# Numerical Investigation of Residual Stresses in Welded Thermoplastic CFRP Structures

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

_{2}emissions. Several methods have been investigated on an experimental and numerical level so far [4,5,6,7,8,9,10,11,12]. While in the paper at hand, the resistance welding method is examined and described in detail later, further relevant technologies will be described in the following as well. One of them is the induction welding method. For the induction welding of thermoplastics, the electromagnetic field of an external inductor heats the heating element in the joining zone. This leads to the melting of the matrix and in consequence, the adherends can be joined under pressure. In [4], a procedure based on numerical methods has been developed, allowing a more precise understanding of the process parameters involved. The joining quality is evaluated based on single-lap-shear tests (SLS tests) and microscopic examination of the failure surfaces [5]. Another well-studied method is the laser welding of thermoplastics, for which a laser as a heat source is used. In [6], a thermal finite element (FE) model of a laser transmission welding process is developed using an unreinforced thermoplastic. This allows determining the size of the heat-affected zone and investigating the resulting internal stresses. Furthermore, a process model under consideration of the composite‘s microstructure was developed, which enables clarifying the correlation between fiber volume content and welding quality [7]. Familiarization with the literature shows that ultrasonic welding could also play an important role in future applications. For ultrasonic welding, the vibrations generated by an ultrasonic generator are converted into mechanical vibrations via sonotrode. The targeted introduction of these vibrations in the area of the joining zone leads to the melting of the matrix. With the help of experimental methods, it has so far been shown that this variant, which is usually implemented in a spot welding topology, could be a useful alternative to conventional rivets [8]. A process modeling procedure was shown in [9]. However, there still is no valid concept for how the ultrasonic welding process could be used for large continuous joints. According to the current state of research, one of the most promising variants, and therefore one of the best understood, is resistance welding. Here, a resistance element located in the joining zone is heated by current feed so that the matrix is melted. Subsequently, the adherends are joined under pressure as a result of cooling [10]. For this process, it was possible to demonstrate, mainly on an experimental level, the potential of its use in aircraft construction. For example, possible process windows could be identified, and the quality of the joint is determined by optical observation of the failure surfaces and SLS tests. In addition, the first numerical investigations were carried out [11,12].

## 2. Materials and Methods

^{®}. Two coupon specimens according to ASTM D1002 standard are used as adherends. To reduce the computational time for the modeling procedure, both adherends are assumed to behave similarly, so that only one coupon specimen is modeled with adequate boundary conditions. The schematic resistance welding process based on a typical experimental setup and the corresponding simplification for modeling is shown in Figure 1.

_{2S}quasi-isotropic layup. Every single unidirectional layer is represented as one quadratic hexahedral coupled temperature-displacement element in the thickness direction. This results in an overall thickness of t = 2 mm. The specimen’s length is l = 101.6 mm, and the width is w = 25.4 mm. The overlap length is assumed to be l

_{lap}= 25.4 mm. Furthermore, the global coordinate system definition (Figure 2a) as well as the layup used for the simulation (Figure 2b) need to be addressed. While the global system is characterized by the x, y, and z coordinates, the local layer system is represented by the I-coordinate in the fiber direction, the II-coordinate in-plane perpendicular to the fiber direction, and the III-coordinate out-of-plane perpendicular to the fiber direction.

## 3. Results

#### 3.1. Welding Simulation

_{melt}= 390 °C) is reached after t

_{weld}= 25 s in the middle of the joining zone (P1). Furthermore, it can be noticed that with this welding parameter configuration, only a section of the joining surface is melted, as the temperature in P2 does not reach the melting temperature. Afterward, the input power is modeled to be turned off, and the cooling of the specimen due to free convection begins. While there is a clear drop in temperature to observe for P1 and P2 after turning off the input power, a slight increase in temperature can be noticed for P3, which results from the heat flow in the material.

^{2}is reached after 25 s, it takes only 18 s for an input power of 80 kW/m

^{2}. The cooling process follows a similar course. However, comparing these data with the ones shown in Figure 5, it can be assumed that due to the thermal resistance of the material, the heat cannot be transported fast enough, resulting in a smaller melted area, as the material needs to be prevented from degradation. Such data have to be taken into account for investigating an optimal processing window for the resistance welding of thermoplastic composites. When it comes to the influence of crystallization and different heating and cooling rates on mechanical properties, the estimation of transient temperature data for the process in an early design stage plays a significant role.

#### 3.2. Residual Stress Analysis

_{II}= 221 MPa is reached. In Figure 7 and Figure 8, the residual stresses for the 90° layers and +45° layer are depicted. It can be stated that all layers show comparable characteristics. The σ

_{I}stresses seem to be highly influenced by the applied pressure, which is needed for the consolidation of the adherends in the joining zone during cooling. Especially the peaks at the edge of the joining zone and the effect of the pressure put on them need to be considered in detail for future design steps.

_{I,ult}= 2070 MPa) and structural integrity of such structures, the transverse residual stresses are assumed to be critical. The maximum value is σ

_{II,max}= 221 MPa, observed in layers 1 and 2, which are the layers right next to the heating element. This is a multiple of the ultimate transverse strength of the used unidirectional CFRP layer (R

_{II,ult}= 90 MPa) and herewith leads to matrix cracks in the loaded area. Based on the determined stresses, matrix cracks will appear in every single layer, especially in the laminate area between the insulator and heating element.

## 4. Discussion and Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) Considered geometry for the Resistance Welding Process Simulation; (

**b**) Simplified FE model.

**Figure 2.**(

**a**) Definition of geometry and used coordinate systems; (

**b**) Layup with z-direction as axis of rotation.

**Figure 3.**Transient temperature data at selected elements resulting from the modeled resistance welding process for an input power of 60 kW/m

^{2}.

**Figure 4.**Temperature distribution in °C in the joining zone for an input power of 60 kW/m

^{2}at (

**a**) 3 s, (

**b**) 10 s, (

**c**) 20 s, and (

**d**) 25 s.

**Figure 6.**Longitudinal and transverse residual stresses along the x-direction in 0° layers at the specimen center y = 0.5w.

**Figure 7.**Longitudinal and transverse residual stresses along the x-direction in 90° layers at the specimen center y = 0.5w.

**Figure 8.**Longitudinal and transverse residual stresses along the x-direction in +45° layers at the specimen center y = 0.5w.

**Table 1.**Mechanical and thermal material properties at room temperature used in the FEM model [16].

Elastic Properties | Thermal Properties | |||||||||
---|---|---|---|---|---|---|---|---|---|---|

Young’s Modulus | Shear Modulus | Poisson’s Ratio | Thermal Conductivity Coefficient | Thermal Expansion coefficient | Specific Heat Capacity | |||||

${\mathit{E}}_{\mathit{I}}$ | ${\mathit{E}}_{\mathit{I}\mathit{I}},{\mathit{E}}_{\mathit{I}\mathit{I}\mathit{I}}$ | ${\mathit{G}}_{\mathit{I},\mathit{I}\mathit{I}},{\mathit{G}}_{\mathit{I},\mathit{I}\mathit{I}\mathit{I}}$ | ${\mathit{G}}_{\mathit{I}\mathit{I},\mathit{I}\mathit{I}\mathit{I}}$ | ${\mathit{\nu}}_{\mathit{I},\mathit{I}\mathit{I}},{\mathit{\nu}}_{\mathit{I},\mathit{I}\mathit{I}\mathit{I}}$ | ${\mathit{\nu}}_{\mathit{I}\mathit{I},\mathit{I}\mathit{I}\mathit{I}}$ | ${\mathit{\kappa}}_{\mathit{I}}$ | ${\mathit{\kappa}}_{\mathit{I}\mathit{I}},{\mathit{\kappa}}_{\mathit{I}\mathit{I}\mathit{I}}$ | ${\mathit{\alpha}}_{\mathit{I}}$ | ${\mathit{\alpha}}_{\mathit{I}\mathit{I}},{\mathit{\alpha}}_{\mathit{I}\mathit{I}\mathit{I}}$ | ${\mathit{C}}_{\mathit{p}}$ |

[MPa] | [MPa] | [MPa] | [MPa] | [-] | [-] | $\left[\frac{\mathrm{mJ}}{\mathrm{s}\mathrm{mm}\mathrm{K}}\right]$ | $\left[\frac{\mathrm{mJ}}{\mathrm{s}\mathrm{mm}\mathrm{K}}\right]$ | $\left[\frac{1}{\mathrm{K}}\right]$ | $\left[\frac{1}{\mathrm{K}}\right]$ | $\left[\frac{\mathrm{kJ}}{\mathrm{kg}\mathrm{K}}{10}^{6}\right]$ |

130,000 | 10,300 | 6000 | 4800 | 0.32 | 0.35 | 3.5 | 0.42 | 1.5 × 10^{−7} | 2.82 × 10^{−5} | 800 |

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**MDPI and ACS Style**

Nagel, L.; Herwig, A.; Schmidt, C.; Horst, P. Numerical Investigation of Residual Stresses in Welded Thermoplastic CFRP Structures. *J. Compos. Sci.* **2021**, *5*, 45.
https://doi.org/10.3390/jcs5020045

**AMA Style**

Nagel L, Herwig A, Schmidt C, Horst P. Numerical Investigation of Residual Stresses in Welded Thermoplastic CFRP Structures. *Journal of Composites Science*. 2021; 5(2):45.
https://doi.org/10.3390/jcs5020045

**Chicago/Turabian Style**

Nagel, Lukas, Alexander Herwig, Carsten Schmidt, and Peter Horst. 2021. "Numerical Investigation of Residual Stresses in Welded Thermoplastic CFRP Structures" *Journal of Composites Science* 5, no. 2: 45.
https://doi.org/10.3390/jcs5020045