1. CRACK GROWTH IN NOTCHED
SPECIMEN UNDER REPETITIVE IMPACTS
Presented By: Gayan Abeygunawardane-Arachchige
Gayan Abeygunawardane-Arachchige
Prof. Vadim Silberschmidt
Wolfson School of Mechanical & Manufacturing Engineering, Loughborough University, UK
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Mechanics of Advanced
Materials Research Group
ISMMS 2015, Augustów, Poland, May 31 – June 3 2015

2. Introduction
MINING COMPANY
LOGINOV AND PARTNERS
VIBRO-IMPACT MACHINES BASED ON
PARAMETRIC RESONANCE:
Concepts, mathematical modelling,
experimental verification and
implementation
Mechanics of Advanced
Materials Research Group

3. 3
Out line
1. Introduction and Motivation
 Mining and construction screening process
 Concept of parametric resonance (PR)
 Effect of notch shapes
 Aim of the study
2. Finite Element Method
 Calculation of Fracture Energy and impact vel.
 Constitutive model
 Material Properties
 Geometry, BCs of the model
 Boundary conditions
3. Results and Discussion
 Impact Energy vs Number of Cycles
 Von-Mises Stress variation ahead Crack Tip
 Shapes of crack paths for different impact
Energies
 Crack propagation rate for different energy
input
4. Conclusions
Mechanics of Advanced
Materials Research Group

4. Introduction
 The Purpose of the machine is to filter the mining product by
means of parametric vibration.
 The screener is a perforated plate which is clamped after
pretension
 The vibration is achieved by means of motors on the side of the
screener
 The screen is normally perforated by standard geometrical holes
( circular, rectangular )
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5. Introduction & Motivation
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 Failure of the screener is frequent and requires the
substitution of the perforated plate
 These failures happen first at the sides of the
screener, then at the middle of the plate
 The main reason for these failure is associated to
the PR conditions, due to the location of the cracks
 The effect of the granular particles on the screener
are still unknown

6. Introduction and Motivation(Cont..)
 A typical example of
Parametric vibration is the
swing due to the exchange of
angular momentum between
the swing and the swinger.
 It is suspected that notches
created by the holes initiates
cracks.
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Amplitudes of the oscillation of the screener
in vertical and horizontal directions

7. Introduction and Motivation(Cont..)
 The critical factor in investigating
the failure of the screen is to
analyse the effect of notch
shapes.
 Different geometries contributes
different stress concentration
levels for peculiar loading
conditions
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Stress Concentration; retrieved from
https://www.teachengineering.org

8. MODELLING OF CRACK GROWTH FOR
REPITITIVE LOADING CONDITIONS
/Finite Element Modelling
8

9. Calculation of Fracture Energy and Impact Velocity
 Fracture energy required - 2γA
 γ – Surface energy (kJ/m2)
 A – Fracture surface area
 From Schiavone et al. γ=1500 kJ/m2 and A=
rectangular cross section;
 This fracture energy should be supplied by
means of kinetic energy = 0.5mV2
 m; is taken as 3.14kg (mass of the pendulum)
 The velocity to complete fracture with a single impact is
361 mm/s.
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Schiavone A., G.Abeygunawardane Arachchige, Vadim Silberschmidt, Crack initiation
And propagation in ductile specimens with notches, Acta Mechanica, Special Issue
Micro mechanics.

10. Constitutive Modelling
 GTN Damage Model: spherical void growth at high triaxilities
developed to associate material plasticity; damage accumulation and could
predict the loss of resistance of porous materials
𝜑 =
𝑞
𝜎 𝑦
2
+ 2. 𝑞1. 𝑓. 𝑐𝑜𝑠ℎ
3. 𝑞2. 𝑝
2. 𝜎 𝑦
− 1 + 𝑞3. 𝑓2
q– effective misses stress 𝑝 – pressure σy= yield stress of fully dense matrix
q1, q2, q3– GTN model parameters 𝑓 – defines the effective porosity
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 *
,
,
,
c
F c
c c c F
F c
F
F
f
if f f
f f
f f f f if f f f
f f
if f f
f



    
 

2
1 1 3
3
F
q q q
f
q
 

fc- Critical value of void volume fraction fF - Critical value of void volume fraction

11. Material Properties
 Material – Al 1050a
 Young’s Modulus = 70 Gpa
 Poisson’s ratio = 0.33
 Hardening characteristic = initial yield stress with
85MPa with multi-linear curve based on experimental
tests
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Parameters of GTN model used in simulations of notched specimens
q1 q2 q3 εn Sn fn ff fc
1.5 1 2.25 0.1028 0.1 0.0249 0.04854 0.03103
Source – Schiavone A.2014

12. Consideration of instrument setup for FE modelling
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13. Specimen Geometry, BCs and /FE - Mesh
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• FE-Software - Abaqus/ Explicit 6.14
• Element – 4- Node bilinear, 2D plane stress,
reduced integration elements.

14. Fatigue Cycle – Shape and its characteristics
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Pendulum travels
into the specimen
along (+y) direction
Pendulum reverse
the direction from
(+) y to (-) y
Pendulum travels in negative direction and
reach to the initial position
Pendulum reverse
the direction from
(-) y to (+) y
Pendulum travels
into the specimen
along (+y) direction

15. Calculation of Stress concentration factor
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For Double edge notched specimen; KI can be calculated as..
I
a
K aF
b
 
 
  
 
Where a and b are length parameters and σ is the applied stress.
𝐹
𝑎
𝑏
= 1.12 + 0.203
𝑎
𝑏
− 1.197
𝑎
𝑏
2
+ 1.930
𝑎
𝑏
3
1
1
1 ASME, the analysis of cracks Hand book, Tada et.al.2000

16. RESULTS AND DISCUSSION
/Finite Element Modelling
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17. Results and discussion
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Impact Energy vs Number of Cycles
0
0.0005
0.001
0.0015
0.002
0.0025
0.003
0.0035
0.004
1 3 6 18 23 35 113
Energy(J)
Number of Cycles
Impact energy reduces in an exponential
Way as the number of fatigue cycles increases

18. Results and discussion
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Von-Mises Stress Distribution on the course during Crack Propagation ( For N=6 case)
N=1 N=2
N=3 N=4

19. Results and discussion
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Von-Mises Stress Distribution on the course during Crack Propagation ( For N=6 case)
N=5
N=6

20. Results and discussion
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Shapes of crack path for different impact energies
4% of E 1% of E
0.5% of E 0.1% of E
E – Energy required to break the specimen from single impact

21. Results and discussion
21
Shapes of crack path for different impact energies
0.06% of E 0.02% of E
0.009% of E

22. Results and discussion
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0
5
10
15
20
25
30
35
0 20 40 60 80 100 120
cracklength(mm)
Number of Cycles (Nf)
4% of E
1% of E
0.5% of E
0.1% of E
0.06% of E
0.02% of E
0.009% of E
Crack Propagation rate for different energy input

23. Results and discussion
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Experimental Results for mixed mode cracks – Al 1050
Employed Push- Pull fatigue
tests at a frequency of 10 Hz.
Makabe, C., et al. "Evaluation of fatigue crack propagation by mode I and mixed mode in 1050 aluminium.“
Fatigue & Fracture of Engineering Materials & Structures 30.4 (2007): 323-332

24. Results and discussion
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0
0.0002
0.0004
0.0006
0.0008
0.001
0.0012
0.0014
0.0016
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
da/dN(m/Cycle)
KI (MPa√m)
1% of E
0.5% of E
0.1% of E
0.02% of E
0.009% of E
0.06% of E
Crack Propagation rate Vs Stress Intensity factor ( From Simulation )

25. Conclusion
 GTN parameters determined under quasi static
conditions was used in this dynamic fatigue analysis.
 Based on the previous study (Schiavone et al.) ; two
types were observed based on crack propagation
direction.
 When the input energy is equal and above 1% of E; the
crack shape is similar to the crack shape observed for
quasi static tensile test.
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26. Conclusion
 GTN model does not include void distortion and inter
void linking in damage evolution.
 Though the location of the crack initiation is correct;
crack propagation rate is significantly rapid with the
GTN model compared with the experiments available.
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