Full-field experimental analysis of a sandwich beam under bending and comparison with theories

Abstract

Sandwich plates with two thin stiff face-sheets and a soft center core have been used in many constructions for which the dominating load is transverse bending. Many theoretical/numerical analyses have been devoted to studying the deformation mechanism of such a structure. But relatively limited experimental investigations are present in this field and they are often self-content with little connection to the existing theoretical pursuits. In this paper, a composite sandwich structure made with carbon fiber woven face sheets and a relatively compliant foam core was loaded in 3-point bending. Images were captured of the specimen before and after deformation, which were then analyzed with a Digital Image Correlation (DIC) program. The full field displacements and strain fields were obtained for the specimen. The experimental deflection of the beam was compared with five theoretical models and one numerical solution. The result shows that only one model predicts the reality well.

Introduction

Sandwich plates and beams can be found in many engineering structures such as ships, bridges, planes, wind turbines, and other structures. Modern sandwich construction usually consists of two stiff face sheets and a soft middle core. Such a construction has a very advantageous weight to stiffness ratio. Research efforts devoted to sandwich structures have a long history [1]. Most investigations are either theoretical or numerical in nature [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13]. Of particular interest in these papers are the work of Kardomateas et al. [4], [5], in these studies, a formulation of the Elasticity solution for the behavior of sandwich beams is presented, then in a following study, the Extended High-Order Sandwich Panel Theory (EHSAPT) is formulated and compared with existing theories of composite sandwich beams. In Kardomateas et al. [6] the authors developed a Finite Element Model (FEM) based on EHSAPT, yielding results that were nearly identical to the analytical solution. Numerous studies have been performed on the bending behavior of composite sandwich beams [3], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23], [24]. Though relatively few experimental investigations have investigated the validity for the numerous existing numeric models and analytic theories. There seems to be a disconnect between theory/numerical studies and experimental investigations in that very little efforts are devoted to checking each other’s results. Most studies, either theoretical/numerical or experimental, place emphasis on the global deformation (deflection) of a plate or beam, even though the dominant failure mode of a sandwich structure is the excessive deformation of the core [21], [22], [23], [24], [25], [26], [27], [28], [29], [30], [31], [32], [33], [34], [35]. The first full-field mapping of a sandwich core deformation is given by Gdoutos et al who employed the in-plane moiré method to mapping the core deformation [20]. With the advent of modern full-field measurement techniques, such a DIC (Digital Image Correlation), DSP (Digital Speckle Photography), DSC (Digital Speckle Correlation) more detailed deformation patterns of the core can be obtained. An example is the work of Fathi, Keller, and Altstaedt [36] in which the shear strain field of the foam core was calculated. In this paper, we present the results of a sandwich beam under three point-bending using DIC to obtain its displacement field and then calculate the strain fields using different displacement–strain relations, that model the linear or nonlinear behavior of elements of a composite sandwich beam, in accordance with the formulations developed by Yuan et al. [37].

In recent years there has been a rich outpouring of theoretical/numerical papers dealing with the deflection of sandwich plates/beams under bending [4], [5], [6], [7], [8], [9]. But no experimental effort, to the best of our knowledge, has been devoted to checking these models to ascertain which of the models matches with reality. In this paper, we present some experimental results in an effort to shed light on the validity of various theoretical/numerical models.