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Thermal analysis of the arc welding process: Part I. General solutions

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Abstract

An analytical solution for the temperature-rise distribution in arc welding of short workpieces is developed based on the classical Jaeger’s moving heat-source theory to predict the transient thermal response. It, thus, complements the pioneering work of Rosenthal and his colleagues (and others who extended that work), which addresses quasi-stationary moving heat-source problems. The arc beam is considered as a moving plane (disc) heat source with a pseudo-Gaussian distribution of heat intensity, based on the work of Goldak et al. It is a general solution (both transient and quasi-steady state) in that it can determine the temperature-rise distribution in and around the arc beam heat source, as well as the width and depth of the melt pool (MP) and the heat-affected zone (HAZ) in welding short lengths, where quasi-stationary conditions may not have been established. A comparative study is made of the analytical approach of the transient analysis presented here with the finite-element modeling of arc welding by Tekriwal and Mazumder. The analytical model developed can determine the time required for reaching quasi-steady state and solve the equation for the temperature distribution, be it transient or quasi-steady state. It can also calculate the temperature on the surface as well as with respect to the depth at all points, including those very close to the heat source. While some agreement was found between the results of the analytical work and those of the finite-element method (FEM) model, there were differences identified due to differences in the methods of approach, the selection of the boundary conditions, the need to consider image heat sources, and the effect of variable thermal properties with temperature. The analysis presented here is exact, and the solution can be obtained quickly and in an inexpensive way compared to the FEM. The analysis also facilitates optimization of process parameters for good welding practice.

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Abbreviations

a :

thermal diffusivity of the medium (cm 2/s)

Ln:

latent heat or heat of fusion

Q rg :

heat liberated by the instantaneous ring heat source (J)

q pt :

heat liberation rate of a point heat source (J/s)

q rg :

heat liberation rate of a ring heat source (J/s)

q pl :

heat liberation rate of a moving disc heat source (J/s)

q 0 :

heat-liberation intensity of a moving disc heat source (J/cm2·s)

R 0 :

distance between the center of the moving disc heat source and the point where the temperature rise at time t is concerned (cm)

R 0, R 1, R 2, R 3, and R 4 :

distances between the center of the relevant-image moving disc heat sources and the point where the temperature rise at time t is concerned (cm)

X (or X 0):

projection of the distance on the X-axis between the center of the moving disc heat source and the point where the temperature rise at time t is concerned (cm)

X 1, X 2, X 3, and X 4 :

projection of the distances on the X-axis between the center of the relevantimage moving disc heat sources and the point where the temperature rise at time t is concerned (cm)

t :

time of observation or the time after the initiation of a moving disc heat source (s)

t s :

the time when the moving disc heat source is shut off after completion of the welding process (s)

X, y, and z :

coordinates of any point M in a moving coordinate system, where the temperature rise is concerned

r 0 :

the radius of the moving disc heat source or moving ring heat source (cm)

r i :

the radius of a segmental ring heat source (cm)

λ :

thermal conductivity of the medium (J/cm · s · °C)

ϑ M :

temperature rise at any point M at any time t (°C)

ρ :

density of the medium (g/cm3)

I 0(p):

modified Bessel function of the first kind, order zero, (=1/2 π ∫ 2π0 e pcosαdα)

when 0≤p<0.2:

I 0(p)=1

when 0.2≤p<1.6:

I 0(p)=0.935 exp (0.352p)

when 1.6≤p<3:

I 0(p)=0.529 exp (0.735p)

when p≥3:

I 0(p)=\(\frac{1}{{\sqrt {2\pi p} }}\)exp (p)

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Authors and Affiliations

  1. the School of Mechanical and Aerospace Engineering, Oklahoma State University, 74078, Stillwater, OK

    R. Komanduri (Professor and MOST Chair in Intelligent Manufacturing) & Z. B. Hou (Visiting Professor)

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  1. R. Komanduri
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Komanduri, R., Hou, Z.B. Thermal analysis of the arc welding process: Part I. General solutions. Metall Mater Trans B 31, 1353–1370 (2000). https://doi.org/10.1007/s11663-000-0022-2

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