Fracture Analysis of Adhesively Bonded Joints as a Function of Temperature

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Paper ID: 4855

International Conference on Mechanical, Manufacturing and Process Engineering (ICMMPE – 2022)

Organizer: Faculty of Mechanical Engineering, Dhaka University of Engineering & Technology (DUET), Gazipur, Bangladesh Website: https://icmmpeduet.com/

Fracture Analysis of Adhesively Bonded Joints as a Function of Temperature

Golam Rabbi, Md. Abdul Hasib*, Arup Kumar Debnath, Md. Ashraful Islam

Department of Mechanical Engineering, Khulna University of Engineering & Technology, Khulna – 9203, Bangladesh.

E-mail: [email protected] ABSTRACT

In this study, adhesively bonded joints’ fracture parameters have been investigated. Double Cantilever Beam (DCB) and End Notch Flexure (ENF) tests have been simulated using ABAQUS^® simulation software to analyze the effect of low temperature on the epoxy adhesive Mode I and Mode II fracture toughness respectively. Varying material properties for different low temperatures have been used to simulate the tests at low-temperature conditions. The fracture load has been determined from the P-δ curve at various low temperatures. The stress intensity factor has been evaluated to get the strain energy release rate which has been used to describe the fracture toughness of the adhesive.

The result showed that the fracture load and fracture toughness for Mode I slightly increases by the reduction in temperature. Whereas with the reduction of temperature fracture load and toughness for Mode II increases greatly.

The fracture load has increased by 12.6% and 65.1% and the fracture toughness has increased by 36.5% and 84.3%

with temperature reduced to -80°C from room temperature for Mode I and Mode II respectively.

Keywords: Double cantilever beam; End notch flexure; Stress intensity factor; Fracture toughness.

1. INTRODUCTION

Epoxy adhesives are excessively used in many industries, including aerospace, automotive, telecommunications, shipbuilding, etc. because of their fascinating characteristics. Most of the products from these industries have to perform under various environmental conditions. In aerospace structures, the high flight altitude contributes to a large temperature gradient for structures in addition to traditional mechanical loading. The normal temperature on a commercial aircraft's body is about -60°C, and the equivalent temperature of military aircraft used for flying at even higher altitudes is below -80°C. Spacecrafts and satellite carrier shuttles experience even lower temperatures [1]. Epoxy adhesive joints perform better under fatigue loads, allow different materials to be joined together and pose lower stress concentrations than alternative joining techniques. Accurate damage models must be available for the design of adhesively bonded joints to predict their fracture behavior. Therefore, it is important to have the material's fracture toughness to apply a fracture mechanics approach. The stiffness of the fractures varies with the type of load. The most important factors influencing the strength and rupture properties of the bonded joints across fluctuations in temperature include changes in the adhesive's mechanical properties and the disparity between the joined portion's thermal expansion coefficients [2]. In addition to the traditional mechanical stresses, the temperature-induced gradient stresses should be taken into consideration during the design phase, as the mechanical properties of the adhesives vary with temperature changes, creating a difference in the adhesive structure. One of the basic

parameters which should be considered in the design process is the impact of temperature on the strength and fracture toughness of the adhesive joints. Different materials have different thermal expansion coefficients. When the adhesive joint is formed between different materials, due to the adhesive bond's motion constraint, the temperature change will cause thermal stresses in both arms.

Adhesive strength refers to an adhesive's ability to adhere to a surface and bond two surfaces together. Fracture toughness is a quantitative way to describe the resistance of a material to the propagation of cracks. Temperature dependence is usually shown by adhesive strength. Research that provides experimental data on adhesive joints with structural adhesives (especially epoxies) as a factor of temperature usually shows a reduction in toughness with rising and lowering temperatures [3-6]. This is due to the reduced strength of the adhesive at high temperatures, while the high thermal stresses and frailty of the adhesive are the cause of this behaviour at low temperatures [7].

It is also expected that fracture toughness will depend on temperature. Some researchers have experimented with fracture toughness in the tension or shearing of fine adhesive layers in adhesive bonds, but most of these studies are confined to research at room temperature. Melcher and Johnson [8] tested the fracture toughness of an adhesively bonded composite–composite joint in a cryogenic environment in Mode I. They found a significant decrease in the toughness of the fracture as opposed to room temperature (RT) at cryogenic temperature. Banea et al. [9] measured the Mode I fracture toughness of high-temperature RTV silicone adhesive joint throughout a large temperature range (from Room temperature to +260°C) indicating that fracture

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International Conference on Mechanical, Manufacturing and Process Engineering (ICMMPE – 2022)

2 toughness and traction separation laws depend on temperature. In an experimental study, Carlberger et al. [10]

found that fracture toughness is not significantly affected by temperature, ranging from -40°C to +80°C (Tg of the epoxy adhesive tested in +90°C), and the maximum stress in the peel load decreases in monotony as the temperature rises in this range. Moreover, Cohesive Zone Models (CZM) have recently been used by researchers around the world to model crack initiation and development to predict the fracture behavior of the bonded joints accurately. Blackman et al.

[11] used a CZM approach on Tapered Double Cantilever Beam (TDCB) and peel tests under Mode I loading, including two parameters Gc and σmax to investigate the fracture of adhesively bonded joints. They observed that the compliance of the specimen and Gc relied on σmax until a relatively high value. To assess the cohesive features of a ductile adhesive sheet used in a double cantilevered beam (DCB) experiment, Andersson and Stigh [12] used a reverse approach.

The relationship between stress and displacement can be split into three sections. Initially, the stress increases proportionally with the elongation (the adhesive layer's linear elastic behavior), till limit stress is reached. A region of the plateau is then observed which corresponds to the adhesive's plastic behavior. The curve ends with an adjustable parabolic component. Tvergaard and Hutchinson and Yang et al. used a similar constitutive principle on softening. Chai [13] studied the temperature effect on the energy of the fracture in the shear and found that the fracture energy in Mode II decreased in the range of 0.7 < T/Tg < 1.0.

For pure Mode II, only a few informations are available regarding the temperature dependency of fracture toughness.

On the other hand, the control of crack duration in Mode II experiments is difficult, as propagation happens rapidly and without a consistent opening. Furthermore, it may be difficult to classify the crack tip due to micro-cracks in the significantly larger fracture phase zone (FPZ) [14].

Therefore, there is increasing interest in comparable or efficient crack methods which consist of using the experimental conformity and a beam theory-based relationship to measure the crack frequency. Banea et al. [7, 9] performed a double cantilever beam (CDM) and end notch flexure (ENF) test for analyzing the temperature dependency of the fracture toughness for Mode I and Mode II respectively. The result of their research exhibits temperature dependency of fracture strain, fracture toughness and fracture strength.

2. NUMERICAL MODELLING

In the FEM kit of ABAQUS^®, a numerical study of the DCB joints and the ENF joints for Mode I and Mode II respectively, as a function of temperature was conducted to determine the feasibility of its CZM formulation. The numerical study was conducted using two-dimensional models taking into consideration of geometrical non- linearities for an accurate representation of the deformation

behavior of the specimens, especially transverse deflection and arm rotation.

In this work, the Double Cantilever Beam (DCB) and End Notched Flexure (ENF) tests are simulated to establish the temperature effect of a low temperature (+22°C to -80°C) epoxy adhesive (Loctite EA-9466) on the adhesive model fracture toughness for Mode I and Mode II, respectively, using ABAQUS^®. Its output i.e., the stress intensity factor was then converted to strain energy release rate. The fracture toughness was defined using the parameter strain energy release rate. The fracture load was determined from the P-δ curve obtained from the simulation.

2.1 Model Creation

The created parts which have been presented on Figure 1, 2 and 3 have been assembled using different constraints.

Tie constraints have been used to tie the surfaces of the adhesive to the surface of the adherend surfaces. Interaction properties have been defined as hard contact for the lower surface of the upper arm and the upper surface of the lower arm to define their behavior during an interaction after the adhesive layer has failed.

Fig. 1: Geometry for Mode I.

Fig. 2: Geometry for Mode II.

Fig 3: Mode I and II force distribution.

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International Conference on Mechanical, Manufacturing and Process Engineering (ICMMPE – 2022)

3 2.2 Material Properties

Banea et al. [7] experimented DCB test with the same material for adherend. The properties used in this work were taken from the mentioned author’s research. The properties were provided by the supplier for their research which have been presented in Table 1.

Table 1: Mechanical and physical properties of steel Tensile failure strength (MPa) 1000-1068

Yield stress (MPa) 861-930

Elongation (%) 14-17

Young’s modulus, E (MPa) 205,000

A Rahmani [16] has performed experimental tests to analyze the properties of epoxy adhesive Loctite EA-9466 at varying low temperatures. The properties used in this work were taken from their research and presented in Table 2.

Table 2: Mechanical properties of the Loctite EA-9466

22 -20 -60 -80

Elasticity

Modulus (MPa) 1910 1957 2207 2524 Yield Strength

(MPa) 41.33 67.73 79.66 93.87 Tensile Strength

(MPa) 44.38 67.73 79.66 93.87 Poisson’s Ratio 0.35 0.35 0.35 0.35 Elongation (%) 3.86 3.70 3.36 3.31

2.3 Boundary condition

From figure 4 for Mode I i.e., opening, as DCB specimen is used, the lower arm of the joint has been kept fixed. Two sets of boundary conditions are possible for keeping the arm fixed. One is to make the lower surface of the arm encastre i.e., fixed and the other is to make the right surface and lower left point of the lower arm encastre. In this work, the second method was used. Displacement was applied to the upper arm at the top left corner. For Mode II i.e., in-plane shear, as

Fig. 4: Boundary conditions for Mode I.

Fig. 5: Boundary conditions for Mode II.

ENF specimen is used the lower arm is given pinned boundary condition at the two ends of the lower surface. The load is applied downward at the midpoint of the upper arm’s upper surface which has been showed in figure 5. For being Pinned the lower surface does not react in the x-direction. It’s free to rotate about the z-axis.

2.4 Mesh Sensitivity

The mess sensitivity should be validated to ensure that the obtained result does not vary with the number of elements in the mesh.

The test arms were designed with plane strain 8- node quadrilateral solid finite elements (ABAQUS^® CPE8) and the epoxy adhesive was modeled with cohesive 6- node elements, including the CZM bilinear mixed mode, consistent with the quadrilateral 8-node elements. For each neck, twelve solid finite elements have been used along the direction of thickness, with a finer mesh near the adhesive area [16,17]. The meshes were developed utilizing the automated meshing facilities of ABAQUS^®, using a manual seeding method that involved biasing effects from the loading points to the crack tip in the horizontal direction, where strong stress gradients are necessary. A more precise mesh was used in the crack tip. From figure 6 it is visible that the value of GC stays the same for element sizes 27967 and 34164. Therefore, using 27967 elements reduce calculation and save time.

Fig. 6: Verifying mesh dependency.

Temperature (ᵒC) Properties

0.25 0.24 0.28

0.26 0.31 0.33 0.33

0.15 0.16

0.140.16 0.17 0.18 0.18

0 0.1 0.2 0.3 0.4 0.5

7000 17000 27000 37000

GC( N/mm2 )

No. of Elements Mode I Mode II

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4 3. RESULT AND DISCUSSION

3.1 Validation

A. Rahmani [16], F. Moroni and A. Pirondi [17]

performed similar studies with different approach. Table 3 illustrates a comperative analysis of the strain energy release rate i.e., the fracture toughness of the adhesive at room temperature with this study. Values from different research shows that, GIC ranges from 0.31 to 0.39 J/mm² where as this study obtained value about 0.33 J/mm² and the value of GIIC is about 0.15 whereas this study obtained value about 0.18 J/mm². So, Table 3 validates the effectiveness of this approach in this study.

Table 3: Comperative analysis with recent studies.

Adherend-Adhesive G^IC (J/mm²) G^IIC (J/mm²)

Al-EA 9466 [16] 0.31 0.15

Al-EA 9466 [17] 0.31 -

St-EA 9466 [This study] 0.33 0.18

3.2 P-δ Curve

Figure 7 displays the P-δ curve for Mode I at varying temperatures. The fracture load for Mode I respectively at 22°C, -20°C, -60°C, -80°C is 1.95 kN, 1.88 kN, 2.22 kN, 2.23 kN and the maximum displacement at fracture load is 0.5 mm, 0.32 mm, 0.25 mm, 0.25 mm. Figure 8 displays the P-δ curve for Mode II at different temperatures. The fracture load for Mode II respectively at 22°C, -20°C, -60°C, -80°C is 2.73 kN, 4.12 kN, 5.52 kN, 7.83 kN and the maximum displacement at fracture load is 2.05 mm, 2.07 mm, 2.07 mm,

Fig. 7: P-δ curve for Mode I.

Fig. 8: P-δ curve for Mode II.

2.16 mm. Figure 8 displays the P-δ curve for Mode II at different temperatures. The fracture load for Mode II respectively at 22°C, -20°C, -60°C, -80°C is 2.73 kN, 4.12 kN, 5.52 kN, 7.83 kN and the maximum displacement at fracture load is 2.05 mm, 2.07 mm, 2.07 mm, 2.16 mm.

In the case of Mode I, the fracture load, displacement at the fracture point, and area under the curve have shown great change with reduced temperature. On the other hand, in the case of Mode II, fracture load, displacement at the fracture point, and the area under the curve show an increasing tendency with reduced temperature.

These findings are concurrent with Cantwell [18] and Scott [19]. They also observed an increase in fracture loads with decreased temperature for polymer and epoxy adhesive.

This is due to the added shear fracture loads. Displacement relates to molecular relaxation at low temperatures.

Fig. 9: Fracture loads at different temperatures for both Mode I and Mode II.

3.2 Fracture Load

Load (KN)

1.952.73 1.88 2.22 2.23

4.12

5.52

7.83

0 2 4 6 8 10

22 -20 -60 -80

Load (kN)

Temperature (°C) Mode I Mode II

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International Conference on Mechanical, Manufacturing and Process Engineering (ICMMPE – 2022)

5 Figure 9 describes the fracture loads of Mode I and Mode II at different temperatures. From the chart, it is clear that for Mode I, fracture load shows very little deviation with the decrease in temperature. On the contrary, for Mode II, fracture load increases with decreased temperature. By lowering the temperature from 22°C to -80°C, fracture load increased 12.6% and 65.1% for Mode I and Mode II respectively.

3.3 Fracture Toughness

Figure 10 shows fracture toughness for Mode I and Mode II at varying low temperatures. From the chart, it can be stated that fracture toughness increases slightly for Mode Iloading conditions but increases drastically with increasing temperature. By decreasing the temperature from 22°C to - 80°C, fracture toughness increased 36.5% and 84.3% for Mode I and Mode II respectively.

Fig. 10: Fracture toughness at different temperatures for Mode I and Mode II.

4. CONCLUSION

The goal of this research was to analyze how the fracture toughness of an epoxy adhesive Loctite EA- 9466 with steel as an adherend changes with the reduction in temperature in two different modes. DCB test and ENF tests were analyzed to create Mode I and Mode II loading conditions. The results at RT were verified by matching with results from similar works. Fracture load was found from the load-displacement curve. And the J-integral was evaluated to get the stress intensity factor which was converted to energy release rate describing the fracture toughness of the cohesive. The fracture load of the adhesive increased by 12.6% and 65.1%

with temperature reduced to -80°C from RT for Mode I and Mode II respectively. The toughness of the adhesive increases by 36.5% and 84.3% by the reduction of temperature from RT to -80°C for Mode I and Mode II respectively. It was also found that the adhesive toughness

increasing rate due to temperature fall is greater in pure Mode II than in pure Mode I. Experimental analysis can be done in future to validate the numerical analysis.

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