Critical Plane Method Research Articles

Multi-axial creep-fatigue life prediction considering history-dependent damage evolution: A new numerical procedure and experimental validation

In this paper, a new numerical procedure based on a cycle-by-cycle analysis has been constructed for creep-fatigue behavior and life prediction of high-temperature structures under multi-axial stress states. Within this framework, a modified unified viscoplastic constitutive model with isotropic hardening and modified kinematic hardening rules is developed to simulate the cycle-by-cycle stress-strain responses. Moreover, the newly constructed creep-fatigue approach calculates fatigue and creep damage variables using the critical plane method (CPM) and the modified strain energy density exhaustion (SEDE) model, respectively. The multi-axial ductility factor and elastic follow-up factor are also introduced into the modified SEDE model to accommodate the special multi-axial and mixed controlled modes, which are widely existed in practical structures. In order to validate the feasibility of the proposed numerical procedure, a series of creep-fatigue tests of notched specimens made from nickel-based GH4169 superalloy were carried out at 650 °C. The predicted numbers of cycles to crack initiation agree well with the experimental data. Evidence of crack initiation under various loading conditions was observed via the electron backscatter diffraction (EBSD) technique, indicating location-dependent crack initiations depending on loading conditions. In detail, the crack initiation sites shifting from surface to subsurface with increasing hold times can be well simulated by the proposed numerical procedure due to a reasonable description of the creep-fatigue damage evolution.

Fatigue analysis of ductile and brittle behaving steels under variable amplitude multiaxial loading

AbstractThe analysis of fatigue behavior under multiaxial variable amplitude stress states, despite its wide applicability, has not been fully studied. Issues such as varying degrees of nonproportionality of the load history, cycle counting, damage accumulation, failure behavior of the material, and mean stress fluctuations which can significantly affect the results of these analyses have not been well understood. In this study, a methodology for the analysis of fatigue behavior under multiaxial variable amplitude loading conditions is employed which accounts for the aforementioned issues. At its core, the applied methodology uses critical plane analysis based on the failure behavior of each material to assess the fatigue damage. In order to evaluate the performance of the analysis method, axial, torsional, and combined axial‐torsional variable amplitude tests were performed on one ductile and one brittle behaving steel. The applied methodology resulted in close estimation of the experimental fatigue life for both ductile and brittle behaving steels.

Investigation of the multiaxial fatigue behaviour of 316 stainless steel based on critical plane method

AbstractIn this work, the multiaxial behaviour of 316 stainless steel is studied under the lens of critical plane approach. A series of experiments were developed on dog bone–shaped hollow cylindrical specimens made of type 316 stainless steel. Five different loading conditions were assessed with (a) only tensile axial stress, (b) only hoop stress, (c) combination of axial and hoop stresses with square shape, (d) combination of tensile axial and hoop stresses with L shape, and (e) combination of compressive axial and hoop stresses with L shape. The fatigue analysis is performed with four different critical plane theories, namely, Wang‐Brown, Fatemi‐Socie, Liu I, and Liu II. The efficiency of all four theories is studied in terms of the accuracy of their life predictions and crack failure plane angle. The best fatigue life predictions were obtained with Liu II model, and the best predictions of the failure plane were obtained with Liu I model.

Computing Tire Component Durability via Critical Plane Analysis

ABSTRACT Tire developers are responsible for designing against the possibility of crack development in each of the various components of a tire. The task requires knowledge of the fatigue behavior of each compound in the tire, as well as adequate accounting for the multiaxial stresses carried by tire materials. The analysis is illustrated here using the Endurica CL fatigue solver for the case of a 1200R20 TBR tire operating at 837 kPa under loads ranging from 66 to 170% of rated load. The fatigue behavior of the tire's materials is described from a fracture mechanical viewpoint, with care taken to specify each of the several phenomena (crack growth rate, crack precursor size, strain crystallization, fatigue threshold) that govern. The analysis of crack development is made by considering how many cycles are required to grow cracks of various potential orientations at each element of the model. The most critical plane is then identified as the plane with the shortest fatigue life. We consider each component of the tire and show that where cracks develop from precursors intrinsic to the rubber compound (sidewall, tread grooves, innerliner) the critical plane analysis provides a comprehensive view of the failure mechanics. For cases where a crack develops near a stress singularity (i.e., belt-edge separation), the critical plane analysis remains advantageous for design guidance, particularly relative to analysis approaches based upon scalar invariant theories (i.e., strain energy density) that neglect to account for crack closure effects.

Numerical analysis of the influence of micro-voids on fretting fatigue crack initiation lifetime

Abstract In this paper, the influence of the heterogeneity in the predicted crack initiation lifetime under fretting fatigue conditions is analysed for a regular and a random distribution of micro-voids. A critical plane analysis with two multiaxial damage criteria is performed to assess the crack initiation lifetime. The predicted initiation lifetime in the heterogeneous material is compared with the results obtained in the homogeneous case. The numerical results show that the heterogeneity has a noticeable influence on the predicted initiation lifetime. Furthermore, the numerical model suggests that a crack may firstly initiate at the upper edge of the micro-voids located close to the contact edge, leading to a mean reduction of the predicted crack initiation lifetime. However, in some cases, the introduction of micro-voids reduces the stress intensity at the contact edge and thus decreasing the predicted crack initiation lifetime.

Multiaxial Fatigue Life Prediction of GH4169 Alloy Based on the Critical Plane Method

The multiaxial fatigue life of GH4169 alloy was predicted based on the critical plane method. In this paper, a new critical plane-damage multiaxial fatigue parameter is proposed, in which the maximum shear strain is considered to be the main damage control parameter, and the correction parameter, including the normal stress and strain of the maximum shear strain plane, is defined as the second control parameter. The axis of principle strain rotates under non-proportional loading. Meanwhile, the mechanism of the variation of material microstructure and slip systems leads to an additional hardening phenomenon. The ratio of cyclic yield stress to static yield stress is used to represent cyclic strengthening capacity, and the influence of the phase difference and loading condition on the non-proportional reinforcement effect is considered. It is also proposed that different materials have different influences on the additional hardening phenomenon. Meanwhile, the model revision results in stress under asymmetrical loading. Experimental data of GH4169 alloy show that the proposed model can provide better prediction than the Smith–Watson–Topper (SWT) and Fatemi–Socie (FS) models.

Method for Predicting the Fatigue Life of Geometrically Discontinuous Structures Under Combined Bending and Torsion

The fatigue damage model based on theory of damage mechanics is capable of predicting the fatigue life under multiaxial loading. Meanwhile, the application of critical plane method in the prediction of multiaxial fatigue life has made certain progress. According to the law of thermodynamics, a new damage evolution equation is developed in the present study to predict the fatigue life of geometrically discontinuous structure under tension-torsion loading based on damage mechanics and the critical plane method. The essence of this approach is that the strain parameter of the uniaxial nonlinear fatigue damage model is replaced with the equivalent strain, which consists of the relevant parameters of the critical plane. However, it is difficult to calculate the stress–strain status and the critical plane position of geometrically discontinuous structure by theoretical methods because of the existence of stress concentration and the multiaxial nonproportional characteristics. Therefore, a new numerical simulation method is proposed to determine the critical plane of geometrically discontinuous structure under multiaxial loading by means of the finite element method and MATLAB software. The fatigue life of notched specimens subjected to combined bending and torsion is predicted using the proposed method, and the result is compared with those from the experiments and the Manson–Coffin law. The comparisons show that the proposed method is superior to the Manson–Coffin law and is capable of reproducing the experimental results reasonably when the geometry of the structure is complex. It completely meets the needs of engineering practice.

Fatigue life assessment of crankshaft with increased horsepower

PurposeThe purpose of this paper is to analyze the fatigue life of the crankshaft in an engine with increased horsepower.Design/methodology/approachThe applied load on the powertrain components was calculated through a dynamic analysis. Then, to estimate the induced stress in every crank angle, the calculated loads in different engine speeds were applied on the crankshaft. Finally, the critical plane fatigue theories in addition to URM standard were used to estimate the damage and fatigue life of the crankshaft with the increased power.FindingsIt was found that a simultaneous increase of gas pressure and engine speed by 30 percent will cause an increase of maximum applied load on the crankshaft by 25 percent. It was also found that while the results of finite element (FE) method predict an infinite life for the crankshaft after increasing the power, the URM method predicts an engine failure for the increased power application. In this study, the crankpin fillet is introduced as the most critical area of the crankshaft.Originality/valueIncreasing the power of the internal combustion engines without changing its main components has been of high interest; however, the failure associated with the increased load as the result of increased power has been a big challenge for that purpose. Moreover, although URM standard provided an efficient practice to evaluate a crankshaft fatigue life, using FE analysis may provide more reliability.

Axial-torsional fatigue and cyclic deformation of 304L stainless steel at room temperature

This work investigates the axial-torsional fatigue and cyclic deformation behaviour of 304L stainless steel at room temperature. Four fully reversed strain-controlled loading paths (axial, torsional, proportional axial-torsional, and 90º out-of-phase axial-torsional) and a fully-reversed shear strain-controlled with static axial stress loading were investigated. For axial, torsional, torsional with static stress and few proportional experiments, an initial cyclic softening was followed by secondary hardening related to martensitic transformation. Secondary hardening was not observed for non-proportional loading nor for some proportional experiments. The influence of the non-stabilized cyclic deformation behaviour on the fatigue life estimates of two multiaxial critical plane fatigue models (Smith–Watson–Topper and Fatemi–Socie) was investigated. Life estimates based on the stress-strain hysteresis loops corresponding to the maximum softening and to the half-life were similar for the two models.

Effects of secondary orientation and temperature on the fretting fatigue behaviors of Ni-based single crystal superalloys

A dovetail fixture for fretting fatigue test was designed. Fretting fatigue experiments were performed for Ni-based single crystal (NBSX) superalloys at 600 and 700 °C in two secondary orientations, [110] and [010]. The influence of secondary orientation and temperature on fretting fatigue behavior was investigated. The crystal plasticity finite element (CPFE) simulation was used to study the stress field at the contact region. The result indicates that the stress distribution is correlated to fretting damage, which is consistent with the crack initiation site. Fretting fatigue life is predicted based on critical plane method, which is in good agreement with the experimental result.

Durability prediction of an ultra-large mining truck tire using an enhanced finite element method

Ultra-class mining trucks used for material haulage in rugged surface mining terrains experience premature tire fatigue failure in operation. Typical failures include belt edge separation, ply turn-up separation, and tread base and sidewall cracking. The use of reinforcing fillers and processing aids in tire compounds result in the formation of microstructural in-homogeneities in the compounds. This article presents an application of the critical plane analysis technique for predicting the fatigue life of the belt package of an ultra-large mining truck (CAT 795F) tire of size 56/80R63 in a surface coal mine. Experimental data obtained from extracted specimens (sidewall, tread, and belt edge region) of the tire are used to characterize the stress–strain and fatigue behavior of the modeled tire. The tire’s duty cycle stresses and strains were obtained from finite element analysis of the rolling tire in Abaqus. Fatigue life calculations were performed in the rubber fatigue solver Endurica CL. Effects of inflation pressure, tire speed, and axle load on the fatigue life of the belt package under strain-crystallizing and non-crystallizing conditions of the belt compound are discussed. Specifically, the results show the belt edges to be critical regarding crack nucleation.

Predicting fretting fatigue in engineering design

The progress in fretting fatigue understanding and predictability is reviewed, with engineering applications in mind. While industrial assessments often relies on simple empirical parameters, research in fretting fatigue should allow the design engineer to improve confidence in the fretting fatigue analysis.Fretting fatigue cracks often form in multiaxial stress fields with severe gradients under the contact area, and are inherently difficult to predict.By describing the fretting stress gradients using comparisons with the mechanical fields surrounding cracks and notches, crack nucleation threshold conditions and finite life can efficiently be determined. Also, non-local stress intensity multipliers provide promising tools for the industrial finite element analysis, often involving complex geometries and loading conditions.The use of multiaxial fatigue criteria to determine fretting fatigue nucleation life is also reviewed. Researchers have shown that critical plane calculations with some stress-averaging method can predict fretting fatigue crack initiation. However, the frictional interface causes non-proportional loading paths, and the application of critical plane methods is not straight forward.

Investigation of the Biaxial Behaviour of 316 Stainless Steel Based on Critical Plane Method

In this work the biaxial behavior of 316 stainless steel is studied under the lens of critical plane approach. A series of ten experiments were developed on dog bone shape hollow cylindrical specimens made of type 316 stainless steel. Five different loading conditions were assessed, with (i) only axial stress, (ii) only hoop stress, (iii) proportional combination of axial and hoop stresses, (iv) non-proportional combination of axial and hoop stresses with square shape and (v) non-proportional combination of axial and hoop stresses with L-shape. The fatigue analysis is performed following four different critical plane theories, namely Wang-Brown, Fatemi-Socie, Liu I and Liu II. The efficiency of all four theories is studied in terms of the accuracy of their life predictions.

A new critical plane-energy model for multiaxial fatigue life prediction of turbine disc alloys

Abstract For engine components under complex loadings, multiaxial fatigue life prediction is critical for ensuring their structural integrity and reliability. Combining the critical plane method with the virtual strain energy concept, a new multiaxial fatigue damage parameter is proposed to characterize the influence of both shear/normal mean stress and non-proportional hardening on fatigue life. Particularly, no extra material constants are needed for model application. Experimental data of TC4 and GH4169 alloys under various loading paths are utilized to evaluate and validate the proposed damage parameter as well as four other models. Results show that the proposed damage parameter yields a higher accuracy on multiaxial fatigue life prediction than others.

Fatigue life predictions of metal structures based on a low-cycle, multiaxial fatigue damage model

A modeling strategy is developed accounting for the simulation of fatigue in metallic structures subjected to multiaxial, cyclic loading conditions. Cyclic plastic deformations are assumed to cause microcrack nucleation and growth, which in turn, lead to a deterioration of the mechanical and thermal properties. Microcrack nucleation and growth are modeled by a continuum damage mechanics formulation which accounts for a progressive loss of material integrity. The formulation utilizes a critical plane method for the prediction of microcrack nucleation. The emerging microcracks are assumed to be aligned with the critical plane orientation causing an anisotropic damage behavior. A second-order damage tensor is defined to approximate the damage behavior by an orthotropic material response. Damage evolution caused by microcrack growth is obtained from an empirical energy criterion based on the inelastic strain energy density. This way, the isotropic material response of a pristine material becomes orthotropic during damage evolution causing a direction dependent loss of material integrity. The continuum damage mechanics formulation in combination with the nonlinear Finite Element Method enables the simulation of structural deterioration caused by a propagating region of material failure. The approach is implemented into the Finite Element Method and extended by a cycle jump technique to reduce the computational time. The modeling strategy is exemplified on micrometer-sized cantilever beams under low-cycle fatigue conditions.

Critical plane analysis for interpreting experimental results on anisotropic rocks

This paper deals with a coherent analytical interpretation of the anisotropic strength of rocks as derived from standard laboratory experimental compression tests on rock samples under confinement. The critical plane approach is herein revisited by reformulating the Mohr–Coulomb failure criterion on a sliding plane when the operative strength parameters are direction dependent. Detailed attention is paid to the solution of the emerging equations that describe an optimization problem where the failure function is maximized with respect to orientation. This encompasses a tangency condition that has to be explicitly solved for as the stress state approaches failure from the inside of the plastic limit surface. However, this tangency condition cannot be graphically represented in the Mohr space as classically done in the isotropic case. A new graphical construction is herein proposed that offers insights to the problem by illustrating how anisotropy of strength juxtaposes with stress variations during a typical loading path to failure. More importantly, a perturbation analysis is conducted to obtain an approximated closed-form solution of the equations arising from the description of anisotropy. Within such a framework, salient features describing anisotropy of strength can be systematically related to inherent material symmetries so that laboratory experimental test data can be thus interpreted on a mathematically sound basis.

Research on extending the fatigue life of railway steel bridges by using intelligent control

This paper investigates the potential of a vibration control-inspired method towards extending the fatigue life of railway steel bridges. Based on coupled thermal-mechanical and vehicle-track analysis, both the residual stresses from welding and these from traffic on the bridge are obtained. Subsequently, a multi-scale approach with a shell Finite Element (FE) model of the whole bridge and a solid FE model of its critical joints is put forward. The equation of motion is established for the controlled bridge, equipped with a Magnetorheological-Tuned Mass Damper (MR-TMD) system, while the combination of excitation, welding and control effects is practiced through own-developed packages and commercial software sub-model routines. The framework is showcased for the study of the Poyang Lake Railway Bridge in China. After obtaining the controlled stress states at the critical welded joint, the fatigue crack initial life is evaluated by using the critical plane method and the linear cumulative damage theory. Simulation results indicate that the multi-scale modelling approach followed, meets the accuracy needs for capturing the cracking process of the welded joint with high computational efficiency. The MR-TMD system, even when moderately reducing the critical joint stress amplitudes, can improve substantially the overall bridge fatigue resistance over the uncontrolled structure.

The Fatigue Life Prediction of Train Wheel Rims Containing Spherical Inclusions

It is a common phenomenon that fatigue crack initiation occurs frequently in the inclusions of wheel rims. Research on the fatigue life of wheel rims with spherical inclusions is of great significance on the reliability of wheels. To find the danger point and working condition of a wheel, the stress state of the wheel rim with spherical inclusions was analyzed using the finite element method. Results revealed that curve conditions are dangerous. The critical plane method, based on the cumulative fatigue damage theory, was used to predict the fatigue life of the wheel rim and whether it contained spherical inclusions or not under curve conditions. It was found that the fatigue life of the wheel rim is significantly shorter when the wheel rim contains spherical inclusions. Analysis of the results can provide a theoretical basis and technical support for train operations and maintenance.

Fatigue life of a railway wheel under uniaxial and multiaxial loadings

In this paper, a railway wheel material is under evaluation using multiaxial fatigue testing. The experiments were conducted using a servo-hydraulic machine with standardized specimens. All samples were machined from a single worn-out railway wheel. The damage scale between normal and shear stresses was evaluated in the normal stress space for proportional and non-promotional loadings. Moreover, the uniaxial SN curves were obtained. A critical plane analysis was performed using theoretical criteria and experimental results. Results show a strong influence of heat treatments on the material fatigue behavior.

Numerical investigation of the influence of rolling texture and microstructure on fatigue crack initiation in BCC polycrystals

The study aims to investigate the influence of the grain morphology and rolling texture on the fatigue crack initiation in BCC polycrystals. Several 2D polycrystalline aggregates having different grain size and shape distributions are generated based on an anisotropic tessellation and an ellipse packing algorithm. Uniform and typical BCC rolled textures containing both the α and γ fibers are considered for the crystallographic texture of the material. Finite element simulations using a crystal plasticity model are performed under cyclic uniaxial tension-compression condition. Twenty simulations are conducted for each type of microstructure in order to obtain significant statistical data. A critical plane fatigue indicator parameter (FIP) following the Tanaka-Mura model is applied to quantify the sensitivity of the microstructure against fatigue crack initiation. The distributions of relevant geometrical, crystallographic and mechanical quantities are analyzed. The effect of the grain size distribution, morphology and texture on the fatigue performance and scattering are discussed.