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equivalent plastic strain

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Effective plastic strain rate: ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 [ ] { } 2 / 1 2 2 2 2 2 2 2 3 2 3 2 p yz p xz p xy p zz p yy p xx p ij p ij p ε ε ε ε ε ε ε ε ε & & & & & & & & & + + + + + = = Effective plastic strain: ∫ = dt p p ε ε & For example uniaxial tension in the x-direction the strain rates are 0 0 0 5 . 0 5 . 0 = = = - = - = = p yz p xz p xy p zz p yy p xx ε ε ε ε ε ε ε ε ε & & & & & & & & & Where the -0.5 factors are from conservation of volume (“Plastic Poisson’s Ratio” = 0.5). The effective plastic strain rate is (29 ( 29 ( 29 { } (29 ε ε ε ε ε ε & & & & & & = = - + - + = 2 2 / 1 2 2 2 2 3 3 2 5 . 0 5 . 0 3 2 p So that for uniaxial loading the effective plastic strain rate is equal to the strain rate in the loading direction (this is the point of the 3 / 2 factor). This is similar conceptually to effective stress.

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Page 1: Equivalent Plastic Strain

Effective plastic strain rate:

( ) ( ) ( ) ( ) ( ) ( )[ ]{ } 2/12222222

3

2

3

2 pyz

pxz

pxy

pzz

pyy

pxx

pij

pij

p εεεεεεεεε &&&&&&&&& +++++==

Effective plastic strain:

∫= dtpp εε &

For example uniaxial tension in the x-direction the strain rates are

0

0

0

5.0

5.0

=

=

=

−=

−=

=

pyz

pxz

pxy

pzz

pyy

pxx

εε

εεε

εεεε

&

&

&

&&

&&

&&

Where the -0.5 factors are from conservation of volume (“Plastic Poisson’s Ratio” = 0.5). The effective plastic strain rate is

( ) ( ) ( ){ } ( ) εεεεεε &&&&&& ==−+−+= 22/1222

2

3

3

25.05.0

3

2p

So that for uniaxial loading the effective plastic strain rate is equal to the strain rate in the

loading direction (this is the point of the 3/2 factor). This is similar conceptually to effective stress.

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