Core crush criterion to determine the strength of sandwich composite structures subjected to compression after impact

In this study a core crush criterion is proposed to determine the residual strength of impacted sandwich structures. The core of the sandwich is made of a Nomex Honeycomb core and the faces are laminated and remain thin. The mechanism of failure of this kind of structure under post-impact compressive loading is due to interaction between three mechanical behaviors: geometrical nonlinearity due to the skin’s neutral line off-set in the dent area, nonlinear response of the core and damages to the skins. For the type of sandwich analysed in this study, initially the core crushes at the apex of the damage. Using a finite element discrete modelling of the core previously proposed by the authors, the load corresponding to the crushing of the first cell can be computed and it gives the value of the residual strength for our criterion. Some geometric and material hypotheses are assumed in the damaged area mainly based on non-destructive inspection (NDI). The criterion is then applied to tests modelled by Lacy and Hwang [Lacy TE, Hwang Y. Numerical modelling of impact-damaged sandwich composites subjected to compression after impact loading. Compos Struct 2003;61:115–128]. It is shown that the criterion allows a good prediction of the tests except in the case of very small dents. Several sensitivity studies on the assumptions were made and it is shown that using this approach, the criterion is robust.     

Simulation of drop-weight impact and compression after impact tests on composite laminates

This paper presents finite element simulations of two standardized and sequential tests performed in polymer–matrix composite laminates reinforced by unidirectional fibers: the drop-weight impact test and the compression after impact test. These tests are performed on laboratory coupons, which are monolithic, flat, rectangular composite plates with conventional stacking sequences. The impact and the compression after impact tests are simulated using constitutive material models formulated in the context of continuum damage mechanics. The material models account for both ply failure mechanisms and delamination. Comparisons with experimental data are performed in order to assess the accuracy of the predictions.     

Failure mechanisms of laminated composites subjected to static indentation

Quasi-static indentation tests on composite laminates have been performed. Thermal deply and C-scan techniques are used to observe the internal damage characteristics of laminates induced by static indentation. The results indicate that the dent depth increases slowly and almost linearly as the force is lower than its maximum. The observation shows that the damage induced at this loading stage includes matrix cracking and delamination only. Once the force exceeds the maximum, the dent depth increases sharply while the force remains almost unchanged. Deply test results demonstrate that the transition to rapid increase in dent depth is due to the fiber breakage produced at this loading stage. The results also indicate that the damage resistance of a composite laminate can be characterized by the maximum contact force. On the basis of this principle and test results, it is concluded that the damage resistance of toughened composite is much higher than that of brittle one.     

Behaviour of multiple composite plates subjected to ballistic impact

An experimental and numerical investigation has been carried out to study the behavior of single and multiple laminated panels subjected to ballistic impact. A pressurized air gun is used to shoot the impactor, which can attain sufficient velocity to penetrate all the laminates in a multiple laminated panel. The incidental and residual velocity of the impactor is measured to estimate the energy absorption in the impact process. The commercially available code ABAQUS has been used for the numerical simulation where the impactor has been modeled as a rigid body and the laminates have been modeled with a simple shell element. A user material model based on a continuum damage mechanics concept for failure mechanism of laminated composites has been implemented. Experimental tests showed that the numerical model could satisfactorily predict the energy absorption. Most interestingly, it has clearly demonstrated a feasible phenomenon behind counterintuitive experimental results for the multiple laminated panels.     

Failure prediction of composite T-beams subjected to lateral load on the web

A study of the design and mechanical behaviour of co-cured T-beams subjected to lateral loading on the web is presented. The T-beams were manufactured by press moulding from pre-pregs of uni-directional and fabric glass reinforced high performance epoxy matrix. A special fixture was designed in order to carry out tests where the T-beams were laterally loaded on the web and clamped on the flange. Analytical and numerical studies were performed to predict the failure load to compare with the experimental results. The multilayer anisotropic continuum theory for delamination analysis of curved beams subjected to end moments and forces was used to compute the delamination stresses in the quarter cylindrical beam of the junction between the flange and the web. Finite element analyses of the T-beams were performed using plate/shell elements and two models were used for the joining between web and flange, to compute the planar stresses in the beam. The scatter obtained in the experimental results can be explained by the presence of two failure modes: one due to delamination associated with the through the thickness stresses developed in the curved part of the beam, the other related with failure occurring due to tangential stresses in the most highly stressed plies.     

Buckling analysis of trapezoidal composite sandwich plate subjected to in-plane compression

The results of the stability analysis of simply supported layered isosceles trapezoidal plate subjected to axial in-plane compression are presented. The layup configuration is confined to symmetric laminates. The solution has been obtained by means of the Galerkin orthogonalisation method combined with the proposed method of the coordinate system transformation. The results of the analytical solution are compared with the verifying FEM calculation. The computed results in the form of graphs of the buckling force as a function of material and geometrical parameters of the panel are included.     

Characterization of fracture modes in stitched and unstitched cross-ply laminates subjected to low-velocity impact and compression after impact loading

The insertion of transverse reinforcing threads by stitching is a very promising technique to restrict impact damage growth and to improve post-impact residual strength of laminates. In order to develop general models capable of addressing the issues of impact resistance and damage tolerance of stitched laminates, detailed understanding of the nature and extent of damage, identification of the dominant fracture modes and assessment of the effect of stitches on the damage development are essential. In this study, both instrumented drop-weight tests and compression-after-impact tests were carried out to examine and compare the damage responses of stitched and unstitched graphite/epoxy laminates subjected to low-velocity impact. The progression of damage and its effect on post-impact performance was investigated in detail in two classes of cross ply laminates ([0₃/90₃]_s and [0/90]_3s) by means of an extensive series of damage observations, conducted with various complementary techniques (X-radiography, ultrasonics, optical microscopy, deply). The results of the analyses carried out during the study to characterize the key fracture modes and to clarify their relationship with the structural performance of both stitched and unstitched laminates are reported and discussed in the paper.     

Spectral strip analysis for composite cylinders subjected to lateral impact

An efficient computational method, combining the spectral element and the finite-strip method (spectral-strip) is developed in order to obtain numerical results to time dependent problems of cylindrical composite structures subjected to lateral impact, within moderate CPU times. The finite strip method is applied to cylindrical structures uses global interpolation in the circumferential direction, and spectral emenents in the meridional cross section. A term superposition solution is obtained, where every iteration refines the solution and is independent of former iterations. In this manner, a full three-dimensional solution to the problem of the dynamic response of cross-ply cylindrical composite shells subjected to a lateral impact, is obtained. The stability and the accuracy of the method are examined. The main goal is to predict the damage caused by a high velocity non penetrating impact of microparticles. Two types of shells are studied—thin and thick cross-ply laminates. The effect of curvature on a high velocity impact is studied. Also, the stress field obtained by the finite element code is investigated and damage evaluation is discussed. The present work focuses on moderate and high velocity impacts and therefore the force duration is of the order of the through-the-thickness propagation time, causing the imapct region to be in tension due to the reflected stress wave. The results demonstrate the dilatational compression wave traverses the shell thickness as a result of the impact and the dilatational tension wave reflected from the interior free surface as well as the propagation of shear waves in different directions. Using failure criteria, one can find that the compressive stress wave causes matrix cracking and the tensile stress wave causes both delamination and matrix cracking. It is shown that for a thin cylinder, the impact phenomenon is concentrated near the striking region while for a thick-walled cylinder the results of the impact are visible in points far from the striking point as well. The interference of the stress waves that circumevent the cylinder create other points of local maxima for the equivalent stresses. The code written for the finite element solution embloys the object oriented programming through the C++ language. A special matrix class is developed to perform various linear algebra operations. Dedicated to the memory of Professor Joab J. Blech (1934–1996)     

Dynamic large deflection response of composite laminates subjected to impact

Impact responses of composite laminates with and without initial stresses are investigated using the finite element method. A nine-node isoparametric quadrilateral element based on the Mindlin plate theory and the von Karman large deflection assumptions is developed. An experimentally established contact law which accounts for the permanent indentation is incorporated into the finite element program to evaluate the impact force. In the time integration, the Newmark constant acceleration algorithm is used in conjunction with successive iterations within each time step. Numerical results, including the contact force histories, deflections and strains in the plate, are presented.     

Numerical simulation of ceramic composite armor subjected to ballistic impact

Armor systems made of ceramic and composite materials are widely used in ballistic applications to defeat armor piercing (AP) projectiles. Both the designers and users of body armor face interesting choices – how best to balance the competing requirements posed by weight, thickness and cost of the armor package for a particular threat level. A finite element model with a well developed material model is indispensible in understanding the various nuances of projectile–armor interaction and finding effective ways of developing lightweight solutions. In this research we use the explicit finite element analysis and explain how the models are built and the results verified. The Johnson–Holmquist material model in LS-DYNA is used to model the impact phenomenon in ceramic material. A user defined material model is developed to characterize the ductile backing made of ultra high molecular weight polyethylene (UHMWPE) material. An ad hoc design optimization is carried out to design a thin, light and cost-effective armor package. Laboratory testing of the prototype package shows that the finite element predictions of damage are excellent though the back face deformations are under predicted.     

Diamond synthesis in graphite/nickel composite powders subjected to shock compression

Characterization of graphite/nickel composite powders subjected to high-pressure shock-wave compression was performed using optical and transmission electron microscopy. Unique spherulites of graphite were observed in the nickel matrix of those specimens in which the nickel apparently melted under the shock-wave loading. The morphology of these spherulites resembles that of nodular graphite found in cast iron. Evidence of diamond formation was found both at the centre of spherulites (polycrystalline) as well as in the remaining graphite flakes (single crystal).     

Failure characteristics of some metals subjected to torsion only,and when subjected to combined torsion and compression

The contents of this paper show that when a metal toreion specimen is subjected to an axially applied compressive stress, then the resulting angle of twist recorded up to fracture will be greater than if tested under plain torsion conditions. Increasing this longitudinal compression results in a further increase in the fracture strain.

The introduction of CCL₄ to the gauge length whilst under test causes a reduction in the strain to failure. The presence of a longitudinal stress or CCL₄ or a combination of both has little or no effect on the fracture strength of the tested materials. Tested materials include pure, two and poly phase and free-machining materials.     

Modelling damage evolution in composite laminates subjected to low velocity impact

In this paper, the impact damage of composite laminates in the form of intra- and inter-laminar cracking was modelled using stress-based criteria for damage initiation, and fracture mechanics techniques to capture its evolution. The nonlinear shear behaviour of the composite was described by the Soutis shear stress–strain semi-empirical formula. The finite element (FE) method was employed to simulate the behaviour of the composite under low velocity impact. Interface cohesive elements were inserted between plies with appropriate mixed-mode damage laws to model delamination. The damage model was implemented in the FE code (Abaqus/Explicit) by a user-defined material subroutine (VUMAT). Numerical results in general gave a good agreement when compared to experimentally obtained curves of impact force and absorbed energy versus time. The various damage mechanisms introduced during the impact event were observed by non-destructive technique (NDT) X-ray radiography and were successfully captured numerically by the proposed damage evolution model.     

Failure loads for model adhesive joints subjected to tension,compression or torsion

The Griffith fracture criterion has been applied to model adhesive joints subjected to tension, compression or torsion. Two model joints are considered: a rigid cylinder partly embedded in and bonded to an elastic cylinder (termed rod joint here), and an elastic cylinder inserted partway into, and bonded to, a rigid tube (termed sleeve joint here). Both types of joint have been constructed, using vulcanized rubber cylinders bonded to aluminium rods and sleeves.Measurements have been made of the failure loads under tension, compression and torsional loading. They were found to be in satisfactory agreement with the theoretical predictions except, in some instances, for rod joints subjected to tension or torsional loading when the failure loads were as much as three times the predicted values. This discrepancy is attributed to friction between the partially-detached rubber cylinder and the embedded rod, enhanced to a great extent by the tendency of the rubber cylinder to shrink in radius on stretching or twisting. A theoretical analysis of the effect of friction is presented. It predicts increasingly large pull-out forces or torques, as the depth of embedment increases, until frictional seizure occurs. Experimentally, frictional effects were limited by applying an internal gas pressure to the region being detached. All of the failure loads were then found to be in satisfactory agreement with the original theory, ignoring frictional effects. Thus, a simple fracture energy criterion is shown to govern the failure of adhesive joints under complex loading conditions, with or without friction acting at the interface.On leave from the Rubber Research Institute of Malaysia, Kuala Lumpur, Malaysia.     

Failure mode maps for composite sandwich panels subjected to air blast loading

Failure mode maps for sandwich panels with composite face sheets are presented. These failure mode maps can provide useful insights on how panel failure depends on the key variables in the problem. To include dynamic effects in the problem the sandwich panel was modeled as a single-degree-of-freedom mass–spring system. This allows one to simulate the effect of blast loading on the panels. A comparison with some quasi-static test results was performed and it was found that the experimental data were consistent with the analysis.     

Modelling of composite sandwich structures with honeycomb core subjected to high-velocity impact

In this study the perforation of composite sandwich structures subjected to high-velocity impact was analysed. Sandwich panels with carbon/epoxy skins and an aluminium honeycomb core were modelled by a three-dimensional finite element model implemented in ABAQUS/Explicit. The model was validated with experimental tests by comparing numerical and experimental residual velocity, ballistic limit, and contact time. By this model the influence of the components on the behaviour of the sandwich panel under impact load was evaluated; also, the contribution of the failure mechanisms to the energy-absorption of the projectile kinetic energy was determined.     

Contact force history analysis of composite sandwich plates subjected to low-velocity impact

Usually the modified Hertzian contact law or experimental static indentation law has been used to analyze low-velocity impact response of composite laminates. In composite laminated plates subjected to low-velocity impact, usually indentation by impact is very small and also energy absorption by indentation is negligible, so ‘spring element method’, which proposed by author recently, can be well applied to investigate impact response. In the present study ‘lumped mass method’ also had been proposed by author to approximately calculate contact force history of composite laminates will be conceptually described as well as the spring element method. And it will be discussed that how the spring element method can be applied to composite sandwich plates. Finally numerical results easily obtained from finite element analysis based on the spring element method using general-purpose commercial FEM software is compared with experimental results. The comparison shows overall agreement.     

On the influence of laminate stacking on buckling of composite cylindrical shells subjected to axial compression

The buckling loads of laminated cylinders can strongly depend on the position of the differently oriented layers within the shell. This paper deals with two different laminated orthotropic cylinders with opposite stacking sequence of the laminate layers. Cylinders of this construction had been thoroughly tested within a BRITE EURAM project. Analytical and semi-analytical methods have been used to predict the buckling loads, and the results are reported in this paper as well as test results for comparison. An explanation of the striking influence of stacking sequence is given. With some more examples the findings are verified. It is suggested that the presented results can be used for benchmarking purpose.