Multiaxial Fatigue Life Prediction Research Articles

Multiaxial Fatigue Life Prediction Based on Nonlinear Continuum Damage Mechanics and Critical Plane Method

A new multiaxial fatigue life prediction model has been proposed in this paper. The concepts of nonlinear continuum damage mechanics and critical plane criteria were incorporated in the proposed model. The shear strain-based damage control parameter was chosen to account for multiaxial fatigue damage under constant amplitude loading. Fatigue tests were conducted on nickel-based superalloy GH4169 tubular specimens at the temperature of 400 °C under proportional and nonproportional loading. The proposed method was checked against the multiaxial fatigue test data of GH4169. Most of prediction results are within a factor of two scatter band of the test results.

Multiaxial notch fatigue life prediction based on pseudo stress correction and finite element analysis under variable amplitude loading

AbstractA new computational methodology is proposed for fatigue life prediction of notched components subjected to variable amplitude multiaxial loading. In the proposed methodology, an estimation method of non‐proportionality factor (F) proposed by authors in the case of constant amplitude multiaxial loading is extended and applied to variable amplitude multiaxial loading by using Wang‐Brown's reversal counting approach. The pseudo stress correction method integrated with linear elastic finite element analysis is utilized to calculate the local elastic‐plastic stress and strain responses at the notch root. For whole local strain history, the plane with weight‐averaged maximum shear strain range is defined as the critical plane in this study. Based on the defined critical plane, a multiaxial fatigue damage model combined with Miner's linear cumulative damage law is used to predict fatigue life. The experimentally obtained fatigue data for 7050‐T7451 aluminium alloy notched shaft specimens under constant and variable amplitude multiaxial loadings are used to verify the proposed methodology and equivalent strain‐based methodology. The results show that the proposed methodology is superior to equivalent strain‐based methodology.

A simple energy‐based model for nonproportional low‐cycle multiaxial fatigue life prediction under constant‐amplitude loading

AbstractFrom the literature concerning the traditional nonproportional (NP) multiaxial cyclic fatigue prediction, special attentions are usually paid to multiaxial constitutive relations to quantify fatigue damage accumulation. As a result, estimation of NP hardening effect decided by the entire history path is always proposed, which is a challenging and complex task. To simplify the procedure of multiaxial fatigue life prediction of engineering components, in this paper, a novel effective energy parameter based on simple material properties is proposed. The parameter combines uniaxial cyclic plastic work and NP hardening effects. The fatigue life has been assessed based on traditional multiaxial fatigue criterion and the proposed parameter, which has been validated by experimental results of 316 L stainless steel under different low‐cycle loading paths.

A Multiaxial Variable Amplitude Fatigue Life Prediction Method Based on a Plane Per Plane Damage Assessment

A multiaxial variable amplitude fatigue life prediction method is proposed in this paper. Three main steps are distinguished. The first one concerns the counting of multiaxial cycles and uses the normal stress to a physical plane as the counting parameter. Then a multiaxial finite fatigue life criterion allows one to assess the material life corresponding to each cycle on any physical plane. A damage law and its cumulation rule describe the damage induced by each cycle plane per plane. By this way the critical plane for a given multiaxial stress history is found out. It is assumed to be the fracture plane and the fatigue life of the material is traduced as the number of repetitions of the sequence up to crack initiation. At this stage, material fatigue criteria and linear and nonlinear damage laws assume that the material is damaged. One distinguishes among these criteria critical plan type whose formalism can identify the crack initiation plan. An application is given for each load. In the context of multiaxial solicitations of variable amplitude, a validation of the estimation of the orientations of the priming planes is carried out based on experimental results on cruciform test pieces; the estimated orientations are close to those observed experimentally.

Local stress gradient approach for multiaxial fatigue behaviour assessment of high strength steels in occurrence of defects

This study is dedicated to the effect of surface defects on the fatigue behaviour of high strength steels and the evaluation of their sensitivity. For that purpose, defects were introduced by Electro-Discharge Machining (EDM) on the edge of sheet metal test samples. Different defect depths are tested on high strength steel grades. A stress-based multiaxial fatigue life prediction method is then developed to assess the fatigue life. Input data are cyclic stress tensor states at the notch root that are calculated by a FEM analysis using the open-source Salome-meca software. In fact elastic–plastic numerical simulations were performed for each defect geometry to determine stresses distribution around the defect. A new class of multiaxial fatigue criteria extended from classical formulation to new ones with stress gradient terms related to the normal stress component is formulated. The Fogue integral approach based criterion is used since it is proved to give pertinent prevision under rotating principal stress directions multiaxial loading. For any material plane P the local stress gradient in its normal direction is calculated by parabolic interpolation and integrated to the normal stress component within the multiaxial fatigue criterion. For investigated multiaxial criteria, accounting for stress gradient effect is assessed from the experimental campaign results on two very high strength steel grades with occurence of surface defects.

Evaluation of fatigue damage with an energy criterion of simple implementation

Many theoretical methods for multiaxial fatigue life prediction are present in literature, most of them based on their effectiveness on knowledge of the entire stress time history. This represents the great applicative limit. The incapacity to study real situations, not only deterministic one, let the authors to develop a simple and rigorous criterion, which helps the designer who works in this area. The criterion is presented focusing the attention on the basic premise, highlighting its applicability, its practicality and its computational power. To do that, the Authors take into account the deterministic or random character of the individual constraint components and their degree of correlation. In order to verify the method, simulations of multiaxial loads conditions, developed in the time domain, will be carried out with various correlation levels between the stress components on which the method will be applied.

Multiaxial fatigue life prediction for powder metallurgy superalloy FGH96 based on stress gradient effect

Both proportional and non-proportional axial-torsion fatigue tests were conducted on powder metallurgy (PM) superalloy FGH96 tubular specimens and round bar specimens at 650 °C. The alloy is widely used to manufacture the aero-engine turbine disk by a process of hot isostatic pressing (HIP). The different stress distributions of thin-walled tubular specimen and the round bar specimen under axial-torsion cyclic loading are discussed. A multiaxial equivalent stress gradient factor is defined based on the tensile stress gradient and the shear stress gradient. A modified Zhong-Wang-Wei (ZWW) model considering the effect of the stress gradient is proposed for multiaxial fatigue of FGH96. Comparing to six multiaxial fatigue models, including the maximum effective strain model, the maximum shear strain model, the Fatemi-Socie (FS) model, the Smith-Watson-Topper (SWT) model, the Itoh model and the ZWW model, the predicted multiaxial fatigue lives of FGH96 by the modified ZWW model based on the effect of the stress gradient agreed better with the experimental results.

Multiaxial Fatigue Life Prediction Based on Short Crack Propagation Model with Equivalent Strain Parameter

The maximum shear strain and the normal strain excursion on the critical plane are regarded as the primary parameters of the crack driving force to establish a new short crack model in this paper. An equivalent strain-based intensity factor is proposed to correlate the short crack growth rate under multiaxial loading. According to the short crack model, a new method is proposed for multiaxial fatigue life prediction based on crack growth analysis. It is demonstrated that the method can be used under proportional and non-proportional loadings. The predicted results showed a good agreement with experimental lives in both high-cycle and low-cycle regions.

Multiaxial high-cycle fatigue life prediction model considering mean shear stress effect under constant and variable amplitude loading

In this paper, load controlled uniaxial, pure torsion, constant and variable amplitude tension–torsion tests on 7075-T651 aluminum alloy tubular specimens were conducted. According to the analysis of the experimental data obtained, a multiaxial high-cycle fatigue life prediction model, based on the critical plane method and considering mean shear stress effect, is proposed. The critical plane is proposed to be determined by a weight average, which is based on the variation of the maximum shear stress. The estimated fatigue lives obtained by applying the proposed model, for the fatigue limits related to 106, 2×106 and 107 cycles, are compared. The results demonstrate that the proposed model shows a good predictive capability.

Multiaxial Fatigue Damage Parameter and Life Prediction without Any Additional Material Constants

Based on the critical plane approach, a simple and efficient multiaxial fatigue damage parameter with no additional material constants is proposed for life prediction under uniaxial/multiaxial proportional and/or non-proportional loadings for titanium alloy TC4 and nickel-based superalloy GH4169. Moreover, two modified Ince-Glinka fatigue damage parameters are put forward and evaluated under different load paths. Results show that the generalized strain amplitude model provides less accurate life predictions in the high cycle life regime and is better for life prediction in the low cycle life regime; however, the generalized strain energy model is relatively better for high cycle life prediction and is conservative for low cycle life prediction under multiaxial loadings. In addition, the Fatemi–Socie model is introduced for model comparison and its additional material parameter k is found to not be a constant and its usage is discussed. Finally, model comparison and prediction error analysis are used to illustrate the superiority of the proposed damage parameter in multiaxial fatigue life prediction of the two aviation alloys under various loadings.

A New Energy-Critical Plane Damage Parameter for Multiaxial Fatigue Life Prediction of Turbine Blades.

As one of fracture critical components of an aircraft engine, accurate life prediction of a turbine blade to disk attachment is significant for ensuring the engine structural integrity and reliability. Fatigue failure of a turbine blade is often caused under multiaxial cyclic loadings at high temperatures. In this paper, considering different failure types, a new energy-critical plane damage parameter is proposed for multiaxial fatigue life prediction, and no extra fitted material constants will be needed for practical applications. Moreover, three multiaxial models with maximum damage parameters on the critical plane are evaluated under tension-compression and tension-torsion loadings. Experimental data of GH4169 under proportional and non-proportional fatigue loadings and a case study of a turbine disk-blade contact system are introduced for model validation. Results show that model predictions by Wang-Brown (WB) and Fatemi-Socie (FS) models with maximum damage parameters are conservative and acceptable. For the turbine disk-blade contact system, both of the proposed damage parameters and Smith-Watson-Topper (SWT) model show reasonably acceptable correlations with its field number of flight cycles. However, life estimations of the turbine blade reveal that the definition of the maximum damage parameter is not reasonable for the WB model but effective for both the FS and SWT models.

Multiaxial fatigue life prediction of composite materials

In order to analyze the stress and strain fields in the fibers and the matrix in composite materials, a fiber-scale unit cell model is established and the corresponding periodical boundary conditions are introduced. Assuming matrix cracking as the failure mode of composite materials, an energy-based fatigue damage parameter and a multiaxial fatigue life prediction method are established. This method only needs the material properties of the fibers and the matrix to be known. After the relationship between the fatigue damage parameter and the fatigue life under any arbitrary test condition is established, the multiaxial fatigue life under any other load condition can be predicted. The proposed method has been verified using two different kinds of load forms. One is unidirectional laminates subjected to cyclic off-axis loading, and the other is filament wound composites subjected to cyclic tension-torsion loading. The fatigue lives predicted using the proposed model are in good agreements with the experimental results for both kinds of load forms.

Low-cycle multiaxial fatigue behaviour and fatigue life prediction for CuZn37 brass using the stress-strain models

The low-cycle, strain-controlled fatigue tests have been conducted on CuZn37 brass (ASTM: C27200, EN: CW508L). Machined specimens have been subjected to uniaxial, proportional and non-proportional axial-torsional loadings. The monotonic and cyclic material properties have been determined for the loadings used. The obtained fatigue lives have been analysed in reference to the total Huber-von Mises equivalent strain ranges, the hysteresis loops energy in the loading cycle and the total plastic strain energy in the fatigue test. The relations between the plastic strain energy and the total as well as the plastic strain have been described. On the basis of the obtained experimental results, the selected stress-strain multiaxial fatigue criteria have been evaluated. In the conclusion it was found that fatigue lives predicted using the Fatemi-Socie and Garud criteria are closest to the experimental ones.

A critical plane‐energy model for multiaxial fatigue life prediction

AbstractA new critical plane‐energy model is proposed in this paper for multiaxial fatigue life prediction of metals. A brief review of existing methods, especially on the critical plane‐based and energy‐based methods, is given first. Special focus is on the Liu–Mahadevan critical plane approach, which has been shown to work for both brittle and ductile metals. One potential drawback of the Liu–Mahadevan model is that it needs an empirical calibration parameter for non‐proportional multiaxial loadings because only the strain terms are used and the out‐of‐phase hardening cannot be explicitly considered. An energy‐based model using the Liu–Mahadevan concept is proposed with the help of the Mróz–Garud plasticity model. Thus, the empirical calibration for non‐proportional loading is not needed because the out‐of‐phase hardening is naturally included in the stress calculation. The model predictions are compared with experimental data from open literature, and the proposed model is shown to work for both proportional and non‐proportional multiaxial loadings without the empirical calibration.

A new life prediction model for multiaxial fatigue under proportional and non-proportional loading paths based on the pi-plane projection

A new multiaxial fatigue damage parameter is proposed based on the projection path on the π-plane of the loading path. The proposed parameter is suitable for any arbitrary loading path in practical problems. Many materials exhibit strain hardening due to the non-proportional cyclic loading. A brief overview of some important non-proportional effects in multiaxial fatigue is presented, and a new non-proportionality description is defined. A modified multiaxial fatigue life prediction model is established based on the Coffin-Masson equation. Comparing to five classic multiaxial fatigue models, including the maximum effective strain model, the maximum shear strain model, the Fatemi-Socie (FS) model, the Smith-Watson-Topper (SWT) model and Itoh model, the predicted multiaxial fatigue lives of three metallic materials using the proposed model agreed better with the experimental results.

Multiaxial Fatigue Life Prediction of Metallic Materials Based on Critical Plane Method under Non-Proportional Loading

The critical plane method is widely discussed because of its effectiveness for predicting the multiaxial fatigue life prediction of metallic materials under the non-proportional loading conditions. The aim of the present paper is to give a comparison of the applicability of the critical plane methods on multiaxial fatigue life prediction. A total of 205 multiaxial fatigue test data of nine kinds of metallic materials under various strain paths are adopted for the experimental verification. Results shows that the von Mises effective strain parameter and KBM critical plane parameter can give well predicted fatigue lives for multiaxial proportional loading conditions, but give poor prediction lives evaluation for multiaxial non-proportional loading conditions. However, FS parameter shows better accuracy than the KBM parameter for multiaxial fatigue prediction for both proportional and non-proportional loading conditions.

多軸一定応力振幅下の高サイクル疲労寿命予測

Multiaxial high cycle fatigue life prediction under constant stress amplitude is proposed. This new criterion, which extends the proposed fatigue limit criterion by the authors in the previous papers, uses the unified equivalent shear stress amplitude. The material properties for the proposed criterion are the axial fatigue limit and the true fracture strength. The multiaxial high cycle fatigue tests for life prediction accuracy verification was carried out with S45C and SCM440. The fatigue tests were conducted under combined axial and torsion stresses with mean stress and phase difference. The criterion error is better than that of the Susmel criterion. The proposed criterion predicted the experimental fatigue life to be within a factor of 3.

Comparison between SSF and Critical-Plane models to predict fatigue lives under multiaxial proportional load histories

Materials can be classified as shear or tensile sensitive, depending on the main fatigue microcrack initiation process under multiaxial loadings. The nature of the initiating microcrack can be evaluated from a stress scale factor (SSF), which usually multiplies the hydrostatic or the normal stress term from the adopted multiaxial fatigue damage parameter. Low SSF values are associated with a shear-sensitive material, while a large SSF indicates that a tensile-based multiaxial fatigue damage model should be used instead. For tension-torsion histories, a recent published approach combines the shear and normal stress amplitudes using a SSF polynomial function that depends on the stress amplitude ratio (SAR) between the shear and the normal components. Alternatively, critical-plane models calculate damage on the plane where damage is maximized, adopting a SSF value that is assumed constant for a given material, sometimes varying with the fatigue life (in cycles), but not with the SAR, the stress amplitude level, or the loading path shape. In this work, in-phase proportional tension-torsion tests in 42CrMo4 steel specimens for several values of the SAR are presented. The SSF approach is then compared with critical-plane models, based on their predicted fatigue lives and the observed values for these tension-torsion histories. KEYWORDS. Multiaxial fatigue life prediction; Critical-plane approach; Polynomial stress scale factor approach.

Multiaxial Fatigue of 6061-T6 Aluminum Alloy under Corrosive Environment

Aluminium alloys are widely used in the fields of automobile, machinery and naval construction. To investigate the effect of non-proportional loadings and corrosive environment on the fatigue resistance of 6061-T6 aluminum alloy, a set of uniaxial and multiaxial low cycle fatigue tests were carried out. Firstly, the results of uniaxial tests showed that the alloy exhibited cyclic hardening then cyclic softening. With the increase of stress amplitude the cyclic softening became pronounced. The increasing of plastic deformation was basically cyclically stable with small plastic strain amplitude accumulation when the stress amplitude was lower than 200MPa ,while it was increasing rapidly when the stress amplitude was higher than 220MPa. Secondly, it was observed that non-proportional cycle additional hardening of 6061-T6 aluminum alloy was little. While the fatigue life was badly affected by the loading paths. Thirdly ,the fatigue corrosion interactions were also talked about in details by performing the tests under the same loading conditions with corrosive environment. The experiment proved that the seawater corrosion has huge impact on fatigue life under pH 3. Finally, a multi-axial fatigue life prediction model was used to predict the fatigue life with or without the corrosive environment which showed a good agreement with experimental data.

Fatigue life prediction for simultaneous cyclic loading with blocks of normal stresses and shear stresses

The problem of effects superposition in the case of simultaneous loadings, an important issue in mechanical structures design, have been analised. A method for the multiaxial fatigue life prediction was developed. This method was applied to fatigue life calculation in the cases of cyclical loading with: – one block of normal stress and one bloc of shear stress; – successive blocks of normal stresses, simultaneous with successive blocks of shear stresses. The influence of deterioration, of mean stress and residual stress upon the fatigue life is introduced. The theoretical results: – have been compared with experimental results reported in literature; – may be used for design, as well as for experimental data evaluation. Numerical examples show how the obtained theoretical results may be used in practical cases.