Derivation of the stress concentrations at holes in orthotropic plates using thermoelastic stress analysis

An experimental study of the stress distribution around holes in orthotropic composite laminates has been conducted using thermoelastic stress analysis (TSA). Quantitative thermoelastic studies of stress concentrations in metallic plates is a straightforward matter, all that is required is the ratio of the response from the hole and a far-field reading. For orthotropic materials the situation is more complex as the response is not simply proportional to the sum of the principal stresses. In general the thermoelastic response of an orthotropic laminate is a function of the stresses in the principal surface material directions and the associated coefficient of thermal expansion. The approach in this paper is to obtain ‘stress factors’ at the hole and identify the maxima in the plot. Specimens manufactured from a variety of different laminate lay-ups (unidirectional (UD), cross-ply (CP), angle-ply (AP) and quasi-isotropic (QI)) are considered. In all these cases the principal stress directions at the hole are not coincident with the principal material directions and it is a challenging proposition to derive meaningful stress data from these configurations. To validate the approach the experimental data are compared to analytical models. To better understand the nature of the response finite element models are produced that mimic the thermoelastic response. Introduction Composite components with holes or cut-outs of various sizes and shapes are frequently used as load bearing members in various engineering structures. The presence of stress concentrators causes substantial perturbation of the stress and strain field in the structure under service loads. Therefore it is of great practical interest to accurately analyse the load bearing capacity of these structures. Numerous numerical studies [1-4] on anisotropic composite plates with holes of various geometries, lay-ups and loading conditions have been conducted. The heterogeneity and directional anisotropy of composite plates complicates the mathematical formulation of the stress concentration factor (SCF) around holes. A theoretical solution to obtain SCF’s in an infinite orthotropic plate for both circular and elliptical holes under tensile load using the complex variable method was presented by Lekhnitskii [5]. In addition, several experimental techniques such as digital image correlation (DIC) [6], Moiré methods [7], thermoelastic stress analysis (TSA) [8] and strain gauging [9] have been used to determine the strain/stress distribution around circular holes in orthotropic plates. Some experimental and theoretical results that attempt to incorporate a finite width correction factor around the hole are presented in Ref. [9], which is important in the interpolation of test data to infinite plate results. The TSA technique is based on infra-red thermography, where the small temperature changes resulting from a change in elastic stress are obtained by measuring the change in infra-red photon emission. TSA has advantages over other experimental techniques since only minimal surface preparation (i.e. coatings, grids or speckle patterns are not needed) is required for obtaining stress data with spatial resolution down to 4 μm [10]. The purpose of this paper is to obtain the stress/strain concentration at holes in orthotropic polymer composite plates from thermoelastic data. To achieve this it is necessary to understand the Figure 1: Uniaxial tensile load applied a) in the principal directions and b) at an angle to the principal material direction of an orthotropic plate with a circular hole nature of the thermoelastic response; three approaches are presented for interpreting the thermoelastic data. A variety of lay-ups are studied and analytical and finite element models are used to aid the interpretation of the TSA data. To achieve accurate insight from the models the material properties required to present the data in the same form as the TSA are derived experimentally for the different material configurations. The results show that the thermoelastic response is most similar to the ‘global’ response of the laminate and not that of the surface ply or resin rich layer. Derivation of the thermoelastic stress and strain concentration factors A stress concentration factor, SCFσ, for a single hole in the centre of a strip of material loaded under uniform uniaxial loading is defined as follows: