# Numerical Simulation and Experimental Validation of the Cladding Material Distribution of Hybrid Semi-Finished Products Produced by Deposition Welding and Cross-Wedge Rolling

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## Abstract

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## 1. Introduction

#### 1.1. Tailored Forming Approach

_{max}, see Figure 1, right. This cyclic loading of the material volume initiates and propagates fatigue cracks in the high-cycle regime (>>10

^{6}cycles), which is referred to as rolling contact fatigue (RCF) [15]. RCF eventually leads to material removal and, if a crack propagates to the surface and forms a chip/pitting, failure of the component. Lundberg and Palmgren [16] assumed the maximum orthogonal shear stress τ

_{O}to be significant in causing fatigue failure. Other authors consider the von Mises–Hencky distortion energy theory [17] and the scalar von Mises stress to be better for predicting RCF failure, with the latter being directly proportional to the octahedral shear stress τ

_{oct}. Figure 1, right, shows that the maximum shear stress occurs at depth z of approximately 0.5b to 0.8b. Here, RCF occurs in a highly localized volume of stressed material, so a high-strength material is required there. The remaining part of the component can be made of a less solid material with higher ductility and lower price.

#### 1.2. Welding and Forming

#### 1.3. Bearing Fatigue Life of Tailored Forming Machine Elements

_{rad}= 2 kN with a resulting Hertzian contact pressure of p

_{max}= 1.8 GPa. The calculated bearing life L

_{50}, where 50% of the specimens are expected to have failed, is L

_{50}= 23.5 × 10

^{6}revolutions. This is within an error margin of 16% of the bearing fatigue life from the experimental studies. The basic trends of the calculated probability of survival are represented by the experimental values L

_{10}and L

_{63}. A too-thin cladding layer reduces fatigue life of multi-material machine elements by a factor of 3. With a cladding height of h > 0.5 mm the difference in fatigue life compared to monolithic parts is within a 15% margin. These preliminary results show that a minimum cladding height in dependence of the load is necessary to achieve the same fatigue life as a monolithic component.

## 2. Materials and Methods

- Depending on the application, even a small amount of high-performance material may be sufficient to produce a multi-material component with a performance comparable to that of conventional manufacturing processes. However, the cladding layer in the region subject to rolling contact loading must not be too thin.
- The process must have an economically viable application rate and quality. This requires precise knowledge of the application and its loads.
- It must be possible to set the layer height as the decisive target value for production within narrow limits.

#### 2.1. Laser Metal Deposition Welding with Wire

#### 2.2. Plasma Powder Transferred Arc Welding

#### 2.3. Cross-Wedge Rolling

#### 2.3.1. Cross-Wedge Rolling Simulation

^{4}W/m²K. The thermal effusivity of the tools was set to 11.76 kJ/m

^{2}·K·s

^{0.5}. The ambient air temperature was set to a constant temperature of 50 °C. The chosen preset “steel hot medium” and the heat-exchange algorithm within Forge NxT take conduction, convection and radiation between the tools, work piece, and ambient air into account. The friction between work piece and tools were set to the preset “very high Tresca”, resulting in a value m = 0.8, which proved to be a good approximation of friction for hybrid CWR processes [32]. As default, thermal expansion calculation is not enabled for material flow simulations in Forge NxT. Additionally, as default, rigid dies are used to simulate a CWR process. To assure the accuracy of the simulation model used, simulations comparing these influences were conducted and the cladding thickness for each set of parameters was measured within Forge NxT (see Figure 13).

#### 2.3.2. Cross-Wedge Rolling Experiment

## 3. Results

## 4. Discussion and Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 1.**Partial section of tailored forming shaft with mounted cylindrical roller bearing (

**left**) and loaded material volume (

**right**).

**Figure 2.**Microstructure of the joining zone after welding (

**a**) and after cross-wedge rolling (CWR) (

**b**).

**Figure 11.**Simulation result of hybrid work piece cross-wedge rolling tool after 1.5 s process time.

**Figure 12.**Cross-wedge rolling process at different time steps, where the base cylinder is in blue and the cladding in red.

**Figure 15.**CAD model of different cladding (red) distributions on base cylinder (blue) forX45CrSi9-3, (

**a**) 1 layer at 15 mm seam width (

**b**) 1 layer at 8 mm seam width (

**c**) 2 layers at 15 mm seam width (

**d**) 2 layers at 8 mm seam width.

**Figure 16.**CAD model of different cladding (red) distributions on base cylinder (blue) for 100Cr6, (

**a**) 10 mm seam width (

**b**) 15 mm seam width (

**c**) 20 mm seam idth.

**Figure 18.**(

**a**) Work pieces with different amounts of cladding; (

**b**) (cold) work piece in starting position.

**Figure 31.**Different amount of cladding material resulting in differently shaped bearing seat material distribution at 1.25 s process time.

**Figure 32.**Analysis of cladding material distribution during cross-wedge rolling over time—cladding material X45CrSi9-3 (red) on C22.8 (blue).

**Figure 33.**Over time analysis of the cladding material distribution within the cross-section of the work piece during cross-wedge rolling—cladding material X45CrSi9-3 (red) on C22.8 (blue).

**Figure 34.**Unsymmetrical cladding distribution (experiment left, simulation right) due to positioning error.

**Figure 35.**Influence of the cladding material amount on the accuracy of the simulation (X45CrSi9-3); (

**a**) Pareto chart of standardized effects, (

**b**) Main effect plot for simulation and experiment deviation

Element | C | Si | Mn | P | S | Cr | Ni | |
---|---|---|---|---|---|---|---|---|

Material | ||||||||

C22.8 | 0.17–0.24 | <0.40 | 0.40–0.70 | <0.045 | <0.045 | <0.40 | - | |

X45CrSi9-3 | 0.4–0.5 | 2.7–3.3 | ≤0.6 | ≤0.004 | ≤0.03 | 8.0–10.0 | ≤0.5 | |

100Cr6 | 0.93–1.05 | 0.15–0.35 | 0.25–0.45 | ≤0.025 | ≤0.015 | 1.35–1.60 | - |

Parameter | LMD-W ^{1} |
---|---|

Welding speed | 1200 mm/min |

Current | 110 A |

Wire feed rate | 2.8 m/min |

Laser power | 2.3 kW |

Shielding gas flow | 8 L/min |

Wire diameter | 1.0 mm |

^{1}Laser Metal Deposition Welding with Wire.

Parameter | Value |
---|---|

Shielding gas flow | 10 L/min |

Plasma gas flow | 1.5 L/min |

Transport gas flow | 6 L/min |

Welding speed | 0.06 m /min |

Length of the welding seam | 30 mm |

Current | 120–100 A |

Voltage | 27–25 V (depends on current) |

Powder material | 100Cr6 |

Grid size of powder particles | 0.06–0.2 mm |

Deposition rate | 0.9 kg/h |

Case ID | Thermal Expansion Calculation ^{1} | Tool Behavior | Thermal Expansion due to Initial Heating ^{1} | Estimated Normalized Calculation Time |
---|---|---|---|---|

#1 | No | rigid | No | 100% |

#2 | Yes | rigid | Yes | 182% |

#3 | Yes | deformable | Yes | 449% |

^{1}of work piece.

Simulation Result | Setup | Cross Section Surface of: | Max. Coating Thickness | Min. Coating Thickness | Avg. Coating Thickness | |
---|---|---|---|---|---|---|

Cladding | Base Cylinder | |||||

#1: No thermal expansion; Rigid tools | 644.082 mm^{2} | 452.646 mm^{2} | 2.263 mm | 2.854 mm | 2.439 mm | |

#2: Thermal expansion; Rigid tools | 644.912 mm^{2} | 455.057 mm^{2} | 2.101 mm | 2.830 mm | 2.426 mm | |

Δ to Setup #1 | 0.10% | 0.50% | 7.20% | 0.80% | 0.50% | |

#3: Thermal expansion; Deformable tools | 643.981 mm^{2} | 430.330 mm^{2} | 2.131 mm | 2.872 mm | 2.381 mm | |

Δ to Setup #1 | 0.00% | 5.20% | 6.20% | 0.60% | 2.40% |

Material | Work Piece Geometry | Tool Velocity | Work Piece Temperature |
---|---|---|---|

Base cylinder: C22.8 | Ø 27 or 29 mm | 240 mm/s | 1250 °C |

Cladding: X45CrSi9-3 or 100Cr6 | 8 or 15 mm width; 1.2; 2.4; or 2.5 mm height |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Kruse, J.; Mildebrath, M.; Budde, L.; Coors, T.; Faqiri, M.Y.; Barroi, A.; Stonis, M.; Hassel, T.; Pape, F.; Lammers, M.; Hermsdorf, J.; Kaierle, S.; Overmeyer, L.; Poll, G. Numerical Simulation and Experimental Validation of the Cladding Material Distribution of Hybrid Semi-Finished Products Produced by Deposition Welding and Cross-Wedge Rolling. *Metals* **2020**, *10*, 1336.
https://doi.org/10.3390/met10101336

**AMA Style**

Kruse J, Mildebrath M, Budde L, Coors T, Faqiri MY, Barroi A, Stonis M, Hassel T, Pape F, Lammers M, Hermsdorf J, Kaierle S, Overmeyer L, Poll G. Numerical Simulation and Experimental Validation of the Cladding Material Distribution of Hybrid Semi-Finished Products Produced by Deposition Welding and Cross-Wedge Rolling. *Metals*. 2020; 10(10):1336.
https://doi.org/10.3390/met10101336

**Chicago/Turabian Style**

Kruse, Jens, Maximilian Mildebrath, Laura Budde, Timm Coors, Mohamad Yusuf Faqiri, Alexander Barroi, Malte Stonis, Thomas Hassel, Florian Pape, Marius Lammers, Jörg Hermsdorf, Stefan Kaierle, Ludger Overmeyer, and Gerhard Poll. 2020. "Numerical Simulation and Experimental Validation of the Cladding Material Distribution of Hybrid Semi-Finished Products Produced by Deposition Welding and Cross-Wedge Rolling" *Metals* 10, no. 10: 1336.
https://doi.org/10.3390/met10101336