Finite Element Modeling for Thermal Stresses Developed in ... · Abstract— include A...

International Journal of Engineering & Technology IJET-IJENS Vol: 11 No: 06 86

115306-5757 IJET-IJENS @ December 2011 IJENS I J E N S

Abstract— A three-dimensional finite element modeling is

developed using ABAQUS® software. This includes riveted and

rivet-bonded joints models. Both models undergo thermal heat

caused by hot-driven rivet process and then are subjected to a

constant velocity at one of its strip edges to simulate the shear

tensile test up to the failure point. The developed FE models were

based on elastic-plastic properties and ductile fracture limit

criteria. In addition, the adhesive layer was modeled based on

traction separation. Detailed experiments were conducted to

evaluate these material properties and provide the FE developed

models with these necessary data. The thermal stresses developed

in riveted and rivet-bonded joints are assessed and reported. The

present work shows that introducing an adhesive layer to riveted

joints vastly reduces the stresses developed in these joints. In

addition, the complete load-displacement curve for each joining

model is obtained and compared with the finite element models

without including the effect of thermal analysis.

Index Term— Adhesive Layer, Load-Displacement Curve,

Rivet, Rivet-Bonded, Thermal Stresses.

I. INTRODUCTION

Rivets are used in many design applications such as joining

together two plates. A full understanding of these joints is

essential in most of automobile and aerospace industries.

When a rivet is heated before being placed in the hole, it is

identified as hot-driven rivet. After the rivet colds, it presses

the connected parts strongly and the rivet pole expands to fill

the hole. Thus, the rivet head becomes under high

concentration of stresses, which the rivet has to resist. The

sharp corner beneath the head may cause the head to be failed.

Tearing between the rivet holes, shearing, or crushing of the

rivet and/ or the joined material are considered to be the major

tension connection failures.

Using an adhesive material as bonding is another way of

joining two different parts. It is used to adhere a wide range of

materials structure such as metal to metal or metal to non-metal.

It has the advantages of reducing stress concentration, resisting

fatigue, and the capability of joining two different thickness

materials as well as joining two dissimilar materials. Bonded

structure could be used alone or together with a mechanical

This work was supported by College of Engineering Research Center,

King Saud University. Essam A. Al-Bahkali is with the Mechanical Engineering Department,

King Saud University, P.O. Box 800, Riyadh 11421, Saudi Arabia (phone:

+9661-4676675; fax: +9661-67-6652; e-mail: [email protected]).

connection. The bonded with a mechanical connection type may

include weld-bonded and rivet-bonded connections.

Barron [1] investigated the effect of clamping forces and grip

on the fatigue strength of rivets in butt joints. Hoffer [2]

determined the load-bearing capacity of a riveted joint by using

statistical analysis. He also evaluated the type of the joint

failures. Schvechkov [3] studied experimentally the effects of

adhesive mechanical properties along with the geometry of

butted sheets on the point of failure and cycle longevity on

rivet-bonded joints.

Fung and Smart [4] examined countersunk and snap riveted

single lap joints experimentally and numerically. They studied

the failures metallurgically to determine the cause of failure and

then they analyzed the joints using the finite element method.

They found that the stress concentration for this joint occurred

at a point away from the point of failure of a riveted joint. They

also determined the stress patterns around the rivet. Bedaira and

Eastaugh [5] proposed a numerical procedure for the analysis of

riveted lap joints taking into account the effect of the secondary

out of plane bending and plates/rivet interaction. Their results

showed that the secondary bending largely affects the maximum

tensile and compressive stresses within the joint with difference

might reach up to 39%. They also presented an experimental

comparison using photo-elastic test.

Gomeza et al. [6] presented a mechanical model to

reproduce the behavior of a structural hybrid adhesive/riveted

single lap joint. They used the Bond-Graph technique in order

to obtain the equations of the model. These equations

depended on four parameters considered to be the

characteristics of the joint. Their model reproduced the

experimental curves with great precision. Sadowski et al. [7]

carried out an experimental investigations of steel adhesive

double lap joints reinforced by rivets. They monitored the

deformation process of the hybrid joint using digital image

correlation system. They also studied the model numerically

and analyzed the whole model behavior up to failure point.

They found that adding a rivet to the adhesive joint led to very

significant energy absorption by about 35% in comparison to a

simple adhesive.

Moroni et al. [8] evaluated the beneficial of using hybrid

weld-, rivet- or clinch-bonded joints in comparison with

simple adhesive, spot-welded, riveted or clinched joints. They

conducted experimental analysis using the design of

experiments methodology. The influence of the material,

geometrical factors, and environment on static strength,

stiffness and energy absorption was assessed through the

Finite Element Modeling for Thermal Stresses

Developed in Riveted and Rivet-Bonded Joints

Essam A. Al-Bahkali



analysis of variance. They compared the hybrid and simple

joints in terms of mechanical response under the various

conditions tested.

Al-Bahkali [9] developed three-dimensional finite element

modeling for spot welded and weld-bonded joints models for

austenitic stainless steel AISI 304 annealed condition sheets of

1.0 mm thickness. In his studied, each model underwent

thermal heat caused by spot welding process and then was

subjected to an axial load up to the failure point. He defined

the properties of elastic and plastic regions, fracture limit,

weld nugget and heat affected zones around the spot welding.

He also obtained the load-displacement curve for each joining

model theoretically and experimentally. The results obtained

for both spot welded and weld-bonded joints affected by

thermal process showed an excellent agreement with the

experimental data.

Although several studies on riveted joints have been carried

out, however, these studies focused on the failure and strength

at room temperature. In the present work, three-dimensional

finite element analysis is considered to calculate the thermal

stresses caused by hot driven rivet for both riveted and rivet-

bonded models. In addition, the stress distribution for each

model at certain load is determined. Finally, the load-

displacement curves for both models with and without

including the effect of thermal analysis are calculated and

compared.

II. MODEL

A. Geometry

The art of the finite element (FE) analysis lies in the

representation of a real structure and its loading by a

mathematical model, which can be analyzed by the particular

analysis program used. An accurate and efficient idealization

can be as similar as possible to the real structure from the

geometric and loading view points. Two finite element models

are considered in the present work. The considered models are a

single lap riveted model and a single lap hybrid rivet-bonded

model. Fig. 1 shows the configurations, dimensions, constraints,

and loading conditions for both models (riveted and rivet-

bonded models).

Throughout the analysis, the following assumptions are

considered:

1) The analysis is based on three dimensional FE model.

2) Each model is subjected to thermal analysis, then to an

elastic analysis. During the thermal analysis, the hot driven

rivet is assumed to be at 160oC uniform temperature, then

it cools until it reaches room temperature. During the

elastic analysis, both models are subjected to a constant

Velocity that the model is subjected to at the right edge of

the right strip to simulate the shear tensile test.

3) A thin isotropic adhesive layer is considered.

4) The line of action force is not initially parallel to the

adhesive layer. Thus, as the load increases the overlap

area bends and therefore the adhesive layer peel at its

ends.

Fig. 1. (a) Riveted, and (b) Rivet-Bonded Models

B. Finite Element Mesh

The finite element computation is carried out using

ABAQUS software [10]. Fig. 2 shows the FE mesh for a

portion of the hyper rivet-bonded model.

Fig. 2. 3D partial finite element mesh of Rivet-Bonded Model

The selection of the mesh size is based on the ability to

represent each model accurately and obtaining the results in

reasonable time. The element type is specified based on the

ability to represent the variation of temperature and the

mechanical behavior of the model. Therefore, the meshes for



each model are generated using eight-node trilinear

displacement and temperature reduced integration with

hourglass control (C3D8RT) for the strips and rivet, and three

dimensional cohesive elements type (COH3D8) for the

adhesive layer. The numbers of elements for both models that

are used in the current study after several refined meshes to

insure the conversion of FE results, are given in Table I.

TABLE I

Elements number used in different models

Model Riveted Model Rivet-Bonded Model

Strip A 3360 3360

Strip B 3360 3360

Adhesive Layer ----- 928

Rivet 4448 4448

C. Model Analysis

In this research, the analysis of each model is divided into

two stages. These stages are thermal analysis and elastic

analysis. In the thermal analysis (first stage), stresses caused

by cooling the rivet from 160oC to room temperature are

determined. In the elastic analysis (second stage), each model

is subjected to a constant velocity (V) at the right edges of

strip (B). Out of this analysis, the stresses at certain load and

the load-displacement curves are determined for each model.

Fig. 3 shows the basic algorithm steps for the analysis

models. Where Ti is initial temperature, To is the room

temperature, V is the velocity that the model is subjected to at

the right edge to simulate the shear tensile test, and hair is the

convection heat transfer coefficient.

Fig. 3. The basic algorithm steps for the analysis model

D. Boundary Conditions

1. Thermal Boundary Conditions

A heat transfer analysis is preformed first to cool the rivet

part until it reaches room temperature. This can be done by

considering a convection heat transfer process as a thermal

boundary condition. Hence, it is assumed that heat is

exchanged with the environment through a convection heat

transfer coefficient hair as:

( ) (1)

2. Elastic Boundary Conditions

The mechanical boundary conditions associated with each

finite element model can be summarized as the following:

1) On the left edges at x = 0, clamped boundary conditions

are imposed. Thus, the displacements ux, uy, and uz are

equal to zero.

2) Both strips are subjected to a fixed y-direction boundary

condition (uy = 0) at the beginning 30 mm segment of

strip A (x = 0 to 30mm) and at the end 30mm segment of

strip B (x = 145 to 175mm).

3) In the overlap area for the rivet-bonded model, tie

constraints are imposed between components of bonded

joints; i.e. both strips and adhesive layer. By doing so, the

translational and rotational boundary conditions of tied

surfaces are made identical, regardless of the way these

parts are meshed.

4) The model is subjected to a constant velocity (V = 1

mm/min.) at the right edges of right base metal strip to

simulate the shear tensile test.

E. Material Properties

Detailed experiments were conducted to evaluate the

material properties and provide the FE developed models with

these necessary data. These data are given in Table 2. The

ductile fracture limits are also defined in terms of stress

triaxiality and corresponding equivalent strain for steel [11-

17]. The corresponding equivalent strain is obtained from the

tensile test of notched specimen and the stress triaxiality is

evaluated using numerical simulation [18-19]. The adhesive

layer is defined based on traction separation mode.

TABLE II

Material properties for steel and adhesive

Material Adhesive Steel

Young’s Modulus (GN/m2) 1.9 193.7

Possion’s Ratio, 0.37 0.30

Yield Stress Sy (MPa) 32 277.3

Ultimate Stress Sut (MPa) 60.4 729.2

Specific heat (J/kg oC) 1667.2 458.48

Thermal expansion (C-1) 60 12

Thermal conductivity (W/moK) 0.7 35

III. RESULT

The results of riveted and rivet-bonded FE simulations

including both thermal and elastic analyses are determined. At

first, the stresses resulted from thermal analysis are obtained.

Secondly, the stresses at certain load during the elastic

analysis are determined. Finally, the load-displacement curves



are obtained and compared with the same models but without

including the thermal analysis which reflect the case of cold-

driven rivet

A. Thermal stress

The results of riveted and rivet-bonded FE models after

running thermal analysis are determined and shown in Fig. 4

and Fig. 5, respectively. Both FE models undergo a heat

transfer analysis until they reach room temperature starting

from temperature Ti=160oC.

Fig. 4. Thermal Stress Contours for Riveted Model

Fig. 4 shows the contour plots for riveted model for the

normal stresses (x & y), the shear stress (xy), and the Von

Mises stress (V.M). While the normal stress x has high stress

concentration underneath the rivet head and in contact with the

strips edges at the top and bottom of the rivet hole as shown in

Fig. 4-(a), the normal stress y has high stress at the rivet

center and in contact with the strips as shown in Fig. 4-(b). On

the other hand, the shear stress contour (see Fig 4-(c))

illustrates that the high stress level (tension and compression)

takes a diagonal shape starting from the contact edge between

strips and underneath the rivet head toward the surface of the

rivet head.

Fig. 5. Thermal Stress Contours for Rivet-Bonded Model



Fig. 4-(d) shows the combined contour stress (V.M )

developed in riveted joint. It can be seen that the rivet head

becomes under high concentration of stresses, which the rivet

has to resist. The locations of these stresses are at the sharp

corner beneath the head and the areas in contact with the edges

of both strips.

Fig. 5 shows the stress contour plots x, y, xy, and V.M

for rivet-bonded model. Although the pattern of the stress

contours is similar to the contours in Fig 4, however, the level

of stresses is very small. This is because of the addition of the

adhesive layer between the strips joint. Again, the combined

contour stress (V.M ) as shown in Fig. 5-(d) demonstrates that

the rivet head becomes under high stress concentration at the

sharp corner beneath the head and in contact with the edges of

both strips.

B. Stress distribution at certain applied load

During the elastic FE simulation, it is very important to

study the stress distribution at the overlap area. Therefore, a

load of 3000N is applied while the model is still running in the

elastic region. This is done for both riveted and rivet-bonded

models.

Stresses Developed in Riveted Joint Model

The predicted stresses (σxx, σyy and σxy) along with σV.M stress

through the mid-layer area of the jointed area are shown in Figs.

6 and 7. Fig. 6 demonstrates the stresses developed in the

longitudinal direction, where the shear stress σxy is dominating

the rest of the stresses (σxx and σyy). The stress σyy is near zero.

The figure also shows that the longitudinal σV.M takes its

minimum value (37.6MPa) at the center of the rivet and rapidly

reaches its maximum value (356.6MPa) at the far ends of the

rivet. Fig.7 shows the stresses developed in the transverse

direction. As can be seen from the figure, the shear stress σxy is

also dominating the rest of the stresses σxx and σyy. The figure

shows that the transverse σV.M stress takes its minimum value

(37.6MPa) at the center of the rivet and its maximum value

(196.5MPa) at the far ends of the rivet’s side.

Fig. 6. Longitudinal stresses (developed along the mid-layer of overlapped

riveted joint).

Fig. 7. Transverse stresses (developed in the center overlapped riveted joint

along the z-direction).

Stresses Developed in Rivet-Bonded Joint Model

The predicted stresses for σxx, σyy σxy, and σV.M stress through

the mid-layer of the joined area are shown in Fig. 8 and Fig. 9.

Fig. 8 displays the stresses developed in the longitudinal

direction. It is seen that the stress σxx is dominating the rest of

stresses. The stress σyy is nearly of zero value. The figure also

shows that the longitudinal σV.M stress takes several local

minimum and maximum values across the joint area. In the

rivet area, the local minimum value occurs at the center of the

rivet with a value of 66.4MPa while the maximum value takes

places at the far ends of the rivet with a value of 131.8MPa.

Fig. 9 demonstrates the stresses developed in the transverse

direction, with σxx being also the dominant stress. The figure

also shows that the transverse σV.M stress for the rivet takes its

minimum value at the center of the overlap area and its

maximum value at the rivet’s side with a value of 144.6MPa.

Fig. 8. Longitudinal stresses (developed along the mid-layer of overlapped

rivet-bonded joint).



Fig. 9. Transverse stresses (developed in the center overlapped rivet-

bonded joint along the z-direction).

Figs. 8 and 9 show that the Von Mises stresses developed in

rivet-bonded joints are nearly of low and uniform value

compare to the riveted model. They also show that the V. M.

stresses of riveted joints are reduced by 63% in the

longitudinal direction and by 26.4% in the transverse direction

when the adhesive layer is introduced.

C. Load-displacement Curve

The results of riveted and rivet-bonded FE simulations

including the effect of thermal analysis are determined. The

results are compared with the same FE models but without

including the effect of the thermal analysis.

Fig. 10 Load-displacement curves for rivet and rivet-bonded models with

or without including the thermal analysis.

Fig. 10 shows four load-displacement curves obtained from

the FE riveted and rivet-bonded models. These four curves

are: riveted model runs at room temperature, riveted model

runs at temperature Ti =160oC, rivet-bonded model runs at

room temperature, and rivet-bonded model runs at temperature

Ti=160oC. By comparing all curves, it is clear that both riveted

models with and without including the effect of thermal

analysis have the same trend. However, for the riveted model

with thermal analysis, the maximum load is increased by 9%

and the displacement is increased by 25%. Similarly, both

rivet-bonded models with and without including the effect of

thermal analysis are alike in general, but the maximum load

and displacement of the rivet-bonded model with thermal

analysis are increased by almost the same amount of 9% and

23%, respectively.

By comparing the trend of the obtained load-displacement

curves with other pervious published work such as Birch et al.

[20], these curves show, in general, a very good agreement

with their results.

IV. SUMMARY AND CONCLUSION

A three-dimensional FE riveted and rivet-bonded models

are developed. Both models undergo thermal analysis caused

by hot-driven rivet and then are subjected to a constant

velocity at one of its strip edges to simulate shear tensile test.

The two-step analysis is used to include the effect of residual

stresses cased by high initial temperature. In addition, stresses

at certain load and load-displacement curve for each joining

model are successfully obtained. The results show that

introducing the adhesive layer to riveted joints increases the

joint strength and significantly reduces the stresses developed in

riveted joints. It is found that, adding the thermal analysis to

the solution seems to have an effect on the steel structure.

During the cooling cycle from Ti=160oC to room temperature,

carbides precipitate more uniformly throughout the steel

structure which improves the strength by at least 9% and the

displacement by 23%.

The analysis in this paper has been executed by running the

Abaqus/Standard procedure. To fully understand the dynamic

behavior of the joints and the failure modes, this study can be

extended by running Abaqus/Explicit procedure to include the

time-domain in the analysis. This will help investigating the

influences of different parameters on riveted and rivet-bonded

joints such as the sensitivity of the strain rate and the fracture

limits. It is recommended to carry out some experimental

works to verify the results.

REFERENCES

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Aluminum,” p. 391, p. 473, 1983. [2] F. Barron and E. W. Larson, “ Comparison of Bolted and Riveted Joints, “

Trans. Am. Soc. Civil Eng., 1955, pp. 1322.

[3] E. I. Schvechkov,” Failure Patterns and Cycle Longevity of Rivet-Bonded Joints,” Masinovedenie, 1984, p. 71.



[4] C-P Fung and J. Smart,” An experimental and numerical analysis of

riveted single lap joints,” Proceedings of the Institution of Mechanical Engineers, Vol. 208, No. G2, 1994, pp.79-90.

[5] O. K. Bedaira and G. F. Eastaugh,” A numerical model for analysis of

riveted splice joints accounting for secondary bending and plates/rivet interaction,” Thin-Walled Structures, Vol. 45, 2007, pp. 251–258.

[6] S. Gomeza, J. Onoro, and J. Pecharroman,” A simple mechanical model

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[7] T. Sadowski, M.Knec´, and P.Golewski,” Experimental investigations

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