The analytical model gives precise results only if experimentally estimated parameters are involved in the model. Furthermore, verification of the analytical model can be done by comparing the results from the analytical model with experimentally estimated results (Ref. 2). The friction coefficient () varies with temperature. However, in the present model for demonstration purposes, it is considered as 0.4. The summary of all pin profiles shown in Table 1, under the following process parameters, are as follows: tool rotational speed – 1000 rev/min, weld speed – 10 mm/s, – 0.4, Rshoulder – 6 mm, Rprobe – 3 mm, and Hprobe – 4.7 mm. The AA2014-T6 thickness is 5 mm, solidus temperature – 780 K, liquidus temperature – 911 K, F - 9.09 kN for TR, 8.97 kN for SQ, 6.98 kN for PEN, and 6 kN for the HEX pin profile. The expression for heat generation in FSW is given below in a generalized form where the value of multiplying factor ‘X’ is 3 (Ref. 4). The value of ‘X’ for different pin profiles is shown in Table 2. From Table 2, it is seen that by increasing the sides of polygon, the value of ‘X’ goes on increasing and finally it stops at value 3. From Table 1, it is seen that heat generation of given pin profiles in ascending order of the edges initially increases from the TR to SQ pin profile, then decreases to the HEX pin profile. From Table 2, it is seen that an increase in the number of edges leads to an increase in the pulsating stirring action, but a decrease in the heat and temperature profile of the weld zone under the given set of process conditions. From Fig. 8, it can be seen that increasing the number of edges, the peak temperature initially increases from the TR to SQ pin profile then decreases to the HEX pin profile. Furthermore, an increase in number of edges that finally forms a circle means the heat generation is lowest for the SC pin profile, beyond which no temperatures rise. Figure 9 and Table 3 shows the modeling heat generation for the SQ pin profile with peak temperature and its comparison with the developed analytical model. The variation in analytical and numerical modeling using Comsol is attributed due to the following two reasons: First, in numerical modeling, material properties such as thermal conductivity, heat capacity, and density of both the workpiece and tool material were considered (i.e., material specific), whereas in analytical modeling only process parameters were considered (i.e., nonmaterial specific). Second, the friction coefficient was assumed and Equation 25 adapted from Ref. 22, when the analytical method is used. From Table 3, it is seen that under constant weld speed and increasing tool rotational speed, heat input increases and hence peak temperature increases. This agrees well with literature (Ref. 8) where it was reported that varying tool rotational speed could raise strain rate, and thereby influence the recrystallization process. Similarly, under constant tool rotational speed and increasing weld speed, heat input decreases and hence peak temperature decreases. This agrees well with literature (Ref. 26), where it was reported that at lower weld speed, overaging takes place in the weld region due to high frictional heat generation and at higher weld speed underaging take place due to low frictional heat generation. Moreover, process maps for different work material (Ref. 23) gives a clear understanding regarding temperature, strain rate, plastic deformation, and behavior, which will be helpful to optimize the FSW tool geometry and process parameters to get defect-free welds. Recently, a similar approach was developed by Backer et al. (Ref. 24) where they used a temperature controller that modifies the spindle speed to maintain a constant welding temperature except predicting the mechanical properties. The correlation of temperature data by considering the deformation with strain rate, Zener-Holloman parameter, and grain size will remain as a future work. Conclusions Understanding the process of heat generation and estimating the amount of heat generated during FSW are complex and challenging tasks that require a multidisciplinary approach. In this study, an analytical model for heat generation in FSW of aluminum alloys using different pin profiles such as TR, SQ, PEN, and HEX are developed. Using an analytical approach, it is seen that by increasing the number of edges, the amount of heat generation initially increases from the TR to SQ pin profile, then decreases to the HEX pin profile. Furthermore, numerical modeling shows that increasing the QTotal = ⋅π⋅ω⋅μ⋅τcontact ⋅(R shoulder + X ⋅R probe ⋅Hprobe ) 2 3 3 2 (26) WELDING RESEARCH APRIL 2015 / WELDING JOURNAL 123-s Table 2 — Different Pin Profiles with Multiplying Factor ‘X’ Pin Profile Multiplying Factor (X) TR 0.72 SQ 0.95 PEN 1.19 HEX 1.43 SC 3 Table 3 — Numerical Modeling of SQ Pin Profile under Different Process Conditions Sr. No. Condition Q(Energy/length), J/mm Q(Energy/length) , Eff. Tmax (K) (Analytical) Tmax (K) (Numerical) A 500–600 89.20 83.85 504 593 B 1000–600 178.40 167.70 516 789 C 1500–600 267.60 251.54 528 864 D 1000–200 535.20 503.09 563 889 E 1000–400 267.60 251.54 528 850 F 1000–500 214.08 201.23 521 822 Note: 500–600 = 500 rev/min (tool rotational speed) – 600 mm/min (weld speed) all at 8.97 kN (vertical force) condition.
Welding Journal | April 2015
To see the actual publication please follow the link above