**4. Numerical results and experimental validation**

#### **4.1 Temperature**

*<sup>ε</sup>*\_*ij* <sup>¼</sup> <sup>1</sup> <sup>þ</sup> *<sup>ν</sup>*

**3.2 Initial and boundary conditions**

the substrate were set as 0.

**3.3 Finite element modeling**

properties appear in **Figure 4**.

*3.3.1 Material properties*

*3.3.2 Element selection*

**Figure 4.**

**96**

*Temperature-dependent mechanical properties of SS 304.*

*<sup>E</sup> <sup>σ</sup>*\_ *ij* � *<sup>ν</sup>*

*New Challenges in Residual Stress Measurements and Evaluation*

*<sup>E</sup> <sup>σ</sup>*\_ *kkδij* <sup>þ</sup> *<sup>α</sup>T*\_ *<sup>δ</sup>ij* <sup>þ</sup> *λ σij* � <sup>1</sup>

The temperature history of all the nodes generated in the thermal analysis was imported as a predefined field into the mechanical analysis. The only boundary condition applied to the domain was that the substrate was fixed on one side to prevent rigid body motion. In ABAQUS, the node displacements on the left side of

Temperature-dependent mechanical properties including the thermal expansion coefficient [23], Young's modulus, Poisson's ratio [21], and yield stress [16] were used to model the thermomechanical behavior of SS 304. The values of these

The order of element and integration method used in the mechanical analysis differed from those used in the thermal analysis, while the element dimension and meshing scheme remained unchanged. To ensure the computational accuracy of the residual stress and deformation, second-order elements were utilized in the heataffected zone, while first-order elements were used in other regions to reduce the computation time. Preventing shear and volumetric locking [14] requires the selection of reduced-integration elements. Therefore, elements "C3D20R" and "C3D8R"

As shown in **Figure 5**, the 3-D 20-node element used in the mechanical analysis

had 12 more nodes than the 3-D 8-node element used in the thermal analysis.

in ABAQUS were combined in use to represent the domain.

3 *σkkδij* 

(23)

#### *4.1.1 Temperature field*

**Figure 6** shows the temperature field of the melt pool and surrounding areas from top view at different times in Case 1 (laser power 607 W, laser travel speed 250 mm/min, powder feed rate 6.3 g/min). Laser beam cyclically moves along +z and –z-direction. At *t* ¼ 0*:*9 s, *t* ¼ 2*:*7 s, and *t* ¼ 4*:*5 s, laser beam is located in the center of the substrate. **Figure 7** shows the temperature field and isotherms of the substrate and deposits from the side view at *t* ¼ 4*:*5 s in Case 1. The peak temperature during the process was around 2350 K, while the lowest temperature was close to room temperature. The big temperature differences and small geometrical dimensions caused very large temperature gradients.

#### *4.1.2 Temperature gradient*

The temperature gradient involved in the DMD process was quantitatively analyzed in details. The temperature of nodes along the *x*<sup>0</sup> and *y*<sup>0</sup> (shown in **Figure 8**) axes in simulation Case 1 at *t* ¼ 4*:*5 s is shown in **Figure 9**. The *x*<sup>0</sup> -direction nodes were selected along the top surface of the substrate (bottom surface of the deposits), while the *y*<sup>0</sup> -direction nodes were selected along the height of the deposits. The temperature of the substrate's top surface reached a maximum of 1069 K just below the center of the laser beam and decreased gradually along the *x*<sup>0</sup> direction. In the *y*<sup>0</sup> -direction, the temperature of the deposits reached a maximum of 2220 K on the top surface of the deposits and decreased rapidly to1069 K . The slopes of the temperature curves represent the thermal gradients along the *x*<sup>0</sup> - and *y*0 -directions. Along *x*<sup>0</sup> , the temperature gradient reached a maximum of483 K*=*mm; along *y*<sup>0</sup> , the maximum temperature gradient occurred near the top surface of the deposits, reaching 1416 K*=*mm and then decreasing along the negative *y*<sup>0</sup> -direction.

**Figure 8.**

**Figure 9.**

**Figure 10.**

**99**

*Contour plots of residual stress field within deposits.*

*Location of points within deposition under consideration.*

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

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

*The temperature of nodes in x- and y-directions in Case 1 at t = 4.5 s.*

#### **Figure 6.**

*Contour plots of temperature field of the melt pool and surrounding areas from top view at different times (Case 1).*

#### **Figure 7.**

*Contour plots of temperature field and isotherms of the substrate and deposits from side view at t* ¼ *4:5 s (Case 1).*

These steep thermal gradients induced large compressive strains within the deposits and substrates [24].

## **4.2 Residual stress**

The nature and magnitude of residual stresses existing in final deposits would affect the integrity of the entire structure. In general conditions, compressive residual stresses are advantageous since they increase the load resistance and

*Residual Stress Modeling and Deformation Measurement in Laser Metal Deposition Process DOI: http://dx.doi.org/10.5772/intechopen.90539*

**Figure 8.** *Location of points within deposition under consideration.*

**Figure 9.** *The temperature of nodes in x- and y-directions in Case 1 at t = 4.5 s.*

**Figure 10.** *Contour plots of residual stress field within deposits.*

These steep thermal gradients induced large compressive strains within the deposits

*Contour plots of temperature field and isotherms of the substrate and deposits from side view at t* ¼ *4:5 s*

*Contour plots of temperature field of the melt pool and surrounding areas from top view at different times*

*New Challenges in Residual Stress Measurements and Evaluation*

The nature and magnitude of residual stresses existing in final deposits would affect the integrity of the entire structure. In general conditions, compressive residual stresses are advantageous since they increase the load resistance and

and substrates [24].

**Figure 6.**

*(Case 1).*

**Figure 7.**

*(Case 1).*

**98**

**4.2 Residual stress**

*4.3.1 Experiment setup*

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

**Figure 12.**

**Figure 13.**

**Figure 14.** *Experimental setup.*

**101**

*Deflection of substrate along y (m).*

*Final shape of substrate.*

As shown in **Figure 14**, in the experiment, the substrate was clamped at the left end to prevent rigid body motion. Keyence's LK-G5000 series laser displacement sensor shown in **Figure 15** was placed just below the right end of the substrate to record the displacement of the free end along the y-direction with a frequency of 25 Hz during the process. The experimental results appear in **Figure 16**. The entire DMD process was controlled by the "Laser Aided Material Deposition System".

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

**Figure 11.** *Contour plots of residual stress field within deposits (y–y cross section).*

prevent crack growth, while tensile residual stresses are detrimental that they reduce the load resistance and accelerate crack growth.

The residual stress (in Pa) distribution within the final deposits is shown in **Figures 10** and **11**, where **Figure 10** shows the whole substrate and deposit, while **Figure 11** shows a *y*–*y* cross section view with half of the deposits hidden to show the internal residual stress. Normal stresses *σ*11, *σ*22, and *σ*<sup>33</sup> along three spatial directions are shown in **Figures 10** and **11(a)–(c)**, respectively, and the von Mises stress is shown in **Figures 10** and **11(d)**. As the figures indicate, residual stresses in the lower part of the deposits were mostly tensile stresses due to the cooldown phase of the molten layers [24]. After the deposition was finished, the remelted lower part of the deposits began to shrink; this shrinkage was restricted by the underlying material, thus inducing tensile stresses. Compressive residual stresses existed at the top free surface of the deposits, caused by the steep temperature gradient. The expansion of the hotter top layer was inhibited by the underlying material, thus introducing compressive stress at the top surface.

Various experimental methods for measuring residual stress have been developed, such as destructive methods, including incremental hole drilling, layer removal, and crack compliance, and nondestructive methods including X-ray diffraction and neutron diffraction [8, 9, 24–27]. These methods could be used to measure the residual stress directly with relatively good accuracy; however, they usually are not cost-effective or easy to set up. Therefore, instead of measuring the residual stress directly, a flexible indirect method has been developed for residual stress validation. A one-one relationship exists between the deflection of the substrate and residual stress; therefore, by validating the deflection of the substrate, the residual stress results can be validated indirectly.

#### **4.3 Deformation**

During the DMD process, the substrate will continuously expand and shrink, finally maintaining a deformed shape (**Figure 12**). In this study, deflection along y was the main deformation under consideration and is shown in **Figure 13**.

*Residual Stress Modeling and Deformation Measurement in Laser Metal Deposition Process DOI: http://dx.doi.org/10.5772/intechopen.90539*

## *4.3.1 Experiment setup*

As shown in **Figure 14**, in the experiment, the substrate was clamped at the left end to prevent rigid body motion. Keyence's LK-G5000 series laser displacement sensor shown in **Figure 15** was placed just below the right end of the substrate to record the displacement of the free end along the y-direction with a frequency of 25 Hz during the process. The experimental results appear in **Figure 16**. The entire DMD process was controlled by the "Laser Aided Material Deposition System".

**Figure 12.** *Final shape of substrate.*

prevent crack growth, while tensile residual stresses are detrimental that they

The residual stress (in Pa) distribution within the final deposits is shown in **Figures 10** and **11**, where **Figure 10** shows the whole substrate and deposit, while **Figure 11** shows a *y*–*y* cross section view with half of the deposits hidden to show the internal residual stress. Normal stresses *σ*11, *σ*22, and *σ*<sup>33</sup> along three spatial directions are shown in **Figures 10** and **11(a)–(c)**, respectively, and the von Mises stress is shown in **Figures 10** and **11(d)**. As the figures indicate, residual stresses in the lower part of the deposits were mostly tensile stresses due to the cooldown phase of the molten layers [24]. After the deposition was finished, the remelted lower part of the deposits began to shrink; this shrinkage was restricted by the underlying material, thus inducing tensile stresses. Compressive residual stresses existed at the top free surface of the deposits, caused by the steep temperature gradient. The expansion of the hotter top layer was inhibited by the underlying

Various experimental methods for measuring residual stress have been devel-

During the DMD process, the substrate will continuously expand and shrink, finally maintaining a deformed shape (**Figure 12**). In this study, deflection along y

was the main deformation under consideration and is shown in **Figure 13**.

oped, such as destructive methods, including incremental hole drilling, layer removal, and crack compliance, and nondestructive methods including X-ray diffraction and neutron diffraction [8, 9, 24–27]. These methods could be used to measure the residual stress directly with relatively good accuracy; however, they usually are not cost-effective or easy to set up. Therefore, instead of measuring the residual stress directly, a flexible indirect method has been developed for residual stress validation. A one-one relationship exists between the deflection of the substrate and residual stress; therefore, by validating the deflection of the substrate, the

reduce the load resistance and accelerate crack growth.

*Contour plots of residual stress field within deposits (y–y cross section).*

*New Challenges in Residual Stress Measurements and Evaluation*

material, thus introducing compressive stress at the top surface.

residual stress results can be validated indirectly.

**4.3 Deformation**

**100**

**Figure 11.**

**Figure 13.** *Deflection of substrate along y (m).*

**Figure 14.** *Experimental setup.*

*4.3.2 Experimental and simulation results*

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

process.

**5. Conclusion**

**Acknowledgements**

**103**

Center is also greatly appreciated.

down, the substrate still maintained its distorted shape.

than Case 1, which is caused by higher laser power.

as laser sintering, laser cladding, and welding.

**Figure 16** illustrates the comparisons of the substrate deflection between the experimental and simulation results for both cases. It is obvious that the simulated deflection matched well with the experimental results. During each deposition layer, the substrate firstly bent down due to thermal expansion on the top surface and then bent up due to thermal shrinkage from the cooling process. After cooling

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

The deflection values from simulation were 28.5 and 24.6% higher than the deflection measured from experiments for Cases 1 and 2, respectively. There are several potential factors that could cause these differences. Firstly, the experimental setup could not perfectly match the setup in the simulation. For example, in the simulation, the laser beam traveled exactly along the centerline of the substrate. While in experiments (**Figure 12**), this cannot be perfectly achieved. These offsets may greatly affect the deflection value since it is very sensitive to the positions of heated zone (where expansion and shrinkage mainly happen) and measuring point. Moreover, the laser displacement sensor did not track the displacement of one particular point on the workpiece. Instead, it sensed the signal reflected by an obstacle, so the positions it tracked were always changing as the substrate continuing to deform. Last but not the least, the simplifications and assumptions considered in both thermal and mechanical analyses could also contribute to the differences between the simulation and experiment. For example, although the substrate material is originally isotropic elastic solid, it may become orthotropic after the DMD

It is also worth noting that for Cases 1 and 2, even the total amount of energy applied to the substrate is the same and Case 2 has significantly higher distortion

To investigate the features of thermal and mechanical behavior of deposited materials involved in the DMD process, a sequentially coupled, thermomechanical finite element model was developed for multilayer DMD process of Stainless Steel 304. The results revealed the characteristics of temperature distribution, residual stress, and deformation within the formed deposits and substrates. A set of experiments were conducted to validate the mechanical effects using a laser displacement sensor. This FEA model can be used to predict the mechanical behavior of products fabricated by the DMD process or similar processes with localized heat sources such

The support from NASA's grant, under NRA NNX11AI73A, is appreciated. The authors would like to acknowledge William Seufzer and Karen Taminger of NASA Langley Research Center for their mentorship. Support from Missouri S&T's Material Research Center, Manufacturing Engineering program, and Intelligent Systems

**Figure 16.** *Simulation and experimental results of substrate deflection. (a) Deflection in case 1 and (b) deflection in case 2.*

*Residual Stress Modeling and Deformation Measurement in Laser Metal Deposition Process DOI: http://dx.doi.org/10.5772/intechopen.90539*

#### *4.3.2 Experimental and simulation results*

**Figure 16** illustrates the comparisons of the substrate deflection between the experimental and simulation results for both cases. It is obvious that the simulated deflection matched well with the experimental results. During each deposition layer, the substrate firstly bent down due to thermal expansion on the top surface and then bent up due to thermal shrinkage from the cooling process. After cooling down, the substrate still maintained its distorted shape.

The deflection values from simulation were 28.5 and 24.6% higher than the deflection measured from experiments for Cases 1 and 2, respectively. There are several potential factors that could cause these differences. Firstly, the experimental setup could not perfectly match the setup in the simulation. For example, in the simulation, the laser beam traveled exactly along the centerline of the substrate. While in experiments (**Figure 12**), this cannot be perfectly achieved. These offsets may greatly affect the deflection value since it is very sensitive to the positions of heated zone (where expansion and shrinkage mainly happen) and measuring point. Moreover, the laser displacement sensor did not track the displacement of one particular point on the workpiece. Instead, it sensed the signal reflected by an obstacle, so the positions it tracked were always changing as the substrate continuing to deform. Last but not the least, the simplifications and assumptions considered in both thermal and mechanical analyses could also contribute to the differences between the simulation and experiment. For example, although the substrate material is originally isotropic elastic solid, it may become orthotropic after the DMD process.

It is also worth noting that for Cases 1 and 2, even the total amount of energy applied to the substrate is the same and Case 2 has significantly higher distortion than Case 1, which is caused by higher laser power.
