**1.4 Simulation and experiment approach**

Based on the finite element (FE) analysis package ABAQUS, a 3-D, sequentially coupled, thermomechanical model was developed to simulate the transient temperature field, residual stress, and final deformation involved in the DMD process of

**Figure 1.** *Flow chart showing the process of numerical modeling.*

Furthermore, this process is very cost-effective compared with traditional

*New Challenges in Residual Stress Measurements and Evaluation*

During DMD processing, highly localized heating and cooling lead to nonuniform thermal expansion and contraction, which further results in a complicated distribution of residual stresses in the heat-affected zone (HAZ) and distortion across the entire structure. These residual stresses could be detrimental—they may cause fractures, promote fatigue, and induce unpredictable buckling during the service of deposited parts; the deformation often is harmful to the dimensional accuracies of structures. Therefore, it becomes critical to predict the two behaviors of materials after the DMD process and to optimize the manufacturing parameters

with little or no machining.

**1.2 Residual stress and distortion**

thermal stress is produced [1].

**1.3 Literature review**

**88**

to reduce the residual stresses and deformation.

residual stresses were modeled and analyzed.

subtractive manufacturing techniques because it can produce near net shape parts

Residual stresses exist in a part while no external loads were applied. When a part is heated evenly from its previous residual stress-free state, it expands evenly, and no thermal stress is generated. However, when a part is heated unevenly,

The thermal behavior of the DMD process has been investigated numerically by

Some researchers have focused on the modeling and simulation of traditional welding processes, which share many similarities with DMD processes. Using a double-ellipsoid heat source, Gery et al. [5] generated the transient temperature distributions of the welded plates. The results demonstrated that the welding speed, energy input, and heat source distributions had important effects on the shape and boundaries of heat-affected zone. Deng [6] investigated the effects of solid-state phase transformation on the residual stress and distortion caused by welding in low carbon and medium steels. The model discovered that the solid-state phase transformation did not have a noteworthy impact on the final residual stress and the welding deformation in low carbon steel. However, the final residual stresses and the welding deformation appear to be significantly affected by the martensitic transformation in medium carbon steels. Feli et al. [7] analyzed the temperature history and the residual stress field in multi-pass, butt-welded, stainless steel pipes. It was found that in the weld zone and its vicinity, a tensile axial residual stress is produced on the inside surface and compressive axial stress at the outside surface. Other researchers have attempted to obtain the distribution of residual stress caused by the DMD process through experiments. For example, Moat et al. [8]

many scholars. In [2], a 2-D finite element model was created to simulate the temperature field during the laser cladding process. The results indicated that quasisteady thermal field could not be reached in a short time. Other scholars have chosen to experimentally investigate thermal behavior. In [3], Griffith et al. employed radiation pyrometers and thermocouples to monitor the thermal signature during laser engineered net shaping (LENS) processing. The results showed that the integrated temperature reheat had a significant effect on the microstructural evolution during the fabrication of hollow H13 tool steel parts. Utilizing a twowavelength imaging pyrometer, Wang and Felicelli [4] measured the temperature distribution in the melt pool and the area surrounding it during the LENS deposition process. It was found that the maximum temperature in the molten pool is approximately 1600. Only thermal behaviors were investigated in these papers, while no

Stainless Steel 304 (SS 304). The numerical modeling consisted of two major steps shown in **Figure 1**. A transient thermal analysis was firstly carried out to produce the temperature history of the entire workpiece. Then, in the second step, using the temperature field file generated in the previous step as load, a mechanical analysis was carried out to calculate the residual stress and deformation of workpiece.

surfaces of the workpiece; and Λ denotes the surface area covered by the

*Residual Stress Modeling and Deformation Measurement in Laser Metal Deposition Process*

following assumptions and adjustments were considered.

*2.3.1 Energy distribution of the deposition process*

experiments conducted, and *r* ¼ 1*:*25 mm.

the beam's center *R* with time *t* as follows

*R* ¼ *x* �

the powder that did not reach the melt pool.

*2.3.4 Modeling the latent heat of fusion*

lent specific heat capacity *c* <sup>∗</sup>

**91**

ð*t t*0 *udt* � � <sup>þ</sup> *<sup>y</sup>* �

*2.3.2 Movement of laser beam*

motion of the laser beam.

*2.3.3 Powder projection*

Accurate modeling of the thermal process yields highly nonlinear coupled equations, which is time-consuming and expensive to solve. To speed up the solution process and reduce the computational time without sacrificing accuracy, the

In this study, a circular-shaped laser beam with a constant and uniform power density was used. Thus, to match the experiment setup, the heat source parameter *Q* in Eq. (1) was considered a constant and uniformly distributed surface heat

*<sup>Q</sup>* <sup>¼</sup> *<sup>α</sup><sup>P</sup>*

*r* is the radius of the laser beam. *α* was set as 0.4 according to the previous

where *α* is the absorption coefficient, *P* is the power of the continuous laser, and

The motion of the laser beam was taken into account by updating the position of

ð*t t*0 *vdt* � � <sup>þ</sup> *<sup>z</sup>* �

where *x*, *y*, and *z* are the spatial coordinates and the laser beam centers, *u*, *v*, and *w*, are the continuous velocities the laser beam travels along *x*-, *y*-, and *z*-direction. In ABAQUS, a user subroutine "DFLUX" [14] was written to simulate the

When modeling, the continuous powder injection process is broken into many small discrete time steps. Using the model change method provided by ABAQUS [14], in each time step, a set of finite elements was added onto the substrate to form deposits along the center line of the substrate. The width of the deposits was assumed to be the same as the diameter of the laser beam, and the thickness of the deposits was calculated from the laser or table travel speed and the powder feed rate. An efficiency of 0*:*3 was assumed for the power feeding process to account for

To account for the effect of the latent heat of fusion during the melting and solidification process, the specific heat capacity is modified to generate an equiva-

*<sup>p</sup>* as [15]

*wdt* � � � � <sup>1</sup>

*<sup>π</sup>r*<sup>2</sup> (5)

ð*t t*0

2

(6)

laser beam.

flux defined as

**2.3 Assumptions and adjustments**

*DOI: http://dx.doi.org/10.5772/intechopen.90539*

A laser displacement sensor was used in the experiment to record the vertical deflection of the workpiece resulted from thermal stresses during the deposition process. The accuracy of the numerical model was checked and validated by comparing the experimental results with the simulation results. This validated model can be applied to a multilayer DMD process of stainless steel under different process parameters and can be used for other materials.
