FEMFAT-MAX: A FE-Postprocessor for Fatigue Analysis of Multiaxially Loaded Components

Transcription

1 FEMFAT-MAX: A FE-Postprocessor for Fatigue Analysis of Multiaxially Loaded Components Christian Gaier, Gerald Steinwender, Helmut Dannbauer Engineering Center Steyr GmbH, Steyr Daimler Puch, Austria Summary: With increasing capacities of computers the prediction of the lifetime of components by numerical methods gets more and more important. The number of testing cycles can be reduced dramatically by finding the crack initiation point with suitable software tools and preoptimization of the components. The software FEMFAT exists since about fifteen years, is widely applied for extensive problems and its development is permanently continued since that time. The assessment of uniaxially and multiaxially loaded components as well as welding seams and spot joints is possible. The theory applied in FEMFAT differs in some aspects from classical approaches like the nominal stress concept or the local one and can be characterized by the term influence parameter method. Several influence parameters can be considered as e.g. stress-gradient to take into account notch effects, mean-stress influence, surface roughness and treatments, temperature, technological size, etc. Also mean-stress rearrangements caused by plastic deformations are taken into account. The user can choose between several analysis methods for the quantification of the influence parameters, e.g. methods which are fixed by German guiding rules (FKM) and such ones which have been developed in our company. A convenient method to consider situations with changing principal stress directions is the Critical Plane Approach. This hypothesis was used to develop a software module called FEMFAT-MAX. The basic idea of the Critical Plane Approach is that cracking starts in the cutting plane with maximum damage. This method can be well applied for each combination of external loads. FEMFAT-MAX can deal with channel based linear quasistatic stress input data, with stress data obtained from a modal FE-analysis and with transient nonlinear stresses. Keywords:, Lifetime Prediction, FEMFAT, Finite Element Method, Nonproportional Load, Multiaxial Load, Vehicle Engineering. 1

2 1 Introduction In todays automotive engineering and development a long computational simulation chain will be performed before prototyping and testing start (see Fig. 1). This chain includes static and dynamic analysis with Finite Element Method (FEM), Multibody Simulation (MBS), Noise and Vibration Harshness (NVH), Modal Analysis, Temperature Analysis, Fluid Analysis, etc. The last limb is represented by the lifetime analysis to fix the weak points of a structure. Damage distributions are the basis for a decision, if and how a redesign should be done. FEMFAT is a software tool for the lifetime prediction of components, which has delivered good result quality for about fifteen years now. Of course the results cannot be better than the huge amount of input data required for a lifetime analysis: FE-model, FE stress results, static and dynamic material data and load data (spectra, histories). All these data must be carefully defined and provided by the user. Material data can be taken from the FEMFAT material database, which contains about 150 materials (steels, cast irons, aluminium, magnesium). FEMFAT consists of several modules for different applications: - FEMFAT BASIC Fatigue analysis for one amplitude-, mean- and constant stress - FEMFAT PLAST Consideration of local plastification based on linear computed stresses and Neuber hyperbola, mean stress rearrangement - FEMFAT BREAK Consideration of the influence of the relative stress gradient and ductility for static loading - FEMFAT MAX Reliable and effective assessment of complex loads - FEMFAT WELD Assessment of arc welded areas - FEMFAT SPOT Assessment of spot jointed areas - FEMFAT STRAIN Calculating the fatigue behaviour at strain gauges Calibrating the stress behaviour of FE-models - FEMFAT HEAT Low cycle fatigue analysis of thermomechanically loaded components - FEMFAT FEDIS Efficient submodelling for detailed stress analysis - FEMFAT EHD A tool for elastohydrodynamic bearing computation - FEMFAT NVH A FE postprocessing-tool for computation of surface noise - FEMFAT LAB Measurement data software With this contribution we will focus mainly on FEMFAT-MAX. From Concept to Prototype Dynamics Finite Elements Design, Road Profile ADAMS Fatigue STEYR Data Base FEMFAT Prototype Test Bench Verification Fig. 1: Simulation in automotive engineering 2

3 2 A Little Bit Theory 2.1 Critical Plane Criterion A common way to perform a fatigue assessment is to generate an equivalent stress (von Mises and maximum principal stress, respectively, depending on the material type - ductile or brittle, e.g. steel versus grey cast iron) from the local stress state. This equivalent stress is compared to the tensile strength of a cylindrical test specimen. But it must be stated, that this procedure is applicable only for proportional loads, i.e. loads which scale the magnitude of the multiaxial stress state, but which do not change the directions of the principal stress axes. For multiaxially loaded components the classical damage-hypotheses are no longer valid. A convenient method to consider situations with changing principal stress directions is the Critical Plane Approach [1-3]. This hypothesis was used to develop a multiaxial damage analysis module FEMFAT- MAX. The basic idea of the critical plane approach is that cracking starts in the cutting plane with maximum damage. This method can be well applied for each combination of external loads. Firstly, the history of a stress vector is generated by transforming the stress tensors into several cutting planes. Depending on the material and the load situation, respectively, the equivalent stress can be equated with the normal or shear component, or it can be defined as a function which is composed of both of them, e.g. as linear combination [4]. Similar to the von Mises-stress, but supplied with a sign, a convenient definition of an equivalent stress seems to be [5] 2 2 σ 2 σ ( σ ) σ τ τ a e = sign n n + (1) a However, it must be stated, that (1) represents a discontinuous function, which can deliver wrong results for special situations. For the case of a large but steady shear component, and for a small normal component which changes its direction periodically, too large amplitudes are obtained from (1). Similar problems arise if the sign is taken from the larger of the two terms below the root. Therefore result plausibility checks should to be done in any case, when using (1). After rainflow-counting and the projection onto an amplitude-mean-stress-rainflow-matrix, a damage calculation is performed in the actual cutting plane, based on the influence parameter method (see next chapter). To reduce the computation effort, some restrictions have to be done. Firstly, only nodes lying on the component s surface are evaluated. Secondly two different cutting plane filters have been implemented. The first one is based on a scheme proposed by Chu et al [6]. The status of the plain stress tensor is marked by points in the stress space, spanned by two normal and one shear component, for each time step, see Fig. 2. The aspect ratio of the least square ellipsoid, spanned by this cloud of points, is a measure for the degree of multiaxiality. A straight line through the origin indicates the special case of uniaxial loading. The directions of the ellipsoid s first principal axis refer to the position of the critical plane. This method is recommended for short load histories. As a second method the upper limits of the channel equivalent stresses are considered for each cutting plane (Fig. 3). The maxima indicate planes, which may be critical. But a secure prediction is not possible, because it is not known in advance, how the channels will be superimposed. Otherwise this method behaves to be a very fast one, because no load histories need to be processed in advance. This method can be applied for both channel-based and transient multiaxial fatigue analysis. For the second one the stresses at each time step are used instead of stresses for each load channel. Fig. 2: Considering local stress state for cutting plane preselection Almost uniaxial stress-distribution Strongly multiaxial stress-distribution 3

4 maximum equivalent stress for channel 1 maximum equivalent stress for channel 2 maximum equivalent stress for channel 3 upper equivalent stress filter limits selected planes Fig. 3: Considering maximum stresses for each load channel 2.2 The Influence Parameter Concept As basic material input data S/N-curves of cylindrical, unnotched and polished specimen are used by FEMFAT. At each node of the FE-mesh a synthetic S/N-curve will be created by modifying the basic specimen S/N-curve in dependence on several influence parameters like stress gradient, surface roughness, mean stress, etc. This method is derived from the nominal stress concept and has been named to Influence Parameter Concept. Usually for complicated geometries it is not possible to define a nominal stress because the cross-section is not determined uniquely. But the stress concentration factor K f (and with it some kind of pseudo nominal stress) can be estimated by the relative stress gradient derived from the FE-stress distribution. The relative stress gradient is calculated by FEMFAT and used for the modification of the local S/N-curve by taking into account the important notch effect, quantified by the notch sensitivity factor K t. A method, how to calculate the ratio K t /K f, has been developed by the Engineering Center Steyr [7], but also other methods are provided (IABG [8], Stieler [9]). For the other influence factors mostly methods fixed by the German FKM-guiding rule ( Forschungskuratorium Maschinenbau = Research Committee Mechanical Engineering) [10] have been implemented into FEMFAT. The list of influence factors include: - Stress Gradient - Surface Roughness - Mean Stress - Constant Stress - Technological Size Influence - Statistics Influence - Isothermal Temperature Influence - Thermomechanical Temperature Influence - Tempering Influence - Surface Treatment Influence Factors: - Shot Peen - Roll - Carburize - Nitrate - Inductive Harden - Flame Harden - General Surface Treatment Factor 4

5 3 Channel Based Multiaxial FEMFAT-MAX is a module for the assessment of multiaxially loaded components, which has been developed about three years ago and applied widely since that time [11-14]. It can deal with two kinds of stress input data: - FEMFAT-ChannelMAX uses channel based FE-stress results - FEMFAT-TransMAX uses transient FE-stress results If a lot of forces and moments are acting independently from each other on a component, and the loads can be assumed to be quasistatic, then ChannelMAX is the right choice. The user has to perform a FE-analysis for each unit load case. The load histories must be provided by measurements or multibody simulations and are taken together with the corresponding stress distributions as input for FEMFAT (Fig. 4). Fig. 4: Example: Three force components for acceleration/braking, curve driving and car weight are acting onto this wheel carrier. Therefore three load channels must be defined as FEMFAT-MAX input The stresses will be transformed into the cutting planes, multiplied with the corresponding load histories and superimposed at each time step. After rainflow counting fatigue analysis will be performed for each cutting plane by applying the concept of synthetic S/N-curves (Influence Parameter Concept). This procedure can be well applied also for a fatigue analysis based on modal stresses. Stress distributions for specific resonance frequencies will be scaled by modal coordinates and superimposed at each time step (Fig. 5). For a pure dynamic analysis in the time domain a channel based fatigue analysis can be done too, if the load histories are acting as switches (Fig. 6). At each time step one load channel is active, whereas all others are switched off. But there is a big disadvantage: Load channel superimposition will be performed, although it is not necessary. That s a very time consuming and inefficient procedure and it was an impulse to develop a more efficient FEMFAT-module called TransMAX. 5

6 Fig. 5: Process of modal analysis and fatigue analysis afterwards Fig 6: Transient stress induced by rotating bearing forces taken as input for a channel based fatigue analysis 6

7 4 Transient Multiaxial A frequently appearing problem in engine, gear and drive train engineering are rotating forces in bearings. A common way for FE-analysis is to create a star of beam elements and to apply the rotating force in the center. The stress distribution is analyzed for several load directions (e.g. in 20 degree steps, see Fig. 6). A time varying stress distribution is obtained in the bearing, for which a lifetime analysis should be performed. An optimized fatigue analysis tool FEMFAT-TransMAX [15] has been developed to deal with such load situations and to overcome the problems mentioned in the previous chapter. No load channel superimposition is performed, therefore the analysis is much faster than ChannelMAX. It must be dealt with a huge amount of stress data (one stress dataset for each time step, required disk space up to several Gigabytes). The disk space requirements for FEMFAT have been minimized by using binary scratch files and storing only necessary informations (stress on surface nodes in the current analysis group, see Fig. 7). Fig. 7: Datastream in FEMFAT-TransMAX 5 Interfaces Interfaces to nearly all wide-spread FE-systems are provided for input (FE-structures, FE-stressdistributions) and output (visualization of damage results and safety factors): - I-DEAS VI-i and Master Series Universal File - NASTRAN Bulk Data File (only FE-structures) - NASTRAN Aries Neutral File (only stresses) - NASTRAN Punch File (only stresses) - NASTRAN OP2 - Intergraph Neutral File (only FE-structures) - ANSYS - PATRAN Neutral and Result (rpt) File - MEDINA - Pro/MECHANICA FEMFAT itself provides facilities to visualize material data (S/N-curves, Haigh-diagram) and load data (spectra, histories), see Fig. 8 and 9. 7

8 Fig. 8: Graphical representation of material data Fig. 9: Visualization of load spectra in FEMFAT 8

9 6 Stress Gradient A lot of problems arise when a stress gradient calculation should be performed for multiaxially loaded components. The calculation a time-dependent stress gradient will be too time consuming and is not practical. Furthermore the stress gradient should be evaluated only from the dynamic part of the signal. The dynamic part is not unique and will be determined just in the cutting planes. Therefore the dynamic part can be different for different cutting planes at the same node. For ChannelMAX, a rather simple but fast and effective procedure has been developed for the calculation of a time averaged stress gradient (Fig. 10). The relative gradients obtained from the unit load cases will be weighted by the maximum amplitudes of the corresponding load histories and linearly superimposed. With this method the dominating load cases will influence the stress gradient distribution strongly, whereas the other ones will be neglected. In TransMAX the user can select between two methods: For the first one a simple constant stress gradient distribution averaged over all time steps will be generated. This method behaves to be fast, but does not distinguish between static and dynamic part of the signal. Therefore a second, more sophisticated method has been implemented (Fig. 11): The histories of the principal stresses are considered and the differences of the maxima and minima yield double stress amplitudes. The maximum stress amplitude is assumed to represent the dynamic part of the signal and will be taken for the stress gradient evaluation. Fig. 10: Stress gradient calculation in ChannelMAX Fig. 11: Stress gradient calculation in TransMAX 9

10 7 Conclusion FEMFAT is a powerful software tool for fatigue analysis by using FE-stresses, which has been proved in practice for several years now. It can identify reliably the weak points of a structure and is essential for save automotive design. A lot of well-known companies of the automotive and rail vehicle industry use successfully FEMFAT for their development and engineering projects. 8 References [1] Capper P. L., Fatigue in Shafts under Combined Bending and Torsion, The Engineer, 1937, pp [2] Zenner H., Heidenreich R., Richter I.: Fatigue Strength under Nonsynchronous Multiaxial Stresses, Z. Werkstofftech. 16, Germany 1985, pp [3] Zenner H., Dauerfestigkeit und Spannungszustand, VDI Berichte Nr. 661, 1987, pp [4] Nokleby J. O., Fatigue under Multiaxial Stress Conditions, Rep. MD-81001, Div. Mach. Elem., The Norw. Inst. Technol., Trondheim (Norway), 1981 [5] Sanetra C., Zenner H., Betriebsfestigkeit bei mehrachsiger Beanspruchung unter Biegung und Torsion, Konstruktion 43, Springer-Verlag, Germany 1991, pp [6] Chu C. C., Conle F. A., Hübner A., An Integrated Uniaxial and Multiaxial Fatigue Life Prediction Method, VDI Berichte Nr. 1283, Germany 1996, pp [7] Eichlseder W., Rechnerische Lebensdaueranalyse von Nutzfahrzeugkomponenten mit der Finite Elemente Methode, Dissertation, University of Technology Graz, 1989 [8] Hück M., Thrainer L., Schütz W., Berechnung von Wöhlerlinien für Bauteile aus Stahl, Stahlguß und Grauguß Synthetische Wöhlerlinien, Verein deutscher Eisenhüttenleute, Bericht Nr. ABF 11, Düsseldorf, Juli 1983 [9] DDR-Standard TGL 19340, Ermüdungsfestigkeit; Dauerfestigkeit der Maschinenbauteile, Verlag für Standardisierung, Berlin, March 1983 [10] German FKM Guiding Rule Rechnerischer Festigkeitsnachweis für Maschinenbauteile, VDMA Verlag Frankfurt/Main, 3 rd edition, 1998 [11] Brune M., Fiedler B., Gaier C., Neureiter W., Unger B., Einsatz der rechnerischen Lebensdauerabschätzung in der frühen Bauteilentwicklungsphase, DVM-Report 123, Cologne, Germany, Oct. 1997, pp [12] Steinwender G., Gaier C., Unger B., Fatigue Simulation of Multiaxially Loaded Suspension Components, 7 th Aachen Colloquium, Germany, 1998 [13] Gaier C., Unger B., Vogler J., Theory and Application of FEMFAT - a FE-Postprocessing Tool for, Proc. 7 th International Fatigue Congress, Beijing, China, June 1999, pp [14] Gaier C., Pramhas G., Dannbauer H., Unger B., Vergleich Rechnung - Versuch eines mehrachsig belasteten Vorderachsbocks, Österreichische Ingenieur- und Architekten- Zeitschrift 4/1999, pp [15] Haas A., Dauerbruchsicherheit und transiente Lebensdauerberechnung mit Femfat-MAX, diploma thesis, Johannes Kepler University Linz,