Torsional fatigue behavior of adhesively joined tubes

Journal of Materials Processing Technology 191 (2007) 339–341

Torsional fatigue behavior of adhesively joined tubes Philip Portillo a,∗ , Dr. Jesa Kreiner b , Dr. Timothy Lancey c a

Wyle Laboratories, San Bernardino, CA 92408, USA Department of Mechanical Engineering, CSU Fullerton, Fullerton, CA 92831, USA c Department of Mechanical Engineering, CSU Fullerton, Fullerton, CA 92831, USA

b

Abstract A commonly utilized method of joining metal tubes to each other is to bond them by the use of adhesives. Structures created in such a manner are frequently subjected to various types of loading, i.e. tension, compression, bending, torsion or combination of these. Of particular interest and significance in many industries is what happens when torsional cyclic loading is applied to such joints, which subject the joint to fatigue. The joint configuration will perform differently depending upon various variables, i.e. bond gap, bond length, etc. . . .. The extended usage of the metal structures mentioned above is frequently encountered in the field and inspections in industrial use are intended to provide information on the soundness of these structures in general and joints in particular and to identify the amount of accumulated damage that is deemed acceptable at the time of inspection. The successful evaluation of these structures without doing destructive testing is of immense value to industrial users. NDT procedures (non-destructive techniques) to evaluate the damage to the structures present a better approach because they lead to better comprehension of the residual stresses present within the joints, lead to an improved and more effective utilization of materials and allow for prediction of the period of the utility of the joint. A comprehensive effort is under way to study the fatigue caused phenomena of adhesively joined aluminum tubular connections subjected to torsional cyclic loading. This includes the testing of a popular and widely utilized adhesive; which entails the design of the test rig, instrumentation, and post data analysis. Assessments of damages to the joints will be carried out upon conclusion of the experimental work as well as the analytical study enabling prediction of the phenomena encountered to assist the designer when planning such joints. © 2007 Published by Elsevier B.V. Keywords: Adhesive bonding; Nondestructive evaluation; Fatigue

1. Introduction The use of adhesives is currently a growing trend. This trend is mostly due in part to engineers realizing that compared to other fastening technologies, adhesion has many more advantages. For example, in the space structure industry the majority of composite parts are bonded together because of strength and machining issues that other fastening technologies cannot address. The downside to adhesives is that once bonded they generally cannot be removed without destroying the adherends. In order to determine if bonding meets standards without destroying the adherends, a number of non-destructive testing (NDT) techniques have been developed, such as ultrasonic testing. These NDT techniques allow engineers to inspect the bond for voids, inclusions, and other aspects that might cause premature failure.

A number of studies have been conducted to determine the behavior of adhesives under different static loadings, and how different NDT techniques can be applied to analyze bonds, but not too many studies have concentrated on torsional adhesive fatigue. Torsional adhesive fatigue occurs in many structures. For example, in spacecraft the use of composite tubular struts are employed throughout the structure. These struts undergo torsional adhesive fatigue. It is critical for engineers to know what kind of behavior adhesives will exhibit under fatigue loading. It is for this purpose that a significant effort be made to analyze the torsional adhesive fatigue of tubular joints. This effort will entail the fatigue testing of a bonded aluminum tubular joint, and before testing an effort will be made to determine if ultrasonic scanning is a viable means of NDT assessment. 2. Testing apparatus and material

∗

Corresponding author. E-mail addresses: [email protected] (P. Portillo), [email protected] (Dr.J. Kreiner), [email protected] (Dr.T. Lancey). 0924-0136/$ – see front matter © 2007 Published by Elsevier B.V. doi:10.1016/j.jmatprotec.2007.03.028

The test rig, shown in Fig. 1, was designed to take on the rigors of high cycle fatigue. An air cylinder will be used to load the test specimen, and a load cell will be used to measure the

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P. Portillo et al. / Journal of Materials Processing Technology 191 (2007) 339–341 Table 1 Shear strain at the inner edge of the bond joint Torque (lb-in)

Shear strain (milliard/rad)

389 346 302

1.91 1.70 1.49

Fig. 1. Fatigue test rig.

force being exerted by the air cylinder. Two strain gages will be bonded to the inner shaft where the bond is located. The adhesive being tested will be EA 9309. This paste adhesive was chosen because of its wide and frequent usage in the aerospace industry. Wire will be used around the bonding area to control the bond gap.

periphery, along the 0.50 in length of the joint.

3. Analytical strain results

τ2 =

An analytical analysis was conducted to make a handshake with the experimental strain results. For this analysis, the shear strain in the adhesive (1) bonding a B.C.F. configuration is calculated. The shaft outside diameter (d1 ) is 1.00 in., and the inner diameter (d2 ) of the ring is 1.02 in., providing a ring of bonded adhesive 0.01 in. radially, with a length of 0.50 in.. Perfect roundness and concentricity of the diameters are assumed. The outer ring provides a driving torsional input (T) to the bond joint of a maximum of 432 lb-in, which yields a shear stress boundary condition to the outer bond joint at (d2 ) and acts along the 0.50 in length (L) of the joint. The system is said to be in plane strain, with the strains and displacements dependent only on the radial (r) direction (2). The equilibrium equation governing this system for the shear stress (τ rθ ) is, with the inner diameter of the joint fixed,

We find that τ 2 = 265 psi maximum, and τ 1 = 276 psi. The maximum shear strain (γ 1 ) with the shear modulus (G) known to be 0.130 Mpsi is:   1 (4) τ1 γ1 = G

2τrθ dτrθ + =0 r dr

(1)

Defining the inside of the joint by subscript (1) and the outside by subscript (2) we integrate over the joint and solve for the shear stress in terms of the inner and outside diameters.  2 r2 τ1 = (2) τ2 r1 The torque acts on the ring outside of the joint. The boundary condition at the outside joint diameter is found by converting the torque to a couple and then spreading the couple over the outer

Fig. 2. Test rig in max. torque test configuration.

T πd22 L

(3)

We find the maximum is 2.12 millirad/rad. The values of the calculated shear strains at 70%, 80% and 90% of the maximum torsional input, are shown in Table 1. 4. Experimental data To determine the maximum torque the bond can handle, the test rig was first setup with a different setup, shown in Fig. 2. A torque meter with a dial was used to get readings from the test. Experimental results for the test were not close to analytical results due to calculation errors. After recalculating, the two results were within 50% of each other. In order for the test rig to work, a smaller bond length and a larger bond line was chosen (Table 2). Fatigue testing has taken place for the first four specimens, see Table 3 for results. Table 2 Max torque results, first samples

Bond length = 1 in. with bond thickness = .005 in. Bond length = 0.5 in. with Bond thickness = .010 in.

Analytical result (lb-ft)

Experimental result (lb-ft)

264

500

36

10, 50

P. Portillo et al. / Journal of Materials Processing Technology 191 (2007) 339–341 Table 3 Fatigue results Specimen number

Applied torque (lb-in)

Number of cycles

1 2 3 4

389 475 648 1080

1 million 1 million 1 million 721922 (test failure)*

* Specimen 4 developed a crack at opposite end of bond joint. Test was stopped prematurely.

Table 4 Max. torque results, second samples Specimen number

Breaking torque (lb-in)

5 6 7 8 9

3440 1443 1649 2576 2268

Since the results show that the specimens were not failing, even at torques above the theoretical max. breaking torque, it was decided to conduct five more maximum breaking torque tests (Table 4). From the data the breaking torque is an average of 530% above the analytical breaking torque. This is probably due to the amount of cure time that these specimens had or the equations used from [4] are invalid.

5. Conclusion More research and testing are ongoing to determine the fatigue life of tubular joints. It can also be seen that more research is needed to determine the torque equations for adhesives. Reference [4] Loctite Worldwide Design Handbook.

Further reading [1] C.Y. Warren, Roark’s Formulas for Stress and Strain, sixth ed., McGrawHill Book Company, 1989.

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