Time Histories Of Contact Force Research Articles

Experiments on the localized interaction at the interface fuel rod/spacer grid in pressurized water reactors

The release of fissile material into the coolant caused by fretting of the fuel rods at the interface with spacer grids is a significant safety issue and cause of financial losses in the operation of Pressurized Water Reactors (PWRs). Each fuel rod is kept in position inside spacer grids through friction from the preload exerted by retaining elements (springs and dimples). Fretting of the fuel rods occurs at the contact with the springs and dimples. In severe fretting cases the integrity of the fuel rod cladding is compromised and fission byproducts enter the primary coolant circuit. The reciprocating motion at the contact interface of the fuel rods and spacer grids resulting in material fretting is due to the Flow-Induced Vibrations (FIV) of fuel rods, caused by the unstable surrounding coolant flow, which in PWRs is predominantly parallel to the length of fuel rods (axial flow). Under specific flow conditions, fretting develops rapidly. The vibrations of fuel rods, as well as the relationship of fretting wear mechanisms with several factors associated with the fission process and coolant flow dynamics and stability (vibration amplitude, preload, oscillating loads, irradiation, axial slip, spring relaxation, temperature, oxidation, material of spacer grids and fuel rods), have been considered in the literature. However, direct experimental measurements of the contact force and axial slip during FIV have not been treated in the literature, likely because of the absence of suitable measurement methods. This gap in experimental measurement techniques is addressed in this work, specifically for the analysis of PWR fuel assemblies, by installing a piezoelectric stack and aiming laser Doppler vibrometers on a one-meter-long fuel rod, supported by two full-scale spacer grids, in-air or immersed in quiescent water. In the presence of small- and large- amplitude forced vibrations, the signal of the piezoelectric force transducer increases with the amplitude of vibration, but it is also affected by vibrations perpendicular to the excitation, which appear for large-amplitude excitations. The axial motion of the fuel rod at the spacer grid has a complex evolution and is significant for large-amplitude vibrations only. At any rate, the time histories of contact force and axial motion display the effects of impacts and slips, particularly during the tests in water. The measurement system shows that the severity of the interaction at the spacer grid interfaces is influenced strongly by the amplitude of the forced fuel rod vibrations. Since fuel rods and fuel assemblies are prone to several nonlinear phenomena, as demonstrated by recent studies, it follows that the usage of nonlinear models will be essential to numerically estimating the severity of fretting.

Ballistic Limit of Sandwich Plates With a Metal Foam Core

Abstract The ballistic perforation of sandwich plates comprising two identical/unidentical aluminum alloy face sheets and an aluminum foam core is investigated to gain insights into the factors governing the penetration processes. The impact velocities of projectiles with conical, flat, and hemispherical noses range from 60 ms−1 to 220 ms−1 in the experiments. Against conical-ended projectiles, petalling failure is found to be an active failure mode at the rear face sheet. Against projectiles with flat and hemispherical noses, both petalling failure and petalling-flipped-cover failure are observed. Finite element simulations considering the effect of foam meso-structure on the ballistic limit of sandwich plates are performed and validated against the experimental results. It is shown that the local bending and fracture of the cell walls significantly dissipate the kinetic energy of the projectile and restrain the occurrence of the high stress regions. Characteristic double-peak and single-peak modes of contact force time histories are observed for projectiles with various nose shapes. It is also found that a sandwich plate with thicker front face sheet has higher ballistic resistance, which may facilitate the instructional arrangement of face sheets with regard to mass distribution to achieve higher ballistic resistance. Finally, a three-stage theoretical model based on energy balance principle is developed for each type of projectile to predict the residual velocities after perforation of sandwich plate.

Delamination in GLARE laminates under low velocity impact

Present paper deals with the finite element (FE) analysis for determination of impact induced delamination in GLARE laminates. Despite the fact that GLARE possesses better impact properties compared to those for both aluminium and glass/epoxy composites, the low interface strengths may lead to failure in the form of delamination and debonding under low velocity impacts (LVIs). In the present work, LVI responses of GLARE 5 and GLARE 4-3/2 are studied to compare the contact force-time history, plate deflection and delamination at the interfaces using a transient dynamic FE code developed incorporating Newmark-β method and Hertzian contact law. Results show that under LVI, GLARE 4-3/2 is more susceptible to delamination at the interfaces compared to GLARE 5-2/1. The effects of outer aluminium layer thickness and laminate configuration on the interfacial delamination in GLARE under LVI are also studied.

Characterization of adhesive joints under high-speed normal impact: Part II – Numerical studies

This two-part article presents an experimental method with numerical verification of the characterization of adhesive bonds under normal impact loading. Part I presented the experimentally measured performance of static and impact behavior of two adhesives (a methacrylate and an epoxy). Part II presents the numerical modeling of the static and dynamic tests performed in Part I. The finite element simulations are used to determine approximate dynamic material modeling parameters. The simulations are also useful in estimating certain critical performance aspects of the adhesive for the proposed impact test such as the estimation of contact force time histories, the dynamic stress time history profiles within the adhesive, and to the various energy components in the adhesives and adherends.

Low Velocity Impact Response of Laminate Rectangular Plates Made of Carbon Fiber Reinforced Plastics

The paper aims to present an experimental study on low velocity impact behavior of composite materials reinforced with carbon fibers. The objectives of investigations are to assess the main characteristics of impact response such as the energy absorbed by the laminate plate, the contact force as well as the indentation corresponding to different initial kinetic energies of the projectile. The experimental tests were conducted on rectangular plate specimens with dimensions of 150x100x2.5mm3, cut off from a symmetric laminate made of 8 unidirectional carbon/epoxy vinyl ester laminate that are stacked in a lay-up configuration of [0/-45/45/90]s. The energy that induced the specimen’s complete perforation as well as the energy corresponding to the level of BVID were determined with regard to typical testing conditions, such as the time varying acceleration, displacement as well as the absorbed impact energy. Moreover, for comparison purposes, the analytically results obtained for the case of an elastic impact with a projectile velocity of 1m/s, by making use of a complete model based on Kirchhoff plate theory, is presented. Within the range of elastic impact, the analytical results demonstrated their good agreement with the experimental testing data in terms of the absorbed impact energy, displacements and contact force time histories.

Numerical investigation on low-velocity impact response of CFRP wraps in presence of concrete substrate

Under the levels of low-velocity impact far below those considered by current design codes, the carbon fiber-reinforced polymer (CFRP) wraps externally bonded for retrofitting reinforced concrete (RC) columns might suffer severe damage. In this study, explicit finite element method was used to fill the knowledge gap, which was verified by experimental tests. Twenty-four transverse impact scenarios related to a CFRP-retrofitted RC column-to-impactor system were investigated, which were designed according to the different combinations of a series of parameters, namely incident kinetic energy of impactor, CFRP thickness, and shape of impactor. The energy distribution among the different parts in the system was presented. The contact force time histories obtained from the scenarios indicated that a damage threshold load associated with a prescribed shape of impactor existed in the case of the CFRP wraps with concrete substrate. Furthermore, the significant differences among the roles of the parameters were revealed, and the reasons behind the differences were analyzed.

Dynamic behavior of particulate metal matrix nanocomposite plates under low velocity impact

The main purpose of this work is to investigate low velocity impact behavior of metal matrix nanocomposite plates reinforced with silicon carbide nanoscale particles. First, a micromechanical model is proposed to predict the effective mechanical properties of metal matrix nanocomposites. Two features of the nanocomposite microstructure affecting the elastic properties, including agglomerated state of silicon carbide nanoparticles and size factor, are taken into account in the micromechanical simulation. Then, finite element method is used to analyze the time histories of contact force and center deflection of silicon carbide nanoparticle-reinforced metal matrix nanocomposite plates. Several detailed parametric studies are accomplished to explore the influence of volume fraction, diameter and dispersion type of silicon carbide nanoparticles, spherical impactor velocity and diameter, plate dimensions, as well as different boundary conditions on the dynamic response of metal matrix nanocomposite plates. The presented approach accuracy is verified with the available open literature results displaying a clear agreement. The results indicate that adding the silicon carbide nanoparticles into the metal matrix materials leads to a reduction in plate center deflection and an increase in contact force between the plate and projectile. Moreover, it is found that the nanoparticle agglomeration dramatically decreases the contact force and increases the center deflection of metal matrix nanocomposite plates.

Eccentric low-velocity impact on fiber-metal laminates under in-plane loading using unified zigzag theory

This paper investigates the eccentric low-velocity impact of Fiber metal laminates (FMLs) subjected to spherical projectile using a unified Zig-Zag plate theory. The presented zig-zag plate theory enforces transverse shear stress continuity through the thickness and can be reduced to conventional plate theories using appropriate shape function. The governing equations and suitable boundary conditions are obtained using the principle of minimum total potenital energy. Runge-Kutta method is employed to solve initial value problem resulted by the method of Ritz. The present model is validated by comparison and good agreement between its results and those of reports in open literature. Influence of various specifications of impact phenomenon such as laminate thickness, projectile radius, projectile velocity, in-plane load and eccentricity parameter is examined on deflection and contact force time history. The obtained results indicate that continuity of transverse shear stress is required to achieve accurate contact force even for moderately thin FMLs.

Probabilistic modelling of forces of hail

Numerical modelling techniques enable forcing function at the point of contact in a hail impact to be predicted, but many models available in commercial software have not been verified by experiments. A recently developed deterministic model is only able to simulate the impact action of an idealised spherical hailstone. Results recorded from the impact testing of non-spherical simulated hail ice specimens show wide scatters and are different to spherical specimens. A stochastic model has been developed in this study to incorporate the variability of the modelling parameters representing the behaviour of non-spherical ice specimens and to generate time histories of contact force for given impact scenarios. A probabilistic model which was developed previously to provide predictions of the distribution of the size of hailstones in a severe category hailstorm has also been further developed to provide predictions of the maximum contact force values in probabilistic terms. For any given pre-defined forcing function denting into the surface of a steel plate can be estimated by finite element analysis or experimentally on a test machine. The new knowledge base introduced in this paper can be used by manufacturers and designers to re-assess existing products and in making improvements to future installations taking into account cost–benefit considerations.

Effects of the number of fatigue cycles on the impact behavior of glass fiber/epoxy composite tubes

Abstract This paper investigates the impact damage behaviors of filament wound glass reinforced plastic (GFRP) tubes that were fatigued under internal pressure. Damage to the GFRP tubes was investigated, and the tubes' bursting pressures were determined. (±55°) 3 E-glass/epoxy composite specimens were manufactured using the filament winding method. Fatigue tests were applied to the specimens at a stress rate of 0.05 and frequency of 0.42 Hz in accordance with the ASTM-D 2992 standard. The specimens were subjected to fatigue tests at a stress level of 35% static burst pressure. Fatigued and non-fatigued composite tube specimens were pre-stressed by applying 32 bar internal pressure. After applying internal pressure, low velocity impact tests at various energy levels (5 J, 10 J and 15 J) were performed on the GFRP tubes. Plots of contact force-time history were obtained. For impact characteristics, such as deflection, absorbed energies were calculated based on the force–time histories. The damaged areas that developed on the specimens were also evaluated. The specimens that fatigued and impacted at the 10 J energy level burst in accordance with the ASTM D 1599 standard. It was concluded that for all of the energy levels employed in this work, as the number of fatigue cycle increases, the rigidity of the tubes decreases.

Finite Element Analysis of Laminated Composite Skewed Hypar Shell Roof Under Oblique Impact with Friction

Impact of foreign objects on laminated composite has become a great concern despite its other advantages. Hypar (hyperbolic-paraboloid), a preferred shell roof geometry is frequently subjectedto such impacts. In most of the practical situations such impacts are oblique. Present study investigates dynamic behaviour of a simply supported composite hypar shell roofs under oblique impact, considering modified Hertzian contact law, for different impact velocities and impact angles allowing for anisotropic friction. Time dependent equations are solved using Newmark's time integration algorithm. Time histories of contact force at point of impact and that of displacement are presented to extract significant engineering conclusions. There are also proposals of practical parameters for designing such shells through static simplification of the problems.

Behaviour of GFRP composite plate under ballistic impact: experimental and FE analyses

In this paper, experimental as well as numerical analysis of Glass Fiber Reinforced Polymer (GFRP) laminated composite has been presented under ballistic impact with varying projectile nose shapes (conical, ogival and spherical) and incidence velocities. The experimental impact tests on GFRP composite plate reinforced with woven glass fiber (<TEX>$0^{\circ}/90^{\circ}$</TEX>)s are performed by using pneumatic gun. A three dimensional finite element model is developed in AUTODYN hydro code to validate the experimental results and to study the ballistic perforation characteristic of the target with different parametric variations. The influence of projectile nose shapes, plate thickness and incidence velocity on the variation of residual velocity, ballistic limit, contact force-time histories, energy absorption, damage pattern and damage area in the composite target have been studied. The material characterization of GFRP composite is carried out as required for the progressive damage analysis of composite. The numerical results from the present FE model in terms of residual velocity, absorbed energy, damage pattern and damage area are having close agreement with the results from the experimental impact tests.

Sequence of damage events occurring in the course of low energy impact

Finite element simulation was carried out to better understand damage formation in CF/epoxy plate in the course of a low velocity 8J impact. The plate under investigation was of [+30/−30]s lay-up. To validate the numerical results a drop test was carried out with the help of a drop tower. The interlaminar damage extent was determined with the help of C-scan. Comparison between the numerical and experimental results showed a good quantitative agreement concerning contact force time history, however, the amount of dissipated energy determined based on the numerical simulation was lower than that from the experiment,consistently, the damage extent determined based on numerical simulation was smaller than that determined by C-scan. Nevertheless, characteristic points on the plot representing contact force time history could be related to the particular damage mechanism onsets and their actions.

A study on low velocity impact response of FGM rectangular plates with 3D elasticity based graded finite element modeling

Low velocity impact behavior of rectangular plates made of functionally graded materials (FGMs) based on three-dimensional theory of elasticity is studied in this paper. The modified Hertz contact law, which is appropriate for graded materials, is employed. On the basis of the principle of minimum potential energy and the Rayleigh Ritz method, the graded finite element modeling is applied. Solution of the nonlinear resulted system of equations in the time domain is accomplished via an iterative numerical procedure based each time on Newmark's integration method. The effects of various involved parameters, such as the graded property profile, projectile velocity and projectile density on time histories of contact force, lateral deflection and normal stresses are investigated in detail. To present efficiency of the present work, several numerical examples are included. The main novelty of the present research, which has not been reported in literature, is considering the difference of lateral deflection through the thickness of the FGM plate due to analyzing three-dimensional elasticity of the plate.

A method for testing railway wheel sets on a full-scale roller rig

Full-scale roller rigs for tests on a single axle enable the investigation of several dynamics and durability problems related with the design and operation of the railway rolling stock. In order to exploit the best potential of this test equipment, appropriate test procedures need to be defined, particularly in terms of actuators’ references, to make sure that meaningful wheel–rail contact conditions can be reproduced. The aim of this paper is to propose a new methodology to define the forces to be generated by the actuators in the rig in order to best reproduce the behaviour of a wheel set and especially the wheel–rail contact forces in a running condition of interest as obtained either from multi-body system (MBS) simulation or from on-track measurements. The method is supported by the use of a mathematical model of the roller rig and uses an iterative correction scheme, comparing the time histories of the contact force components from the roller rig test as predicted by the mathematical model to a set of target contact force time histories. Two methods are introduced, the first one considering a standard arrangement of the roller rig, the second one assuming that a differential gear is introduced in the rig, allowing different rolling speeds of the two rollers. Results are presented showing that the deviation of the roller rig test results from the considered targets can be kept within low tolerances (1% approximately) as far as the vertical and lateral contact forces on both wheels are concerned. For the longitudinal forces, larger deviations are obtained except in the case where a differential gear is introduced.

Experimental investigation on transverse low-speed impact behavior of adhesively bonded similar and dissimilar clamped plates

This experimental study investigates the low-speed impact behavior of adhesively bonded similar (Al–Al, St–St) and dissimilar (Al–St, St–Al) plates. The after-impact geometries of the front and back faces of the bonded plates, which were visualized by measuring the displacements, were in good agreement with the simulated surface geometries obtained by using explicit finite element method. The plate stiffness was affective on the deflections of the bonded plates; thus, the bonded Al–Al plates exhibited maximum deflections, contact durations, and minimal contact force levels, whereas the bonded St–St plates had minimum deflections, contact durations, and maximum contact force levels. As the impact energy is increased, the impact forces, durations, and deflections increased naturally; however, the impact force-time histories were not affected evidently. The bonded Al–Al plates can dissipate the impact energy more effectively than the bonded St–St plates. The experimental and simulated contact force-time histories were generally in good agreement. Based on the cross-section photographs of the damaged impact regions the bonded Al–Al plates with low stiffness can deform plastically and dissipate most of the impact energy, and the adhesive layer remains compatible with the deformation of the plates. The interfacial fractures appear along the back plate–adhesive interface for the low impact energy but along both front and back plate–adhesive interfaces and cracks propagated to the back interface to lower interface through the adhesive thickness near the boundaries of the impactor trace. The bonded St–St plates behave more rigid, transmit the impact energy directly to the adhesive layer and the high impact force distributions result severe fractures not only interfacially but also through the adhesive thickness. The color transformations, which are indications of fracture formation and propagation speed in some way, were observed around the adhesive fractures. Although the bonded St–Al and Al–St plates had a fracture mechanism similar to those of the bonded Al–Al plates but the color transformation near the fractures and the crack opening displacement levels were more evident. The existence of a stiffer plate affects considerably the damage formation in the adhesive layer and in the plates, whereas the less stiff plates can dissipate the impact energy by deforming plastically and the adhesive layer experiences less local damages.

Analysis of Low-Velocity Impact on Composite Sandwich Panels Using an Assumed Strain Solid Element

Low-velocity impact on composite sandwich panels has been investigated. The contact force is computed from a proposed modified Hertzian contact law. In the proposed contact law, the exponent is adjusted and the through-the-thickness elastic constant of honeycomb core is reduced properly to approximately predict the measured contact force-time history during the impact. The equivalent transverse elastic constant is calculated from the rule of mixture. Nonlinear equation to calculate the contact force is solved by the Newton-Raphson method and time integration is done by the Newmark-beta method. A finite element program for the low-velocity impact analysis is coded by implementing these techniques and an 18-node assumed strain solid element. Behaviors of composite sandwich panels subjected to low-velocity impact are analyzed for various cases with different geometry and lay-ups. It has been found that the present code with the proposed contact law can predict measured contact forces and contact times for most cases within reasonable error bounds, especially for thick sandwich plates.

Substructure Analysis of a Flexible System Contact-Impact Event

In this paper, the application of the substructure methodology to contact-impact analysis of flexible multibody systems is validated. Various impact model parameters that affect the model’s accuracy are presented. A contact-impact system is used that consists of a flexible cantilever bar longitudinally struck at its free end by a rigid body moving at a finite velocity. First, a dynamic model using the substructure method is established. Second, the initial conditions of the system’s dynamic responses during contact-impact are derived. Finally, a numeric contact-impact simulation is performed. The excellent agreement between the numeric solutions to both the substructure model and the analytical solutions demonstrates that the substructure model can successfully describe stress wave propagation within flexible bodies during contact-impact. The method can also clearly display the contact force time history and deformation distribution along the bar during contact-impact time and correctly predict the displacement of the contact surface of the flexible bar and the contact duration of the two bodies. It is shown that a larger substructure number will improve the accuracy of the numerical solutions, but an excessive number will lower the model’s accuracy since increasingly fine substructures increase the number of modal coordinates and lead to more serious computational round off errors and longer computational time.

Smooth static and dynamic indentation of a cantilever beam

Abstract The static and dynamic indentation of structural elements such as beams and plates continue to be intriguing problems, especially for scenarios where large area contacts are expected to occur. Standard methods of indentation analyses use a beam theory solution to obtain an overall load–displacement relationship and then a Hertzian contact solution to calculate local stresses under the indenter. However, these techniques are only applicable in a fairly limited class of problems: the stress distribution in the contact region will differ significantly from a Hertzian one when the contact length exceeds the thickness of the beam. The indentation models developed herein are improvements over existing GLOBAL/LOCAL models for static and dynamic indentation of cantilever beams. Maximum contact stresses, beam displacements, and contact force time histories are obtained and compared with the predictions of current static and dynamic indentation models. The validity of the solutions presented herein is further assessed by comparing the results obtained to the predictions of modified beam theory solutions.