jntukucev.ac.in · Web viewConventional monolithic materials have limitations with respect to achievable combinations of strength, stiffness, and density. In order to overcome these

52

SYNTHESIS AND CHARACTERIZATION OF NANO PARTICLE REINFORCED ALUMINIUM COMPOSITES

F.No.42 – 902/2013(SR)

Major Research Project Report

Submitted to

The University Grants Commission

New Delhi

By

Prof. G. Swami Naidu

Principal Investigator

Department of Metallurgical Engineering

University College of Engineering,Vizianagaram

JNTU Kakinada

Andhra Pradesh

INDIA

CONTENTS

SL. NO

CONTENT

PAGE NO

1

1.0 Introduction

02

2

2.0 Objectives

02

3

3. 0 research methodology and experimental studies

03

4

3.1 Raw Materials

03

5

3.2. X-Ray Diffraction Studies

03

6

3.3 Stir Casting

08

7

3.4 Homogenization

09

8

3.5 Hardness and upset tests

09

9

3.6 Wear Tests

09

10

4.0 Results and Discussion

11

11

4.1 Effect of composition on wear rate

11

12

4.1.1 Wear tests on pure Al

11

13

4.1.2 Wear tests on Al+5% red mud (micro)

12

14

4.1.3 Wear tests on Al+5% red mud (nano)

13

15

4.1.4 Wear tests on Al+10% red mud (micro)

14

16

4.1.5 Wear tests on Al+10% red mud (nano)

15

17

4.2 Deformation Studies

21

18

4.2.1 Effect of deformation on wear rate (Al+5% micro red mud)

21

19

4.2.2 Effect of deformation on wear rate (Al+5% nano red mud)

27

20


32

21


38

22

4.3 Microstructural observations

40

23

4.4. Regression Modelling

42

24

4.5. Artificial neural network modelling

43

25

4.5.1 Network training and testing

44

26

5.0 Conclusions

47

27

References

48

28

List of Publications

51

1.0 INTRODUCTION

Conventional monolithic materials have limitations with respect to achievable combinations of strength, stiffness, and density. In order to overcome these shortcomings and to meet the ever-increasing engineering demands of modern technology, metal matrix composites are gaining importance. In recent years, discontinuously reinforced aluminium metal matrix composites have attracted worldwide attention as a result of their potential to replace their monolithic counterparts primarily in automobile and energy sector. In the present work, nano red mud particke reinforced aluminium matrix composites are synthesized by stir casting successfully. Different weight fractions of red mud was mixed with the matrix material and tested for wear, mechanical properties and corrosion resistance studies. The merits of nano red mud reinforcement over micro red mud reinforcement will be determined. The best fraction of red mud reinforcing phase required in the composites for optimum properties will be determined. The proposed research work will be undertaken with an objective to explore the use of red mud as a reinforcing material as a low cost option.

The aluminium metal matrix composites are produced either by casting route or by powder metallurgy. Stir casting is widely used due to its simplicity, flexibility and applicability to large quantity production, hence the final cost of the product can also be minimized.

Redmud is the caustic insoluble waste residue generated by alumina production form bauxite by Bayer’s Process. The use of nano redmud as reinforcement material for preparation of MMC has not been explored till date.

The present work is focussing on the utilization of abundant available industrial waste redmud in useful manner by dispersing it into aluminium matrix to produce composites by liquid metallurgy route.

2.0 OBJECTIVES

The main objective of this work is to synthesize and characterize MMCs using nano redmud as reinforcement and aluminium as matrix material by liquid metallurgy route.

· To prepare samples with different weight fractions of both nano and micro structured redmud particles as reinforcement.

· To determine various mechanical properties of both nano and micro structured redmud reinforced Aluminium metal matrix composite.

· To conduct the upset tests to give different deformations to the samples.

· To conduct wear tests on a pin on disc wear testing machine to determine the wear characteristics of both micro and nano structured redmud reinforced Aluminium MMC.

3. RESEARCH METHODOLOGY AND EXPERIMENTAL STUDIES:

3.1 Raw Materials:

Red mud is obtained from NALCO, Bhubaneswar and its chemical analysis is furnished in Table 1.

CONSTITUENTS

% weight (wt)

CONSTITUENTS

% weight (wt)

Al2O3

15.0

Fe2O3

54.8

TiO2

3.7

SiO2

8.44

Na2O

4.8

CaO

2.5

P2O5

0.67

V2O5

0.38

Ga2O3

0.096

Mn

1.1

Zn

0.018

Mg

0.056

Organic C

0.88

L.O.I

Balance

Table 1. Chemical analysis of red mud

The redmud is subjected to sieve analysis using mechanical sieve shaker. Different particle sizes of 53 microns, 75 microns and 106 microns were obtained. Redmud of particle size 106 microns is taken for preparation of MMCs with microstructured reinforcement.

Micro structured redmud is reduced to nano structured using High energy Planetary Ball mill (Model Retsch, PM 100, Germany) at IIT, Chennai in a stainless steel chamber using tungsten carbide and zirconia balls of 10 mm Ø and 3mm Ø. The milling is carried for 30 hours by maintaining the rotation speed of the planet carrier at 200 rpm. The ball mill is loaded with ball to powder ratio (BPR) of 10:1. Toluene is used as the medium with an anionic surface agent to avoid agglomeration. The milled sample powder is taken out at intervals of 5 hrs and subjected for XRD analysis. .

3.2. X-Ray Diffraction Studies

The fresh as well as milled Red mud is characterized with an X-Ray Diffractometer (Model: 2036E201; Rigaku, Ultima IV, Japan). JADE software is used to investigate the structural changes and phase transformations of powders occured during mechanical milling. Sample preparation of XRD is done as per the standard practice. Sample packing is carried out by filling the Red mud on a glass slit of 12 X 12 X 2 mm size. Precautions are taken to have a tight powder packing on the glass slit and no manual contamination with the powder specimens. The X-ray diffraction measurements are carried out with the help of a Goniometer model 2036E201 using Cu Kα radiation (Kα= 1.54056 A0) at an accelerating voltage of 40 kV and a current of 20 mA. In this test the sample is kept in stationary condition, only the arms of the X- ray tube was rotating in the opposite direction up to 900 of 2θ during the test. The samples were scanned in the range from 30 to 900 of 2θ with a scan rate of 20 / min. The analysis is carried out to find out crystallite size, peak height, and amount of induced strains in the milled Red mud.

The average crystallite size is calculated from the full width at half maximum (FWHM) of the X-ray diffraction peak using Scherer’s equation (Cullity, 1978).

D = (k λ) / (B cosθ)

Where D is the particle diameter, λ is the X – Ray wavelength, B is the FWHM of the diffraction peak, θ is the diffraction angle and K is the Scherer’s constant of the order of unity for usual crystals. The existence of stress in the materials results in lattice distortions of crystals; consequently, the diffraction peaks of the crystals are broadened. The relationship between the half width of the broadened diffraction peaks, Bd and the distortion of lattice, (Δd/d) was described by Yang et al. (2000). The lattice distortion (Δd/d) can be obtained from the following equation.

(Δd/d) = Bd / (4 tanθ)

Where Bd, is half width of the broadened diffraction peaks, θ is half of the diffraction angle. During ball milling the intense mechanical deformation experienced by the Red mud leads to generation of lattice strains, crystal defects. The balance between cold welding and fracturing operations among the powder particles is expected to affect the structural changes in the powder. The measurement of crystallite size and lattice strain in the mechanically milled powders is very important since the phase constitution and transformation characteristics appear to be critically depending on them (Suryanarayana, 2001). A steady decrease in the crystallite size is observed and it is found that the crystallite size has been reduced from 400 nm to 40 nm for 30h milling time. The relative lattice strain is increasing with increasing the duration of milling time. This lattice strain is increased from 0.12 to 0.28 for as received and 30 h milled Red mud respectively.

The X-Ray diffractograms obtained at various time intervals of milling are shown in Figures 1-6 respectively. The X-ray diffractograms have revealed a small tungsten carbide contamination in the milled Red mud sample. This entry might be from the tungsten carbide balls which were used as milling media during milling; It is also evident that the intensity of the peaks in the XRD pattern got reduced and the peak broadening increased as the duration of milling increases. Three major phases were identified for all the milling times; which are MnSiO2, MgAl.79Fe1.21O4 and Al2Mg O4.

Fig 1. X-Ray Difractogram Obtained before Milling

Fig 2. X-Ray Difractogram Obtained after 6 hrs of Milling



Fig 5. X-Ray Diffractogram obtained after 24 hours of milling

Fig 6. X-Ray Diffractogram obtained after 30 hours of milling

Diffraction peak positions are accurately measured with XRD, which makes it the best method for characterizing homogeneous and inhomogeneous strains. Homogeneous or uniform elastic strain shifts the diffraction peaks positions. From the shift in peak positions, one can calculate the change in d-spacing, which is the result of the change of lattice constants under a strain. Inhomogeneous strains vary from crystallite to crystallite or within a single crystallite and this cause a broadening of the diffraction peaks. The XRD graphs illustrate that with increasing milling time the peak height intensity shift slightly to the lower heights and increasing the peak broadening. This is the indication of high energy milling decreases the crystallinity of the Red mud, thus increasing the amorphous phase in it.

3.3 Stir Casting

Pure aluminium is preheated in muffle furnace at around 2000C for 2 hours to remove any contamination. The required quantities of redmud (5, 10, 15 percent by weight) is taken and is preheated in a furnace upto 1000 C. The weighted quantity of pure aluminium is melted to the desired temperature of 8000C and redmud is then added to the molten metal and stirred continuously using mechanical stirrer. Argon gas is used to avoid any agglomeration. The melt with the nano redmud reinforced particulates is poured into cylindrical metal moulds. Using the similar method samples with the micro redmud reinforced particulates are also prepared.

After solidification, the castings are taken out form the moulds and are cut to the required shape and sizes for mechanical testing and for wear testing. To ascertain the distribution of reinforcement of redmud, the polished samples are inspected under optical microscope and the microstructures of the samples are shown in figures 7-8, the distribution of the reinforced redmud particles is uniform in the aluminium metal matrix.

Fig. 7. Optical micrograph (Al + 10% nano structured redmud)

Fig. 8. Optical micrograph (Al + 15% micro structured redmud)

3.4 Homogenization:

The samples are homogenized at 1000 C for 24 hours in a muffle furnace.

3.5 Hardness and upset tests:

Upset tests are conducted on compression testing machine and deformations of 10%, 20%, 30%, 40% are obtained for all the composites. The hardness tests are conducted usingVickers hardness tester and the results are furnished in table 2.

Metal/Composite

VHN.

10% def

20% def

30% def

40% def

Al + 5% micro structured Redmud

46.68

52.12

57.42

66.08

69.12


51.8

52.24

60.46

67.52

72.62


53.6

58.06

62.92

73.14

78.00

Al + 5% nano structured Redmud

49.8

54.44

65.97

75.20

76.27


54.08

63.76

77.81

80.42

80.90


59.28

65.17

79.20

80.56

82.26

Table 2. Hardness measurements

3.6 Wear Tests:

Wear Tests are conducted as per ASTM G-99 Standard under unlubricated condition in a normal laboratory atmosphere at 50-60% relative humidity and a temperature of 28-350C. Each test is carried for 5 hrs run. The mass loss in the specimen after each test is estimated by measuring the weight of the specimen before and after each test using an electronic weighing machine having an accuracy up to 0.01 mg. Care has been taken that the specimens under the test are continuously cleaned with woollen cloth to avoid entrapment of wear debris and to achieve uniformity in experimental procedure.

The tests have been carried under the following conditions:

The specimens under tests were fixed to the collect. The collect along with the specimen (Pin) is positioned at a particular track diameter. Load is applied through a dead weight loading system to press the pin against the disc. Frictional force arises at the contact can be read out from the controller. The speed of the disc or motor rpm can be varied through the controller. Each set of test was carried out for a period of 5 hours run. After each one hour run, the test pieces were removed from the machine and weighed accurately to determine the loss in weight.

Wear Calculations:

Wear rate was estimated by measuring the mass loss in the specimen after each test and mass loss, ∆m in the specimen is obtained. Wear rate which relates to the mass loos to sliding distance (L) is calculated using the expression

Wr = ∆m/L

The Volumetric wear rate Wv of the composite is relate to density (ρ) and the abrading time (t), was calculated using the expression,

Wv = ∆m/ρt

The friction force is measured for each pass and then averaged over the total number of passes for each wear test. The average value of co-efficient is calculated using the expression

µ = Ff / Fn

Where Ff is the average friction force and Fn is the applied load.

For characterisation of the abrasive wear behaviour of the composite, the specific wear rate is employed. It is defined as the volume loss of the composite per unit sliding distance and per unit applied normal load. The specific wear rate expressed in terms of the volumetric wear rate as

Ws = Wv / Vs Fn

Where Vs is the sliding velocity.

4.0 RESULTS AND DISCUSSION

4.1 Effect of composition on wear rate

4.1.1 Wear tests on pure Al:

Wear tests are conducted on pure aluminium samples using various loads ie., 10N, 20N, 30N at different speeds of 200 RPM, 400 RPM, 600 RPM and a few results are tabulated below.

Pure AlLoad – 10 NSpeed – 200 RPMρ = 2.62x103 Kg/m3

m1(gm)

m2(gm)

∆m(gm)

Time

Ff(N)

µ

R.D x 103(m)

Wrx10-6(N/m)

Wvx10-12(m3/sec)

Wsx10-13(m3/N-m)

1.384

1.37

0.014

3600

3.3

0.33

0.942478

0.145722

1.484047

5.668644

1.384

1.358

0.026

7200

3.3

0.33

1.884956

0.135314

1.378044

5.263741

1.384

1.342

0.042

10800

2.9

0.29

2.827433

0.145722

1.484047

5.668644

1.384

1.328

0.056

14400

3.3

0.33

3.769911

0.145722

1.484047

5.668644

1.384

1.32

0.064

18000

3

0.3

4.712389

0.133232

1.356843

5.18276

Table 3


m1(gm)

m2(gm)

∆m(gm)

Time

Ff(N)

µ

R.D x 103(m)

Wrx10-6(N/m)

Wvx10-12(m3/sec)

Wsx10-13m3/N-m

1.452

1.421

0.031

3600

4.9

0.49

1.884956

0.161335

3.286105

6.275998

1.452

1.399

0.053

7200

3.1

0.31

3.769911

0.137916

2.80909

5.364966

1.452

1.386

0.066

10800

4.7

0.47

5.654867

0.114496

2.332075

4.453934

1.452

1.362

0.09

14400

4.7

0.47

7.539822

0.117098

2.385076

4.55516

1.452

1.341

0.111

18000

4.3

0.43

9.424778

0.115537

2.353275

4.494425

Table 4


m1(gm)

m2(gm)

∆m(gm)

Time

Ff(N)

µ

R.D x 103(m)

Wrx10-6(N/m)

Wvx10-12(m3/sec)

Wsx10-13(m3/N-m)

1.658

1.61

0.048

3600

4.6

0.46

2.827433

0.16654

5.088163

6.47845

1.658

1.566

0.092

7200

4.8

0.48

5.654867

0.159601

4.876156

6.208515

1.658

1.526

0.132

10800

3.9

0.39

8.4823

0.152661

4.664149

5.938579

1.658

1.482

0.176

14400

4.4

0.44

11.30973

0.152661

4.664149

5.938579

1.658

1.434

0.224

18000

4.2

0.42

14.13717

0.155437

4.748952

6.046553

Table 5

4.1.2 Wear tests on Al+5% red mud (micro):

Wear tests are also conducted on Al+5% red mud (micro) samples using various loads ie., 10N, 20N, 30N at different speeds of 200 RPM, 400 RPM, 600 RPM and a few results are tabulated below.

Al+5% Micro RMLoad – 10 NSpeed – 200 RPMρ = 2.42x103 Kg/m3

m1(gm)

m2(gm)

∆m(gm)

Time

Ff(N)

µ

R.D x 103(m)

Wrx10-6(N/m)

Wvx10-12(m3/sec)

Wsx10-13(m3/N-m)

1.362

1.352

0.01

3600

3.4

0.34

0.942478

0.104087

1.143271

4.366975

1.362

1.344

0.018

7200

3.8

0.38

1.884956

0.093679

1.028944

3.930278

1.362

1.336

0.026

10800

4.2

0.42

2.827433

0.090209

0.990835

3.784712

1.362

1.327

0.035

14400

3.6

0.36

3.769911

0.091076

1.000362

3.821103

1.362

1.318

0.044

18000

4.8

0.48

4.712389

0.091597

1.006079

3.842938

Table 6

Al+5% Micro RM Load – 10 NSpeed – 400 RPMρ = 2.42x103 Kg/m3

m1(gm)

m2(gm)

∆m(gm)

Time

Ff(N)

µ

R.D x 103(m)

Wrx10-6(N/m)

Wvx10-12(m3/sec)

Wsx10-13m3/N-m

1.452

1.43

0.022

3600

4.7

0.47

1.884956

0.114496

2.515197

4.803673

1.452

1.412

0.04

7200

5.6

0.56

3.769911

0.104087

2.286543

4.366975

1.452

1.397

0.055

10800

5.5

0.55

5.654867

0.095413

2.095998

4.00306

1.452

1.378

0.074

14400

5.6

0.56

7.539822

0.096281

2.115052

4.039452

1.452

1.356

0.096

18000

5.9

0.59

9.424778

0.099924

2.195081

4.192296

Table 7


m1(gm)

m2(gm)

∆m(gm)

Time

Ff(N)

µ

R.D x 103(m)

Wrx10-6(N/m)

Wvx10-12(m3/sec)

Wsx10-13(m3/N-m)

1.448

1.412

0.036

3600

5.8

0.58

2.827433

0.124905

4.115777

5.24037

1.448

1.38

0.068

7200

6.4

0.64

5.654867

0.117966

3.887123

4.949238

1.448

1.357

0.091

10800

6.2

0.62

8.4823

0.105244

3.467923

4.415497

1.448

1.329

0.119

14400

7.2

0.72

11.30973

0.10322

3.401232

4.330584

1.448

1.291

0.157

18000

7.3

0.73

14.13717

0.108945

3.589872

4.570767

Table 8

4.1.3 Wear tests on Al+5% red mud (nano):

Wear tests are also conducted on Al+5% red mud (nano) samples using various loads ie., 10N, 20N, 30N at different speeds of 200 RPM, 400 RPM, 600 RPM and a few results are tabulated below.

Al+5% Nano RMLoad – 10 NSpeed – 200 RPMρ = 2.37x103 Kg/m3

m1(gm)

m2(gm)

∆m(gm)

Time

Ff(N)

µ

R.D x 103(m)

Wrx10-6(N/m)

Wvx10-12(m3/sec)

Wsx10-13(m3/N-m)

1.484

1.476

0.008

3600

3.3

0.33

0.942478

0.08327

0.937018

3.579143

1.484

1.469

0.015

7200

3.4

0.34

1.884956

0.078065

0.878454

3.355447

1.484

1.463

0.021

10800

3.2

0.32

2.827433

0.072861

0.81989

3.13175

1.484

1.457

0.027

14400

2.8

0.28

3.769911

0.070259

0.790609

3.019902

1.484

1.449

0.035

18000

3.3

0.33

4.712389

0.072861

0.81989

3.13175

Table 9


m1(gm)

m2(gm)

∆m(gm)

Time

Ff(N)

µ

R.D x 103(m)

Wrx10-6(N/m)

Wvx10-12(m3/sec)

Wsx10-13m3/N-m

1.682

1.667

0.015

3600

4.7

0.47

1.884956

0.078065

1.756908

3.355447

1.682

1.653

0.029

7200

5.5

0.55

3.769911

0.075463

1.698344

3.243599

1.682

1.638

0.044

10800

5.6

0.56

5.654867

0.076331

1.717866

3.280881

1.682

1.623

0.059

14400

5.5

0.55

7.539822

0.076764

1.727626

3.299523

1.682

1.608

0.074

18000

5.3

0.53

9.424778

0.077025

1.733482

3.310708

Table 10


m1(gm)

m2(gm)

∆m(gm)

Time

Ff(N)

µ

R.D x 103(m)

Wrx10-6(N/m)

Wvx10-12(m3/sec)

Wsx10-13(m3/N-m)

1.494

1.466

0.028

3600

4.6

0.46

2.827433

0.097148

3.279561

4.175667

1.494

1.444

0.05

7200

5.2

0.52

5.654867

0.086739

2.92818

3.728274

1.494

1.426

0.068

10800

5.4

0.54

8.4823

0.078644

2.654883

3.380302

1.494

1.402

0.092

14400

5.6

0.56

11.30973

0.0798

2.693925

3.430012

1.494

1.378

0.116

18000

5.8

0.58

14.13717

0.080494

2.717351

3.459839

Table 11

4.1.4 Wear tests on Al+10% red mud (micro):

Wear tests are also conducted on Al+10% red mud (micro) samples using various loads ie., 10N, 20N, 30N at different speeds of 200 RPM, 400 RPM, 600 RPM and a few results are tabulated below


m1(gm)

m2(gm)

∆m(gm)

Time

Ff(N)

µ

R.D x 103(m)

Wrx10-6(N/m)

Wvx10-12(m3/sec)

Wsx10-13(m3/N-m)

1.416

1.408

0.008

3600

4.2

0.42

0.942478

0.08327

0.906805

3.463742

1.416

1.402

0.014

7200

3.8

0.38

1.884956

0.072861

0.793455

3.030774

1.416

1.396

0.02

10800

4.6

0.46

2.827433

0.069392

0.755671

2.886451

1.416

1.388

0.028

14400

4.4

0.44

3.769911

0.072861

0.793455

3.030774

1.416

1.38

0.036

18000

4.3

0.43

4.712389

0.074943

0.816125

3.117367

Table 12


m1(gm)

m2(gm)

∆m(gm)

Time

Ff(N)

µ

R.D x 103(m)

Wrx10-6(N/m)

Wvx10-12(m3/sec)

Wsx10-13m3/N-m

1.452

1.435

0.017

3600

7.2

0.72

1.884956

0.088474

1.926962

3.680225

1.452

1.423

0.029

7200

5.8

0.58

3.769911

0.075463

1.643585

3.139016

1.452

1.411

0.041

10800

6.4

0.64

5.654867

0.071126

1.549126

2.958613

1.452

1.396

0.056

14400

7.4

0.74

7.539822

0.072861

1.58691

3.030774

1.452

1.382

0.07

18000

6.8

0.68

9.424778

0.072861

1.58691

3.030774

Table 13


m1(gm)

m2(gm)

∆m(gm)

Time

Ff(N)

µ

R.D x 103(m)

Wrx10-6(N/m)

Wvx10-12(m3/sec)

Wsx10-13(m3/N-m)

1.458

1.432

0.026

3600

5.9

0.59

2.827433

0.090209

2.947118

3.752387

1.458

1.41

0.048

7200

6.2

0.62

5.654867

0.08327

2.720416

3.463742

1.458

1.388

0.07

10800

6.4

0.64

8.4823

0.080957

2.644849

3.367527

1.458

1.362

0.096

14400

7.2

0.72

11.30973

0.08327

2.720416

3.463742

1.458

1.342

0.116

18000

6.8

0.68

14.13717

0.080494

2.629736

3.348284

Table 14

4.1.5 Wear tests on Al+10% red mud (nano):

Wear tests are also conducted on Al+10% red mud (nano) samples using various loads ie., 10N, 20N, 30N at different speeds of 200 RPM, 400 RPM, 600 RPM and a few results are tabulated below


m1(gm)

m2(gm)

∆m(gm)

Time

Ff(N)

µ

R.D x 103(m)

Wrx10-6(N/m)

Wvx10-12(m3/sec)

Wsx10-13(m3/N-m)

0.97

0.964

0.006

3600

3.7

0.37

0.942478

0.062452

0.685937

2.620087

0.97

0.96

0.01

7200

4.3

0.43

1.884956

0.052044

0.571614

2.183406

0.97

0.956

0.014

10800

4.7

0.47

2.827433

0.048574

0.533507

2.037846

0.97

0.95

0.02

14400

1.2

0.12

3.769911

0.052044

0.571614

2.183406

0.97

0.94

0.03

18000

2.9

0.29

4.712389

0.062452

0.685937

2.620087

Table 15


m1(gm)

m2(gm)

∆m(gm)

Time

Ff(N)

µ

R.D x 103(m)

Wrx10-6(N/m)

Wvx10-12(m3/sec)

Wsx10-13m3/N-m

0.941

0.939

0.002

3600

1.38

0.138

1.884956

0.010409

0.228646

0.436681

0.941

0.935

0.006

7200

1.6

0.16

3.769911

0.015613

0.342969

0.655022

0.941

0.929

0.012

10800

2.2

0.22

5.654867

0.020817

0.457292

0.873362

0.941

0.914

0.027

14400

1.7

0.17

7.539822

0.035129

0.771679

1.473799

0.941

0.909

0.032

18000

1.5

0.15

9.424778

0.033308

0.731666

1.39738

Table 16


m1(gm)

m2(gm)

∆m(gm)

Time

Ff(N)

µ

R.D x 103(m)

Wrx10-6(N/m)

Wvx10-12(m3/sec)

Wsx10-13(m3/N-m)

1.201

1.195

0.006

3600

2.5

0.25

2.827433

0.020817

0.685937

0.873362

1.201

1.193

0.008

7200

2.1

0.21

5.654867

0.013878

0.457292

0.582242

1.201

1.189

0.012

10800

2.3

0.23

8.4823

0.013878

0.457292

0.582242

1.201

1.185

0.016

14400

2.2

0.22

11.30973

0.013878

0.457292

0.582242

1.201

1.183

0.018

18000

2

0.2

14.13717

0.01249

0.411562

0.524017

Table 17

The plots drawn between wear rate and sliding distance at different loads and sliding speeds for various materials are shown in Fig. 9-17.

(Load : 10NSpeed 200 RPM)

Fig. 9. Plots showing wear rate at 10 N and 200 rpm

















From the above plots, it is clear that at constant sliding speed and constant load the wear rate is decreased with the increased fraction of red mud particles in the composite. From the above investigations, significant increase in wear resistance is observed with the addition of nano structured remud particles compared to that of micro structured redmud particles in the composites. The addition of 5% weight fraction of nano redmud particles have given improved wear resistance than 10% weight fraction of micro structured redmud particles. Highly significant improvement in the wear resistance is observed in the case of composites with 10% weight fraction of nano redmud particles. The surface properties of red mud changes considerably with increased ball milling and hence the surface energy and inter atomic bonding will also increase.

4.2 Deformation Studies


Upset tests are conducted on Al+5% red mud (micro) samples using compression testing machine and 10%, 20%, 30% and 40% deformations are obtained. Wear tests are conducted for the above samples with various loads ie., 10N, 20N, 30N at different speeds of 200 RPM, 400 RPM, 600 RPM and a few results are tabulated below.


Deformation – 10%

m1(gm)

m2(gm)

∆m(gm)

Time

Ff(N)

µ

R.D x 103(m)

Wrx10-6(N/m)

Wvx10-12(m3/sec)

Wsx10-13(m3/N-m)

1.408

1.397

0.011

3600

6.9

0.69

0.942478

0.114496

1.257599

4.803673

1.408

1.389

0.019

7200

6.8

0.68

1.884956

0.098883

1.086108

4.148626

1.408

1.38

0.028

10800

7.2

0.72

2.827433

0.097148

1.067053

4.075843

1.408

1.372

0.036

14400

8.2

0.82

3.769911

0.093679

1.028944

3.930278

1.408

1.361

0.047

18000

6.5

0.65

4.712389

0.097842

1.074675

4.104957

Table 18


Deformation – 10%

m1(gm)

m2(gm)

∆m(gm)

Time

Ff(N)

µ

R.D x 103(m)

Wrx10-6(N/m)

Wvx10-12(m3/sec)

Wsx10-13m3/N-m

1.495

1.472

0.023

3600

7.8

0.78

1.884956

0.1197

2.629524

5.022021

1.495

1.454

0.041

7200

5.9

0.59

3.769911

0.10669

2.343706

4.476149

1.495

1.44

0.055

10800

7.2

0.72

5.654867

0.095413

2.095998

4.00306

1.495

1.421

0.074

14400

6.4

0.64

7.539822

0.096281

2.115052

4.039452

1.495

1.401

0.094

18000

6.5

0.65

9.424778

0.097842

2.14935

4.104957

Table 19


Deformation – 10%

m1(gm)

m2(gm)

∆m(gm)

Time

Ff(N)

µ

R.D x 103(m)

Wrx10-6(N/m)

Wvx10-12(m3/sec)

Wsx10-13(m3/N-m)

1.456

1.424

0.032

3600

6.4

0.64

2.827433

0.111026

3.658468

4.658107

1.456

1.398

0.058

7200

5.4

0.54

5.654867

0.100618

3.315487

4.221409

1.456

1.37

0.086

10800

5.8

0.58

8.4823

0.099461

3.277378

4.172887

1.456

1.337

0.119

14400

6.4

0.64

11.30973

0.10322

3.401232

4.330584

1.456

1.302

0.154

18000

6.8

0.68

14.13717

0.106863

3.521276

4.483428

Table 20

(Al + 5% Micro RMLoad : 10NSpeed : 200 RPM)

Fig. 18. Plots showing wear rate at 10 N and 200 rpm (Al + 5% Micro RM)


















Upset tests are conducted on Al+5% red mud (nano) samples using compression testing machine and 10%, 20%, 30% and 40% deformations are obtained. Wear tests are conducted for the above samples with various loads ie., 10N, 20N, 30N at different speeds of 200 RPM, 400 RPM, 600 RPM and a few results are tabulated below.


Deformation – 10%

m1(gm)

m2(gm)

∆m(gm)

Time

Ff(N)

µ

R.D x 103(m)

Wrx10-6(N/m)

Wvx10-12(m3/sec)

Wsx10-13(m3/N-m)

1.482

1.474

0.008

3600

6.9

0.69

0.942478

0.08327

0.937018

3.579143

1.482

1.468

0.014

7200

6.8

0.68

1.884956

0.072861

0.81989

3.13175

1.482

1.462

0.02

10800

7.2

0.72

2.827433

0.069392

0.780848

2.982619

1.482

1.455

0.027

14400

8.2

0.82

3.769911

0.070259

0.790609

3.019902

1.482

1.447

0.035

18000

6.5

0.65

4.712389

0.072861

0.81989

3.13175

Table 21


Deformation – 10%

m1(gm)

m2(gm)

∆m(gm)

Time

Ff(N)

µ

R.D x 103(m)

Wrx10-6(N/m)

Wvx10-12(m3/sec)

Wsx10-13m3/N-m

1.485

1.47

0.015

3600

7.8

0.78

1.884956

0.078065

1.756908

3.355447

1.485

1.456

0.029

7200

5.9

0.59

3.769911

0.075463

1.698344

3.243599

1.485

1.441

0.044

10800

7.2

0.72

5.654867

0.076331

1.717866

3.280881

1.485

1.426

0.059

14400

6.4

0.64

7.539822

0.076764

1.727626

3.299523

1.485

1.412

0.073

18000

6.5

0.65

9.424778

0.075984

1.710057

3.265968

Table 22


Deformation – 10%

m1(gm)

m2(gm)

∆m(gm)

Time

Ff(N)

µ

R.D x 103(m)

Wrx10-6(N/m)

Wvx10-12(m3/sec)

Wsx10-13(m3/N-m)

1.478

1.453

0.025

3600

5.8

0.58

2.827433

0.086739

2.92818

3.728274

1.478

1.432

0.046

7200

6.2

0.62

5.654867

0.0798

2.693925

3.430012

1.478

1.411

0.067

10800

6.4

0.64

8.4823

0.077487

2.615841

3.330592

1.478

1.391

0.087

14400

5.8

0.58

11.30973

0.075463

2.547516

3.243599

1.478

1.367

0.111

18000

6.6

0.66

14.13717

0.077025

2.600224

3.310708

Table 23

(Al + 5% Nano RMLoad : 10NSpeed : 200 RPM)

Fig. 27. Plots showing wear rate at 10 N and 200 rpm (Al + 5% Nano RM)


















Upset tests are conducted on Al+10% red mud (micro) samples using compression testing machine and 10%, 20%, 30% and 40% deformations are obtained. Wear tests are conducted for the above samples with various loads ie., 10N, 20N, 30N at different speeds of 200 RPM, 400 RPM and 600 RPM and the results are tabulated below.


Deformation – 10%

m1(gm)

m2(gm)

∆m(gm)

Time

Ff(N)

µ

R.D x 103(m)

Wrx10-6(N/m)

Wvx10-12(m3/sec)

Wsx10-13(m3/N-m)

1.408

1.4

0.008

3600

6.9

0.69

0.942478

0.08327

0.906805

3.463742

1.408

1.394

0.014

7200

6.8

0.68

1.884956

0.072861

0.793455

3.030774

1.408

1.388

0.02

10800

7.2

0.72

2.827433

0.069392

0.755671

2.886451

1.408

1.381

0.027

14400

8.2

0.82

3.769911

0.070259

0.765117

2.922532

1.408

1.373

0.035

18000

6.5

0.65

4.712389

0.072861

0.793455

3.030774

Table 24


Deformation – 10%

m1(gm)

m2(gm)

∆m(gm)

Time

Ff(N)

µ

R.D x 103(m)

Wrx10-6(N/m)

Wvx10-12(m3/sec)

Wsx10-13m3/N-m

1.454

1.438

0.016

3600

6.8

0.68

1.884956

0.08327

1.813611

3.463742

1.454

1.425

0.029

7200

7.2

0.72

3.769911

0.075463

1.643585

3.139016

1.454

1.412

0.042

10800

5.4

0.54

5.654867

0.072861

1.58691

3.030774

1.454

1.4

0.054

14400

6.4

0.64

7.539822

0.070259

1.530234

2.922532

1.454

1.386

0.068

18000

6.6

0.66

9.424778

0.070779

1.541569

2.94418

Table 25


Deformation – 10%

m1(gm)

m2(gm)

∆m(gm)

Time

Ff(N)

µ

R.D x 103(m)

Wrx10-6(N/m)

Wvx10-12(m3/sec)

Wsx10-13(m3/N-m)

1.485

1.458

0.027

3600

6.4

0.64

2.827433

0.093679

3.060468

3.896709

1.485

1.437

0.048

7200

6.2

0.62

5.654867

0.08327

2.720416

3.463742

1.485

1.415

0.07

10800

6.3

0.63

8.4823

0.080957

2.644849

3.367527

1.485

1.392

0.093

14400

6.8

0.68

11.30973

0.080668

2.635403

3.3555

1.485

1.368

0.117

18000

5.4

0.54

14.13717

0.081188

2.652406

3.377148

Table 26



















The deformation studies have shown that, for all the compositions, the wear resistance is increased with deformation. This could be due to the increased dislocation density with increased deformation. The strain hardening increases with the increased deformation and caused for the reduced wear. The decreased wear indicates that the addition of red mud to aluminium matrix caused for the increase in ductility and no brittleness enhancement.

4.2.4 Effect of deformation on wear rate (Al+10% nano red mud):

The hardness of the pure aluminium as well as Al-Red mud composites was increased with increase in deformation. This might be due to the existence of strain hardening effects form matrix materials and also from the rule of mixture of composite strengthening (Callister, 2007). The coefficient of friction in all cases decreases with the increase of normal load. This decrease in value occurs likely as a result of particulate standing above the surface making contacting area of the specimen smaller. In addition, this decrease in coefficient of friction may be attributed to the wear of the matrix from the pin surface leaving the particulates standing proud. A similar change in coefficients of friction has been observed by M.H. Korkut (2003) for the newly developed Al 2024 composites. The effect of deformation on wear rate with sliding distance at various loads and sliding velocities are furnished in Fig 45.

Fig 45. The effect of deformation on wear rate with sliding distance

4.3 Microstructural observations:

The worn-out surfaces of some selected specimens after the wear test are observed under optical microscope and are shown in Fig 46 and 47. It is observed that cavities are formed in the matrix of the composite and have aligned parallel to the direction of sliding during slow sliding velocity i.e. at 200 RPM. The amount of cavities is reduced with increase in sliding velocities and minimum cavities are observed with sliding velocity 600RPM. In some regions, the substructures are aligned parallel to the sliding direction. The worn surfaces at higher sliding speeds are relatively smoother than at lower sliding speeds. Cracks have appeared for the same sliding speed with increased load and these might have helped in chipping of hard red mud particles. With increase in applied load although the amount of cavitations appears to be low but deep cracks and grooves are clearly visible in the optical micrographs at higher loads. The optical micrographs depict that when the sample is rubbed, against steel wheel, at low sliding speed and low applied load hard particles might have chipped off and the aluminium grains are grown into bigger sizes with increase in applied load and the aluminium matrix appears to be smeared along the direction of the sliding. From the micrograph, it is seen that some cracks are originated at the grain boundaries of aluminium. This might be due to (Savchenko et al., 2002) strain hardening of aluminium during sliding with the applied load and due to pulling up of hard red mud particles from the aluminium grain boundaries (Korkut, 2004). With increasing the applied load this effect is more pronounced. This might have been caused also due to embrittlement of hard particles during sliding.

(10µ) (10µ) (b) (a)

(c) (10µ)

Fig 46. Optical micrographs of Al-10% nano structured red mud composite after wear tests at 10N load (a) 200 RPM (b) 400 RPM (c) 600 RPM

(10µ) (a)

(10µ) (b) (cw) (10µ)

Fig. 47 Optical micrographs of Al-10% nano structured red mud composite after wear tests at 600 RPM speed (a) 10N (b) 20N (c) 30N

4.4. Regression Modelling

Polynomial additive and multiplicative models were tried and the following model has been developed using regression analysis.

Where F is the load applied, Vs is the sliding velocity, C is the percent composition of redmud and D is the percent deformation.

The consistency and fitness with the experimental data was tested using R-Software. The following empirical values were obtained for the above model.

A0 = 0.6257456, A1 = -0.0548196, A2 = -0.00390050, A3 = 0.00247220, A4 = 0.00006446

The model fitness is measured with R square value and accuracy of forecast is measured with mean absolute percent error (MAPE). The R square value for the above model is 0.9775 and MAPE is 12.96%. If MAPE calculated is less than 10%, it is interpreted as excellent accurate forecasting, between 10-20% good forecasting, between 20-50% acceptable forecasting and over 50% inaccurate forecasting [20]. An R square value of 0.9 or above is very good, a value above 0.8 is good, and a value of 0.6 or above may be satisfactory in some applications [21]. The R square and MAPE values obtained are in the well acceptable range and hence the present model can be adapted effectively.

4.5. Artificial neural network modelling

The main components of artificial neuron are, weights, addition function, activation function and outputs and is represented in figure 48. Input data can be obtained from external environment or the other artificial neurons. The quantities (wij) demonstrate the effect of a data point when it arrives at artificial neural cell. The addition function netij calculates the net input on a neural cell.

..... (3)

Where Ɵi is the threshold value of ith process element, xi indicates the i input, wij is the connection weight from j element to i element.

The artificial neuron output value, which depends on the selected activation function employs a sigmoid function as the activation function and is calculated using eq.4

..... (4)

The sigmoid function is the most common activation function in the ANN because it combines nearly linear behaviour, curvilinear behaviour, and nearly constant behaviour [22,23].

Fig. 48 Mathematical model of neuron cell

In the present investigations, volumetric wear of the composite is modelled using ANN. Deformation, Composition, Load and sliding velocity are taken as the inputs and the volumetric wear is the output for the model. The experimental data is grouped into training data and test data. The training data is used for training the ANN and the test data is used for validating the ANN. Root mean square error and mean absolute percentage error is calculated using the following equations.

(5)

...... (6)

Where ti is the experimental value and tdi is the model prediction value and N is the number of testing data.

The ANN architecture used for modelling is shown in fig. 49 with four input variables, two hidden layers with 7 and 6 neurons in the two hidden layers respectively and volumetric wear as output variable.

Fig. 49 Artificial Neural network arcitecture

4.5.1 Network training and testing

A forward feed backward propagation multilayer ANN is used for modelling and the network training and testing was carried out using MATLAB. The hyperbolic tangent sigmoid function (tansig) eq no.4 and the linear transfer function (purelin) are used as activation transfer functions. The back propagation function that updates weight and bias values according to Levenberg-marcendet optimization (trainlm) is used as training algorithm due to its high accuracy in prediction and fast convergence. The experiments in the present investigations have yielded 144 results, out of which 124 were used for training the network and 20 were used to test the ANN model. Different network configurations are evaluated by varying the number of neurons in the hidden layers between 2 and 20. The mean absolute percent error (MAPE) and Root mean square error and correlation coefficient were used to evaluate the performance of ANN model for prediction. The model with 7 and 6 neurons in the hidden layer resulted in MAPE of 7.30%, correlation coefficient of 0.989 and RMSE of 0.3177 which are in the well acceptable range and hence the model with above combination of neurons is selected. The regression analysis of the selected ANN model is furnished in figure 50.

Fig. 50 Regression analysis of the ANN model

The regression and ANN models were adapted for the experimental results and a comparative study is made. The error percentage is calculated with respect to experimental results and it is observed that both the models are in consistent with experimental results. MAPE and RMSE values reflect that the ANN model is more accurate as compared to regression model. The results obtained from the comparative study are depicted in table 27 and its graphical representation is shown in figure 51.

Table. 27: Experimental data and predicted values using regression model and ANN model

percent deformation

% composition

load

sliding velocitym/sec

Volumetric wear x 10-12 m3/sec

experimental value

reg model

% error

ann model

%error

10

10

20

0.523599

3.521145

3.060027

13.10

3.563598

-1.21

30

5

20

0.523599

3.607518

3.711845

-2.89

3.423788

5.09

10

15

30

0.523599

4.834279

5.138675

-6.30

4.55278

5.82

0

10

20

0.261799

1.60052

1.70049

-6.25

1.58974

0.67

40

5

20

0.523599

3.654368

3.775931

-3.33

3.623701

0.84

30

10

30

0.261799

1.737708

2.08737

-20.12

1.880595

-8.22

0

5

30

0.523599

5.739232

6.494499

-13.16

5.829162

-1.57

10

15

10

0.785398

2.293472

2.569337

-12.03

2.435157

-6.18

10

5

30

0.261799

2.975031

2.991535

-0.55

2.672682

10.16

0

15

20

0.523599

3.777483

3.766736

0.28

3.868963

-2.42

0

0

10

0.523599

2.353275

3.276396

-39.23

2.251735

4.31

0

10

30

0.785398

7.911143

7.652206

3.27

7.944785

-0.43

40

15

20

0.785398

5.328949

4.819502

9.56

6.221719

-16.75

20

5

10

0.785398

2.576798

2.837079

-10.10

2.714028

-5.33

30

5

30

0.785398

8.456583

8.351651

1.24

9.188548

-8.66

20

5

30

0.523599

5.996912

5.674159

5.38

5.929547

1.12

40

5

20

0.785398

5.692382

5.663896

0.50

5.414032

4.89

20

10

20

0.785398

5.075936

4.281131

15.66

4.795642

5.52

40

10

10

0.785398

2.034947

2.135434

-4.94

2.176135

-6.94

30

15

20

0.523599

3.327782

3.148916

5.37

3.349029

-0.64

MAPE

12.32091

7.294696

RMSE

0.358549

0.317371

Fig. 51. Graphical representation of regression and ANN models.

5.0 CONCLUSIONS

· Nano structured redmud is successfully synthesised by High energy Ball Milling.

· Nano and micro structured redmud particle reinforced alumimium matrix composites are synthesised successfully by stir casting route.

· Improved Hardness is observed in the composites with increased redmud fraction. The addition of nano redmud particles have shown improved hardness than the micro structured redmud particle reinforced composites.

· The composites with nano structured redmud particle reinforced composites have shown significant improvement in wear resitance than the micro structured redmud of same fraction.

· About 60% inmprovement in wear resistance is observed between pure aluminium and the composite with 10% nano redmud particle reinforcement.

· Wear resitance has been significantly increased with increased deformation. The wear loss remained constant for the composites with 30% and 40% deformation with respect to sliding distance. The optimum results were obtained for the composites with 10% nano redmud particle reinforcement.

· Regression and ANN models have been successfully developed and have shown high accuracy and consistency. It is also observed that the ANN model is more accurate than the regression model.

· The R square value and MAPE value obtained for the regression model are 0.9775 and 12.96% respectively, which are in the well acceptable range and hence the developed regression model can be adapted effectively.

· The ANN model with 7 and 6 neurons in the hidden layer resulted in MAPE of 7.30%, correlation coefficient of 0.989 and RMSE of 0.3177 which are in the well acceptable range and hence can be adapted for the prediction of wear behaviour, which considerably saves the project time, effort and cost

Acknowledgements

The authors sincerely express their thanks to the UGC for extending the financial support for carrying the research work.

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List of Publications

1. G. Satyanarayana; G. Swami Naidu; N. Hari Babu, The effect of deformation on wear behaviour of Al-5% red mud particle reinforced nano composites synthesised by stir casting, Int. J. of Materials Engineering Innovation, Inderscience Publishers, 2016 Vol.7, No.2, pp.115 - 129

2. Satyanarayana G, Narayana Rao K, Swami Naidu G and Bhargava N R M R, “Nano structured Red mud – Synthesis and XRD studies”, International Journal of Mechanical Engineering and Material Sciences, Serials Publications, ISSN 0974-584X, Volume 7, No. 1, pp.63-65

3. Satyanarayana G., Swami Naidu G., Hari Babu N., “Deformation behaviour of al-10 wt% red mud particle reinforced nano Composites – wear studies”, International conference on Material Processing Technology MPT-2016, Organized at Pune, during 5-7, January 2016, pp. 13-20

Al0.942477796076937491.88495559215387612.82743338823081423.76991118430776024.71238898038469230.145722265894937780.13531353261672840.145722265894939310.145722265894939470.133231785961087095% Micro0.942477796076937491.88495559215387612.82743338823081423.76991118430776024.71238898038469230.104087332782099659.3678599503890375E-29.020902174448675E-29.1076416184337566E-29.1596852848248242E-25 % Nano0.942477796076937491.88495559215387612.82743338823081423.76991118430776024.71238898038469238.3269866225680347E-27.8065499586574161E-27.2861132947469529E-27.025894962791697E-27.2861132947469751E-210% Micro0.942477796076937491.88495559215387612.82743338823081423.76991118430776024.71238898038469238.3269866225680347E-27.2861132947469931E-26.9391555188066514E-27.2861132947469931E-27.4942879603111898E-210% Nano0.942477796076937491.88495559215387612.82743338823081423.76991118430776024.71238898038469236.2452399669259785E-25.2043666391049834E-24.8574088631646507E-25.2043666391049834E-26.2452399669259785E-2

Sliding Distance x 103 m

Wear rate x 10-6 N/m

Al1.88495559215387613.76991118430776025.65486677646162767.53982236861550359.42477796076936870.161335365812253910.137915715936281910.114496066060309720.117098249379861820.115536939388130785% Micro1.88495559215387613.76991118430776025.65486677646162767.53982236861550359.42477796076936870.114496066060309720.104087332782099659.5413388383591161E-29.6280782823442185E-29.9923839470815526E-25 % Nano1.88495559215387613.76991118430776025.65486677646162767.53982236861550359.42477796076936877.8065499586574161E-27.5463316267022004E-27.6330710706873084E-27.6764407926798825E-27.7024626258753795E-210% Micro1.88495559215387613.76991118430776025.65486677646162767.53982236861550359.42477796076936878.8474232864784147E-27.5463316267022004E-27.1126344067767869E-27.286113294746982E-27.286113294746982E-210% Nano1.88495559215387613.76991118430776025.65486677646162767.53982236861550359.42477796076936871.0408733278209964E-21.561309991731466E-22.0817466556419802E-23.5129474813958478E-23.3307946490271814E-2



Al2.82743338823081425.65486677646162768.482300164692441411.30973355292332414.1371669411540480.166539732451359250.159600576932552170.152661421413745890.152661421413745970.15543708362126995% Micro2.82743338823081425.65486677646162768.482300164692441411.30973355292332414.1371669411540480.124904799338520070.117965643819713220.105243858701900960.103219938342248550.108944741645264625 % Nano2.82743338823081425.65486677646162768.482300164692441411.30973355292332414.1371669411540489.7148177263293015E-28.6739443985083695E-27.8643762546475302E-27.9800288466276403E-28.0494204018157059E-210% Micro2.82743338823081425.65486677646162768.482300164692441411.30973355292332414.1371669411540489.0209021744486528E-28.326986622568032E-28.0956814386078019E-28.3269866225680195E-28.049420401815692E-210% Nano2.82743338823081425.65486677646162768.482300164692441411.30973355292332414.1371669411540482.0817466556420031E-21.3878311037613321E-21.3878311037613321E-21.3878311037613321E-21.249047993385196E-2



Al0.942477796076937491.88495559215387612.82743338823081423.76991118430776024.71238898038469230.364305664737351880.338283831541825620.291444531789881110.260218331955250510.241482612054471415% Micro0.942477796076937491.88495559215387612.82743338823081423.76991118430776024.71238898038469230.249809598677039750.218583398842410570.201235510045393220.21337903220330370.216501652186767425 % Nano0.942477796076937491.88495559215387612.82743338823081423.76991118430776024.71238898038469230.228992132120619780.176948465729570180.159600576932552670.161335365812254440.1623762391400754610% Micro0.942477796076937491.88495559215387612.82743338823081423.76991118430776024.71238898038469230.218583398842411650.176948465729570180.170009310210763210.176948465729570180.1748667190739274210% Nano0.942477796076937491.88495559215387612.82743338823081423.76991118430776024.71238898038469234.1634933112839882E-23.1226199834629893E-23.8165355353436924E-23.6430566473735021E-23.3307946490271891E-2


















0% deformation0.942477796076937491.88495559215387612.82743338823081423.76991118430776024.71238898038469230.104087332782099659.3678599503890306E-29.0209021744486528E-29.1076416184337525E-29.1596852848248228E-210% deformation0.942477796076937491.88495559215387612.82743338823081423.76991118430776024.71238898038469230.114496066060308469.8882966142994549E-29.7148177263293015E-29.3678599503889806E-29.7842092815173448E-220% deformation0.942477796076937491.88495559215387612.82743338823081423.76991118430776024.71238898038469230.104087332782099658.8474232864784147E-28.326986622568032E-28.326986622568032E-28.5351612881321495E-230% deformation0.942477796076937491.88495559215387612.82743338823081423.76991118430776024.71238898038469239.3678599503889001E-28.326986622568032E-27.9800288466276029E-27.8065499586574744E-27.9106372914395914E-240% deformation0.942477796076937491.88495559215387612.82743338823081423.76991118430776024.71238898038469239.3678599503891388E-27.286113294746982E-27.2861132947470139E-27.286113294746982E-27.4942879603111801E-2

Sliding distance x 103 m


0% deformation1.88495559215387613.76991118430776025.65486677646162767.53982236861550359.42477796076936870.114496066060309720.104087332782099659.5413388383591161E-29.6280782823442185E-29.9923839470815526E-210% deformation1.88495559215387613.76991118430776025.65486677646162767.53982236861550359.42477796076936870.119700432699415150.106689516101652439.5413388383591549E-29.6280782823442185E-29.784209281517367E-220% deformation1.88495559215387613.76991118430776025.65486677646162767.53982236861550359.42477796076936870.109291699421205840.101485149462547529.3678599503890306E-29.4979691163666266E-29.6801219487352749E-230% deformation1.88495559215387613.76991118430776025.65486677646162767.53982236861550359.42477796076936870.104087332782099659.6280782823441519E-29.3678599503890306E-29.3678599503890084E-29.3678599503890125E-240% deformation1.88495559215387613.76991118430776025.65486677646162767.53982236861550359.42477796076936879.8882966142995368E-29.1076416184337525E-29.0209021744486528E-28.9775324524561245E-28.9515106192605748E-2



0% deformation2.82743338823081425.65486677646162768.482300164692441411.30973355292332414.1371669411540480.124904799338520070.117965643819713220.105243858701900960.103219938342248550.1089447416452646210% deformation2.82743338823081425.65486677646162768.482300164692441411.30973355292332414.1371669411540480.111026488300906320.100617755022696329.9461229102895024E-20.103219938342248550.1068629949896221620% deformation2.82743338823081425.65486677646162768.482300164692441411.30973355292332414.1371669411540480.104087332782099659.8882966142994744E-29.7148177263293015E-29.6280782823442032E-29.8536008367055172E-230% deformation2.82743338823081425.65486677646162768.482300164692441411.30973355292332414.1371669411540480.107556910541502729.7148177263292626E-29.7148177263292751E-29.4545993943741025E-29.4372515055770198E-240% deformation2.82743338823081425.65486677646162768.482300164692441411.30973355292332414.1371669411540480.104087332782099659.5413388383591161E-29.3678599503890222E-29.3678599503890306E-29.367859950389025E-2



0% deformation0.942477796076937491.88495559215387612.82743338823081423.76991118430776024.71238898038469230.249809598677039750.218583398842410570.201235510045393220.21337903220330370.2165016521867674210% deformation0.942477796076937491.88495559215387612.82743338823081423.76991118430776024.71238898038469230.249809598677039750.21337903220330370.21511382108300520.221185582161961460.2206651454980508320% deformation0.942477796076937491.88495559215387612.82743338823081423.76991118430776024.71238898038469230.218583398842409490.19776593228598940.197765932285988930.197765932285988790.2060929189085564430% deformation0.942477796076937491.88495559215387612.82743338823081423.76991118430776024.71238898038469230.197765932285991260.17174409909046620.170009310210763210.171744099090465560.1707032257626434340% deformation0.942477796076937491.88495559215387612.82743338823081423.76991118430776024.71238898038469230.166539732451360.145722265894940060.145722265894940060.145722265894940060.14572226589494006


















0% deformation0.942477796076937491.88495559215387612.82743338823081423.76991118430776024.71238898038469238.326986622568032E-27.8065499586574161E-27.2861132947469404E-27.025894962791697E-27.2861132947469529E-210% deformation0.942477796076937491.88495559215387612.82743338823081423.76991118430776024.71238898038469238.326986622568032E-27.286113294746982E-26.9391555188066431E-27.025894962791697E-27.2861132947469529E-220% deformation0.942477796076937491.88495559215387612.82743338823081423.76991118430776024.71238898038469237.2861132947468918E-26.7656766308364202E-26.5921977428662723E-26.7656766308364771E-26.8697639636185734E-230% deformation0.942477796076937491.88495559215387612.82743338823081423.76991118430776024.71238898038469237.2861132947468918E-26.2452399669259785E-26.2452399669259785E-26.2452399669259785E-26.4534146324901551E-240% deformation0.942477796076937491.88495559215387612.82743338823081423.76991118430776024.71238898038469236.2452399669259785E-25.7248033030155382E-25.8982821909857014E-25.9850216349707865E-25.8288906357975803E-2












0% deformation1.88495559215387613.76991118430776025.65486677646162767.53982236861550359.42477796076936870.249809598677039750.202970298925094410.180418043488973810.192561565646884370.181111959040853210% deformation1.88495559215387613.76991118430776025.65486677646162767.53982236861550359.42477796076936870.260218331955250510.19776593228598940.173478887970166640.170443007430688210.1727849724182851920% deformation1.88495559215387613.76991118430776025.65486677646162767.53982236861550359.42477796076936870.223787765481513690.174346282410017370.164804943571657590.162636457472031310.1634171124678974230% deformation1.88495559215387613.76991118430776025.65486677646162767.53982236861550359.42477796076936870.223787765481514830.169141915770912230.159600576932552670.160034274152478730.1602944924844345340% deformation1.88495559215387613.76991118430776025.65486677646162767.53982236861550359.42477796076936870.218583398842410570.166539732451360.15613099

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jntukucev.ac.in · Web viewConventional monolithic materials have limitations with respect to achievable combinations of strength, stiffness, and density. In order to overcome these