Issue 76

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

Maximum strain max 

Average strain ave 

Minimum strain min 

Lengths of the second channel (mm)

Friction Coefficient f

Varition factor V (%)

0

1.70 1.69 1.76 1.68 1.68 1.68 1.81 1.61 1.64 1.66 1.76 1.61 1.63 1.65 1.76 1.7

1.53 1.56 1.61 1.51 1.54 1.58 1.64 1.45 1.49 1.54 1.61 1.45 1.48 1.6

1.09 1.18 1.38 1.13 1.04 1.16 1.33 1.07

11.8 10.7 6.14 11.3 12.8 11.3 7.71 12.4 14.4 14.4 10.4 11.3 13.9 13.4 12.6

0.1 0.2 0.3 0.1 0.2 0.3 0.1 0.2 0.3 0.1 0.2 0.3 0 0 0

L=20

L=30

0.951 1.03 1.22 0.987 1.01 1.11 1.13 1.2

L=40

L=50

1.5 1.6

12.3 Table 5: Evolution of the punch force, equivalent plastic strain, and variation factor as a function of L and f for an inner angle φ = 15° in the case of the 105° die 2-ECAE. Evolution of pressing force The evolution of the pressing force as a function of time for different channel lengths and friction conditions is presented in Fig. 18. It is evident that the maximum punch force increases with the rise in the friction coefficient, reflecting the additional resistance introduced at the billet–die interface. Quantitatively, the maximum pressing force varies between 13.1520 kN and 86.6768 kN for all simulated cases (see Tab. 6). This trend is consistent with the mechanics of the ECAE process, where higher friction enhances energy dissipation and impedes smooth sliding of the material along the die walls, thereby requiring greater extrusion loads. However, excessive friction may also promote flow localization, leading to non-uniform strain fields and potential surface damage. Interestingly, the analysis shows that the most homogeneous plastic strain distribution was obtained when the pressing force reached 50.4739 kN, corresponding to a channel length of L = 20 mm and a friction coefficient of f = 0.2. This result highlights the critical balance between applied load and strain uniformity: moderate friction levels contribute to improved strain homogenization without excessively increasing the extrusion force. Consequently, this case can be considered as an optimal compromise between mechanical efficiency and microstructural refinement.

100000

100000

f = 0 f = 0.1 f = 0.2 f = 0.3

f = 0 f = 0.1 f = 0.2 f = 0.3

80000

80000

60000

60000

40000

40000

Perssing Force ( N )

Perssing Force ( N )

20000

20000

0

0

0

20

40

60

80 100

0

20

40

60

80 100

Time ( s )

Time ( s )

(a) L=20mm

(b) L=30mm

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