Fatigue Life Assessment of Automotive Leaf Springs

The creation of a new mechanical component, such as a high-performance leaf spring, is a very challenging procedure that consists of many stages over a long timeframe from concept to production. High performance leaf springs are components with high complexity at the areas of failure. This complexity is derived from the multiple manufacturing processes that the raw material undergoes to reach its final geometrical and microstructural form. The paper shows the assessment of fatigue life of high-performance leaf springs, from different manufacturers with different geometrical and loading parameters. The assessment uses the fatigue life calculations which are described at the FKM Guideline as a basis. Limitations of the FKM Guideline, concerning the material’s ultimate tensile strength and the exclusion of the stress shot peening process, are restricting the fatigue life calculations of such components, therefore, a new theoretical tool is needed for more accurate calculations.


Introduction
The modern society is heavily based on transportation of both people and goods.Big portion of transportation is performed by commercial heavy vehicles driving on the roads [1].These vehicles use internal combustion engines that produce carbon dioxide and other air pollutants.Therefore, European union has introduced the last three decades regulations that the automotive industry must comply with, the EURO standards [2].These standards dictate the minimization of fuel consumption and air pollutants, not only by optimizing their engine functionality and their aerodynamic shape, but also by minimizing the vehicle's net weight.As a result of these regulations, automotive industries want to minimize the structural weight of all components by pushing the technological boundaries.One of the structural parts that is greatly affected by the weight minimization, is the leaf spring from the vehicle's suspension systems which is designed to operate within a specific fatigue life to minimize its weight even more [3].These lightweight leaf springs are called high performance leaf springs and are produced through multiple manufacturing processes that the raw material undergoes to reach its final geometrical and microstructural form.The complexity of the material at the failure critical area of the spring is high and cannot be easily described analytically, thus, engineers must perform multiple fatigue tests throughout the development and production stage of each spring.Leaf springs are elongated steel structures that connect the axle to the vehicle's chassis.In figure 1, the leaf spring is highlighted inside a circle, and to be more precise this leaf spring is a tow leaf spring consisted of two beams.The leaf spring major loading type is bending; therefore, the failure critical area is located on the tensile surface of the spring.The present paper will demonstrate how the FKM guideline [4] perform on calculating fatigue life of a leaf spring, using simple material data from the springs and then compare the theoretical fatigue lives to the experimental fatigue data of the same components.The fatigue life experimental data and their material properties come from a batch of 10 leaf spring testing specimens.

Manufacturing and Material
The leaf springs manufacturing is a long and complicated procedure that includes many steps.The raw material comes in the form of a spring steel bar, either 52CrMoV4 or 51CrV4 [5], with the respective thickness and width, which is cut into the wanted length.After the cut the bar is heated up to a high enough temperature (>900°C) to become malleable and to let the changes to its microstructure begin.As is, the leaf spring gets hot rolling which gives to the spring the specified thickness along its length and the spring's curvature is given.The next step is quenching in an oil bath with controlled temperature, during which the spring's microstructure turns into 100% martensite and the material gets much harder, as well as brittle, figure 2. To regulate its brittleness the spring is heated up again for a certain duration to get tempered.When the heat treatment is finished the spring's tensile surface needs to be enhanced.The spring is bent so that its surface gets almost to the material's ultimate tensile strength, and then it gets shot peening to further plastically deform the surface to introduce compressive residual stresses, figure 3.This procedure is called stress shot peening and when it is finished the spring is released to get its final curved form.After release the compressive residual stresses get even higher, thus, getting higher fatigue life.On the downside, the spring's surface gets rougher allowing the creation of cracks.The last step of the manufacturing process is called setting, during which the leaf spring is bent once again to a higher level to plastically deform the tensile surface to normalize the residual stress field and get its final shape.After all these manufacturing steps and material transformations it is difficult to assign parameter values to any analytical guideline to calculate the spring's fatigue life.

Testing
Leaf spring's operation is simple, under normal operation a leaf spring is considered to experience 3point bending cyclic loadings with load ratios between R=0 and 0.5.Meaning that the minimum loading value is close to zero during vehicle rebound or when the vehicle is lifted.Therefore, when automotive manufacturers need fatigue life data, they fatigue test the leaf springs using standard cyclic loading levels.
Fatigue tests are performed on 3-point bending test rigs using a servo hydraulic actuator [6], figure 4. The leaf spring is clamped in the centre with steel blocks that connect to the actuator.On each side, the spring is mounted on bearings, to allow free movement of the spring when it is loaded.To determine the loading level, strain gages are attached to the tensile surface to monitor exactly the strain values.When the loading level is reached and cycles are stabilized, the leaf spring is tested to failure and the number of cycles is counted.A total of 10 specimens were tested with two different load levels.These specimens are representative of the produced leaf spring.To achieve that, the specimens share similar dimensions to the truck leaf spring except for the length.They have the same thickness at the clamping area and the parabolic area starts and ends with the same thickness.The specimens are designed so that during a load cycle the tensile surface is stressed equally, figure 5, by giving a parabolic thickness distribution to the spring.Of the 10 specimens, 5 were tested on 800±550Mpa, and 5 specimens were tested on the high level of 800±600MPa.On the low level, fatigue lives vary from cycles to failure up to N=198.897, while on the high level from N=60.380 cycles to failure up to N=128.630.The performed fatigue lives are typical to this type of leaf spring with no extraordinary values and can be used to test the performance of the FKM guideline calculations.

FKM guideline fatigue life calculation
The calculations suggested by the FKM guideline specify the fatigue limit of the component, a load level at the knee point of the life curve at N=10 6 cycles.To calculate fatigue life at higher loads the guideline suggests the use of a standardised slope k=-5.At this point it has to be highlighted that the FKM calculations provide a probability of survival Ps=97.5%.
To perform the calculation basic information of the leaf spring is needed, parameters such ultimate tensile strength, roughness, geometrical characteristics, and manufacturing procedures.The first parameter needed to initiate the calculation is the leaf spring's material ultimate tensile strength.For the tested specimens the material has an Rm of 1600MPa.This value is well over the guidelines limit for steel of 1200MPa, therefore the results will be treated cautiously.The next parameter is roughness at the critical failure area which is the tensile surface, and the measured value is Rz=28μm.The leaf spring's thickness is variable, 47mm to the clamping area, while the thickness of the investigated area is about 28mm.The thickness is used to calculate the statistical size effect factor, which together with the effect of the bending loading is included in the Kf,b factor.Finally, as previously stated the leaf spring's tensile surface has been stress shot peened to increase its fatigue life.This surface treatment can be included in the calculations as the factor Kv.According to the guideline, this factor takes values depending on the quality of the surface treatment, and the highest value is assigned to plain shot peening (Kv=1.3).In the case of the leaf spring surface treatment, this value is underestimating the true effect of stress shot peening, which, as stated before, increases even more the fatigue life, when compared to plain shot peening.Every other factor in the calculation takes the value 1.In figure 6, the direct comparison between the theoretical S-N curve and the experimental fatigue lives can be seen.According to FKM guideline the fatigue limit (with stress amplitude value 409MPa) is reached in two stages, firstly by applying the mentioned factors to find fatigue limit of the leaf spring for fully reversible loading cycles with R=-1, and then with the use of mean stress sensitivity factor as stated in the guideline, to reach the respective R.After fatigue limit is found the theoretical S-N curve can be designed using the slope value k=-5.The experimental lives, which can be seen with the circular points, clearly lie below the theoretical S-N curve.Though the two results seem to be close to each other, the experimental data rest on the unsafe side.

Conclusion
In the contemporary era we live in, more and more attention is given to weight optimization, towards a more sustainable future.With the implementation of the EURO regulations, structural components are expected to weight less and less, driving the manufacturers to push the boundaries of both material properties and manufacturing processes.Therefore, the new boundaries must be studied, and new analytical tools must be developed.Until the establishment of a new analytical tool, engineers are heavily relying on extensive fatigue life tests that a) cost a lot and b) are time consuming, delaying the development of such high-tech components.
The FKM guideline is a widely accepted set of fatigue life safe calculations that, despite the limitations stated in it, could fill the gap created by the new developments.Though the new applications lay outside the guideline's limits, it would be a helpful tool to engineers who deal with them.Despite the fact that, the chosen parameters are not too extreme, the FKM guideline calculations produced a result that is not safe.The calculated S-N curve lies above all the experimental results.This means that the specimens failed earlier than the calculation expected.Thus, an engineer cannot rely on them to design a new leaf spring.Further investigations could be performed using the FKM guideline for springs and spring elements [7].

Figure 5 .
Figure 5. Stress distribution at the tensile surface of a parabolic leaf spring test specimen.

Figure 6 .
Figure 6.Theoretical S-N curve direct comparison to experimental fatigue life data.