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 is the ratio of 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 modemixity
in this FRMM test and other similar beam-like
geometries.