Multiaxial Cycle Counting Method Research Articles

Multiaxial cycle counting method based on path-dependent line integral

A multiaxial cycle counting method was proposed by path-dependent line integral (PDLI). In the proposed PDLI multiaxial cycle counting method, the length increment of loading path is assigned a positive or negative sign in the strain space, and the interval from zero to the maximum value of PDLI is defined as a half-cycle. A very concise recursive algorithm is provided to implement the proposed multiaxial cycle counting method. The experimental verification showed that the proposed multiaxal cycle counting method was used to count multiaxial cycle, which can obtain satisfactory life prediction results under multiaxial variable amplitude loading. In addition, the PDLI multiaxial cycle counting method can be reduced to a uniaxial rainflow counting form.

Data-driven modeling of multiaxial fatigue in frequency domain

A data-driven approach to modeling multiaxial fatigue in frequency domain is proposed. The paper presents a methodology through which models can be built to predict fatigue damage based on a multiaxial cycle counting method and the associated life assessment approach in frequency domain. Through apt parameterization of spectrum in conjunction with principal component analysis transformation, every biaxial stress state in frequency domain can be represented as a point on a common feature space. The proposed methodology consists of three phases: exploratory study, data generation and model development. Two structural components are used for the demonstration. The performance of the models are evaluated in comparison with time domain approaches, and results are compared. The proposed methodology is able to predict multiaxial fatigue damage in frequency domain within acceptable error limits, allowing for a fast and efficient method to tackle multiaxial fatigue analysis in frequency domain.

Assessing variable amplitude multiaxial fatigue lifetime of notched components based on the notch critical plane approach

In the present paper, the notch critical plane method proposed by the authors is extended from 2D- to 3D-cases. The plane passing through the assumed critical point and experiencing the maximum variance of the resolved shear stress is defined as the the notch critical plane. The linear-elastic stress fields around the notch root are fitted via polynomial functions. The relationship between critical distance, l, and fatigue damage, Db, under variable amplitude loading blocks is proposed. Susmel’s parameter and a specific multiaxial cycle counting method are incorporrated into this approach to estimate multiaxial variable amplitude fatigue life. Numerous fatigue data generated by testing five different notched metallic materials were collected from the literature to check the accuracy of the proposed approach. This validation exercise allowed us to demonstrate that this method is highly accurate, with the majority of the predicted experimental results falling within an error band of 2.

An improved critical plane and cycle counting method to assess damage under variable amplitude multiaxial fatigue loading

AbstractThe plane with the maximum variance of the resolved shear stress is taken as the critical plane. Two algorithms are used along with the maximum variance method (MVM) to determine the orientation of the critical plane. The maximum variance of the normal stress on the potential critical planes is calculated to determine the one experiencing the maximum extent of fatigue damage. A new multiaxial cycle counting method is proposed to count cycles on the critical plane. The modified Wöhler curve method is used to assess fatigue damage. About 200 experimental results were collected from the technical literature to validate the approaches being proposed. The results show that the improved design technique being proposed is successful in assessing fatigue damage under variable amplitude multiaxial cyclic loading.

Online fatigue damage evaluation method based on real-time cycle counting under multiaxial variable amplitude loading

To realize on-line multiaxial fatigue damage evaluation for the servicing mechanical components, a real-time multiaxial cycle counting method is proposed, meanwhile, an online multiaxial fatigue damage evaluation method based strain-critical plane model is given and validated by the fatigue experimental data of En15r steel. Investigation showed that the proposed on-line multiaxial fatigue damage evaluation method could provide satisfactory evaluation results, and the real-time performance of the proposed cycle counting method is path-dependent.

Real-time damage evaluation method for multiaxial thermo-mechanical fatigue under variable amplitude loading

A real-time multiaxial thermo-mechanical damage evaluation method was proposed under variable amplitude loading. In order to achieve real-time damage evaluation, a real-time multiaxial cycle counting method that can take into account temperature loading history was proposed. The proposed multiaxial cycle counting method can obtain the reversals one by one in order with the reading of the load-time history data, which can realize the damage calculation immediately as a single reversal is counted out. At the same time, to consider the effect of temperature loading on the damage accumulation, an equivalent temperature was determined for the time period of the counted reversal. A fatigue-oxidation-creep damage model that can consider the influence of the non-proportional additional hardening on the fatigue, oxidation and creep damages was used to predict the lives in cases of isothermal axial-torsional fatigue, uniaxial thermo-mechanical fatigue and axial-torsional thermo-mechanical fatigue under constant and variable amplitude loadings. The results showed that the prediction errors were within a factor of 2.

Online multiaxial fatigue damage evaluation method by real‐time cycle counting and energy‐based critical plane criterion

AbstractTo realize online multiaxial fatigue damage assessment for the mechanical components in service, an online multiaxial cycle counting method is proposed coupled with the segment processing technique and Wang‐Brow's relative equivalent strain concept. Meanwhile, considering all the stress and strain components, which contribute to the fatigue damage on the critical plane, a multiaxial fatigue damage model without any weight coefficients is also proposed in an equivalent form of shear strain energy. Then, an online fatigue damage evaluation method for multiaxial random loading is developed by combining with the proposed damage model and online cycle counting method. The experimental results showed that the proposed online cycle counting method can be successfully applied to the calculation of multiaxial fatigue damage under random loading. Moreover, the proposed online multiaxial fatigue damage evaluation method can provide satisfactory predictions.

Algorithms for multiaxial cycle counting method and fatigue life prediction based on the weight function critical plane under random loading

Based on the critical plane determined by the weight function method, two algorithms for multiaxial cycle counting method are proposed by modifying the rainflow and range cycle counting methods. The proposed two algorithms can be applied to multiaxial random loading, and be suitable to any critical plane-based fatigue life prediction models, since the counted cycles or reversals are represented by the start time and end time. The proposed two algorithms are used to predict multiaxial fatigue life by the experimental data of 7075-T651 aluminum alloy, En15R steel and 7050-T7451 aluminum alloy conducted under multiaxial random loading in both high-cycle and low-cycle fatigue region. The life prediction results are in good agreement with the experimental data.

Multiaxial cycle counting method for non-proportional multiaxial variable loading signals based on modified maximal shear stress

One of the most challenging task in field of multiaxial fatigue is fatigue lifetime estimation of components loaded with multiaxial non-proportional variable amplitude loading. While this task consists of multiple smaller problems, one of the most crucial ones is loading cycles identification (and extraction) for future use with multiaxial damage criterions. By now, several cycle counting methods have been proposed for multiaxial loading conditions. The most wildly accepted methods are Bannantine-Socie’s method and Wang-Brown’s method (which has been later modified by Meggiolaro and Castro). The aim of this paper is the comparison of newly developed method with Bannantine-Socie’s method and Wang-Brown’s method. The new cycle counting method is based on cycle identification in relative maximum shear stress histories (calculated from multiaxial loading histories). The extracted data than composes part of each loading channel of multiaxial loading histories corresponding to identified loading cycle. The comparison of chosen methods has been done by using data sets created by authors as well as using real measured data from real operation.

A weight function method for multiaxial low-cycle fatigue life prediction under variable amplitude loading

A weight function method based on strain parameters is proposed to determine the critical plane in low-cycle fatigue region under both constant and variable amplitude tension–torsion loadings. The critical plane is defined by the weighted mean maximum absolute shear strain plane. Combined with the critical plane determined by the proposed method, strain-based fatigue life prediction models and Wang-Brown’s multiaxial cycle counting method are employed to predict the fatigue life. The experimental critical plane orientation and fatigue life data under constant and variable amplitude tension–torsion loadings are used to verify the proposed method. The results show that the proposed method is appropriate to determine the critical plane under both constant and variable amplitude loadings.

Performance of chosen multiaxial cycle counting method under non-proportional multiaxial variable loading.

One of the most crucial tasks in fatigue life-time estimation of components loaded with multiaxial variable amplitude loading is to correctly identify loading cycles that can be used with multiaxial damage criterions. During past years, several cycle counting methods have been proposed for multiaxial loading conditions. The aim of this text is the comparison of selected multiaxial cycle counting methods, namely Wang-Brown’s method, Modified Wang-Brown’s method, Bannantine-Socie’s method and then a critical analysis of the obtained results. For the comparison of chosen methods, a new data set, consisting of experimentally obtained results from multiaxial non-proportional variable amplitude loading tests carried on by authors, has been used. The tested specimens were made from S355J0 structural steel and the testing procedure has been carried out on the MTS Axial/Torsion servo hydraulic testing machine. Findley and McDiarmid multiaxial criterion with Palgren-Miner summation rule have been used for fatigue life-time estimation of the tested specimens.

Fatigue damage and life evaluation of SS304 and Al 7050-T7541 alloys under various multiaxial strain paths by means of energy-based Fatigue damage models

Three energy-based models of Macha, Ellyin and Varvani, respectively, are employed to evaluate fatigue life of SS304 and Al 7050-T7451 alloys undergoing variable multiaxial loading spectra. The Macha damage approach assesses the lives based on the equivalent strain energy densities over counted reversals on the critical plane. The Ellyin model evaluates fatigue life data based on the total strain energy density per cycle, consisting of two parts (elastic and plastic strain energies). These energies are quantified from areas within the axial and shear stress-strain hysteresis loops. The Varvani damage approach assesses fatigue lives through summation of the normal and shear energy ranges calculated on the critical plane where the largest stress and strain Mohr's circles over the counted reversals are determined. The reversals over variable multiaxial loading spectra are counted based on the Wang-Brown multiaxial cycle counting method. Damage values are calculated over reversals and then accumulated over a block loading spectrum. The total damage over block histories is then related to fatigue life Nf in the right-hand side of the damage model equations proposed by Macha, Ellyin, and Varvani, respectively. The choice of damage assessment models and how to determine the fatigue life of structural components under variable loading spectra are discussed.

Comparative study of multiaxial fatigue damage models for ductile structural steels and brittle materials

Fatigue damage prediction under a general multiaxial service loading consists of three main steps: multiaxial cycle counting, damage evaluation for an identified cycle (or reversal), and damage accumulations. The accuracy of fatigue life predictions depends on all the above steps. This paper reviews the evolutions of various multiaxial fatigue damage models, a comparative study is conducted about the physical basis, the computational efficiency, and the application range of the approaches. Based on the comparative studies, a new procedure is proposed to evaluate fatigue damage under general multiaxial random loading, which uses the Wang and Brown´s multiaxial cycle counting method for identifying cycles (or reversals), the modified procedure of the minimum circumscribed ellipse (MCE) approach for fatigue damage evaluation for an identified cycle (or reversal), and the Miner´s linear damage law for fatigue damage accumulations. By comparisons of the predicted life results with experimental results and with other approaches, it is shown that the proposed procedure is very efficient and suitable for computer aided structural optimization against fatigue.

Multiaxial cycle counting for critical plane methods

The critical plane method has proven to be a popular analytical tool for estimating multiaxial fatigue. Based on the strain-life approach to fatigue, the method relies on a cycle counting routine to identify cycles and a damage model to assess damage for each cycle. Researchers have traditionally borrowed cycle counting methods from established uniaxial methods. This work will show how uniaxial rainflow methods are inappropriate for cycle counting on the critical plane. A multiaxial cycle counting method, based on a simple uniaxial rainflow algorithm, is then presented.

A Procedure for Fast Evaluation of High-Cycle Fatigue Under Multiaxial Random Loading

This paper presents a fast evaluation procedure for high-cycle fatigue (HCF) under multiaxial random loading. The recent multiaxial cycle counting method of Wang and Brown is used to identify the loading reversals. For each identified reversal, the effective shear stress amplitude is directly calculated from the component stress ranges by an equation derived from the MCE approach, which is a newly developed method to account for nonproportional loading effect. This shear stress amplitude and the maximum hydrostatic stress during the time period of an identified reversal are used to evaluate the fatigue damage for that reversal by Crossland’s criterion. The fatigue damage of the loading block is then calculated by summing the damages of all the identified reversals by Miner’s rule. Comparisons with other multiaxial HCF approaches show that the procedure is a computationally efficient and conservative engineering approach.