Slip Lines

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Slipe line a method in plasticity

Transcript of Slip Lines

  • (slip lines)

    [ ]

  • , (friction hill)

    (upper bound analysis).

    ,

    .

    ,

    .

    1)

    2)

    3)

    ,

    (xy) .

    z Levy Misses

    .

    Tresca

    k->

    Von misses

    *k

    Tresca Von

    misses

  • .

    Mohr

    (Dieter)

    +

  • (1)

    (2)

    (3)

    1,2,3

    (4)

    (5)

    (6)

  • (7)

    (8)

    7,8

    .

    :

    (9)

    H l

    9

    (7) (8)

    .

    7,8

    (9)

    (10)

  • 9 10

    (11)

    (12)

    11 12

    (13)

    (14)

    1)

    2)

    ( Hencky)

    A D

    Hencky: ) (15)

    B C

    (16)

    15 16

  • (17)

    , C

    (18)

    3)

    ,

    Hencky .

    . .

    Hencky .

    4) ,,

    =

    5) Hencky:

    S :

    (19)

    R :

    (20)

    . M.Levy

    11 12

    7 8

    (21)

    (22)

  • .

    ,

    ,

    ,

    (23)

    ,

    (hosford)

    4

    .

    1

  • (hosford)

    OC: ( )

    () K

    Hencky

    P=2k(

    o

    .

  • (Hosford)

    .

    H/L

    .

    ,

  • Hencky , .

    P

    (0,1)

    Hencky . (1,1)

    (25)

    . (n,n)

    25.

  • .

    ]dy=0=>

    .

  • ,

    .O Hill

  • (R.Hill)

    .

    ,

    h .

    .

  • r<

    .

    .

    .

    x,y

    .

    (0,1)

    (n,n+1) , Hencky

    .

    , h=

  • ,

    .

    :

    .

    R.Hill: The Mathematical Theory of Plasticity

    Caddel-Hosford: Metal Forming Mechanics and Metallurgy

    L.M Kachanov: Fundamentals of the Theory of Plasticity

    Dieter: Mechanical Metallurgy

    W.W Sokolovsky :Theory of plasticity