Issue 76

H. Houri et alii, Fracture and Structural Integrity, 76 (2026) 238-264; DOI: 10.3221/IGF-ESIS.76.15









1

  

  

  

  

  

  



i 



 





ec

2cos

cos

(1)

2 2

2 2

3

where  is the corner angle. The total equivalent plastic strain for N cycles is: i N    

(2)

In the case of the modified ECAE process, known as equal-channel multiple angular extrusion (ECMAE) [20], the billet is extruded through a die consisting of several channels of identical cross-sections intersecting at fixed angles. Under these conditions, the equivalent plastic strain can be expressed as:

n



2



i





cot

(3)

2

3



i

1

where n is the number of intersection angles of the channels, it should be noted that. ECAE equipment realizes simple shear deformation with varied orientation of shear planes and extrusion with varied deformation intensity.

C ONSTITUTIVE MODELING

T

he mechanical response of polyamide under compression and various strain rates exhibits pronounced time dependent and rate-sensitive characteristics that cannot be accurately captured by conventional elastic–plastic formulations. To represent this behavior more realistically, the present study employs the Perzyna viscoplastic model [21], combined with a Voce-type nonlinear isotropic hardening law [22]. This constitutive framework provides a physically consistent description of the rate-dependent plastic flow and the saturation of hardening typically observed in polymeric materials. The model is formulated under small strain assumptions and assumes an additive decomposition of the total strain rate into its elastic and plastic components.

e p   ε ε ε   

(4)

where e ε  and p ε  denote the elastic and plastic strain rates, respectively. This decomposition assumes that the material response can be separated into a recoverable (elastic) part and a time dependent irreversible (plastic or viscoplastic) part, as commonly adopted in rate-dependent plasticity formulations. [21,22,23] The elastic behavior of the polyamide is considered linear and isotropic, following Hooke’s law:

: e p  σ C ε  

(5)

where e C is the isotropic elasticity tensor defined by Young’s modulus E and Poisson’s ratio ν . The tensor components can be expressed as:   e ijkl ij kl ik jl il jk C           (6) where ij  is Kronecker delta ( ij  =1 if i=j, otherwise 0),  and  are the Lamé parameters. This formulation ensures that the stress–strain relationship remains consistent with the principles of small deformations and isotropic elasticity.

241