**4. Fatigue analysis (Senthilkumar & Vijayarangan, 2007)**

Main factors that contribute to fatigue failures include number of load cycles experienced, range of stress and mean stress experienced in each load cycle and presence of local stress concentrations. Testing of leaf springs using the regular procedure consumes a lot of time. Hence (SAE manual,1990) suggests a procedure for accelerated tests, which give quick results, particularly for SLSs. As per the outlined procedure(SAE manual,1990 & Yasushi,1997), fatigue tests are conducted on SLSs and CLSs. Fatigue life(Yasushi,1997) is expressed as the number of deflection cycles a spring will withstand without failure (Fig. 8).

### **4.1 Fatigue life of Steel Leaf Spring (SLS)**

Fatigue life calculation of SLS is given as follows: stroke available in fatigue testing machine, 0-200 mm; initial deflection of SLS, 100 mm; initial stress (measured by experiment), 420 MPa; final deflection of SLS (camber), 175 mm; maximum stress in the final position (measured by experiment), 805 MPa. Fatigue life cycles predicted for SLS is less than 10,00,000 cycles (Fig. 8) by the procedure outlined in (SAE manual,1990).

### **4.2 Fatigue life of Composite Leaf Spring (CLS)**

A load is applied further from the static load to maximum load with the help of the electrohydraulic test rig, up to 3250 N, which is already obtained in static analysis. Test rig is set to operate for a deflection of 75 mm. This is the amplitude of loading cycle, which is very high. Frequency of load cycle is fixed at 33 mHz, as only 20 strokes/min is available in the test rig. This leads to high amplitude low frequency fatigue test.

Design, Manufacturing and Testing

**4.2.2 Life time distribution** 

referred to as scale parameter.

or 'scale' parameter.

life prediction.

The reliability of Weibull distribution is given by,

Table 7. Median rank of composite leaf springs.

of Polymer Composite Multi-Leaf Spring for Light Passenger Automobiles - A Review 69

**Leaf spring No. Cycles to fail Stress level** 1 10,800 0.65 2 6,950 0.65 3 19,240 0.65 4 14,350 0.65

Weibull life distribution model is selected which has previously been used successfully for the same or a similar failure mechanism. The Weibull distribution is used to find the reliability of the life data and it helps in selecting the particular data that is to be used in life prediction model. The Weibull distribution uses two parameters, namely, 'b' and 'Ө' to estimate the reliability of the life data. 'b' is referred to as shape parameter and 'Ө' is

( ) 1-exp[- / ]*<sup>b</sup> Rt x*

where, X is the life; b is the Weibull slope or 'shape' parameter and Ө is the characteristic life

The parameters of the Weibull distribution are calculated using probability plotting (Weibull, 1961). The life cycles of leaf spring are arranged in increasing order and the

> **Order No. Cycles to fail Median rank** 1 6,950 15.9 2 10,800 38.5 3 14,350 61.4 4 19,240 84.1

The value of Ө is found to be 14,600 cycles. The reliability of the life data is calculated and shown in Table 8. It is found that the reliability of 3rd GFRP spring is higher than that of other leaf springs and the fatigue life data of 3rd GFRP spring has been considered for fatigue

The fatigue test is conducted up to 20000 cycles and it is examined that no crack initiation is visible. The details of test results at 0 and 20000 cycles are as follows: maximum load cycle range, 1850-3250 N; amplitude, 75 mm; frequency, 33 mHz; spring rate, 27.66 N/mm; maximum operating stress, 240 MPa; minimum operating stress, 140MPa and time taken 17 h. The experimental results are available only up to 20000 cycles. With no crack initiation,

median rank is calculated using the Equation (3) and are shown in Table 7.

where, j is the order number and N is the total quantity of sample.

*Medianrank j* 100 \* ( -0.3)/(N 0.4) (3)

(2)

Table 6. Number of cycles to failure for composite leaf spring.

Fig. 8. Estimation of fatigue life cycles of steel leaf springs (SAE manual,1990).

Maximum and minimum stress values obtained at the first cycle of the CLS are 222 MPa and 133 MPa respectively. As the cycles go on increasing, stress convergence is happening only after 25000 cycles. These maximum and minimum operating stress values are 240 MPa and 140 MPa respectively. Because of very low stress level, fatigue life of CLS is very high under simulated conditions.

#### **4.2.1 Life data analysis**

Life data analysis (Weibull,1961) which is a statistical approach is used to find the reliability of predictions about the life of composite leaf springs by fitting a statistical distribution to life data from representative sample units. For the GFRP leaf spring, the life data is measured in terms of the number of cycles to fail for the four leaf springs and are presented in Table 6.


Table 6. Number of cycles to failure for composite leaf spring.

#### **4.2.2 Life time distribution**

68 Materials Science and Technology

Fig. 8. Estimation of fatigue life cycles of steel leaf springs (SAE manual,1990).

simulated conditions.

in Table 6.

**4.2.1 Life data analysis** 

Maximum and minimum stress values obtained at the first cycle of the CLS are 222 MPa and 133 MPa respectively. As the cycles go on increasing, stress convergence is happening only after 25000 cycles. These maximum and minimum operating stress values are 240 MPa and 140 MPa respectively. Because of very low stress level, fatigue life of CLS is very high under

Life data analysis (Weibull,1961) which is a statistical approach is used to find the reliability of predictions about the life of composite leaf springs by fitting a statistical distribution to life data from representative sample units. For the GFRP leaf spring, the life data is measured in terms of the number of cycles to fail for the four leaf springs and are presented Weibull life distribution model is selected which has previously been used successfully for the same or a similar failure mechanism. The Weibull distribution is used to find the reliability of the life data and it helps in selecting the particular data that is to be used in life prediction model. The Weibull distribution uses two parameters, namely, 'b' and 'Ө' to estimate the reliability of the life data. 'b' is referred to as shape parameter and 'Ө' is referred to as scale parameter.

The reliability of Weibull distribution is given by,

$$R(t) = 1 \cdot \exp[-\mathbf{x} \;/\; \theta]^b \tag{2}$$

where, X is the life; b is the Weibull slope or 'shape' parameter and Ө is the characteristic life or 'scale' parameter.

The parameters of the Weibull distribution are calculated using probability plotting (Weibull, 1961). The life cycles of leaf spring are arranged in increasing order and the median rank is calculated using the Equation (3) and are shown in Table 7.

$$\text{Medianramk} = 100 \, \text{\*} \, (\text{j-0.3}) / (\text{N} + 0.4) \tag{3}$$

where, j is the order number and N is the total quantity of sample.


Table 7. Median rank of composite leaf springs.

The value of Ө is found to be 14,600 cycles. The reliability of the life data is calculated and shown in Table 8. It is found that the reliability of 3rd GFRP spring is higher than that of other leaf springs and the fatigue life data of 3rd GFRP spring has been considered for fatigue life prediction.

The fatigue test is conducted up to 20000 cycles and it is examined that no crack initiation is visible. The details of test results at 0 and 20000 cycles are as follows: maximum load cycle range, 1850-3250 N; amplitude, 75 mm; frequency, 33 mHz; spring rate, 27.66 N/mm; maximum operating stress, 240 MPa; minimum operating stress, 140MPa and time taken 17 h. The experimental results are available only up to 20000 cycles. With no crack initiation,

Design, Manufacturing and Testing

of Polymer Composite Multi-Leaf Spring for Light Passenger Automobiles - A Review 71

**Maximum stress MPa Applied stress level Number of cycles to** 

Optimisation of weight reduction in CLS has been carried out(Senthilkumar & Vijayarangan,2007). The nite element analysis of composite multi leaf spring with 7 leaves shows that maximum deection of the leaf spring and the bending stress induced are well within the allowable limit (factor of safety 2.8). So, it is decided to optimize the number of leaves with minimum of 2 leaves and maximum of 7 leaves using ANSYS 7.1 itself, for the

0 5000000 10000000 15000000 20000000

Number of Cycles to Failure

(Stress ratio = 0.24, > 10,00,000 cycles)

Table 9. Fatigue life at different stress levels of composite leaf spring.

Fig. 9. S-N curve for composite leaf spring.

**5. Optimisation** 

Applied Stress, MPa

Applied Stress, MPa

100 0.1 8143500 200 0.2 3515500 300 0.3 1354800 400 0.4 450900 500 0.5 122700 600 0.6 25000 700 0.7 3200 800 0.8 200 900 0.9 - 1000 1.0 -

**failure** 


Table 8. Reliability of fatigue life data.

there is a necessity to go for analytical model for finding number of cycles to failure from analytical results. An analytical fatigue model to predict the number of fatigue cycles to failure for the components made up of composite material has been developed (Hwang and Han,1986). They have proposed two constants in their relation on the basis of experimental results. It is proved that the analytical formula predicts the fatigue life of component with E-Glass/epoxy composite material.

$$\text{Hwang and Han relation: N} = \text{[B(1-r)]}^{1/\text{C}} \tag{4}$$

where, N is the number of cycles to failure; B= 10.33; C= 0.14012; r = max/U; max is the maximum stress; U is the ultimate tensile strength and r is the applied stress level. Equation (4) is applied for different stress levels and fatigue life is calculated for the composite leaf spring. The results are obtained based on the analytical results (Table 9) and the resulting S-N graph is shown in Fig.9. From Fig.9, it is observed that the composite leaf spring, which is made up of E-glass/epoxy is withstanding more than 10 Lakh cycles under the stress level of 0.24.

The test was conducted for nearly 17 hours to complete 20000 cycles. The variations in stress level were reduced to very low level after 20000 cycles. There was no crack initiation up to 20000 cycles. The stress level of 0.24 is obtained from experimental analysis. This is very much helpful for the determination of remaining number of cycles to failure using fatigue model (Hwang and Han,1986). According to this fatigue model, the failure of the composite leaf spring takes place only after 10 Lakh cycles. Since the composite leaf spring is expected to crack only after 10 Lakh cycles, it is required to conduct the leaf spring fatigue test up to 10 Lakh cycles for finding type and place of crack initiation and propagation. For completing full fatigue test up to crack initiation with the same frequency, nearly 830 hours of fatigue test is required.

From the design and experimental fatigue analysis of composite multi leaf spring using glass fibre reinforced polymer are carried out using life data analysis, it is found that the composite leaf spring is found to have 67.35% lesser stress, 64.95% higher stiffness and 126.98% higher natural frequency than that of existing steel leaf spring. The conventional multi leaf spring weighs about 13.5 kg whereas the E-glass/Epoxy multi leaf spring weighs only 4.3 kg. Thus the weight reduction of 68.15% is achieved. Besides the reduction of weight, the fatigue life of composite leaf spring is predicted to be higher than that of steel leaf spring. Life data analysis is found to be a tool to predict the fatigue life of composite multi leaf spring. It is found that the life of composite leaf spring is much higher than that of steel leaf spring.


Table 9. Fatigue life at different stress levels of composite leaf spring.

Fig. 9. S-N curve for composite leaf spring.

#### **5. Optimisation**

70 Materials Science and Technology

**Leaf spring no. Life (cycles) Median rank Reliability (%)**  1. 10,800 38.5 43 2. 6,950 15.9 39 3. 19,240 84.1 73 4. 14,350 61.4 62.7

there is a necessity to go for analytical model for finding number of cycles to failure from analytical results. An analytical fatigue model to predict the number of fatigue cycles to failure for the components made up of composite material has been developed (Hwang and Han,1986). They have proposed two constants in their relation on the basis of experimental results. It is proved that the analytical formula predicts the fatigue life of component with E-

where, N is the number of cycles to failure; B= 10.33; C= 0.14012; r = max/U; max is the maximum stress; U is the ultimate tensile strength and r is the applied stress level. Equation (4) is applied for different stress levels and fatigue life is calculated for the composite leaf spring. The results are obtained based on the analytical results (Table 9) and the resulting S-N graph is shown in Fig.9. From Fig.9, it is observed that the composite leaf spring, which is made up of E-glass/epoxy is withstanding more than 10 Lakh cycles under the stress level

The test was conducted for nearly 17 hours to complete 20000 cycles. The variations in stress level were reduced to very low level after 20000 cycles. There was no crack initiation up to 20000 cycles. The stress level of 0.24 is obtained from experimental analysis. This is very much helpful for the determination of remaining number of cycles to failure using fatigue model (Hwang and Han,1986). According to this fatigue model, the failure of the composite leaf spring takes place only after 10 Lakh cycles. Since the composite leaf spring is expected to crack only after 10 Lakh cycles, it is required to conduct the leaf spring fatigue test up to 10 Lakh cycles for finding type and place of crack initiation and propagation. For completing full fatigue test up to crack initiation with the same frequency, nearly 830 hours

From the design and experimental fatigue analysis of composite multi leaf spring using glass fibre reinforced polymer are carried out using life data analysis, it is found that the composite leaf spring is found to have 67.35% lesser stress, 64.95% higher stiffness and 126.98% higher natural frequency than that of existing steel leaf spring. The conventional multi leaf spring weighs about 13.5 kg whereas the E-glass/Epoxy multi leaf spring weighs only 4.3 kg. Thus the weight reduction of 68.15% is achieved. Besides the reduction of weight, the fatigue life of composite leaf spring is predicted to be higher than that of steel leaf spring. Life data analysis is found to be a tool to predict the fatigue life of composite multi leaf spring. It is found that the life of composite leaf spring is much higher than that of

Hwang and Han relation: 1/C N={B(1-r)} (4)

Table 8. Reliability of fatigue life data.

Glass/epoxy composite material.

of 0.24.

of fatigue test is required.

steel leaf spring.

Optimisation of weight reduction in CLS has been carried out(Senthilkumar & Vijayarangan,2007). The nite element analysis of composite multi leaf spring with 7 leaves shows that maximum deection of the leaf spring and the bending stress induced are well within the allowable limit (factor of safety 2.8). So, it is decided to optimize the number of leaves with minimum of 2 leaves and maximum of 7 leaves using ANSYS 7.1 itself, for the

Design, Manufacturing and Testing

ANSYS 7.1. Manual, (1997). Ansys Inc, New York

0133182398, New York.

No.6,pp.(4759-4764), ISSN 0975-5462.

pp. (163 – 176), ISSN 0263-8223

*US pat 4,565,356* 

0045-7949

ISSN 1392–1320

spring, *US pat 4*, 560, 525

**8. Acknowledgement** 

0266-3538

provided by DRDO.

**9. References** 

of Polymer Composite Multi-Leaf Spring for Light Passenger Automobiles - A Review 73

This work is carried out as part of research project supported by Defense Research and Development Organisation (DRDO), India. Author is grateful for the financial support

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minimum weight. The number of leaves is reduced one by one, without changing any of the dimensions, and found out results for same full bump load. The results are shown in Table 10. From the FEM results in Table 10, it is understood that the leaf spring with 3 leaves violates the constraints of deection and stress. Therefore, further optimization is terminated at this point. It is evident that only 4 leaves (2 full length leaves and 2 graduated leaves) are sufcient to withstand the applied load. The composite leaf spring with 4 leaves weighs about 3.18 kg only. It gives a weight reduction of 76.4%.


Table 10. Results of optimization of number of leaves.
