Numerical and Theoretical Analysis for Investigation of Shear strength of A Joint Established Using Adhesive for Automotive Application

IJSRD - International Journal for Scientific Research & Development| Vol. 2, Issue 09, 2014 | ISSN (online): 2321-0613
All rights reserved by www.ijsrd.com 505
Numerical and Theoretical Analysis for Investigation of Shear strength of
A Joint Established Using Adhesive for Automotive Application
Mr.P.V.Dashwant1 Mr.Y.R.Patil2 Mr.P.R.Patil3
1
P.G.Student 2,3
Assistant Professor
1
Department of Mechanical Engineering
1,2,3
Dr. J. J. Magdum College of Engineering, Jaysingpur, India
Abstract— It is becoming increasingly important to
accurately predict the behavior of adhesive joints. Adhesive
joints are widely used in industries e.g. automobiles,
aircrafts, home appliances and so on. They are being used as
a closure system in the packaging industry, through the use
of adhesives as a system for construction of complex
structures such as skyscrapers, airplanes, trains or buses etc.
In adhesive bonding, the load is transmitted from one
adherend to another adherend smoothly through the
adhesive layer in the overlap region i.e. the adhesive serves
as medium for load transmission. The research is presented
with variants of different adhesive materials proposed for
the shear strength investigation of adhesive joint to be used
in the automotive industry. The problem is investigated
using mathematical analysis as well as analytical
methodology with Finite Element Analysis. For meshing of
the geometry of the brake shoe assembly hyper mesh
software is used. In FEA, the competent software ‘Abacus’
is used for determining the shear stress induced in two
different materials of adhesive layer applied to the brake
shoe. Different variants with different adhesive materials
and geometry of base material are analyzed for concluding
the research work.
Keywords: Adhesives, Shear stress of a joint, Brake shoe
I. INTRODUCTION
In the last two decades, adhesive bonding has become more
common in engineering. The advantages of the adhesive
joint over the conventional mechanical fasteners are savings
in weight and cost. The common type of joint in use today,
is the lap joint where two adherends overlap and are fixed
together by a layer of adhesive between them. Failure in a
joint may occur either in the adherend or in the adhesive or
at the interface. A failure at the interface is termed as
'adhesive, ' since it involves the failure of the bond between
the adhesive and the adherend. When the fracture occurs
either inside the adhesive or inside the adherend, the failure
is then termed as ‘cohesive’ [5]. In a cohesive failure, the
material at the two fracture surfaces is the same. The
interfacial adhesion of modern adhesives is high so that
failure mostly occurs either in the adhesive as in the case of
metal to metal joints, or in the adherends as happens with
wood joints. Adhesively bonded joints offer the aerospace
designer an attractive mass efficient alternative to the
mechanical fastening of structural components.
In the past, however, the poor reliability of bonded
joints has in general dissuaded designers from taking full
advantage of the projected benefits of bonded structural
designs. Thus, growth in the use of bonded systems in load-
carrying components is not keeping pace with the
continuing development and improved reliability of new
high strength adhesives. Bonded joints should be designed
to transfer load in shear with a minimum of peel across the
bond line, since adhesives are generally more efficient in
supporting shear forces and perform poorly when supporting
peel type forces. Design of bonded joints thus requires
knowledge of the shear and peel stress distributions in the
bond line as well as the shear strength of the adhesive [1].
The failure strength of adhesively bonded joints depends on
many factors such as material properties (both adhesive and
adherend), specimen geometries, test environments, surface
preparation procedures, etc. Among them, adhesive
properties can be regarded as the most dominating factor
affecting the failure strength.
II. NUMERICAL ANALYSIS
The finite element method (FEM), is sometimes referred to
as finite element analysis (FEA), is a computational
technique used to obtain approximate solutions of boundary
value problems in engineering. Due to the complexity of the
structures stresses are usually calculated by numerical
methods such as the finite element method. The finite
element analysis (FEA) is a numerical technique for finding
approximate solutions of partial differential equations (PDE)
as well as of integral equations [2]. The solution approach is
based either on eliminating the differential equation
completely, or rendering the PDE into an approximating
system of ordinary differential equations, which are then
numerically integrated.
A finite element analysis is able to determine stress
and strain distributions throughout a bonded structure
resulting from an applied force or displacement. It is
possible to calculate the stiffness of the joint and to locate
regions of stress and strain concentration where failure is
expected to initiate. Using a suitably fine mesh the influence
of geometrical features, such as the size and shape of fillets
at the ends of the adhesive layer, on stress and strain
distributions can be evaluated. Certain steps in formulating
finite element analysis of a problem are common to all such
analyses whether structural, heat transfer, fluid flow or some
other problem. These steps are embodied in commercial
finite element software packages. Figure shows general
procedure for finite element method. These steps are
described below,
Fig 1: Stages of Analysis
A. 3D Modelling in CATIA:
The three dimensional model of brake shoe is prepared in
CATIA V5 R16 environment. For analysis we have created
3D model and with the help of CATIA software it can
generate model of each geometry in three dimensions views

Numerical and Theoretical Analysis for Investigation of Shear strength of A Joint Established Using Adhesive for Automotive Application
(IJSRD/Vol. 2/Issue 09/2014/113)
and that will help to visualize properly and to clear idea
about model quickly.
CATIAInterface
Fig 2: 3D model of brake shoe
B. Meshing of Geometry using Preprocessor (Hyper
Mesh):
Hyper Mesh user-interface is easy to learn and supports
many CAD geometry and finite element model files -
increasing interoperability and efficiency. Advanced
functionality within Hyper Mesh allows users to efficiently
mesh high fidelity models. This functionality includes user
defined quality criteria and controls, morphing technology
to update existing meshes to new design proposals, and
automatic mid-surface generation for complex designs with
of varying wall thicknesses. Automated tetra-meshing and
hexa-meshing minimizes meshing time while batch meshing
enables large scale meshing of parts with no model clean up
and minimal user input. For analysis purpose we have to
discretised the geometry in to number of parts. For this
purpose we used the pre-processor Hyper Mesh. The
element used is C3D8R hexahedral element for meshing of
the geometry. There are total no of 113493 nodes and
130510 elements in the meshing geometry.
Fig 3: Meshing of brake shoe
Fig 4: Loading condition of brake shoe
Fig 5: Meshing using grooves on base
Torque is applied at the centre of the wheel and
upper surface of adhesive joint is constrained to simulate the
shear. For this purpose all degrees of freedom are arrested
except rotation about Z axis for calculating the shear stresses
induced in the joint. Six different design variants are created
by changing the adhesive materials and by changing the
base design of the shoe. The surface texture shall be offered
manipulator using grooves or criss-cross construction. The
change in geometry is likely to affect the performance in a
favorable manner. Since the adhesive can lodge in the
crevices and improve the retention of the joint. Figure below
shows the numerical results obtained for one of the design
variant.
Fig 6: Shear stresses induced in the adhesive layer
III. THEORETICAL ANALYSIS
An adhesive is a material used for holding two surfaces
together. An adhesive must wet the surfaces, adhere to the
surfaces, develop strength after it has been applied, and
remain stable. The stress in the adhesive layer is dependent
on the geometrical proportions and the elastic constants of
the materials of the joint, and on the nature of the forces
acting on the joint. In this case study shear stresses are
developed in the adhesive of the brake shoe due to torque
applied. The shear stresses can be calculated by using the
formula given below,
M=Mass of the Vehicle is kg.
V=maximum speed velocity of vehicle in kmph.
K.E = ½ mv2 ... (3.1)
We know that, work done is nothing but kinetic energy.
So, Work done = Braking force * Displacement.
W.D. = Fb x d... (3.2)
Putting values of Work done and displacement we get
Braking force.
Now, Torque = Braking force * radius.
T = Fb x R... (3.3)
T = is in N-M
Putting values of Braking force and radius we get value of
torque.
Applied Force,
F = T/R…. (3.4)
R= Radius of drum.
Load per unit Width,

Numerical and Theoretical Analysis for Investigation of Shear strength of A Joint Established Using Adhesive for Automotive Application
(IJSRD/Vol. 2/Issue 09/2014/113)
P = F/W… (3.5)
W= Width of Drum.
σ = P/t …. (3.6)
c = L/2…. (3.7)
τmax =
σ
8
∗ (1 + 3k) ∗ √(8Gat ÷ E ∗ ta)… (3.8)
k=
cosh(u2∗c)∗sinh(u1∗L)
[cosh(u2∗c)∗sinh(u1∗L) + 2∗√2∗cosh(u1∗L)∗ sinh(u2∗c)]
… (3.9)
u2 = √ [3*σ*(1 – μ2
)/ (2*E*t2
)] … (3.10)
u1 = 2*√2*u2 … (3.11)
Where,
P = load per unit width.
L = length of overlap (bond length).
t = adherend thickness.
E = adherend modulus.
Ga = adhesive shear modulus.
ta = adhesive layer thickness.
µ = Poisson’s Ratio of Adhesive.
The table below shows the results for values of
shear stresses calculated by numerical and theoretical
analysis of the two materials for base design of the brake
shoe base material. The values of shear stresses are
calculated for torque value of 2930 N-M by considering
maximum speed of the vehicle.
parameter
s
Disp
(mm).
Shear
stress(Mpa
)
Relativ
e slip
Cont.stres
s
(Mpa)
Material 1
1.84E
-2
13.13
1.375E-
13
7.054
Material 2
7.18E
-2
10.21
1.323E-
13
6.449
Table 1: Numerical analysis results for materials
Sr.No.
Numerical
(Mpa)
Theoretical
(Mpa)
Material 1 13.23 11.01
Material 2 10.21 7.17
Table 2: Comparative shear stress values of Theoretical,
Numerical Analysis
IV. RESULTS AND CONCLUSION
The provision of an accurate failure criterion for adhesives
would greatly facilitate accurate modeling of adhesively
bonded structures. Much work has been performed on
structural adhesives and still no universal criterion has been
established. The structural analysis of adhesive joint of the
brake shoe is carried out and the shear stresses induced in
the adhesives layers are calculated in this study. The results
for the different variants evolved during the study assert the
significance of the parameters determined for this work.
From the numerical and mathematical analysis out of the
two different materials the material 2 gives lower value of
shear stress. Maximum values of shear stresses are observed
at the side end of the adhesive layer but permissible limit of
shear stresses has not been exceeded at any point. The base
design satisfies the criteria of no slippage. The
recommended variant needs to be implemented in practice.
This might solve several problems in terms of designing
adhesive joint over the designated mating area of the brake
shoe and the brake pad.
REFERENCES
[1] Paul A. Cooper and James Wayne Sawyer “A
Critical Examination of Stresses in an Elastic
Single Lap Joint” NASA Technical Paper 1507
September 1979.
[2] “Fatigue Analysis of Helical Spring using CATIA
V5 And FEA Software”, International Journal of
Engineering Research & Technology (IJERT) Vol.
2 Issue 10, October.
[3] A Text Book of Machine Design, R. S. Khurmi and
J. K. Gupta, Eurasia Publishing House Ltd., New
Delhi.
[4] W R Broughton and G Hinopoulos “Evaluation of
the Single-Lap Joint Using Finite Element
Analysis”
[5] Murlidhar h. pahoja “Stress analysis of an
Adhesive Lap Joint Subjected to Tension, Shear
Force and Bending Moments”.
[6] Rahman and H. Roh,H. Qian, C. T. Sun Stress
analysis of Adhesive Joints Using Peel Stress and
CTOA 52nd
AIAA/ASME/ASCE/AHS/ASC
Structures, Structural Dynamics and Materials
Conference April 2011, Denver, Colorado.
[7] Simon George, Arun LR, Guru Prasad BS”
Analysis of Composite Drum Brake Using FEA
Approach” International Journal of Engineering
Trends and Technology (IJETT) – Volume 4 Issue
8- August 2013.
[8] W R Broughton, L E Crocker and J M Urquhart
“Strength of Adhesive Joints: A Parametric Study”
July 2001.

Numerical and Theoretical Analysis for Investigation of Shear strength of A Joint Established Using Adhesive for Automotive Application

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