STUDY ON RELATIONSHIP BETWEEN AVERAGE DELAMINATION STRESS ON INTERFACE AND NON-DIMENSIONAL INTENSITY OF STRESS SINGULARITY FOR BONDED STRIPS

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STUDY ON RELATIONSHIP BETWEEN AVERAGE DELAMINATION STRESS ON INTERFACE AND NON-DIMENSIONAL INTENSITY OF STRESS

SINGULARITY FOR BONDED STRIPS

T.Kurahashi ¹ , S.Oshima ² , K.Ibe ³ , Y.Watanabe ⁴ , T.Kondo ⁵ and H.Koguchi ⁶

1, 6

Department of Mechanical Engineering, Nagaoka University of Technology, Niigata 940-2188, Japan

4

Electrical and Mechanical Systems Engineering Advanced Course, Advanced Course of Nagaoka National College of Technology, Niigata 940-8532, Japan

2,3,5

Department of Mechanical Engineering, Nagaoka National College of Technology, Niigata 940-8532, Japan

We present estimation equation of average delamination stress on interface for bonded strips using non- dimensional intensity of stress singularity. Aluminum bonded strips are employed in the delamination test, and variation of delamination force with respect to adhesive layer thickness is investigated. In addition, stress analysis based on the finite element method using Akin singular element is carried out. The intensity of stress singularity is obtained by fitting for results by stress analysis. Finally, the estimation equation of average delamination stress on interface for bonded strips was derived by relationship between average delamination stress on interface and non-dimensional intensity of stress singularity.

Keywords: Intensity of stress singularity, order of singularity, delamination test, finite element method, Akin singular element

1 Introduction

In this study, we investigate relationship between average delamination stress on interface and intensity of stress singularity obtained by stress analysis for delamination test for the aluminum bonded strip. The delamination test is carried out for the specimens whose adhesive layer thickness is changed, and the delamination stress on interface is calculated by the measured delamination force and the area of the interface. In addition, the intensity of stress singularity is obtained by the stress distribution on interface by the FEM, and the relation equation between average delamination stress on interface and the intensity of stress singularity is derived. In general, exponentiation of the distance is included in the unit of the intensity of stress singularity, and the value of the exponentiation is referred to as the order of singularity. The order of singularity is determined by the material properties of both materials and shape of interface edge. Hence, in this study, non-dimensional intensity of stress singularity is derived such that the average delamination stress on interface can be estimated regardless of the combination of the bonded materials and shape of interface edge. The stress analysis is carried out based

on the finite element method, and the Akin singular element is applied to the elements including the singular point[1],[2],[3]. In addition, the Bogy’s characteristic equation is employed to calculate the order of singularity [4].

2 Delamination test

The aluminum bonded specimen shown in Fig.1 is employed. The adhesive layer thickness is set as 0.4mm，

0.7mm，1.2mm, and the delamination test is carried out four times. The variation of the obtained delamination force with respect to the adhesive layer thickness is shown in Fig.2. Consequently, it is found that the delamination force increases with decreasing the value of the adhesive layer thickness.

3 Evaluation of intensity of stress singularity

The stress analysis is carried out based on the finite

element method using Akin singular element. The

material properties and the computational model is

shown in Tab.1 and Fig.3.

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Figure 1: Specimen model for tensile test

Figure 2: Relationship between delamination force and adhesive layer thickness

The order of singularity near interface edge of aluminum and resin is obtained λ=0.19329 by the Bogy’s characteristic equation. The value of the order of singularity is applied to the Akin singular element, and the stress analysis is carried out by the finite element method. The distribution of stress component σ

yy

from singular point on interface is shown in Fig.4 in case that the adhesive layer thickness is 0.4, 0.7 and 1.2mm. In Fig.4, lines indicate the fitting result by the equation σ

yy

=K

yy

r

^-λ

in case of λ=0.19329. It is seen that stress component σ

yy

decreases with decreasing the value of adhesive layer thickness. Fig.5 shows the relationship between the intensity of stress singularity K

yy

obtained by fitting calculation and the adhesive layer thickness.

It is found that the intensity of stress singularity K

yy

increases with increasing the value of adhesive laye thickness t.

Table 1: Material properties Young’s

modulus E(GPa)

Poisson’s ratio ν

Aluminum 70.60 0.340

Resin 1.94 0.252

Material1

Material2 Interface

Singular point

A5052

DP-460 d=0.04mm

Figure 3: Computational model (upper : computational model,

lower : finite element mesh around singular point)

Figure 4: Distribution of stress component σ

yy

from

singular point on interface for each adhesive thickness

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Figure 5: Relationship between adhesive layer thickness t and intensity of stress singularity K

yy

Fig.6 shows the relationship between the delaminaton force F and the intensity of stress singularity K

yy

for each case of adhesive layer thickness t. Consequently, it is seen that the relationship between the

delamination force F and the the intensity of stress singularity K

yy

can be expressed by the linear equation.

Here, the non-dimensional intensities of stress singularity K

w-yy

and K

t-yy

are derived by the boundary condition σ

External-force

and the interfacial width w and adhesive layer thickness t (Eqs. 1 and 2). The non- dimensional intensities of stress singularity K

w-yy

and K

t-yy

indicate the intensity of stress singularity K

yy

normalized by the interface width w and adhesive layer thickness t, respectively. Fig. 7 shows the relationships between average delamination stress on interface σ*

and non-dimensional intensity of stress singularity K

wyy

and K

tyy

. The average delamination stress on interface σ indicate that the delamination force F is divided by* the interfacial area. It is found that the relationships between average delamination stress on interface σ*

and non-dimensional intensity of stress singularity K

wyy

can be expressed by the linear equation, i.e., σ*=- 38.438K

w-yy

+25.607. On the other hand, it is seen that there is no tendency between average delamination stress on interface σ* and non-dimensional intensity of stress singularity K

tyy

. The reason why these results is obtained is that the interfacial width w is constant value in this study. On the other hand adhesive layer thickness t is chanced for each result. Therefore, it appears that the constant distance parameter should be used in normalization process of the intensity of stress singularity.

Figure 6: Relationship between intensity of stress singularity K

yy

and delamination force F

19329 . 0

19329 . 19329 0

. 0

0 . 25

0 . 25 0

. 1 0 . 25



 



 

 



 

 

 



 

 

 



 





K r K r

w w r

K

r w K w

K r

yy w

yy

force External

yy force External

yy force

External yy

 





 (1)

19329 . 0

19329 . 19329 0 . 0

0 . 1

0 . 25



 

 



 

 

 



 

 

 



 





t K r

t w r K

r t K t K r

yy t

yy

force External

yy force External

yy force

External yy

 





 (2)

（1）

（2）

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Figure 7: Relationship between average delamination stress on interface σ* and non-dimensional intensity of

stress singularity K

wyy

and K

tyy

( upper : Relationship between σ* and K

w-yy

. lower : between σ* and K

t-yy

)

4 Conclusions

In this study, we investigated the relationship between the average delamination force on interface and the non- dimensional intensity of stress singularity. The average delamination force was calculated by the delamination force and interfacial area, and the non-dimensional intensity of singularity K

w-yy

was defined by the intensity of stress singularity K

yy

normalized by the boundary condition σ

External-force

and specimen width w.

Consequently, the relationship between the average delamination force on interface and the non-dimensional intensity of stress singularity K

w-yy

could be expressed by the linear equation σ*=-38.438K

w-yy

+25.607. It appears that the average delamination force on interface can be estimated by using this linear equation. In the future, it is necessary to verify the validity of the estimation equation of the average delamination force on interface by changing the material combination and shape near singular point.

Acknowledgments

This work was supported by Grant-in-Aid for Young Scientists (B) (No. 25820015) and Grant-in-Aid for

Scientific Research (B) (No. 26289003). We wish to thank staff of research institute for information technology at Kyushu university for use of super computer system, FUJITSU PRIMERGY CX400.

References

[1] Akin,J.E., The generation of elements with singularities, International Journal for Numerical Methods in Engineering, Vol.10, pp.1249-1259, 1976.

[2] Wang,S., Shiratori,M. and Yu,Q., Evaluation of Singular Stress Field at the End of the Interface of Dissimilar Materials Using Akin's Singular Element, Transactions of the Japan Society of Mechanical Engineers Series A, Vol.63, No.606(1997), pp.110- 115. (in Japanese)

[3] Kurahashi,T., Watanabe,Y., Kondo,T. and Koguchi,H., Evaluation of stress singularity field near vertex on interface of dissimilar material joints based on Akin singular element using three- dimensional order of singularity (Comparison of results in case of tetrahedron and singular elements), Transactions of the Japan Society of Mechanical Engineers, Vol.80, No.809(2014), pp.1-18. (in Japanese)

STUDY ON RELATIONSHIP BETWEEN AVERAGE DELAMINATION STRESS ON INTERFACE AND NON-DIMENSIONAL INTENSITY OF STRESS SINGULARITY FOR BONDED STRIPS

STUDY ON RELATIONSHIP BETWEEN AVERAGE DELAMINATION STRESS ON INTERFACE AND NON-DIMENSIONAL INTENSITY OF STRESS

SINGULARITY FOR BONDED STRIPS

T.Kurahashi 1 , S.Oshima 2 , K.Ibe 3 , Y.Watanabe 4 , T.Kondo 5 and H.Koguchi 6

Department of Mechanical Engineering, Nagaoka University of Technology, Niigata 940-2188, Japan

Electrical and Mechanical Systems Engineering Advanced Course, Advanced Course of Nagaoka National College of Technology, Niigata 940-8532, Japan

Department of Mechanical Engineering, Nagaoka National College of Technology, Niigata 940-8532, Japan

Keywords: Intensity of stress singularity, order of singularity, delamination test, finite element method, Akin singular element

1 Introduction

on the finite element method, and the Akin singular element is applied to the elements including the singular point[1],[2],[3]. In addition, the Bogy’s characteristic equation is employed to calculate the order of singularity [4].

2 Delamination test

The aluminum bonded specimen shown in Fig.1 is employed. The adhesive layer thickness is set as 0.4mm，

3 Evaluation of intensity of stress singularity

The stress analysis is carried out based on the finite

element method using Akin singular element. The

material properties and the computational model is

shown in Tab.1 and Fig.3.

Figure 1: Specimen model for tensile test

Figure 2: Relationship between delamination force and adhesive layer thickness

from singular point on interface is shown in Fig.4 in case that the adhesive layer thickness is 0.4, 0.7 and 1.2mm. In Fig.4, lines indicate the fitting result by the equation σ

=K

r

in case of λ=0.19329. It is seen that stress component σ

decreases with decreasing the value of adhesive layer thickness. Fig.5 shows the relationship between the intensity of stress singularity K

obtained by fitting calculation and the adhesive layer thickness.

It is found that the intensity of stress singularity K

increases with increasing the value of adhesive laye thickness t.

Table 1: Material properties Young’s

modulus E(GPa)

Poisson’s ratio ν

Aluminum 70.60 0.340

Resin 1.94 0.252

Material1

Material2 Interface

Singular point

A5052

DP-460 d=0.04mm

Figure 3: Computational model (upper : computational model,

lower : finite element mesh around singular point)

Figure 4: Distribution of stress component σ

from

singular point on interface for each adhesive thickness

Figure 5: Relationship between adhesive layer thickness t and intensity of stress singularity K

Fig.6 shows the relationship between the delaminaton force F and the intensity of stress singularity K

for each case of adhesive layer thickness t. Consequently, it is seen that the relationship between the

delamination force F and the the intensity of stress singularity K

can be expressed by the linear equation.

Here, the non-dimensional intensities of stress singularity K

and K

are derived by the boundary condition σ

and the interfacial width w and adhesive layer thickness t (Eqs. 1 and 2). The non- dimensional intensities of stress singularity K

and K

indicate the intensity of stress singularity K

normalized by the interface width w and adhesive layer thickness t, respectively. Fig. 7 shows the relationships between average delamination stress on interface σ*

and non-dimensional intensity of stress singularity K

and K

. The average delamination stress on interface σ* indicate that the delamination force F is divided by the interfacial area. It is found that the relationships between average delamination stress on interface σ*

and non-dimensional intensity of stress singularity K

can be expressed by the linear equation, i.e., σ*=- 38.438K

+25.607. On the other hand, it is seen that there is no tendency between average delamination stress on interface σ* and non-dimensional intensity of stress singularity K

Figure 6: Relationship between intensity of stress singularity K

and delamination force F

0 . 25

0 . 25 0

. 1 0 . 25

 

 



 

 

 



 

 

 



 





K r K r

T.Kurahashi ¹ , S.Oshima ² , K.Ibe ³ , Y.Watanabe ⁴ , T.Kondo ⁵ and H.Koguchi ⁶

. The average delamination stress on interface σ indicate that the delamination force F is divided by* the interfacial area. It is found that the relationships between average delamination stress on interface σ*