Dan Zenkert

Fatigue of foam core sandwich beams—1: undamaged specimens

The present paper addresses the fatigue characteristics of two cellular foam core materials as used in load carrying sandwich structures. The fatigue loading studied is a constant shear stress which corresponds to the main type of loading that the core in a sandwich structure exhibits. Based on results from testing stress-life curves are presented for a number of stress ratios (R) and are fitted to a simple two-parameter Weibull function. The influence of the R-value is emphasized and standard Haigh diagrams are constructed. It is seen that the fatigue behaviour of the core materials investigated herein well can be described in manners similar to that of classical metal fatigue. A thorough investigation is performed on the behaviour of fatigue crack formation and growth.

Fatigue of foam core sandwich beams—2: effect of initial damage

This paper addresses the influence of sub-surface core damage in sandwich beams subjected to fatigue loading. Using results from static and fatigue tests of undamaged beams a model for the prediction of the fatigue life of damaged beams are proposed. Sandwich beams subjected to transverse loading inducing a shear stress field in the core material with two typical sub-surface damages, a flawed butt-joint and a interface disbond, are investigated. The fatigue life of damaged sandwich beams is investigated through numerous tests which are presented in standard S/N diagrams. Curve fitting to the experimental data is performed using a two parameter Weibull function. In order to capture the effects of crack opening and crack closure loads and their relations two different loading ratios are employed. Also, a modified stress life function is proposed using notch factors to predict the fatigue life of damaged beams. The notch factor is calculated as the ratio of the failure loads of damaged to undamaged beams obtained from static tests. The results indicate that the proposed simple approach can be used to accurately predict the reduction in the fatigue life due to the inflicted damages. Also, an alternative and very general method based on point stress criterion is proposed which seems rather promising. The fracture paths are monitored and the fracture initiation in fatigue is discussed.

Strength of sandwich beams with interface debondings

Abstract The adhesive joint bonding the faces to the core material in a sandwich structure ensures that the loads are transferred between the components. However, debondings may arise either during the manufacturing process or due to overloading. These will reduce both the stiffness and the load bearing capacity of the structure. In the present paper, debondings in foam core sandwich beams are investigated assuming that cracks in the interface between the face and core are present. Stress intensity factors are found from an analytical model and compared to solutions from several finite element calculations. Fracture toughness values, determined from simple specimens, are used to predict the fracture loads for beams with simulated debondings subjected to four-point bending.

Failure Mechanisms and Modelling of Impact Damage in Sandwich Beams - A 2D Approach: Part I - Experimental Investigation

This paper addresses the effect of low velocity impact damage on post-impact failure mechanisms and structural integrity of foam core sandwich beams subjected to edgewise compression, shear and bending load cases. The study deals with a 2D configuration, where a sandwich beam is impacted by a steel cylinder across the whole width of the specimen. The impact damage is characterised as indentation of the core with sub-interface damage seen as a cavity while the GFRP faces remain virtually unaffected by the impact. Digital speckle photography (DSP) analysis is employed for in situ monitoring of crushing behaviour in the foam core during static indentation of sandwich specimens. The static shear strength of impact-damaged sandwich beams is compared with specimens with fabricated sub-interface cracks of the same length. DSP analysis reveals that the face-core interface in the peripheral regions of 2D impact damage is not entirely separated. The crack analogy is thus not fully representable since the surfaces remain bridged resulting in higher strength, when compared with fabricated cracks. The post-impact resistance to compressive loads is lower than for the specimens with fabricated cracks due to the presence of the cavity and the crushed core with reduced foundation stiffness support. The properties of crushed foam core are experimentally determined as they appear to be important for accurate modelling and analysis of the residual strength of sandwich beams. Modelling and post-impact analysis of the specimens with impact damage is elaborated in detail in part II of this study.

PVC sandwich core materials: Mode I fracture toughness

Abstract The fracture of a cracked PVC sandwich core material has been investigated. Mode I fracture toughness is evaluated using linear elastic fracture mechanics (LEFM), nonlinear fracture mechanics and a damage zone model. For the crack sizes and structural dimensions relevant to sandwich constructions, LEFM is not applicable according to the ASTM standard requirements for metals. However, the results show that the deviation between nonlinear analyses and LEFM is relatively small. Therefore, K Ic and G Ic can still be used for engineering purposes. It is also found that the fracture toughness depends on the average cell size.

Fatigue of closed cell foams

This paper deals with fatigue of closed cell foams. The main idea is to use a few simple tests to predict the tension-tension fatigue properties of foams. The required testing consists of crack propagation rate measurements and one tension-tension fatigue test performed at yield stress for the foam. This data can then be combined to construct a synthetic S-N Curve for the foam. Tests on three densities of Divinycell H-grade foam are performed and the results Support this approach. Some preliminary results from two densities of Rollacell WF-grade are given as well. Static properties of foams scale with relative density and once this scaling can be obtained through various static tests and the same scaling appears to be valid for both crack propagation rates and fatigue properties of foams. The implication of this is that once the fatigue behaviour of one relative density foam is established, one can predict the fatigue behaviour of all other relative density foams within the same class of materials.

Strength of sandwich beams with mid-plane debondings in the core

Abstract Sandwich beams containing cracks in the mid-plane of the core are investigated. The cracked part is subjected to a constant remote shear stress field. Beams with different cross-section geometries and materials were analyzed by the finite element method (FEM) in order to compute the stress intensity factors at the crack tips. An analytical approach for estimation of the energy release rate, based on a potential energy calculation, is presented that agrees well with results from the FE analyses. Results from four-point bending tests with cracked beams show that the fracture load can be accurately predicted. The simplicity of the analytical model makes it possible to compute critical crack lengths and safety factors for various types of sandwich beams.

Failure Mechanisms and Modelling of Impact Damage in Sandwich Beams - A 2D Approach: Part II - Analysis and Modelling

This study addresses the effect of low velocity impact damage on the post-impact residual strength and failure mechanisms of sandwich beams with Rohacell WF51 foam core. The considered impact damage has a form of a subinterface cavity surrounded by crushed core while the face sheet remains virtually undamaged. Part I of this study deals with experimental investigation of impact-damaged beams tested in transverse shear, bending and edgewise compression. It is shown that the crushed core and the bridging condition in the peripheral regions of the impact damage exert a significant effect on the post-impact critical loads and failure mechanisms. In this paper, parameterised finite element (FE) models of impact damage with implemented crushed core properties are developed for numerical analyses of post-impact failure. In the analysis of the shear case, a model for II bridging condition in the peripheral regions of impact damage is introduced. A point-stress criterion is applied for predictions of failure loads and crack kink angle. Geometrically nonlinear FE analysis is employed for evaluation of critical loads for local buckling in the beams with impact damage. The FE analyses demonstrate good agreement with experimental results.

Poly(vinyl chloride) sandwich core materials: Fracture behaviour under mode II loading and mixed-mode conditions

Abstract In a sandwich construction the core material carries transverse loads and transfer loads between the faces as shear stresses. A crack in the core material will therefore be subjected to mode II loading or a state of mixed-mode conditions. In the present paper, fracture of a cracked poly(vinyl chloride) core material with crack sizes and structural dimensions relevant to sandwich constructions under such conditions is investigated. It is found that the apparent mode II fracture toughness is slightly larger than for mode I. Both fracture stress and propagation angle can be satisfactorily predicted with the strain energy density criterion for the mixed-mode case. A failure assessment diagram can be used when high ligament stresses arise and where linear elastic fracture mechanics therefore are not valid.

Imperfection-induced Wrinkling Material Failure in Sandwich Panels

In this paper, sandwich wrinkling or local face sheet instability is treated in the context of material failure. Traditionally, test results rarely complied well with the predicted failure load and a knock down factor often had to be used. The reason for this is often referred as the effect of initial geometric imperfections. In this paper, imperfections are included in the natural waveform given by the linear stability analysis, i.e., a short wavelength sinusoidal buckling shape. These initial imperfections lead to increased displacements during loading giving rise to both, an in-plane compressive strain and a varying bending strain. These strains can then be related to material failure criteria, one for the face sheet compressive strain and one for the core normal strain. An analytical model is derived and compared with experimental results and several issues are revealed. The panel strength measured using a realistic initial imperfection amplitude agrees very well with the derived model, giving a prediction somewhat below the values obtained from the traditional approach. This verifies that the actual wrinkling failure is below the theoretical instability load. The model is able to distinguish between different failure modes, face sheet compression failure or core-adhesive joint tensile failure, giving good correlation with the experimental findings. Thus, it appears that using initial imperfections as a basis for wrinkling analysis provides a better foundation for the failure analysis than the ordinary stability analysis, and it also allows to determine which failure mode is predominant. Finally, it is shown that the choice of the core material can be made based on the theory presented to obtain a more efficient sandwich panel.