Tensile Electroforming Model - Electrically Assisted Forming - page 133

Manipulating

σ m A o , m
σ m + 1 A o , m + 1

= e − ε L , m + 1
e − ε L , m

(6.48)

σ m A o , m
σ m + 1 A o , m + 1

= e ( ε L , m − ε L , m + 1 )

(6.49)

ln σ m A o , m

− ln

σ m + 1 A o , m + 1

− ε L , m + ε L , m + 1 = 0

(6.50)

where the stress ( σ ) is defined by a modified power law relation that is a function
of temperature and strain for Mg AZ31:

σ m ε L , m ,total , T m

= K m ε n L , m ,total e ε L , m ,total s m

(6.51)

σ m + 1 ε L , m + 1,total , T m + 1

= K m + 1 ε n m + 1

L , m + 1,total e ε L , m + 1,total s m + 1

(6.52)

and

ε L , m ,total = ε i − 1

L , m ,acc + ε L , m

(6.53)

ε L , m + 1,total = ε i − 1

L , m + 1,acc + ε L , m + 1

(6.54)

where ε L , m ,total and ε L , m + 1,total are the total accumulative strain in element m and
m + 1 developed during forming at time step i , respectively. ε i − 1

L , m ,acc and ε i − 1 L , m + 1,acc

represent the total accumulative strain in element m and m + 1 from the start of
forming to the prior time step ( i − 1). ε L , m and ε L , m + 1 are the incremental strains
occurring during time step i for elements m and m + 1, respectively.
Such that K , n , and s are as follows:

T ≤ 25 ◦ C : K = K RT

25 ◦ C < T < 150 ◦ C : K = K 1 T + K 2
T ≥ 150 ◦ C :

K :=

(6.55)

K = K 3 exp ( K 4 T )

T ≤ 25 ◦ C : n = n RT

25 ◦ C < T < 150 ◦ C : n = n 1 T + n 2
T ≥ 150 ◦ C :

n :=

(6.56)

n = n 3 T + n 4

T < 120 ◦ C: s = 0

120 ◦ C ≤ T ≤ 327 ◦ C : s = s 1 T 2 + s 2 T + s 3
T > 327 ◦ C :

s :=

(6.57)

s = 0

where the coefficients are given in Table 6.4 .