Lamination Direction Research Articles

Determination of the size of the local region for efficient global/local modeling in a large composite structure under impact loading

Virtual testing of large composite structure requires multi-scale analysis techniques due to the involved high computational challenges. Global/local modeling is a possible solution in which the size of the local region is a key-aspect to approximate the solution with accuracy and efficiency; however no defined solution for the initial prediction for the size of the local region exists. In this study, wave propagation based analytical approach is proposed for an impacted laminated structure to estimate the size of the local region. Stress wave formulation and damping along the different directions of laminate can describe the shape and area of the local region. The speed for shear and flexural waves is determined along the fiber orientations and their damping characteristics are studied. Wave propagation is dependent on the mechanics of selected materials along with laminate layup and can be different in different directions, defining different shapes of the local region. The analytical approach is formulated and implemented using MATLAB code. It can figure out the distance traveled by the flexural wave front in the in-plane directions of the laminated structure. A validation is performed from three examples for the contact force and damaged area predictions. Then the study is extended for a 3D leading edge of a wing under bird striking for finding the dynamic response. The prediction is compared with the experimental results obtained in our Lab. It is shown that the current approach can not only reduce the computational effort by predicting the contact force and damaged area for high as well low speed impact scenarios, but with satisfied accuracy and efficiency. The approach can be a base for defining the size of the local area in the Global/Local modeling methodology for large composite structures. The technique can also be employed to find out the shape of the affected and damaged area in the composite structure by implementing the methodology at different angles from the impact center.

Observation of vector solitary waves in soft laminates using a finite-volume method

Soft materials with engineered microstructure support nonlinear waves which can be harnessed for various applications, from signal communication to impact mitigation. Such waves are governed by nonlinear coupled differential equations whose analytical solution is seldom trackable, hence emerges the need for suitable numerical solvers. Based on a finite-volume method in one space dimension, we here develop a designated scheme for nonlinear waves with two coupled components that propagate in soft laminates. We apply our scheme to a periodic laminate made of two alternating compressible Gent layers, and consider two cases. In one case, we analyze a motion whose component along the lamination direction is coupled to a component in the layers plane, and discover vector solitary waves in a continuum medium. In the second case, we analyze a motion with two coupled components in the plane of the layers, and observe a train of linearly polarized solitary waves, followed by a single circularly polarized wave. The framework we developed offers a platform for further investigation of these waves and their extension to higher dimensional problems.

Application of unlimited and limited anisotropic core compression results for wellbore stability calculations

The study touches upon the issue of wellbore stability in wells drilled in anisotropic rocks. Initial data for solving this task is the results of anisotropic core samples testing for unlimited and limited compression taken from one section of the whole core and drilled in different directions. These data are taken from the works of foreign authors that are collected and presented in [1]. The problem of wellbore stability drilled in multi-layer highly anisotropic rocks is solved by applying a strength criterion that includes stress tensor components and the angle between the normal line to the slip area and the direction of lamination. Given that the values of the elastic modulus and Poisson’s ratio for the anisotropic rocks under consideration in the main directions of anisotropy differ insignificantly, the stress distribution around the wellbore is accepted without taking into account the anisotropy of the elastic properties. It is believed that strength anisotropy is the cause of rock destruction. Thus, the components of the stress tensor are determined using the superposition method by summing the solutions of the classical Kirsch and Lame problems.

On the micromechanics of deep material networks

We investigate deep material networks (DMNs), recently introduced by Liu et al. [Comput. Method Appl. M., vol. 345, pp. 1138–1168, 2019], from the viewpoint of classical micromechanics at small strains. We aim to establish the basic micromechanical principles of deep material networks, shed light on the characteristics of the building blocks and introduce a simple, robust and fast solution technique for inelastic deep material networks.In their original formulation, DMNs are solely trained by linear elastic data, but applied to nonlinear and inelastic problems with astonishing accuracy. We clarify this phenomenon theoretically by showing that, to first order in the strain rate, the effective inelastic behavior of composite materials is determined by linear elastic localization. Our argumentation applies to arbitrary microstructures comprising nonlinear generalized standard materials at small strains. The main technical tool is a Volterra series approximation of the stress of a generalized standard material, which we adapt from nonlinear dynamical systems theory.Next, we establish that deep material networks inherit thermodynamic consistency and stress-strain monotonicity from their phases. These properties root in the definition of the DMN as a tree of hierarchical laminates and contrast with other applications of neural networks to the approximation of material laws, where consistency and monotonicity typically cannot be guaranteed far away from the training set.Last but not least, we introduce rotation-free DMNs with arbitrary directions of lamination and exploit a novel formulation, uniting the implementation of DMNs of arbitrary tree topology and multi-phase laminates, and apply our insights to microstructures of industrial complexity.

Electromagnetic performance analysis of flux-switching permanent magnet tubular machine with hybrid cores

The performance of traditional flux switching permanent magnet tubular machine (FSPMTM) are improved by using new material and structure in this paper. The existing silicon steel sheet making for all mover cores or part of stator cores are replaced by soft magnetic composite (SMC) cores, and the lamination direction of the silicon steel sheet in stator cores have be changed. The eddy current loss of the machine with hybrid cores will be reduced greatly as the magnetic flux will not pass through the silicon steel sheet vertically. In order to reduce the influence of end effect, the unequal stator width design method is proposed. With the new design, the symmetry of the permanent magnet flux linkage has been improved greatly and the cogging force caused by the end effect has been reduced. Both 2-D and 3-D finite element methods (FEM) are applied for the quantitative analysis.

Experimental Study on the Fabrication of 3D Microelectrodes for Electrochemical Micromachining

The use of three-dimensional (3D) microelectrodes to machine micro-cavities in electrochemical micromachining (ECMM) can greatly improve processing efficiency. The 3D microelectrodes that are difficult to fabricate by traditional methods can be prepared by laminated object manufacturing and vacuum thermal diffusion bonding (VTDB). However, the VTDB process is very time-consuming, resulting in a long preparation cycle. To solve this problem, the present study proposed an approach combining wire electrochemical micromachining (WECMM) with micro-electric resistance slip welding to fabricate 3D microelectrodes. The machining surface quality and dimensional accuracy of 2D microstructures under different WECMM conditions were investigated. Moreover, the effects of the welding parameters on the bonding quality were studied. The experimental results show that with a 6 V machining voltage, 1.33 μm/s feed rate, and 30 μm movement amplitude for the wire electrode, the machining gap was approximately 10 μm and the machining surface was flat when using a tungsten wire 8 μm in diameter to machine 30 μm thick #304 stainless steel foils by WECMM. Under a 0.3 V welding voltage, 0.2 MPa welding pressure, 20 ms welding time and 160 times slip welding discharge, the error in 3D microelectrodes in lamination direction was smaller than 3 μm. Based on the proposed approach, two typical 3D microelectrodes were successfully fabricated and subsequently applied in ECMM to machine 3D micro-cavities in nickel plates.

A New 3D Method for Reactor Core Vibration Based on Silicon Steel Lamination Rules and Application in UHV Shunt Reactors

A new three-dimensional (3D) analysis method is proposed as the existing two-dimensional (2D) method has low accuracy in analysing the vibration characteristics of oil-immersed shunt reactors, such as ultrahigh-voltage (UHV) shunt reactors. First of all, a set of 3D laminated coordinate systems was defined based on silicon steel lamination rules, in which the anisotropy of magnetic properties for laminated silicon steel in the rolling direction (RD), the transverse direction (TD), and the lamination direction (LD) were considered. Then, the mapping between laminated coordinate systems and space rectangular coordinate system was established to unify the parameters in different laminated coordinate systems. With the mapping, the anisotropy of the magnetic properties in the laminated coordinate systems was transformed into a rectangular coordinate system. Next, two sets of comparative studies between the new 3D method and the traditional 2D method were carried out, which show that the 3D method has high precision and a wide application range. Finally, the relationship between air gap number and core vibration of UHV shunt reactors was studied by the new 3D method. The results show that, as the number of air gaps increases, the magnetic flux density and the total force area of Maxwell force are increased, resulting in the intensification of core vibration. The conclusions of this paper are helpful for the design of large oil-immersed reactors.

Electrical resistivity response of unidirectional thin-ply carbon fiber reinforced polymers

In this study, we investigate the effects of the thin-ply on electrical resistivity and its response to the tensile loading of carbon fiber reinforced polymers (CFRPs). Our results show that the resistivity in the thickness direction of the unidirectional laminate (UDL) made from thin-ply rises linearly at a small rate with the increase of the load until the load reaches 77.7% of the tensile strength calculated with the mix law of the composites, which is 1.43 times that of the thick-ply UDL. For thick-ply UDL, such linear response presents two phases. The resistivity increases at a small rate in the first stage in which the maximum load is low. The rate increased in the second stage is twice that of the first stage, and the threshold of the load corresponding to the stage is 54.4% of the tensile strength calculated with the mix law. It was found that the electrical resistivity of the CFRP in the thickness direction was related to the morphology of the resin-rich zone in between two plies and is less dependent of fiber volume fraction if fiber volume fraction is greater than a critical value in the composites.

The influence of the rolling direction on the elastic characteristics of the bending samples

There are a number of factors influencing the bending process such as: the rolling direction of the blank; the minimum bend radius of the piece; the radii of the bending plate (of the mold); the play between the die and the punch, the recoverable strain of the piece after bending. The paper presents the experimental results regarding the influence of the lamination direction on the rheological behaviour of the cold bending parts, using the Lloyd LS100 Plus universal machine and the Nexygen Plus program. Thus, two categories of samples were analyzed: some being cutted off in the direction of rolling of the sheet at which the bending occurred on an axis perpendicular to the direction of rolling and others cutted on cross direction of rolling, the bending being produced along the axis parallel to the rolling direction. As an elasto-plastic process, after the loading process during experiment, the samples recorded an elastic strain recovery due to the kinetic energy stored during stresses. Thus, the recovered elastic deformation (springback) is more pronounced in the case of specimens cutted of in cross direction on the rolling fiber where the bending moment is produced in the direction parallel to the laminating fiber of materials.

Failure Observation of 3D-Printed Thrust Bearing Specimens with Inner Defects in Water Conditions

Additive manufacturing (AM) methods are developing and have become popular, but questions remain about the strength of parts made by this method. We have already investigated the effect of the lamination direction on the fractures in bearing specimens. In this study, we made inner defects in the 3D-printed bearing specimens and performed rolling contact fatigue (RCF) tests on this specimens immersed in a water bath in order to investigate the fracture of 3D printed bearings.

P‐136: Research of COP Film shrinkage on Flexible Touch Sensor Process

This paper mainly studied the influence of the preparation process conditions (temperature, lamination direction, film structures, etc.) on the shrinkage of COP (Cycio Olefins Polymer) film flexible touch sensor The temperature is the main influence factor of the shrinkage of COP film flexible touch sensor With the temperature increasing from 100 ° C 60 min to 130° C 60 min, the shrinkage factor increases from 0.07% to 0.39%. Also, the lamination direction has a great influence on the shrinkage of COP film. After 130° C 60 min baking, the shrinkage factor of TD (perpendicular to the direction of Lami) is 0.39%, while the shrinkage factor of MD is 0.43%. The shrinkage factor has 0.04% difference between the TD&MD. Meanwhile, the OC (organic coating) film and ITO thickness cause less than 0.01% shrinkage factor. Compared to the effects of temperature, this 0.01% shrinkage factor can be ignored. Therefore, in the flexible touch sensor process, temperature management is very important.

Monitoring of Multidirectional and Cure-Induced Strain in CFRP Laminates Using FBG Sensors

During the curing cycle, the residual stress has influence on cure-induced deformation for carbon fiber reinforced plastics (CFRP) laminates, which is highly susceptible to the ply design. Therefore, the change laws of strain and the effect of residual stress in CFRP laminates after curing, which is of great significance to ply design, were cleared by using the combining pattern of thermocouple and fibre Bragg grating (FBG) sensors. For the FBG sensors embedded with different directions in lay-up CFRP laminates, the temperature and strain in different directions of composite laminates were obtained in real-time. Monitoring results show that compared with strain in 45° direction, the carbon fibers (CF) act stronger to inhibit strain in 0° direction and weaker to inhibit strain in 90° direction of resin. After curing, the residual strain in 0° direction is tensile strain, and the residual strain in 45° direction and 90° direction are compressive strain. Meanwhile the value of residual strain in 90° direction is greater than that in 45° direction.

Influence of Fiber Volume Content on Thermal Conductivity in Transverse and Fiber Direction of Carbon Fiber-Reinforced Epoxy Laminates.

Thermal conductivity is an important material property for thermo-mechanical calculations, as mechanical properties strongly depend on the temperature and heat distribution in the manufactured parts. Although several suggestions for approximation formulae have been made, existing experimental data are rare and are not comparable due to different measurement methods. In addition, scarcely has the thermal conductivity in both the fiber direction and transverse direction been studied. The aim of the current research is to show the influence of carbon fiber volume content on the thermal conductivity of laminates. The values are then used to verify the micromechanical models used in the literature. A strong influence on the thermal conductivity could be determined. For the transverse thermal conductivity, the correlation was exponential; for the conductivity in the fiber direction, a linear correlation was found.

A Two-Dimensional Labile Aether Through Homogenization

Homogenization in linear elliptic problems usually assumes coercivity of the accompanying Dirichlet form. In linear elasticity, coercivity is not ensured through mere (strong) ellipticity so that the usual estimates that render homogenization meaningful break down unless stronger assumptions, like very strong ellipticity, are put into place. Here, we demonstrate that a L^2-type homogenization process can still be performed, very strong ellipticity notwithstanding, for a specific two-phase two dimensional problem whose significance derives from prior work establishing that one can lose strong ellipticity in such a setting, provided that homogenization turns out to be meaningful.A striking consequence is that, in an elasto-dynamic setting, some two-phase homogenized laminate may support plane wave propagation in the direction of lamination on a bounded domain with Dirichlet boundary conditions, a possibility which does not exist for the associated two-phase microstructure at a fixed scale. Also, that material blocks longitudinal waves in the direction of lamination, thereby acting as a two-dimensional aether in the sense of e.g. Cauchy.

Effect of Capillary Induced Flow on CO2 Residual Trapping

Residual trapping is one of the main mechanisms for immobilizing CO2 after the injection phase of a geological sequestration project. Residual trapping results from capillary forces at the pore scale which lead to snap-off and bypass of CO2. For heterogeneous systems, there is, in addition to the capillary potential at the pore scale, a capillary potential at the scale of the heterogeneity which will result in capillary induced flows and trapping. We investigate the impact of capillary induced flow on multiphase flow behavior and its implications for residual trapping of CO2 by performing experimental and numerical core-flood tests. Results show that the magnitude and spatial extent of the heterogeneity impact the local capillary forces and, therefore, the capillary pressure and saturation distribution. In certain cases, even in the capillary dominated regime, local capillary disequilibrium was observed, leading to capillary induced flow when the system relaxed. This work shows that for layered rock with small variations in permeability, laminations direction has minimal impact on the local capillary forces and does not effect the residual trapping potential. Further research is needed to investigate if lamination direction impacts the residual trapping potential in the case of layered rocks with larger variations in permeability.

Laboratory Investigation of Dynamic Strain Development in Sandstone and Carbonate Rocks Under Diametrical Compression Using Digital-Image Correlation

Summary Understanding the mechanical behavior (compression, shear, or tension) of rocks plays an important role in wellbore-stability design and hydraulic-fracturing optimization. Among rock mechanical properties, strain is a critical parameter describing rock deformation under stress with respect to its original condition, yet conventional methods for strain measurement have several deficiencies. In this paper, we analyze the application of the optical method digital-image correlation (DIC) to provide detailed information regarding fracture patterns and dynamic strain development under Brazilian testing conditions. The effects of porosity, rock type, lamination, and saturation (freshwater and brine) on indirect tensile strength are also discussed. To examine the effect of rock type, 60 samples of sandstone (Parker, Nugget, and Berea) and carbonate rocks (Winterset Limestone, Silurian Dolomite, Edwards Brown Carbonate, and Austin Chalk) were tested under dry and saturated conditions with regard to lamination angle in laminated samples. A photogrammetry system was used to monitor the samples in a noncontact manner while conducting the indirect tensile experiment. DIC depends on the photogrammetry system, which helps to visualize and examine rock-fracture patterns from the recorded images of the rock before and after deformation by assessing the strain development in samples. The experimental results show the following. Average tensile strength declines with increasing porosity for homogeneous, laminated, and heterogeneous rock specimens. Lower tensile strengths are observed in carbonate-rock samples compared with sandstones, except for Silurian Dolomite. Saturation reduces rock strength; for homogeneous samples, the highest strength decline (28%) was observed in Berea Sandstone, whereas the largest decrease (65%) for heterogeneous samples was observed in fully heterogeneous Edwards Brown Carbonate samples. Increase of lamination angle (from 0 to 90°) affects the tensile strength. Average tensile strength observed for the Parker and Nugget Sandstones was greater in the direction perpendicular to the lamination direction (θ = 90°) compared with that of the parallel direction (θ = 0°). Fracture patterns examined for homogeneous rocks are nearly centrally propagated and relatively linear. Three different fracture patterns (central fracture, layer activation, and noncentral or mixed mode) were investigated for laminated and heterogeneous samples. Finally, DIC results illustrated the fracture creation and propagation with consistent strain mapping. The homogeneous samples produced a uniform fracture strain until the diametrical split, where the laminated samples were influenced by planes of weakness and fully heterogeneous anisotropic rocks produced winding and erratic fractures.

Numerical Modeling of Iron Loss Considering Laminated Structure and Excess Loss

In this paper, an excess loss modeling method of the laminated iron core is proposed. The 1-D single sheet silicon steel plate analysis is combined with the 3-D solid-core analysis to model the laminated structure. The modeling is improved by including the domain wall bowing due to pinning effect, which is considered as the main cause of excess loss. The domain wall bowing due to pinning is considered in the 1-D steel plate analysis because the excess loss generated by the flux density in the parallel direction of the stack is dominant compared with that in the perpendicular direction. In the 1-D analysis, an initial bowing flux distribution along the thickness direction of one lamination is introduced. The results of iron losses show that the hysteresis and eddy current losses vary with the flux and eddy current distribution in the laminated iron cores. Finally, the 1-D–3-D combined method is applied to a single-phase reactor; the magnetic flux and eddy current distribution are analyzed in detail. The eddy currents generated by the parallel flux are increased, hence, the skin effect of flux in the parallel direction of laminations is enhanced; thus, the hysteresis and eddy current losses are increased and the iron loss is increased by 8%.

Damage Mechanism Analysis of Carbon Fiber Composites under Compressive Load

Carbon fiber composite material with light weight, high strength, corrosion resistance and other characteristics of its impact damage mechanism is different from the traditional metal materials. In this paper, the quasi-static compression of carbon fiber composites was carried out by using a material testing machine to analyze the damage mechanism. The Hopkinson bar technology was used to test the dynamic mechanical properties. The damage mechanism of the carbon fiber composites under dynamic compressive loading was studied. Stress - Strain relationship of composites under Quasi - static and dynamic compressive load. It is found that the main failure mode of out-of-plane direction of carbon fiber composite laminates is brittle shear failure, while the in-plane failure mode shows the properties of brittle materials.

Macroscopic out-of-plane auxetic features of a laminated open-cell structure with in-plane negative Poisson’s ratios induced by bridging beam components

This paper presents the out-of-plane mechanism of a laminated open-cell structure that is exerted by a simple control of the geometric configuration. We propose two types of structural units that are assembled with beam and column members in a tetragonal system, and with the geometric difference between them being the presence of a reinforced beam. For the two unit cells, we develop finite element models according to a homogenization method and analyze the macroscopic linear and nonlinear elastic properties. The numerical results show that the cellular structure, which is bridged by additional beams, exhibits strong auxeticity with high negative values of Poisson’s ratio in the lamination direction, while retaining the in-plane negative Poisson’s ratios. We assess the sensitivity of the linear and nonlinear out-of-plane response to changes in the component geometry. Finally, we discuss the large deformation behaviors of the out-of-plane mechanisms to quantify the amounts of three-dimensional rotations of the internal components.

Effect of Needle Punching Process on a Chopped Strand Mat Composite with an Open Hole

The easiest and most reliable joining method is the mechanical joint with a bolt and nut or rivet. However, in the case of composite laminates, mechanical joint properties decrease because of lower interlaminar properties compared to in-plane properties around hole. This study investigated needle punching process with the aim of improving the mechanical properties in the thickness direction of fiber-reinforced plastic composite laminates with an open hole. Needle punching process was applied to glass fiber chopped strand matused as the reinforcement for the composite laminates. Open-hole tensile tests and observations of end cross-sections after the tests were performed. The tensile properties and fracture mechanism of the specimens subjected to needle punching process were investigated. In addition, characteristic distance (a parameter for evaluating resistance to fracture in open-hole tensile test specimens) was also calculated to examine the effects of needle punching process conditions on fracture toughness. Tensile strength was improved by more than 15% by needle punching process. However, when a certain needle punching density was exceeded, the mechanical properties worsened. In addition, characteristic distance increased with increasing needle punching density. Thus, these results suggest that there is an optimal needle punching density with respect to strength and characteristic distance.