GRANT
journal
ISSN 1805-062X, 1805-0638 (online), ETTN 072-11-00002-09-4
EUROPEAN GRANT PROJECTS | RESULTS | RESEARCH & DEVELOPMENT | SCIENCE
The glued joints have a high shear resistance. Very badly tolerated
tensile force. Therefore we shape them so that the joint is loaded
only by shearing.
The glued joint is loaded with force F (Figure 3). In this case
(assuming the flange material is inelastic), both parts are shifted by
length e. If Hook's law applies to the adhesive, the voltage
τ is the
same over the entire length of the connection l.
Fig. 3 Glued joint stressed on shear
The basic calculation equation is based on the mean stress
τ equally
distributed over the length of the joint and we compare it with the
allowable stress
τ
D
.
=
∙
≤
(1)
=
(2)
where k - safety factor, F – force, l - length of the connection, b -
joint width,
τ - tensile stress, τ
D
- allowable tensile stress.
Experiments showed these values
τ
p
for steel are
=(23÷54)∙10
6
(3)
Recently, at ever faster evolving computer technology and available
literature, we can encounter modern numerical methods, such as
finite element method (FEM) [19]. It is one of the most widespread
numerical mathematical methods used to solve the problems of
elasticity and strength, the dynamics of pliable bodies, heat transfer,
fluid flow, electromagnetism, and many other problems in
engineering.
Knowledge of the behavior of glued joints is essential for their
subsequent application in practice. For effective prediction of the
properties of glued joints it is necessary to use suitable tools
allowing to accurately model various modes of failure that may
occur in the structure [20]. The failure of glued joints includes the
area from the beginning of loading to the initiation of the crack,
followed by the area of development of the failure.
The possibility of numerical simulation of the glued joint is the main
requirement for its successful design. If a suitable numerical method
was found, it would be possible to replace a large part of the glued
joint experiments with this simulation. This would lead to a
reduction in the times involved in the development, production and
production cost of the product. The simpler tools offered by FEM
analysis allow you to model only the area from the beginning of the
load to the initiation of damage. The principles of linear elastic
fracture mechanics apply in this area. The behavior in this area is
described by the cohesive stiffness of the adhesive layer. The failure
initiation state occurs at a critical value of the stress at the crack
front. In the FEM model, this state describes the tension between the
nodes of an idealized adhesive layer caused by their critical
displacement and critical load.
In addition to the strength approach, advanced analyzes can also be
based on the elasto-plastic fracture mechanics approach to describe
the area of failure development. These principles apply especially in
a situation where the adhesive layer is very thin between two parts
to be glued and its behavior cannot be described by macroscopic
properties, such as tensile modulus or Poisson's constant (E, ν) [21,
22]. In these cases, the behavior of the bonded joint by the energy
required for crack propagation, or the rate of release of the strain
energy G, is described. These approaches make it possible to predict
the onset and spread of failure without prior knowledge of the
location of the crack and the direction of crack propagation in the
structure. The quality of the calculation and the accuracy of the
results are directly dependent on how ideally the adhesive layer can
be idealized using conventional and advanced tools offered by FEM
analysis. In addition to the accuracy of the results, the duration of
the calculation, these can also differ in the user-friendliness of the
results.
Elements commonly available in FEM analyzes can be used to
idealize the adhesive layer. Their behavior is described in terms of
material parameters, which in some cases can be obtained from glue
producers, but more often it is necessary to find out more difficult
by means of experiments. Specifically, the adhesive layer can be
replaced by contact, 3D elements, 2D elements, a linear spring
system, or simply replacing the adhesive, such as the SSG element
in Siemens NX or the TIE element in Abaqus.
The first step is to create a CAD model. This model is then
converted into a preprocessor, which converts the geometric model
into the form necessary for the calculation itself. In this phase, the
main task is to create an adequate computer network and to define
the initial conditions correctly. The preparation of the whole
calculation model follows the rules that each company creates itself
and must be strictly observed. The rules are set to achieve a
compromise between computational complexity and result accuracy.
The next step is to load the file into the solver and start the
calculation itself. The calculation is started using the command line
and follows the mathematical operations described above. The
results are written to files during the calculation.
The last step is to load and process the results in the postprocessor.
The postprocessor allows viewing the simulated process, plotting
acceleration, stress, strain and many other variables depending on
the selected variable.
Fig. 4 2D plain strain finite element model of bonded joint
In recent years, models using the so-called cohesive joint model
have been used in the research of glued joints. The cohesive Model
can be used to model adhesives, bonded surfaces, seal models,
patches, or delamination processes (Fig.4). The cohesive model
exploits some of the advantages of common FEM elements and is
based on Griffith's refraction theory. The aforementioned common
elements included in the FEM creation tools are characterized by the
absence of a criterion for predicting the evolution of violations for
any violation mode. The cohesive model is innovative and used
approach for the calculation and prediction of the evolution of
bonding failure, specifically this model includes, compared to the
Vol. 9, Issue 1
108