### 1. Introduction

^{1)}conducted a statistical mult-response study on electron beam welding of stainless steel samples in order to optimize the process. Zhu et al.

^{2)}in 2002 studied the effect of temperature-dependent material properties on weldments through 3D nonlinear analysis of welding taking advantage of finite element method. In 2003, Couedel et al.

^{3)}modeled a moving heat source through 2D finite element modeling. Ferro et al

^{4)}in 2004 carried out a numerical and experimental research on plates made from the nickel-based super-alloy of Inconel 706 in order to study the effect of electron beam welding parameters on geometrical and microstructural properties. In the same year, Ram et al

^{5)}presented design of experiments and parameter optimization in electron beam welding making use of variance analysis. In 2005, Ho

^{6)}analytically studied the effects of conical specifications of the electron beam on the fusion zone. The same author in 2007 in another paper

^{7)}proposed an analytical 3D solution for prediction of temperatures in the welding pool of electron beam welding. One year later, Zhao et al.

^{8)}studied residual stress and distortion reductions in electron beam welding taking advantage of multiple beams technique, and investigated the topic through finite element analysis and experimental studies. In the same year Qi et al.

^{9)}took advantage of high energy density, high absorption rate and vacuum environment of electron beam technology in Electron beam selective melting316 stainless steel powders. In 2009, Luo et al.

^{10)}simulated the thermal effect of electron beam welding in a magnesium alloy through 3D modeling of the heat source in vacuum. Liu et al.

^{11)}in 2011 studied variation of welding residual stresses after material removal from a 50 mm thick plate of a titanium alloy welded through electron beam welding. In a recent study in 2011, Jha et al.

^{12)}conducted different experiments on 304 stainless steel plates in order to control welding outputs in terms of yield strength and ultimate tensile strength through monitoring input parameters namely accelerating voltage, beam current, and welding speed. They took advantage of neural networks in their optimization.

^{4)}, in order to validate the model. The agreement observed between the results provided confidence in the validity of the model.

### 2. Heat Source Model For EBW

_{1}denotes the volume of the spherical heat source, and R represents the effective radius of the electron beam. According to the rotating body property, x

^{2}+y

^{2}=r

^{2}, where r is the radial distance of each point in the heat source from the center.

^{2}+u

^{2}=r

^{2}.

_{2}denotes the volume of the conical heat source. The other parameters are provided in Table 1.

##### Table 1

Heat source | Spherical | Conical |
---|---|---|

q_{0}(W/mm^{2}) |
215 | - |

R1(mm) | 0.9 | - |

R2(mm) | 1.3 | - |

Ri(mm) | - | 0.47 |

Re(mm) | - | 0.49 |

Zi(mm) | - | 2.7 |

Ze(mm) | - | 8.8 |

### 3. Finite element simulation of ebw

*sequentially coupled analysis*, the thermal results are first extracted through solution of a pure heat transfer problem, and the thermal history of nodes and elements are applied as the input to the next phase which is the mechanical analysis in which the resulting stresses are calculated based upon the thermal history of weldments through incorporation of thermal expansion coefficient. In the other approach, fully coupled analysis, the thermal and mechanical fields are studied at the same time through solution of all the thermal and mechanical equations in their initial coupled format. The latter approach is more complicated in comparison with the sequentially coupled analysis, and thus, it is justified when the nonlinearity of equations are too high to be treated in an uncoupled manner

^{13)}.

### 3.1 Welding parameters

^{4)}have been utilized in validation of the finite element model. The geometry and dimensions of the plates in this experimental work are depicted in Fig. 2.

^{4)},

*V*= 150

*kv*,

*I*=10

*mA*and

*v*= 10

*mm/s*have been considered, and the same parameters were included in the present work.

### 3.2 Thermal analysis of ebw process

^{14)}.

### 3.3 Mechanical analysis of ebw process

##### Table 3

### 4. Results and discussion

^{4)}. After enough confidence is reached about validity of the model, further predictions and investigations about the effect of plate thickness on the residual stresses are made.

### 4.1 Validation of the model

### 4.2 pre-heat treatment

^{16)}.

### 4.3 Pre-heat treatment procedures]

^{17)}.

### 4.4 Effect of base metal heat treatment prior to welding on residual stresses

^{4)}. An important question to be answered is how heat treatment of initial materials affects the final residual stresses. In other words, does heat treatment which allows for much higher strength for the material include any drawbacks? Heat treatment imposes dramatic changes in the plastic properties of the material. In this regard, the mechanical properties of non-heat treated Inconel 706 were incorporated and the residual stresses were calculated and compared to the initial results. The results are presented in Figs. 7 and 8 for longitudinal and transverse stresses, respectively.

### 4.5 Effect of plate thickness on residual stresses

### 5. Conclusions

^{4)}were utilized to validate the finite element model. Through fulfillment of this study, the following conclusions were drawn: