Process modeling

The movement and flow behavior of the work piece material around the pin during FSW has been a very interesting subject. Scientists have tried various methods, such as tracer technique by markers, to understand the material flow behavior. The heating source and temperature distribution during FSW are also important subjects because the temperature distribution would influence the final welding zone microstructure. These mechanical and thermal models would be introduced in the following section.

1.6.3.1 Material flow behavior in the stirred zone

The method of tracking the material flow behavior in the stirred zone is to use a marker material as tracer to track the material flow during FSW. In the past few years, different tracer materials, such as small steel balls [97], Al-SiC (particles), Al-W (particles) composites [98], and Al alloy that etches differently from the base material [99], have been used as the tracer.

In addition to the tracer technique, FSW of dissimilar materials has been used to visualize the complex flow phenomenon [100-103].

From these researches, the material flow in the stirred zone exhibited some common characteristics, as described below. First, the flow was not symmetric about the weld centerline [99]. Second, the “stirring “ of material occurred only at the top of the weld where the material transportation is directly influenced by the rotating tool shoulder [99], and the flow pattern at the approximately upper one-third region exhibited the more complex behavior [100]. Third, the material ahead of the pin was moved through the retreating side to the back of the pin and deposited along the semi-circle arc in the stirred zone [98,99]. In addition, the material close to the advancing side front of a weld entered into a zone that rotated and advanced simultaneously with the pin. The material in this zone was very highly deformed and sloughed off behind the pin in the arc shaped features [98]. Fourth, many researches all suggested that the friction stir welding process can be roughly described as in situ extrusion wherein the tool shoulder, the pin, the weld backing plate and cold base metal outside the weld zone formed an “extrusion chamber” which moves relative to the workpiece.

The material was simply extruded from the retreating side to the back of the pin [97-99].

Seidel and Reynolds [99] also reconstructed the three-dimension flow behavior from the marker insert technique, as shown in Fig. 1-11. Fifth, material ahead of the pin was significantly uplifted because of small tilt angle of the tool, which created a “plowing action”

of the metal ahead of the weld [98]. Sixth, the material exhibited the behavior of flowing downward to backing plate due to the influence of the thread of the pin [98-100].

The research results also showed that FSW had the effect of mixing the dissimilar materials in the stirred zone [100-103]. From Fig. 1-12, it is very clear that these marker inserts were mixed together after FSW. Li et al. [102,103] also reported that such a mixing behavior in the FSW-joined 2024 and 6061 Al alloys. In addition, it is worth noting that the nugget zone area would increase with decreasing weld pitch (here, the pitch in their paper is referred to the distance advanced during each rotation), meaning an increased rotation speed or a decreased advancing speed and would mix more uniformly. The practical experiment for Al alloys by FSW also revealed this trend [101].

1.6.3.2 Material flow modeling

Except for the above experimental approaches to investigate the material flow behavior during FSW, utilizing computer simulation based on the fluid dynamics or metalworking model is also a method to explore the material flow.

Colegrove and Shercliff [104] used the Computational Fluid Dynamic (CFD) code to model the metal flow. They suggested that FSW is similar to the “slip model”, where the interface conditions were governed by the local shear stress, rather than the past assumption of material stick. The simulation result showed that the deformation region for the slip model was much smaller on the advancing side than retreating side, and was consistent with the observation of the experimental. It was also pointed out that the slip model needed the larger traversing force and the lower welding force, in comparing the difference of “stick” and

“slip” model. The lower the local shear stress is, the lower torque and higher traversing force

for the slip model does need. Goetz and Jata [105] used a two-dimensional finite element method code to simulate material flow in FSW of 1100 Al and Ti-6Al-4V alloys. The simulations predicted a strain rate of 2-12 s^-1 and a strain of 2-5 in the localized flow zone.

Arbegast [106] developed a model to describe the metal flow during FSW in terms of five conventional metal working zones: (a) preheat, (b) initial deformation, (c) extrusion, (d) forging, and (e) post heat/cool down, as shown in Fig. 1-13. In the preheat zone ahead of the pin, the temperature will rise due to the friction heating of the rotating tool and adiabatic heating because of the deformation of material. As the tool moves forwards, an initial deformation zone forms when material is heated to above a critical temperature and the magnitude of stress exceeds the critical flow stress of material, resulting in material flow. The material in this zone is forced both upwards into shoulder zone and downwards into the extrusion zone, as shown in Fig. 1-13 (a). Inside the extrusion zone with a finite width, material flows around the pin from the front to rear. A critical isotherm on each side of the tool defines the width of extrusion zone where the magnitudes of stress and temperature are insufficient to allow metal flow outside the extrusion zone. Following the extrusion zone is the forging zone where the material from the front of tool is forced into cavity left by the forwards moving pin under the hydrostatic pressure condition. The shoulders also help to constrain material in this cavity and apply a downwards forging force. Behind the forging zone is the post heat/cool zone where the material cools under either passive or forced cooling conditions.

Arbegast [106] speculated that the extrusion zone model based on the above metal working process, as shown in Fig. 1-14. The extrusion zone geometry can be assumed as shown in Fig. 1-15. Therefore, the extrusion ratio, R, can be calculated as

( )

(

) (

)

= +

r r p

W Z h

W R

R h , (14)

where Rp is the radius of pin, h the pin length, λ the threads pre lenghth, δ² the projected thread area, Wr the width of extrusion zone on retreating side, and ΔZ is the distance that material moved down per revolution. The mean strain, ε, can be written as

ε=ln (R). (15)

The average strain rate can be approximated by dividing the mean strain by the time,

( ) ( )

( )

[ ] ( ) [ ]

(

)

r r f

r p f

t R W

W / W v / w h

W R ln h

v

+

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

+

−

+

= 6 2

λδ

ε& λ , or (16)

( )f

( )

t =ε /t=6v ln R / R +W

ε& . (17)

where vf is forward travel speed. The predicted mean strain rate lies between 10⁰-10² s^-1 based on the above equation (Eq. 17). It is suggested [106] that the strain rate is independent of the forward travel speed at low rotation speeds and high travel speeds. However, the strain rate appears to converge on a liner relationship with higher rotation speeds (above 500 rpm).

It is suggested that the strain rate is strongly dependent on the forward travel speed at higher rotations where the extrusion zone width becomes small.

1.6.3.3 Input energy and temperature prediction

Schmidt et al. [107] analyzed the heat generation in FSW based on the analytical model developed by them. The analytic results suggested that the part of shoulder generated 86%

heat to the total heat generation, the side of the pin is 11%, and the tip of the pin is 3%. The experiment results also demonstrated that the temperature difference was small no matter if the tool is attached with or without the pin.

The average heat input per unit area and time according to the research of Frigaad et al.

[108] is

3 2

0 3

4

Rp

P

q = π μ ω , (18)

where q0 is the net power (W, in unit of P), μ the friction coefficient, P the pressure (Pa), w the tool rotational speed (rot/s), and Rp is the tool radius (m). Frigaad et al. [108] suggested that the rotational speed and the shoulder radius are the main process variables to the heat input. The pressure P, in practice, cannot exceed the actual flow stress of the material at the operating temperature if a sound weld without depression is to be obtained.

As for the maximum temperature during FSW, Arbegast [106] speculated an experiential equation as a function of the rotation speed (w, in unit of rpm) and forward travel speed (vf, in unit of IPM, inch per minute) given by :

a

f

m v

K w T

T ⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

= ⋅² ₄

10 , (19)

where the exponent “a” is found to range between 0.04 and 0.06, the constant K lies the between 0.65 and 0.75, and T_m (^oK) is the melting point of the alloy. The maximum temperature observed during the FSW of aluminum alloys is between 0.6 Tm and 0.9 Tm.