Andrey Shipsha

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.

The inelastic quasi-static response of sandwich structures to local loading

The paper addresses the inelastic quasi-static response of sandwich beams and panels with foam core to localized loads. The plane and axisymmetric formulations for local indentation or local low-velocity impact by a rigid body are considered; no overall bending is assumed. The governing equations for the face are derived using the Kirchhoff–Love static theory under the assumption that the core crushing follows elastic–ideally-plastic behavior. Analytical solutions are constructed on the basis of the principle of minimum work. The solutions allow predicting the face deflection, size of crushed core area and contact force. In general, the solutions are in good agreement with experimental data and finite element analysis.

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.

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.

The elastic response of sandwich structures to local loading

The paper addresses the elastic response of sandwich panels to local static and dynamic loading. The bottom face is assumed to be clamped, so that the overall bending is eliminated. The governing equations are derived using the static Lame equations for the core and the thin plate Kirchoff–Love dynamic theory for the faces. The plane and axisymmetric formulations are considered. The closed-form solutions are obtained using Fourier–Laplace (Hankel–Laplace) integral transformations for the cases of forced excitation and impact by a rigid body. The solutions allow to predict the stress–strain state of the structure. The analytical solutions demonstrate a good agreement with experimental data and finite element analysis.

Effect of Physical Nonlinearity on Local Buckling in Sandwich Beams

This article deals with experimental, theoretical, and FE characterization of the local buckling in foam-core sandwich beams. In the theoretical approach, this phenomena is considered in a periodic formulation (unbounded wrinkle wave); a nonlinear stress—strain response of the face material is accounted for. In the FE approach, nonlinearity of the core material is also modeled. Full-field strain measurement is employed in the tests showing that the commonly used edgewise compression set-up can cause premature waviness of the faces, and therefore, nonlinear local deformations in the core layer.

Fatigue Behavior of Foam Core Sandwich Beams with Sub-Interface Impact Damage

The fatigue life of impact-damaged foam core sandwich beams with GFRP faces is investigated for constant load-amplitude cyclic loading. The damage produced by the low velocity/energy impact is characterised as a sub-interface cavity with surrounding crushed core whereas the face sheet is undamaged. The effect of bridging owing to the crushed core in the peripheral regions of impact damage, revealed in the preceding static study Shipsha et al. [1,2] is assessed under cyclic loading. The fatigue test results are analysed in a stress-life S-N diagram and compared with published data from undamaged beams. The effect of two load ratios R = 0.1 and -1 is investigated. The fatigue threshold load levels are experimentally quantified from the S-N curves. Furthermore, a modified point-stress criterion based on the threshold stress intensity factor, Kth, is proposed to estimate the “no-crack growth” limit loads. The results show good agreement with performed experiments.

Deformation of Foam Cores in Uniaxial Compression-Tension Cycle:

This article deals with experimental and analytical analysis of the mechanical behavior of crushed foam cores. Three rigid cellular core materials are tested in a uniaxial compression-tension cycle. An analytical model is proposed describing the stress-strain curve in tension and secondary compression. A special emphasis is laid on the relaxation behavior of a crushed foam core in tension.

Wrinkling in sandwich panels - an analytical approach

This article deals with theoretical modeling of the local buckling in foam–core sandwich panels. This phenomenon is considered mainly in the periodic (unbounded wrinkle wave) and linearly elastic formulation. The analytical solutions are in agreement with results of finite element analysis and can be applied with a good precision for many finite-size panels, as well as for many sandwiches having honeycomb cores.

Residual In-plane Mechanical Properties of Transversely Crushed Structural Foams

The mechanical properties of structural polymer foams are investigated after crushing in the rise direction (out-of-plane axis of a foam material block). The crushed foams are loaded in uniaxial compression, tension, or shear. All tests are performed in the plane of the foam block, i.e., perpendicular to the crushing direction. For comparison, virgin foams are also characterized. The results are discussed featuring the properties of crushed foams, which can be important for the damage tolerance analysis of a foam core sandwich structure.