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Numerical simulation of friction stir-assisted incremental forming with synchronous bonding of heterogeneous sheet metals

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Abstract

Friction stir-assisted incremental sheet forming with synchronous bonding is developed as a novel variant of incremental sheet forming, by which the two sheet metals form incrementally and get bonded simultaneously. Numerical simulation of this process is crucial in revealing the forming mechanism and optimizing the process compared with expensive physical tryouts. A coupled thermo-mechanical finite element model was established to take the contact and heat transformation in every interface into consideration, and VUINTER contact subroutine which can express the heat partition coefficient and coefficient of friction was complied, validated and revised by groove tests. The effectiveness of the numerical simulation was verified by experiments. Furthermore, a comparative study based on numerical simulation is conducted to analyze the effects of process variables including feed rate, spindle speed, wall angle and vertical step size on temperature, thickness, and central bulge.

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Abbreviations

d :

vertical step size (mm)

v f :

feed rate of the tool (mm/min)

v s :

spindle speed of the tool (RPM)

v :

sliding velocity of the contact point in the tool/sheet interface (mm/s)

ΔD :

distance of relative motion between the contact nodes on master surface and slave surface (mm)

g N :

penetration distance (mm)

n s :

value of penalty stiffness for each node

T :

temperature (°C)

T 0 :

ambient temperature (°C)

T 1 :

temperature of the upper sheet (°C)

T 2 :

temperature of the lower sheet (°C)

T 3 :

temperature of the back sheet (°C)

T 4 :

temperature of the forming tool (°C)

T 5 :

temperature of the blank holder (°C)

f :

friction stress (MPa)

τ max :

shear stress limit (MPa)

q fric :

heat generated by friction (mW/mm2)

q →t :

heat flowing into the tool (mW/mm2)

q →u :

heat flowing into the upper sheet (mW/mm2)

q →l :

heat flowing into the lower sheet (mW/mm2)

q →b :

heat flowing into the back sheet (mW/mm2)

β →t :

friction heat partition coefficient

h c 1 :

heat conductivity in tool/upper-sheet interface (mW/mm2 ∙  ° C)

h c 2 :

heat conductivity in upper-sheet/lower-sheet interface (mW/mm2 ∙  ° C)

h c 3 :

heat conductivity in lower-sheet/back-sheet interface (mW/mm2 ∙  ° C)

h s 1 :

coefficient of heat dissipation for air (mW/mm2 ∙  ° C)

h s 2 :

coefficient of heat dissipation for blank-holder (mW/mm2 ∙  ° C)

η :

efficiency of the heat converted by the work done by friction

β :

coefficient of heat partition

μ :

coefficient of friction

ρ :

density (kg/m3)

E :

elastic modulus (GPa)

γ :

Poisson ratio

c p :

specific heat (J/kg/°C)

λ :

thermal conductivity of material (W/m/°C)

σ n :

contact stress (MPa)

σ s :

yield stress (MPa)

α :

wall angle (°)

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Acknowledgements

The authors are grateful for the financial support from National Natural Science Foundation of China through grant no. 51675332 and the Program of Shanghai Excellent Academic Research Leadership through grant no. 19XD1401900.

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Authors and Affiliations

  1. Department of Plasticity Technology, School of Materials Science and Engineering, Shanghai Jiao Tong University, Shanghai, 200030, China

    Sheng Cai, Renhao Wu, Zhiheng Wang, Meng Li & Jun Chen

  2. National Engineering Research Center of Die & Mold CAD, School of Materials Science and Engineering, Shanghai Jiao Tong University, Shanghai, 200030, China

    Sheng Cai, Renhao Wu, Zhiheng Wang, Meng Li & Jun Chen

Authors
  1. Sheng Cai
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  2. Renhao Wu
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  3. Zhiheng Wang
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  4. Meng Li
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  5. Jun Chen
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Correspondence to Jun Chen.

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Cai, S., Wu, R., Wang, Z. et al. Numerical simulation of friction stir-assisted incremental forming with synchronous bonding of heterogeneous sheet metals. Int J Adv Manuf Technol 106, 2747–2763 (2020). https://doi.org/10.1007/s00170-019-04792-x

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