Experimental investigation and quantitative prediction in interference-fit size of CFRP riveted joints under a transversal ultrasonic vibration-assisted riveting

In this study, a transversal ultrasonic vibration-assisted riveting (TUVAR) process was developed to improve the uniformity of CFRP riveted lap joint interference-fit size, which provided a possibility for the quantization of riveted joint interference-fit sizes. The relationship between the process parameters of vibration amplitude, vibration duration, and roughness with interference-fit sizes by algorithms, through the minimum coefficient variance of interference-fit size (ICV-min) to confirm the riveting process parameters of the quantized average interference-fit sizes (IA). The experimental verification results showed that the mean absolute percentage error of measured IA and predicted IA is less than 10%. Furthermore, the tensile tests were carried out to investigate the effect of interference-fit size {1.4%, 1.6%, 1.8%, and 2.0%} on mechanical performances of CFRP riveted lap joints by TUVAR, and the tensile strength presents first-up then down with the interference-fit size increase, the maximum ultimate tensile strength is the riveted lap joint with the interference-fit size of 2.0%. Hence, the quantitative optimization method can well predict the riveting process parameters corresponding to the most uniform interference-fit size.


Experimental procedures Transversal ultrasonic vibration-assisted riveting system
In Fig. 1, the developed transversal ultrasonic vibration-assisted riveting (TUVAR) system mainly consists of a drive unit, an ultrasonic vibration assistance unit, and a data acquisition unit.The ultrasonic vibration assistance unit is in charge of providing acoustic energy.Specifically, when connecting with the power, the ultrasonic generator transfers the low-frequency electric energy to high-frequency electric energy.Then the ultrasonic transducer is used to transfer the electric energy to mechanical energy, furtherly the ultrasonic horn amplifies the vibration amplitude.Finally, the high-frequency mechanical vibration with an amplified amplitude is applied to rivets, until the compression is completed.In the TUVAR process, the vibration amplitude has a significant effect on the plasticity improvement of the Ti-alloy rivet based on the previous study 4 , which would further affect the rivet deformation and joint performance.The amplitudes with different power were measured by a dial indicator (Syntek-JR3), and the measured results are shown in Fig. 2.

Specimen preparation
The T700 CFRP laminates and Ti-45Nb rivets were selected for interference-fit sizes optimization and tensile specimens.T700 CFRP was using a unidirectional carbon fiber/epoxy with a thickness of 0.15 mm per ply (provided by GW COMPOS Company Ltd., China).The fabricated T700 CFRP laminate processes a thickness of 2.3 mm with 16 piles, the ply orientation of T700 CFRP is[0°/90°/45°/− 45°/− 45°/45°/90°0°] 2 s , and the weight fraction of carbon fiber is about 60%.Material properties of the fabricated CFRP laminates are presented in Table 1.Moreover, the Fabricated Ti-45Nb rivets (provided by CAG Company Ltd., China) were annealed by heating in a vacuum (less than 0.1um mercury) to a temperature within the range of 1450-1600 °F, holding at heat for sufficient time to produce a recrystallized structure that will meet the requirements of 3.5.Material properties of the Ti-45Nb are presented in Table 1.In addition, the sizes of CFRP riveted specimens according to the ASTM D5661 21 are shown in Fig. 3, and W/D ≥ 6, E/D ≥ 3.

Experimental procedure
The experimental procedure is divided into three parts, as shown in Fig. 4. Part 1: the experiments of orthogonal and single factor were carried out, and the diameters of the deformed rivet bar were measured with three positions 1, 18 , as shown in Fig. 5. Furthermore, the relative interference-fit size {I 1 , I 2 , I 3 } of three positions were calculated by Eq. (1), and the average relative interference size (I A ) and coefficient of variance of relative  where D and D 0 are the diameters of the deformed rivet shaft and initial riveting hole.
where I A presents the average relative interference size; N is the number of the measured positions of each deformed rivet; I i is the relative interference size with different measured positions.
where I CV presents the coefficient of variance of relative interference size, i.e. the evaluation index of interference-fit size uniformity.To accurately evaluate the contribution value of the TUVAR process parameters, the random forest, and extremely randomized trees are adopted to quantize the weight magnitude of the process parameters 22,23 .Considering the disadvantages of the algorithm analysis, the random forest and extremely randomized trees are used to authenticate and take the mean of multiple cycles superposition calculation. (1)

Interference-fit size analysis
Interference-fit size has a significant effect on the mechanical properties of CFRP riveted lap joints 25 .The relative interference-fit sizes {I 1 , I 2 , I 3 } correspond to the measured positions (P 1 , P 2 , P 3 ) based on Fig. 5.Each position of the deformed rivet bar was repeated three times at intervals of 120° using a Vernier caliper with the precision of 0.01 mm.Furthermore, the {I 1 , I 2 , I 3 , I A , I CV } are calculated with Eqs.(1, 2, 3), respectively.The calculated results of {I 1 , I 2 , I 3 , I A , I CV } were listed in Table 2, where scheme 0 is the conventional riveting process without ultrasonic vibration, the scheme 1-28 are the transversal ultrasonic vibration-assisted riveting (TUVAR).But scheme 16 is disqualification, because of the severe damage around the CFRP riveted hole.It could be seen that the I CV of scheme 0 is 0.369, which is much larger than the I CV of TUVAR schemes.Therefore, the uniformity of the interference-fit size can be well improved by transversal ultrasonic vibration.It also could be seen that the I A of scheme 16 is 0.0504, which is much larger than the upper limit value of 0.02 of interference-fit size for CFRP laminates riveted lap joints.It is because the acoustic energy with the largest amplitude 31 μm and vibration time 2.0 s, which make the Ti-45Nb rivet soften and promote the severe deformation of the rivet, and leadqa to the I A of scheme 16 remarkable increase.As shown in Fig. 6, the {I 1 , I 2 , I 3 , I A , I CV } of conventional riveting (scheme 0) and the typical TUVAR (scheme 9) at the same pressure and velocity are compared.It could be seen that the interference-fit size of P 1 declined, and the interference-fit size of P 2 improved under TUVAR.Hence, the TUVAR can well overcome an aperture constraint and promote the hole entrance material to flow into the P 2 region, which improves the uniformity of interference-fit size a lot, and it has been identified from the microscale 24 .Besides, the I A of TUVAR increases by about 14.7%, because more material from the driven head flows into the riveted hole under TUVAR.The comparison of I CV of conventional riveting and TUVAR showed that the I CV decreases about 9 times.Hence, a much more uniform interference-fit size of CFRP riveted lap joint can be achieved with the assistance of transversal ultrasonic vibration, which contributes a possibility for the interference-fit size quantization of riveted lap joint.

Interference-fit size optimization by response surface algorithm
The user-defined RSA is used for the process data set in Table 2, and the variance analysis result (Model, C 1 , C 2 , C 3 ) of the {I 1 , I 2 , I 3 , I A , I CV } are displayed in Table 3.It is acknowledged that the P ≤ 0.05, the model, and factors  8) cannot be straightly applied to the reserve solving and optimizing the TUVAR process parameters, Eq. ( 3) is still adopted to calculate the I CV .
According to the independent P-value of (C 1 , C 2 , C 3 ) on {I 1 , I 2 , I 3 , I A }, it could be obtained that C 1 and C 2 have a significant effect on {I 1 , I 2 , I 3 , I A }, except C 3 .For I CV , the independent P-values of (C 1 , C 2 , C 3 ) are larger than 0.05, which is insignificant.Besides, the significance ranking of (C 1 , C 2 , C 3 ) on {I 1 , I 2 , and the significance ranking of (C 1 , C 2 , C 3 ) on The reason for the significance ranking of I 3 is considering that the ultrasonic vibration attenuation transfer mode leads to softening effect reduction in the P 3 area.Meanwhile, the random forest algorithm and the extremely randomized trees were used to verify and quantify the contribution values of process parameters (C 1 , C 2 , C 3 ) for the RSA results.After several times training by random forest algorithm, the results are shown in Fig. 7.It could be seen that the contributions of process parameters (C 1 , C 2 , C 3 ) have a good consistency with the P values of (C 1 , C 2 , C 3 ) by RSA, which further identify the analysis results RSA is reliability.In Fig. 7, the effect weight values of process parameters (C 1 , C 2 , C 3 ) for {I 1 ,  www.nature.com/scientificreports/Vol According to the RSM analyzed results, the relationship between parameters and {I 1 , I 2 , I 3 , I A , I CV } are built by the least square method (as shown in Eq. 4).To reveal the interaction of process parameters (C 1 , C 2 , C 3 ) on the I A , the four-dimensional bubble charts and RSA charts are combined based on experimental results and Eqs.(5,  6, 7, 8), as displayed in Fig. 8.In Fig. 8a, it could be seen that the larger of amplitude and time is, the larger I A is achieved.In Fig. 8b-d, it can be seen that amplitude and time have a larger effect on I A , and the effect of roughness on I A is minimal.Due to the insignificant effect of parameters on I CV , the corresponding four-dimensional bubble charts, and RSA charts are not analyzed.
where x i is the process parameter, ε is a residual error, and β 0 β i β ii β ij are undetermined coefficients.
Therefore, according to the RSA and interpolation method, a user subroutine is defined by Python.4. It could be seen that the value of I CV-min is less than 0.1, except for predicted schemes 1 and 11.But the maximum deviation of (I 1 , I 2 , I 3 ) for predicted schemes 1 and 11 are 0.0033 and 0.0048, respectively, compared with the maximum deviation of (I 1 , I 2 , I 3 ) for conventional riveting is 0.0128, the uniformity of interference-fit size significantly improves.
Considering the unavoidable measurement error leading to I A out of tolerance, the predicted schemes {2, 4, 6, 8, 10} were verified by TUVAR experiments.And Eq. ( 9) is used to calculate the mean absolute percentage error (MAPE) of I A and I CV .The results of verification experiments and the MAPE analysis of I A and I CV are listed in (4)   where ŷi represents the predicted value of I A by interpolation algorithm, y i is the measured value of I A by experiments.

Mechanical property analysis
Tensile tests of TUVAR riveted lap joint specimens were carried out with the relative interference size I A = {1.4%,1.6%, 1.8%, 2.0%, and 2.2%}.The repeated results of tensile tests for different relative interference-fit sizes are listed in Table 6.The typical average load-displacement curves of five groups of specimens are displayed in    In stage 1, the maximum tensile strength of the interferencefit sizes I A = {1.6%,1.8%, 2.0%, 2.2%} have a good consistency, and the elastic maximum tensile load is about 3800N.However, the maximum bearing load of the interference-fit size I A = 1.4% in stage 1 is lower than the interference-fit sizes I A = {1.6%,1.8%, 2.0%, 2.2%}, and the elastic maximum tensile load is about 3600 N. In stage 2, it could be obtained that the tensile load of I = 1.4% is still less than others.The ultimate strength of different interference-fit sizes is listed and marked with red rectangular regions.
To straightly analyze the variation tendency of tensile strength with the different interference-fit sizes, the relationship between the relative interference-fit sizes and maximum load is displayed in Fig. 10b.It could be seen that the tensile strength increases at first and then declines with the increase of interference-fit size.There is a maximum ultimate strength when the interference-fit size I A = 2.0%, and the difference in tensile strength is not significant with I A = 1.8%.An appropriate interference-fit size is beneficial to the stiffness improvement of the CFRP riveted lap joints.However, the maximum tensile strength of the specimen with the interference-fit size I A = 2.2% is lower than I A = {1.8%,2.0%}.This phenomenon may be attributed to the severe damage to the hole wall surface by the rivet rod expansion after the TUVAR, especially the micro-scale carbon fiber damage in local regions.Moreover, earlier researches 13,26 showed that micro-scale damage near the hole surface area varies with interference-fit size.As a consequence, appropriate interference-fit size can well realize a close fit between the deformed rivet shaft and the hole wall.Meanwhile, uniform interference-fit size can increase the actual contact and provide a reaction force of the hole wall, and decline the stress value and uniform stress distribution.However, the large interference-fit size (e.g.I A = 2.2%) will induce delamination, fiber fracture et al., which resulted in the reduction of riveted lap joints.As a result, proper interference-fit size is beneficial to the improvement of the ultimate tensile strength of CFRP laminates riveted lap joints, whereas an excessive interference fit can reduce the maximum tensile strength.

Conclusion
In this paper, the TUVAR experiments were carried out to investigate the effect of process parameters on the interference-fit size of the CFRP riveted lap joints.Multiple arithmetics are combined to optimize the TUVAR process parameters and quantized the interference-fit size.Meanwhile, the tensile tests were carried out to identify the accuracy of the optimized results.the main conclusions were drawn as follows: (1) Compared with conventional riveting, the P 2 position interference-fit size of TUVAR increases, significantly, and the P 1 position interference-fit size declines a lot. the coefficient of variance of relative interference size decreases about 9 times, and the uniformity of interference-fit size under the TUVAR improves significantly (2) The results of the quantitative weight coefficient show that process parameters have a significant effect on {I 1 , I 2 , I 3 , I A }.In addition, the vibration amplitude is the maximum weight coefficient, then the time and roughness, and the average weight coefficients are 0.497, 0.336, and 0.167, respectively (3) The MAPE results of the I A and I CV by the inverse solving algorithm and the experiment showed that the MAPE of the I A is lower than 10%, which has a good prediction accuracy.But the MAPE of the I CV is larger than 20% when the interference-fit size is over 2.0%, which showed that uniform interference-fit sizes of TUVAR are difficult to achieve by combining with the MAPE of the I A .(4) The results of tensile tests showed that the best interference-fit size of the riveted specimen under the TUVAR is 1.8% or 2.0%, and the maximum tensile load arrives at 4562.564 N. Compared with the interference size of the riveted specimen under conventional riveting, the tensile load improves by 6.94%.

Figure 1 .
Figure 1.The schematic of the TUVAR system 27 .

Figure 2 .
Figure 2. The relationship between input power and amplitude 27 .

Figure 3 .
Figure 3. Dimensions of the CFRP laminates riveted lap joint (dimension in mm).

Figure 4 .
Figure 4. Experimental process of interference-fit size optimization.
First, the I A is the quantized target of interference-fit size to obtain the data set {(C 11 , C 22 , C 33 ) … (C 1i , C 2i , C 3i )}.Then the data set {(C 11 , C 22 , C 33 ) … (C 1i , C 2i , C 3i )} are transferred to Eqs. (4, 5, 6) to achieve data set {(I 11 , I 22 , I 33 ) … (I 1i , I 2i , I 3i )}.Furthermore, the data set {(I 11 , I 22 , I 33 ) … (I 1i , I 2i , I 3i )} are inputted in Eq. (3) to calculate and output data set {I CV1 … I CVi }, then looping comparison the I CV1 to I CVi and confirming the I CV-min , as shown in Fig. 4. Finally, based on I CV-min to confirm the optimal process parameters (C 1 , C 2 , C 3 ).The optimized and predicted {I A-p , I CV-min , (I 1 , I 2 , I 3 ), (C 1 , C 2 , C 3 )} are listed in Table Furthermore, the bar charts of I A and I CV MAPE are displayed in Fig. 9, which could be a more intuitive comparison of MAPE values.Comparing with the predicted I A (I A-p ) and experimental measurement I A (I A-m ), it could be seen that the values of I A MAPE are lower than 10%.Therefore, the I A-p and I A-m have good consistency.In addition, the minimum I A MAPE of 1.099% is achieved, when the I A is 0.018.However, the values of I CV MAPE are larger than 10%, except the Scheme 6, the values of I CV MAPE for Scheme 2 and Scheme 4 are less than 20%, and the values of I CV MAPE for Scheme 8 and Scheme 10 are larger than 20%.Therefore, the consistency of I CV-m and I CV-p is poor, but the minimum I CV MAPE is 5.630% when the I A is 0.018.To sum up, when the I A is 0.018, both the MAPE(I A ) and MAPE(I CV ) are minimum.

Fig. 10a .
Fig.10a.The load-displacement curves are divided into three-stage, i.e. stage 1: hole elastic deformation, stage 2: hole plastic deformation, and stage 3: hole failure.In stage 1, the maximum tensile strength of the interferencefit sizes I A = {1.6%,1.8%, 2.0%, 2.2%} have a good consistency, and the elastic maximum tensile load is about 3800N.However, the maximum bearing load of the interference-fit size I A = 1.4% in stage 1 is lower than the interference-fit sizes I A = {1.6%,1.8%, 2.0%, 2.2%}, and the elastic maximum tensile load is about 3600 N. In stage 2, it could be obtained that the tensile load of I = 1.4% is still less than others.The ultimate strength of different interference-fit sizes is listed and marked with red rectangular regions.To straightly analyze the variation tendency of tensile strength with the different interference-fit sizes, the relationship between the relative interference-fit sizes and maximum load is displayed in Fig.10b.It could be seen that the tensile strength increases at first and then declines with the increase of interference-fit size.There is a maximum ultimate strength when the interference-fit size I A = 2.0%, and the difference in tensile strength is not significant with I A = 1.8%.An appropriate interference-fit size is beneficial to the stiffness improvement of the CFRP riveted lap joints.However, the maximum tensile strength of the specimen with the interference-fit size I A = 2.2% is lower than I A = {1.8%,2.0%}.This phenomenon may be attributed to the severe damage to the hole wall surface by the rivet rod expansion after the TUVAR, especially the micro-scale carbon fiber damage in local regions.Moreover, earlier researches13,26 showed that micro-scale damage near the hole surface area varies with interference-fit size.As a consequence, appropriate interference-fit size can well realize a close fit between the deformed rivet shaft and the hole wall.Meanwhile, uniform interference-fit size can increase the actual contact and provide a reaction force of the hole wall, and decline the stress value and uniform stress distribution.However, the large interference-fit size (e.g.I A = 2.2%) will induce delamination, fiber fracture et al., which resulted in the reduction of riveted lap joints.As a result, proper interference-fit size is beneficial to the improvement of the ultimate tensile strength of CFRP laminates riveted lap joints, whereas an excessive interference fit can reduce the maximum tensile strength.

Figure 10 .
Figure 10.Analysis of tensile experiments: (a) typical average tensile curve with different I A , (b) maximum load analysis.

�I i Table 1 .
Mechanical properties of the sample 4 .

Table 2 .
The calculated results of the {I 1 , I 2 , I 3 , I A , I CV }.The predicted models for {I 1 , I 2 , I 3 , I A , I CV } are shown in Eqs.(4, 5, 6, 7, 8).According to the evaluation index of P-value, the models of {I 1 , I 2 , I 3 , I A } are significant, except the I CV .It means that the model relationship between the I CV and (C 1 , C 2 , C 3 ) is poorly reliable, hence the process parameter (C 1 , C 2 , C 3 ) cannot be directly optimized by the I CV model.Therefore, the predicted function of Eq. ( Vol.:(0123456789) Scientific Reports | (2023) 13:14408 | https://doi.org/10.1038/s41598-023-41578-4are significant.

Table 3 .
Variance analysis of the {I 1 , I 2 , I 3 , I A , I CV }.

Table 4 .
Predicted results of relative interference sizes by interpolation algorithm.

Table 5 .
The results of verification experiments and the MAPE analysis of I A and I CV .

Table 6 .
The repeated results of tensile tests for different interference sizes.