It is clear that the cooling rate is reduced significantly by preheating. Preheating is a common practice in welding high‐strength steels because it reduces the risk of HAZ cracking. In multiple‐pass welding the inter‐pass temperature is equivalent to the preheat temperature T 0 in single‐pass welding.
Thus, Eq. (2.17) shows that the cooling rate decreases with increasing Q/V, and Eq. (2.15) shows that the temperature gradient decreases with increasing Q.
Example 2.2 Consider 2D (x, y) heat flow and 3D (x, y, z) heat flow in the workpiece. (a) When heat flow in the workpiece is 2D, does the temperature distribution (including the weld width) change much in the depth direction of the workpiece? (b) What about 3D heat flow? (c) Which equation works better for the thick plate (25 mm thick) in Figure E2.2, and why? (d) How about the thin sheet (3.2 mm thick)? (e) At the same Q and V, how does preheating affect the weld width and cooling rate?
Figure E2.2 Transverse cross‐sections of welds.
Answer:
1 (a) No, with 2D heat flow the temperature distribution changes little in the depth direction.
2 (b) With 3D heat flow, the temperature distribution changes significantly in the depth direction.
3 (c) 2D equation works better because the weld width is essentially uniform in the depth direction, suggesting 2D heat flow.
4 (d) 3D equation works better because the weld width changes significantly in the depth direction, suggesting 3D heat flow.
5 (e) Increasing preheating temperature increases the weld width but decreases the cooling rate.
Example 2.3 Consider the transverse cross‐section of the weld pool based on Rosenthal's 3D heat flow equation. What is the shape of the transverse cross‐section of a weld based on Rosenthal's 3D equation?
Answer:
From Rosenthal's 3D equation
At a fixed value of x, x = c, where c is a constant. For a given material under a given welding condition, T o , k, Q, V, and α are all constant. Furthermore, T = T m (the melting point) at the fusion boundary. Therefore, everything in Eq. (2.20) is constant, and the radial distance R between the origin and a point at the fusion boundary must, therefore, also be constant.
(2.21)
Since R and x are both constant, y 2 + z 2 = constant. Thus, the transverse cross‐section of the weld pool is round. In reality, however, the transverse cross‐section of a bead‐on‐plate weld is often not round, even when the plate is very thick.
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