**1. Introduction**

H13 steel is widely used as a kind of hot die steel. It can be used for manufacturing various hot extrusion and forging dies [1,2] because of its high thermal strength, hardness, abrasion resistance, toughness, good heat resistance, and fatigue performance. But the surface performance will be significantly reduced if the H13 steel mold is exposed to high temperature for a long time [3–5]. Laser cladding technology can effectively improve the surface performance of the metal, but the process of cladding is affected by many factors. If only a single experimental study is carried out, the work efficiency will be low and resources will be wasted [6]. By combining computer simulation and experiment, the research cycle can be greatly reduced and the efficiency can be improved [7].

In the past two decades, scholars domestic and abroad have established numerous laser cladding simulation models and conducted relevant studies [8]. Kong et al. [9] adopted the enthalpy-pore method to deal with the phase transition phenomenon in the cladding process, adopted the horizontal set method to track the movement of the molten pool. The forced convection and thermal radiation on the surface of the cladding layer were incorporated into the simulation model, while the heat transfer process in the laser multilayer cladding process of H13 section steel was studied. Liu Hao et al. [10] developed a simulation model of laser cladding temperature field for simultaneous powder delivery.

**Citation:** Yao, F.; Fang, L. Thermal Stress Cycle Simulation in Laser Cladding Process of Ni-Based Coating on H13 Steel. *Coatings* **2021**, *11*, 203. https://doi.org/10.3390/ coatings11020203

Academic Editors: Pradeep Menezes and Pankaj Kumar

Received: 2 November 2020 Accepted: 4 February 2021 Published: 10 February 2021

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**Copyright:** © 2021 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 (https:// creativecommons.org/licenses/by/ 4.0/).

The model processed the additive effect in the entire cladding process through the life and death element method, the shielding effect of the powder flow on the high-energy laser beam and the heat transfer of the laser beam in the powder conveying process were considered by calculating the shading rate [11–15].

Kar and Mazumder [16] proposed a one-dimensional conduction model to determine the alloy composition and cooling process. Hoadley and Rappaz [17] developed a twodimensional model to calculate the steady-state temperature in the laser cladding process, which gave a quasi-steady-state numerical model of the substrate temperature field. The calculation takes into account the changes in the liquid molten pool, the gas–liquid for the shape and position of the free surface, in order to simplify the model, it is considered that the substrate melts very little and uses the line energy form of the laser, so that the approximate linear relationship between the laser power, the scanning speed, and the thickness of the repair layer is obtained. Han et al. [18] solved the two-dimensional fluid and energy equations, predicted the temperature distribution and geometry of the molten pool during the laser cladding process. Cho and Pirch [19] published a three-dimensional steady-state finite element model of coaxial powder feeding. A self-consistent method is used to calculate the temperature field and coating shape. The obtained temperature gradient and cooling rate are used to predict the coating solidification structure. Jendrzejewski [20] discussed the influence of the preheating temperature on the temperature field and stress field of the repair layer, and adopted a linear approximation to its temperature characteristics. After preheating, the thermal stress value of the substrate repair layer reduced from 1800 MPa to 900 MPa, and go<sup>t</sup> a crack-free repair layer. Toyserkani [21] et al. developed a three-dimensional transient finite element model of coaxial powder feeding. The coating is a multilayer structure, its width and height are determined by the area of the previous layer and laser powder. The model ignores the effect of surface tension and gravity on the shape of the coating. He [22,23] et al. studied the three-dimensional numerical model of the molten pool temperature and fluid flow during the laser cladding process of H13 steel, and used the level set method to simulate the molten pool. Kovacevic [24] and others at the Laser Aided Manufacturing Center of Southern Medical University USA used ANSYS to establish a finite element model. The law of temperature distribution and cooling rate in the molten pool under positive and negative defocusing conditions was studied. Compared with the Gaussian laser beam, it is found that the hollow laser beam (defocus) can effectively prevent the center of the molten pool from overheating, but the model does not consider the powder input impact when it reaches the molten pool. Parisa Farahmand studied the single multi-layer temperature field, strain stress field, and pool size evolution rule for laser cladding [25]. Gao W calculated the temperature variation, cooling rate, and solidification rate at the solid/liquid interface, but he did not consider the effect of Marangoni convection on the weld pool [26]. The Indian Institute of Technology and Monash University used H13 tool steel as the matrix to perform a single-pass laser cladding of CPM9V powder. It was found that the surface hardness of the cladding layer under single-layer and multi-layer conditions are the same. Researchers from Harazmi University in Tehran, Iran and Kaye Nasir Tutsi University of Technology in Tehran, Iran, used ABAQUS to simulate the laser cladding process of WC powder on the surface of Inconel 718. Analyzing the temperature field and residual stress distribution, it is concluded that the laser power and scanning rate have a greater influence on the dilution rate and residual stress of the cladding layer. The increase of input energy increases the residual stress of the cladding layer and the number of cracks decreases [27].

In this study, a planar continuous heat source model was used to conduct numerical simulation on the single-pass laser cladding process of H13 steel based on COMSOL software, the optimal process parameter scheme was determined, the thermal stress and thermal cycle curves were drawn and analyzed, which are used to study the influence of thermal stress cycle on the cladding layer, the residual stress of the cladding layer is also simulated.
