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CRACK GROWTH IN NOTCHED SPECIMEN UNDER REPETITIVE IMPACTS

Presented By: Gayan Abeygunawardane-Arachchige

Gayan Abeygunawardane-ArachchigeProf. Vadim Silberschmidt

Wolfson School of Mechanical & Manufacturing Engineering, Loughborough University, UK

Mechanics of Advanced Materials Research Group

ISMMS 2015, Augustów, Poland, May 31 – June 3 2015

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

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Out line1. 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

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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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

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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.

Amplitudes of the oscillation of the screenerin vertical and horizontal directions

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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

conditionsStress Concentration; retrieved fromhttps://www.teachengineering.org

MODELLING OF CRACK GROWTH FORREPITITIVE LOADING CONDITIONS

/Finite Element Modelling

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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 initiationAnd propagation in ductile specimens with notches, Acta Mechanica, Special IssueMicro mechanics.

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

q– effective misses stress– pressure σy= yield stress of fully dense matrix

q1, q2, q3– GTN model parameters – defines the effective porosity

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*

,

,

,

c

F cc c c F

F cF

F

fif f f

f ff f f f if f f f

f fif f f

f

2

1 1 3

3F

q q qf

q

fc- Critical value of void volume fraction fF - Critical value of void volume fraction

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

Consideration of instrument setup for FE modelling

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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.

Fatigue Cycle – Shape and its characteristics

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Pendulum travelsinto the specimenalong (+y) direction

Pendulum reversethe direction from(+) y to (-) y

Pendulum travels in negative direction andreach to the initial position

Pendulum reversethe direction from(-) y to (+) y

Pendulum travelsinto the specimenalong (+y) direction

Calculation of Stress concentration factor

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For Double edge notched specimen; KI can be calculated as..

I

aK aF

b

Where a and b are length parameters and σ is the applied stress.

𝐹 (𝑎𝑏 )=1.12+0.203 (𝑎𝑏 )−1.197 (𝑎𝑏 )2

+1.930( 𝑎𝑏 )3

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1

1 ASME, the analysis of cracks Hand book, Tada et.al.2000

RESULTS AND DISCUSSION/Finite Element Modelling

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Results and discussion

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Impact Energy vs Number of Cycles

1 3 6 18 23 35 1130

0.0005

0.001

0.0015

0.002

0.0025

0.003

0.0035

0.004

Number of Cycles

Ener

gy (J

)

Impact energy reduces in an exponentialWay as the number of fatigue cycles increases

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

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

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

Results and discussion

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Shapes of crack path for different impact energies

0.06% of E 0.02% of E

0.009% of E

Results and discussion

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0 20 40 60 80 100 1200

5

10

15

20

25

30

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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

Number of Cycles (Nf)

crac

k le

ngt

h (

mm

)

Crack Propagation rate for different energy input

Results and discussion

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Experimental Results for mixed mode cracks – Al 1050

Employed Push- Pull fatiguetests 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

Results and discussion

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0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20

0.0002

0.0004

0.0006

0.0008

0.001

0.0012

0.0014

0.0016

1% of E

0.5% of E

0.1% of E

0.02% of E

0.009% of E

0.06% of E

KI (MPa√m)

da/d

N (m

/Cyc

le)

Crack Propagation rate Vs Stress Intensity factor ( From Simulation )

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. 25

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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