X CONGRESO INTERNACIONAL DE INGENIERÍA DE PROYECTOS

VALENCIA, 13-15 Septiembre, 2006

METHODOLOGY FOR A WHOLE ANALYSIS OF THE FATIGUE BEHAVIOUR ON AUTOMOTIVE COMPONENTS

J. Romo García, E. Cañibano Álvarez, C. Maestro Martín, L de Prada Martín(p)

Abstract Nowadays, the great improvement in finite element methodology development has changed the way of solving fatigue problems. The automotive world is not out of this development. In this paper a methodology to make a whole analysis of the fatigue behaviour on several automotive components is described. In order to get this aim it is used a feed back circle between the FEM simulation and the experimental results.

The basic schedule for this analysis consists on making a statical study with unitary loads over the component, this step is made with a finite element code. If the geometry or load make necessary to mesh a submodel of the most critical zone in order to know more accurately the location and distribution of stress concentration it will be done.

In order to make the fatigue simulation with the finite elements method three main inputs are necessary: First of them is the strain state obtained from the statical analysis. The second one is the curve describing the strain-life behaviour of the material considered. The last input is the temporal signal beared by the component. At the same time experimental testing is made in order to validate the results from the simulation.

Keywords: Fatigue, FE simulation, Validation, Durability Methodology, Design optimisation.

Resumen El gran desarrollo de los programas de elementos finitos en los últimos años ha cambiado el modo de resolver los problemas de fatiga. Este desarrollo incluye a la industria de automoción, a lo largo del presente artículo se describe el análisis completo de varios componentes de automoción. Para poder completar esta tarea, se usará un ciclo realimentado entre las simulaciones de FE y los resultados experimentales.

El esquema básico para este análisis incluye un estudio estadístico con cargas unitarias, paso que se lleva a cabo con el código de FE. Si la geometría o la carga hacen necesario mallar un submodelo de la zona más crítica, de modo que se conozcan con más exactitud la posición y distribución de la concentración de tensiones, este submodelo se realizará.

Para poder realizar la simulación de fatiga, con el método FE, es necesario conocer tres datos de entrada: El primero es el estado de deformaciones, obtenido a través de un análisis estadístico. El segundo es la curva de deformación-vida del material considerado. Por último la señal temporal de carga que soporta el componente. Al mismo tiempo se llevarán a cabo experimentos para poder validar los resultados que se obtengan de la simulación.

Palabras clave: Fatigua, FEM, Validación, Durabilidad, Optimización de diseño..

1.- Introduction During the last years the finite elements methodology and the computers have suffered a large evolution that has changed the way of solving the calculations in the engineer’s world.

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One of the last places to be reached by the finite elements has been the fatigue. In this technical field it is been made the first move towards the consolidation of a reliable methodology with a great ratio of correlation with the experimental tests. This paper follows this direction, a methodology for the fatigue simulation of metallic components has been established and later experimental tests have been made in order to validate the procedure.

With the development of this methodology some important advantages are obtained, for example time into market reduction and decrease of the number of prototypes. And also, with this analysis the durability of the component is warranted and this fact increases the added value of the final product. Other important advantage is that the number of the long and expensive durability test is drastically reduced.

2.- Methodology Schedule The schedule of the methodology developed is shown in this picture.

GEOMETRYMESH

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Figure 1: Methodology schedule

2.1.- Geometry and mesh For the methodology development a hexaedral mesh has been used. Our experience in finite elements contact simulation shows that the quality of the results is improved with this kind of elements. The effort in the meshing process is compensated by the accuracy of the result.

2.2.- Residual stresses A previous step to the simulation of the static load is to consider the stress and strain field due to the manufacturing and the assembly processes. The consideration of these processes have a great influence on the fatigue behaviour of the component, because a initial stress field can vary the main stress value when the variable load are been applied and this parameter has a great influence on the component life.

2.3.- Static characterisation The mechanical properties characterisation of the materials when a static load is applied is very important for any finite elements simulation, but in the case of a fatigue analysis this importance is greater because a small deviation in the static simulation can introduce large

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errors in the fatigue analysis. The reason is that the static results are one of the inputs of the fatigue simulation.

The static characterisation is made through the application of a tensile load on standard specimens, the test is made with an extensometer following the standard EN 10002. From the test the engineering curve is obtained, and also some characteristics values like the Young modulus, the yield stress, the ultimate stress or the maximum strain before breaking. With the curve from the test and a simulation program it is possible to obtain the real behaviour curve, that is the one introduced as an input in the finite elements code for the static simulation.

2.4.- Static load For the static load consideration there are two different cases. First of them is when the simulation is totally linear, there are no contacts, no plasticity, no large strain and no rubber like behaviour in any components around. In this case, it is possible to use a unitary load for the static simulation and later it would be enough to multiply the stress and strain field obtained by the load history in order to obtain the input for the fatigue analysis software.

When some non-linearties exist, in the static simulation, it is necessary to make one calculation for every load state that will be considered in the fatigue analysis. This fact is a direct consequence of the non-linearty.

2.5.- Stress and strain For the stress strain field determination, it is possible to use any of the finite elements codes available in the market. In the Centre for Automotive Research and Development, CIDAUT, we usually use NASTRAN for the linear cases and MARC for the non-linear.

As it was shown in the previous schedule the main inputs for the determination of the stress and strain state are the mesh, the static properties and the loads. Other important data to take into account are the boundary conditions and the choice of the right element type to be used.

2.6.- Critical zone submodel In some occasions the zone of the component where the fatigue behaviour is critical can be quite small compared with the whole size of the component, for this reason the size of the mesh can be not adequate for the determination of the stress and strain in the critical zone. There are two alternatives to solve this problem. The first one is to make a finer mesh of the whole component, this fact implies an important increase in the computational cost and it may overcome the maximum capacity of the equipment. The second option is to make a submodel of the critical zone. This one has been the alternative chosen for the methodology, so it will be explained in greater detail.

The most important step of this process is the boundary conditions application. The displacements on the nodes of the initial static simulation are applied on the nodes in the border of the critical zone and are extrapolated to the new mesh. With the new static simulation we are able to get a great accuracy in the stress and strain results in the critical zone of the component.

2.7.- Cyclic characterisation This has been one of the more important points in the methodology development. It has been probed that small variations in the cyclic properties of the material imply large errors in the fatigue life estimation. There are three main techniques to obtain the material properties of the material:

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The main advantage of the bibliography is the low cost, although it has important disadvantages that recommend against its use. There is a lack of accuracy because it is very difficult to find the same material with the same manufacturing process and treatment.

Another possibility is to estimate the fatigue behaviour curve from the static properties of the material. Many researchers have developed their own method, the more important ones are Baumel and Seeger, Universal Slopes and the Four-Points Correlation. The main advantage is that the estimated curve fits better with reality than the bibliography curve. The disadvantage is that there is still a large deviation and since those methods are to be applied to any material, the deviations follow no tendency.

The third way, testing the material, is the most accurate, although it is also the most money and time consumming. To carry the test out, several specimens with uniform section are needed, the sape, size and surface finish are ruled by the standards ASTM E-466 “Standard Practice for Conducting Force Controlled Constant Amplitude Axial Fatigue Test of Metallic Materials” and ASTM-606 “Standard Practice for Strain-Controlled Fatigue Testing”, depending on which property is controlled.

Figure 2: Left: Specimens for cyclic characterisation. Centre: Broken specimen. Right crack in specimen

Several tools have been used during the test, the most important are the load cell, the LVDT and the extensometer. The results from this test are the specimen life, the plastic strain, the total strain, the hysteresis cycles, the stress, the force and the displacement, all of them as a function of time and number of cycles.

Figure 5: Elastic and plastic estimated curves

For the statistical treatment of the results, the standard ASTM E-739 “Standard Practice for Statistical Analysis of Linear or Linearized Stress-Life (S-N) and Strain-Life (ε -N) Fatigue Data” is used. From this standard the statistical values that define the behaviour of the elastic and plastic part of the strain-life curve can be calculated, as it is shown in figure 5.

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2.8.- Load history The load history shows the differents loads beared by the component through its life and in-service conditions. It can be calculated in two main ways. First of them is to make experimental measures over the component that we want to simulate. It is a very accurate procedure, but it can be difficult to make. Sometimes the component it is on a develop stage so it is not possible to test it. Or there can be a lack of accessibility to the measure point.

In those cases we can use a second way, by means of building a virtual multibody model. The main advantage of this tool is the low cost and the quick response. It is possible to build complex models of cars that reproduce with high reliability the behaviour when some manoeuvres or solicitations are imposed.

2.9.- Durability and damage analysis Once the strain state in the most critical zone of the component, the evolution of the load along the time and the cyclic properties of the material are known, the damage and the life of the component can be determined using specific software for fatigue.

An important utility of this kind of software is that It is possible to analyse the temporal signal and determine which are the cycles producing less damage, so they can be deleted from the signal, as an example, a road signal, after been edited, can be reduced to a 10% of its time, being the damage 95% or more of the initial one. That means that tests that initially were 6 months long can be carried out in two weeks .

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3.- Validation Once the methodology was defined, it was necessary to make experimental testing in order to get the validation. There were two levels where the validation should be done.

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GEOMETRYMESH

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Figure 8: Methodology schedule showing the validation levels

For the first validation level we will consider parameters like displacement, strain and stress, while for the second level we will compare the estimated life and the one obtained by test.

3.1.- Experiment design. Geometry and meshing The first step for the validation was to design a test suitable for the study requirements. The chosen component was a ball stud, and after we optimised the design in order to ensure that the failure would happen by fatigue and in a point easy to be measured. The component was defined as it is shown in figure 9.

Figure 9: Design chosen for the validation

The way of loading the component has been similar to a Cantilever beam. The thread has been constrained and a vertical load is been applied in the opposite side.

the mesh has been made of hexaedral elements because there is contact in the simulation. It has also been considered the presence of the structural tooling, in the simulation, in order to consider the elasticity due to this part of the assembly and to eliminate the uncertainty in the experimental results. In the next figure the mesh of the component and of the complete assembly is shown.

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Figure 10: Mesh of the component and of the whole experiment device

3.2.- Residual stresses The manufacturing of the components has been done by milling, those components have been polished in order to get a mirror finish, so the residual stresses due to the forming process are not important for the component. The component and tool geometries are conical in the fastening zone; the component is fixed by a screw with a torque of 12Nm. This initial stress that has been taken into account in all calculations. The stress state due to the assembly is the one shown in figure 10.

3.3.- Static characterisation The material chosen for the component manufacturing was steel F1140. The reasons for choosing were availability, easy machinability and knowledge of its behaviour.

Figure 12: Specimens used for the tensile tested and curves obtained

It is importance to notice that the test is very repetitive. The most relevant properties from the static characterisation are:

• Yield stress: 504 MPa

• Ultimate stress: 800 MPa

• Young modulus: 204000 MPa

3.4- STATIC LOAD The chosen example for the validation presents two kinds of non linearties, the contact and the plastic strain in the critical zone. The whole load was applied in the static analysis;

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boundary conditions, contact definitions and the other parementer were appliedIn the finite elements code to reproduce the experimental test.

3.5- STRESS AND STRAIN STATE Once that all the inputs have been introduced in the software, the simulation is made in order to get all the results needed for the validation. In our case, the most important results are the displacement, the stress and the strain.

3.6- CRITICAL ZONE SUBMODEL As it was previously explained, the finite model considered includes also the tooling, for this reason the mesh in the critical zone is not fine enough. So it is necessary to make a submodel of this critical zone in order to get more accurate results. For determininig the mesh size, the shape and dimensions of the validation gauges were taken into account to be sure that the measurements are made exactly in the same point.

The figure 11 shown the difference between the model and submodel. It is important to recall that the displacement field of the initial model is the starting point for the submodel.

Figure 13: Mesh, displacement and strain. On the left initial model on the right submodel

3.8- CORRELATION OF THE STRESS AND STRAIN To establish the ratio of correlation between the simulation and the experimental test, several measurements methods have been used. The most important ones:

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• Displacement capacitive transducer

• LVDT

• Load cell

• Extensometric gauges

• Thermoelasticity measurement equipment (SPATE)

The use of so many different systems follows a double aim. First of all, the validation of the static results, and also the correlation of the different methods between them. In the pictures below there are some details of the measurement equipment used.

Figure 14: Capacitive transducer and extensometric gauges

Two gauges were glued to the component, one of them in the most critical zone and the other out of this zone. The lecture made in the gauges, along the process of linear load application, is shown below.

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Galga X1 Galga Y1 Galga X2 Galga Y2 Figure 16: Strain measured in the gauges

The dark blue line corresponds to the longitudinal direction measurement for the gauge out of the critical zone, the pink one is for the transversal direction of the same gauge. The red

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line corresponds to the longitudinal direction measurement for the gauge on the critical zone, the light blue one is for the transversal direction of the same gauge.

The next step was to consider the strain obtained by simulation in the same points of the finite element model. In this picture is shown which these points are.

Figure 17: Gauges in the component and measure points in the finite element model

If we calculate the strain, and make a comparison with the measured by the gauges, we obtain the results shown in the next table. It is important to notice that the correlation ratio for both gauges is very high, the error is always lower than 2%.

Simulation Experimental Difference (%)

Out of critical zone x -6.0561e-4 6.1530e-4 9.69e-6 (1.6)

Out of critical zone y 1.8967e-4 -1.9299e-4 3.32e-6 (1.7)

Critical zone x -1.7065e-3 1.7111e-3 4.6e-6 (0.27)

Critical zone y 2.7527e-4 -2.7517e-4 -1e-7 (-0.036)

According to this results, the correlation ratio is very high, so we can conclude that the simulation method for the stress and strain field determination for the static load is been validated.

3.9.- CYCLIC CHARACTERISATION The material chosen for this analysis is F1140. In order to make the simulations when variable loads are applied, it is necessary to know the strain life curve. In the following lines it is shown, as a summary, the main results reached during the characterisation process.

The strain levels for the cyclic characterisation were determined from the static properties. In every specimen different information was recorded, the most important were the stress and strain variation versus the cycles number, the hysteresis loop and the number of cycles before the crack appearance.

Making a statistical analysis of all the results from the characterisation, we are able to determine the shape of the curve and the main parameters defining the cyclic behaviour of the material. In the rigth part of figure 23 the regression line for the elastic and the plastic strain, and also the behaviour of the strain life curve are shown.

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Figure 23: Left: Result obtained during the cyclic characterisation process. Right: Elastic strain, plastic

strain and total strain versus number of cycles obtained from characterisation

3.10.- Load history As it was explained before, in the static load description, in this case all the load levels have been considered in the static analysis, so it is no necessary to develop this point of the methodology.

3.11.- Durability analysis In this moment all the inputs necessary for the durability test of the component are available. So the simulation was done considering the strain results and the Morrow main stress correction, because it is the most suitable method according to our own experience. The simulation was made with different load levels, the same ones that were tested later.

In the picture we can observe some of the results that can be obtained with the fatigue software based in the finite element method.

Figure 26: Left: damage representation. Right: life distribution

3.12.- DURABILITY ANALYSIS CORRELATION Following the criteria as in the static simulation, it is necessary to establish the correlation ratio between the simulation and the experimental test in order to validate the methodology. For this reason forty components were tested at ten different strain levels in order to get a statistical curve defining the material behaviour when cyclic loads are applied over the component.

If we compare the experimental and the simulated curve representing the strain versus the life, it can be concluded that the correlation is very high in all the strain range considered in the analysis.

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DEFORMACIÓN-VIDA

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Curva deformación-vida experimental Curva deformación-vida simulada Figure 27: Comparison of the tested and the simulated strain live curve

4.- SUMMARY In this paper, a methodology for the simulation the fatigue behaviour, using the finite element method, has been described. Then this methodology was validated, using experimentation for establishing the correlation ratio with the simulated results.

This correlation is really, basicly due to three reasons:

1. The load history, in this case, it was previously defined, so the experimental and the simulated loads are exactly the same.

2. The strain state, was accurately determined, using the most advanced simulation techniques.

3. And finally, the material cyclic characterisation. In this case the uncertainty source has been reduced to the minimum, because all the specimens have been obtained from the same material and have been manufactured with the same process.

The great correlation ratio obtained allows us to affirm that the described methodology is validated.

References [1] Bastow, D., Howard, G. “Car suspension and handling”, Ed. Arnold, 1996.

[2] Darrel F. Socie, Gary B. Marquins. “Multiaxial fatigue”, Ed. SAE, 2000.

[3] Ellis, J.R. “Vehicle dynamics”, Ed. Business Book Limited.

[4] Wulpi, J. “Understanding how components fail”, Ed. ASM, 2001.

[5] “Fatigue and Fracture”, Ed. ASM, 1996

[6] “Guide for fatigue testing and the statistical analysis of fatigue data”, ASTM 91-A, 1963.

Contact.

Fundación CIDAUT, Parque Tecnológico de Boecillo, Parcela 209, 47151, Boecillo (Valladolid), Spain. Phone: (+34) 983 54 80 35 Fax: (+34) 983 54 80 62. www.cidaut.es

E-mail: luipra@cidaut.es, cesmae@cidaut.es, javrom@cidaut.es, estcan@cidaut.es.

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