Available online at Materials and Design 29 (2008)

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1 Available online at Materials and Design 29 (2008) Materials & Design Fatigue life prediction of ZE41A magnesium alloy using Weibull distribution M. Sivapragash a, *, P.R. Lakshminarayanan b, R. Karthikeyan b, K. Raghukandan b, M. Hanumantha c a Department of Mechanical Engineering, Jayamatha Engineering College, Aralvaimozhi, Tamil Nadu, India b Department of Manufacturing Engineering, Annamalai University, Chidambaram, Tamil Nadu, India c Foundry and Forging Division, HAL, Bangalore, Karnataka, India Received 23 September 2007; accepted 29 January 2008 Available online 14 February 2008 Abstract In this investigation, the fatigue life prediction of ZE41A magnesium alloy has been statistically analyzed by Weibull distribution. The mechanical fatigue tests are conducted under R = 0.1 axial tension condition on specimen machined at as cast and welded materials. The micro structural investigations performed shows strong influence of precipitation on the fatigue failure of material. The curve for maximum stress and cycles to failure has been constructed for above stated materials. Using Weibull, the probability distribution according to which the material will fail is obtained. The fracture surface of the specimens is studied using scanning electron microscope. Ó 2008 Elsevier Ltd. All rights reserved. Keywords: Magnesium alloy; Gas tungsten arc welding; Weibull distribution; Fatigue life prediction 1. Introduction As a lighter structural alloy, magnesium alloys offer very attractive materials in order to enhanced performance and energy saving of machines and structures. Magnesium alloys are attractive because of their advantages such as light weight, high strength to weight ratio and high specific stiffness [1]. The cast magnesium alloys are extremely useful structural materials for automobiles, aerospace industries because of their high strength, low density and good machinability as compared with other metals and alloys [2 5]. Cast have clear economic advantage compared to wrought materials for mass production of components due to their lower long term processing and assembly costs [6]. Joining technology is important for materials development and excellent joining is an effective solution for * Corresponding author. address: mspragash@rediffmail.com (M. Sivapragash). simplifying product design and decreasing the cost, which affects the application of magnesium alloys. For the advantages of utility and economy, Gas Tungsten Arc Welding (GTAW) has been used extensively and some studies on GTAW of magnesium alloys have been reported [7,8]. The varying strengths of the material are due to their internal structure, inferring that there is no specific strength value to represent their mechanical behaviour. This leads to the necessity of employing statistical analyses for their safe utilisation in design and manufacturing. One of these analyses is the Weibull distribution, which has recently been used for the determination of static and dynamic mechanical properties of materials [9]. Weibull distribution has the capability to model experimental data of very different characters. In recent years, these statistical methods are widely used in research papers and books dealing with the historical development and applications. Fatigue life of any specimen, component or structure is the number of stress or strain cycles to cause failure in /$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi: /j.matdes

2 1550 M. Sivapragash et al. / Materials and Design 29 (2008) anticipated stress amplitude. It is a function of many variables, including environmental and metallurgical conditions of the material, and exhibits scattered results, even where the specimens are from the same lot and the applied stress or strain cycles are equal. Due to this scattered nature it is difficult to predict the fatigue life or to establish the prediction interval from a limited number of sample data. Many researchers have developed graphical and analytical methods to evaluate the fatigue life or strength and S N curve from a limited amount of data [10,11]. Lassen et al. [12] proposed statistical models for fatigue life prediction for welded joints are discussed and fitted to experimental data for fillet-welded steel joints where cracks emanate from the weld toe. The models assume the existence of a fatigue limit given as a stress range below which no failure will take place. The conclusion is that the rulebased S N curves may be overly pessimistic in the stress regime where service stresses frequently occur. A more correct statistical model based on a random fatigue-limit model results in S N curves that give decreased dimensions for a given fatigue design factor under constant amplitude loading. In this study, Weibull distribution was used to predict fatigue strength for the as cast and welded ZE41A magnesium alloy. 2. Experimental techniques 2.1. Materials and welding The sand-cast ZE41A magnesium alloy composed of wt% Zn, wt% RE, wt% Zr and remaining wt% as magnesium and is supplied by Hindustan Aeronautical Limited, Bangalore, India. Welding plates are machined to the size of 90 mm 50 mm 12 mm and welding experiments are conducted using gas tungsten arc welding (GTAW) method. Argon is used as the shielding gas. The welding process is carried out on optimum conditions. In earlier work, the welding parameters are optimized through Taguchi based grey analysis method for tensile, hardness and fracture toughness studies. The welding parameters are 200A current, argon gas flow of 19 l/min and filler diameter of 4 mm. The filler metal is cut from the base plate size of 310 mm 250 mm 18 mm which has same composition of base metal. The edges to be joined are designed to double V with 1mm root thickness. Prior the welding, the plates are preheated to 200 C to preventing the distortion. Leftward welding technique is followed and two passes on each side is adopted to fuse the edges and to fill the gap. After the completion of welding process, the welded plate for this experiment is heat-treated by the solutionizing at a temperature of 330 C for 2 h to improve the strength, toughness and shock resistance of the magnesium alloy. The ageing is done after solutionizing treatment of magnesium alloy at 180 C for 16 h to improve hardness and strength [13] Metallographic examination The initial microstructure of the as cast and welded materials are characterized by optical microscopy. The specimen are first polished with silicon carbide sheet paper of grade and subsequently mechanically polished with 1 lm diamond oil suspension. [14]After polishing, nital solution (5 ml HNO 3 (conc.), 95 ml Methanol) is used as the etchant and briefly applied to the surface of samples, which are then thoroughly rinsed with water and dried [15] Fatigue testing Fatigue strength data were obtained at a stress ratio (SR) of 0.1 with different maximum stresses ranges of MPa at a frequency of 20 Hz. The tests are carried out in the Instron fatigue testing machine in laboratory air at ambient temperature. The standard specimens are prepared as per ASTM standard E 466 [15]. Test specimens are machined from as cast and welded material as per the standard. After testing the fracture specimens are examined using JEOL scanning electron microscope (SEM). 3. Theoretical analysis Weibull distribution is being used to model extreme values such as failure times and fracture strength. In this study, the two-parameter Weibull distribution, which can be used in fatigue life prediction, will be considered. The distribution function in this case can then be written as follows [16]: F ðx; b; cþ ¼1 expð ðx=bþ c Þ; b P 0; c P 0 ð1þ In the context of this study, F ðx; b; cþ, represents the probability that the fatigue life is equal to or less than x. Using the equality F ðx; b; cþþrðx; b; cþ ¼1, the reliability Rðx; b; cþ, that is, the probability that the fatigue life is at least x, is defined as (Dodson 1994) F ðx; b; cþ ¼expð ðx=bþ c Þ; b P 0; c P 0 ð2þ The parameters scale parameter (b) and shape parameter (c) of the distribution function F ðx; b; cþ are estimated from observations. 4. Results and discussion Fig. 1 shows the microstructures of the as cast and welded materials, which are characterized by optical microscopy. The initial grains of as cast material are mostly irregular, uneven and coarse with distribution inhomogeneous. All grains are recrystallized. Fig. 1a shows that the average grain size of cast material are about 44 lm. The edges are not sharp and the grain boundaries are uneven. The microstructure displays evidence of porosity and fragmented grains. Fig. 1b shows that average grain size of weld metal are about 40.5 lm. All weld metal leads to grain refinement compare to initial structure due to post treatment. A clear and well defined boundary is seen existing between the fusion zone and the heat affected zone. In fusion zone the edges of the grains are not well defined and the boundaries are hazy. Large numbers of particles are precipitated in the network largely which breaks down the grain into separate fragments in fusion zone. This quaternary alloy containing zirconium and rare earth metals which plays vital role to achieve better properties. In this alloy, zirconium compound is separating from the liquid above the peritectic temperatures. This undergoes a peritectic reaction resulting in grain refinement. Zirconium addition completely eliminates the coarse grained, columnar cast structure, thus increasing the mechanical properties [17].

3 M. Sivapragash et al. / Materials and Design 29 (2008) Fig. 1. Optical images of as cast and welded material. (a) Optical image of as cast and (b) optical image of FZ of material welded material after heat treated. The Weibull plots of the test data of as cast and welded materials are shown in Figs. 2a and 2b The linear regression model with the regression line is used to obtained figures. All first point in figures appears to fit the line well. However, this is an expected situation in the method of linear regression; among consecutive (Y(i), Y(i + 1)) pairs, (Y(1),Y(2)) has the largest absolute difference. The Weibull modulus, which is determined using Minitab package, has a value of shape factor and scale factor for as cast material and for welded material the shape factor is and scale factor is The cumulative distribution failure (CDF) plots of the test data of as cast and welded materials are shown in Figs. 3a and 3b Through the CDF plot the value of each observation against the percentage of values in the sample that are less than or equal to that value. In this respect, an empirical CDF is similar to a probability plot except both axes are linear, which can make interpreting the empirical CDF more intuitive. Create an empirical CDF graph to compare the fitted distributions for each treatment and estimate the percentile of failure. The Weibull cumulative probability plots of the test data of as cast material and welded materials are shown in Figs. 4a and 4b Minitab package is used to calculate the plot points using a nonparametric method. The observed failure times are plotted on the x-axis vs. the estimated cumulative probabilities (p) on the y-axis. To make the fitted line, Minitab first calculates the percentiles for the various percents, based on the chosen distribution. The associated probabilities are then transformed and used as the y-variables. The percentiles may be transformed, depending on the distribution, and are used as the x-variables. The transformed scales, chosen to linearize the fitted line, differ depending on the distribution used. Approximate 95.0% confidence intervals for the fitted line are considered. Fig. 2a. Weibull plot of as cast material. Fig. 2b. Weibull plot of welded material.

4 1552 M. Sivapragash et al. / Materials and Design 29 (2008) Fig. 3a. Empirical CDF to failure of as cast material. Fig. 4a. Probability plot for cycles of as cast material. Fig. 3b. Empirical CDF to failure of welded material. Apparently, the shape factor was affected by the test stress and decreases with a decrease in the stress. A decreasing shape factor value shows that the measured data were more scattered and widely distributed. In other words the presence of precipitates and larger size of grain greatly affect the cycles to failure. The predictions of fatigue life, along with 10 percent probability of failure are extrapolated to 10 3 cycles for both as cast and welded materials. The predictions of fatigue life, along with percent probability of failure are extrapolated to cycles for as cast and cycles for welded materials. At 10 percent Fig. 4b. Probability plot for cycles of welded material. probability of failure are extrapolated to cycles for both as cast and welded materials. Similarly, Shih et al. [18] was predicted fatigue strength of extruded AZ91A magnesium alloy using Weibull distribution. The macroscopic fracture surfaces of the samples shown in Fig. 5 are observed carefully after fatigue testing. Most fracture surface demonstrates cleavage fracture, with a small fraction of ductile fracture. Fig. 5a reveals plastic deformation zone with secondary cracks and voids. The Fig. 5b reveals more micro voids than secondary cracks. The fractures are observed as quasi cleavage or cleavage and this tends to lower the fatigue life of the material.

5 M. Sivapragash et al. / Materials and Design 29 (2008) Fig. 5. Samples of SEM showing facture surface: (a) as cast material at (0.1) SR at 90 MPa and (b) welded material at (0.1) SR at 90 MPa. 5. Conclusion The Weibull distribution is employed here to predict the probability of failure of as cast and welded materials to maximum stress. The microstructure shows that the fusion zone of welded material has large numbers of precipitated particles in the network. This breaks down the grain into separate fragments in fusion zone and they weaken the material properties. The predictions of fatigue life, along with percent probability of failure are extrapolated to cycles for as cast and cycles for welded materials. At 10 percent probability of failure are extrapolated to cycles for both as cast and welded materials. The SEM result of fatigue life shows that all fractures are observed as quasi cleavage or cleavage. The presences of more micro voids in the welded material lead to lower the fatigue life of the material. Acknowledgement The authors are grateful to the Department of Forging and Foundry Division, Hindustan Aeronautical Limited, Bangalore, for providing Magnesium alloy material for carrying out the work. References [1] Froes Young FH, Won Kim, Krishnamurthy S. Rapid solidification of light weight metal alloys. Mater Sci Eng A 1989;117: [2] Smith WE. Structure and properties of engineering alloys. NewYork: Mc Graw Hill; [3] Mordike BL, Ebert T. Magnesium properties-application-potential. Mater Sci Eng A 2001;302: [4] Vijai Mohan V, Gopalakrishna V. Applications of magnesium alloys castings. In: KrishnadasNair CG, Gopalakrishna V, Dwarakadasa ES, editors. Source book on magnesium alloys technology, Bangalore, India; p.1 3 [paper no. 34]. [5] Paul DeGarms E, Black JT, Kohser Ronald A. Materials and processes in manufacturing. USA: Prentice-Hall Inc; [6] Luo A, Pekguleryuz MO. Cast magnesium alloys for elevated temperature application. J Mater Sci 1994;29: [7] Su SF, Huang JC, Lin HK, Ho NJ. Electron-beam welding behaviour in Mg Al based alloys. Metall Mater Trans A 2002;33A: [8] Lee WB, Kim JW, Yeon YM, Jung SB. The joint characteristics of friction stir welded AZ91D magnesium alloy. Mater Trans 2003;44: [9] Hallinan Jr AJ. A review of the Weibull distribution. J Qual Technol 1993;25(2): [10] Gope PC. A method for sample size determination to estimate average fatigue life. Proc IX ISME Conf Mech Eng 1994;1: [11] Parida N, Das SK, Gope PC, Mohanty ON. Probability, confidence, and sample size in fatigue testing. J Test Eval 1990;18(6): [12] Lassen T, Darcis Ph, Recho N. Fatigue behavior of welded joints Part 1 statistical methods for fatigue life prediction. Weld J 2005: 183s 7s. [13] Rajan TV, Sharma CP, Sharma A. Heat treatment principles and techniques. India: Prentice-Hall of India Private Ltd; [14] Avedesian M, Baker Hugh, editors. ASM specialty hand book magnesium and magnesium alloys. Materials Park (OH): ASM International; [15] ASTM Standard E-466. Practice for conducting force controlled constant amplitude axial fatigue tests of metallic materials. Philadelphia: American Society For Testing And Materials; [16] Dirikolu MH, Aktas A, Birgoren B. Statistical analysis of fracture strength of composite materials using Weibull distribution. Turk J Eng Environ Sci 2002;26:45 8. [17] Emley EF. Principles of magnesium technology. London: Pergamon Press; [18] Shih TS, Liu WS, Chen YJ. Fatigue of as-extruded AZ61A magnesium alloy. Mater Sci Eng A 2002;325: