Thickness Imperfections Research Articles

Contactless geometric and thickness imperfection measurement system for thin-walled structures

The load carrying capacity of thin-walled shell structures, when designed unstiffened, is highly sensitive to imperfections. In order to study the impact of geometric and thickness imperfections on the load carrying capacity of a thin-walled structure, these imperfections need to be measured. Therefore, in this paper, the development of a measurement system for measuring geometric and thickness imperfections of cylindrical structures with two laser sensors is introduced. Application, design and functionality of the measurement system are discussed in detail in this paper. In addition, the measurement of an unstiffened isotropic test specimen is evaluated. A measurement noise of 30 μm was detected and filtered using a median filter. The maximum measurement error is 68 μm. The imperfection magnitude for the PL1 shell structure lies in the order of w∈[-0.317mm,0.299mm]. The maximal thickness deviation is in the range of treal∈[0.155mm,0.226mm].

2-D Modeling of Dual-Gate MOSFET Devices Using Quintic Splines

This paper is the first known composition to demonstrate the application of quintic splines in the development of a dual-gate MOSFET model based on the well-known drift-diffusion system of differential equations used in semiconductor analysis. The techniques and methodologies presented advance the current state of the art in this particular area by implementing improved 2-D numerical techniques and avoiding the use of common accuracy reducing assumptions to decrease semiconductor equation complexity and execution time. This results in a model that is valid in all regions of operation, includes Non-Quasi static transient behavior, accounts for short channel effects, and allows researchers to predict the real world manufacturing effects of gate oxide thickness imperfections and applied gate voltage disparities. Model validation was accomplished by comparing simulation results to previously published experimental data for long and short channel devices as well as data generated using an established commercial product. In addition, a subsequent paper submission is planned to demonstrate the application of this modeling method in determining frequency response for simple CMOS circuits.

Buckling load prediction of grid-stiffened composite cylindrical shells using the vibration correlation technique

The vibration correlation technique (VCT) is one of the most important nondestructive methods to calculate the buckling load of imperfection sensitivity in thin-walled structures. VCT is widely used for beam and plate structures, but the technique is still under development for thin-walled shells. In this paper, an experimental and numerical validation of VCT approach was presented and discussed for the prediction of the buckling load of the grid-stiffened composite cylindrical shells loaded in compression. From the experimental point of view, three specimens were fabricated using a new silicone rubber mold, and specially-designed filament winding setup. The modal behavior of the grid-stiffened composite cylindrical shells was investigated by exciting the structures using modal hammer method in different applied compression load. Then, the variation of the first natural frequency of vibration with the applied compressive load was measured up to buckling during testing. Furthermore, a series of Finite Element Models (FEMs), including nonlinear effects such as geometric and thickness imperfection, are carried out in order to characterize the variation of the natural frequencies of vibration with the applied load and also compare it with the experimental results. Finally, the buckling test was performed to validate the experimental and numerical results of VCT approach. The results showed that the difference between the predicted buckling load using the VCT approach on the experimental results and numerical results with an experimental buckling load is 3.1% and 5.0%, respectively. Also, the current VCT approach has a very good correlation for grid-stiffened composite cylindrical shells when the maximum applied load is higher than 68% of the experimental buckling load.

Material hardening of a high ductility aluminum alloy from a bulge test

This study employs the hydraulic bulge test in combination with analysis to extract the stress–strain response of an anisotropic Al-6022-T43 sheet metal. Tests are performed in a facility with a 150 mm aperture and the deformation of the bulge is continuously monitored via 3D digital image correlation. The relatively high ductility of this alloy enabled the bulge to deform well past a pressure maximum, reaching a strain of 0.66 at rupture. After the pressure maximum, deformation localized around the apex and the strain profile acquired an increasingly conical shape. Anisotropy is modeled with Barlat's Yld04-3D yield function, calibrated through a set of independent experiments. The measured strains and curvatures at the apex are used in conjunction with membrane equilibrium and Yld04-3D to extract the material stress–strain response. The procedure adopted does not assume an equibiaxial state of stress or strain. A finite element model of the bulge test that includes the draw bead and clamping hardware is used to simulate the experiments. The model accurately reproduces all aspects of the experiment including the strain profile and its localization after the pressure maximum. A parametric study of the problem revealed that the particular anisotropy of the analyzed sheet did not influence the overall behavior of the bulge, but affects the onset of failure in the presence of MK-type thickness imperfections. The amount of material slipping over the draw bead during pressurization, however, is shown to have a more significant impact on the bulge response and the extracted stress–strain response.

Propagation of phase transformation fronts in pseudoelastic NiTi tubes under uniaxial tension

Under tension a pseudoelastic NiTi tube traces a closed hysteresis with an upper stress plateau associated with transformation from the austenitic to the martensitic phase during loading, and the reverse with a lower stress plateau on unloading. The transformations induce multi-helical localization patterns of higher/lower strain that propagate as the two stress plateaus develop. The experiment is simulated numerically by implementing a recently developed constitutive model for the pseudoelastic behavior of NiTi in a finite element analysis using solid elements. The unstable behavior of the material is modeled by introducing softening that spans the two stress plateaus recorded in the structural response. Localized deformation of nearly 7% initiates from a small thickness imperfection at one end of the model and propagates via a multi-helical front with ten prongs symmetric about a plane passing through the imperfection and the center of the circular tube. The specimen initially unloads homogeneously, but reverts to a single helical band of lower strain, which broadens as it propagates along the length of the tube. A parametric study demonstrates that the shape of localization patterns is influenced by the type and location of the imperfection used to initiate instability, by the imposed boundary conditions, and to some degree by the strength of the softening modulus adopted.

Buckling of axially compressed CFRP cylinders with and without additional lateral load: Experimental and numerical investigation

Thin-walled structures are widely used in aerospace, offshore, civil, marine and other engineering industries. Buckling of such thin-walled imperfection sensitive structures is a very important phenomenon to be considered during their design phase. Existing design guidelines, being the most known the NASA SP-8007 for cylinders dated from the late 1960's are currently used in the aerospace industry and employ conservative lower-bound knock-down factors. These empirically based lower-bound methods do not include important mechanical properties of laminated composite materials, such as the stacking sequence. New design approaches that allow taking full advantage of composite materials are therefore required.This study deals with buckling experiments of axially compressed, unstiffened carbon fiber–reinforced polymer (CFRP) cylinders with and without an additional lateral load. Two geometrically identical cylinders with the same layup were designed, manufactured and tested. Before testing, the thickness of the cylinders was measured with ultrasonic inspection and the geometry was measured utilizing a 3D scanning system based on photogrammetry. During testing, a digital image correlation system was employed to monitor deformations, strain gage readings and load-shortening data was taken. Modelling of shape mid-surface and thickness imperfections as well as fiber volume fraction correction are included into the Finite Element Analysis (FEA) of the test structures, and the experimental results are compared against FEA results.

Collapse Analysis of Perforated Pipes Under External Pressure

This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 184946, “Collapse Analysis of Perforated Pipes Under External Pressure,” by K. BeltrÁn and T. Netto, Federal University of Rio de Janeiro, prepared for the 2017 SPE Latin American and Caribbean Mature Fields Symposium, Salvador, Bahia, Brazil, 15–16 March. The paper has not been peer reviewed. This work is a study of collapse pressure of perforated pipes to evaluate the effect of lateral perforations on the radial resistance of pipes under external pressure. These types of pipes represent a simple and economical technology widely used as sand-control meshes or perforated liners. Introduction One of the most common challenges to high flow rates in mature fields is the migration of sand to the well. High rates of oil production together with maximum sand retention is the optimal result. In accomplishing this complex goal, perforated pipes play a vital role because they are a simple and inexpensive application, and they are widely used in the industry. Failures of such pipes are directly related to the collapse resistance of a pipe weakened by the perforations. Such failures can occur because of the plugging of holes or changes in differential pressure. This study might contribute to future prediction of collapse pressures of perforated pipes without resorting to costly full-scale experiments. Methodology Development Geometric Properties. This study involves four intact and eight perforated specimens as study bodies. All of them were obtained from four pipes designated as T3, T4, T5, and T6. A special nomenclature was defined to identify each one with a sequence of letters and numbers. An explanation of this nomenclature is shown in Fig. 1. The geometrical properties were obtained by means of a physical mapping, taking 10 measurements in the longitudinal direction and five in the circumferential direction to calculate the average thickness, average diameter, and initial imperfections (ovalization and eccentricity) of each specimen. Material Properties. The mechanical properties were also determined for each specimen by means of traction tests on 18 proof bodies, including some in the longitudinal direction and others in the circumferential direction. After processing the results, the average curves and values for the mechanical properties for each tube were defined. Because of the remarkable differences in shape and behavior of the curves, an average curve was calculated also. The results of monotonic traction tests in the circumferential direction are shown in Table 4 of the complete paper, and the plots are shown in Figs. 3 and 4 of the complete paper.

A thermal forming limit prediction method considering material damage for 22MnB5 sheet

Hot stamping of high-strength steel is an innovative technology to achieve automobile lightweight and guarantee security simultaneously. However, the formability of high-strength steel is still limited at elevated temperatures by the evolution of void damage inside materials. Thus, the establishment of an efficient forming limit prediction method is urgently demanded. In the present work, the Gurson-Tvergaard-Needleman (GTN) model is extended by containing Hosford anisotropic yield criterion which can characterize void damage in normal anisotropic materials. The flow behavior of matrix material 22MnB5 at different forming temperatures is simulated by the modified Norton-Hoff hardening law. And the damage-related parameters are calibrated through FEM inverse analysis. Furthermore, the prediction method of forming limit combined with void damage is realized within the framework of the Marciniak and Kuczynski (M-K) model. Meanwhile, the high-temperature Nakazima test is conducted to obtain experimental thermal forming limit diagram (TFLD). The comparison of results by theoretical prediction and experimental test shows good consistency. Based on the proposed method, the effects of temperature, void damage, initial thickness imperfection, and anisotropy on the forming limit are analyzed. The formability improved with the increasing of deformation temperature but worse for other factors.

Epsilon-near-zero behavior from plasmonic Dirac point: Theory and realization using two-dimensional materials

The electromagnetic response of a two-dimensional metal embedded in a periodic array of a dielectric host can give rise to a plasmonic Dirac point that emulates Epsilon-Near-Zero (ENZ) behavior. This theoretical result is extremely sensitive to tructural features like periodicity of the dielectric medium and thickness imperfections. We propose that such a device can actually be realized by using graphene as the 2D metal and materials like the layered semiconducting transition-metal dichalcogenides or hexagonal boron nitride as the dielectric host. We propose a systematic approach, in terms of design characteristics, for constructing metamaterials with linear, elliptical and hyperbolic dispersion relations which produce ENZ behavior, normal or negative diffraction.

Influence of material models on theoretical forming limit diagram prediction for Ti–6Al–4V alloy under warm condition

Forming limit diagram (FLD) is an important performance index to describe the maximum limit of principal strains that can be sustained by sheet metals till to the onset of localized necking. It offers a convenient and useful tool to predict the forming limit in the sheet metal forming processes. In the present study, FLD has been determined experimentally for Ti–6Al–4V alloy at 400 °C by conducting a Nakazima test with specimens of different widths. Additionally, for theoretical FLD prediction, various anisotropic yield criteria (Barlat 1989, Barlat 1996, Hill 1993) and different hardening models viz., Hollomon power law (HPL), Johnson–Cook (JC), modified Zerilli–Armstrong (m-ZA), modified Arrhenius (m-Arr) models have been developed. Theoretical FLDs have been determined using Marciniak and Kuczynski (M–K) theory incorporating the developed yield criteria and constitutive models. It has been observed that the effect of yield model is more pronounced than the effect of constitutive model for theoretical FLDs prediction. However, the value of thickness imperfection factor (f0) is solely dependent on hardening model. Hill (1993) yield criterion is best suited for FLD prediction in the right hand side region. Moreover, Barlat (1989) yield criterion is best suited for FLD prediction in left hand side region. Therefore, the proposed hybrid FLD in combination with Barlat (1989) and Hill (1993) yield models with m-Arr hardening model is in the best agreement with experimental FLD.

Constant single-buckle imperfection principle to determine a lower bound for the buckling load of unstiffened composite cylinders under axial compression

Unstiffened cylindrical shells are very sensitive to geometric imperfections such as production-related deviations from the ideal geometry (conventional imperfections) as well as imperfect boundary conditions, material and wall thickness imperfections (non-conventional imperfections). The load carrying capability of unstiffened shells is reduced significantly by those imperfections. The NASA SP-8007 design guideline from 1968 is currently used for shell design. This guideline provides knock-down factors for the buckling loads and is based on experimental data of isotropic and orthotropic test specimen. Therefore the structural behavior of composite material is not considered adequately.Based on the single-perturbation load approach (SPLA), this paper introduces a new physical based approach, to determine a lower bound for the buckling load of unstiffened composite cylindrical shells with respect to conventional and non-conventional imperfections, the constant single-buckle imperfection (CSBI) principle. The CSBI principle is based on the theory of the metastability of the geometric imperfect cylindrical shell which is introduced within this paper. The results indicate that the CSBI principle has the potential to provide an improved shell design in order to reduce weight and cost of thin-walled shells.

Measurement and Characterization of the Initial Geometric Imperfections in High Strength U-ing, O-ing and Expanding Manufactured Steel Pipes

The geometric imperfections in high strength U-ing, O-ing and expanding (UOE) manufactured pipes are investigated in this paper using a high-resolution 3D surface scanner, and a reverse engineering and inspection software. The geometric analyses show that the initial imperfection patterns in the UOE manufactured pipes are not at all random, although the magnitudes of imperfections may vary across specimens. These patterns of outside radii and pipe wall thickness imperfections consistently appear along the length of the specimens regardless of their D/t ratios and manufacturer. The sources of these imperfections can potentially be traced back to the UOE manufacturing process.

Modified MK model combined with ductile fracture criterion and its application in warm hydroforming

A modified MK model combined with ductile fracture criterion (DFC-MK model) is proposed to compute the forming limit diagrams (FLDs) of 5A06-O aluminum alloy sheet at different temperatures. The material constant (C) of ductile fracture criterion and initial thickness imperfection parameter (f0) at various temperatures are determined by using a new computing method based on wide sheet bending test. The FLDs at 20 and 200 °C are calculated through the DFC-MK model. The DFC-MK model, which includes the influence of through-thickness normal stress, is written into the subroutine VUMAT embedded in Abaqus/Explicit. The cylindrical cup hydroforming tests are carried out to verify the model. The results show that compared with experimental observations, the predicted FLDs based on DFC-MK model are more accurate than the conventional MK model; the errors between the simulations and experiments in warm hydroforming are 8.23% at 20 °C and 9.24% at 200 °C, which verify the effectiveness of the proposed model.

Design and Manufacture of Conical Shell Structures Using Prepreg Laminates

The design and manufacture of unstiffened composite conical structures is very challenging, as the variation of the fiber orientations, lay-up and the geometry of the ply pieces have a significant influence on the thickness imperfections and ply angle deviations imprinted to the final part. This paper deals with the manufacture of laminated composite cones through the prepeg/autoclave process. The cones are designed to undergo repetitive buckling tests without accumulating permanent damage. The aim is to define a process that allows the control of fiber angle deviations and the removal of thickness imperfections generated from gaps and overlaps between ply pieces. Ultrasonic scan measurements are used to proof the effectiveness of the proposed method.

Experimental Waviness Evolution of Interstitial Free - IF Steel Sheet under Biaxial Stretching

The purpose of present study is to present experimental results and a mathematical model for the evolution of surface waviness parameters with plastic strain of Interstitial Free - IF steel sheet under uniaxial and biaxial stretching tests. Roughness and waviness are very important quality parameters to be evaluated in sheet metal forming. Various waviness profile parameters such as the arithmetic average waviness Wa, the total height peak-valley waviness Wt, maximum peak height Pp and maximum valley depth Pv were measured during uniaxial and biaxial tests. Tensile test specimens at 0º, 45º and 90º to the direction of rolling and Nakazima type specimens of IF steel were fabricated. After preparing the test specimens, incremental simple tensile and Nakazima biaxial tests with flat punch were performed to characterize the negative and positive quadrant of the Map of Principal Surface Limit Strains, MPLS, of IF steel sheet. Measurements of waviness parameters of the specimen surface at incremental plastic strain stages were performed at the same surface site. Also, during the uniaxial and biaxial tests, the following plastic strains were calculated from printed circular mesh at each incremental step: ε1 longitudinal major strain and ε2 transverse minor strain. From these data, curves of waviness parameters versus equivalent strain were plotted to obtain a phenomenological equation of 4th or 3rd degree polynomial type. Furthermore, the growth rates of Wa and Wt parameters with the equivalent plastic strain were assessed. From the growth rate curves, it was possible to verify how the sheet thickness imperfections evolves during straining, being possible to predict the influence of plastic strain on the waviness values of IF steel sheets. From the analysis of Wa and Wt growth rates during straining, it was possible to proposed a criteria for the onset of local necking or limit strains in the MPLS. The waviness parameters Wt is the best for characterizing the onset of local necking in sheet metal forming.

Improved stochastic methods for modelling imperfections for buckling analysis of composite cylindrical shells

Imperfection sensitive CFRP cylindrical shells are used in a variety of civil and aerospace applications and feature a large scatter in buckling load levels induced from imperfections introduced from their manufacture. Currently, there are no complete methods that can realistically simulate cylinders with a full spectrum of imperfection types for a complete diagnosis of possible buckling loads. This forces shell designers to utilise an outdated, inefficient and conservative design philosophy that is unsuitable for modern manufacturing methods and materials. Stochastic analyses can optimise and improve the robust design and reliability of such cylinders through accurate prediction of the range of conceivable buckling loads by realistic simulation of structural imperfections. Such imperfections include initial shell-wall geometric, thickness and material imperfections and non-uniform applied end-loads. A procedure which aims to improve the stochastic modelling of thickness and material imperfections in imperfection sensitive composite cylindrical shells is proposed. Monte-Carlo simulations of axially compressed cylinders are performed to show that the stochastic methods described here are able to capture the scatter introduced from the imperfections. The results show that the axial buckling load of the specific cylinder analysed here can be reduced to 29.5kN and increased to over 40kN from a perfect load of 38.2kN from material and thickness imperfections alone.

Experimental and numerical estimation of buckling load on unstiffened cylindrical shells using a vibration correlation technique

Nondestructive methods, to calculate the buckling load of imperfection sensitive thin-walled structures, are one of the most important techniques for the validation of new structures and numerical models of large scale aerospace structures. The vibration correlation technique (VCT) allows determining the buckling load for several types of structures without reaching the instability point, but this technique is still under development for thin-walled plates and shells.This paper presents and discusses an experimental and numerical validation of a novel approach, using the vibration correlation technique, for the prediction of realistic buckling loads on unstiffened cylindrical shells loaded in compression. From the experimental point of view, a batch of three composite laminated cylindrical shells are fabricated and loaded in compression up to buckling. An unsymmetric laminate is adopted in order to increase the sensitivity of the test structure to initial geometric imperfections. In order to characterize a relationship with the applied load, the first natural frequency of vibration and mode shape is measured during testing using a 3D laser scanner. The proposed vibration correlation technique allows one to predict the experimental buckling load with a very good approximation, without actually reaching the instability point. Furthermore, a series of numerical models, including non-linear effects such as initial geometric and thickness imperfection, are carried-out in order to characterize the variation of the natural frequencies of vibration with the applied load and compare the results with the experiment findings. Additional experimental tests are currently under development to further validate the proposed approach for metallic and balanced composite structures.

Prediction of forming limit diagram of AA7075-O aluminum alloy sheet based on modified M-K model

To accurately predict the forming limit diagram of AA7075-O aluminum alloy sheet,a modified M-K model was put forward based on the ductile fracture criterion and the traditional M-K model. By using the method which combined the uniaxial tension simulation with experiment,the history of stress-strain of the dangerous element was substituted into the C-L ductile fracture criterion which was implemented into Abaqus / Explicit to get the material constant. Based on the forming limit data obtained by the uniaxial tensile,the initial thickness imperfection in the modified M-K model was obtained by the method which was programed in MATLAB. At room temperature,the experimental forming limit data of AA7075-O aluminum alloy sheet were tested through the uniaxial tensile,wide plate bending and hydraulic bulging experiments. Meanwhile,the theoretical forming limit curves obtained by the modified M-K model and the traditional M-K model were computed respectively. By comparison,the modified M-K model is proved to be feasible and more accurate.

Analytical Study on the Buckling of Cylindrical Shells With Arbitrary Thickness Imperfections Under Axial Compression

This paper presents an analytical study on the buckling of axially compressed cylindrical shells with arbitrary thickness imperfections (nonaxisymmetric and axisymmetric). First, the basic governing partial differential equations, which consider thickness imperfections, are obtained. Second, a unified method that combines the perturbation method and Fourier series expansion is developed to derive buckling load, radial displacement and stress function, that are expressed by triple series in terms of thickness imperfection parameter and buckling modes up to arbitrary order. Third, two patterns of nonaxisymmetric thickness imperfections, which are modal and exponential, are, respectively, investigated. These results are absolutely new to literature. When modal thickness imperfection becomes axisymmetric, the buckling loads degenerate to the known results. In addition to the analytical investigation, analyses and comparisons are also carried out.

The single perturbation load approach applied to imperfection sensitive conical composite structures

The importance of taking into account geometric imperfections for cylindrical and conical thin-walled structures prone to buckling had been already recognized by the first authors dealing with new formulations. Nowadays, the analysts still use empirically based lower-bound methods such as the NASA SP-8007 guideline to calculate the required knock-down factors (KDFs), which does include important mechanical properties of laminated composite materials, such as the stacking sequence. New design approaches that allow taking full advantage of composite materials are required.The single perturbation load approach (SPLA), a new deterministic approach first proposed by Hühne, will be investigated with unstiffened composite conical structures varying the geometry, lamina and layup. The SPLA׳s capability for predicting KDF is compared with the NASA approach. The SPLA was applied to the geometrically perfect structures and to the structure with geometric imperfections of two types, mid-surface imperfections and thickness imperfections. The study contributes to the European Union (EU) project DESICOS, whose aim is to develop less conservative design guidelines for imperfection sensitive thin-walled structures.