Page 120 - Template Tesis UTM v2.0

True stresses of the specimen at the front face, and back face, are
2
1
calculated based on Equation 3.7 and 3.8, respectively [117].

( ) = x ( ( ) + ( )) (3.7)

1

( )

x
( ) = ( ) (3.8)
2

( )

Where ;

( ) - True stress of the specimen at the front face
1
( ) - True stress of the specimen at the back face
2
- Elastic modulus of the bar
- Areas of the bar

- Incident wave

- Transmitted wave

- Reflected wave

( ) - Instantaneous area of the specimen up to the point of fracture

Theoretically, stress ( ), strain ( ), and strain rate ( ̇) of the specimen can be

determined using Equation 3.9, 3.10 and 3.11, as found in the previous literatures

[113–115], with a few assumptions as follows [137];

i. Wave propagation in the Hopkinson bars is assumed to be in the axial direction,

as suggested by one-dimensional wave theory. Meanwhile, the wave dispersion
is negligible.

ii. A uniform and pure stress and strain are assumed for the cross-sectional areas

of the incident and transmitted bars.
iii. Radial and frictional effects are negligible during the collision.

iv. Both specimens have a flat surface and supposed to be in flawless contact
during the collision with the Hopkinson bars.

90