In this presentation describe finite element analysis of single lap joint.

1. 1
Finite Element Modelling of
Polymer Nanocomposites as an
Adhesive
Submitted by-
Vikas Mishra
2017CC13
Under the Guidance of-
Dr. D.K. Shukla
Associate Professor
MED,MNNIT Allahabad
Mechanical Engineering Department
Motilal Nehru National Institute of Technology
Allahabad-211004, INDIA

2. Table of Contents-
• Introduction
• Literature Survey
• Conclusions of Literature Survey
• Research Gaps
• Objectives
• Finite Element Modeling
• Remaining work
2

3. Introduction
• Adhesives are used for joining and assembling of structures. A modern adhesive is a polymer based
material that can be used to join a wide variety of different surfaces together without the need to
create discontinuities in the substrate material.
Types of adhesives
Adhesives
3
Adhesive
By Structure
Thermosetting
Adhesive
Thermoplastic
Adhesive
Elastomeric
Adhesive
By Curing Method
Heat activated curing
adhesives
Light/UV activated
curing adhesives
Moisture activated
curing adhesives
Pressure sensitive
adhesives (PSA)
By Origin
Synthetic
adhesives
Natural adhesives
(glues)

4. • In an adhesive joint, adhesive are applied between two plates known as adherend. If the load is not very
large adhesive joints become very useful in joining metallic or non–metallic dissimilar materials.
• It is possible to produce high strength, durable joints using polymer adhesive without the need for fasteners
such as rivets and screw. Adhesives are used to join metal to metal, composite to composite and metal to
composite component.
Adhesive joints
Types of adhesive joints
(a) Single lap joint (b) Balanced double lap adhesive joint
(c) Unbalanced double lap joint
(d) Scarf joints
Fig 1. Different types of adhesive joint
4

5. Polymer nano composite
• Composite material is a material composed of two or more distinct phases (matrix phase and dispersed
phase) and having bulk properties significantly different form those of any of the constituents.
• Matrix phase-The primary phase, having a continuous character, is called matrix. Matrix is usually
more ductile and less hard phase.
• Dispersed (reinforcing) phase-The second phase is embedded in the matrix in a discontinuous form. This
secondary phase is called dispersed phase. Dispersed phase is usually stronger than the matrix, therefore it
is sometimes called reinforcing phase.
• Polymer nanocomposites consists of polymer matrix that has nanofillers dispersed into it. Nanofillers may
be of different shapes (eg, platelets, fibers, and spheroids), and at least one dimension must be in the range
of 1-50 nm. Nanofillers provide very high interfacial area for better adhesion to polymer matrix.
Fig.2.Types of nano phases
a. Nanoparticles b.Nano tubes c.Nano plates
5

6. Literature Survey-
• The literature Survey performed is divided into following categories-
1. Research paper based on Experimental approach.
I. The effect of nanoparticles on the adhesion of epoxy adhesive by Lanlan Zhai, Guoping Ling,
Jian Li and Youwen Wang.
II. On adhesive properties of Nano-silica/epoxy bonded single-lap joints by He-Le-Zi Zhou, Hong-
Yuan Liu, Huamin Zhou, Yun Zhang, Xiping Gao, Yiu-Wing Mai.
2.Research papers based on finite element modeling.
I. A review of finite element analysis of adhesively bonded joints by Xiao Cong He
II. Simplified finite element modelling of structural adhesive joint by Guofeng Wu and A. D.
Crocombet.
3. Research paper based on finite element modeling and validation
with experiment.
I. Mechanical properties and adhesive behaviour of epoxy-graphene nanocomposites
by C. Saloma, M.G. Prolongoa S.G. Prolongob.
6

7. S.No Title Author Name Material System Finding
Year/Reference no Adherend Adhesive
1. The effect of
nanoparticles on the
adhesion of epoxy
adhesive.
International Journal
of Materials Letters
(2006)
Lanlan Zhai, Guoping
Ling, Jian Li and
Youwen Wang.
The low
carbon
Steel.
Epoxy
adhesive
Nanoparticles
were used
nanoAl2O3,
nanoCaCO3,
nano-SiO2.
Modified by 2% nano-
Al2O3, the strength on
the surface abraded
with 150# was visibly
improved by about 5
times.
2. Dynamic strength of
single lap joints with
similar and dissimilar
adherends.
International Journal
of Adhesion &
Adhesives(2015)
H.Ravi Sankar. Steel(SS304)
Aluminium
(6106)
Araldite 2014 The dynamic strength
under dynamic loading
is higher for stiffer
adherend .
7

8. S.No Title Author Name Material System Finding
Year/Reference no Adherend Adhesive
3. On adhesive
properties of Nano-
silica/epoxy bonded
single-lap joints.
International Journal
of Materials and
Design(2016)
He-Le-Zi Zhou,
Hong-Yuan Liu,
Huamin Zhou, Yun
Zhang, Xiping Gao,
Yiu-Wing Mai
Stainless
steel
plates
Epoxy
Incorporation of 10 and 20 wt.%
of nano-silica into epoxy matrix
improved the adhesive joint
strength by 20%.
4. Mechanical
properties and
adhesive behaviour
of epoxy-graphene
nanocomposites.
International Journal
of Adhesion and
Adhesives (2018)
C. Saloma, M.G.
Prolongoa S.G.
Prolongob.
Epoxy Polymer
matrix filled
with silica
nanoparticles
.
A slight increase of
strength and decrease of
ductility is observed for the
composite compared
to the pure epoxy.
8

9. S.No Title Author Name METHOD Types of Testing Finding
Year/Reference no Modelling
Software
5 A review of finite
element analysis of
adhesively bonded
joints.
International Journal
of Adhesion &
Adhesives(2011)
Xiao Cong He. Using finite
element
modelling on
commercial FEM
software ANSYS.
Finite element analysis
of adhesively bonded
joints is reviewed in
this paper, in terms of
static loading analysis,
environmental
behaviours, fatigue
loading analysis and
dynamic characteristics
of the adhesively
bonded joints.
It is concluded that the FEA
of adhesively bonded joints
will help future applications
of adhesive bonding by
allowing different
parameters to be selected to
give as large a process
window as possible for joint
manufacture.
6. Simplified finite
element modelling of
structural adhesive
joint.
Journal of computer
and structureVol. 61.
No. 2. pp. 383-391.
Guofeng Wu and A. D.
Crocombet
Using finite
element
modelling on
commercial FEM
software ANSYS.
The design analysis
of structural adhesive
joints.
Adhesive stresses from a
relatively coarse mesh can
be used for design purposes
and quadrilateral elements
for adhesive provide reliable
results for a representative
range of material
properties for single and
9

10. S.No Title Author Name METHOD Types of Testing Finding
Year/Reference no Modelling Software
7. Finite element inversion
method for interfacial stress
analysis of composite
single-lap adhesively bonded
joint based on full-field
deformation.
International Journal of
Adhesion and Adhesives
(2017)
Ruixiang Bai,
Shuanghua,
BaoZhenkun
Lei, Cheng Yan,
Xiao Han.
A three-
dimensional FEM
model of a single-
lap joint was
constructed using
the commercial
software ABAQUS.
Shear stress
distributions at the
interface and in the
middle of the adhesive
layer obtained by the
inverse FEM model.
In this paper, an inverse
hybrid method
combining the optical
measurement and FEM
numerical analysis was
proposed to obtain the
stress distribution at the
adhesive layer in a
composite single-lap
adhesively bonded joint.
8. Numerical modelling of
adhesively-bonded double-
lap joints by the
eXtended Finite Element
Method.
Journal of finite elements in
analysis and design.(2017)
T.F. Santos,
R.D.S.G.
Campilhoa.
Using the
commercial
software ABAQUS.
Subjected
to a tensile load, in
order to evaluate their
performance.
The XFEM analysis
revealed that it is
possible to accurately
predict the joints’
strength using the MAXS
and QUADS damage
initiation criteria.10

11. S.No Title Author Name Material System Types of
Testing
Finding
Year/Reference no
Adherend
Adhesive
9. Experimental and FEM
Studies on Mechanical
Properties of Single-
lap Adhesive Joint
with Dissimilar
Adherends Subjected
to Impact Tensile
Loadings.
International Journal
of Adhesion &
Adhesives(2013)
Lijuan Liao, Toshiyuki
Sawa, Chenguang
Huang.
aluminum
(A5052)
steel
(S45C)
epoxy resin Impact
tensile
tests.
It can be concluded
that the strength of
the joint with
dissimilar adherends
is smaller than that
of the joint with
similar adherends.
10. Adhesive joining of
copper using nano-
filler composite.
Journal of Polymer
(2016)
P.K. Ghosh, Avantak
Patel, Kaushal Kumar.
Copper Epoxy
based
nano-
filler
adhesi
ve
Nanoparticles
used were
titanium
dioxide (TiO2)
nanoparticles
Shear
strength
The use of nano-
filler composite
adhesive enhances
lap shear strength
and toughness of
the joint.
11

12. A review of finite element analysis of adhesively bonded joints by Xiao Cong He.
International Journal of Adhesion & Adhesives(2011)
• Finite element analysis of adhesively bonded joints is reviewed in this paper, in terms of static loading analysis,
environmental behaviours, fatigue loading analysis and dynamic characteristics of the adhesively bonded joints.
• Fig. 5 shows some typical classifications of adhesively bonded joints, which are commonly found in current
engineering practice.
Fig. 5. Some common engineering adhesive joints 12

13. Static loading analysis-
Environmental conditions-
Moisture effects on adhesively bonded joints and temperature effects on adhesive joints
Fig. 6.a Sketch of a standard SLJ and a SLJ with a
101 preformed angle.
Fig. 6. b Effects of the chamfer height on stress
distribution in the joint
Fig. 7.a Predicted failureloadsfromthe2-Dand3-D MMF
models using the continuum damage model with the
different mesh sizes.
Fig. 7.b Stress–strain curves for sheet steel at 40, +20 and
+90 1C along with the adhesive strain to failure a the corresponding
temperatures.
13

14. • Dynamic Analysis-
• In this paper the research and progress in FEA of adhesively bonded joints are critically reviewed and
current trends in the application of FEA are mentioned. It is concluded that the FEA of adhesively bonded
joints will help future applications of adhesive bonding by allowing different parameters to be selected to give as
large a process window as possible for joint manufacture.
Fig.8 . Location of nodes at the free edge of the single lap-
jointed cantilevered beam
Fig. 9. FRFs predicted by FEA and measured using the test rig (a) FRF for node
60621 & 151 ,(b) FRF for node 2060621 & 153 and (c) FRF for node 4060621 &
155.
14

15. Simplified finite element modelling of structural adhesive joint by Guofeng Wu and A.
D. Crocombet.
• In this paper a simplified finite element modelling approach is presented for the design analysis of structural
adhesive joints, in which either all the substrates (the beam version) or most of the substrates (the hybrid
version) are modelled by means of beam elements and the adhesive is modelled by using four-noded iso
parametric elements.
• The joints investigated here include a single lap joint and a double lap joint.
• A comparison of the stress results between the simplified analyses and detailed full two-dimensional finite
element analyses for all the joints is made by using the commercial engineering analysis system ANSYS.
• Finite element modelling of adhesive joints-
• Applying the beam version of simplified modelling to a joint, all the substrates will be modelled by beam
elements with the two connecting nodes of any element located along the centroid of the element.
• To account for the effects of the local deformation of the substrates and accommodate complete
displacement compatibility along the interfaces of substrates and adhesive, the following modelling
approach is adopted, which is called two-dimensional continuum modelling
15

16. • Single lap joint
Fig. 10. Schematic finite element meshes for a single lap joint
Fig. 11. A single lap joint and the boundary conditions used
for different modelling schemes.
Fig. 11.b Adhesive stress distributions along the bond line of the
single lap joint. 16

17. 17
• Es, and Ys, to represent the Young’s modulus and Poisson’s ratio of substrates, respectively, and Ea, and Ya, for
those of adhesive. It is also assumed that only unit width (1 mm) of the model is considered for all the joints
studied.
• Figure 11a shows the geometric dimensions and loading conditions of the single lap joint studied, the ratio of theYoung’s
modulus Es, for substrates to that for adhesive E,, r = Es/Ea, is the only parameter in this study of the joint. In this example,
Es, = 7OOOOMPa,.!Z, = Es/r is allowed to change, vs, = 0.3, va, = 0.32. Plane stress conditions are assumed.
• 1050 two-dimensional elements are used to mesh the overlap part, in which 1000 elements are for the substrates and
50 elements for adhesive for two dimensional continuum model.
• For the simplified beam model, the whole joint is idealised with 50 two-dimensional elements and 100 beam
elements.
• A fine mesh is adopted (i.e. using nearly square shaped elements) near the two joint ends such that the end effects
can be accurately modelled, and a relatively coarse mesh is used for the most central part.

18. • Double lap joint
• .
Fig.12.A double lap joint and the boundary conditions
used for different modelling schemes
Fig. 13. Adhesive stress distributions along the bond
line of the double lap joint.
18
See Fig12. a for the double lap joint studied. Since the joint is symmetric about the centre of the inner
substrate, only the upper half of the joint needs to be modelled.

19. • In this example, Es = 70000 MPa, Ea, = Es/r is allowed to change, vs, = 0.3, va, = 0.4. Plane strain conditions are
assumed.
• Fig. 12b and c shows the two-dimensional continuum model and the simplified beam model for theupper
half of the double lap joint. Similar to the single lap joint case, 950 two-dimensional elements are adopted
for the two-dimensional continuum model, 100 beam elements and 50 two-dimensional elements are used
for the simplified beam model.
• When Ea. = 2100 (i.e. r = 33.3), Fig. 13 depicts the peel and shear stresses within the adhesive obtained by
simplified beam model (SBM) and two-dimensional continuum model (2CM).
• It is concluded that Simplified finite element models using beam elements for substrates and quadrilateral
elements for adhesive provide reliable results for a representative range of material properties for single and
double lap joints. Adhesive stresses from a relatively coarse mesh can be used for design purposes.
19

20. CONCLUSIONS OF LITERATURE SURVEY
• It is concluded that the FEA of adhesively bonded joints will help future applications of adhesive bonding by
allowing different parameters to be selected to give as large a process window as possible for joint
manufacture.
• It is concluded that Simplified finite element models using beam elements for substrates and quadrilateral
elements for adhesive provide reliable results for a representative range of material properties for single and
double lap joints. Adhesive stresses from a relatively coarse mesh can be used for design purposes.
• It was demonstrated here that incorporating epoxy adhesive with nanoparticles can distinctly increase the
adhesion strength of epoxy adhesive, nanoparticles' kinds and counter faces roughness also had some
influence on the strength of epoxy adhesive.
• It can be concluded that the strength of the joint with dissimilar adherends is smaller than that of the joint
with similar adherends.
20

21. RESEARCH GAPS
• There is very limited work for estimation of shear strength of adhesively bonded metal joints to
best of our knowledge.
• Polymer nano composite is used as an adhesive in very limited researches.
• Very limited variety of adherend material is explored for adhesively bonded metal joints .
21

22. OBJECTIVES
The adhesively bonded single lap joint will be considered for this analysis-
• Two dimensional finite element model of adhesively bonded single lap joint is analyze.
• Morphology of nanoparticles and the effect of nanoparticles on the adhesion of epoxy adhesive.
• Investigate the influence of nanoparticles on shear strength of adhesive using finite element method
on commercial FEM software ANSYS.
• Investigate the influence of different size of nano particle on shear strength of adhesive using finite
element method on commercial FEM software ANSYS.
22

23. Finite Element Modelling
23
Geometric Modelling of single lap joint
Fig.14 Geometry of single lap joint for neat epoxy
adhesive.
Fig.15 Geometry of single lap joint with
nanosphere nanoparticles as inclusion in
adhesive.
The model used for the analysis is made as per ASTM standard D1002 which is used to test the shear
strength of single lap joint experimentally. All dimension is given in the figure .

24. Material model of single lap joint
24
Properties of adherend material, adhesive and nanoparticles considered for FEM analysis are
mentioned in Table I. An average diameter of 35nm, 70nm, 100nm,500nm, 10micro meter was taken
in present FEA.
Description Materials Density(g/cm3)
Young’s Modulus
(GPa)
Poisson’s ratio (ν)
Adherend
Aluminium
alloy
2.7 71 0.35
Adhesive Epoxy 1.17 3.8 0.375
Nanoparticles Alumina 3.7 375 0.23
Table 1. Properties of adherend, adhesive and nanoparticles

25. Adhesive was considered as an isotropic material with nonlinear stress strain curve modelled as multilinear
elastic problem in ANSYS 17. Whereas, the adherend and alumina nanoparticles were considered as linear
isotropic materials . Stress- strain data was obtained from tensile test of bulk adhesive .
25
Fig. 16. Stress- strain curve of neat epoxy

26. Dispersion of Nanoparticle
26
A MATLAB code was written to generate ANSYS APDL script file for generation of randomly
distributed Nano particle in nanocomposite adhesive. It was ensured that the distance between particles
was not less than a diameter of nanoparticle. Number of particles required for the analysis of single lap
joints having 0.5, 1.0, 1.5 and 2.0 wt.% of nanosphere.
Fig.17. Dispersion of nanoparticle on adhesive in single lap joint.

27. Element type and meshing
27
Element type
For FEA analysis of single lap joint in ANSYS ,the element type PLANE 82 was considered.
PLANE 82 provides accurate results for mixed (quadrilateral-triangular) automatic meshes and can tolerate
irregular shapes without as much loss of accuracy. The eight node elements have compatible displacement
shapes and are well suited to model curved boundaries. The 8-node element is defined by 8 nodes having two
degrees of freedom at each node. The element has plasticity, creep, swelling, stress stiffening, large deflection,
and large strain capabilities
Fig.18. PLANE82 ,2D 8-node structural solid

28. Meshing of single lap joint
28
Eight noded quadrilateral elements having two degree of freedom at each node was used for meshing
the adherends, adhesive and nanoparticles for multilinear elastic analysis.
Fig. 19 Representative FE mesh of single lap joint with pure epoxy
adhesive
Finite element mesh of single lap joint with pure epoxy adhesive
Finite element mesh of nanocomposites adhesive layer having nanospheres
To achieve proper mesh it was insured that the distance between particles was not less than a diameter
of nanospheres for nanocomposites adhesive having nanospheres.

29. Number of particle required for the analysis of single lap joint having 0.5, 1, 1.5 and 2.0 wt% of
nanospheres are listed in table 2.
29
Table.2 Number of nanoparticle and number of elements in FE model of
nanocomposites adhesive for diameter 35nm.
Description Wt. % of
Nano-alumina
Number of
particles in
RVE
Number of elements No. of times domain size
reduced
Nanospheres
0.5 209 88290 100
1 420 163986 100
1.5 632 275514 100
2 846 483678 100

30. Table 3 Number of nanoparticle and number of elements in FE model of nanocomposites adhesive for
diameter 70nm.
30
Description
Wt. % of Nano-alumina Number of
particles in RVE
Number of Elements No. of times domain
size reduced
Nanospheres
0.5 52 110930 100
1 105 195954 100
1.5 158 255780 100
2 211 340765 100
Table 4 Number of nanoparticle and number of elements in FE model of nanocomposites adhesive
for diameter 100nm.
Description
Wt. % of Nano-alumina Number of
particles in RVE
Number of Elements No. of times domain
size reduced
Nanospheres
0.5 25 135149 100
1 51 210348 100
1.5 77 310478 100
2 103 423679 100

31. Table 3. Number of nanoparticle and number of elements in FE model of nanocomposites
adhesive for diameter 10 micro meter.
31
Description
Wt. % of
Nano alumina
Number of
particles in
RVE
Number of
Elements
No. of times domain
size reduced
Nanospheres
0.5 25 120403 No reduction
1 51 212546 No reduction
1.5 77 310567 No reduction
2 103 453245 No reduction
Figure 20 Representative FE mesh of adhesive layer having nanospheres

32. Boundary condition
32
The boundary conditions applied on single lap joints are shown in Fig. 4. Left end of joint was
constrained (degree of freedom in all the directions was kept zero i.e. Ux=0, Uy=0). A displacement
“d” was applied on right face of the adherend. Right end of bottom adherend was constrained in y
direction (i.e. Uy=0).
Fig. 21 Boundary condition applied on single lap joint
The displacement applied to the right end of the joint was calculated on the basis of von- Mises theory of failure
i.e. the von-Mises stress in the adhesive was not allowed to exceed the von-Mises stress at the time of failure in
a tensile test of neat epoxy (bulk adhesive). On the basis of von -mises theory of failure the value of
displacement is 0.33mm.

33. Convergence of finite element mesh
33
Fig.22 Convergence of finite element mesh checked for single lap joint with pure epoxy
adhesive by varying the number of elements
From the above graph it can seen that the value started converge after 6324 number of elements. At
this point onwards and afterwards almost remain constant.

34. 34

35. 35

36. • Left end of the joint was kept fixed in all the directions i.e. Ux = Uy = 0. The unbounded end of the
second adherend was constrained in y direction (i.e. Uy=0) along its entire length. A force of 380
N was applied on the right end of the joint. A static stress analysis was performed with these
boundary conditions on ANSYS.
36
Fig. 3. Boundary conditions and load application

37. Convergence study
• Convergence of finite element mesh was checked for single lap joint with pure epoxy adhesive by
varying the number of elements and plotting the curve of shear stress in the adhesive at an
overlap length of 25 mm as a function of number of elements.
37
Fig. 4. Variation in shear stress in adhesive as a function of number of elements
in finite element mesh.
NUMBER OF ELEMENT

38. RESULT
Shear stresses in the adhesive layer along the overlap length of lap joint were analyzed
for neat epoxy.
The value of shear stress varies along the overlap length of the adhesive joints. Shear stresses
were maximum at the ends and were minimum at the center of joints.
Overlap length (mm)

39. Remaining work
• T dimensional finite element model of adhesively bonded single lap joint is analyze.
• A MATLAB code will write to generate ANSYS APDL script file for generation of randomly
distributed nanoparticles in nanocomposite adhesives.
• Investigate the influence of nanoparticles on shear strength of adhesive using finite element
method on commercial FEM software ANSYS.
39

40. 3D MODEL OF SINGLE LAPJOINT
40

41. REFERENCES
• A. D. Crocombe, G. F. Wu and D. H. Sinclair, A structural design analysis for adhesive joints Journal of
computer and structureVol. 61. No. 2. pp. 383-391 (1996).
• Lanlan Zhai, Guoping Ling, Jian Li and Youwen Wang, The effect of nanoparticles on the adhesion of epoxy
adhesive,journal of Materials Letters 60 (2006) 3031–3033.
• Xiaocong He, A review of finite element analysis of adhesively bonded joints , International Journal of
Adhesion & Adhesives 31(2011) 248-264..
• Lijuan Liao, Toshiyuki Sawa, Chenguang Huang, Experimental and FEM Studies on Mechanical Properties of
Single-lap Adhesive Joint with Dissimilar Adherends Subjected to Impact Tensile Loadings International
Journal of Adhesion & Adhesives (2013).
• H.Ravi Sankar, Dynamic strength of single lap joints with similar and dissimilar adherends International
Journal of Adhesion & Adhesives 56(2015) 46-52.
• P.K. Ghosh, Avantak Patel, Kaushal Kumar, Adhesive joining of copper using nano-filler composite Journal of
Polymer87 (2016) 159-169.
41

42. Cont..
• Ruixiang Bai, Shuanghua, BaoZhenkun Lei, Cheng Yan, Xiao Han ,Finite element inversion method for
interfacial stress analysis of composite single-lap adhesively bonded joint based on full-field deformation
International Journal of Adhesion and Adhesives (2017).
• T.F. Santos, R.D.S.G. Campilhoa, Numerical modelling of adhesively-bonded double-lap joints by the
eXtended Finite Element Method Journal of finite elements in analysis and design133(2017) 1-9.
• C. Saloma, M.G. Prolongoa S.G. Prolongob, Mechanical properties and adhesive behaviour of epoxy-
graphene nanocomposites , International Journal of Adhesion and Adhesives 84 (2018) 119-125.
42

43. 43