Optimum design of cross-sectional profiles of pultruded box beams with high ultimate strength

Pultruded box beams under bending may be subjected to local buckling which causes premature failure of the beams. As such it is important to design pultruded box beams with high local buckling resistance to increase their ultimate strength. This paper presents an optimum design approach for cross-sectional profiles of pultruded box beams of (approximately) the same mass with emphasis on accomplishment of high local buckling resistance through finite element analysis. Five different sectional profiles have been designed by stiffening a simple box, and finite element analysis is used to study linear buckling and postbuckling of the beams. Results for the critical loads of linear buckling and local buckling judged by stress variation, stresses and deformations in postbuckling are presented. The computational results show one of the proposed sectional profiles does not develop local buckling and produces much smaller stresses and deformations within the load range of interest.     

Thermal preconditioning study for bolted tension joints in pultruded GRP plate

Thermocouples have been used to monitor the time versus temperature rise response at the centre of four sizes of pultruded GRP plate used in bolted tension joints in order to demonstrate that all of the GRP plate is at the required temperature prior to testing the joints to failure. A simple one-dimensional finite element (FE) model has also been developed and used to predict time versus temperature rise response. The experimental and numerical results confirm that a thermal preconditioning period of 30 min duration is more than adequate for all of the pultruded GRP plates to achieve the actual test temperatures of 40, 60 and 80 °C.     

Design and evaluation of various section profiles for pultruded deck panels

Local high stresses and buckling may be critical to the composite deck panels with moderately thick walls. Design and evaluation of section profiles for pultruded deck panels with the reduced local stress and improved buckling strength are discussed. The deck panels with several different cross-sectional profiles are assessed based on finite element analysis. The assessment covers the global and local stiffness, the maximum stresses and buckling strength. Compared to the original design, one of the panels with the modified profiles possesses significant improvement in all aspects evaluated. Most profiles provide lower compressive stress and higher local stiffness and significantly higher buckling strength.     

Metallographic investigation of the damage caused to GRP by the combined action of electrical,mechanical and chemical environments

The use of glass fibre-reinforced polymers in electrical insulator components has gradually been taking place. Problems may arise where such insulators are in service at very high voltage, e.g. 200 kV and above, are under significant mechanical loads, and the environment (rain, and various pollutants) is able to gain access to the surface of the GRP. With the aid of optical and scanning electron microscope techniques, a detailed examination has been carried out on the nature of damage which has taken place in GRP pultruded rods that have operated for various periods of time in the above service conditions. These pultruded rods can receive significant levels of damage under the action of electrical fields, and the attendant environment; this takes the form of erosion, melting, burning and displacement of both glass and polymer phases. When a mechanical stress, which may be less than 10% of the breaking stress of the rod, is applied in conjunction with the above conditions a different form of insulator breakdown can take place. Instead of material displacement on the scale mentioned above, brittle failure of the GRP takes place. Such a failure mode can be compared with the process of stress corrosion which takes place when GRP is tested in 0.1 N acid solutions. It is suggested that the combined action of electrical activity and the presence of minor amounts of pollutants are able to influence the surface of glass fibres and promote stress corrosion in an analogous fashion to that described for concentrated acid solutions.     

Analysis of pultruded glass reinforced plastic beams with semi-rigid end connections

The influence coefficient method of analysis has been used to derive closed-form expressions for the mid-span deflection and end rotations of shear deformable uniform section beams with semi-rigid end connections. The formulae have been recast into performance indices which define the reduction in mid-span deflection, the increase in load carrying capacity and the increase in span relative to an otherwise identical simply supported beam for two practical load distributions: (1) a point load at mid-span and (2) a uniform load over the entire span. Expressions are also presented for the required rotation capacity of the semi-rigid end connections. Initial rotational stiffness data, derived from full-scale tests on web and web and flange cleat connections between two sizes of pultruded glass reinforced plastic (GRP) WF-section are used in the formulae to evaluate the performance indices for the practical range of span-to-depth ratios for load case (1). The values obtained quantify the benefits to be derived from exploiting semi-rigid end connection stiffness in the design of pultruded GRP beams with the current, very limited, range of section sizes.     

Failure of pultruded GRP single-bolt tension joints under hot–wet conditions

An experimental study of the effects of hot–wet conditions on the load carrying capacity of pultruded GRP (glass reinforced plastic) single-bolt tension joints has been carried out. The bolted joints were failed in tension after being immersed in water at three temperatures for two periods of time. Two joint geometries, defined in terms of end distance and width to bolt diameter, were tested with the pultrusion and tension axes coincident. The reductions in the load capacities of the joints due to the hot–wet conditions were quantified and shown to be very large. For example, it was found that more than 60% of the load carrying capacity of a single-bolt tension joint was lost after being immersed in water for 6.5 weeks at 60 °C. This temperature is lower than the manufacturer’s recommended maximum service temperature for this type of pultruded GRP material.     

Experimental and computed natural frequencies of square pultruded GRP plates: effects of anisotropy, hole size ratio and edge support conditions

Experiments have been carried out to determine the free vibration frequencies and mode shapes of 3.2 mm thick, pultruded GRP, square plates with six combinations of clamped (C), simply supported (S) and free (F) edge supports. Comparison of experimental and theoretical/numerical frequencies confirms that thin homogeneous orthotropic/anisotropic plate theory provides a reasonable model for predicting the free vibration response of pultruded GRP plates. Additional vibration experiments were carried out on plates with central circular cutouts. The hole size ratios were varied from about 0.1 to 0.4 for three combinations of clamped (C) and simply supported (S) edge conditions. Finite-element (FE) frequency and mode shape predictions based on orthotropic plate theory were again shown to be in reasonable agreement with the experimental frequencies and modes.     

Single-bolt tension joint tests on pultruded GRP plate - effects of tension direction relative to pultrusion direction

The literature on single-bolt tension joints in structural grade pultruded GRP plate is reviewed and the differences between the main investigations are highlighted. Details are given of the test setup and the joint configurations used in a series 54 such tests on single-bolt joints in which the angle between the pultrusion and tension axes (the off-axis angle) and the joint geometry are varied. Ultimate strength, intial stiffness, initial bolt slip and bolt displacement at failure data are presented as functions of the joints' principal geometric ratios. The observed joint failure modes show that, for off-axis angles ≥ 30 °, bearing failure (a relatively benign failure mode) does not arise. Instead, tension mode failure predominates and cracks tend to propagate parallel to the rovings diagonally across the width of the joint. It is concluded that the rovings play a significant role in controlling the crack propagation and this has implications for joint layout and design in pultruded GRP plate.     

Through thickness stress distributions in pultruded GRP materials

This paper describes an experimental methodology for determining the through thickness properties of pultruded GRP materials and their application in finite element analysis (FEA) of adhesively bonded joints. The finite element analysis is validated using an infra-red thermography based experimental mechanics technique known as thermoelastic stress analysis. The obtained results show that the measured through thickness values fall within the assumed bounds of previous work and have highlighted that interactions between the fibres and resin in the through thickness direction are present but not in a particularly intuitive manner. Moreover, the work presented herein highlights that the value of shear modulus used in the numerical model is an important consideration.     

Pre-buckling and post-buckling failure at web-flange junction of pultruded GFRP beams

Separation at the web-flange junction is a common failure mode of pultruded glass fiber-reinforced (GFRP) beams subjected to bending. The causes of this separation appear to depend on the presence of lateral supports to prevent lateral buckling. To clarify the driving mechanisms, four-point bending experiments were carried out on pultruded GFRP girders. Lateral buckling was prevented by using lateral supports. Web-flange separation failure due to exceeding the shear strength was observed before any buckling was seen. Furthermore, nonlinear FEA was performed to identify the critical stress states of GFRP beams from the research literature, without any lateral supports in the post-buckling phase. In this case, based on numerical calculation, the critical stress states and their locations depended significantly on the shape of initial imperfections. The ultimate loads, with or without lateral supports, were predicted by a modified von Mises criterion applied to the stress states at the web-flange junction.     

Flexural-torsional buckling of pultruded fiber reinforced plastic composite I-beams: experimental and analytical evaluations

In this paper a comprehensive experimental and analytical approach is presented to study flexural-torsional buckling behavior of full-size pultruded fiber-reinforced plastic (FRP) I-beams. Two full-size FRP I-beams with distinct material architectures are tested under midspan-concentrated loads to evaluate their flexural-torsional buckling responses. To monitor rotations of the cross-section and the onset of critical buckling loads, transverse bars are attached to the beam crosssection and are subsequently connected to LVDTs; strain gages bonded at the edges of the top flange are also used. The analysis is based on energy principles, and the total potential energy equations for the instability of FRP I-beams are derived using nonlinear elastic theory. The equilibrium equation in terms of the total potential energy is solved by the Rayleigh-Ritz method, and simplified engineering equations for predicting the critical flexural-torsional buckling loads are formulated. A good agreement is obtained between the experimental results, proposed analytical solutions and finite-element analyses. Through the combined experimental and analytical evaluations reported in this study, it is shown that the testing setup used can be efficiently implemented in the characterization of flexural-torsional buckling of FRP shapes and the proposed analytical design equations can be adopted to predict flexural-torsional buckling loads.     

Buckling failure modes of FRP thin-walled beams

A study on buckling phenomena in pultruded Fiber Reinforced Polymer (FRP) beams, based on two mechanical models recently formulated by the authors with regard to composite thin-walled beams, is presented in this paper. Global buckling behavior is analyzed by means of a one-dimensional model in which cross-section torsional rotation is divided into two parts: the first one, associated with Vlasov’s axial warping, the second one, associated entirely with shear strains. The study of local behavior is based on the individual buckling analysis of the components of FRP profile, assumed as elastically restrained transversely isotropic plates. Both mechanical models take into account, within the field of small strains and moderate rotations, the contribution of shear deformation in the kinematic hypotheses. Design charts suitable to evaluate the buckling load of FRP “I” beams with either narrow or wide flanges are obtained and presented in this paper.     

A phenomenological analysis of Mode I fracture of adhesively-bonded pultruded GFRP joints

The fracture behavior of adhesively-bonded pultruded joints was experimentally investigated under Mode I loading using double cantilever beam specimens. The pultruded adherends comprised two mat layers on each side with a roving layer in the middle. An epoxy adhesive was used to form the double cantilever beam specimen. The pre-crack was introduced in three different depths in the adherend in order to induce crack initiation and propagation between different layers and thus investigate the effect of these different crack paths on the strain energy release rate. Short-fiber and roving bridging increased the fracture resistance during crack propagation. Specific levels of critical strain energy release rates could be attributed to each of the crack paths, with their levels depending on the amount of short-fiber bridging and the presence of a roving bridge. The different levels of critical strain energy release rate could be correlated to the morphology of the fracture surface and the strain energy release rate can thus be determined visually without any measurement.     

Atomic-resolution imaging in liquid by frequency modulation atomic force microscopy using small cantilevers with megahertz-order resonance frequencies

In this study, we have investigated the performance of liquid-environment FM-AFM with various cantilevers having different dimensions from theoretical and experimental aspects. The results show that reduction of the cantilever dimensions provides improvement in the minimum detectable force as long as the tip height is sufficiently long compared with the width of the cantilever. However, we also found two important issues to be overcome to achieve this theoretically expected performance. The stable photothermal excitation of a small cantilever requires much higher pointing stability of the exciting laser beam than that for a long cantilever. We present a way to satisfy this stringent requirement using a temperature controlled laser diode module and a polarization-maintaining optical fiber. Another issue is associated with the tip. While a small carbon tip formed by electron beam deposition (EBD) is desirable for small cantilevers, we found that an EBD tip is not suitable for atomic-scale applications due to the weak tip-sample interaction. Here we show that the tip-sample interaction can be greatly enhanced by coating the tip with Si. With these improvements, we demonstrate atomic-resolution imaging of mica in liquid using a small cantilever with a megahertz-order resonance frequency. In addition, we experimentally demonstrate the improvement in the minimum detectable force obtained by the small cantilever in measurements of oscillatory hydration forces.     

Stress corrosion cracking of GRP pultruded rods in acid environments

Stress corrosion cracking of GRP pultruded rods has been investigated in 0.0001 to 5.0 N hydrochloric acid environments under bending and tensile loading modes. Crack initiation takes place at exposed glass fibres in the surface of the rod, and crack propagation is planar and at right angles to the rod axis. Leaching of calcium and aluminium from the fibres takes place during the cracking process, and time-to-failure is dependent on the acid concentration, the stress level and the ease of access of the acid to the glass fibre surface. Possible mechanisms of crack propagation through the glass fibres and resin are discussed.     

Semi-rigid––simply supported shear deformable pultruded GRP beams subjected to end moment loading: comparison of measured and predicted deflections

A single span shear deformable beam is analysed. One end is simply supported and subjected to an external moment and the other is supported by a semi-rigid joint with a linear moment––rotation characteristic. An expression for the mid-span deflection is derived in order to predict deflections recorded in tests on pultruded GRP beams with four types of semi-rigid joint. Using rotational stiffnesses derived from moment––rotation tests on similar joints it is shown that semi-rigid, shear deformable beam analysis is generally able to predict the measured deflections to within less than 10%. The mid-span deflection formula is recast to allow a back analysis to be carried out to determine the actual stiffness of two of the semi-rigid joints. It is shown that the joint tests significantly under-estimate the rotational stiffness of the bolted web cleat joint, whereas the predicted stiffness of the bolted web and flange cleat connection differs only by about 20% from that determined in one of the joint tests on this connection.     

Cantilever tip-surface contact as a catastrophe machine

The contact of a cantilever tip with a sample surface in a scanning-probe microscopy is considered for the first time as a catastrophe machine. Using an approach of the catastrophe theory, behavior of the tip-surface system is analyzed depending on the internal parameters (stiffness and coordinates of the cantilever holder). The tip jumps and the adhesion force variations in the course of the vertical and lateral cantilever motions are calculated. Projections of the equilibrium surface are constructed and the regimes are established that eliminate the “jumps to contact” and “ microslips.” A new method for the surface vacancy diagnostics and a new algorithm for the controlled tip approach to the surface are proposed.     

Nanomachining by rubbing at ultrasonic frequency under controlled shear force

This study proposes a new method of proximal-probe machining that uses a rubbing process by introducing concentrated-mass (CM) cantilevers. At the second resonance of the CM cantilever vibration, the tip site of the cantilever becomes a node of the standing deflection wave because of the sufficient inertia of the attached concentrated mass. The tip makes a cyclic motion that is tangential to the sample surface, not vertical to it, as in a tapping motion. This lateral tip motion that is selectively excited by CM cantilevers was effective for the material modification of a sample due to the friction between the tip and the sample. Imaging and nanomachining under controlled shear force were demonstrated by means of the modified cantilever and a normal atomic force microscope. We were able to write a micron-sized letter "Z" having a line width of 30-100 nm on a resin surface.     

Scanning electrochemical microscopy monitoring in microcantilever platforms

The deflection of cantilever systems may be performed by an indirect electrochemical method that consists of measuring the local cantilever activity and deflection in a feedback generation-collection configuration of the SECM. This is illustrated during the electrochemically assisted adsorption of Br onto a gold-coated cantilever, either in its pristine state or previously coated with a thin organic barrier. It is further extended to the adsorption of an antibody in a heterogeneous immunoassay at an allergen-coated microcantilever platform. In both reactions, the cantilever deflection is qualitatively detected from the SECM tip current measurement and a quantitative estimate is obtained through modeling. This electroanalytical strategy provides an alternative approach to standard optical detection. It can overcome some limitations of the optical method by allowing electrochemical characterization of nonconductive cantilevers and appropriate use for closed systems.     

Progressive damage and nonlinear analysis of pultruded composite structures

This study combines a simple damage modeling approach with micromechanical models for the progressive damage analysis of pultruded composite materials and structures. Two micromodels are used to generate the nonlinear effective response of a pultruded composite system made up from two alternating layers reinforced with roving and continuous filaments mat (CFM). The layers have E-glass fiber and vinylester matrix constituents. The proposed constitutive and damage framework is integrated within a finite element (FE) code for a general nonlinear analysis of pultruded composite structures using layered shell or plate elements. The micromechanical models are implemented at the through-thickness Gaussian integration points of the pultruded cross-section. A layer-wise damage analysis approach is proposed. The Tsai–Wu failure criterion is calibrated separately for the CFM and roving layers using ultimate stress values from off-axis pultruded coupons under uniaxial loading. Once a failure is detected in one of the layers, the micromodel of that layer is no longer used. Instead, an elastic degrading material model is activated for the failed layer to simulate the post-ultimate response. Damage variables for in-plane modes of failure are considered in the effective anisotropic strain energy density of the layer. The degraded secant stiffness is used in the FE analysis. Examples of progressive damage analysis are carried out for notched plates under compression and tension, and a single-bolted connection under tension. Good agreement is shown when comparing the experimental results and the FE models that incorporate the combined micromechanical and damage models.