Strength prediction of self-pierce riveted joint in cross-tension and lap-shear

    Strength prediction of self-pierce riveted joint in cross-tension and lap-shear Rezwanul Haque, Yvonne Durandet PII: DOI: Reference:

S0264-1275(16)30920-0 doi: 10.1016/j.matdes.2016.07.029 JMADE 2033

To appear in: Received date: Revised date: Accepted date:

10 June 2016 4 July 2016 7 July 2016

Please cite this article as: Rezwanul Haque, Yvonne Durandet, Strength prediction of self-pierce riveted joint in cross-tension and lap-shear, (2016), doi: 10.1016/j.matdes.2016.07.029

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ACCEPTED MANUSCRIPT Strength prediction of self-pierce riveted joint in CrossTension and Lap-Shear

Faculty of Science, Health, Education and Engineering, University of the Sunshine Coast, Sippy

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Downs, QLD 4556, Australia 2

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Rezwanul Haque1, a*, Yvonne Durandet2, b

Faculty of Science, Engineering and Technology, Swinburne University of Technology, Hawthorn, VIC 3122, Australia [email protected], [email protected]

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*Corresponding author Address: University of the Sunshine Coast, 90 Sippy Downs Drive, Sippy Downs, Queensland 4556, Australia.

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Abstract

This paper describes a parametric study of the mechanical behaviour of self-pierced

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riveted (SPR) joints of steel sheets in two loading conditions (lap-shear and crosstension). Higher strength was always observed in lap-shear testing than in crosstension. In both loading conditions, the strength of a joint was greatly influenced by

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the hardness and thickness of sheet materials and die depth. An empirical model was developed to predict the joint strength in cross-tension loading using characteristic joint data determined directly from the SPR process (force-displacement) curve. All predictions of joint strength fell within 10% of the measured joint strength. Finally, a relationship was established between the joint strength in lap shear and cross-tension with less than 8% error. The developed relationship provides a useful tool for further studies especially for different rivet and die geometry.

Key words: Self-piercing riveting, SPR, Joint strength, Analytical model, Crosstension, Lap-shear.

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Introduction

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ACCEPTED MANUSCRIPT Self-Pierce Riveting (SPR) is a cold forming process used to fasten two or more sheet materials as shown in Fig. 1. A mechanical interlock is created by the rivet through piercing the top sheet and flaring in the bottom sheet under the guidance of the rivet

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internal geometry and a die [1]. As SPR relies on the formation of a mechanical

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interlock rather than a fusion bond, the process is capable of joining mixed grades of

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materials and multiple material stacks [2, 3].

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Fig. 1 Schematic illustration of SPR process adopted from [4-6] The strength of a SPR joint is primarily determined by the interlock between the rivet shank and sheet materials. The interlock has been shown to depend on many factors

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such as die geometry, thickness and properties of sheets, rivet properties, coatings and piercing direction. For instance, Pickin et al. [7] investigated the effect of die parameters on rivet flaring (i.e. interlock) in different joints comprising steel, aluminium and aluminium composite panel with polypropylene core (known as Hylite LSS) with thicknesses ranging from 0.74 mm to 1.2 mm. They found that the rivet flaring increased when the die diameter was increased and height of internal die tip was decreased. Xu [8] studied the effect of rivet length (5 mm and 6.5 mm) and ply materials’ thickness (1+1 mm, 1+2 mm and 2+2 mm of aluminium alloy 5754-O) on the amount of interlock. They concluded that the amount of rivet flaring increased with increased rivet length and increased thickness of bottom sheet. The amount of flaring in SPR joints of steel sheet is influenced by rivet hardness [9]. An increase in rivet hardness shortens the flaring stage of the riveting process and reduces the amount of flaring. Coatings on sheet material can also effect the amount of rivet 2

ACCEPTED MANUSCRIPT flaring [10]. It was observed that the rivet flaring increased with the addition of coating on steel and aluminium sheets while keeping all other parameters unchanged.

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The piercing direction (riveting order) can improve the join-ability by increasing the

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flaring. A join-ability study of aluminium alloy with steel comprised of different thicknesses was conducted by Abe et al. [11]. The amount of rivet flaring was

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increased when the hard steel sheet was placed at the top. A similar study was conducted by He et al. [12] to evaluate the join-ability of similar and dissimilar titanium sheets with aluminium and copper alloys of 1.5 mm thickness. The amount

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of rivet flaring and the joint strength were higher when hard titanium sheet was placed

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at the top.

Like the amount of rivet flaring, joint strength was also influenced by rivet properties (hardness, diameter and length). Fu and Mallick [13] reported the effect of rivet

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hardness on the strength of a SPR joint. By analysing variance (ANOVA), they found

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that the contribution of the rivet hardness to the strength of the joint was 4.53%. In their experiments they used 4 and 5 mm long rivets for joining 1 + 1 mm Al 5754-O

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and 6 and 6.5 mm long rivet for joining 2 + 2 mm Al 5754-O. However, they considered only three levels of hardness: normalized (rivet as produced, without any heat treatment), 410HV and 480HV.

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A long rivet with a large diameter can absorb more impact energy [14, 15]. Xu [14] examined the effect of rivet parameters (diameter and length) on joint quality and strength. Aluminium alloy AA 5754 was joined in four different stack thicknesses (1 + 1 mm, 1 + 2 mm, 2 + 1 mm and 2 + 2 mm) with 480 HV rivets of 3.3 or 5.3 mm diameter, and 5 mm or 6.5 mm length. A significant increase in joint strength was observed with the larger diameter and long rivet. Hence, the performance of a riveted joint can be optimized by increasing the rivet length. Sun and Khaleel [15] reported that the joint strength was increased from 3.7 to 5.3 kN when a 6.5 mm long rivet was used instead of 6.0 mm long rivet to join 2 mm AA5182-O (top sheet) + 1.6 mm DP600 (bottom sheet).

Another parameter which influences the joint strength is sheet material thickness. Zhao et al. [16] investigated this aspect for aluminium alloy (AA5052) of 1.5, 2.0 and 3

ACCEPTED MANUSCRIPT 2.5 mm thickness. With increasing sheet thickness, the joint fatigue life was increased and the failure positions moved from the top sheet to the bottom sheet. The test data was verified by statistical analysis. Calabrese et al. [17] also studied the influence of

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sheet thickness on joint strength focussing on the top sheet thickness and proposed a

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failure map. They used aluminium alloy (AA6082) of four different thicknesses (1, 1.5, 2 and 3 mm). A 6.5 mm rivet (460 HV) was used to join a stack thickness of 3

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and 4 mm. Failure in the sheet occurred for a very thin top sheet, head pull-out occurred with a thin top sheet, and tail pull-out occurred for a thick top sheet. They reported a change in failure mode due to ageing of materials causing softening, which

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ultimately affected the magnitude of the joint strength.

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Edge distance plays a significant role on the quality and the strength (both static and fatigue) of self-piercing riveted joint [18, 19]. The distance of rivet centre to the sheet edge was varied from 5 mm to 14.5 mm for joints of aluminium alloy AA5754 (2 + 2

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mm). Results showed that a smaller edge distance offered less constraint in the bottom

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sheet and hence greater joint distortion, and an optimum edge distance of 11.5 mm

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was recommended for less joint distortion and high joint strength.

The mechanical behaviour of SPR joints is influenced by specimen configuration. Han et al. [20] studied the effect of specimen configuration in SPR joints of multi layered aluminium alloy (2 mm AA6111 + 1.5 mm NG5754 +2 mm NG5754). Six

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different configurations were examined, comprising three in shear test and three in peel test. Some tests were also conducted by replacing one of the aluminium top sheet by HSLA350 steel. Results showed that the joint strength was higher for shear configuration, and within shear configuration (also in peel configuration) strength was higher when aluminium was used as a top sheet instead of steel. In the lap-shear condition the bearing load was mainly transferred by the rivet, but in cross-tension the bearing load was mainly transferred by the shearing between the rivet leg and materials. As a result the energy absorption and load were higher for lap-shear than cross-tension.

Joint design is another factor that influences the joint strength. An examination by Iyer et al. [21] showed that the strength of a double riveted joint was no better than a similar single-rivet joint for the same value of applied stress per rivet. For a double 4

ACCEPTED MANUSCRIPT riveted joint (length-wise), the highest strength was exhibited when the rivet heads were close to the loading ends. Other studies [18, 22, 23] showed that rivet pitch influences the strength of a double riveted joint (both length-wise and width-wise).

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The strength of the joint was highest when the rivet pitch equalled half of width and

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half of overlap for width-wise and length-wise double riveted joints respectively.

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In order to predict the strength of a SPR joint, Porcaro et al. [24-26] used finite element simulation using commercial software LSDYNA. At first, they identified the parameters required for numerical analysis by material testing. Then they investigated

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the failure loads of the rivet. Finally they tested the strength of the joint in different loading conditions and compared their results with numerical simulation. The results

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of the model directly depended on the accurate determination of material properties. To determine the properties of the rivet material, a tubular specimen was obtained by

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removing the head and the lower part of the rivet skirt.

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Another different approach to strength estimation, depending on the head height, was studied by Matsumura et al. [27]. They used 1.3 mm aluminium (AA 6000 series) as

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the top sheet, 0.65 mm soft mild steel as the middle sheet, and 1.2 mm high strength steel (yield strength 590 MPa) as the bottom sheet. They reported that for a large head height the failure mode was head pull-out and the strength was low. The strength increased with a decrease in head height to a certain limit. The strength decreased

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with further reduction in head height and the failure mode changed from head pull-out to tail pull-out.

Sun and Khaleel [28] proposed an analytical approach to predict the strength assuming that the rivet periphery was under perfect axisymmetric loading just before failure. They also assumed that sufficient interlock had been achieved during the riveting process. Nine different cases consisting of different thicknesses and grades of aluminium and steel were examined to validate the strength estimator. Similar analytical approach was also used to predict the joint strength of welded joints [29]. These analytical methods required some geometrical dimensions which were obtained by physically measuring the cross-sections of joints. Most of the previous research was conducted either in lap-shear or cross-tension loading condition. Sun and Khaleel

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ACCEPTED MANUSCRIPT [28] mentioned that a joint’s strength under lap-shear condition can be related to its cross-tension strength, but the relationship was not made available.

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A simple and effective model was developed by Haque et al. [30] to determine the

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amount of rivet flaring inside SPR joints without the need for cross-sections. Both interrupted and un-interrupted SPR experiments, consisting of three different

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thicknesses of steel (2.5 +2.5, 2.0 +2.0 and 1.5 +1.5 mm) and rivet with three different hardnesses ( 555, 480 and 410 HV), were performed with recording of force and punch displacement data. A relationship was established between rivet flaring and ply

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thicknesses, nominal die dimensions, and two key data points from the force-

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displacement curve that were identified to mark the start and end of rivet flaring.

Since rivet flaring is a measure of the interlock between rivet shank and sheet materials, it is a leading factor in determining the strength of SPR joints. The aim of

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the present study was to establish a relationship between SPR process parameters

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(force-displacement) and joint strength by using the rivet flaring model [30], and to develop a correlation between the strengths in the two loading conditions (lap-shear

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and cross-tension), based on the tensile resistance formulae presented in Euro-code 9 [31] for different failure modes. Here, the effect of different process parameters (ply material properties, rivet hardness and die dimensions) on the static strength of SPR joints in cross-tension and lap-shear loading conditions was investigated

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systematically for steel sheets.

Specimen Preparation

Nine different combinations of joints (cases A to I in Table 1) were considered for this study, which comprised three stack thicknesses (5.0, 4.0 and 3.0 mm), two coated low-carbon steel strips (G300 with hardness of 198 HV and yield strength of 300 MPa; G450 with hardness of 270 HV and yield strength of 450 MPa), and two values of steel rivets hardness (555 and 480 HV). More details on the properties of the steel sheets can be found on Bluescope website [32]. Three different lengths of rivet were used depending on the joint total thickness: 6, 7 and 8 mm long rivet for 3, 4 and 5 mm stacks respectively. A die with a flat profile was used for all conditions, but with

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ACCEPTED MANUSCRIPT a high die recess volume for the thick joint and a low die recess volume for the thin joint.

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Five single-point joint specimens were produced for each test piece configuration

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(cross-tension and lap-shear) as described in Figs. 2 and 3. SPR joints were produced using Henrob’s 2-stage hydraulic rivet setter with pre-clamp. A load cell, a linear

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variable differential transformer (LVDT) and pressure transducers were used to measure the force, punch displacement, rivet setting and pre-clamp pressure respectively, as a function of time. Data logging was performed at a rate of 1000 Hz.

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The experimental setup and method of producing the characteristic force– displacement curve (Fig. 4) are described in detail in Haque et al. [9]. The effective

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length of the rivet in the bottom sheet (teff) and the deformed rivet diameter (Dt) were measured from metallographic cross-sections, as shown in Fig. 5.

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Table 1 Summary of different joining combinations for static strength analysis. A

Material

G450 steel

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Thickness of the joint (Top sheet + bottom sheet, mm) Length (mm) Rivet Hardness (HV) Diameter (mm) Flat die Depth (mm) Effective length of rivet in bottom sheet, teff (mm) Deformed rivet diameter, Dt (mm)

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Case no.

G300 steel

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F

G450 steel

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G300 steel

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I

G450 steel

G300 steel

2.5 + 2.5

2.0 + 2.0

1.5 +1.5

8

7

6

555

480

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2.35 3.20 3.04 ± ± 0.13 0.12 7.66 7.60 ± ± 0.11 0.09

555

480

10 3.00 3.68 ± 0.09 7.26 ± 0.13

2.66 ± 0.07 7.54 ± 0.04

2.10 2.44 2.73 ± ± 0.05 0.11 7.72 7.52 ± ± 0.09 0.03

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2.73 ± 0.06 7.72 ± 0.08

2.00 2.25 2.25 ± ± 0.09 0.04 7.40 7.40 ± ± 0.12 0.05

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Fig. 2 Diagram of a single point cross-tension SPR joint test piece (a) schematic and (b) experimental.

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Fig. 3 Diagram of a single point lap-shear SPR joint test piece (a) schematic and (b) experimental.

Fig. 4 Cross-section and characteristic curve of 1.5 mm + 1.5 mm G300 carbon steel joint with a 6 mm long rivet of 480 HV hardness (case I in Table 1).

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Fig. 5 Cross-section of a riveted joint (case A in Table 1) showing the different

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quality parameters.

Wood et al. [33] studied the dynamic strength of SPR joint at 5 different speeds (0.01,

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0.1, 0.5, 2 and 5 m/s) and found that the joint strength was practically constant below the speed of 0.5 m/s. According to ASTM [34], static condition is considered when the strain is below 5 X 10-5 S-1. To represent the static loading, several researchers

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[17, 35] used the loading speed of 1mm/min in their examination of SPR joint strength. Thus, in the present study, mechanical testing was performed on a MTS machine under displacement control at a rate of 1 mm / minute to represents the static loading condition of SPR joints. The experiment was programmed so that the testing stopped automatically when the joint failed. The force and the displacement were recorded during testing with a logging rate of 20 Hz, and the force was then plotted as a function of displacement. Test results demonstrate good reproducibility and all data reported in the subsequent sections are average and standard deviation values calculated from five repeats.

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Results and Discussion

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In this paper, the results obtained in both cross-tension and lap-shear tests for all joints’ conditions are reported first. The effect of ply materials properties is also discussed. The effect of rivet hardness on the joint strength is then reported and

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finally, the effect of die depth on the energy required before the failure of a joint is

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analysed. The extension of the rivet flaring model presented in Haque et al. [30] to

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estimate the strength of a riveted joint is examined. In the last section of this paper, the relationship between cross-tension and lap-shear in terms of maximum force

Mechanical behaviour of joints

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3.1.

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needed to initiate failure is developed.

Two types of failure modes were observed. Similar failure mode was observed in

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Porcaro et al. [26]. Thus, the literal description of the failure mode was adopted from Porcaro et al. [26]:

Failure mode 1: Pull-out of the rivet tail from the bottom sheet (Fig. 6)

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Failure mode 2: Tilting and pull-out of the rivet from the bottom sheet and

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

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further pull-out of the rivet head from the top sheet (Fig. 7)

Fig. 6 Rivet pull-out (failure mode 1) from the bottom sheet in cross-tension test (a) experimental steel joint , (b) aluminium joint adopted from [26]

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Fig. 7 Tilting and pull-out of rivet from bottom sheet with additional rivet head pullout from top sheet (failure mode 2) in lap-shear test (a) experimental steel joint , (b) aluminium joint adopted from [26].

The cross-tension test repeatedly showed pull-out of the rivet from the bottom sheet

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(failure mode 1), and in the case of thick joints, rivet failure also occurred (Fig. 8).

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Failure mode 2 was always encountered in the lap-shear tests. Unlike the crosstension condition, rivet failure (Fig. 9) only occurred for thick and hard joints (2.5 +

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2.5 mm G450).

Fig. 8 Rivet failure with tail pull-out from the bottom sheet (failure mode 1) in crosstension testing of joint with thick sheet material (2.5 mm).

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Fig. 9 Rivet failure with tilting and tail pull-out from bottom sheet with additional rivet head pull-out from top sheet (failure mode 2) in lap-shear test of joint with thick and hard sheet material (2.5 mm G450 carbon steel).

Test results of the two extreme conditions, Case A (harder and thickest joint) and

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Case I (softer and thinnest joint) in Table 1 are presented below to demonstrate the

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reproducibility and general behaviour of the SPR joints.

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Case A: 2.5 mm + 2.5 mm G450 carbon steel joint with 555 HV rivet

These joints were produced with 8 mm long rivets and a flat die (11.0 mm diameter

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and 2.35 mm deep). Force-displacement curves of the cross-tension and lap-shear tests are shown in Fig. 10.

Fig. 10 Force-displacement curves of (a) cross-tension and (b) lap-shear tests of 2.5 + 2.5 mm G450 carbon steel sheet joints with 8mm long 555 HV rivets (case A in Table 1). 13

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Case I: 1.5 mm + 1.5 mm G300 carbon steel joint with 480 HV rivet Compared to the above Case A, the 2.5 mm G450 sheets were replaced with the 1.5

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mm G300 carbon steel. A similar flat die was used, but with a smaller die recess

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volume (9.0 mm diameter and 2.00 mm deep), and the rivet length was reduced to 6

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mm due to the thin sheets. Force-displacement curves of the cross-section and lap-

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shear tests are shown in Fig. 11.

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Fig. 11 Force-displacement curves of (a) cross-tension and (b) lap-shear tests of 1.5 + 1.5 mm G300 carbon steel sheet joints with 6 mm long 480 HV rivet (case I in Table 1).

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It should be noted that since results demonstrated the reproducible behaviour of SPR joints, as shown in Figs. 10 and 11, all graphs presented thereafter show the median curve representing the maximum force among the five test curves for any joint tested.

It was clear that the force-displacement curves from all cross-tension tests showed similar patterns whereby three distinctive stages occurred for all cases. For example, the force-displacement curve of the 1.5 + 1.5 mm G300 carbon steel joint (Fig. 12) shows that during the first stage, the force increased linearly with displacement indicating that bending of the sheet materials occurred elastically. In the middle stage, plastic bending of the materials occurred and the slope of the curve was reduced. Hence, the force increased with a much lower gradient. Finally, the force started to increase again with a higher gradient due to the resistance to plastic deformation from the sheet material surrounding the rivet leg. In this case, the flared portion of the rivet 14

ACCEPTED MANUSCRIPT tail sheared along the effective length of rivet in the bottom sheet (Fig. 5) and the joint failed by pull-out of the rivet from the bottom sheet. It is thus expected that the maximum force needed to cause failure depends on the effective length of rivet in the

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bottom sheet (teff) and the deformed rivet diameter (Dt). Lap–shear test results also

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showed a similar pattern of force-displacement curves for all cases.

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Fig. 12 Median force-displacement curve of a cross-tension test for 1.5 + 1.5 mm G300 carbon steel joint showing the three distinctive stages. However, the maximum force was always higher in lap-shear than in cross-tension

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loading condition, while the total displacement was larger in cross-tension than in lap-

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shear. This is typically shown in Fig. 13.

Fig. 13 Effect of loading condition on force-displacement curves of 2.5 + 2.5 mm G300 carbon steel joint. In both conditions (lap-shear and cross-tension) the strength of a joint was greatly dependent on the hardness and thickness of the sheet materials. As expected, the harder and thicker a ply material, the higher is the strength of a joint in terms of both 15

ACCEPTED MANUSCRIPT maximum force and energy absorbed. The key points for each joint condition are summarized in Table 2.

Cross-tension

B Lap-shear Cross-tension

C Lap-shear Cross-tension

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3.2.

92.50 ± 0.90

17.90 ± 0.73

4.34 ± 0.15

126.23 ± 0.77

10.34 ± 1.04

15.66 ± 0.48

97.31 ± 1.20

12.90 ± 0.53

4.07 ± 0.10

98.27 ± 0.95

11.33 ± 1.02

16.67 ± 0.62

125.46 ± 1.41

Mode 2

14.17 ± 0.83

3.99 ± 0.12

105.11 ± 1.33

Mode 1

9.78 ± 0.64

15.52 ± 0.64

89.09 ± 0.88

Mode 2

14.28 ± 0.14

3.99 ± 0.09

102.33 ± 0.22

failure Mode 2 + rivet failure Mode 1 + rivet failure Mode 2

Mode 1 + rivet failure

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12.45 ± 0.55

Mode 1 + rivet

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Lap-shear Cross-tension

Mode 1

9.76 ± 0.24

16.76 ± 0.37

97.19 ± 0.52

Lap-shear

Mode 2

14.35 ± 0.81

3.99 ± 0.07

91.53 ± 1.05

Cross-tension

Mode 1

7.97 ± 0.70

17.22 ± 0.49

83.14 ± 1.13

Lap-shear

Mode 2

11.36 ± 0.31

3.53 ± 0.11

82.31 ± 0.85

Cross-tension

Mode 1

7.32 ± 0.22

15.92 ± 0.34

73.37 ± 0.59

Lap-shear

Mode 2

10.73 ±0.63

3.53 ± 0.06

77.51 ± 1.03

Cross-tension

Mode 1

6.84 ± 0.94

14.23 ± 0.04

56.29 ± 1.31

Lap-shear

Mode 2

10.54 ± 0.71

3.25 ± 0.02

69.10 ± 1.23

Cross-tension

Mode 1

4.69 ± 0.13

13.98 ± 1.14

38.03 ± 1.02

Lap-shear

Mode 2

8.33 ± 0.82

2.56 ± 0.02

41.13 ± 0.88

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11.16 ± 0.61

Failure mode

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Lap-shear

Energy absorbed before failure (kN-mm)

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A

Displacement at maximum force (mm)

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Cross-tension

Maximum force (kN)

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Case no.

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Table 2 Failure mode, maximum force and absorbed energy in cross-tension and lapshear test conditions of joints listed in Table 1.

Effect of ply materials’ properties and thickness on joint strength

The effects of material properties on the static strength in cross-tension of SPR joints with three different thicknesses are shown in Fig. 14. It can be observed that for a 16

ACCEPTED MANUSCRIPT 50% increment in the yield strength of the material, the maximum force was increased by 8%, 22% and 45% for 5.0 (2.5 + 2.5) mm, 4.0 (2.0 + 2.0) mm and 3.0 (1.5 +1.5) mm joint stacks respectively. The effective length of the rivet in the bottom sheet (teff

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= 2.25 mm) and the deformed rivet diameter (Dt = 7.4 mm) for a 3.0 mm joint were

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found to be the same for joints of either G300 or G450 steel. Thus, the increase in joint strength was related to the rate of increase in the yield strength of the ply

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materials. However, with the 4.0 mm joint, the effective length of the rivet in the bottom sheet was less for the G450 joint (teff = 2.66 mm) than the G300 joints (2.73 mm), as shown in Table 1, while the deformed rivet diameter was the same (Dt = 7.50

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mm). As a result, the strength of the 4.0 mm joint did not increase proportionately with the yield strength. For the 5.0 mm joints, the failure mode was different for the

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G450 joint (rivet failure observed in addition to failure mode 1), which is why the

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joint strength was not increased with the rate of increase in yield strength.

Fig. 14 Effects of material grade and thickness on joints strength in cross-tension

It is clear from Fig. 14 that the displacement during elastic bending was similar for each joint of the same material. However, the plastic bending and yielding of material 17

ACCEPTED MANUSCRIPT varied for different thicknesses due to stiffness. For the joints of G 300 steel, maximum forces were 10.34, 7.97 and 4.69 kN for 5.0, 4.0 and 3.0 mm stack joints respectively (Table 2). An increase in joint thickness needed a longer rivet to be used

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which led to differences in the deformed rivet diameter and the effective length of the

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rivet in the bottom sheet. Thus, for a 33% and 67% increase in thickness (from 3.0 to 4.0 and 5.0 mm), the maximum force increased by 70% and 120% respectively. The

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displacements before complete failure were 15.66, 17.22 and 13.98 mm for 5.0, 4.0 and 3.0 mm stack joints respectively.

For G450 steel joints, the displacements before complete failure were 12.45, 15.52

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and 14.23 mm for 5.0, 4.0 and 3.0 mm stack joints respectively. The displacement for the 5.0 mm joint was low as rivet failure occurred in addition to rivet pull-out as

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shown in Fig. 8). Maximum forces were 11.16, 9.78 and 6.84 kN for 3.0, 4.0 and 3.03.0 mm stack joints respectively.

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The effect of material properties on the lap-shear static strength of SPR joints of three

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different thicknesses are shown in Fig. 15. The increase in maximum force due to material properties was found to be similar for all different thicknesses (Fig. 15). Like

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the cross-tension condition, the effective length of the rivet in the bottom sheet (teff) was not the only crucial factor for lap-shear loading condition; the deformed rivet diameter (Dt) was also another crucial factor. In general, it was observed that the effective length of rivet in the bottom sheet (teff) was high when the deformed rivet

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diameter (Dt) was low. The energy was mainly dependent on the deformed rivet diameter, and the pull out strength was mainly characterized by the effective length of the rivet in the bottom sheet (teff in Fig. 5). As a combination of the three factors (effective length of the rivet in the bottom sheet, the deformed rivet diameter and material properties) the peak loads in lap shear of G450 joints were overall 30% greater than G300 joints.

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Fig. 15 Effects of material grade and thickness on joints strength in lap-shear.

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It is clear from Fig. 15 that for the joints of G300 steel, the maximum force increased with the increase in joint thickness. Peak forces were 12.9, 11.3 and 8.3 kN for 5.0, 4.0 and 3.0 mm joints respectively. The joint strengths increased by 36% and 56% for

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an increase in thickness of 33% and 66% respectively. All the above joints showed similar failure mode. Thus the force increased proportionately with an increase in thickness.

3.3.

Effect of Rivet hardness on joint strength

Force-displacement curves for the cross-tension tests of joints of 2.0 + 2.0 mm G450 carbon steel sheet produced with rivets of different hardness are shown in Fig. 16.

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Fig. 16 Force-displacement curves for a 2.0 + 2.0 G450 carbon steel sheet joint in cross-tension condition.

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It was clear that the two joints behaved identically during the elastic bending of the sheet material. However, a small increase in the force was observed for the joint with

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the softer rivet. This was due to the higher deformed rivet diameter (Dt = 7.72 and 7.54 mm for 480 and 555 HV rivet respectively, Table 1). The final displacements at failure were 15.52 mm and 16.76 mm for 555HV and 480HV rivet joints respectively. As the deformed rivet diameter was higher for 480 HV rivet, it required more

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displacement of material before failure. Thus the displacement at failure was higher for the joint with the softer rivet. The failure mode for both joints was rivet pull out from the bottom sheet (failure mode 1), which occurred mainly by shear failure of the material. Therefore, rivet hardness (for the range of HV examined) does not appear to be a critical factor for joint cross tension strength.

Force- displacement curves for the lap-shear tests of 4.0 mm (2.0 + 2.0 mm) G450 carbon steel sheet are shown in Fig. 17. It is evident that the maximum force was slightly higher for the harder rivet (14.35 and 14.28 kN for 555 and 480 HV rivets respectively, Table 2). In the lap-shear condition, initially the energy was absorbed by the rivet while tilting of rivet occurred, so it was easy to deform the sheet material for the harder rivet. Initially the force was higher for the same amount of displacement for the softer rivet. However, the effective length of the rivet in the bottom sheet (teff = 20

ACCEPTED MANUSCRIPT 2.66 and 2.44 mm for G450 and G300 joint respectively, Table 1) was higher for the 555 HV rivet and due to this aspect, the maximum force was also high. On the other hand, the deformed rivet diameter (Dt =7.54 and 7.72 mm for G450 and G300 joint

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respectively, Table 1) was lower for the 555 HV rivet). As a result, Though the

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hardness of the rivet was increased by 15%, the maximum force was increased by only 0.4%. It can be concluded that the rivet hardness (within the range of HV

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examined) played an insignificant role in terms of the joint strength.

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Fig. 17 Joint strength depending on rivet hardness for a 2.0 + 2.0 mm G450 carbon

3.4.

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steel sheet joint in lap-shear condition.

Effect of die depth on joint strength

Die depth plays an important role on the effective length of rivet in the bottom sheet (teff) of a SPR joint which ultimately leads to a high static force. Force- displacement curves for the cross-tension tests of 2.5 + 2.5 mm G300 carbon steel joints are shown in Fig. 18. It was clear that the force was higher for joints made with the 3.0 mm deep die (11.33 kN) than with the 2.35 mm deep die (10.34 kN). This was mainly due to the effective length of rivet in the bottom sheet (teff = 3.68 and 3.04 mm for the 3.0 and 2.35 mm deep dies respectively, Table 1, also in Fig .19). Thus, a deep die should be used where possible. However, it was observed that a deep die can also lead to cracking of hard material with low elongation [36]. So, extreme care should be taken

21

ACCEPTED MANUSCRIPT when selecting a proper die for a given set of riveting parameters (ply material

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thickness and hardness, rivet length and hardness).

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Fig. 18 Effect of die depth on the strength in cross-tension tests of joints of 2.5 + 2.5

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mm G300 carbon steel sheet.

Fig. 19 Effect of die depth on joint characteristics of joints of 2.5 + 2.5 mm G300 carbon steel sheet.

The force-displacement curves for the lap-shear condition tests of 2.5 + 2.5 mm G300 carbon steel joints with different die depths are shown in Fig. 20. Like the crosstension condition, the force in lap shear condition was also higher for joints made 22

ACCEPTED MANUSCRIPT with the 3.0 mm deep die. Though the deformed rivet diameter was greater with the 2.35 mm deep die (Dt = 7.6 mm vs 7.26 mm for the 3.0 mm deep die, Table 1, also in Fig. 19), the lower force can be related to the lower effective length of rivet in the

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bottom sheet (teff = 3.04 mm). Similar effect of die depth on joint strength was

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observed for different thickness of materials in Haque [36]. From this result and consistent with Sun & Khaleel [28], it can be concluded that the effective length of

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rivet in the bottom sheet should be included as a quality parameter for a riveted joint whereas most literature had reported only the deformed rivet diameter as a quality

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parameter [7, 8, 13].

Fig. 20 Effect of die depth on lap shear strength of 2.5 + 2.5 mm G300 carbon steel joint.

3.5.

Joint strength estimation

A rivet flaring model was developed in Haque et al. [30], where it was shown that the rivet flaring can be calculated by using the empirical equation (1).

(1)

23

ACCEPTED MANUSCRIPT where,

is the amount of rivet flaring;

and

are coefficients that depend on

rivet hardness and length respectively; t1and t2 are the top and bottom sheets’ thickness respectively; h is the die depth; Rr is the undeformed (initial) rivet radius

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T

and Dd is the die diameter.

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Finally, d0 and dmax are the relative punch displacements before and after flaring respectively, and can be determined from the characteristic SPR process curve (Fig. 4) for any given joint. It was found that the rivet flaring model can successfully predict

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the rivet flaring (deformed rivet diameter) albeit the simple nature of that equation. It was clear from the previous section (section 3.2) that the joint strength under cross-

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tension directly depends on the material thickness. Sun and Khaleel [28] proposed an empirical equation to estimate the static strength of SPR joint (Equation 2).

D

(2)

TE

where FCT is the joint strength for tail pull-out failure; Dt is the deformed rivet diameter and teff is the effective length of the rivet in the bottom sheet; ƞ t is the

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empirical coefficient of material degradation due to the piercing process for the tail side (ƞ t = 0.6 if the elongation is >9% and ƞ t = 0.5 for materials having elongation <9%); βt is an empirical coefficient of the sheet bending induced thickness reduction

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for the tail side materials (βt=1 for t2>1.5 mm and βt ≅0.8 for t2 ≤1 5 mm, see Fig. 5); and σt is the yield strength of the sheet material.

In equation 2, two factors are unknown unless the rivet cross section is available: teff and Dt. The tail pull out strength estimator thus depends on the accurate measurements of very small dimensions of deformed rivet diameter (Dt) and effective length of rivet in the bottom sheet (teff) as shown in Fig. 5. Precise sectioning and adequate specimen preparation are required to get those measurements. A small error in the process of measurement can thus lead to significant error on the estimation of the joint strength. In the present study, since the riveting process requires no piercing through the bottom sheet, the deformed rivet diameter (Dt) and the effective length of rivet in the bottom sheet (teff) were approximated by the following equations with the

24

ACCEPTED MANUSCRIPT help of the rivet flaring model (

in equation 1), provided good interlock has been

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T

achieved:

(3)

(4)

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can be rewritten in the following form.

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Substituting values of Dt and teff given by equations 3 and 4 respectively, equation 2

(5)

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For a given die and rivet, the die depth (h) and rivet radius (Rr) are known. For a

and rivet flaring (

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given joint, the top sheet thickness (t1) and bottom sheet thickness (t2) are also known, ) can be calculated by equation 1. Thus equation 5 is an adapted

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strength estimator that eliminates the need for metallographic measurements from cross-sections.

The nine different experimental cases listed in Table 1 were used to check the validity

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of the adapted strength estimator. The values of the empirical coefficients for material thickness (βt) and degradation due to the piercing process (ƞ t) were the same as used by Sun and Khaleel [28] as the materials are of similar elongation and thickness. The rivet radius (Rr = 2.75 mm) was the same for all experiments. An example of joint strength calculation is given below for case A and the calculated joint strengths for all the cases are summarized in Table 3.

Case A: The yield strength of the material was σt = 450 MPa. The geometrical factors were: Rr = 2.75 mm, h = 2.35 mm, t2 = 2.5mm and rivet flaring, (

= 1.19 mm), as

determined by equation 1. Equation 5 produces

25

ACCEPTED MANUSCRIPT 5 1 5

11

5

1

1

T

1

5

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The experimentally measured joint strength was found to be 11.16 ± 0.61 kN.

Die

of bottom

depth, h

sheet, σt

(mm)

(MPa)

Top/Bottom sheet thickness,

2.35

B

300

2.35

2.5/2.5

C

300

3.00

2.5/2.5

D

450

2.10

2.0/2.0

E

450

2.10

2.0/2.0

F

300

2.10

2.0/2.0

300

2.10

2.0/2.0

450

2.00

1.5/1.5

300

2.00

1.5/1.5

I

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H

2.5/2.5

TE

450

Calculated

Rivet flaring,

joint

Measur

calculated by

strength,

ed joint

equation 1,

from

strength

equation 5,

(kN)

t2/t2 (mm)

A

G

d0 / dmax

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Case no.

strength

D

Yield

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Table 3 Joint strengths in cross-tension for all cases listed in Table 1

(mm)

5.22/7.95

FCT (kN) 12.00

1.13

9.54

0.86

10.19

0.79

9.29

1.11

9.52

0.80

7.44

1.25

7.67

0.95

5.92

0.90

4.73

4.40/7.80

1.19

5.85/8.00 4.10/6.60 4.00/6.70 3.60/6.65 3.50/7.00 3.10/5.90 3.00/5.85

11.16 ± 0.61 10.34 ± 1.04 11.33 ± 1.02 9.78 ± 0.64 9.76 ± 0.24 7.97 ± 0.70 7.32 ± 0.22 6.84 ± 0.94 4.69± 0.13

Considering the simple nature of equations 1 and 5, a reasonably good correlation was obtained between experimental and predicted strengths. A comparison between the calculated and measured joint strengths is shown in Fig. 21.

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Fig. 21 Comparison of calculated and measured joint strengths in cross-tension.

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Results show that most of the calculated joint strengths fall within 10% of the respective measured joint strength. The adapted joint strength estimator depends on

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the rivet flaring model and estimation of effective rivet length (teff). Nevertheless, the

3.6.

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above estimator is simple in nature and could be a useful tool in industrial practice.

Relationship between cross-tension and lap-shear strengths

Eurocode 9 (prEN1999-1-4) allows the design of cold-formed joints to be assessed by theoretical model [31]. According to Eurocode 9 (prEN1999-1-4), the strength of blind rivet joint can be determined as follows:

(6)

(7)

27

ACCEPTED MANUSCRIPT where FPO is the pull-out resistance and FB is the joint bearing resistance for crosstension and lap-shear loading respectively;

is the minimum ultimate tensile

strength of both sheets; d is the diameter of the blind rivet; tmin is the thickness of the is the factor for resistance of the connection;

is the

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thinner connected sheet;

is the yield strength of the bottom sheet.

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sheet; and

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correction factor with respect to the location of rivet; t is the thickness of the bottom

It should be noted that the above design formulas prescribed in Eurocode 9 [31] were only suitable for blind rivets and no recommendation was found for self-piercing rivet. However, it was observed that the failure mode in the present study was mainly

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by rivet tail pull out, to which the design formula available for the blind rivet in Eurocode 9 may be applied. Considering the similarity of the failure mode (tail pull-

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out), two equations were proposed in this study. For the cross-tension loading condition (failure mode 1), equation (8) was developed based on the pull-out resistance, while for the lap-shear loading condition (failure mode 2), equation (9)

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was developed based on the bearing resistance of the rivet. The equations are as

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follows:

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(8)

(9)

where FCT and FLS are the maximum force for the cross-tension and lap-shear loading conditions respectively.

is the yield strength of the material. Dt and teff are the

deformed rivet diameter and the effective length of the rivet in the bottom sheet respectively. αCT and αLS are empirical strength coefficients for the cross-tension and lap-shear conditions respectively. By dividing equation 9 with equation 8, the expression for the maximum force for the lap-shear condition becomes:

28

ACCEPTED MANUSCRIPT

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(10)

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The coefficient αCT was found from equation 8 by replacing FCT with the

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experimentally obtained values for the cross-tension condition, while the coefficient for the lap-shear condition (αLS) was found from equation 9 by using the experimental FLS values. Four different joining conditions were considered to determine the above

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coefficients, comprising two types of hardness of materials and two levels of rivet hardness (cases D, E, F and G in Table 1). The calculation of the constants for the cross-tension and the lap-shear is shown below and the values for different cases are

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summarized in Table 4.

= 0.79 mm and teff

=

2.66 mm. The experimentally obtained forces were:

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were:

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Case D: The yield strength of the material was 450 MPa. The geometrical factors

FCT=9.78 ± 0.64 kN and FLS= 14.28 ± 0.14 kN. Equations 3, 8 and 9 produced the as follows:

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and

) = 2 * (2.75 + 0.79) = 7.08

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Deformed rivet diameter, Dt = 2 * (Rr + Constant for cross-tension,

1 5

1

1

1

1

Constant for lap-shear, 1 5

1

1 1

1

1

Table 4 Constants for cross-tension and lap-shear loading for the different cases in Table 1 29

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Yield

no.

of bottom sheet,

Deformed

Effective

Constant

Constant

flaring,

rivet

length of rivet

for cross-

for lap-

diameter,

in bottom

tension,

shear,

(mm)

Dt (mm)

sheet, teff (mm)

0.79 1.11 0.80 1.25

7.08 7.72 7.10 8.00

2.66 2.50 2.65 2.43

,

450 450 300 300

1.89 1.98 2.31 2.28

1.69 1.66 2.01 1.84

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D E F G

αLS

αCT

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(MPa)

T

Case

Rivet

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strength

The coefficients for the cross-tension (αCT) and lap-shear (αLS) conditions were

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determined as the average of the above calculated coefficients.

= 2.11 ± 0.21

Prediction of strength for lap-shear condition by equation 10

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3.7.

= 1.80 ± 0.16

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Coefficient for cross-tension,

D

Coefficient for cross-tension,

The coefficients αCT and αLS from the experimental measurement were needed to verify equation 10. Five different joining conditions were considered sufficient to validate

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equation 10, comprising two values of thickness and hardness of materials, and with two different values of hardness of the rivet (cases A, B, C, H and I in Table 1). The calculations for case A is shown below and the experimental and calculated joint strengths for all the conditions are summarized in Table 5. The strengths for cases DG in Table 1 were back calculated again by using the average coefficients αCT and αLS. Case A: The geometrical factors were:

=1.19 mm and teff

=

3.08 mm. The

experimentally obtained force for the cross-tension condition was: FCT=11.16 ± 0.61 kN. Equations 10 becomes

30

1

1

11 1

1

1

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11

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ACCEPTED MANUSCRIPT

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15 1

The experimentally measured joint strength for the lap-shear condition was found to be

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17.90 ± 0.73 kN.

Table 5 Lap-shear joint strength for different cases in Table 1

calculated

no.

by equation 1,

1.19 1.13 0.86 0.79 1.11 0.80 1.25 0.95 0.90

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A B C D E F G H I

Effective length of

joint

lap shear

rivet in bottom

strength

joint

calculated

sheet calculated by

calculated

strength

by

equation 4, teff

by equation

(kN)

(mm)

10, (kN)

3.04 3.11 3.57 2.66 2.50 2.65 2.43 2.03 2.05

15.18 ± 0.82 13.89 ± 1.38 13.70 ± 1.23 13.6 ± 0.30 14.6 ± 1.30 11.1 ± 0.53 11.3 ± 0.92 11.12 ± 1.52 7.52 ± 0.21

rivet diameter

equation 3, Dt (mm)

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, (mm)

Measured

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Case

Lap shear

D

flaring

Deformed

TE

Rivet

7.88 7.76 7.22 7.08 7.72 7.10 8.00 7.40 7.40

17.90 ± 0.73 12.90 ± 0.53 14.17 ± 0.83 14.28 ± 0.14 14.3 ± 0.81 11.36 ± 0.31 10.73 ± 0.63 10.54 ± 0.71 8.33 ± 0.82

It was observed that equation 10 gives a reasonable prediction of lap shear strength. A comparison between the predicted and experimental strengths for the lap-shear condition is shown in Fig. 22.

31

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ACCEPTED MANUSCRIPT

D

Fig. 22 Comparison between predicted and measured joint strengths for the lap-shear loading conditions for the nine different cases as tabulated in Tables 4 and 5.

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It is clear from Fig. 22 that equation 10 relates the joint strength between lap-shear and cross-tension with less than 8% error. Case E showed some discrepancy between

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the predicted and measured strengths. It should be noted that the failure mode in the lap-shear condition for case E was different from the other eight cases. The failure mode was tilting and pull-out of the rivet from the bottom sheet and pull-out of the

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rivet head from the top sheet (failure mode 2) for cases B-I as tabulated in Table 1. However, for ‘case E’ rivet failure occurred in addition to the failure mode 2. Thus, a significant difference between the calculated and measured strengths was observed for this case. Discrepancy was also observed for cases C, D, F and G, but this was due to the averaging of the co-efficient for lap-shear condition (αLS). It should be noted that the coefficients for the cross-tension and lap-shear conditions were determined using data from joints with 2.0 mm thick sheet, while equation 10 was validated for completely different thickness combinations. This demonstrates that the coefficients are not dependent on the material thickness. However, the coefficients (αCT and αLS) were strictly related to the parameters studied in this investigation (rivet and die geometry) and cannot be generalized. Still, the developed relationship between the cross-tension and lap-shear conditions represents a useful reference to be considered for further studies especially for different rivet and die geometries. 32

ACCEPTED MANUSCRIPT

4.

Conclusions

A systematic investigation was conducted of the effects of different process

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parameters on the static strength of single point SPR joints of steel sheets in cross-

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tension and lap-shear loading on. Rivet pull-out was the main failure mode in cross-

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tension while rivet pull-out with tilting of rivet was the main failure mode in lapshear. Additionally, rivet failures occurred in joints of thick and hard sheet material in

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both loading conditions.

The joint strength increased non-proportionally with increased hardness and thickness of materials for all loading conditions as other factors like rivet flaring and effective

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length of the rivet in the bottom sheet (teff) also influence the joint strength. The depth of the die plays a significant role in the deformation behaviour of the material: the

D

effective length of the rivet in the bottom sheet (teff) was greater with a deeper die,

TE

which resulted in increasing the joint strength.

Since the riveting process requires no piercing through the bottom sheet, the deformed

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rivet diameter (Dt) and the effective length of rivet in the bottom sheet (teff) were approximated by rivet flaring model (equations 3 and 4) which leads to the development of joint strength estimator (equation 5) in static loading condition. This

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estimator can be used effectively to predict the joint strength in cross-tension loading (static) as it was successfully linked to the characteristic SPR process forcedisplacement curve. A relationship (equation 10) was also developed between the lap shear and cross-tension strengths in static loading condition. These strength models represent a useful reference to be considered for further studies especially for different rivet and die geometries.

Acknowledgements

The authors would like to thank Henrob (UK) Pty Ltd for supplying the rivets and materials to produce the joints, and also for giving permission to publish this work. The support of CAST CRC and Swinburne, and the provision of a PhD scholarship

33

ACCEPTED MANUSCRIPT are acknowledged. CAST was established under, and was supported in part by the

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Australian Government’s Cooperative Research Centre Program.

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Nomenclature

C1 = Coefficient depends on rivet hardness (0≤C1≤1). C2 = Coefficient depends on rivet length (0≤C2≤1).

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d0 = Displacement of rivet before flaring (mm).

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Dd = Die diameter (mm). Deformed rivet diameter (mm).

dmax = Maximum rivet displacement (mm).

D

= Joint strength in cross-tension loading (kN).

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h = Die depth (mm).

TE

= Joint strength in lap-shear loading (kN).

Rr = Rivet radius (mm).

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t1 = Top sheet thickness (mm). t2 = Bottom sheet thickness (mm). = Effective length of the rivet in the bottom sheet (mm). α

= Strength coefficient for cross-tension.

α

= Strength coefficient for lap-shear.

βt = Empirical coefficient of the sheet bending induced thickness reduction for the tail side materials. Δd = Rivet flaring (mm). ƞ t = Empirical coefficient of material degradation due to the piercing process for the tail side.

34

ACCEPTED MANUSCRIPT

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σt = Yield strength of the sheet material (MPa).

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products/metallic-coated-steel (accessed on 17th November, 2015). 2015. [33] Wood PKC, Schley CA, Williams MA, Rusinek A. A model to describe the high rate performance of self-piercing riveted joints in sheet aluminium. Materials & Design. 2011;32:2246-59. [34] American Society of Metals (ASM) Handbook online vol:8, Mechanical Testing and Evaluation, accessed on 4th July, 2016

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ACCEPTED MANUSCRIPT [35] Ueda M, Miyake S, Hasegawa H, Hirano Y. Instantaneous mechanical fastening of quasi-isotropic CFRP laminates by a self-piercing rivet. Composite Structures. 2012;94:3388-93.

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[36] Haque R. Residual stress and deformation in SPR joints of high strength

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materials: Swinburne University of Technology; 2014.

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Graphical Abstract

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Highlights  Influence of sheet thickness and yield strength, rivet hardness and die depth variation on strength of SPR joints were studied.  An analytical model to estimate SPR joint strength directly from forcedisplacement curve was developed.  A relationship between cross-tension and lap-shear loading conditions was established.

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