5 Dry Laser Peening: Ultrashort Pulsed Laser Peening …
179
5.4 Plastic Deformation Induced by Ultrashort Pulsed
Laser-Driven Shock Wave
By taking the time derivative of the Orowan equation γ = kρbl [113], dγ
dt =
kb(ρdl/dt +ldρ/dt) is obtained, where γ is the plastic strain, ρ is the mobile dislocation density, b is the Burgers vector, l is the mean distance traveled by a dislocation,
t is the time, and k is a proportionality constant. The plastic strain rate dγ
dt is
expressed by the sum of the term for the velocity of dislocations dl
dt and the
generation of dislocations dρ
dt. In shock compression above the Hugoniot elastic
limit or high strain-rate deformation, the generation of dislocations dominates this
phenomenon premising that the velocity of dislocations does not exceed the sound
velocity. Dislocation nucleation takes place just behind the shock front to relieve
the stress caused by the lattice mismatch between regions in front and behind the
shock front [114]. In the case of conventional shocks, a part of the dislocations once
generated behind the shock front and multiplied in a release process is annihilated
due to residual heat, resulting in a residual density of one tenth of the highest density
once induced. In the case of femtosecond laser-driven shock, the major part of the
dislocations once induced remains due to much less dislocation annihilation because
of negligible heat effects, resulting in massive peening effects. This appears to be
the unique mechanism of dry laser peening without a sacrificial overlay under atmospheric conditions in comparison with other peening methods such as nanosecond
laser peening, shot peening, and ultrasonic peening.
When a peak pressure of a shock wave exceeds a threshold that depends on a
material, the pressure increases as a function of the time or the travel distance exhibits
a single structure, where the plastic component overtakes the elastic component. The
threshold stress for aluminum when the single structure of the shock front is clearly
formed is 25 GPa [37]. It was reported that the single structure was observed in the
surface layer of 500 nm in pure aluminum, which was irradiated using the intensity
of 8.7 × 10
12 W/cm
2 with the pulse duration of 150 fs [34]. Therefore, the shock
wave with a single structure over 25 GPa should be driven and propagated in the
2024 aluminum alloy, which was irradiated at the intensity of 1.2 × 10
14 W/cm
2
with the pulse duration of 130 fs in this research.
It was empirically observed that the strain rate η of the shock wave with the single
structure was proportional to the fourth-power of the shock stress σ [115, 116]. For
the aluminum alloy, η = 9100σ
4 has been reported [37]. Therefore, the strain rate
η of 3.5 × 10
9 s
−1 was obtained for the shock stress of 25 GPa. The dimensionless
Bland number B = 3hsη/8c was defined [115], where h is the sample thickness, c is
the bulk sound velocity under normal pressure, and s is the slope of the u p -u s relation,
u s = c + su p , where u p is the particle velocity and u s is the shock velocity. When
B is greater than 1, steady-wave conditions are expected [37]. The thickness h was
estimated to be 3.0 μm for B = 1, η = 3.5 × 10
9 s
−1 , s = 1.338, c = 5.328 km/s [117].
Therefore, the shock wave with the single structure propagates in the surface layer
of 3.0 μm. The single structure splits into two structures, elastic and plastic waves,
179
5.4 Plastic Deformation Induced by Ultrashort Pulsed
Laser-Driven Shock Wave
By taking the time derivative of the Orowan equation γ = kρbl [113], dγ
dt =
kb(ρdl/dt +ldρ/dt) is obtained, where γ is the plastic strain, ρ is the mobile dislocation density, b is the Burgers vector, l is the mean distance traveled by a dislocation,
t is the time, and k is a proportionality constant. The plastic strain rate dγ
dt is
expressed by the sum of the term for the velocity of dislocations dl
dt and the
generation of dislocations dρ
dt. In shock compression above the Hugoniot elastic
limit or high strain-rate deformation, the generation of dislocations dominates this
phenomenon premising that the velocity of dislocations does not exceed the sound
velocity. Dislocation nucleation takes place just behind the shock front to relieve
the stress caused by the lattice mismatch between regions in front and behind the
shock front [114]. In the case of conventional shocks, a part of the dislocations once
generated behind the shock front and multiplied in a release process is annihilated
due to residual heat, resulting in a residual density of one tenth of the highest density
once induced. In the case of femtosecond laser-driven shock, the major part of the
dislocations once induced remains due to much less dislocation annihilation because
of negligible heat effects, resulting in massive peening effects. This appears to be
the unique mechanism of dry laser peening without a sacrificial overlay under atmospheric conditions in comparison with other peening methods such as nanosecond
laser peening, shot peening, and ultrasonic peening.
When a peak pressure of a shock wave exceeds a threshold that depends on a
material, the pressure increases as a function of the time or the travel distance exhibits
a single structure, where the plastic component overtakes the elastic component. The
threshold stress for aluminum when the single structure of the shock front is clearly
formed is 25 GPa [37]. It was reported that the single structure was observed in the
surface layer of 500 nm in pure aluminum, which was irradiated using the intensity
of 8.7 × 10
12 W/cm
2 with the pulse duration of 150 fs [34]. Therefore, the shock
wave with a single structure over 25 GPa should be driven and propagated in the
2024 aluminum alloy, which was irradiated at the intensity of 1.2 × 10
14 W/cm
2
with the pulse duration of 130 fs in this research.
It was empirically observed that the strain rate η of the shock wave with the single
structure was proportional to the fourth-power of the shock stress σ [115, 116]. For
the aluminum alloy, η = 9100σ
4 has been reported [37]. Therefore, the strain rate
η of 3.5 × 10
9 s
−1 was obtained for the shock stress of 25 GPa. The dimensionless
Bland number B = 3hsη/8c was defined [115], where h is the sample thickness, c is
the bulk sound velocity under normal pressure, and s is the slope of the u p -u s relation,
u s = c + su p , where u p is the particle velocity and u s is the shock velocity. When
B is greater than 1, steady-wave conditions are expected [37]. The thickness h was
estimated to be 3.0 μm for B = 1, η = 3.5 × 10
9 s
−1 , s = 1.338, c = 5.328 km/s [117].
Therefore, the shock wave with the single structure propagates in the surface layer
of 3.0 μm. The single structure splits into two structures, elastic and plastic waves,