Abstract
While there are many different methods known for determining the flow curves of materials for bulk metal forming, only a limited number of experiments can be applied for thin sheet metal. There are several reasons for this:
-
1.
For sheet metal the plastic anisotropy usually is of greater importance than for bulk metal forming. Therefore methods for determining flow curves of sheet metal should also enable one to obtain some information on anisotropy.
-
2.
The tensile test on sheet metal allows for the determination of the flow curve only for strains below uniform elongation because it is not possible to measure the contour of the neck with good accuracy. The upsetting test on sheet metal is limited to sheet thicker than 5 to 7 mm because otherwise the relative error of the measurements is too large. In ASTM E 9–81 /2.17/ also the compression of rectangular sheet specimens in planar direction is included whereby a jig is needed for lateral support of the test piece. Such tests, however, are somewhat complicated and the result may be influenced by friction.
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Abbreviations
- α:
-
zero approximation for the angle of twist
- B:
-
length of the head of a rectangular tension specimen (Fig. 3.1)
- β̄:
-
mean value of constant ß, see Eq. (3.27)
- C:
-
width of head of rectangular tension specimen (Fig. 3.1)
- C*:
-
constant in Eq..(‘3.10)
- ε1; ε2 :
-
engineering strain at forces F1 and F2, respectively, in tensile test on sheet specimens
- F1; F2 :
-
values of force F in tensile test on sheet specimens, see Eq. (3.5)
- f(τ):
-
“correction function”, defined by Eq. (3.14)
- f’ (τ):
-
derivate of f(τ); f’ (τ) = df (τ)/dτ
- f̄(M):
-
averaged value of f(τ), defined by Eq. (3.17)
- γ0 :
-
zero approximation for shear strain γ
- γ2 :
-
second approximation for shear strain γ
- h:
-
pole height in the hydraulic bulge test
- Lt :
-
total length of rectangular tension specimen (Fig. 3.1)
- p:
-
hydraulic pressure
- pk :
-
coefficient in Eq. (3.13)
- r:
-
distance from axis in the plane torsion test
- r:
-
actual radius of a reference circle in the hydraulic bulge test
- r0 :
-
initial value of r
- ri :
-
radius of inner clamp in the plane torsion test
- ra :
-
radius of outer clamp in the plane torsion test a
- rn :
-
“critical” radial distance in the plane torsion test n
- r̄:
-
mean normal anisotropy
- s0 :
-
initial value of sheet thickness
- s:
-
actual sheet thickness
- τn :
-
shear stress at the critical” radial distance in the plane torsion test
- ξ:
-
angle of inclination to the axis of a bar, see Fig. 3.9
- w0 :
-
initial width of rectangular tension specimen (Fig. 3.1)
- φs :
-
strain in thickness direction in tensile test on sheet metal
- φw :
-
strain in width direction in tensile test on sheet metal
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Pöhlandt, K. (1989). Determining Flow Curves of Sheet Metal. In: Materials Testing for the Metal Forming Industry. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-50241-5_3
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