analysis starting from the level of individual collagen fibers organized into bundles, and then into fascicles at the next scale. A configuration of a collagen bundle is conceived in terms of a representative unit cell including a collagen fiber surrounded by a viscous membrane and a physiological fluid. The mixing of solid and fluid components gives rise to an equivalent stress-strain response in tensor format highlighting a long term memory, in addition to instantaneous viscous effects. The kernel function of the hereditary response is determined thanks to the theory of homogenization, relying on the solution of the localization problem over the selected unit cell. Homogenization is the principal factor responsible for both the relaxation phenomena and the nonlinearity due to recruitment of fibrils observed at the fascicle level, although none of the components present at the lower scales is endowed with these properties. The nature of the matrix surrounding the collagen fiber – described as either viscous solid or a biological fluid - is shown to strongly influence the transverse response, but it has a weaker influence on the tensile response of fascicles. The initial waviness and progressive recruitment of the collagen fibers under the effect of the local strain has been integrated in the expression of the elastic and viscous stresses at the scale of the collagen fiber bundle, allowing simulating the nonlinear response of a fascicle. The computed response is able to reproduce the measured physiological response of a real tendon to a uniaxial tensile test for a proper choice of the parameters of the recruitment statistical function.

A three-dimensional micro-mechanical model for predicting the layer longitudinal compression strength of composite laminates

A three-dimensional micro-mechanical model for predicting the compressive strength of composite laminates is presented in this paper. The effect of initial misalignment of fiber angle on the compressive strength of fibrous composites is investigated. The compressive strength of fibrous composites is estimated using the actual initial misalignment of fibers in the rotated plane. The initial misalignment angles in both directions are defined as a curve in the form of a cosine function. Equilibrium equations are then derived for a Representative Volume Element (RVE) along the axis of the fibers using total potential energy principle. Minimization of the total potential energy with respect to the amplitudes defined by the initial waviness function of the fibers yields a formula used to define the maximum compressive strength of fibrous composite materials. The formula obtained in this paper is used to study continuous fiber/polymer matrix composites. The results obtained by the model presented in this paper are in a good agreement with experimental data obtained from compression tests on [±60°/0°] specimens and theoretical results available in the literature.

Experimental investigation of kink initiation and kink band formation in unidirectional glass fiber-reinforced polymer specimens

The failure mechanism of non-slender glass fiber-reinforced epoxy prismatic specimens subjected to axial compression and different temperatures was investigated. Digital image correlation was used to map and derive the failure modes. The failure mode changed from splitting failure at ambient temperature to kinking at the onset of the glass transition temperature. The kink initiation mechanism could be clearly observed. Based on the initial waviness of the fibers, the wave amplitude disproportionally increased at one specific location up to fiber microbuckling and surrounding matrix failure; the wavelength of the initial imperfection was thereby maintained. The kink band then rapidly propagated through alternating horizontal and inclined segments leading to an overall inclined kink band of 31° on average. The kink band width doubled from around three to six times the average wavelength of the initial imperfection.

Line-edge roughness increase due to wiggling enhanced by initial pattern waviness

To clarify whether pattern waviness due to line-edge-roughness enhances wiggling, distortion of straight and wavy patterns was numerically analyzed by the three-dimensional (3D) elastic finite element method. Wiggling occurs only in wavy patterns but not in straight patterns at a stress or aspect ratio much lower than their buckling thresholds. More severe wiggling occurs when the wavelength of initial waviness approaches a value that is 3.3 times the pattern height. These phenomena were experimentally confirmed in the etching of amorphous carbon with a SiON mask. We consider that precise etching without wiggling is achieved by the elimination of the original line-edge roughness and the reduction in mechanical stress in an underlying film to which the pattern is transferred.

Experimental study on the effect of varying focal offset distance on laser micropolished surfaces

Laser micropolishing (LμP) is an innovative part-finishing process that reduces machining roughness by melting a thin layer of material on the micromilled surface using a focused laser beam. The quality of the final polished surface is dependent upon the part material, initial surface topography and roughness, and the energy density of the beam. The focal offset distance (FOD) is one critical parameter that controls the amount of energy delivered to the workpiece. The impact of varying the FOD on final laser-polished surface quality is investigated by performing a series of experiments on carefully prepared AISI H13 test samples with known initial surface roughness and waviness due to the milled track periodicity. Three well-defined polishing regimes were observed when adjusting the FOD for a Q-switched Nd/YAG LμP system between 1.3 and 2.9 mm. Given the same initial micromilled surface geometry, each LμP regime (i.e., short FOD, 2.2 mm; and intermediate FOD) reduced the surface roughness and periodic waviness in a distinct manner. For a micromilled sample with a 33-μm periodicity, the LμP with FOD of >2.2 mm was determined to be the most effective regime by improving surface quality by 39.7 %. The affects of repetitive exposure to the beam and increasing the applied laser power on improving surface quality are also investigated for the 3 LμP regimes.

Influence of pre-strain on the formability of 2024 aluminium alloy

Present work investigates the influence of pre-strain on the limiting strains in sheet metal forming, using the strain gradient evolution model that predict the onset of local necking from initial thickness imperfections, roughness waviness and thickness gauge. The theoretical analysis is compared with the experimental results for fully annealed and three pre-strain levels of 4%, 8% and 12% in 2024 aluminium alloy sheet with thickness of 2.5 mm presented by Leacock et al. at ESAFORM 2008. The effect of strain and strain rate hardening behaviour, pre-strain and anisotropy parameters in material formability are analyzed. The experimental forming limit curves indicate an immediate drop in the limiting strains in the pre-strained specimen when compared with the full annealed condition material as expected from the theoretical prediction by a new model. Other relevant aspects of the new approach to modeling FLC are also discussed.

Micromechanics and macromechanics of carbon nanotube-enhanced elastomers

The effects of carbon nanotubes on the mechanical behavior of elastomeric materials is investigated. The large deformation uniaxial tension and uniaxial compression stress–strain behaviors of a representative elastomer are first presented. This elastomer is then reinforced with multi-wall carbon nanotubes (MWNTs) and the influence of weight fraction of MWNTs on the large deformation behavior of the resulting composite is quantified. The initial stiffness and subsequent strain-induced stiffening at large strains are both found to increase with MWNT content. The MWNTs are also found to increase both the tensile strength and the tensile stretch at break. A systematic approach for reducing the experimental data to isolate the MWNT contribution to the strain energy of the composite is presented. A constitutive model for the large strain deformation behavior of MWNT-elastomer composites is then developed. The effects of carbon nanotubes are modeled via a constitutive element which tracks the stretching and rotation of a distribution of wavy carbon nanotubes. The MWNT strain energy contribution is due to the bending/unbending of the initial waviness and provides the increase in initial stiffness as well as the retention and further enhancement of the increase in stiffness with large strains. The model is shown to track the stretching and rotation of the CNTs with macroscopic strain as well as predict the dependence of the macroscopic stress–strain behavior on the MWNT content for both uniaxial tension and uniaxial compression.

Resonant and Stationary Waves in Rotating Disks

The analytical conditions for resonant and stationary waves in rotating disks are presented. These conditions are derived from a nonlinear plate theory pertaining to initial configurations and are applicable to rotating disks with initial waviness and/or undergoing large- amplitude displacements. The rotational speeds at which the resonant and stationary waves occur for a 3.5-inch diameter computer memory disk are computed. The resonant waves for linear and nonlinear, rotating disks are simulated numerically. It is found that some disk modes exhibit a hardening effect under which the rotational speeds for the resonant and stationary waves increase with increasing wave amplitude, while other modes experience a softening effect with those rotational speeds decreasing with increasing wave amplitude. The rotating-disk resonant spectrum presented in this paper is relevant to the disk drive industry for determining the range of operational rotation speed.

Nonlinear Vibration of Rotating Thin Disks

The response and natural frequencies for the linear and nonlinear vibrations of rotating disks are given analytically through the new plate theory proposed by Luo in 1999. The results for the nonlinear vibration can reduce to the ones for the linear vibration when the nonlinear effects vanish and for the von Karman model when the nonlinear effects are modified. They are applicable to disks experiencing large-amplitude displacement or initial flatness and waviness. The natural frequencies for symmetric and asymmetric responses of a 3.5-inch diameter computer memory disk as an example are predicted through the linear theory, the von Karman theory and the new plate theory. The hardening of rotating disks occurs when nodal-diameter numbers are small and the softening of rotating disks occurs when nodal-diameter numbers become larger. The critical speeds of the softening disks decrease with increasing deflection amplitudes. [S0739-3717(00)02004-3]

Towards a numerical model of the compressive strength for long fibre composites

The compressive failure of long fibre composites is tackled as a structural instability that is initiated by plastic microbuckling. A homogenised model is proposed to take into account the fibre initial waviness, the non-linear matrix behaviour and some structural effects. The problem is formulated at the ply scale by using a two-scale displacement field and a specific finite element is developed to reduce the extent of computations. This numerical tool permits us to rapidly determine the failure of various unidirectional ply configurations by use of a maximum load criterion. The results establish the influence of some structural parameters on the compressive failure strains, as has been observed in related experiments. They also explain the high compressive strength achieved under flexural loading.

Nonlinear effects in the extension of an elastic space containing a wavy layer inclusion

The two-dimensional problem of extension of an infinite isotropic elastic space (the matrix) containing an infinite, solitary, elastic, periodically wavy layer inclusion, having both bending and axial rigidities, is considered. Geometric nonlinearity of the layer and the matrix are taken into account as well as physical nonlinearity of the matrix material. A general procedure for an arbitrary periodic inclusion is developed. Explicit analytical solutions for a typical case of a cosinusoidal inclusion having small initial waviness are presented and are found to depend solely on parameters defined by stiffness and thickness ratios of the matrix/inclusion system. Numerical results describing the deformation of the layer and the stress field in the matrix are presented for a wide range of the matrix/inclusion parameters. It is shown that within the range of small to moderate strains physical nonlinearity can have significant influence on the behavior and be a controlling factor in possible modes of failure, namely by delamination or crack initiation in the matrix.

Nonlinear behavior of wavy composites under tension

A composite structure consisting of doubly periodic moderately wavy layers under tension is considered. The periodic cell of the composite is represented by two layers of different materials, but having the same arbitrary initial shape. As opposed to theories with full homogenization, the thickness of the periodic cell with respect to its length is not assumed to approach zero in the analysis. The influence of this structural parameter is shown to be especially significant if the material of one of the layers is much weaker than the other. Using a geometrical nonlinear Cosserat rod model to describe the layers, we take into account extension flexure and shear deformation in the layers. The problem is reduced to a boundary value problem for a scalar nonlinear ODE of second order for the rotational degree of freedom. The determination of the deformed shape of the layers, as well as the relation between the elongation of the periodic cell and the applied tension force is then reduced to nonlinear quadratures. For the case of small initial waviness, an analytical solution is obtained for an arbitrary initial shape of the layers. For moderate initial waviness numerical results are presented relating stress, strain and amplitude of waviness. The influence of material and structural parameters is investigated and discussed.