Critical Plane Damage Parameter Research Articles

Fretting fatigue crack nucleation analysis under a variable coefficient of friction

Fretting fatigue is a phenomenon that occurs when two surfaces come into contact and experience oscillatory stresses and displacements of small amplitude. This can lead to a significant reduction in mechanical parts’ lifetime. The complexity of this type of problems relies on the many variables that can affect the results. One of its most important variables is the Coefficient of Friction (CoF), which has been observed to vary throughout a single fretting test. However, this variation is rarely considered in fretting fatigue finite element analyses. In order to analyse the effects of a Variable Coefficient of Friction (VCoF) on nucleation lifetime, a cylinder-on-plane finite element model is developed. To predict nucleation lifetime, two critical plane damage parameters, Fatemi-Socie (FS) and Findley parameter (FP), are used along with an evolving CoF during the first stress cycles. These parameters are evaluated by calculating initiation lifetime where the maximum value of the damage parameter occurs (hotspot method) and by the quadrant averaging method, because of its capability of predicting lifetime with relative accuracy and negative crack angles. To simulate the evolution of the CoF, a Python script that changes the value of CoF before each simulation is developed. This coefficient varies between 0.3633 and 0.65, following arbitrary points on the coefficient’s evolution curve. Once the simulation is concluded, the script evaluates the damage parameters and their equivalent lifetime throughout the contact surface and saves those values in an accumulation parameter that follows Miner’s rule. This process is repeated until CoF reaches its maximum value. The lifetime to nucleation is statistically analysed for all methodologies. The results suggest that, regarding the hotspot method, FP values remain within ± 3 N deviations from the experimental results, while FS results are nearer, within ± 2 N deviations. In addition, the quadrant method results remain at ± 3 N deviations, but providing more accurate results for the FP parameter. The application of a VCoF to these methods leads to less conservative and less deviated results, providing more accuracy for conservative approaches and more consistency for predictions in general. It is concluded that VCoF analysis is an interesting tool to determine more accurately nucleation lifetime for conservative approaches. Additionally, it reduces the predictions variation for differently loaded fretting setups regardless the desired approach.

A fatigue life prediction method distinguishing fracture modes for Ni-based single crystal superalloys considering porosity defect

Microporosity is one of the most common defects in nickel base single crystal (N-SC) superalloys, which is a great threat to fatigue performance. In this paper, nine porosity-related fatigue damage parameters for N-SC superalloys were selected by referring to those parameters originally proposed for casting and 3D printing metal materials as well as the critical plane damage parameters commonly used in N-SC superalloys. According to the plastic constitutive model of single crystals, a crystal plastic finite element (CPFE) model was established to evaluate these different fatigue damage parameters, and the parameters of CPFE were calibrated by the low cycle fatigue (LCF) hysteresis loop obtained from the fatigue test. The evaluation results showed that the geometric mean of stress–strain concentration factor (GCF) kg was a satisfactory parameter to quantify the effect of porosity defects on fatigue. Inspired by the discovery and considering the slip systems characteristics of N-SC superalloys, the geometric mean of resolved stress–strain concentration factor (GRCF) krg on slip systems was proposed, and it was found that the max(krg,kg) could be used to predict the fracture modes of N-SC superalloys. Based on the max(krg,kg), a porosity-related fatigue life prediction method which can distinguish the fracture modes was put forward. The prediction results showed that the fracture mode prediction results were consistent with the test results, and the life prediction results were also improved compared with the GCF parameter.

A novel model for low-cycle multiaxial fatigue life prediction based on the critical plane-damage parameter.

Multiaxial fatigue of the components is a very complex behavior. This analyzes the multiaxial fatigue failure mechanism, reviews and compares the advantages and disadvantages of the classic model. The fatigue failure mechanism and fatigue life under multiaxial loading are derived through theoretical analysis and formulas, and finally verified with the results of multiaxial fatigue tests. The model of multiaxial fatigue life for low-cycle fatigue life prediction model not only improves the prediction accuracy of the classic model, but also considers the effects of non-proportional additional hardening phenomena and fatigue failure modes. The model is proved to be effective in low-cycle fatigue life prediction under different loading paths and types for different materials. Compared with the other three classical models, the proposed model has higher life prediction accuracy and good engineering applicability.

Multi-axis low-cycle creep/fatigue life prediction of high-pressure turbine blades based on a new critical plane damage parameter

To study the multi-axis low-cycle creep/fatigue life of high-pressure turbine blades, a multi-axis low-cycle fatigue life prediction model based on a new critical plane damage parameter is proposed in this paper. Firstly, based on the thermal-structural coupling analysis of high-pressure turbine blades, the law of stress-strain distribution under the complex load of centrifugal load, temperature load and the aerodynamic load is obtained. Secondly, the multi-axis low-cycle fatigue life prediction model and the L-M equation are applied to predict the fatigue life and creep life of blade respectively. Furthermore, different experimental loading schemes are used to study the fatigue damage mechanism for the creep/fatigue interaction under high temperature condition, and a creep/fatigue interaction life prediction model is simultaneously provided. And finally, the experiment results demonstrate the rationality of the multi-axis low-cycle fatigue life prediction model and the creep/fatigue interaction should not be ignored.

Multiaxial Fatigue Life Prediction on S355 Structural and Offshore Steel Using the SKS Critical Plane Model

This work analyses the prediction capabilities of a recently developed critical plane model, called the SKS method. The study uses multiaxial fatigue data for S355-J2G3 steel, with in-phase and 90° out-of-phase sinusoidal axial-torsional straining in both the low cycle fatigue and high cycle fatigue ranges. The SKS damage parameter includes the effect of hardening, mean shear stress and the interaction between shear and normal stress on the critical plane. The collapse and the prediction capabilities of the SKS critical plane damage parameter are compared to well-established critical plane models, namely Wang-Brown, Fatemi-Socie, Liu I and Liu II models. The differences between models are discussed in detail from the basis of the methodology and the life results. The collapse capacity of the SKS damage parameter presents the best results. The SKS model produced the second-best results for the different types of multiaxial loads studied.

Effect of stress gradient and quadrant averaging on fretting fatigue crack initiation angle and life

Abstract Fretting fatigue involves multiaxial stress field due to presence of contact between two bodies. Near the contact edge, high stress gradient may be present depending on load and geometrical conditions. To account for high stress gradient or singular results, a regularization method may be required for better prediction of crack initiation angle and life. In the present work, conventional point and volume averaging methods are compared with a proposed quadrant averaging method to predict crack initiation angle and life. It is found that quadrant method produce more realistic results for initial crack orientation than other methods. Two multiaxial critical plane damage parameters, McDiarmid (MD) and Fatemi Socie (FS) are employed for this purpose. In addition, the influence of stress averaging on crack initiation life is analysed for two different geometries. It is observed that critical radius for stress averaging depends on stress gradient or rate of decay of damage parameter under the surface of the contact.

A damage model based on the critical plane to estimate fatigue life under multi-axial random loading

A multi-axial random vibration fatigue damage parameter was proposed based on a critical plane damage parameter for multi-axial high cycle fatigue, which is an equivalent stress power spectral density (PSD). The fatigue life calculation under multi-axial random loading could be conducted based on the equivalent stress PSD, combined with the spectral method under uniaxial random loading. The multi-axial random vibration fatigue experiment was conducted on the thin-walled circular tube with slots on the side. The fatigue life results obtained from the experiment were compared with the ones calculated from the proposed model, which indicated that the proposed parameter did a good job in predicting the multi-axial random vibration fatigue life.

On the consideration of normal and shear stress interaction in multiaxial fatigue damage analysis

Due to the abundance of engineering components subjected to complex multiaxial loading histories, being able to accurately estimate fatigue damage under multiaxial stress states is a fundamental step in many fatigue life analyses. In this respect, the Fatemi-Socie (FS) critical plane damage parameter has been shown to provide satisfactory fatigue life correlations for a variety of materials and loading conditions. In this parameter, shear strain amplitude has a primary influence on fatigue damage and the maximum normal stress on the maximum shear plane has a secondary, but important, influence. Additionally, in order to preserve the unitless feature of strain, the maximum normal stress is normalized by the material yield strength. However, in examining some data from literature it was found that, in certain situations, the FS parameter can result in better fatigue life predictions if the maximum normal stress is normalized by the shear stress range on the maximum shear plane instead. These data include uniaxial loadings with large tensile mean stress, and some combined axial-torsion load paths with different normal-shear stress interactions. This modification to the FS parameter was investigated by using fatigue data from literature for 7075-T651 aluminum alloy and a ductile cast iron, as well as additional data from 2024-T3 aluminum alloy fatigue tests performed in this study.

Interaction of shear and normal stresses in multiaxial fatigue damage analysis

Due to the abundance of engineering components subjected to complex multiaxial loading histories, being able to accurately estimate fatigue damage under multiaxial stress states is a fundamental step in many fatigue life analyses. In this respect, the Fatemi-Socie (FS) critical plane damage parameter has been shown to provide excellent fatigue life correlations for a variety of materials and loading conditions. In this parameter shear strain amplitude has a primary influence on fatigue damage and the maximum normal stress on the maximum shear plane has a secondary, but important, influence. In this parameter, the maximum normal stress is normalized by the material yield strength in order to preserve the unitless feature of strain. However, in examining some literature data it was found that in certain situations the FS parameter can result in better fatigue life predictions if the maximum normal stress is normalized by shear stress range instead. These data include uniaxial loadings with large tensile mean stress, and some non-proportional axial-torsion load paths with different normal-shear stress interactions. This modification to the FS parameter was investigated by using fatigue data from literature for 7075-T651 aluminum alloy, as well as additional data from 2024-T3 aluminum alloy fatigue tests performed in this study.

Notch deformation and stress gradient effects in multiaxial fatigue

This paper investigates notch mechanics under multiaxial fatigue loading conditions with respect to notch stress–strain estimation rules and stress gradient effects. A pseudo stress-based plasticity modeling technique, incorporating a structural yield surface concept, was applied to predict local stress distributions for a 2024-T3 aluminum alloy notched tubular specimen, as well as for two different AISI 1141 steel alloy notched shaft specimen geometries. Stress–strain predictions were generated for several nominal loading conditions and compared to nonlinear FEA solutions. Most predictions were found to be within ±15% error for loading levels relevant to typical fatigue loading applications. To evaluate stress gradient models, fatigue life predictions were performed for each specimen geometry using Neuber’s rule with fatigue notch factor, as well as several different interpretations of Theory of Critical Distances (TCD) approaches. The effect of critical distance value on life predictions was also studied. The Fatemi–Socie critical plane damage parameter was used to calculate fatigue lives. While the TCD approaches were found to provide improved multiaxial fatigue data correlation when compared to fatigue notch factor, negligible differences between the different TCD approaches were observed. Life prediction trends were found to be consistent regardless of notch geometry and material, thus suggesting some generality of the findings.

A simple unified critical plane damage parameter for high-temperature LCF life prediction of a Ni-based DS superalloy

A simple unified critical plane damage parameter (i.e., the modified resolved shear strain range ∆γ mod) based on a slip mechanism-related critical plane concept was proposed in this paper, integrating life prediction of low cycle fatigue (LCF) behavior affected by anisotropy, load ratio and stress concentration into one framework, where the critical plane is determined as the slip plane on which the damage parameter is the maximum during the cycle. For notched specimens, this procedure was specially carried out at the fatigue initiation sites located on the notch surface, which were well predicted by the distribution of Von-Mises stress range ∆σ Mises. The applications of this damage parameter in a directionally solidified superalloy at high temperatures showed that the LCF lives resulting from complicated loading conditions (i.e., variable material orientation, temperature, loading ratio and notch feature) were well simulated consistently, and the predicted fatigue life is within a scatter band of ±3.

A computer simulation of four-point bending fatigue of a rear axle assembly

The bending fatigue test of a rear axle assembly is simulated by using a FE-integrated fatigue analysis methodology. The presented technique is based on local stress–strain approach in conjunction with two critical plane damage parameters. The stress–strain response at a material point is computed with a cyclic plasticity model coupled with a notch stress–strain approximation scheme. Linear elastic FE stress analyses are used in the calculation of local fatigue loading. All computational modules are implemented into the software tool and used in the four-point bending fatigue test simulation of rear axles made of a high-strength alloy steel. In fatigue models, proportional loadings with a static preload are considered, and the effects of residual stresses are neglected. The fatigue test cycles and crack initiation locations are predicted using Smith–Watson–Topper and Fatemi–Socie fatigue damage parameters. Both damage parameters provided conservative test cycle estimates for the test conditions simulated. It is also observed that von Mises stress distributions cannot be used to predict fatigue crack initiation locations while Smith–Watson–Topper critical plane parameter estimated the cracking location suitably. Comparisons with the prototype tests showed the applicability of the proposed approach.

Low-cycle fatigue life prediction of various metallic materials under multiaxial loading

This paper proposed a simple life prediction model for assessing fatigue lives of metallic materials subjected to multiaxial low-cycle fatigue (LCF) loading. This proposed model consists of the maximum shear strain range, the normal strain range and the maximum normal stress on the maximum shear strain range plane. Additional cyclic hardening developed during non-proportional loading is included in the normal stress and strain terms. A computer-based procedure for multiaxial fatigue life prediction incorporating critical plane damage parameters is presented as well. The accuracy and reliability of the proposed model are systematically checked by using about 300 test data through testing nine kinds of material under both zero and non-zero mean stress multiaxial loading paths.

Numerical modeling and simulation of wheel radial fatigue tests

A computational methodology is proposed for fatigue damage assessment of metallic automotive components and its application is presented with numerical simulations of wheel radial fatigue tests. The technique is based on the local strain approach in conjunction with linear elastic FE stress analyses. The stress–strain response at a material point is computed with a cyclic plasticity model coupled with a notch stress–strain approximation scheme. Critical plane damage parameters are used in the characterization of fatigue damage under multiaxial loading conditions. All computational modules are implemented into a software tool and used in the simulation of radial fatigue tests of a disk-type truck wheel. In numerical models, the wheel rotation is included with a nonproportional cyclic loading history, and dynamic effects due to wheel–tire interaction are neglected. The fatigue lives and potential crack locations are predicted using effective strain, Smith–Watson–Topper and Fatemi–Socie parameters using computed stress–strain histories. Three-different test conditions are simulated, and both number of test cycles and crack initiation sites are estimated. Comparisons with the actual tests proved the applicability of the proposed approach.

A critical plane gradient approach for the prediction of notched HCF life

A new approach, which uses the Findley critical plane damage parameter along with the stress gradient at the notch, was developed for predicting notched HCF life. The proposed approach and methodology for HCF notch analysis accounts for: (i) the multiaxial stress state at the notch, (ii) the notch size effect, and (iii) the effect of fatigue stress ratio. Two fatigue failure criteria based on the critical distance method were used to define a notch gradient parameter, G F. It was shown that G F is invariant with notch geometry and fatigue stress ratio. This invariance of G F was used to successfully and consistently analyze and predict notched HCF life of the titanium alloy Ti–6Al–4V for: (i) different notch geometries, and (ii) different fatigue stress ratios. For a notch under a general 2-dimensional stress state subjected to constant amplitude fatigue loading, the current approach can be performed in closed-form. Closed-form equations were developed for the fatigue notch factor K f, and the Findley gradient factor, G F, as a function of the critical distance, a c, the notch radius, ρ, the stress concentration factor K t, and the stress ratio, R. The proposed approach can be applied equally well using either finite element analysis or the closed-form analysis. A relationship was also established between G F and the notch sensitivity of a material. A new Findley notch sensitivity parameter, Q F, given by (2- G F) was proposed as a convenient and a more robust measure of the notch sensitivity than the classical notch sensitivity parameter, q, which can vary with the applied fatigue stress ratio.