Al-Khwarizmi Engineering Journal Al-Khwarizmi Engineering Journal, Vol. 9, No. 2, P.P. 1- 11 (2013) Drilling of FR-4 Composite Materials Using Single Pulse of Nd:YAG Laser Osamah F. Abdulateef* Enas A. Khalid** Amer G. Hoss*** *,**,***Department of Automated Manufacturing Engineering/ AL-Khwarizmi College of Engineering/ University of Baghdad *Email: drosamah@kecbu.uobaghdad.edu.iq **Email: enaslaser77@yahoo.com ***Email: amer_gazee@yahoo.com (Received 9 April 2012; Accepted 24 March 2013) Abstract Laser drilling is capable of producing small, precisely positioned holes with high degree of reproductively. In this paper , IR millisecond Nd:YAG single pulsed laser was used to determine the effect of laser parameters on the drilled hole of the glass - fiber reinforced epoxy composite FR-4 sample of 2 mm in thickness . The type of laser source was GSI lumonics JK760TR Series laser 1.064μm system in a CNC cabin. The JK760TR series has a 0.3- 50ms pulse length and a maximum repetition rate 500Hz with an average power of 600W. The investigation of single pulse laser drilling in this paper was based on theoretical and experimental solutions. In single pulse technique, the investigation included focal plane position fpp, pulse shape, laser peak power, and pulse duration. It was found that (-1) was the best fpp due to less taper for the drilled holes made by this level (Entrance hole =0.68, Exit hole = 0.27). To predict pulse shape effects; three types were : rectangular , rump-up and cool down, it were examined found that rectangular pulse was efficient more than the other types due to its ability to produce holes with less tapering as compared with others types. Also its found that all pulse shapes had the same effect on the materials microstructure . Laser peak power and pulse duration had the predominant affects on the hole dimensions and edge quality without any defect except hole tapering. Keywords: Nd:YAG Laser, FR-4 Composite materials, Laser Drilling. 1. Introduction FR-4 composite material is a fiber reinforced epoxy resin made from an epoxy resin matrix reinforced by fine glass. They have attracted a significant amount of attention from both industry and academia. The excellent tensile strength of glass fibers, however, may deteriorate when loads are applied for long periods of time. Laser hole drilling in composite materials has been applied widely in industry and became an essential tool for micro-drilling in many components used in the technologically advanced industries. Basic material removal mechanism in laser drilling is based on the absorption of laser energy from a series of laser pulses at the same spot. As a result of which, material gets melted and ejected to form a hole [1, 2]. Laser micro-drilling does not need expensive cutting tools and does not produce mechanical forces that can damage delicate work pieces. The use of laser micro-drilling or micromachining in manufacturing industry can be attributed to its flexibility and ability to process variable quantities and qualities of materials in a very short time with very high surface finish, accuracy, and minimum amount of wastage. Laser machining could drill a hole in very small diameter size, but it will require well controlled laser parameters in order to produce a high quality of hole. Defects that could occur due to inappropriate parameters setting are like overheating, fiber swelling, large heat affected zone HAZ and air plasma spraying APS. Most of the defects are caused mailto:drosamah@kecbu.uobaghdad.edu.iq http://en.wikipedia.org/wiki/Fiber_reinforced_plastic http://en.wikipedia.org/wiki/Fiber_reinforced_plastic Osamah F. Abdulateef Al-Khwarizmi Engineering Journal, Vol. 9, No. 2, P.P. 1- 11(2013) 2 by the rapid heating of the laser beam. The material removal rate MRR for laser machining is not limited by constraints such as maximum tool force, built-up edge formation, or tool chatter. However, due to the presence of thermal effects, the spatial resolution available from conventional, wider pulse lasers operating at visible and infrared wavelengths of the spectrum is limited. Since the absorption coefficient of different materials is highly wavelength dependent, by selecting the laser beam wavelength from deep ultra-violet (UV) to infrared (IR), one can precisely control the material processing [3]. Many researches deal with the micro drilling of composite materials. M.M.Noor, T.T.Mon, K.Kadirgama, 2009 , [4] , non- traditional machining method was employed by using CO2 laser to drill the fiber-glass composite sheet of 2 mm in thickness having four layers of glass-fiber with orientation <0, 90, 0, 90>. The machining parameters under consideration were laser power and pulse duration. Hole quality were then compared for each parameter combination. It was found that the laser power had predominantly affected the quality of the hole in fibre-glass composite material during laser-drilling. A. Demir, L. Candan, T. Canel, V. Gunay, and T. Sınmazcelik, 2009[5], predicted and evaluated the effect of pulse duration and peak power of Nd:YAG laser to find optimum laser parameter in the drilling operation. The average hole diameters and the average taper angles are examined as a function of the laser pulse duration and the laser peak power. The experimental results indicated the diameters of the craters show approximately linear proportion with the pulse duration and the peak power. Avanish, K. D. & Vinod Y., 2007, [6], predicted and evaluated the effect of laser parameter in the drilling of composite material using Nd:YAG laser. This study concluded that HAZ was directly proportional to laser power, where an increase in power would result in an increase in HAZ and it works in the opposite for the cutting speed. W.S.O. Rodden, S.S. Kudesia, D.P. Hand, J.D.C. Jones, 2002, [7], the results of an extensive experimental study of the free running Nd:YAG laser drilling of a multi-layer carbon fiber composite, where adjacent layers had differently orientated fibers. For holes drilled with the laser operating in fixed-Q mode at 1064 nm, parallel sections of blind holes illustrated discontinuities in the hole size along a given section direction Detailed single pulse drilling characteristics presented illustrating the exit hole diameter as a function of pulse energy and material thickness. Zheng Hongyu , Eric Gan Kok Wah 2000 [3], presented the experimental investigation of drilling FR4 , polyimide and alumina substrates using the RF and TEA CO2, 3rd-harmonic Nd: YAG, and KrF excimer lasers, respectively. Both blind and through- vias were drilled and evaluated for taper, wall- angle and smoothness through optical microscope, SEM and cross sectional analyses. In this paper we identifying the most significant parameters governing the quality of the holes in FR-4 composite materials drilled by millisecond Nd:YAG laser by varying the laser parameters pulse peak power, pulse energy , pulse duration, focal plane position(fpp) , and pulse shape to produces a high quality hole with minimal residue and consistent edge quality from entry to exit point. And studying the effects of varying laser beam parameters on the hole dimensions (diameter and depth) and hole quality. 2. One-Dimensional Model for Laser Drilling Drilling can be divided into two stages: heating and material removal, as shown in Figure1. In the heating stage, the temperature of the work piece surface, Ts, is increased up to the phase transition temperature, Tm, by the laser beam. The heating stage is usually very short because the laser beam intensity is very high. In the material removal stage, the hole depth is increased through molten material removal. Heating stage Drilling stage Fig. 1. Heating and Material Removal Stages of Laser Drilling [9]. Osamah F. Abdulateef Al-Khwarizmi Engineering Journal, Vol. 9, No. 2, P.P. 1- 11(2013) 3 During the heating stage, the work piece surface is not thermally eroded. It is difficult to obtain a simple analytical solution for drilling as a non steady process with three-dimensional heat transfer characteristics. Thus, it is assumed that drilling is a one dimensional process and that the laser beam intensity is uniform. The boundary conditions are: At z = 0 → I= - κ (dT/dz)z=0 …(1) and At z → ∞, T=T0 where I0 is the laser beam intensity(W/m 2 ), and T0 is the initial temperature( o K). The temperature distribution inside the workpiece can be derived, to be [8] T-T0 = 2𝐼0 𝐾 𝐾𝑡 𝜋 1 2 𝑒 −𝑍2 4𝑘𝑡 − 𝐼0𝑧 𝑘 …(2) where κ is the thermal diffusivity (cm -2 s -1 ) and I0 is the laser beam intensity. The temperature distribution given by Eq. 2 is valid under the condition that (κt) 1/2 <ω [8], which can be achieved either through low diffusivities or short drilling times. The time for the workpiece surface to reach the solid-liquid phase transition temperature Tm can be determined from Eq.2. Applying Ts = T at z = 0, the following relation can be obtained [8] T – T0 = 2𝐼0 𝑘 𝑘𝑡 𝜋 1 2 …(3) The duration of the heating stage, th in second, can be calculated as [8] th= 𝜋 𝑘 𝑘 𝑇𝑚−𝑇0 2𝐼0 2 …(4) where Tm is a melting temperature( o K). During the heating stage, a hole is not made because phase transition does not occur. After the surface temperature reaches the melting point, drilling starts. In order to determine the hole depth as a function of time and process variables, a one-dimensional analysis is considered, Figure 2 a laser beam is assumed to have a uniform intensity distribution I0 defined as [8] I0 = 𝑃 𝜋𝑤 2 …(5) where P is the laser power (N/m 2 ) and w is laser beam radius at the surface of a workpiece (mm). Fig. 2. One-Dimensional Drilling [8]. 3. Experimental Work In this paper, FR-4 sheet of 2 mm in thickness was drilled by using millisecond pulsed Nd:YAG laser. The schematic diagram of the experimental setup is shown in Figure 3 .Machining is done on the FR-4 composite material samples by changing the laser parameters. The type of laser source was GSI lumonics JK760TR Series Laser (Class 4) (IR) wavelength 1.064λ system in a CNC cabin sees Figure.4. It has a 0.3-50ms pulse length and a maximum repetition rate 500Hz with an average power of 600W.Laser output power is delivered via a 600 μm radius fiber optic cable to the focus head at the work station for processing. The laser beam was focused on to the FR-4 sheet using 160mm focal length Plano convex lens investigate the drilling process of composite materials . glass fiber/epoxy composites sheet type 2116 FR-4 having twelve layers of glass-fiber with orientation <0, 90 respectively > .Single pulse laser drilling method was used. Crater investigations such as crater diameter, depth were performed at five laser peak powers, six pulse duration, four fpp, and three pulse shapes. The laser beam mode is TEM 00 . The spot size of the laser beam on the composite materials substrate is 480 μm. The applied parameters in the experiments are given in Table 1. Osamah F. Abdulateef Al-Khwarizmi Engineering Journal, Vol. 9, No. 2, P.P. 1-11 (2013) 4 Table 1, Laser Parameter in Single Pulse Technique Applied During Experimental. Wave length 1.064μm Nd:YAG pulsed laser Peak power Pulse duration Pulse energy Pulse shape Fpp From 3kw to 9kw with 1.5 kw increment From 1ms to 4ms with 1ms increment From 3j to 36j Rup-up Cool down Rectangular from +1 to -2 mm with 1 mm steps Fig. 3. Experimental Setup for Nd-YAG JK760TR. Osamah F. Abdulateef Al-Khwarizmi Engineering Journal, Vol. 9, No. 2, P.P. 1-11 (2013) 5 Fig. 4. Millisecond Pulsed Nd:YAG Laser Head. The minimum spot size is calculated as follows [8]: 𝐬𝐩𝐨𝐭 𝐬𝐢𝐳𝐞 = 𝐥𝐞𝐧𝐬𝐞 𝐟𝐨𝐜𝐚𝐥 𝐥𝐞𝐧𝐠𝐭𝐡 𝐜𝐨𝐥𝐥𝐢𝐦𝐚𝐭𝐨𝐫 𝐨𝐩𝐭𝐢𝐜𝐬 𝐟𝐨𝐜𝐚𝐥 𝐥𝐞𝐧𝐠𝐭𝐡 + 𝐛𝐞𝐚𝐦 𝐞𝐱𝐩𝐚𝐧𝐬𝐢𝐨𝐧 𝐟𝐚𝐜𝐭𝐨𝐫 ∗ 𝐟𝐢𝐛𝐞𝐫 𝐝𝐢𝐚𝐦𝐞𝐭𝐞𝐫 = (160 mm /200mm)*600µm = 480μm …(6) The glass fiber used in this paper is made from an epoxy glass laminate, which employs a resin based on BT/epoxy with 12-layer woven fabrics of glass fiber and epoxy resin that has orientation (90 o , 0 o ) “E-glass” reinforcement (see Figure 5). The relatively low dielectric constant and low manufacturing cost of the glass-epoxy system make it ideal for many printed circuit applications. 52-56% silicon oxide, 12-16% aluminum oxide and 16-25% calcium oxide [2].The elemental analysis of the selected materials at the specific point was tested by using Energy-dispersive X-ray spectroscopy connected to a scanning electron microscopy (SEM) .The mechanical and physical properties of the FR-4 are listed in Table.2. The experimental procedures are as follows: 1. Fixing the workpiece and identifying the lines of drilling. 2. Drilling the workpiece. 3. Cutting and coating the workpiece. 4. 4. Taking images by the scanning electron microscopy (SEM) and optical microscope for analysis purpose. Osamah F. Abdulateef Al-Khwarizmi Engineering Journal, Vol. 9, No. 2, P.P. 1-11 (2013) 6 Fig. 5. A: 2116 Glass Fiber Composite FR-4 Work Piece: B: High Magnification (16x) Showing Glass Fiber. Table 2, Mechanical and Physical Properties of the FR-4 [11]. Tensile strength MPa 1,770 Rockwell Hardness 110 M scale Temperature Limit ( o C) Up to 120 Glass Melting temperature ( o C) Resin Above 1590 Not Applicable Density (g/cm 3 ) 1.85 Specific heat (J/kg 0 k) 960 Heat Capacity(J/m3-K) 1.703*10 -6 Thermal Conductivity (W/m-°C) 0.16 – 0.20 Permittivity-A 4.8 Thermal expansion coefficient 10 -6 1/ 0 k 0.9 - 1.5 x 10 -5 4. Results and Discussion Laser macro drilling on the FR-4 sheets are presented and discussed for the study of the effect of laser parameters on micro drilling results. There are a total of 24 holes in the final actual experiment based on the parameter range under consideration. Prior to this, trial holes were drilled in order to acquire minimum amount of laser power, pulse duration, and pulse shape that can penetrate the composite specimen of 2mm thickness and to see the effects on the materials microstructure. To determine the effects of the laser parameters; starting reference parameters were first been determined as; 2 ms pulse width, 3 kW peak power, 10 Hz repetition rate, and -1 focal position. All experiments were applied at 160 mm focal length. These parameters have were changed systematically to investigate these effects on macro drilling results. The holes were drilled by unique pulse, first fpp was changed to obtain the optimum surface level for drilling operation, and then the laser parameters (peak power, pulse duration) were changed to obtain ties effects on macro drilling results. http://en.wikipedia.org/wiki/Permittivity Osamah F. Abdulateef Al-Khwarizmi Engineering Journal, Vol. 9, No. 2, P.P. 1-11 (2013) 7 4.1. Effect of Focal Plane Position (fpp) In laser processing, intensity (power per unit area) of the laser beam at the material surface is of prime importance. Intensity is great enough to melt or vaporize any material generated by focusing a laser beam. The maximum irradiance is obtained at the focal point of a lens, where the beam is at its smallest diameter. Intensity values of billion of Watts per square centimeter can be obtained at the focal spot. During this experiment the fpp is considered zero on the workpiece surface and above or below the surface is considered positive or negative, respectively. The fpp was changed from +1 to -2 in a single drilling. As shown in Figure 6 the hole not drilled at +1 fpp and the entrance diameter of the hole was maximum value 0.955, so +1 fpp is already eliminated, but it did not change much at -1 and - 2 mm focal plane positions when compared to the other positions. Circularity of the hole for -1mm focal position was better than the one with -2 mm. It is possible to say that -1 mm focal position was a more suitable position for single drilling due to minimum entrance hole and maximum exit hole (less tapering). Fig. 6. (1) Effect of fpp on the Dimensions of Laser Drilled Microholes (f = 10 Hz), (2) Optical Picture Showing Changing Crater Dimensions for Different Fpp. 4.2. Heating Stage When a laser pulse interacts with a solid target, the electrons are heated to a high temperature by the absorption of laser energy. By the electron- photon interactions, the hot electrons transfer energy to the lattice on a few picoseconds time scale for most materials [9–10]. The equilibrium between these two energies depends on the laser pulse duration. The energies transformation occur in the stage before hole beginning to drill by very short time and this stage is called heating time . The theoretical calculation for heating time that was gathered according to Equation (4) showed high reduction in heating time with increase in laser peak power (see Fig.7). A significant decrease in the heating time as peak power was increased from 3kW to 6kW, and the heating time is decreased slightly from 6kW to 9kW, the heating time relationship is inversive with laser power. This 0.96 0.75 0.68 0.88 0 0.245 0.27 0.25 0 0.2 0.4 0.6 0.8 1 1.2 1 2 3 4 h o le d im e n ti o n m m focal plan position Entrance diameter single Exit diameter single1 2 +1 0 -1 -2 Osamah F. Abdulateef Al-Khwarizmi Engineering Journal, Vol. 9, No. 2, P.P. 1-11 (2013) 8 decrease continues until it reaches to the lowest value before drilling process starts as shown in the values from 3-6(kW), after 6kW and due to high power transfer to the surface, the time is very close to the minimum value for start of the drilling process. So any increase in laser power even if a sudden it will be accompanied by a small decrease in the heating time. Another observation is that heating time was increased as pulse width increased as shawn in Figure 2. Fig. 7. Effect of Laser Power on the Heating Stage. 4.3. Effect of Laser Parameters After predicting the best fpp for single pulse methods (-1) , hole dimensions were examined under different laser parameters and the results show that crater diameter was influenced strongly by changing laser parameter as shown in Figure 8. It was found that Laser power is the predominant effect on the hole size, burn mark and edge quality. At 1ms pulse width the laser didn’t reach to the back side of the FR-4 sample even at high peak power of 9 kW due to less interaction time between the material and the workpiece. For other pulse widths from 3kW to 6 kW the crater dimension was increased slightly and from 6 kW to 9kW the crater dimension was increased significantly. The holes made by a single pulse drilling had more tapering (see Fig.9). Fig. 8. Effect of Laser (Peak Power, Pulse Duration) on the Dimensions of Laser Drilled Micro Holes in FR-4, ( f = 10 Hz , and fpp = -1). 0.00E+00 1.00E-02 2.00E-02 3.00E-02 4.00E-02 5.00E-02 6.00E-02 7.00E-02 1 2 3 4 5 H e a ti n g t im e μ s peak power kw 2ms 3ms 4ms 1ms 3 4 . 5 6 7 . 5 9 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 1 2 3 4 5 H o le d im e n ti o n Peak power KW 2 msEntrance 3msEntrance 4msEntrance 1msEntrance 4msExit 3msExit 2msExit 3 4 . 5 6 7 . 5 9 Osamah F. Abdulateef Al-Khwarizmi Engineering Journal, Vol. 9, No. 2, P.P. 1-11 (2013) 9 Fig. 9. A- Optical Images of the Cross-Section of FR-4 Drilled Hole at 2 ms Pulse Width. B- Effect of Peak Power at 2ms Pulse Width on the Hole Dimension. 5. Conclusions The effect of the four variables on micro-hole drilling in the IR millisecond Nd:YAG laser ablation regimes were investigated theoretically and experimentally in single method. Changes in the pulse length, pulse peak power, and pulse shape were correlated for holes depths and diameters on FR-4 composite materials. The results show: 1- (-1) fpp was the best level to accomplish drilling operation, due to less tapering produced. 2- Heating time increases as pulse width increases while its decrease as peak power increase. 3- In all cases of this experimental work, high laser power density affects the hole in two ways; depth and width, it also increase melt. This implies imparting energy quicker and maintaining higher temperatures within the hole makes the process more efficient. 4- Increased ablation times have two effects on hole creation, first, the removal rate is increased, and second, the hole quality experiences degradation. For holes requiring high removal rates yet not as perfect hole quality, longer pulses become ideal. 6. Acknowledgment We would like to thank the staff of Kocaeli University, Laser Technologies Research and Application Center,Turkey , specially Prof. Dr Arif Demir , Dr. E. Kacar, Erhan Akman, and B. Genc Oztoprak for inviting us and giving us this opportunity to use laser devices and different materials in Laser Technologies laboratory / Kocaeli University to complete our experiment work. 7. References [1] William T. Silfvast , University of Central Florida , Orlando, Florida, The National Science Foundation , Fundamentals of Photonics ,1995 ; Grant # DUE 9752029 [2] Emre Teoman, Dana Lee Church, General Laser Micro Machining Principles, Oxford Press, Great Britain ,1985. [3] Zheng Hongyu, Eric Gan Kok Wah, Investigation of Laser Micro-Drilling of PCB Substrates, Advanced Machining Group, Process Technology Division, 2000. [4] M.M.Noor, T.T.Mon, K.Kadirgama, M.R.M.Rejab, Drilling on Fibre-Glass Composite using CO2 Laser, Faculty of Mechanical Engineering, University of Malaysia Pahang (2009). [5] E. Kacar, M. Mutlu, E. Akman, A. Demir, L. Candan, T. Canel, V. Gunay, T. Sınmazcelik, A B 0.5 mm. Osamah F. Abdulateef Al-Khwarizmi Engineering Journal, Vol. 9, No. 2, P.P. 1-11 (2013) 10 Characterization of the drilling alumina ceramic using Nd:YAG pulsed laser University of Kocaeli, Laser Technologies Research and Application Centre, 41380 Umuttepe, Kocaeli, Turkey(2009). [6] Avanish, K. D. & Vinod, Y.,“Laser Beam Machining – A Review”. International Journal of Machine Tools & Manufacture, vol. 48, pp 609 - 628 (2007). [7] W.S.O. Rodden*, S.S. Kudesia, D.P. Hand, J.D.C. Jones , A comprehensive study of the long pulse Nd:YAG laser drilling of multi- layer carbon fiber composites, Department of Physics, Heriot-Watt University, Edinburgh EH14 4AS, UK, Optics Communications 210, 319–328(2002). [8] H. S. Carslaw and J. C. Jaegar, Conduction of heat in solids, Oxford Press, Great Britain (1975). [9] W. Han, J. S. Yokum, and R. J. Pryputniewicz, "Parametric study of laser micro-drilling process for MEMS fabrication”, (2004). [10] B. Martin, A. Loredo, M. Pilloz, and D. Grevey, “Characterization of CW Nd:YAG laser keyhole dynamics,” Optics and Laser Technology, 33:201-207(2001). [11] Nayyar, Piping Handbook, 6th Edition except for FRP-Glass which is based on SiO2 from Handbook of Chemistry and Physics. (2013) 1- 11، صفحت 2، العذد9هجلت الخوارزهي الهنذسيت الوجلذ اساهت فاضل عبذ اللطيف 11 ياك –باستخذام النبضت الوفردة لليسر النيذهيوم ( فايبر كالش)تثقيب الوادة الوركبت *** عاهر غازي هوش ** يناش عبذ الكرين خالذا * اساهت فاضل عبذ اللطيف جاٍؼح تغذاد / ميٞح اىْٖذسح اىخ٘اسصٍٜ/ قسٌ ْٕذسح اىرصْٞغ اىَؤذَد***،**،* drosamah@kecbu.uobaghdad.edu.iq : االىنرشّٜٗ اىثشٝذ * enaslaser_77@yahoo.com : اىثشٝذ االىنرشّٜٗ ** amer_gazee@yahoo.com : االىنرشّٜٗ اىثشٝذ*** الخالصـــــــت ٝاك اىْثضٜ تاىَيٜ شاّٞح ىذساسح ذغٞش -فٜ ٕزا اىثحس اسرخذً ىٞضس اىْٞذًٍٞ٘. ػَيٞح اىرصقٞة تاىيٞضس ىٖا اىقذسج ػيٚ إّراض شق٘ب صغٞشج، ػاىٞح اىذقح ّذ ذصقٞثٖا تاسرخذاً ذقْٞح اىْثضح ٍيَٞرش ع 2تسَل ( اىَادج األساط ٗاألىٞاف ) خصائص اىيٞضس ػيٚ أتؼاد اىصق٘ب ٗػيٚ اىثْٞح اىَجٖشٝح ىؼْٞاخ اىَادج اىَشمثح ٗاط ٗأػيٚ ٍسر٘ٙ ذشدد ٝصو اىٚ 600ٍيٜ شاّٞح تَؼذه قذسج 50-0.3تط٘ه ٍ٘جٜ GSI lumonics JK760TRّ٘ع اىيٞضس اىَسرخذً ماُ . اىَفشدج ىْثضح، ٗقذسج اىْثضح، ٗط٘ه اىْثضح ٗىقذ ٗشنو ا،فٜ حاىح اىْثضح اىَفشدج فاُ خصائص اىيٞضس اىرٜ ذٌ ذغٞٞشٕا ٕٜ ٍ٘قغ اىَسر٘ٙ اىثؤسٛ. ٕٞشذض 500 ٗرىل ( 2-، 1-، 0، 1)+ٍِ تِٞ استغ ٍسر٘ٝاخ ذٌ اسرخذاٍٖا ٕٜٗ تاىرسيسو ( 1)-ٗجذ أّ فٜ حاىح اىرصقٞة تاىْثضح اىَفشدج فاُ افضو ٍسر٘ٙ ىيرصقٞة ٕ٘ الخرثاس ذأشٞش . 0.27= اٍا فٜ ّقطح اىخشٗض فناُ 0.86= اىذخ٘ه الػطائٔ شق٘ب اقو اسرذقاقا ٍقاسّح تاىَسر٘ٝاخ االخشٙ حٞس ماُ قطش اىصقة فٜ ٍْطقح ّح تاألشناه األخشٙ شنو اىْثضح، فقذ اسرخذٍد شالز اشناه ٗذٌ ٍالحظح أُ اىْثضح اىَسرطٞيح أمصش مفاءج ٗرىل ىقاتيٞرٖا ػيٚ إّراض شق٘ب اقو اسرذقاقا ٍقاس إُ طاقح اىيٞضس ٍٗذج اىْثضح ىٖا اىرأشٞش اىسائذ ػيٚ أتؼاد ٗحجٌ اىصق٘ب ٗمزىل ػيٚ اىَْطقح اىَرأششج . اٍا ذأشٞشٕا ػيٚ اىثْٞح اىَجٖشٝح ىيَادج فناُ ٍرشاتٖا . تاىحشاسج تذُٗ أٛ ػٞ٘ب ٍاػذا اسرذقاق اىصقة اىزٛ ماُ صفح ٍالصٍح ىنو اىصق٘ب اىرٜ أجشٝد تٖزٓ اىطشٝقح mailto:drosamah@kecbu.uobaghdad.edu.iqالبريد mailto:drosamah@kecbu.uobaghdad.edu.iqالبريد mailto:amer_gazee@yahoo.com***البريد mailto:amer_gazee@yahoo.com***البريد