# Optimizing Ultrasonic Welding Parameters for Multilayer Lap Joints of PEEK and Carbon Fibers by Neural Network Simulation

^{1}

^{2}

^{*}

## Abstract

**:**

_{UTS}= 80.5 MPa, ε = 4.2 mm, A = 273 N·m, and Δh = 0.30 mm).

## 1. Introduction

## 2. Problem Statement

## 3. Research Methodology

- Analysis of the reliability of the results of each experiment and, if necessary, rejection of incorrect data;
- Analysis of the completeness of the summarized information or, with a small sample, determination of limitations on the simulation results; and
- Analysis of the data dimensions.

## 4. Materials and Methods

- The USW duration (t) range was set between 800 and 1200 ms because it was not possible to join the PEEK plates at lower values; however, the prepreg could be damaged at higher levels, resulting in faulty USW joints;
- Ranges of the clamping pressure (P) and its (holding) duration after applying US vibrations (τ) were determined based on the technical characteristics of the USW machine, as well as by visual control of the USW joints.

## 5. Research Results

^{®}software package, which includes tools for their synthesis, training, and analysis. All models relied on direct propagation with one hidden layer (example shown in Figure 3). The number of neurons in the hidden layer and the applied activation functions was varied. The use of the linear activation function resulted in designing untrained networks. Therefore, only networks with a hyperbolic tangent as an activation function of both hidden and output layers are discussed below.

_{i}− (t − t

_{i})/(t

_{j}− t

_{i})), where P

_{i}, t

_{i}, and t

_{j}are the values of parameters of the i-th and j-th experiments, respectively.

- The USW modes that provided low ultimate tensile strength levels of the USW joints were considered unacceptable. In particular, the lowest threshold level of 60 MPa was assigned by the authors. On the other hand, failure of the USW joints showed ultimate tensile strength values slightly higher than that for neat PEEK (~93 MPa), occurred over the base material but not in the fusion zone due to its over-strengthening. The most likely reason for of this phenomenon was damage and partial melting of the prepreg. Therefore, the maximum threshold of 93 MPa was assigned.
- Based on the same considerations, the modes providing brittle fracture at low elongation at break levels (ε < 2 mm) were excluded. On the other hand, fusion-zone over-strengthening caused strains with the formation of a “neck” in the base material at ε > 7 mm.
- Because the work of strain value combines both strength and ductility properties, the range of its acceptable values was assigned 150 N·m < A < 560 N·m by analogy with the above considerations.
- USW joint thinning was related to the pattern of the formed macro- and microstructure. In the case of USW joint-thinning values above 0.5 mm, the prepreg was melted, causing fracture of the CFs. On the other hand, the USW joint components, primarily the EDs, clearly did not melt when the USW joint-thinning level was less than 0.3 mm. In such cases, the USW joints were characterized by poor mechanical properties. Thus, the USW joint-thinning range was assigned as 0.3 mm < Δh < 0.5 mm.

## 6. Discussion

## 7. Conclusions

- The definition of “the optimality combination of the USW parameters” was introduced as a condition for satisfaction of the inequality system (1). The mathematical problem of determining the optimal combination of USW parameters was formulated for the formation of USW lap joint with improved mechanical and structural properties.
- A methodology for studying the mechanical properties of USW lap joints was proposed based on the design of an experiment via the Taguchi method and experimental data approximation with the use of neural network simulation (NNS).
- Experiments were performed, and the threshold values of the optimality conditions for the USW parameters were chosen. NNS was accordingly carried out to determine their ranges.
- We demonstrated that according to the Taguchi method, the rational USW parameters corresponded to the P = 3.0 atm/t = 1200 ms combination. This evidence was based on consideration of the mechanical characteristics of the USW joints. However, intense prepreg melting and fracture of CFs occurred during the USW process. Therefore, this mode could not be considered optimal.
- We proved that verification of the computer simulation results obtained with a small sample can be carried out only by experimental analysis of their reliability. To obtain formal criteria to assess such facts, it is necessary to conduct additional studies.
- We analyzed the optimal combination of USW parameters proposed on the basis of NNS. Based on the example of two modes, we demonstrated that the developed optimality condition was insufficient and required correction, taking into account other significant structural characteristics of the formed USW joints. However, the NNS enabled specification of an extra area of USW parameters, which were not previously considered as optimal when designing the experiment. The NNS-predicted optimal US welding mode (P = 1.5 atm, t = 800 ms and τ = 1500 ms) ensured formation of lap joints with the required mechanical and structural properties (σ
_{UTS}= 80.5 MPa; ε = 4.2 mm; A = 273 N·m; Δh = 0.30 mm). - The results of this study are related to the use of additional valuable structural characteristics, as well as attracting more complex neural network models. In terms the PEEK-CF layered composite fabrication with the use of US-welding, CF fabric prepregs are suitable for the design of “CF prepreg—PEEK composite” laminates.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 2.**Dependencies of the mechanical and structural characteristics based on USW parameters: ultimate tensile strength (

**a**), elongation at break (

**b**), work of strain (

**c**), and USW joint thinning (

**d**).

**Figure 3.**Architecture of artificial neural network (model 2). W—matrices of synaptic weights, B—vectors of bias weights.

**Figure 4.**Correlation between the training sample data and the neural network output; neural network No.2 (

**a**); No.4 (

**b**); No.7 (

**c**).

**Figure 5.**Simulation results over the space cross section of the USW parameters: (

**a**,

**c**,

**e**) τ = 1000 ms; P = (3 − (t − 800)/400) atm; (

**b**,

**d**,

**f**) τ = 1500 ms; P = (4 − 2(t − 800)/200) atm.

**Figure 7.**The graphs in the isolines for the sections of the space of ANN parameters; the clamping duration after US vibrations of 1500 ms: (

**a**) model 2; (

**b**) model 3; (

**c**) model 4; (

**d**) model 5.

**Figure 8.**Macrostructure of the test coupons’ cross sections at the central part of the USW joints formed using the modes according to Table 1 (

**a**–

**g**) and micrographs of their fusion zones (

**h**–

**k**).

**Table 1.**Combination of the USW parameters and their levels (according to the Taguchi table in L9 format for a three-factor experiment).

Experiment Number | Level/Factor | ||
---|---|---|---|

USW Duration (t), ms | Clamping Duration after US Vibrations (τ), ms | Clamping Pressure (P), atm | |

1 | 1/800 | 1/500 | 1/ 2 |

2 | 1/800 | 2/1000 | 2/3 |

3 | 1/800 | 3/ 1500 | 3/4 |

4 | 2/1000 | 1/500 | 2/3 |

5 | 2/1000 | 2/1000 | 3/4 |

6 | 2/1000 | 3/1500 | 1/2 |

7 | 3/1200 | 1/500 | 3/4 |

8 | 3/1200 | 2/1000 | 1/2 |

9 | 3/1200 | 3/1500 | 2/3 |

Experiment (Mode) Number | Ultimate Tensile Strength $\left({\mathit{\sigma}}_{\mathit{U}\mathit{T}\mathit{S}}\right)$, MPa | Elongation at Break (ε), mm | Work of Fracture (A), N·m | USW Joint Thinning (Δh), mm |
---|---|---|---|---|

1 | 76.2 ± 0.4 | 3.4 ± 0.1 | 156.2 ± 12.2 | 0.42 ± 0.02 |

2 | 94.4 ± 0.8 | 6.4 ± 0.2 | 424.7 ± 24.5 | 0.35 ± 0.02 |

3 | 51.3 ± 0.5 | 2.0 ± 0.1 | 51.7 ± 4.6 | 0.18 ± 0.01 |

4 | 92.6 ± 0.5 | 4.9 ± 0.2 | 284.3 ± 15.3 | 0.38 ± 0.02 |

5 | 66.9 ± 0.4 | 2.6 ± 0.2 | 95.6 ± 6.7 | 0.32 ± 0.02 |

6 | 96.5 ± 0.5 | 7.7 ± 0.3 | 558.6 ± 37.7 | 0.54 ± 0.02 |

7 | 94.1 ± 0.6 | 9.4 ± 0.3 | 694.4 ± 38.1 | 0.48 ± 0.03 |

8 | 91.2 ± 0.8 | 6.1 ± 0.4 | 386.3 ± 24.4 | 0.81 ± 0.03 |

9 | 95.9 ± 0.7 | 12.1 ± 1.0 | 958.0 ± 52.1 | 0.60 ± 0.02 |

Property | USW Duration (t), ms | Clamping Duration after US Vibrations (τ), ms | Clamping Pressure (P), atm |
---|---|---|---|

Ultimate tensile strength | 2 | 3 | 1 |

Elongation at break | 1 | 3 | 2 |

Work of strain | 1 | 3 | 2 |

USW joint thinning | 1 | 3 | 2 |

Total | 5 | 12 | 7 |

“Best” level | 1200 | 1500 | 3 |

Characteristic, z | Experimental Data Range | Normalization Range | ||
---|---|---|---|---|

min $\left(\mathit{z}\right)$ | max $\left(\mathit{z}\right)$ | Min | Max | |

t, ms | 800 | 1200 | 600 | 1400 |

τ, ms | 500 | 1500 | 400 | 2500 |

P, atm | 2 | 4 | 1 | 5 |

${\sigma}_{UTS}$, MPa | 51.3 | 96.5 | 20 | 100 |

ε, mm | 2.0 | 12.1 | 1 | 14 |

A, N·m | 51.7 | 950 | 30 | 1230 |

Δh, mm | 0.26 | 0.87 | 0.1 | 0.9 |

Model (Neural Network) Number | Number of Neurons | R | MSE |
---|---|---|---|

1 | 4 | 0.99773 | 1.1678 × 10^{−4} |

2 | 5 | 0.9982 | 6.2615 × 10^{−5} |

3 | 6 | 0.99857 | 4.9248 × 10^{−5} |

4 | 7 | 0.99888 | 3.4767 × 10^{−5} |

5 | 9 | 0.99911 | 7.0265 × 10^{−5} |

6 | 11 | 0.99918 | 4.3210 × 10^{−5} |

7 | 13 | 0.99921 | 5.0921 × 10^{−5} |

Characteristic | Thresholds | |
---|---|---|

Min | Max | |

${\sigma}_{UTS}$, MPa | 60 | 93 |

ε, mm | 2.0 | 7.0 |

A, N·m | 150 | 560 |

Δh, mm | 0.3 | 0.5 |

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**MDPI and ACS Style**

Panin, S.V.; Stepanov, D.Y.; Byakov, A.V.
Optimizing Ultrasonic Welding Parameters for Multilayer Lap Joints of PEEK and Carbon Fibers by Neural Network Simulation. *Materials* **2022**, *15*, 6939.
https://doi.org/10.3390/ma15196939

**AMA Style**

Panin SV, Stepanov DY, Byakov AV.
Optimizing Ultrasonic Welding Parameters for Multilayer Lap Joints of PEEK and Carbon Fibers by Neural Network Simulation. *Materials*. 2022; 15(19):6939.
https://doi.org/10.3390/ma15196939

**Chicago/Turabian Style**

Panin, Sergey V., Dmitry Yu. Stepanov, and Anton V. Byakov.
2022. "Optimizing Ultrasonic Welding Parameters for Multilayer Lap Joints of PEEK and Carbon Fibers by Neural Network Simulation" *Materials* 15, no. 19: 6939.
https://doi.org/10.3390/ma15196939