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Analysis of surface crack on forward extruding bar during axisymmetric cup-bar combined extrusion process

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Abstract

In this paper, the kinematically admissible velocity field with surface crack on forward extruding bar is put forward during the axisymmetric cup-bar combined extrusion process, in accordance with the results of model experiments.

On the basis of velocity field, the necessary condition for surface crack formation on the forward extruding bar is derived, with the help of upper bound theorem and the minimum energy principle. Meanwhile, the relationships between surface crack formation and combination of reduction in area for the part of forward and backward extursions (ε b, εf),relative residual thickness of billet (T/R 0),frictional factor (m) or relative land length of ram and chamber (l b/R0, lf/R0)are calculated during the extrusion process. Therefore, whether the surface crack on forward exturding bar occurs can be predicted before extruding the lower-plasticity metals for axisymmetric cup-bar combined extrusion process.

The analytical results agree very well with experimental results of aluminium alloy LY12 (ASTM 2024) and LC4 (ASTM 7075).

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Abbreviations

J * :

total power consumption for plastic deformation

W i :

power of internal deformation

W s :

power to overcome shear losses on boundaries of velocity discontinuity

W f :

power to overcome friction losses

\(\dot \varepsilon _{ij} \) :

component of strain-rate tensor

¦ΔV ¦:

value of velocity discontinuity

U i :

velocity component in thei-direction

Γ i :

thei-th velocity discontinuity boundary

V :

volume of deformation zone

S d :

surface of velocity discontinuity

S f :

surface on which the friction exists

p ave/σ0 :

average relative ram pressure

σ 0 :

yield strength in uniaxial tension

\(\bar \sigma _s \) :

flow stress of the material being formed

ψ j :

reduction in area before necking occurs in uniaxial tension

ψ :

reduction in area

σ b :

ultimate tensile strength

ε 0 :

dimension of defect

R 0 :

chamber radius

R f :

exit radius of workpiece

R b :

ram radius

T f :

height of the deforming zone in the forward extrusion part (pseudo-independent parameter)

T 0 :

original height of billet

T :

height between ram and bottom of chamber

V b(Vf):

exit velocity of the backward (forward) extrusion part

H 0 :

height of Chamber wall

U 0 :

ram velocity

l b(lf):

land length of ram (chamber)

m :

friction factor, 0⩽m⩽1

ε b(εf):

reduction in area of the backward (foward) extrusion part of the combined extrusion

R n :

dividing radius

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Authors and Affiliations

  1. Northwest Polytechnical University, Xi'an

    Li Miao-quan, Wu Shi-chun & Tang Cai-rong

Authors
  1. Li Miao-quan
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  2. Wu Shi-chun
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  3. Tang Cai-rong
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Additional information

Communicated by Chien Wei-zang

The Projects Supported by the National Natural Science Foundation of China.

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Miao-quan, L., Shi-chun, W. & Cai-rong, T. Analysis of surface crack on forward extruding bar during axisymmetric cup-bar combined extrusion process. Appl Math Mech 11, 733–741 (1990). https://doi.org/10.1007/BF02015147

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  • DOI: https://doi.org/10.1007/BF02015147

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