Penelitian tentang Simulasi Split Hopkinson Pressure Bar (SHPB)

1. Dynamic Simulations of a Split
Hopkinson Pressure Bar
Leonardo Gunawan Sahril Afandi Sitompul Tatacipta Dirgantara Ichsan Setya Putra
Lightweight Structure Research Group
Faculty of Mechanical and Aerospace Engineering
Institut Teknologi Bandung
Ganesa 10, Bandung 40132, Indonesia.
Email: gun@ae.itb.ac.id

2. Presentation Outline
• Introduction
• Objectives
• Theory of SHPB
• Design of SHPB
• FEM Model of SHPB
• Simulations: Results and Analysis
• Concluding Remarks

3. Introduction
• Mechanical properties of material at high strain rates are
needed in the analysis of structures loaded in a very short
time such as impact loads.
600
500
True Stress (MPa)
400
Strain Rate
300 (/sec)
100
200 10
1
0.1
100 0.001
0
0.0 0.1 0.2 0.3 0.4
Effective Plastic Strain
• This data is usually measured by using Split Hopkinson Pressure Bar (SHPB).

4. Intro (cont.)
400
D120-V9 Exp.
D120-V9 LS DYNA
300
Crushing Force, kN
200
100
0
-100
0 20 40 60 80 100 120
Crushing Distance, mm
• Research on the design of crush box is being
performed at Lightweight Structure RG of ITB
• Results at low impact speed have been obtained and
in good agreements with experimental results
• Prediction of response of crush box at high impact
speed need material model at high strain rates
• A SHPB is being developed. The design has been
established and some verification is needed to ensure
that it can perform as expected.

5. Objective
To verify the performance of SHPB design by
using numerical simulations
• The simulations were carried out by using FEM
software: LS-DYNA
• Ideal testing conditions: bar system and
specimen were aligned, and the striker hits the
incident bar uniformly.

6. Split Hopkinson Pressure Bar
• SHPB comprises three bars: striker bar, the incident
bar and the transmitter bar
• Sample of material is put between incident and
transmitter bar.
• A uni-axial compressive strain wave is generated in the
incident bar by shooting striker bar to the incident bar.
• The wave propagates to specimen. A part of strain
wave is reflected to incident bar in the form of tension
strain wave and other part is transmitted to the
Department for Strength of Materials, specimen and then to the transmitter bar in the form
Institute of Fundamental Technological of compressive wave.
Research - Polish Academy of Sciences • The strain waves in the input and transmitter bar are
sensed by strain gages bonded to those bars.
v1 v2
I
T
R
Incident bar LS Transmitter bar
Specimen
v Strain gage Strain gage
Striker bar Incident bar Specimen Transmitter bar

7. The wave traveling in the bar system is assumed to be 1-dimensional wave
The bars remain in elastic condition during the test
Strain rate, strain, and stress of specimen can be related to the strain of the
incident and transmitter bar
2C B
 S (t )  
  R (t ) LS: length of striker bar
LS
CB: speed of elastic wave in the bar
t
2C AB: area of bar
 S (t )   B   R (t ) dt
LS 0 AS: area of specimen
EB: Elastic modulus of bar
AB
 S (t )  E B  T (t )
AS

8. SHPB Design Equation
Main parameters in the design of SHPB: strain rate, strain and stress of
specimen. Speed of the striker bar can be determined from specified
stress and strain rates:
And by assuming that reflected strain is constant, then pulse length
needed to produce specimen strain is determined as function of
specimen length:
Length of striker bar = 0.5 Length of pulse
Length of incident and transmitter bar ≥ Length of pulse
(to avoid overlap between incident and reflected wave measured by
strain gage)

9. Initial design of SHPB was performed based on two critical
conditions:
• Test at maximum strain rate involves the highest stress in the
bar system which determines the maximum speed of the
striker bar. Since the bar system should be in elastic region,
this condition can also be used to determine the material of
the bars by selecting materials with yield strength higher than
the maximum stresses of the bar.
• Test at minimum strain rate which determines the minimum
length of the bars.

10. SHPB Design
Spec: max : 1 GPa, max : 0.5, d/dt : 103 – 104
• Diameter of incident, transmitter and striker bar was set to 25 mm.
• Diameter and thickness of specimen were set to 7 mm and 6 mm
respectively, to obtain high stress level.
Maximum strain case: Minimum strain case:
s= 1 GPa, s= 0.5, ds/dt = 104 s= 1 GPa, s= 0.2, ds/dt = 103
• vst = 64 m/s, Lp = 0.256 m • vst = 9.9 m/s, Lp = 1.027 m
• tp 5105 s, I = 1288 Mpa, • tp  2.6104 s
→ Lst = 0.128 m → Lst = 0.128 m
From this calculation:
Length of incident and transmitter bar = 1.5 m.
Material: 4340 Steel with y = 1620 MPa, E = 207 GPa, and r =
7850 kg/m3, for striker, incident and transmitter bar.

11. Numerical Simulations
Striker bar
Incident bar Specimen Transmitter bar
FEM model of the SHPB
Component Elements
Contact conditions:
Number Type Material Automatic node to surface contact
Striker bar 9000 Elastic between striker to incident bar,
Incident bar 36000 Constant Elastic
Transmitter bar 36000 stress solid Elastic
incident bar to specimen, and
element specimen to transmitter bar
Specimen 1800 Piecewise Boundary conditions:
Linear
Plasticity Node in plane of symmetry can not
move out of their plane
Initial Conditions:
Bar material: 4340 steel Striker bar has initial velocity and other
Specimen: DDQ steel bar have zero velocity

12. Simulation for high strain rate
• The strain waves generated in
the incident and transmitter
bar when the incident bar was
hit by 12.8 cm long striker
with velocity of 64 m/s (high
strain rate test case).
• tp  0.05 ms which was
predicted in the initial design
• Max I = -1380 MPa and T =-
77 Mpa
• The simulations indicated that
the bars are loaded in the
elastic region.

13. Simulation for low strain rate
• The strain waves generated in the
incident and transmitter bar
when the incident bar was hit by
51 cm long striker bar with
velocity of 9.9 m/s
• tp  0.26 ms which was predicted
in the initial design
• Max I = -187 MPa and T =-41
MPa
• The simulations indicated that the
bars are loaded in the elastic
region.

14. Calculation of strain rate, strain and stress
(shown only for high strain rate)
2C B
 S (t )  
  R (t )
LS
t
2C
 S (t )   B   R (t ) dt
LS 0
AB
 S (t )  E B  T (t )
AS

15. Stress and strain rates vs strain
• For high strain rate, the stress reaches 1 Gpa, strain 0.5 with strain rate around
104
• For low strain rate, the stress reaches 0.5 Gpa, strain 0.27 with strain rate around
103
• These results are in agreement with the specification of the device

16. Concluding Remarks
• A numerical simulations of a Split Hopkinson
Pressure Bar design has been carrried out with
satisfactory results.
• The results of the simulations indicated that the
designed SHPB can be used to perform
experiments with strain rates from 103 – 104, and
maximum stress 1 GPa.
• Further simulations for different type and size of
specimen can be performed to explore the
capability of the designed SHPB.

17. Thank you for your kind attention
This research is supported by ITB through “Riset KK” 2011.