Worked example Stamping a rectangular panel

and the stress ratio is, from Equation 2.14, α = 2β + 1 2 + β = 0.802 4.24 From Equations 2.18b and 2.19, we obtain σ = 0.917σ 1 and ε = 1.532ε 1 4.25 The effective stress at the end of the process is σ = 700 0.009 + 1.532 × 0.0198 0.22 = 344 MPa and hence σ 1 = 3440.917 = 375 MPa and σ 2 = α.σ 1 = 0.802 × 375 = 301 MPa. The thickness is t = t exp [ − 1 + β ε 1 ] = 0.9 exp [− 1 + 0.505 0.0198] = 0.874 mm and as T = σ t, T 1 = 375 × 0.874 = 326 kNm and T 2 = 301 × 0.874 = 263 kNm Summing the tension around the side-wall and neglecting frictional effects, the punch force is, approximately, F = 2 326 × 0.8 + 263 × 0.4 = 732 kN = 0.73 MN

4.5 Exercises

Ex. 4.1 A material is deforming in plane strain under a major tension of 340 kNm. The initial thickness is 0.8 mm and the material obeys an effective stress–strain relation σ = 700ε 0.22 MPa. What is the major strain at this point? [Ans: 0.062] Ex. 4.2 In the two-dimensional stamping operation shown in Figure 4.13, the side-walls are vertical and the face of the punch is flat. If the blank-holder force B is increased, determine the maximum strain that can be achieved at the centre-line if the coefficient of friction is 0.15 and the sheet obeys the stress strain law σ = 600ε 0.2 MPa. What is the blank-holder force required to reach this if the initial sheet thickness is 0.8 mm? [Ans: 0 .026 ; 2 B = 1780 kNm] B B e 1 × max. Figure 4.13 Section of a draw die with vertical sidewalls. Simplified stamping analysis 59 Ex. 4.3 For the operation in Ex. 4.2, determine the punch force at the maximum side-wall tension and obtain the ratio of blank-holder force to punch force. Ans: 676 kNm; 2.6] Ex. 4.4 At a point in a stamping process the sheet that is in contact with the punch is shown in Figure 4.3, but the sheet makes an angle of 60 ◦ at the tangent point. The strain at the mid-point O is 0.025. The punch has a face radius of 2 m, semi-width of 600 mm, and corner radius of 10 mm. The material obeys an effective stress strain relation of σ = 400ε 0.17 MPa and the initial thickness is 0.8 mm. Determine the tension at O, A and B if the coefficient of friction is 0.10. [Ans: 197, 203 and 219 kNm] 60 Mechanics of Sheet Metal Forming