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.     

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.

     

Optimization of a crankshaft rolling process for durability

A crankshaft is often designed with a small fillet radius. The crankshaft fillet rolling process is one of the commonly adopted methods in engineering to improve fatigue life of the crankshaft. Compressive residual stresses on and below the fillet radius surface are induced through the fillet rolling operation. Consequently, fatigue life of the crankshaft is improved. An analytical technique is used to optimize the crankshaft rolling process to comply with a crankshaft design criterion for durability. A nonlinear finite element analysis is implemented to approximate the stress distributions induced by the crankshaft rolling process, and a crack modeling technique is developed to calculate the equivalent stress intensity factor ranges based on the combined residual and operational stress distributions along various crack growth planes. The threshold equivalent stress intensity factor range is obtained from previous staircase testing on crankshaft sections. The durability design criterion is met if the threshold equivalent stress intensity factor range exceeds the largest calculated equivalent stress intensity factor range. Due to the complexity of the modeling techniques in simulating the rolling process and calculating the equivalent stress intensity factors, a meta-model is generated based on the uniform design method for the choice of sample points and the quadratic polynomial fitting technique for a response surface generation. In the meta-model optimization process, rolling force, rolling angle, and fillet radius are the control factors, while the variations of the threshold equivalent stress intensity factor range, rolling force, rolling angle, and fillet radius are considered as the noise factors. By using the Hooke–Jeeves direct pattern search method and the Monte Carlo simulation technique, the optimal design is obtained for the highest reliability and the smallest coefficient of variation (COV).     

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.     

A mixed hardening rule coupled with Hill48’ yielding function to predict the springback of sheet U-bending

A mixed hardening model has been used to model the Bauschinger effect. This hardening model is based on Lemaitre and Chaboche nonlinear kinematic hardening theory to consider cyclic behavior and the Bauschinger effect. Hill’48 yielding criterion is used because of the general stress state and relative ease of formulation. The backward Euler return mapping algorithm is applied to calculate the stress and strain increment. The mixed hardening model is implemented based on UMAT subroutine of FEA code ABAQUS. The NUMISHEET’93 benchmark shows that the mixed hardening model coupled with anisotropic yield criteria can give a favorable springback angle prediction.     

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.     

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.     

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.     

Stochastic fatigue damage accumulation in a T-welded joint accounting for the residual stress fields

The residual stresses that occur as a result of nonhomogeneous heating and cooling during welding may have a significant effect on the accumulation of fatigue damage in a welded joint. The problem is complicated not because of the complex spatial distribution of the residual stress fields, but because those fields typically change under an applied load. The present study considers the effect of residual stresses on fatigue damage accumulation in a welded joint subjected to stochastic loading.The influence of residual stresses on stochastic fatigue damage accumulation is accounted for by a simple approach based on an elastic–perfectly-plastic material model and the Gerber correction factor. The model assumes that the residual stress remaining at the critical location depends on the largest nominal stress ever endured by a welded joint. The model predicts that the residual stresses during stochastic loading randomly decay to zero. The effect of material yielding is additionally investigated by considering an elastic–plastic material model with linear kinematic hardening. The residual stresses in this case are computed through Monte Carlo simulations. It is demonstrated that the effect of material hardening is to reduce the rate of residual stress decay and thus to accelerate the rate of fatigue damage accumulation.     

Springback investigation of anisotropic aluminum alloy sheet with a mixed hardening rule and Barlat yield criteria in sheet metal forming

A mixed hardening model has been implemented based on Lemaitre and Chaboche non-linear kinematic hardening theory to consider cyclic behavior and the Bauschinger effect. The Chaboche isotropic hardening theory is incorporated into the non-linear kinematic hardening model to introduce a surface of nonhardening in the plastic strain space. The bending and reverse bending case study has verified the effectiveness of the mixed hardening model by comparison with the proposed experiment results. Barlat’89 yielding criterion is adopted for it does not has any limitation while Hill’s non-quadratic yield criterion is for the case that the principal axes of anisotropy coincides with principal stress direction. The Backward–Euler return mapping algorithm was applied to calculate the stress and strain increment. The mixed hardening model is implemented using ABAQUS user subroutine (UMAT). The comparisons with linear kinematic hardening model and isotropic hardening model in NUMISHEET’93 benchmark show that the mixed hardening model coupled with Barlat’89 yield criteria can well reflect stress and strain distributions and give a more favorable springback angle prediction.     

Surface modifications induced by shot peening and their effect on the plane bending fatigue strength of a Cr-Mo steel produced by powder metallurgy

The effect of shot peening on the plane bending fatigue strength of a 7.1 g/cm³ sintered Cr-Mo steel was investigated. Shot peening provides surface densification, strain hardening, compressive residual stresses up to −700 MPa, without impairing the dimensional and geometrical precision of specimens. Plane bending fatigue strength increases of 30%, irrespective to the different residual stress profiles obtained by changing the shot peening parameters. The improvement is mainly due to the surface densification and strain hardening.     

Experimental strain-hardening behaviors and associated computational models with anisotropic sheet metals

Several anisotropic hardening models with simple loading conditions are proposed, including exponential hardening model, linear hardening model and multi-linear hardening model (which also suits for using the experimental data directly). Three special hardening curves, in the 0°, 45° and 90° angles, respectively, measured against the rolling direction, are the special cases of the proposed hardening models. These models make sense to be applied for simulating forming processes of the planar anisotropic hardening sheet metals, in particular for determining the springback and FLD of formed parts. In order to describe this view further, the constitutive relations of stress and strain, based on the plastic potential flow rule with isotropic hardening and kinematic hardening assumptions, have been discussed briefly. And then, the corresponding results of constitutive relations dependent on the proposed hardening models of materials will be represented, respectively.     

Stress–strain time-dependent behavior of A356.0 aluminum alloy subjected to cyclic thermal and mechanical loadings

This article presents the cyclic behavior of the A356.0 aluminum alloy under low-cycle fatigue (or isothermal) and thermo-mechanical fatigue loadings. Since the thermo-mechanical fatigue (TMF) test is time consuming and has high costs in comparison to low-cycle fatigue (LCF) tests, the purpose of this research is to use LCF test results to predict the TMF behavior of the material. A time-independent model, considering the combined nonlinear isotropic/kinematic hardening law, was used to predict the TMF behavior of the material. Material constants of this model were calibrated based on room-temperature and high-temperature low-cycle fatigue tests. The nonlinear isotropic/kinematic hardening law could accurately estimate the stress–strain hysteresis loop for the LCF condition; however, for the out-of-phase TMF, the condition could not predict properly the stress value due to the strain rate effect. Therefore, a two-layer visco-plastic model and also the Johnson–Cook law were applied to improve the estimation of the stress–strain hysteresis loop. Related finite element results based on the two-layer visco-plastic model demonstrated a good agreement with experimental TMF data of the A356.0 alloy.     

Analysis on the fatigue damage evolution of notched specimens with consideration of cyclic plasticity

This paper presents a damage mechanics method applied successfully to assess fatigue life of notched specimens with plastic deformation at the notch tip. A damage‐coupled elasto‐plastic constitutive model is employed in which nonlinear kinematic hardening is considered. The accumulated damage is described by a stress‐based damage model and a plastic strain‐based damage model, which depend on the cyclic stress and accumulated plastic strain, respectively. A three‐dimensional finite element implementation of these models is developed to predict the crack initiation life of notched specimens. Two cases, a notched plate under tension‐compression loadings and an SAE notched shaft under bending‐torsion loadings including non‐proportional loadings, are studied and the predicted results are compared with experimental data.     

Evaluation of residual stress relaxation and its effect on fatigue strength of AISI 316L stainless steel ground surfaces: Experimental and numerical approaches

This paper is aimed at evaluating the residual stress relaxation and its effect on the fatigue strength of AISI 316L steel ground surfaces in comparison to electro-polished surfaces. An experimental evaluation was performed using 3-point and 4-point bending fatigue tests at R_σ = 0.1 on two sets of notched specimens finished by electro-polishing and grinding. The residual stress fields were measured at the notch root of specimens, before and after fatigue tests, by means of the X-ray diffraction technique. It was found a degradation of about −35% for the 4-point bending fatigue limit at 2 × 10⁶ cycles of the ground specimens in comparison to the electro-polished ones. This degradation is associated with a slight relaxation of the grinding residual stresses which remain significant tensile stresses at the stabilized state. While under the 3-point bending test, these residual stresses relax completely and provoke a noticeable increase of the fatigue limit estimated at about 50% in comparison to the 4-point bending fatigue test. The numerical evaluation of residual stress relaxation was carried out by FE analyses of the cyclic hardening behaviour of the ground layer. The isotropic and nonlinear kinematic model proposed by Chaboche was used and calibrated for the base material and the ground layer. The results show that residual stresses relax to a stabilized state characterized by elastic-shakedown response. This stabilization is occurred after the first cycle of the 4-point bending test corresponding to the higher stress concentration (K_t-4p = 1.66), while it requires many cycles under the 3-point bending test corresponding to the lower stress concentration (K_t-3p = 1.54). The incorporation of stabilized residual stress values into the Dang Van’s criterion has permitted to predict with an acceptable accuracy the fatigue limits under both bending modes.     

Fatigue and ratcheting assessment of AISI H11 at 500°C using constitutive theory coupled with damage rule

Hot extrusion is one of the most commonly used manufacturing methods for metal plastic deformation, and the consumption of extrusion tooling is considerably high due to its fatigue damage under cyclic serving condition. Hot‐work tool steel AISI H11 is one of these typical materials employed in extrusion tooling. This work is dedicated to calculating the stress/strain state of AISI H11 and predicting its lifetime at high temperature 500°C by building a unified constitutive model coupled with Lemaitre's damage law. Tensile tests and strain/stress reversed cycling tests have been conducted at 500°C to investigate mechanical properties and damage evolution. A unified constitutive model with Armstrong‐Fredrick/Ohno‐Wang kinematic hardening rule and a new proposed isotropic hardening rule is built; Lemaitre's damage law is employed as well. Parameters are determined based on tests and are temperature dependent. Finite element simulation of the deformation behaviour and fatigue lifetime is implemented into commercial software ABAQUS Standard v6.14‐2 with user material subroutine to validate the proposed method. The comparison shows good agreement with experimental results, and this part of work is essential and crucial to subsequent structure analysis.     

基于不同强化模型的GTN损伤模型及其在板料回弹有限元分析中的应用

为了进一步提高板料成形中的回弹预测精度,分别建立了基于Ziegler 线性随动强化模型、Lemaitre-Chaboche 非线性随动强化以及非线性混合强化模型的Gurson-Tvergaard-Needleman(GTN)细观损伤本构模型,并给出有限元数值积分方法。通过用户自定义材料子程序VUMAT 将损伤模型嵌入到有限元软件ABAQUS 中,以NUMISHEET’93 板料U 型弯曲考题为例,应用显隐相结合的方法模拟分析了不同材料强化模型和损伤对板料回弹量的影响。结果表明:在相同GTN 损伤模型情况下,线性随动和非线性随动强化模型预测得到的板料回弹量较小,等向强化预测的板料回弹量偏大,非线性混合强化预测的板料回弹量介于它们之间。材料模型在考虑损伤因素后,预测的回弹严重程度比无损伤情况时略小,与实验值更相近。     

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.     

A finite element analysis of plane strain dynamic crack growth in materials displaying the Bauschinger effect

In this paper dynamic crack growth in an elastic-plastic material is analyzed under mode I plane strain small-scale yielding conditions using a finite element procedure. The main objective of this paper is to investigate the influence of anisotropic strain hardening on the material resistance to rapid crack growth. To this end, materials that obey an incremental plasticity theory with linear isotropic or kinematic hardening are considered. A detailed study of the near-tip stress and deformation fields is conducted for various crack speeds. The results demonstrate that kinematic hardening does not oppose the role of inertia in decreasing the plastic strains and stresses near the crack tip with increase in crack speed to the same extent as isotropic strain hardening. A ductile crack growth criterion based on the attainment of a critical crack opening displacement at a small micro-structural distance behind the tip is used to obtain the dependence of the theoretical dynamic fracture toughness with crack speed. It is found that for any given level of strain hardening, the dynamic fracture toughness displays a much more steep increase with crack speed over the quasi-static toughness for the kinematic hardening material as compared to the isotropic hardening case.