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.     

Constitutive modeling of woven composites considering asymmetric/anisotropic, rate dependent, and nonlinear behavior

The mechanical performance of woven composites was analyzed focusing on their nonlinear and rate dependent asymmetric/anisotropic deformation behavior. Three key characteristics were identified which are indispensable for realistically simulating the mechanical performance of woven composites: the asymmetric material behavior between tension and compression, its anisotropic and nonlinear evolution and rate dependency. To include all three characteristics into the nonlinear finite element analysis for woven composites, a phenomenological constitutive equation was developed based on an elasto-viscoplastic theory using the modified Drucker–Prager yield criterion and, in particular, developing the anisotropic nonlinear hardening law. A characterization method using both uniaxial tensile and compressive tests at different strain rates was proposed to determine the material properties for the constitutive equation. Then, the developed constitutive equation was incorporated into a finite element code and was validated by comparing the finite element simulation of the three points bending test with experiments.     

Criteria of multiaxial random fatigue based on stress,strain and energy parameters of damage in the critical plane

In this paper generalized criteria of multiaxial random fatigue based on stress, strain and strain energy density parameters in the critical plane have been discussed. The proposed criteria reduce multiaxial state of stress to the equivalent uniaxial tension–compression or alternating bending. Relations between the coefficients occurring in the considered criteria have been derived. Thus, it is possible to take into account fatigue properties of materials under simple loading states during determination of the multiaxial fatigue life. Presented models have successfully correlated fatigue lives of cast iron GGG40 and steel 18G2A specimens under constant amplitude in‐phase and out‐of‐phase loadings including different frequencies.     

The evolution of the stress–strain fields near a fatigue crack tip and plasticity-induced crack closure revisited

The evolution of the stress–strain fields near a stationary crack tip under cyclic loading at selected R‐ratios has been studied in a detailed elastic–plastic finite element analysis. The material behaviour was described by a full constitutive model of cyclic plasticity with both kinematic and isotropic hardening variables. Whilst the stress/strain range remains mostly constant during the cyclic loading and scales with the external load range, progressive accumulation of tensile strain occurs, particularly at high R‐ratios. These results may be of significance for the characterization of crack growth, particularly near the fatigue threshold. Elastic–plastic finite element simulations of advancing fatigue cracks were carried out under plane‐stress, plane‐strain and generalized plane‐strain conditions in a compact tension specimen. Physical contact of the crack flanks was observed in plane stress but not in the plane‐strain and generalized plane‐strain conditions. The lack of crack closure in plane strain was found to be independent of the material studied. Significant crack closure was observed under plane‐stress conditions, where a displacement method was used to obtain the actual stress intensity variation during a loading cycle in the presence of crack closure. The results reveal no direct correlation between the attenuation in the stress intensity factor range estimated by the conventional compliance method and that determined by the displacement method. This finding seems to cast some doubts on the validity of the current practice in crack‐closure measurement, and indeed on the role of plasticity‐induced crack closure in the reduction of the applied stress intensity factor range.     

Elasto-plastic analysis for cyclic loading and tresca yield condition

Incremental theory of plasticity along with the finite element direct stiffness method is used for inelastic structural analysis. Tresca yield surface suitable for kinematic hardening formulation of the incremental theory of plasticity is presented. A uniaxial symmetric Tresca yield condition is used to formulate a small displacement theory of the incremental plasticity for material with both equal and unequal tension and compression yield strength.Constitutive laws for plane stress problem based on the linear kinematic hardening and associated flow rule are derived for sides and corners of the yield surface. In this formulation Ziegler's modification of Prager's rule has been used. Finite element formulation, numerical solution and applications are discussed.     

Development of disc bending fatigue test technique for equi-biaxial loading

The disc bending fatigue test technique was developed to investigate the fatigue life under an equi-biaxial loading condition. In this test, a uniform thickness disc specimen was subjected to a bending load by applying air pressure on the specimen surface. Eleven specimens made of Type 316 stainless steel were tested in a room temperature ambient environment. The crack initiation and growth behaviors during the test were observed through a transparent window. The fatigue life was defined when the peak pressure measured near the specimen surface was reduced to 95% of the supplied air pressure. The fatigue life obtained by the disc bending fatigue test was shorter than that obtained by the uniaxial and plate bending fatigue tests for the same principal strain range. It was confirmed that the equi-biaxial loading condition reduced the fatigue life. The finite element analysis together with test results revealed that the crack was initiated at the edge of the specimen when the specimen thickness was less than 1.0 mm. The specimen thickness should be 1.2 mm in order to maximize the strain range at the specimen center. It was concluded that the disc bending fatigue test can derive the fatigue life under an equi-biaxial loading condition, for which strain range is measured at the specimen center.     

Low-cycle fatigue of 1Cr–18Ni–9Ti stainless steel and related weld metal under axial, torsional and 90° out-of-phase loading

The fatigue behaviour of base metal and weld joints of 1Cr–18Ni–9Ti stainless steel has been studied under uniaxial, torsional and 90° out‐of‐phase loading. A significant degree of additional hardening is found for both base metal and weld metal under 90° out‐of‐phase loading. Both base metal and weld metal have the same cyclic stable stress–strain relationship under torsional cyclic loading and 90° out‐of‐phase cyclic loading. Base metal exhibits higher cyclic stress than weld metal under uniaxial loading, and Young's modulus and yield stress of weld metal are smaller than those of base metal. Weld metal exhibited lower fatigue resistance than base metal under uniaxial and torsional loading, but no significant difference was found between the two materials under 90° out‐of‐phase loading. A large scatter of fatigue life is observed for weld metal, perhaps because of heterogeneity of the microstructure. The Wang–Brown (WB) damage parameter and the Fatemi–Socie (FS) damage parameter, both based on the shear critical plane approach, were evaluated relative to the fatigue data obtained.     

Evaluation of constitutive models for textured aluminium alloys using plane-strain tension and shear tests

The constitutive modelling of the strongly textured aluminium alloys AA6063-T6 and AA7003-T6 is studied. The materials were delivered in the form of flat extruded profiles. Plane-strain tension and shear tests in the plane of the flat profiles are performed. The tests are then used to evaluate a constitutive model including an anisotropic yield function, the associated flow rule and a nonlinear isotropic work-hardening rule. The parameters of the yield criterion and the work-hardening rule were identified primarily from uniaxial tension tests in different in-plane directions. It is suggested how analytical considerations and the results from the plane-strain tension and shear tests may be used to obtain a more accurate calibration of the anisotropic yield criterion. To further assess the constitutive model, finite element simulations of the plane-strain tension and shear tests are carried out and the results compared with the experimental force-elongation curves. Significant deviations in the experimental and predicted results are disclosed, and attributed partly to the parameter identification, primarily based on uniaxial tension tests, and partly to the assumption of isotropic work-hardening. Polycrystal plasticity calculations are carried out for simple shear of the AA7003-T6 material, indicating that texture evolution plays an important role in determining the response in this test already at moderate strains.     

Analysis of Fatigue Damage under Block Loading in a Low Carbon Steel

Abstract: The fatigue damage accumulation behaviour of the P355NL1 steel is characterised using block loading fatigue tests. First, the constant amplitude low‐cycle fatigue behaviour of the P355NL1 steel is evaluated through strain‐controlled fatigue tests of smooth specimens. Both fatigue and cyclic elastoplastic behaviours are analysed. Then, block loading is applied to identify the key features of the fatigue damage accumulation phenomena for the P355NL1 steel. The block loading is composed of two distinct low‐cycle constant amplitude strain‐controlled blocks. The first block is applied for a predefined number of loading cycles, being followed by a second block which is applied until failure. The block loading illustrates that fatigue damage evolves nonlinearly with the number of load cycles as a function of the strain amplitude. These observations suggest a nonlinear damage accumulation rule with load sequence effects. The linear Palmgren–Miner's rule used extensively in design is not verified for the P355NL1 steel. Finally, using the generated experimental data, the cyclic elastoplastic behaviour of the P355NL1 steel is modelled using a continuum plasticity model with nonlinear kinematic hardening, available in the commercial finite element code ansys ®.     

弹塑性随机有限元在低周疲劳分析中的应用

推导了交变载荷下弹塑性随机有限元的迭代格式,计算了局部多轴应力应变的随机响应。迭代格式中,针对复杂的交变载荷,采用运动强化模型反映塑性变形引起的各向异性和包辛格效应,运用Jhansale模型描述材料的瞬态应力应变关系。弹塑性有限元分析,克服了以往近似方法只能计算单轴局部应力应变响应的缺陷,为多轴疲劳分析奠定了基础。考虑零构件的随机因素,将随机有限元方法引入到交变载荷下弹塑性有限元的迭代格式中,得到局部应力应变的随机响应,为低周疲劳可靠性分析提供了更精确的依据。MontCarlo模拟结果证实了提出的弹塑性随机有限元方法是可靠的。     

A robust kinematic hardening rule for cyclic plasticity with ratchetting effects Part II. Application to nonproportional loading cases

Summary Performance of the proposed kinematic hardening rule is examined using several examples of cyclic plasticity phenomena observed in experiments. Results obtained and compared with experimental observations on various loading histories are presented. With the memory effects added to the model, impressive results are obtained without using an anisotropic yield model. Drifting of the yield surface occurs during the numerical computation of the plastic response due to nonproportional loading paths. The drift due to the finite increments of stress or strain is corrected using a simple and efficient method proposed in this paper. The new kinematic hardening rule proposed for the limit surface as being related directly to the yield surface kinematic hardening rule ensures nesting using the blended rule discussed in the part presenting the theoretical formulation [14].     

Plastic dissipation in mixed-mode fatigue crack growth along plastically mismatched interfaces

A new theory of fatigue crack growth in ductile solids has recently been proposed based on the total plastic energy dissipation per cycle ahead of the crack. This and previous energy based approaches in the literature suggest that the total plastic dissipation per cycle can be closely correlated with fatigue crack growth rates under mode I loading. In a recent paper, the authors have extended the dissipated energy approach to the case of fatigue crack growth in a homogeneous material under sustained mixed-mode loading conditions. The goal of the current study is to further extend the approach to mixed-mode fatigue delamination of ductile interfaces in layered materials. Attention is restricted to material combinations with identical elastic properties, but with mismatches in plastic properties (both yield strength and hardening modulus) across the interface. Such systems can occur in brazing, soldering, welding, and a variety of layered manufacturing applications, where high-temperature material deposition can result in a mismatch in mechanical properties between the deposited material and the substrate. In this study, the total plastic dissipation per cycle is obtained through plane strain elastic–plastic finite element analysis of a stationary crack in a general layered specimen geometry under constant amplitude, mixed-mode loading. Numerical results for a dimensionless plastic dissipation per cycle are presented over the full range of relevant material combinations and mixed-mode loading conditions. Results suggest that while applied mode-mix ratio is the dominant parameter, mismatches in yield strength and hardening modulus can have a significant effect on the total plastic dissipation per cycle, which is dominated by the weaker/softer material.     

Evolution of mechanical properties for a dual-phase steel subjected to different loading paths

The evolution of the mechanical properties of a dual-phase (DP590) steel sheet after being prestrained by uniaxial tension, plane strain and equal biaxial stretching was investigated. Specimens were first loaded using the three prestraining modes. Then, from the prestrained specimens, a few sub-sized samples were machined along the rolling direction and the transverse direction for further uniaxial tension testing. Six loading paths were provided. Equal biaxial stretching was performed using a cruciform specimen. The evolution of work hardening performance, elastic modulus, yield stress and tensile stress under the six loading paths were discussed in detail. The results indicate that loading paths can affect the latent work hardening performances, strain hardenability, yield stress and tensile stress evolution as well as the elastic modulus decrease during plastic deformation. The uniaxial tension–uniaxial tension path results in a cross-softening phenomenon, the largest yield stress enhancement and a mild maximum tensile stress increase. The equal biaxial stretching-uniaxial tension path leads to a cross-hardening phenomenon, the least yield stress enhancement and the largest tensile strength increase maximum tensile strength. The elastic modulus of DP590 steel not only changes with the accumulated plastic strain but also varies with the loading paths. The largest decrease of the elastic modulus equal biaxial stretching–uniaxial tension can reach 12.7% beyond 8% equivalent strain, which is 5.2% greater than that in the monotonic uniaxial tension path.     

可收卷复合材料层板大变形弯曲性能研究

该文研究了玻璃纤维编织复合材料制成的可收卷层板在大变形条件下的弯曲静力性能和疲劳性能。通过弯曲静力试验得到了试验件在大变形条件下的应变和位移的关系;通过有限元模拟静力试验并与试验结果对照,确定了疲劳试验的载荷;研究了在大变形条件下不同铺层层板的弯曲疲劳寿命及失效模式和相同铺层层板的疲劳寿命曲线。结果表明:复合材料层板在大变形弯曲时具有明显的非线性行为,且(±45°)铺层层板弯曲疲劳性能明显优于(0°/90°)铺层层板;在最小应变和最大应变比不变的情况下,相同铺层层板的弯曲最大应变和对数疲劳寿命之间存在线性关系。     

Approximate yield criteria for anisotropic porous ductile sheet metals

An approximate macroscopic yield criterion for anisotropic porous sheet metals is developed under plane stress conditions in this paper. The metal matrices are assumed to be rigid perfectly plastic and incompressible. The Hill quadratic and non-quadratic anisotropic yield criteria are used to describe the matrix normal anisotropy and planar isotropy. The voids in sheet metals are assumed in the form of through-thickness holes. Under axisymmetric loading, a closed-form upper bound macroscopic yield criterion is derived as a function of the anisotropy parameter R, defined as the ratio of the transverse plastic strain rate to the through-thickness plastic strain rate under in-plane uniaxial loading conditions. The plane stress upper bound solutions for different in-plane strain ratios can be fitted well by the closed-form macroscopic yield criterion.     

Experimental and numerical study on dynamic fracture behaviour of AISI 1045 steel for compressor crankshaft

Dynamic fracture behaviour of AISI 1045 steel for compressor crankshaft was studied by experimental and numerical methods. True stress–strain relations of the material under different strain rates were measured, and dynamic constitutive model with consideration to strain‐hardening and strain‐rate hardening was proposed. Dynamic fracture tests loaded by Hopkinson pressure bar were carried out, and fracture toughness was determined using a finite element method with the combination of ABAQUS and Zencrack software. Loading states of the specimen and determination methods of the dynamic fracture toughness were discussed. By comparing the fracture behaviours under quasi‐static and dynamic conditions, it was found that the fracture modes exhibited a transition from ductile to brittle fracture with the increasing loading rate, and the dynamic fracture toughness value was less than the quasi‐static one.     

Creep fatigue of a directionally solidified Ni‐base superalloy – smooth and cylindrically notched specimens

Turbine blade life modelling is complicated by the presence of notches, dwells, high temperatures, thermal cycles and temperature gradients. Furthermore, directionally solidified (DS) Ni‐base superalloys are highly anisotropic. This work seeks to characterize the response of the DS Ni‐base superalloy CM247LC subjected to isothermal low cycle fatigue at either 750 or 950 °C. This study considers the effects of strain rate, dwells at the maximum temperature, and stress concentrations. Experiments were conducted under uniaxial loading on smooth and cylindrically notched round‐bar specimens in both longitudinal and transverse orientations. The location of the creep‐fatigue crack is at the maximum Hill's effective stress in the notched specimens. In addition, the notch behaviour is discussed in light of finite element analysis using an anisotropic elastic‐crystal viscoplastic material model.     

Twist springback characteristics of dual-phase steel sheet after non-axisymmetric deep drawing

This paper aims to investigate the twist springback characteristics of advanced high strength steel sheet subjected to deep drawing. A C-rail benchmark, which leads to a particularly pronounced twist springback characteristics, was developed. For an accurate numerical modeling of the process, a non-quadratic anisotropic yield criterion integrated with combined isotropic and kinematic hardening model was used to describe the strain-stress behavior including anisotropy and Bauschinger effects. The corresponding mechanical experiments, namely uniaxial tension and forward-reverse simple shear tests were performed to determine the material parameters. The digital image correlation technique was applied for component tests as well as the deformation and stress-strain analysis. The experimental validation of the elastic-plastic finite element model was assessed by comparing maximum in-plane strain, thickness reduction distribution and twist springback of the drawn rail. To explore the source of twist springback, the deformation associated with in-plane stress and bending moment was analyzed. The results indicate that the bending moment before springback caused by non-symmetric stress states play an important role in twist springback and control. Certain regions of the die radius were varied in a numerical analysis to control the bending moment for the minimization of twist springback as well as the preliminary results of the relationship between the ratio of variable die radius and twist springback.     

PREDICTION OF BENDING FATIGUE BEHAVIOUR BY THE REFERENCE STRESS APPROACH

Abstract— A technique is presented for prediction of low-cycle fatigue behaviour under bending conditions from the knowledge of uniaxial fatigue data. The technique utilizes the reference stress approach used in the analysis of creeping components. The results enable determination of nominal elastic bending stress in terms of the observed saturation stress amplitude in an uniaxial fatigue test conducted at a reference value of strain amplitude. The reference parameters are determined for beams with both rectangular and circular cross-sections. The predictions of fatigue bending behaviour are in excellent agreement with closed form solutions reported recently. The merits of this alternative approach lie in its potential applicability to other structural situations once their reference uniaxial parameters are determined. Since the reference parameters are nearly the same for both creep and fatigue, the approach can be a useful experimental tool for relating creep-fatigue interaction effects in structural components with uniaxial creep-fatigue tests conducted under the reference conditions.