Local water slamming impact on sandwich composite hulls

The local water slamming refers to the impact of a part of a ship hull on stationary water for a short duration during which high local pressures occur on the hull. We simulate slamming impact of rigid and deformable hull bottom panels by using the coupled Lagrangian and Eulerian formulation included in the commercial software LS-DYNA. We use the Lagrangian formulation to describe plane-strain deformations of the hull panel and consider geometric nonlinearities. The Eulerian formulation is used to analyze deformations of the water. Deformations of the hull panel and of the water are coupled through the hydrodynamic pressure exerted by water on the hull, and the velocity of particles on the hull wetted surface affecting deformations of the water. The continuity of surface tractions and the inter-penetrability of water into the hull are satisfied by using a penalty method. The computer code is verified by showing that the computed pressure distributions for water slamming on rigid panels agree well with those reported in the literature. The pressure distributions computed for deformable panels are found to differ from those obtained by using a plate theory and Wagner's slamming impact theory. We have also delineated jet flows near the edges of the wetted hull, and studied delamination induced in a sandwich composite panel due to the hydroelastic pressure.     

Low-velocity impact of sandwich composite plates

In this paper we investigate impact and compression after impact properties of plain weave carbon fiber sandwich composites. Impact tests were conducted on different sample types to obtain information about absorbed energy and maximum impact force. The different samples consisted of foam-filled and hollow honeycomb cores with four-layer carbon fiber facesheets on one or both sides. The impact and compression after impact data provided valuable information to allow for comparisons between the different sample types. Also, the compression after impact tests were conducted in order to determine the reduction in compressive strength when comparing impacted to non-impacted samples. In conclusion, a two-degrees-of-freedom spring/mass model was compared to experimental results. The comparison helped illustrate the limitations of current impact theory. This paper was presented, in part, at a symposium honoring Dr Christian P. Burger, Novel Applications of Experimental Methods in Mechanics, held at the 2003 SEM Annual Conference and Exposition on Experimental and Applied Mechanics, June 2–4, 2003, Charlotte, North Carolina.     

Low-energy impact response of composite and sandwich composite plates with piezoelectric sensory layers

An efficient model reduction based methodology is presented for predicting the global (impact force, plate deflection and electric potential) and through-thickness local (interfacial strains and stresses) dynamic response of pristine simply-supported cross-ply composite and sandwich composite plates with piezoelectric sensory layers subjected to low-energy impact. The through-thickness response of the laminate is modelled using coupled higher-order layerwise displacement-based piezoelectric laminate theories. Linearized contact laws are implemented for simulating the impactor–target interaction during impact. The stiffness, mass, piezoelectric and permittivity matrices of the plate are formulated from ply to structural level and reduced by applying a Guyan reduction technique to yield the structural system in state space. This reduction technique enables the formulation of a plate–impactor structural system of minimum size (1 term per vibration mode for composite plates – 2 terms for sandwich plates) and reduces computational cost, thus facilitating applicability for real-time impact and vibration control.     

The dynamic response of composite sandwich beams to transverse impact

The dynamic response of glass fibre–vinylester composite beams is measured by impacting the beams at mid-span with metal foam projectiles. The beams exist in composite monolithic form, and in sandwich configuration with composite face-sheets and a core made from PVC foam or end-grain balsa wood. High-speed photography is used to measure the transient transverse deflection of the beams and to record the dynamic modes of deformation and failure. For both monolithic and sandwich configurations, a flexural wave travels from the impact site towards the supports. Ultimate failure of the monolithic and sandwich beams is by tensile tearing of the faces. The sandwich beams also exhibit cracking of the core, and face-sheet delamination. The dynamic strength of the beams is quantified by the maximum transient transverse deflection at mid-span of the beams as a function of projectile momentum. It is demonstrated that sandwich beams can outperform monolithic beams of equal mass. The trade-off between core strength and core thickness is such that a low density PVC foam core outperforms a higher density PVC foam core. End-grain balsa wood has a superior stiffness and strength to that of PVC foam in compression and in shear. Consequently, sandwich beams with a balsa core outperform beams with a PVC foam core for projectiles of low momentum. The order reverses at high values of projectile momentum: the sandwich beams with a balsa wood core fail prematurely in longitudinal shear by splitting along the grain.     

Delamination in sandwich panels due to local water slamming loads

We study delamination in a sandwich panel due to transient finite plane strain elastic deformations caused by local water slamming loads and use the boundary element method to analyze motion of water and the finite element method to determine deformations of the panel. The cohesive zone model is used to study delamination initiation and propagation. The fluid is assumed to be incompressible and inviscid, and undergo irrotational motion. A layer-wise third order shear and normal deformable plate/shell theory is employed to simulate deformations of the panel by considering all geometric nonlinearities (i.e., all non-linear terms in strain–displacement relations) and taking the panel material to be St. Venant–Kirchhoff (i.e., the second Piola–Kirchhoff stress tensor is a linear function of the Green–St. Venant strain tensor). The Rayleigh damping is introduced to account for structural damping that reduces oscillations in the pressure acting on the panel/water interface. Results have been computed for water entry of (i) straight and circular sandwich panels made of Hookean materials with and without consideration of delamination failure, and (ii) flat sandwich panels made of the St. Venant–Kirchhoff materials. The face sheets and the core of sandwich panels are made, respectively, of fiber reinforced composites and soft materials. It is found that for the same entry speed (i) the peak pressure for a curved panel is less than that for a straight panel, (ii) the consideration of geometric nonlinearities significantly increases the peak hydrodynamic pressure, (iii) delamination occurs in mode-II, and (iv) the delamination reduces the hydroelastic pressure acting on the panel surface and hence alters deformations of the panel.     

Indentation failure in composite sandwich structures

A combined analytical and experimental investigation of the indentation failure of a composite sandwich panel has been undertaken. Two cases have been studied: a sandwich panel with carbon/epoxy facing and a PVC foam layer supported on a rigid base and indented at the center with a cylindrical indentor; and a sandwich beam with symmetrical facing and core materials as in the sandwich panels. The load-deflection behavior of the loaded facing was monitored during the test. Strains were also measured near the load on both surfaces of the facing using embedded strain gages. A full-field analysis of the in-plane displacements in the foam was conducted using the moiré method. The problem was modeled as an elastic beam resting on an elastic-plastic foundation. Initiation of indentation failure occurs when the foundation yields, while catastrophic failure takes place when the compression facing fractures. The experimental results are in good agreement with the results of the analytical modeling based on the Winkler foundation.     

Dynamic buckling and plastic collapse of rectangular strips under axial slamming impact

The dynamic buckling and plastic collapse of elastic-plastic rectangular strips under axial slamming impact are investigated experimentally. The dynamic response of the specimens is measured by several back-to-back paris of strain gages located at different positions. According to the experimental records, the compressive and bending motions of the rectangular strips are analyzed. The strips exhibit three different critical dynamic conditions: buckling, plastic incipience and plastic collapse. Based on the response characters, three criteria are proposed which completely define the elastic-plastic dynamic behavior of rectangular strips under axial slamming impact with loading durations ranging from 14 to 18 milliseconds. These conditions are estimated by introducing three critical axial compressive strains. Moreover, the effect of geometric imperfection on the dynamic behavior of the strips is discussed.     

The composite damping capacity of sandwich cantilever beams

The governing equation of the flexural forced vibration of a cantilever sandwich beam excited by a sinusoidal displacement at the clamped end is developed by utilizing the conventional Hamilton's Principle. The effect of damping of the composite beam is incorporated into the elastic equation of motion by utilizing the Correspondence Principle of the linear viscoelastic theory. Several plots for different values of the composite damping factor are presented. For comparison, an experimental setup was utilized to test different composite beams. The variation of the experimental results with those derived theoretically seem to be in agreement within the frequency range of the first few modes.     

Nonlinear behavior of composite sandwich beams in three-point bending

The load-deflection behavior of a composite sandwich beam in three-point bending was investigated. The beam was made of unidirectional carbon/epoxy facings and a polyvinyl chloride closed-cell foam core. The load-deflection curves were plotted up to the point of failure initiation. They consist of an initial linear part followed by a nonlinear portion. A nonlinear mechanics of materials analysis that accounts for the combined effect of the nonlinear behavior of the facings and core materials (material nonlinearity) and the large deflections of the beam (geometric nonlinearity) was developed. The theoretical predictions were in good agreement with the experimental results. It was found that the effect of material nonlinearity on the deflection of the beam is more pronounced for shear-dominated core failures in the case of short span lengths. It is due to the nonlinear shear stress-strain behavior of the core. For long span lengths, the observed nonlinearity is small and is attributed to the combined effect of the facings nonlinear stress-strain behavior and the large deflections of the beam.     

Failure behavior of composite sandwich structures under local loading

Usually when analyzing the mechanical response of foam-cored fiber-reinforced composite sandwich structures to localized static loading, the face sheets are treated as a linear-elastic material and no damage initiation and growth is considered. However, practice shows that at higher indentation magnitudes damage develops in the face sheet in the area of contact with the indentor, which could lead to local failure of the face laminate due to the loss of bending stiffness and strength. Therefore, the main objective of the present study is to develop a damage model for predicting the local failure in the composite face sheet and its influence on the load–displacement behavior of sandwich structures under local loading. For this purpose, the Hoffman failure criterion is incorporated into a finite element modeling procedure using the ABAQUS program system. Results deducted from the modeling procedure are compared with experimental data obtained in the case of static indentation tests performed on sandwich beam specimens using steel cylindrical indentors. It is shown that taking into account the damage in the face sheet leads to a substantial improvement in the performance of the model when simulating the mechanical behavior of the sandwich structures at higher indentation values.     

Higher-order impact modeling of sandwich structures with flexible core

In this study, a higher-order impact model is presented to simulate the response of a soft-core sandwich beam subjected to a foreign object impact. A free vibration problem of sandwich beams is first solved, and the results are validated by comparing with numerical finite element modeling results of ABAQUS and the solution by Frostig and Baruch [Frostig, Y., Baruch, M., 1994. Free vibration of sandwich beams with a transversely flexible core: a high order approach. Journal of Sound and Vibration 176(2), 195–208]. Then a foreign object impact process is incorporated in the higher-order model, and the contact force and deflection history as well as the propagation of transverse normal, shear, and axial stresses during the impact are analyzed and discussed. The validity of the model in the impact response predictions is demonstrated by comparing with finite element solutions of LS-DYNA. The calculated stresses caused by a foreign object impact are then used to assess failure locations, failure time, and failure modes in sandwich beams, which are shown to compare well with the available experimental results. The effects of impact mass, initial velocity, core stiffness, and core height on the impact stresses generated in the beams are discussed. The influences of impact mass and initial velocity on the contact force history are close to those by the linearized impact solution, but the proposed higher-order impact model captures the non-linear impact process and different generated stresses. Compared to the fully backed sandwich case, the core height shows a great influence over the impact process of a simply supported sandwich system, in which the global behavior of the sandwich is dominant; while the core stiffness shows minor effect over the impact process. The higher-order impact model of sandwich beams developed in the study provides accurate predictions of the generated stresses and impact process and can be used effectively in design analysis of anti-impact structures made of sandwich materials.     

Penetration of sandwich plates with hybrid-cores under oblique ballistic impact

The oblique penetration performance of lightweight hybrid-cored sandwich plates are investigated numerically. To compose the hybrid-core, ceramic prisms are inserted into pyramidal metal lattice trusses and fixed using epoxy resin. Three-dimensional finite element simulations are carried out for the hybridcored sandwich impacted at 15°, 30°, 45°, and 60° obliquity by a hemispherical projectile. The ballistic limit, the energy absorbed by the constituting elements, and the critical oblique angle are quantified. The physical mechanisms underlying the failure and the influence of fundamental system parameters are explored. The angle of obliquity is found to have significant influence on the ballistic trajectory and erosion of the projectile, thus it is important for the impact response and penetration resistance of the sandwich. For oblique angles equal to or larger than 45°, the projectile moves mainly horizontally and can not effectively penetrate across the sandwich.     

Low-velocity impact response of sandwich beams with functionally graded core

The problem of low-speed impact of a one-dimensional sandwich panel by a rigid cylindrical projectile is considered. The core of the sandwich panel is functionally graded such that the density, and hence its stiffness, vary through the thickness. The problem is a combination of static contact problem and dynamic response of the sandwich panel obtained via a simple nonlinear spring-mass model (quasi-static approximation). The variation of core Young’s modulus is represented by a polynomial in the thickness coordinate, but the Poisson’s ratio is kept constant. The two-dimensional elasticity equations for the plane sandwich structure are solved using a combination of Fourier series and Galerkin method. The contact problem is solved using the assumed contact stress distribution method. For the impact problem we used a simple dynamic model based on quasi-static behavior of the panel—the sandwich beam was modeled as a combination of two springs, a linear spring to account for the global deflection and a nonlinear spring to represent the local indentation effects. Results indicate that the contact stiffness of the beam with graded core increases causing the contact stresses and other stress components in the vicinity of contact to increase. However, the values of maximum strains corresponding to the maximum impact load are reduced considerably due to grading of the core properties. For a better comparison, the thickness of the functionally graded cores was chosen such that the flexural stiffness was equal to that of a beam with homogeneous core. The results indicate that functionally graded cores can be used effectively to mitigate or completely prevent impact damage in sandwich composites.     

Local buckling of composite channel columns

Continuum Mechanics and Thermodynamics - The investigation concerns local buckling of compressed flanges of axially compressed composite channel columns. Cooperation of the member flange and web is...     

Dynamic response of composite sandwich plates subjected to time-dependent pressure pulses

The dynamic response of orthotropic sandwich composite plates impacted by time-dependent external blast pulses is studied by use of numerical techniques. The theory is based on classical sandwich plate theory including the large deformation effects, such as geometric non-linearities, in-plane stiffness and inertias, and shear deformation. The equations of motion for the plate are derived by the use of the virtual work principle. Approximate solutions are assumed for the space domain and substituted into the equations of motion. Then the Galerkin Method is used to obtain the non-linear differential equations in the time domain. The finite difference method is applied to solve the system of coupled non-linear equations. The results of theoretical analyses are obtained and compared with ANSYS results. Effects of the face sheet number, as well as those related to the ply-thickness, core thickness, geometrical non-linearities, and of the aspect ratio are investigated. Detailed analyses of the influence of different type of pressure pulses on dynamic response are carried out.     

蜂窝夹层板撞击极限方程预测能力的提升

蜂窝夹层板撞击极限方程是空间碎片撞击航天器风险评估的关键技术,目前描述其预测能力的指标主要有总体、安全预测正确率和绝对、相对误差。基于131个蜂窝夹层板的实验数据,分别描述各个预测指标在方程系数空间的变化特征,并采用层次化思路进行方程预测指标提升的探讨。结果发现,进行方程优化时,预测概率型指标可精确优化,而预测误差型指标可快速优化;总体预测正确率作为首要预测指标可优先用于研究航天器的在轨防护特性,而安全预测正确率作为首要指标则可优先用于其设计安全性。