Mode-mixity in beam-like geometries: global partitioning with cohesive zones
In-service adhesive joints and composite laminates are often subjected to a mixture of mode I (tensile opening) and mode II (in-plane shear) loads. It is generally accepted that the toughness of such joints can vary depending on the relative amounts of mode I and mode II loading present. From a design perspective, it is therefore of great importance to understand and measure joint toughness under a full range of mode-mixities, thus obtaining a failure locus ranging from pure mode I to pure mode II. The pure mode toughnesses (I, II) can be measured directly from experimental tests, the most common tests being the double cantilever beam (DCB) for mode I and end loaded split (ELS) for mode II. Unfortunately, the analysis of a mixed mode test is not straightforward. In any mixed mode test, one must apply a partition in order to estimate the contributions from each mode. The particular test under study in this work is the fixed ratio mixed mode test (FRMM) with a pure rotation applied to the top beam (fig. 1). In this test, a range of mode-mixities can be obtained by varying γ, where γ = h1/h2. This test is normally analysed using analytical or numerical methods, each of which suffers from a number of uncertainties. The present work attempts to shed some light on both analytical and numerical approaches and ultimately develop a testing protocol and recommendations for the accurate determination of mode-mixity in the FRMM test and other similar beam-like geometries.