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\title{Failure Analysis of Semi-elliptical Master Leaf Spring of Passenger Car using Finite Element Method}
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             \author[1]{Ratnam  Uppala}

             \author[2]{fellow  yohannes}

             \author[3]{R. Srinivasa  Moorthy}

             \affil[1]{  Bahir Dar University}

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\date{\small \em Received: 12 December 2012 Accepted: 31 December 2012 Published: 15 January 2013}

\maketitle


\begin{abstract}
        


The design of leaf spring has been a constant challenge for automotive and manufacturing engineers and it has undergone multiple revisions [2, 3 and 4]. The aim of this paper is to investigate and analyze how failure occurs on the semi-elliptical master leaf spring of a commercial car by analytical approach and using FEM simulation to ascertain the failure condition and to provide a cost-effective design modification for the same. The currently used 10 mm thick master leaf fails repeatedly at a particular zone close to the spring hanger end. After multiple trials for different thickness values and materials, recommendations were given for a better and modified design of the master leaf spring. 

\end{abstract}


\keywords{failure analysis, leaf spring, von mises stress, spring steel.}

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\let\tabcellsep& 	 	 		 
\section[{Introduction}]{Introduction}\par
eaf springs are crucial suspension elements used on light passenger vehicles to give a riding comfort. The leaf spring should absorb the vertical vibrations and impacts due to road irregularities by means of variations in the spring deflection so that the potential energy is stored in spring as strain energy and then released slowly, ensuring a more compliant suspension system. Leaf springs can serve both damping as well as springing functions. The leaf spring can either be attached directly to the frame at both ends or attached at one end, usually the front, with the other end attached through a shackle, a short swinging arm. The shackle takes up the tendency of the leaf spring to elongate when compressed and thus makes for softer springiness.\par
Failure prediction in large-scaled structures that are subjected to extreme loading conditions has been of utmost interest in the scientific and engineering community over the past century \hyperref[b3]{[4]}. Failure of mechanical assembly component is a common phenomenon due to fracture that occurs almost everywhere in mechanical structures. The main cause of failure of leaf spring is due to large bending behavior \hyperref[b4]{[5]}\hyperref[b5]{[6]}.   
\section[{Literature Review}]{Literature Review}\par
The shape of leaf springs has undergone multiple changes and revisions over time from 'flat' to 'elliptical' to the present-day shape of being parabolic. The parabolic spring is light-weighted, has superior capacity to store strain energy and offers better riding comfort and is widely used now-a-days in automotive applications. But it has manufacturing complications.\par
Different sub-assembly of vehicles, including leaf springs are made of steels with low strength and high ductility. Their failure modes are usually characterized by ductile tearing. Fatigue life prediction is based on knowledge of both the number of cycles the part will experience at any given stress level during that life cycle and environmental factors. The local strain-life method can be used pro-actively for a component during early design stage \hyperref[b6]{[7,}\hyperref[b7]{8]}. For strain-based fatigue life prediction, Coffin-Manson relationship is normally applied \hyperref[b7]{[8]}, which is,( ) ( ) c f f b f f a N N E 2 ' 2 ' ? ? ? + = (1)\par
Where, E is the material modulus of elasticity, a ? is the true strain amplitude, 2N f is the number of reversals to failure, ?' f is the fatigue strength coefficient, b is the fatigue strength exponent, ?' f is the fatigue ductility coefficient and c is the fatigue ductility exponent.\par
Mathematically, the Morrow model is defined by,( ) ( ) c f f b f f m f a N N E 2 ' 2 ' 1 ' ? ? ? ? ? + ? ? ? ? ? ? ? ? ? = (2)\par
The SWT model is defined by,( ) ( ) ( ) c b f f f b f f a N N E + + = 2 ' ' 2 ' 2 2 max ? ? ? ? ? (3)\par
In 2008, Fuentes et al., studied leaf spring failure and concluded that the premature failure in the studied leaf springs which showed the fracture failure on a leaf was the result of mechanical fatigue and it was caused by a combination of design, metallurgical and manufacturing deficiencies \hyperref[b8]{[9]}. 
\section[{III.}]{III.} 
\section[{Failure Analysis}]{Failure Analysis}\par
The existing design parameters are listed in Table \hyperref[tab_1]{1}. The leaf spring considered is of simply supported beam type, where the central location of the spring is fixed to the wheel axle. Therefore, the wheel exerts the force F on the spring and support reactions at the two ends of the spring come from the carriage. Maximum deflection, bending stress and Von-Mises stress distribution were estimated by considering the master leaf as a simply supported beam.\par
For uniform width of master leaf, the maximum stress and displacement were analytically calculated using,  
\section[{Modified Design}]{Modified Design}\par
The spring steels commonly used for making leaf springs are low alloy steels like Carbon steel, Si steel, Mn steel, Si-Mn steel, Si-Cr steel, Mn-Cr steel, Cr-V steel, Si-Cr-V steel, Si-Ni-Cr steel, Ni-Cr-Mo steel and Cr-Mo steel. In this paper the material property selected for analysis is a Carbon steel of 56SiCr7, tempered in the temperature range of 400°C\textasciitilde 550°C \hyperref[b9]{[10,} {\ref 11]}.\par
Table \hyperref[tab_1]{1} : Spring steel standards -ISO683-14(1992-08-15) [6]   No  
\section[{FEM -Based Failure Analysis}]{FEM -Based Failure Analysis}\par
The semi-elliptical master leaf was modeled using Solidworks 2012 software. Shackle and bushing were considered for boundary conditions only. Shotpeening and Nip stresses and the frictional effect were also omitted.     
\section[{Results And Discussion}]{Results And Discussion}\par
The post processing of the modeled master leaf (existing), gave the stress, strain and displacement plots as shown in Fig.  {\ref 6}.\par
It is evident that the Von-Mises stress at the hanger end is critical (604 MPa) and is close to the yield stress value (650 MPa), even in static loading conditions. Reversed fatigue loading affects the life of master leaf causing pre-mature failure in the same zone (near hanger end) reported in the passenger car service station.\par
To overcome this failure, multiple trials have been made in terms of change of material and thickness of the semi-elliptical master leaf. Si steel substantially increases the elastic limit of the steel and improves the resistance to permanent set of springs.\par
Hence Si steel of ISO specification 56SiCr7 is chosen from the ISO spring steel standard shown in Table \hyperref[tab_1]{1}. Similarly, after repeated trials for varying thicknesses, 14 mm thickness is chosen for the uniform thickness of master leaf. The FEA results for the modified design were depicted in Fig.  {\ref 7}.\par
The fatigue test result (S-N curve) for dynamic loading of master leaf and the comparison of the results obtained were shown in Fig.  {\ref 8} and Table  {\ref 3} respectively. 
\section[{( )}]{( )}\par
A Year\begin{figure}[htbp]
\noindent\textbf{1}\includegraphics[]{image-2.png}
\caption{\label{fig_0}Figure 1 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{}\includegraphics[]{image-3.png}
\caption{\label{fig_2}Failure}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{2}\includegraphics[]{image-4.png}
\caption{\label{fig_3}Figure 2 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{3}\includegraphics[]{image-5.png}
\caption{\label{fig_4}Figure 3 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{}\includegraphics[]{image-6.png}
\caption{\label{figure6}}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{}\includegraphics[]{image-7.png}
\caption{\label{figure7}}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{1} \par 
\begin{longtable}{P{0.5981481481481481\textwidth}P{0.2518518518518518\textwidth}}
Parameter\tabcellsep Value\\
Material selected\tabcellsep 20MoCr4 (ISO grade)\\
Total span length (eye to eye)\tabcellsep 1200 mm\\
Camber height\tabcellsep 137 mm\\
Width of master leaf leaves\tabcellsep 60 mm\\
Normal static load\tabcellsep 1500 N\end{longtable} \par
 
\caption{\label{tab_1}Table 1 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{2} \par 
\begin{longtable}{}
\end{longtable} \par
 
\caption{\label{tab_3}Table 2 :}\end{figure}
 			\footnote{Meanwhile, two mean stress effect models commonly used are the Morrow\hyperref[b7]{[8]} and Smith-Watson-Topper (SWT)\hyperref[b4]{[5]} strain-life models.? ? ?} 			\footnote{© 2013 Global Journals Inc. (US)} 			\footnote{Failure Analysis of Semi-elliptical Master Leaf Spring of Passenger Car using Finite Element Method} 		 		\backmatter   			 
\subsection[{Acknowledgment}]{Acknowledgment}\par
The authors would like to thanks Assistance Prof. Yonas Mitiku for his valuable guidance, and for Mr. Wolelaw Endalew for his continuous encouragement to challenge things. All thanks made next to my lord Jesus chrysies. 			  			 \par
The following inferences can be taken from the above results: ? The revised design shows a marked reduction in Von Misses stress. The maximum Von Misses stress induced reduced by 33\%.\par
The yield strength of 56SiCr7 steel used in revised design is 1962 MPa, which is nearly 5 times that of maximum Von-Mises stress induced. This ensures high factor of safety and reliable operation even under dynamic conditions. 
\subsection[{? The maximum bending stress induced (analytical)}]{? The maximum bending stress induced (analytical)}\par
for static loading conditions reduced by 49\%.\par
? FEM based resultant displacement registered 33\% reduction.\par
Thus the modified design involving change of material with an increased thickness of 14 mm has substantial improvements in terms of reduction of V o n M i s e s stress, higher yield strength, lessened resultant displacement and higher factor of safety. Hence the authors recommend this as a cost-effective solution, as desired by the customer.\par
The other alternatives like use of parabolic master leaf with varying thickness and use of composite materials are not advocated, since the objective was to give an economic and feasible design revision for the existing semi-elliptical master leaf, which is prone to frequent failure. 
\subsection[{VII.}]{VII.}			 			  				\begin{bibitemlist}{1}
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\bibitem[Conway and Sjodahl ()]{b9}\label{b9} 	 		‘Analysis and representation of fatigue data’.  		 			J B Conway 		,  		 			L H Sjodahl 		.  	 	 		\textit{Materials}  		1991. ASM International.  	 
\bibitem[Kothari ()]{b1}\label{b1} 	 		‘Comparison of Performance of Two Leaf Spring Steels Used for Light Passenger Vehicle’.  		 			Dakshraj Kothari 		.  	 	 		\textit{)},  		VSRD-MAP  		2012. 2 p. .  	 
\bibitem[Malaga and Kumar ()]{b0}\label{b0} 	 		\textit{Design Optimization of Leaf Spring},  		 			Malaga 		,  		 			Kumar 		.  		2012. 2 p. .  	 
\bibitem[Elber]{b6}\label{b6} 	 		‘Fatigue crack closure under cyclic tension’.  		 			W Elber 		.  	 	 		\textit{Eng Fract Mech}  		1970 p. .  	 
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