Mechanics, Materials Science & Engineering, March 2016 – ISSN 2412-5954

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Sankt Lorenzen 36, 8715, Sankt Lorenzen, Austria

Mechanics, Materials Science & Engineering Journal

March 2016

Mechanics, Materials Sciences & Engineering Journal, Austria, Sankt Lorenzen, 2016

Mechanics, Materials Science & Engineering Journal (MMSE Journal) is journal that deals in peer- reviewed, open access publishing, focusing on wide range of subject areas, including economics, business, social sciences, engineering etc.

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ISSN 2412-5954 e-ISSN 2414-6935

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Mechanics, Materials Science & Engineering, March 2016 – ISSN 2412-5954

CONTENT

 

I. Materials Science. MMSE Journal Vol. 3……………………………………………………….6

Characterization and Thermo – Elasto – Viscoplastic Modelling of Cunip Copper Alloy in Blanking

Process .................................................................................................................................................

7

Technology of Modifying a Machine Element ..................................................................................

14

II. Mechanical Engineering & Physics. MMSE Journal Vol. 3 ...................................................

19

Modeling of Heat Transfer and Self-Heating Phenomenon In Materials With High Dissipation .....

20

Rolling Contact Fatigue Life Evaluation Using Weibull Distribution ..............................................

28

The Boltzmann Equation Of Phonon Thermal Transport Solved In the Relaxation Time

 

Approximation – I – Theory ..............................................................................................................

34

Elements of Calculus Quaternionic Matrices And Some Applications In Vector Algebra And

 

Kinematics .........................................................................................................................................

46

The Boltzmann Equation Of Phonon Thermal Transport Solved In the Relaxation Time

 

Approximation – II – Data Analysis ..................................................................................................

57

Automation of Analysis And Structural-Parametric Synthesis of Planetary Gearboxes With Two

 

Degrees Of Freedom ..........................................................................................................................

67

Intellectual Drive With Electric Engines On a Stock Car..................................................................

81

A Numerical-Analytical Approach to the Analysis of Non-Stationary Temperature Fields in

 

Multiply-Connected Solids ................................................................................................................

90

Modeling Curvilinear Motion of Tracked Vehicle with the Dual-Flux Electromechanical Turning

Mechanism .......................................................................................................................................

107

A Fast Algorithm to Solve Nonlinear Hypersingular Integral Equations Arising in a Crack Problem

..........................................................................................................................................................

120

A Virtual Stage-Gate Approach to Developing Injection Moulds for Polymer-Based Drug-Delivery

Systems ............................................................................................................................................

135

IV. Electrical Complexes and Systems. MMSE Journal Vol. 3 .................................................

148

Secondary Power Resources of the Fuel and Energy Complex in Ukraine……………………….149

VI. Power Supply Technologies. MMSE Journal Vol. 3 ............................................................

155

Monitoring of the thermal state of induction motors with low quality power supply .....................

156

VII. Environmental Safety. MMSE Journal Vol. 3 ....................................................................

163

Nasal Bone Fractures In Children And Adolescents. Patient Demographics, Etiology of The

 

Fracture and Evaluation of Plain Film Radiography as a Diagnostic Method in Children’s Clinical

University Hospital.....................................................................................................................................

164

New Basis Points of Geodetic Stations for Landslide Monitoring ..................................................

171

MMSE Journal. Open Access www.mmse.xyz

 

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Mechanics, Materials Science & Engineering, March 2016 – ISSN 2412-5954

IX. Economics & Management. MMSE Journal Vol. 3 .............................................................

178

The Current State of Taxation and Regulation of Land Plot Size of Industrial Areas in Ukraine ..

179

X. Philosophy of Research and Education. MMSE Journal Vol. 3 ...........................................

185

Physics and Optics in Dante’s Divine Comedy ...............................................................................

186

A Matlab Toolbox For Grey Clustering Probability Model Of Postgraduate’s

 

Innovative Ability ...........................................................................................................................

193

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Mechanics, Materials Science & Engineering, March 2016 – ISSN 2412-5954

I . M a t e r i a l s S c i e n c e

M M S E J o u r n a l V o l . 3

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Mechanics, Materials Science & Engineering, March 2016 – ISSN 2412-5954

Characterization and Thermo – Elasto – Viscoplastic Modelling of Cunip

Copper Alloy in Blanking Process

A. Touache1, S. Thibaud2, J. Chambert2, P. Picart2

1 – Mechanical Engineering Laboratory, Faculté des Sciences et Techniques, Sidi Mohammed Ben Abdellah University, Fez, Morocco

2 – Institute FEMTO-ST, Applied Mechanics Laboratory, University of Franche-Comté, 24 rue de l’Epitaphe, 25000 Besançon, France

DOI 10.13140/RG.2.1.3289.0645

Keywords: strain rate/temperature sensitivity, blanking process, copper alloys, FEM

ABSTRACT. Numerical simulations of blanking process are performed to investigate CuNiP copper alloy behavior under blanking conditions. Numerical simulations are mostly dependant of a correct modeling of the material behavior with thermo-mechanical sensitivity. A thermo-mechanical characterization by a set of uniaxial tensile tests at different temperatures and strain rates is presented. A thermo – elasto - viscoplastic approach was investigated to propose the mechanical behavior model based on a phenomenological way in the framework of the thermodynamic of irreversible processes. This model is implemented in finite element software untitled “Blankform” dedicated to the numerical simulation of precision blanking operations and developed at the Applied Mechanics Laboratory. Numerical results are presented and compared with experiments.

1.Introduction. In precision blanking for very thin sheet about 0.254mm thickness, accurate predictions of maximal blanking load and cut edge profile are essential for designers and manufacturers. A finite element code untitled Blankform [1-2] has been developed at the Applied Mechanics Laboratory to simulate the blanking operation from elastic deformation to the complete rupture of the sheet.

In blanking operation like many metal forming processes the material undergoes very large strains, high strain rates and significant variations in temperature. So to obtain an acceptable prediction of the maximal blanking load by FEM simulation, it needs an adapted model for mechanical behavior which takes into account large strains, strain rate and thermal effects. In this paper, a specific thermo-elasto- viscoplastic modelling has been developed for CuNiP copper alloy used for manufacturing electronic components by high precision blanking.

In first, tensile tests are carried out at room temperature with various strain rates. The temperature distribution in the specimen is observed using a thermal CCD camera. Then a second set of tensile tests are carried out in various isothermal conditions. Considering locally the temperature evolution as a function of the strain rate, the analysis of the tensile curves obtained for these experiments allows to propose a new thermo-elasto-viscoplastic modelling for a copper alloys. The identification of the associated material parameters is investigated and presented. The proposed mechanical behavior is implanted in the finite element code Blankform. Finally the capability of the new modelling to predict the maximum blanking force is presented and discussed.

2.Experiments. To study strain rate sensitivity, tensile tests are performed at room temperature with four strain rates: 2 · 10−3−1, 4 · 10−3−1, 8 · 10−3−1 and 9 · 10−2−1. During each tests, a thermal

camera allows the measurement of the heating in the specimen due to the mechanical energy dissipation. The second set of tests is performed at a constant strain rate (2 · 10−3−1) with three different temperatures T=20 °C, 50°C and 150 °C.

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Mechanics, Materials Science & Engineering, March 2016 – ISSN 2412-5954

Even the strain rate and thermal effects are strongly coupled two sets of experiments are carried out to investigate separately the strain rate and temperature effects on the flow stress. The strain rate range investigated by experiments is lower than those observed in industrial blanking process (about 10 s-1). The extension of the modelling in term of large strain rate domain is made by introducing a Johnson- Cook-like modelling [2]. The stress/strain curves obtained for the first (various strain rates) and second set (various temperatures) of experiments are shown respectively on figures 1 and 2.

Fig. 1. Stress-strain curves with different strain rates at room temperature (20 °C)

Fig. 2. Stress/Strain curves with different temperatures (�̇=2.1 10-3 s-1).

The flow stress decreases with temperature increasing and increases with strain rate increasing. Furthermore the deformation at rupture decreases with temperature increasing and increases with strain rate increasing. For tensile tests achieved at a temperature below 150 °C show a fast decreasing of the stress flow. The rupture of specimens appears quickly. The testing device does not allow test in the range of strain rates corresponding to industrial blanking conditions. However these tests show the influence of strain rate and temperature on the mechanical behavior of CuNiP copper alloy.

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Mechanics, Materials Science & Engineering, March 2016 – ISSN 2412-5954

The mean heating of the specimen due to the strain rate evolution which was calculated by thermal camera is presented on figure 3. The heating increases with the strain rate. So the mechanical modeling should take in account temperature and strain rate coupling.

Fig. 3. Specimen heating for different strain rates (20 °C).

3.Modeling. A number of models of thermo-elasto-viscoplastic behavior, for example the models of Johnson-Cook, Prandtl-Ludwik, Zener-Holomon and Armstrong-Zerilli [4], these models were

generally developed for mechanical behavior at very high strain rate so higher than speeds in blanking process which are about 10s-1. We will propose a new model as well as possible reproducing experimental tests and the sensitivities at the strain rate and temperature. We propose following multiplicative low for predicting the thermo-elasto-viscoplastic yield stress:

 

 

 

 

−�������

 

��0

 

���

 

 

 

����

 

 

��

 

��

= (�� + �(1 − �

) +

) (1 + �

 

�� (1 +

��̇

)) �

 

 

 

 

��

 

�� .

(1)

 

 

 

 

0

 

 

 

 

��

 

 

 

 

��0

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

With: ��0 the equivalent stress,

���

the equivalent strain,

 

 

 

���

the strain rate and ��,

 

the temperature, �̇

, , 0, ��, 0 and �� are material hardening parameters.

The first exponential term makes possible to take into account the beginning of the hardening curve as well as the quasi-saturation of this one. The second linear represents the slope of the curve. The term in 1/T represents the fall of the hardening curve with the rise in the temperature. The strain rate influence is proposed according to a term in logarithm. It makes possible to formulate saturation effect of strain rate. Finally a term proportional to exponential of the reverse of the temperature represents saturation and softening due to the temperature.

At low velocity, the term of strain rate in equation (1) tend to one. In first, we set ��at the yield point at ambient temperature. The use of a genetic algorithm allows parameter identification with the experimental results at imposed temperatures and strain rate. The results of this inverse identification are listed in table 1. Experimental and predicted stress flow curves are in good agreements (see figure 1 and 2)

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Mechanics, Materials Science & Engineering, March 2016 – ISSN 2412-5954

Table 1. Identified material parameters for CuNiP copper alloy.

Material parameters

Value

 

 

E (MPa) Young’s modulus

99500

 

 

ν (MPa) Poisson’s ratio

0,31

 

 

��(MPa) Yield stress

199

(MPa)

97

 

 

1300

 

 

(MPa.°C-1)

8200

0

 

��

0,02

(s-1)

2.1 10-3

0

 

α (°C-1)

0,9

4. Numerical Implementation

To take into account temperature and strain rate effects observed during tensile tests, a phenomenological modeling is proposed. A like-plasticity model described by the way of the Von- Mises criterion:

� =

1

 

��: : ��

1

��2 .

(2)

 

 

2

 

 

3

0

 

Where is the yielding surface, �� is the Cauchy stress tensor, is the 4th order deviatoric tensor and ��0 the flow stress.

We consider that the blanking process is carried out in adiabatic conditions. With these assumptions, the local heating is simply computed from the strain and stress state by:

����

 

��

���

 

 

=

 

��: ̇ .

(3)

���

��

 

 

��

 

 

With , and are respectively the density, the specific heat and the transfer coefficient of the material. The parameter ξ permits to take into account the heating. The values of these parameters are given by literature in table 2.

Table 2. Identified material parameters for CuNiP copper alloy.

Material properties

Value

 

 

(kg.m-3) Density

8900

(J.kg-1.°C-1) Specific heat

22,32

 

0,05

 

 

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Mechanics, Materials Science & Engineering, March 2016 – ISSN 2412-5954

In the finite element software Blankform, equation (3) is not strongly coupled with the mechanical solution. The temperature is computed after loading increment by resolution of equation (3).

The new modelling is implanted in Blankform software by a standard numerical procedure as presented in [5]. This software allows the numerical simulation of 2D problems including large strains and inelastic materials. The time integration is based on an implicit algorithm. To solve the equilibrium and the non linear constitutive equations, a Newton Raphson method is used.

5.Blanking FEM simulation. The blanking test geometry is described on figure 4 and table 3. Sliding contact conditions are assumed between tools and specimen. The simulation has been performed in 2D plane strain conditions. The initial mesh is made up 3118 triangular 3 nodes elements with one integration point.

In blanking process a localized shear band appears between the punch and die. This band presents locally very significant values of the equivalent plastic strain about 4 at a punch penetration of 50%. To reduce the influence of the mesh distortion, a global periodic remeshing of the specimen is generated after every 5% of punch penetration. The average size of the elements in the band of shearing is about 1.3% of the thickness.

Table 3.Geometric parameters of the blanking test

 

Value (mm)

 

 

Punch width

1.7

 

 

Hole die width

1.72

 

 

Punch radius

0.01

 

 

Die radius

0.01

 

 

Punch-die clearance

0.01

 

 

Specimen thickness

0.2

 

 

Fig. 4. Schematic description of the blanking operation.

6.Results. Fig. 5, a presents the equivalent strain according to the penetration of the punch. We observe a band of localized plastic deformations. This band is located between the cutting edges of the punch and the die. In the centre of the band, the equivalent deformation is approximately 4 if the punch penetration is 47%. The temperature increases up to 215 °C (see fig. 5, c) near punch and die corners and the strain rate is about 1.5s-1 (see fig. 5, b).

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Mechanics, Materials Science & Engineering, March 2016 – ISSN 2412-5954

In the tensile tests carried out to characterize the behavior, the values of the strain, strain rate and temperature are much lower than the values is thus to check obtained in blanking FEM simulation. The validity of the thermo-elasto-viscoplastic law used in this range of deformation is thus to check. For that we have to compare numerical results and experimental blanking test.

Figure 6 gives experimental and numerical load-displacement curves for two different punch speed

0.1mm.s-1 and 6 mm.s-1. The prediction of the blanking load curve is rather correctly carried out until the initiation of the phase of cracking. This difference can be explained because in the proposed model we do not taking into account the damage phenomena [6]. The relative error on the maximum value of the blanking load is about 2.3 % which is very acceptable (see table 4).

(a)(b)

Fig. 5. Field of the equivalent deformation (a), strain rate in s-1(b) in the shear band.

(c)

and temperature in °C (c)

Punch load (N)

1400

 

 

NUM 0.1mm/s

1200

EXP 0.1mm/s

NUM 6mm/s

 

 

EXP 6mm/s

1000

 

800

600

400

200

00

0.05

0.1

0.15

0.2

0.25

0.3

 

 

 

Displacment (mm)

 

 

 

Fig. 6. Experimental and predicted load/displacement curves

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Mechanics, Materials Science & Engineering, March 2016 – ISSN 2412-5954

Table 4. Experimental and predicted maximal blanking load for tow value of punch speed

Punch speed

Numeric (N)

Experiment (N)

Error (%)

 

 

 

 

0.1mm/s

1163

1136

+2.3%

 

 

 

 

6mm/s

1227

1200

+2.2%

 

 

 

 

6.Conclusion. The thermo–elasto–viscoplastic behaviour of the CuNiP copper alloy was characterized by the use of a set of tensile tests at imposed strain rates and temperatures. A multiplicative behaviour law is proposed to take into account the material sensitivity at the strain rate and the temperature. After having identified by genetic algorithm the parameters of the proposed law, it was implemented in the computer finite elements software Blankform. The application in simulation of the blanking process shows that the thermo-elasto-viscoplastic model for the CuNiP copper alloy allows a correct prediction of the sensitivity of the maximum blanking load at versus punch speed. However, it will be necessary to validate the experimental step for the characterization of the sensitivity at the speed and the temperature on other copper alloys in order to improve the proposed thermo – elasto – viscoplastic model for similar coppers alloys.

References

[1]V. Lemiale, Contribution à la modélisation et à la simulation numérique du découpage des métaux,

PhD Thesis, University of Franche-Comté (2004), France [in french].

[2]A. Touache, "Contribution à la caractérisation et à la modélisation de l’influence de la vitesse et de la température sur le comportement en découpage de tôles minces", Ph.D. Thesis, Université de Franche-Comté, France, December (2006) [in French].

[3]G.R. Johnson, W.H. Cook, A constitutive model and data for metals subjected to large strains, High Strain Rates and High Temperature, In 7th International Symposium on Ballistics, The Netherlands, 1983.

[4]M. Micunovic, M. Radosavljevic, C. Albertini, M. Montagnani, Viscoplastic behaviour of damaged AISI 316H from dynamic experiments, Facta Universtatis, Vol. 2 n° 10: 1299-1317, 1997.

[5]J.C. Simo, T.J.R. Hugues, Computational Inelasticity, Springer Verlag Edition (1998).

[6]Hambli R., Comparison between Lemaitre and Gurson damage models in crack growth simulation during blanking process, International Journal of Mechanical Sciences, 43: 2769-2790, 2001.

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Mechanics, Materials Science & Engineering, March 2016 – ISSN 2412-5954

Technology of Modifying a Machine Element

R. P. Didyk1,a, R. S. Puhach2,b

1 – Dr. Sci. (Tech.), Professor, State Higher Educational Institution “National Mining University”, Dnepropetrovsk, Ukraine

2 – Postgraduate, State Higher Educational Institution “National Mining University”, Dnepropetrovsk, Ukraine

a – didyk@nmu.org.ua

b – dracov-pugach@yandex.ua

DOI 10.13140/RG.2.1.1561.7683

Keywords: basis points, landslide processes, local geodetic network, recalculation of coordinates, the coordinate system.

ABSTRACT. For the first time, products of serpentine decomposition have been identified on the basis of fundamental structural research. These products form a protective ceramic metal layer on the metallic surface. During sliding contact surfaces is formed on a protective layer having anti unique characteristics. There is a restoration of the functional state of the friction surface of the unit due to the initiation of self-organizing processes. Results of industrial tests prove the high effectiveness of the use of natural minerals as machine elements modifiers. They allowed making the service life of mining and metallurgical equipment 2,5 - 5 times longer because of the reduction or elimination of repair works and increase in functional properties of engineering products.

Introduction. Methods of strengthening machine element surfaces subjected to friction are based on various physical, chemical and mechanical processes, resulting in the increase in wear resistance, strength, hardness and corrosion resistance, which ensures a specified service life and minimization of energy losses during the friction unit operation.

Since there is no universal way of strengthening tribological units, it is important to consider the factors specific for each single case: for example, the allowable distortion of machine elements, the occurrence and type of residual stresses, the impact of technological environment, ecological and financial parameters. Some strengthening methods are widely known: chemical and thermal treatment, diffusion, surfacing, chemical deposition from gas medium, implantation, thermal vacuum methods, ion plasma methods and laser methods. A detonation method allows obtaining coatings with enhanced operational properties. Each of the above methods has its advantages, disadvantages and a particular field of application [1].

The new direction in solving this problem is the mechano-chemisty influence of tribotechnical powdercompositions - geomodifiers of friction (GMF) - on the working surfaces of machine elements.

Research results. High loads, extreme speed, a wide temperature range and the presence of aggressive media determine new requirements for the performance and operation of friction units of modern mining and metallurgical equipment. To ensure the efficient work of gears, rolling contact bearings, skid bases, cam shaft mechanisms, guide members, sealing elements, junctures, locks and docking devices, it is necessary to create special self-lubricating materials and coatings, friction modifiers, durable coatings with high chemical resistance and new ways of friction unit treatment.

The result of the received mechanoactivation effect became apparent at the following stages of the technological process of friction geomodifier manufacturing. Fine dispersed powders (0.5 - 1 µm) having been crushed in a special manner and having passed the mechanoactivation stage, are brought

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