Simulations of stress distributions in crankshaft sections under fillet rolling and bending fatigue tests

The residual stresses due to fillet rolling and the bending stresses near the fillets of crankshaft sections under bending fatigue tests are important driving forces to determine the bending fatigue limits of crankshafts. In this paper, the residual stresses and the bending stresses near the fillet of a crankshaft section under fillet rolling and subsequent bending fatigue tests are investigated by a two-dimensional plane strain finite element analysis based on the anisotropic hardening rule of Choi and Pan [Choi KS, Pan J. A generalized anisotropic hardening rule based on the Mroz multi-yield-surface model for pressure insensitive and sensitive materials (in preparation)]. The evolution equation for the active yield surface during the unloading/reloading process is first presented based on the anisotropic hardening rule of Choi and Pan (in preparation) and the Mises yield function. The tangent modulus procedure of Peirce et al. [Peirce D, Shih CF, Needleman A. A tangent modulus method for rate dependent solids. Comput Struct 1984;18:875–87] for rate-sensitive materials is adopted to derive the constitutive relation. A user material subroutine based on the anisotropic hardening rule and the constitutive relation was written and implemented into ABAQUS. Computations were first conducted for a simple plane strain finite element model under uniaxial monotonic and cyclic loading conditions based on the anisotropic hardening rule, the isotropic and nonlinear kinematic hardening rules of ABAQUS. The results indicate that the plastic response of the material follows the intended input stress–strain data for the anisotropic hardening rule whereas the plastic response depends upon the input strain ranges of the stress–strain data for the nonlinear kinematic hardening rule. Then, a two-dimensional plane-strain finite element analysis of a crankshaft section under fillet rolling and subsequent bending was conducted based on the anisotropic hardening rule of Choi and Pan (in preparation) and the nonlinear kinematic hardening rule of ABAQUS. In general, the trends of the stress distributions based on the two hardening rules are quite similar after the release of roller and under bending. However, the compressive hoop stress based on the anisotropic hardening rule is larger than that based on the nonlinear kinematic hardening rule within the depth of 2 mm from the fillet surface under bending with consideration of the residual stresses of fillet rolling. The critical locations for fatigue crack initiation according to the stress distributions based on the anisotropic hardening rule appear to agree with the experimental observations in bending fatigue tests of crankshaft sections.     

曲轴弯曲疲劳试验裂纹研究与失效判定

通过对疲劳裂纹的产生、扩展机理研究和试验,结合疲劳试验数据分析了疲劳裂纹扩展与疲劳寿命的关系。试验结果及分析表明,大量经圆角滚压强化的球墨铸铁曲轴,疲劳试验运行107次在连杆颈与曲柄臂过度圆角产生微裂纹,该裂纹属于非扩展裂纹,继续试验时裂纹不扩展,试样在该载荷下具有无限疲劳寿命。     

PREDICTION OF FATIGUE FAILURE IN A CRANKSHAFT USING THE TECHNIQUE OF CRACK MODELLING

Abstract— A new technique, known as crack modelling, is used here to predict fatigue failure in a crankshaft component. The technique uses a linear elastic finite element (FE) analysis to derive a stress intensity factor ( K ) for the component under load. The novel feature of the technique is that K is calculated without introducing a crack into a component; the stress field around the maximum stress point is examined and compared to that for a standard centre-cracked plate. The fatigue limit for a crankshaft was successfully predicted, when compared to experimental data. The only material parameter required for this prediction was the threshold stress intensity range, ΔK_th.     

Numerical simulation of fatigue crack propagation in compressive residual stress fields of notched round bars

In this paper, the influence of the residual compressive stresses induced by roller burnishing on fatigue crack propagation in the fillet of notched round bar is investigated. A 3D finite element simulation model of rolling has allowed to introduce a residual stress profile as an initial condition. After the rolling process, fatigue loading has been applied to three‐point bending specimens in which an initial crack has been introduced. A numerical predictive method of crack propagation in roller burnished specimens has also been implemented. It is based on a step‐by‐step process of stress intensity factor calculations by elastic finite element analyses. These stress intensity factor results are combined with the Paris law to estimate the fatigue crack growth rate. In the case of roller burnished specimens, a numerical modification concerning experimental crack closure has to be considered. This method is applied to three specimens: without roller burnishing, and with two levels of roller burnishing (type A and type B). In all these cases, the computational finite element predictions of fatigue crack growth rate agree well with the experimental measurements. The developed model can be easily extended to crankshafts in real operating conditions.     

Effects of pressure-sensitive yielding on stress distributions in crankshaft sections under fillet rolling and bending fatigue tests

In this paper, the evolution equation for the active yield surface during the unloading/reloading process based on the Drucker–Prager yield function and a recently developed anisotropic hardening rule is first presented. A user material subroutine based on the anisotropic hardening rule and the constitutive relation was written and implemented into the commercial finite element program ABAQUS. Computations were first conducted for a simple plane strain finite element model under uniaxial monotonic and cyclic loading conditions. The results indicate that the anisotropic hardening rule with the non-associated flow rule describes well the strength-differential effect and the asymmetric closed hysteresis loops as observed in the uniaxial cyclic loading tests of cast irons. Then, a two-dimensional plane strain finite element analysis of a crankshaft section under fillet rolling and subsequent bending was conducted. For the pressure sensitivity corresponding to the cast iron crankshaft of interest, the critical locations for fatigue crack initiation according to the stress distributions for pressure-sensitive materials agree with the experimental observations in bending fatigue tests of crankshaft sections.     

Truck Diesel Engine Crankshaft Failure Analysis

A diesel engine crankshaft fractured in service after 76010 km of operation. The fracture took place on the first crankpin, and the fracture surface has a 45° inclination with respect to the axial. The results indicate that fatigue is the dominant failure mechanism of the crankshaft. It was observed that the fatigue crack initiated at the fillet region of the first crankpin-web. This crankpin is the one among the six crankpins which bear operational load. Absence of the induction hardening case in the fillet region decreased the fatigue strength and led to fatigue initiation and propagation in the weakened region. Although hard-rolling process was conducted in the fillet region, the depth of hard-rolling layer was insufficient to produce the desired residual compressive stress in the fillet region, and therefore the fillet could not offer resistance to the applied load. In addition, the presence of network-like ferrite in the microstructure facilitated the fatigue crack to be initiated and propagated.     

Fatigue strength assessment of partial and full‐penetration steel and aluminium butt‐welded joints according to the peak stress method

In fatigue design of welded joints, the local approach based on the notch stress intensity factors (NSIFs) assumes that the weld toe profile is a sharp V‐notch having a tip radius equal to zero, while the root side is a pre‐crack in the structure. The peak stress method (PSM) is an engineering, FE‐oriented application of the NSIF approach to fatigue design of welded joints, which takes advantage of the elastic peak stresses from FE analyses carried out by using a given mesh pattern, where the element type is kept constant and the average element size can be chosen arbitrarily within a given range. The meshes required for the PSM application are rather coarse if compared with those necessary to evaluate the NSIFs from the local stress distributions. In this paper, the PSM is extended for the first time to butt‐welded joints in steel as well as in aluminium alloys, by comparing a number of experimental data taken from the literature with the design scatter bands previously calibrated on results relevant only to fillet‐welded joints. A major problem in the case of butt‐welded joints is to define the weld bead geometry with reasonable accuracy. Only in few cases such geometrical data were available, and this fact made the application of the local approaches more difficult. Provided the local geometry is defined, the PSM can be easily applied: a properly defined design stress, that is, the equivalent peak stress, is shown (i) to single out the crack initiation point in cases where competition between root and toe failure exists and (ii) to correlate with good approximation all analysed experimental data.     

A study of fatigue crack growth from artificial corrosion pits at welded joints under complex stress fields

The paper studies the effects of artificial corrosion pits and complex stress fields on the fatigue crack growth of full penetration load‐carrying fillet cruciform welded joints with 45° inclined angle. Parameters of fatigue crack growth rate of welded joints are obtained from S‐N curves under different levels of corrosion. A numerical method is used to simulate fatigue crack growth using different mixed mode fatigue crack growth criteria. Using polynomial regression, the crack shape correction factor of welded joints is fitted as a function of crack depth ratios. Because the maximum circumferential stress criterion is simple and easy to use in practice, fatigue crack growth rate is modified using this criterion. The relationship of effective stress intensity factor, crack growth angle and crack depth is studied under different corrosion levels. The simulated crack growth path obtained from the numerical method is compared with the actual crack growth path observed by fatigue tests. The results show that fatigue cracks do not initiate at the edge or bottom of pits but at the weld toes where the maximum stress occurs. The artificial corrosion pits have little effect on the effective stress intensity factor ranges and crack growth angle. The fatigue crack growth rates of welded joints with pits 1 and 2 are 1.15 times and 1.40 times larger than that of the welded joint with no pit, respectively. The simulated crack growth path agrees well with the actual one. The fatigue life prediction accuracy using the modified formulation is improved by about 18%. The crack shape correction factor obtained using the maximum circumferential stress criterion is recommended being used to calculate fatigue life.     

Analysis of a crankshaft fatigue failure

The reason of the crankshaft fracture of the air compressor has been analyzed through the chemical composition, mechanical properties, macroscopic feature, microscopic structure and theoretical calculation methods. The analysis results show that the crankshaft which has obvious fatigue crack belongs to fatigue fracture. The fatigue crack initiated from the fillet region of the lubrication hole because of the high bending stress concentration which is caused by both the small fillet and the misalignment of main journals. The crankshaft fatigue fracture was only attributed to the initiation and propagation of the fatigue cracks on the lubrication hole under cyclic bending and torsion. The high bending loading bending level is the root cause of the failure.     

Lebensdauerberechnung festgewalzter Kerbproben unter Axialbelastung auf der Basis eines Rißfortschrittskonzepts

Axial fatigue life calculation of fillet rolled specimens by means of a crack growth model Fillet rolling is a method which significantly improves the fatigue strength of members. Residual compressive stresses induced in the surface layer during the fillet rolling process are able to retard or prevent crack propagation. An elastic‐plastic on the J‐integral based crack growth model considering the crack opening and closure phenomenon in nonhomogeneous plastic stress fields is described. Experimentally determined crack growth curves and fracture fatigue life curves at constant amplitude loading were used to verify the developed model.     

Rim Thickness Effects on Gear Crack Propagation Life

Analytical and experimental studies were performed to investigate the effect of gear rim thickness on crack propagation life. The FRANC (FRacture ANalysis Code) computer program was used to simulate crack propagation. The FRANC program used principles of linear elastic fracture mechanics, finite element modeling, and a unique re-meshing scheme to determine crack tip stress distributions, estimate stress intensity factors, and model crack propagation. Various fatigue crack growth models were used to estimate crack propagation life based on the calculated stress intensity factors. Experimental tests were performed in a gear fatigue rig to validate predicted crack propagation results. Test gears were installed with special crack propagation gages in the tooth fillet region to measure bending fatigue crack growth. Good correlation between predicted and measured crack growth was achieved when the fatigue crack closure concept was introduced into the analysis. As the gear rim thickness decreased, the compressive cyclic stress in the gear tooth fillet region increased. The retarded crack growth and increased the number of crack propagation cycles to failure. This revised version was published online in August 2006 with corrections to the Cover Date.     

Analysis of subsurface crack propagation under rolling contact loading in railroad wheels using FEM

A general subsurface crack propagation analysis methodology for the wheel/rail rolling contact fatigue problem is developed in this paper. A three-dimensional elasto-plastic finite element model is used to calculate stress intensity factors in wheels, in which a sub-modeling technique is used to achieve both computational efficiency and accuracy. Then the fatigue damage in the wheel is calculated using a previously developed mixed-mode fatigue crack propagation model. The advantages of the proposed methodology are that it can accurately represent the contact stress of complex mechanical components and can consider the effect of loading non-proportionality. The effects of wheel diameter, vertical loading amplitude, initial crack size, location and orientation on stress intensity factor range are investigated using the proposed model. The prediction results of the proposed methodology are compared with in-field observations.     

Numerical modelling of deep rolling influence over crankshaft bending and correlation with fatigue behaviour

The requirements for mechanical reliability of automotive crankshafts are continuously increasing, thus pushing the demand for an optimized processing. Nonetheless, the manufacturing‐induced residual stresses at critical sites for fatigue enhancement are not clarified in the state‐of‐the‐art on the topic. In particular, there is a lack of information on the effect of final manufacturing stages to improve the component life endurance, such as deep rolling, in the overall stress state while the component is under operational loads. This study deepens the validation of a finite element deep rolling model under development with the aid of an in‐house developed crankshaft resonance fatigue test rig. The stress state obtained from the deep rolling simulation was input as a predefined stress field for the simulation of operational conditions experimented at the test rig. Test results produced cracks at the fillet radii of the cast iron crankshafts as anticipated. Overlapping the fractography with the simulation's final stress field yielded interesting correlation with the crack morphology. This contributed with a strong indication of the model correctness. Moreover, it can be further implemented to indicate whether the process parameters such as roller force and angle are fully optimized for each particular crankshaft application.     

Analysis of the crack growth propagation process under mixed-mode loading

In the present paper, a computational model for crack growth analysis under Mode I/II conditions is formulated. The focus is on two issues – crack path simulation and fatigue life estimation. The finite element method is used together with the maximum principal stress criterion and the crack growth rate equation based on the equivalent stress intensity factor. To determine the mixed-mode stress intensity factors, quarter-point (Q-P) singular finite elements are employed. For verification purposes, a plate with crack emanating from the edge of a hole is examined. The crack path of the plate made of 2024 T3 Al Alloy is investigated experimentally and simulated by using the finite element method with the maximum tangential stress criterion. Then, the validation of the procedure is illustrated by applying the numerical evaluation of the curvilinear crack propagation in the polymethyl methacrylate (PMMA) beam and the Arcan specimen made of Al Alloy for which experimental results are available in the literature. In order to estimate fatigue life up to failure of the plate with crack emanating from the edge of a hole, the polynomial expression is evaluated for the equivalent stress intensity factor using values of stress intensity factors obtained from the finite element analysis. Additionally, the fatigue life up to failure of the Arcan specimen is analyzed for different loading angles and compared with experimental data. Excellent correlations between the computed and experimental results are obtained.     

FATIGUE ANALYSIS AND PREDICTION IN FILLET WELDED JOINTS IN THE LOW THICKNESS RANGE

Abstract— The paper reports the results of a comprehensive research project concerning fatigue life prediction in fillet welded joints. Geometry variables such as main plate thickness, radius of curvature at the weld toe and leg to leg distance were analysed in detail. Fatigue life computations were carried out for semi-elliptical cracks using appropriate FE techniques. The range of results covered several types of welded joints loaded in tension and in bending. A comparison of results was made using two methods of stress intensity determination. Experimental data was also obtained and that included measurements of weld toe radius, monitoring of crack shape and S-N curves. Correlation of results with the theoretical predictions gave generally good agreement. A set of fatigue design curves for fillet welded joints is proposed and in these the designer can introduce the geometry of the weldment.     

Crack growth prediction and non-linear analysis for an elasto-plastic solid

In this paper, a variable radius for the plastic zone is introduced and a maximum principal stress criterion is proposed for the prediction of crack initiation and growth. It is assumed that the direction of crack initiation coincides with the direction of the maximum principal stress. The von Mises yield criterion is applied to define the plastic zone, instead of assuming a plastic zone with a constant distance r from the crack tip. An improvement is made to this fracture criterion, and the criterion is extended to study the crack growth characteristics of mixed mode cracks. Based on the concept of frictional stress intensity factor, k_f, the rate of fatigue crack propagation, db/dN, is postulated to be a function of the effective stress intensity factor range, Δk_eff. Subsequently, this concept is applied to predict crack growth due to fatigue loads. The proposed crack growth model is discussed by comparing the experimental results with those obtained using the maximum principal stress criterion.     

Berechnung der Schwingfestigkeit festgewalzter Kurbelwellen

Predicting the fatigue strength of fillet-rolled crankshafts Since three years Darmstadt University of Technology uses finite element method for simulation of fillet rolling process. Now, together with Daimler-Benz AG, a fracture mechanics based concept has been successfully applied predicting the fatigue strength of fillet-rolled crankshafts. For these parts conventional assessment of fatigue behaviour shows several disadvantages. The new concept reduces time and costs for development and design. It consists of three parts:

• calculation of residual stresses induced by fillet rolling and affected by crankshaft and roller geometry, rolling load and work hardening data of material
• simulation of residual stress redistribution due to cyclic load
• assessment of fatigue cracks starting from notch root and propagating under compressive residual stresses by means of linearelastic fracture mechanics.

     

影响球墨铸铁曲轴质量的因素

通过对失效的球墨铸铁曲轴的分析和统计,认为造成球铁曲轴断裂失效的主要因素有铸态下存在孔洞类缺陷、等温淬火态时组织脆性较大和正火态时圆角不强化,而曲轴磨损失效的主要因素是润滑不足。提高等温淬火组织的韧性和强化曲轴圆角是防止曲轴断裂失效的主要措施。     

Surface and subsurface rolling contact fatigue characteristic depths and proposal of stress indexes

The rolling contact fatigue is distinguished into subsurface initiated (spalling and case crushing) and surface initiated (pitting and micropitting). A characteristic depth was identified for each of these mechanism. The characteristic depth of the case crushing is the hardening depth, while for the spalling it is the maximum cyclic shear stress depth. The pitting depth is the size of the crack for which the mode I stress intensity factor range, due to the fluid pressurization, is higher than the threshold. This depth can be similar to the micropitting depth, in the order of 10 μm, for heavily loaded small radius contacts. Rolling contact fatigue cyclic shear stress indexes are then defined on the basis of the characteristic depths, and they identify the load intensity of each rolling contact fatigue mechanism. The characteristic depths and the stress index approach can be used to relate specific tests to component design, without any size effect misinterpretation.     

FE‐Festwalzsimulation und Dauerfestigkeitsberechnung festgewalzter Bauteile mit Konzepten der Schwingbruchmechanik

FE‐Simulation of Fillet Rolling and Fatigue life Calculation based on Fracture Mechanics Concepts Fillet rolling is a method which significantly improves the fatigue strength of members. Residual stresses induced in the surface layer during the fillet rolling process are able to retard or prevent crack propagation. For fatigue strength prediction of fillet rolled notched members a fracture mechanics based concept is described. It consists of three parts: • Finite element simulation of the fillet rolling process to calculate the residual stresses • Simulation of residual stress redistribution due to cyclic load • Assessment of fatigue cracks starting from notch roots and propagating under compressive residual stresses by means of fracture mechanics.