PSI - Issue 68

Tuncay Yalçinkaya et al. / Procedia Structural Integrity 68 (2025) 325–331 Yalc¸inkaya et al. / Structural Integrity Procedia 00 (2024) 000–000

327

3

and the rollers had no axial and radial o ff set. While the diameter of the mandrel is 40 mm, the wall thickness of the preform is 4.12 mm. One end of the preform is clamped and forming by rotating rollers with a constant feed rate of 0.833mm / s and a rotational speed of 125 rpm.

2.2. Plasticity and Damage Models

J2 plasticity with isotropic hardening is used in modeling the plastic behavior of the IN718 alloy. The flow stress is described by the extended Voce hardening law that includes the e ff ect of temperature and strain rate: σ y = σ 0 + q 1 1 − c 1 e ( − b 1 ¯ ε p ) + q 2 1 − c 2 e ( − b 2 ¯ ε p ) 1 + C ln ˙¯ ε p ˙ ε 0 1 − θ − θ trans θ melt − θ trans m (1) where σ 0 is the initial yield stress (MPa) and ¯ ε p is the equivalent plastic strain, ˙ ε 0 is the reference strain rate ( s − 1 ) and q i , c i , b i are dimensionless material-specific parameters for hardening. C , θ , θ trans , θ melt and m are the parameters that define the strain rate; the current, transition and melting temperature and temperature sensitivity of the material, respectively. In the current study, the forming limit of IN718 in the flow forming process is assessed by applying ten distinct failure models which are calibrated against the experimental data that have been collected to predict the initiation of damage for di ff erent stress stares. All damage criteria and corresponding equations are given in the Table 1.

Table 1: Brief summary of selected typical uncoupled damage criteria.

Criterion

Damage relation

1 C 1 1 C 2 1 C 3 1 C 4 1 C 5 1 C 6 1 C 7 1 C 8 1 C 9 1 C 10

¯ ε p 0 ⟨ ¯ ε p 0 ⟨ ¯ ε p

Ayada

σ m ¯ σ ⟩ d ¯

D = D = D = D = D = D = D = D = D = D =

ε p

1 3 ⟩ d ¯ ε p d ¯ ε p

Ayada-m

σ 1 ¯ σ

+

2 σ 1 3( σ 1 − σ m )

Brozzo

0

¯ ε p

Ko-Huh (KH) Le-Roy (LR)

σ m ¯ σ ⟩ d ¯

σ 1 ¯ σ ⟨ 1

+ 3

ε p

0

¯ ε p 0 ( ¯ ε p 0 ¯ ε p

σ 1 − σ m ) d ¯ ε p

sinh

¯ σ

¯ σ d ¯

√ 3 2(1 − n ) ¯ σ d ¯

√ 3 2(1 − n )

McClintock (MC)

σ 1 − σ 2

3 4

σ 1 + σ 2

ε p

+

⟨ σ 1 ⟩

OH

ε p

0 ¯ ε p 0 exp ¯ ε p 0 ⟨ ¯ ε p 0 ¯ σ d ¯ ε p

3 σ m 2¯ σ d ¯

Rice-Trace (RT)

ε p

CL

σ 1 ⟩ d ¯ ε p

Freudenthal

σ 1 and σ 2 are the principal stresses. σ m is the mean stress ( σ m = ( σ 11 + σ 22 + σ 33 ) / 3) and ¯ σ is the von-Mises equivalent stress. C i ’ are the critical value of damage to be calibrated from experiments and ⟨ . ⟩ is the Macauley bracket. Although the damage criteria do not have any temperature related term, they are indirectly related to temperature through the stress term. For all models, the material is assumed to be initially defect free ( D = 0) and failure occurs when D reaches 1. The Ayada model introduces a description of void growth through a stress triaxiality parameter, while cut-o ff value of 1 / 3 is supplemented in the Ayada-m model as a modification. Both the e ff ects of normalized maximum principal stress and stress triaxiality are combined in the KH model. In the LR model, the nucleation, shape change, and coalescence of voids are considered incorporating the maximum principle and hydrostatic stress di ff erence. The Oh model normalizes the first principle stress with equivalent stress. The RT model relies on an exponential function of stress triaxiality. The McClintock’s model considers the equivalent stress, transverse principal stresses, and an exponent for strain hardening. The maximum principal stress is incorporated in the CL, while the von Mises equivalent stress is considered in the case of the Freudenthal. Remarkbly, all criteria includes only a single parameter to be calibrated from a single experiment.