# Effect of Process Parameters on Distortions Based on the Quantitative Model in the SLM Process
## 1 Introduction  
Additive manufacturing (AM) is a promising approach for rapid prototyping [1]. As a precision AM technology, selective laser melting (SLM) is widely employed in medical instruments, aerospace, and auto industries [2, 3, 4]. However, the thermal stresses accumulated within the process lead to defects such as distortions, laminations, and cracks [5, 6]. The distortion is a common problem for SLM technology [7]. In addition, it decreases the dimensional accuracy of the SLM-printed component and may hinder the laying of the powder bed [8].  
Many researchers have attempted to explain the mechanism of the distortion. [PERSON] et al. [9] first proposed the temperature gradient mechanism (TGM) to explore the residual stress mechanism in the powder bed fusion. The method is then widely used to qualitatively analyze transient distortions during the process [10, 11, 12]. However, it focuses on micro-temperature distribution, which determines local residual stresses and distortions and cannot explain the distortion after the process or even after cut from the substrate. [PERSON] et al. [13] assumed constraining force between the deposited layers to analyze the distortion. The theoretical prediction results have the same trend as the experimental results. However, plastic strains dramatically formed in the AM process were not considered in the method,and they might differ among deposited layers. Therefore, it is still essential to propose a reasonable model to illustrate the mechanism of distortion.  
The numerical simulation method has been commonly utilized to study the distortion of additive manufacturing. [PERSON] et al. [14] proposed a numerical model to simulate cantilever deformations, matching the experimental results. [PERSON] et al. [15], [PERSON] et al. [16], [PERSON] et al. [17], and [PERSON] et al. [18] proposed 3D models using the finite element method (FEM) to predict residual stresses and distortions of AM parts. Many studies have been made to investigate the characteristics of distortion. [PERSON] et al. [19] found that decreasing laser power was beneficial to reduce residual stresses and distortions. [PERSON] et al. [20] investigated the distortion of porous structures and concluded that increasing the thickness and porosity of added layers could reduce the distortion of the substrate. [PERSON] et al. [14] studied the distortion of a twin cantilever using the simulation model, which was verified by experiments, and found that residual stresses along the scan direction mainly determine the distortion. [PERSON] et al. [21] conducted island scanning methods with various sizes and sequences. The 20 \(\times\) 20 mm\({}^{2}\) outside-in island method contributed to the slightest distortion but increased the residual stress. In addition, pre-heating the substrate is valuable to alleviate the distortions of AM parts [22]. Although many efforts to explore the distortion's regularity have been made, it is still required to illustrate the effects of process parameters and scan strategies on the distortion.  
Thus, in this paper, a theoretical model considering plastic strains in deposited layers is proposed to reveal the distortion mechanism, and the influence of process parameters and scan strategies on the distortion is investigated. The experimentally verified transient thermo-mechanical model, which was developed in the previous study of the present authors [23], is employed to calculate stresses and distortions of the SLM-printed component. First, thin-walled components with various build heights, scanning speeds, and stiffness of the support structures and plate parts printing with different scan strategies are simulated. Then, the distortion mechanism is revealed by a quantitative model considering displacements, plastic strains, residual stresses, and thermal strains in each layer. Finally, the effect of process parameters and scan strategies on distortion is studied with the help of simulation results and the theoretical model.