The objective of this study is to evaluate the effect of a CFRP composite layer on the buckling behavior of metallic cylindrical shells. To enhance the bearing capacity of steel shells, classical solutions consider internal or external metallic stiffeners (stringers and/or rings) welded or riveted to the shell. Here, an external skin of composite material which wraps the whole metallic skin of the shell is studied. To be valid for metallic shells structures (storage tanks like silos) as well as for metal pipes (gas or oil pipeline), the procedure for setting up and implementing the composite must be simple. The recommended solution is therefore tested through experimental tests to find their limits and the configuration of optimal behavior. A consistent enhancement of bearing capacity is observed. This experimental base serves also to consolidate a numerical model which corroborates the experimental results. The good correlation between experimental and numerical results is confirmed for the whole loading process, for unstiffened and stiffened shells. For metallic unstiffened shell, an adequacy between experiment and simulation is noticed in the mainly membrane precritical behavior, during the buckling initiation characterized by the boundary layer problem corresponding to axisymmetric wavelength appearance near boundaries and in the postcritical domain associated to localization of the buckling mode at one extremity of the shell. For stiffened configuration, the enhancement of the bearing capacity of the shell is correctly gauged; this confirms the possibility to use finite element simulation for the design.
Metallic shells structures are particularly sensitive to buckling or geometric instability. The design, based on the initial geometry, takes into account possible initial geometrical imperfections through knockdown factors. However, this initial configuration can suddenly or gradually evolve over time conducting to a no conservatism of the initial design. During the functioning, new shape defects can appear induced by accidental overloads or creep; also local corrosion due to severe environmental attacks can affect the material conducting to a decrease of the shell thickness. This can lead to diminution of the structure’s lifetime. Furthermore, sometimes, due to the evolution of design rules that impose higher safety margins, for example, a new seismic design requirement by Eurocode 8 [
The composite is a textile of carbon fibers oriented at 90° in accordance with ISO 7211 standard; 70% of the fibers are in the warp direction, and 30% in the weft direction. For the composite carbon reinforced polymer layer, an epoxy resin with two EPONAL 380 components, serves as a matrix. The CFRP is a dry strip applied on a wet resin layer; setting up is manual (Figures
Bonding of CFRP.
(a) Tension: test setup and specimen; (b) compression: test setup.
For composite material characterization, specimens consisting of 1 to 4 composite layers are cut from laminated plates made under the same thermal and hydric conditions as the composite using for the shells reinforcement. The specimen geometry is defined according to the European standard NF EN 527-4.1997.
Two campaigns of classic uniaxial tests were conducted (six tests per configuration: the warp or weft direction and per loading mode: tension or compression). These tests allowed us to confirm the orthotropic elastic character of the composite until the ultimate failure. For certain tensile tests, localized failures of fibers are observed before reaching the ultimate stress. In the optimum direction of composite, an average ultimate stress of 1400 MPa is obtained, and local fibers failures appear systematically beyond a stress of about 800 MPa. Variations between tensile tests are low, below 10% for the elastic modulus in the warp and weft direction. For ultimate stress, the values are widely scattered in the case of samples having only one CFRP layer. This dispersion is less in the case of the specimens having more than two layers of CFRP. Table
Characterization of CFRP composite.
Tension | Compression | |||||
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Modulus | Average ultimate stress | Ultimate strain | Modulus | Average ultimate stress | Ultimate strain | |
Warp direction |
|
|
|
|
|
|
104700 | 1440 | 1.46 | 11400 | 365 | 2.65 | |
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Weft direction |
|
|
|
|
|
|
44700 | 290 | 0.90 | 12000 | 280 | 2.36 | |
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45° direction | — | — | — |
|
— | — |
— | — | — | 5645 | — | — |
The compression behavior is very different from that in tension. The compression tests are very difficult to achieve because of the buckling phenomenon and microbuckling or delamination. For one layer under the compression, the modulus is almost that of the resin. However, when the layers number increases, the compression modulus increases which means that the fibers have a significant contribution. In Table
The mild steel cylindrical shells’ geometrical parameters are defined in Figure
(a) Geometry characteristics of specimens tested; (b) boundary conditions (simply supported).
Tensile curve and mean characteristics of mild steel.
The study of the buckling of the unstrengthened shell allows us to confirm a progressive plastic buckling resulting by the appearance and grow of an axisymmetric wavelength (harmonic
Unstrengthened shell: (a) extensional axisymmetric mode (
In our test, the ovalization of the section develops also at the upper part of the shell at the level of the boundary section, knowing that the radial displacement at the boundary is not perfectly clamped. The mode 2, which appear as a second bifurcation during the softening part of the load deflection curve, as observed also for some tests and reported by Bardi and Kyriakides [
According to the provided cross-sectional dimension of the shell and yield stress (315 MPa) of the constitutive material, the axial yield capacity of the compressed cylinder was estimated as 522 kN and clearly shown in Figure
The setting up of the composite aims essentially for a gain on the bearing capacity. The objective is therefore to block or delay the onset and the evolution of the critical mode. The strengthening in the axial direction cannot lead to a substantial gain. Firstly, the compression stiffness of selected composite is low compared to the steel layer. Secondly, the progressive plastic buckling involves an important radial evolution of the displacement on zero mode or axisymmetric localized mode near the boundary. This kind of buckling mode known as “extensional modes,” conducts to an important circumferential strain and to an equivalent Von Mises stress equal to the yielding limit at the beginning of the buckling process and far from the stress corresponding to the yielding plateau (strain hardening part of the curve) for the final buckling or collapse of the shell. The optimum direction or warp direction is therefore positioned at the shell circumference to induce a confinement which will limit the radial expansion of the buckling mode and plastic strain.
The preliminary tests have permitted to identify the most critical parameters. The delamination of the interlayer and steel/composite essentially occurs when the compression load is applied directly to the composite reinforcement (in this case, the damage of the composite layer is immediate) (Figure
(a) Damage to the steel/composite interface; (b) interlayer delamination due to localized loading on CFRP; (c) null or insufficient covering conducts to inhibit “belt effect” of the CFRP layer.
The mechanical behavior of the shell strengthened by two CFRP layers can be characterized by three phases as described in Figure
Load-deflection curves and mechanical behavior of unstrengthened and strengthened configurations. (a) Series I. (b) Series II.
Load/displacement curves: effects of the number of layers. (a) Series I. (b) Series II.
The problem of steel/CFRP adhesion is one of the concerns in which this study wanted to answer. For the reinforcement to be effective, is it necessary to have the adhesion on the metal shell? Or is the contact enough, even if slip is permitted? The question is legitimate, because metal tanks or silos do not always have the same surface state. Mild steel, stainless steel, or aluminum does not have the same surface roughness. Moreover, a surface paint can completely change this roughness. Sometimes, the cleanliness of the surface, necessary to the development of the adhesion, is not guaranteed. In several cases, the presence of hydrocarbons or oil or even corrosion products can strongly affect the adhesion locally, and this imperfection can spread in time. Therefore, it seems essential to evaluate the contribution of the CFRP in the case where there is no adhesion. That’s why appropriate experimental tests dedicated to this configuration without adhesion were studied.
To gauge the adhesion effect of the reinforcement on the metal, two configurations were tested (only for Series II). For the first configuration, the reinforcement is applied directly on the steel, while for the second one, the presence of a plastic film prevents the bond of CFRP on the steel (Figure
Application of a plastic film on external surface of the metal shell.
Effect of adhesion for 1 and 2 CFRP layers—Series II.
Effect of adhesion for 3 and 4 CFRP layers—Series II.
After adjustment (Figure
Adjustment of postcritical behavior—Series II.
Numerical simulations are conducted with ABAQUS finite element code. The S8R shell element, based on Koiter-Sanders shell theory, is well adapted for thin or intermediate thick shells. The steel and the CFRP have been modelled by the multilayer S8R shell element. The multilayer shell type approach has been chosen to exclude the interface problems, as perfect bonding of the composite layer to the steel layer is considered and debonding or interface damage are excluded. The CFRP is modelled by an external 0.43 mm thickness layer, perfectly bonded to a 4 mm thick steel shell layer. For the case strengthened with several layers of CFRP, the layers number considered in the numerical model is equal to the one used in the experimental test. The perfect adhesion was also assumed between the CFRP layers. As Figure
The multilayer shell model.
The boundary conditions are the symmetry on both vertical edges; this choice is compatible with the expected buckling mode in the unstrengthened case or strengthened case with one or two layers (axisymmetric mode). In the case of the buckling with a nonaxisymmetric mode, this hypothesis remains valid. It is confirmed by a calculation with the antisymmetric conditions on one or both vertical edges. The shell base is clamped, as well as the upper part where only Uz (vertical displacement) is free. The incremental calculation is thus carried out in imposed displacement in order to be able to pass the limit point.
The constitutive law behavior of materials is defined by layer. For mild steel, an elastoplastic law with isotropic hardening was considered. Although the finite element model is based on a 2D mesh model, the updating of the thickness has been taken into account. This artifice is necessary in the case of the large deformations inherent to the critical behavior associated with progressive plastic buckling. The radial evolution of the axisymmetric bulge which traduces the progressive plastic buckling leads to circumferential strains about 5%. For the CFRP, an orthotropic elastic behavior was considered. Neither the ultimate stress nor the various damages (fibers ruptures) that precede the critical threshold or layer failure are considered here. The consideration of damage associated to fibers failure or layers delamination or failure will be the object of a further studies.
The numerical simulation confirms the buckling on axisymmetric mode or elephant foot mode. Axisymmetric wavelength develops at each end of the structure. In the initial linear phase, the behavior is classic with the “barrel effect” or Poisson effect; then the axisymmetric wave appears and evolves to the plastic hinge which corresponds to the limit point.
The correlation between experiment and simulation is quite good in terms of initial behavior (precritical), ultimate load (deviation is <1%), and critical mode (Figure
Unstrengthened shell—Series (I) comparison of experiment/simulation behavior and numerical buckling mode.
In the case of reinforcement with one and two layers of CFRP, the calculations perfectly reproduce the first elastic branch, the beginning of plasticity, the first part of the nonlinear behavior, and the buckling mode (Figures
Numerical and experimental load/displacement curves.
Experimental obtained extension mode (composite removal) and numerical one (Von Mises stresses in the steel layer) of one and two layers of CFRP.
For the case of one-layer CFRP reinforcement, stress and strain state of the multilayer (steel/CFRP) were analysed for different reference points positioned on the load/deflection curve (Figure
Numerical stresses and strains for each layer.
Five reference points | 1 | 2 | 3 | 4 | 5 | |
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Steel layer |
|
319.2 | 321.2 | 392.2 | 430 | 430 |
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0.069 | 0.18 | 1.4 | 3.6 | 5.1 | |
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CFRP layer |
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65.3 | 172.4 | 1440 | 3799 | 4971 |
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0.069 | 0.18 | 1.4 | 3.6 | 5.1 |
Table
In the case of strengthening with three or more layers of CFRP, the numerical model associated to incremental calculation (Newton-Raphson) does not detect the bifurcation in the third or fourth mode observed experimentally. Even Riks calculation failed to catch the bifurcated branch equilibrium. In order to better correlate the numerical results to the experiments in the strengthening case involving three or more layers of CFRP, a structure perturbed by an initial defect collinear to mode 4 of the Euler bifurcation analysis has been considered. This artifice allows to correlate in part of the experimental results (Figures
Numerical and experimental inextensional buckling mode: (a) 3 CFRP layers; (b) 4 CFRP layers.
Experiment and simulation: (a) 3 CFRP layers; (b) 4 CFRP layers.
The gain on the bearing capacity can be described by a bilinear function of the layers number (Figure
Bearing capacity gain function of the CFRP layers—experiment/simulation.
This study allowed us to validate the concept of strengthened thick metallic shells using external layer of composite strip impregnated with epoxy resin. A substantial increase of the buckling load is here demonstrated. For the mild steel thick shells ( Starting from three layers, the buckling mode changes; the axisymmetric extensional mode gives way to inextensional mode 3 or 4. Knowing that for in situ reinforcement, the perfect adherence of the composite reinforcement to the steel shell cannot be systematically guaranteed, and the effect of the CFRP layer adhesion on the metal shell has been carefully studied. The conducted tests allowed us to conclude that the steel/composite bonding is not fundamental in terms of bearing capacity. The numerical simulation, although integrating restrictive hypotheses with regard to the choice of kinematics (no delamination or metal/composite or composite/composite interface debonding) and behavior laws (no damage of composite as fiber failure was considered), leads to the results which correlate correctly the experiments, at least in the precritical domain, as well as buckling initiation. However, according to this simplified modeling, the final gain in bearing capacity induced by the CFRP reinforcement is overestimated. The numerical simulation of steel/composite multilayer shells must be improved by considering a behavior law integrating the different damages of the composite, in particular localized failure of fibers induced by tensile stress and layers delamination induced by local bending as well as fragile failure of composite layer. A model integrating these aspects is necessary for the good estimation of the bearing capacity as well as the successions of local softening and upward branches until the final collapse of the shell.
The data used to support the findings of this study are included within the article.
The authors declare that there are no conflicts of interest regarding the publication of this paper.
The authors gratefully acknowledge Freyssinet France for providing the CFRP and their technical staff for the application of the reinforcement following the recommended application procedure.