Global mechanical properties

Single lap shear testing was carried out to analyze the quasi-static mechanical performance of joints. The joint strength was evaluated in accordance with ASTM D5961-17 [176] using a universal testing machine (model 1478, Zwick Roell, Germany) with a load capacity of 100 kN. The transverse test speed was 2 mm/min and testing was carried out at room temperature (21 °C). The experiments were assisted by a digital image correlation (DIC) system (ARAMIS-4m, GOM, Germany) to record the displacement of joint surface under tensile loading. The joint surfaces were painted to create a stochastic speckle pattern that is used to monitor joint deformation by comparing the relative distance between black dots over different stages of deformation. The set-up described in Section 5.2.4 was adopted.

To determine the plastic deformation and damage accumulation in the joint under quasi-static loading, a consecutive loading and unloading approach was used. Each specimen was loaded five times at levels of 25 %, 50 %, 70 %, 85 %, and 90 % of the ULSF. Three specimens were tested at each load level, with one sample cross-section analyzed by microscopy. After each level, all the joints were qualitatively inspected by the non-destructive techniques (NDT) of the ultrasonic (US) method.

5.2.9.2 Fatigue experiments

The fatigue tests were carried out using a servo-hydraulic machine (Instron/Schenk, Germany) with ±10 kN load capacity in a tension-tension regime at R = 0.1. A constant amplitude sinusoidal loading at a frequency of 5 Hz was set. Load levels of 60 %, 65 %, 70 %, and 80 % of the ULSF were used to determine the Wöhler (S-N) curve. For post-impact fatigue tests, the load levels used were 60 %, 70 %, 80 %, and 90 % of the joint’s residual strength. A minimum of three specimens for each level was tested. The single overlap joint configuration, whose geometry is depicted in Figure 5.4, was used. Complete joint failure and the joint withstanding 10⁶ cycles were used as conditions to stop the test. The joints that survived 10⁶ cycles without failure (termed run-out specimens) were subsequently tested under quasi-static conditions, as described in Section 5.2.9.1, and their residual strength reported.

For friction riveted joints, joint strength is expressed as a ratio of the load level in newtons to the average of the real area (Ar) of the hole, as depicted in Figure 5.12. The real area of the hole was measured from X-ray micro-computed tomography images before mechanical testing by using ImageJ software. This approach was successfully used by Blaga et al. in [27].

Figure 5.12 A cross-sectional view of the single lap joint obtained by X-ray micro-computed tomography that was used to measure the real bearing area (Ar).

A variation in the joint stiffness was used as an indication of damage accumulation throughout the joint fatigue life. The calculation for stiffness degradation Ds = 1-(E/E0), with E0 as the initial joint stiffness, was applied.

Statistical analysis of the fatigue life data

A Weibull distribution was used to model fatigue life of the friction riveted joints according to the DIN 50100:2016-12 [177] standard. The two-parameter Weibull modeling approach, which considers a set of samples rather than individual results, was applied to the model and confidence estimation. This distribution has been reported in the literature as a useful tool to evaluate the broad scattered fatigue data of composite structures and their reliability [178–180].

The probability density function (PDF) of the two-parameter Weibull distribution is presented in Equation 4. An integration of the PDF results in a cumulative density function (CDF) (Equation 5) gives the probability of joint failure. Equation 6 is derived from Equation 5, with the latter corresponding to the probability of the survival, or reliability, of a set of joints [178].

𝑓(𝑥) =^𝛽

where x is the fatigue life; β is the Weibull slope; α is the characteristic life or the number of cycles in which 63.2 % of the sampling is expected to fail; 𝐹_𝑓(𝑥) is the probability of failure; and 𝐹_𝑠(𝑥) is the probability of survival or reliability (Rx).

Based on the above-mentioned equations, a Weibull distribution and reliability analysis were carried out. In this study, S-N plots were drawn for R99, R90, and R50.

5.2.9.3 Drop weight impact testing

To study impact damage tolerance of the friction riveted joints, drop weight impact tests were carried out using an instrumented impact machine, following the ASTM D7136-15 [181] standard, at room temperature. Figure 5. 13 illustrates the set-up for the drop weight impact test. The specimen geometry depicted in Figure 5.4 was used. A pneumatic clamping system was employed to ensure better distribution of the impact energy and prevent movement of the specimens. A hardened steel dart impactor with a hemispherical 12.5 mm diameter tip fixed to the weight was impacted on the center of the joint’s back surface. The edges of such surface were clamped between circular rings of 15 mm inner diameter. An anti-rebound system was coupled to the machine, to prevent multiple impacts during testing. The impact energies of 5 J, 10 J, 20 J, and 30 J were selected and achieved by

varying the drop weight, while the height was kept constant at 300 mm. The load over time was acquired and used to calculate the absorbed energy (Ut).

Figure 5. 13 a) Set-up of the drop weight impact test; b) neutral plane of the set-up, showing the dimensions of the indenter and the inner diameter of the ring from the clamping system.

The post-impact strength and post-impact fatigue behavior were obtained, following the testing described in Section 5.2.9.1 and Section 5.2.9.2, respectively. The impact damage was characterized by impact area (Ai) and residual dent depth (Drd), using confocal laser scanning microscopy (see Section 5.2.5.2), ultrasonic inspection (see Section 5.2.6.2), and X-ray micro-computed tomography (see Section 5.2.6.1). A cross-section of the impacted joints was prepared using a standard materialography procedure and impact-induced through-thickness defects were characterized by means of light optical microscopy (LOM) and scanning electron microscopy (SEM).

5.2.10 Durability experiments