Multiaxial Random Loading Research Articles

Fatigue life prediction considering conversion of mean stress for titanium alloy under multiaxial thermo-mechanical random loading

This paper presents a thermo-mechanical fatigue (TMF) life prediction method for titanium alloy TA15 under multiaxial random amplitude loading. Through strain-controlled TMF tests, it was found that under full-reversed cyclic loading, there was a significant presence of mean stress in the stress response. The induced mean stress led to the anomalous phenomenon where the fatigue life of thermal phase angle out-of-phase (TOP) was shorter than that of thermal phase angle in-phase (TIP). Therefore, a new damage calculation model was proposed, which can take into account the pure fatigue damage considering mean stress conversion and the cumulative environmental damage. Uniaxial TMF tests, constant amplitude multiaxial TMF tests, and random amplitude multiaxial TMF tests are conducted to verify the proposed method. The predicted results for all types of tests are in a good agreement with the experimental data.

Fatigue behaviors and life evaluation of AISI304 stainless steel under non-proportional multiaxial random loading

Fatigue tests on AISI304 stainless steel under non-proportional multiaxial random loading conditions were conducted with uniform hollow specimens at room temperature. The results revealed initial hardening and subsequent cyclic softening under uniaxial loadings and additional hardening under non-proportional multiaxial loadings. This shift from softening to additional hardening significantly reduced the failure life. Fractographic analysis and Electron Backscatter Diffraction (EBSD) observations identified planar slip as the dominant deformation mechanism under uniaxial loading. Multiple slip system activations, strong slip interactions, and martensitic transformation were key factors influencing changes in cyclic deformation behavior under non-proportional loadings. A novel life evaluation method based on the Itoh–Sakane (IS) method was established, demonstrating accurate evaluations for both uniaxial and non-proportional multiaxial fatigue life under random loading conditions.

Bearing life prediction based on critical interface method under multiaxial random loading

The bearing was a key component of the mining machine tire unloader machine and was subjected to random multiaxial stress during operation. Therefore, the life prediction of bearing was of safety guidance. In this paper, a bearing life prediction method based on the critical plane method under multiaxial random loading was proposed. Firstly, a virtual prototype model was built based on the actual working conditions of the tire unloader machine to obtain the time load history of the bearing. Transient dynamic analysis of the bearing was carried out to obtain the triaxial stress-strain time histories at the hazardous locations of the bearing. A new coordinate system was established using the hazard node as the coordinate origin, and the location of the critical plane was searched for based on the critical plane multiaxial fatigue theory, combined with the maximum shear strain amplitude on the critical plane for multi-axial rain flow cycle counting to obtain the damage amount in each direction. At the same time, the life calculated from the maximum damage amount was used as the final life, resulting in a cycle count of the bearing of 268,303 cycles and a duration of 1490.58h. The results of this study could be used as a guide to predict the service life of the bearing in large machinery subjected to multiaxial random stress conditions.

Low-cycle multiaxial random fatigue life prediction model based on equivalent stress transformation

PurposeUnder multiaxial random loading, the material stress–strain response is not periodic, which makes it difficult to determine the direction of the critical plane on the material. Meanwhile, existing methods of constant loading cannot be directly applied to multiaxial random loading; this problem can be solved when an equivalent stress transformation method is used.Design/methodology/approachFirst, the Liu-Mahadevan critical plane is introduced into multiaxial random fatigue, which is enabled to determine the material's critical plane position under random loading. Then, an equivalent stress transformation method is proposed which can convert random load to constant load. Meanwhile, the ratio of mean stress to yield strength is defined as the new mean stress influence factor, and a new non-proportional additional strengthening factor is proposed by considering the effect of phase differences.FindingsThe proposed model is validated using multiaxial random fatigue test data of TC4 titanium alloy specimens and the results of the proposed model are compared with that based on Miner's rule and BSW model, showing that the proposed method is more accurate.Originality/valueIn this work, a new multiaxial random fatigue life prediction model is proposed based on equivalent stress transformation method, which considers the mean stress effect and the additional strengthening effect. Results show that the predicted fatigue lives given by the proposed model are in well accordance with the tested data.

Critical plane-based fatigue life model under multiaxial random loading

PurposeEngineering components/structures are usually subjected to complex and variable loads, which result in random multiaxial stress/strain states. However, fatigue analysis methods under constant loads cannot be directly applied to fatigue life prediction analysis under random loads. Therefore, the purpose of this study is how to effectively evaluate fatigue life under multiaxial random loading.Design/methodology/approachFirst, the average phase difference is characterized as the ratio of the number of shear strain cycles to the number of normal strain cycles, and the new non-proportional additional hardening factor is proposed. Then, the determined random typical load spectrum is processed into a simple variable amplitude load spectrum, and the damage in each plane is calculated according to the multiaxial fatigue life prediction model and Miner theory. Meanwhile, the cumulative damage can be calculated separately by projection method. Finally, the maximum projected cumulative damage plane is defined as the critical plane of multiaxial random fatigue.FindingsThe fatigue life prediction capability of the method is verified based on test data of TC4 titanium alloy under random multiaxial loading. Most of the predicting results are within double scatter bands.Originality/valueThe objective of this study is to provide a reference for the determination of critical plane and non-proportional additional hardening factor under multiaxial random loading, and to promote the development of multiaxial fatigue from experimental studies to practical engineering applications.

Fatigue life calculation of notched specimens by modified Wöhler curve method and theory of critical distance under multiaxial random loading

AbstractReformulation of a critical plane‐based multiaxial fatigue criterion named as Modified Wöhler Curve Method (MWCM) in the frequency domain is proposed; moreover, it is combined with the theory of critical distance (TCD) to implement vibration fatigue lifetime prediction of notched specimens subjected to complex multiaxial random loading. Firstly, a frequency‐domain formulation of the maximum variance method (MVM) is proposed for determining the critical plane with high computational efficiency. Then, a reference fatigue curve is defined through the frequency‐domain formulation of the reference stress ratio corresponding to the critical plane. Finally, the power spectral density (PSD) function of the resolved shear stress along the maximum variance direction is applied with the Bendat/Tovo–Benasciutti (TB) method to implement fatigue damage estimation of mechanical components. Both the time‐domain formulation and the proposed frequency‐domain formulation of the MWCM combined with the TCD are applied to the experimental results from the literature, concerning notched specimens made of 2024‐T4 aluminum alloy tested under various nonproportional bending‐torsion random vibration fatigue loading.

Energy‐based time derivative damage accumulation model under uniaxial and multiaxial random loadings

AbstractA new fatigue life prediction method using the energy‐based approach under uniaxial and multiaxial random loadings is proposed. The uniqueness of the proposed model is based on a time‐derivative damage accumulation unlike classical cycle‐based damage accumulation models. Thus, damage under arbitrary random loading can be directly obtained using time‐domain integration without cycle counting. First, a brief review of existing models is given focusing on their applicability to uniaxial/multiaxial, constant/random, and high cycle fatigue/low cycle fatigue loading regimes. Next, formulation of time‐derivative damage model is discussed in detail under uniaxial random loadings. Then, an equivalent energy concept for general multiaxial loading conditions is used to convert the random multiaxial loading to an equivalent random uniaxial loading, where the time‐derivative damage model can be used. Finally, the proposed model is validated with extensive experimental data from open literature and in‐house testing under various constant and random spectrum loadings.

A multiaxial fatigue life prediction method for metallic material under combined random vibration loading and mean stress loading in the frequency domain

A spectral method for the determination of the critical plane is proposed for metallic material under random vibration loadings based on the criterion of maximum shear stress amplitude, where the direction of critical plane is obtained by solving the maximum value of a function using mathematical optimization method and the fatigue critical location of the structure can be determined. A multiaxial fatigue damage parameter is proposed for combined random vibration loading and mean stress loading cases based on Susmel’s criterion, which is a Power Spectral Density (PSD) of the equivalent shear stress and can be adopted for fatigue life evaluation. The fatigue life estimation of structures under multiaxial random vibration loadings with mean stresses in the frequency domain could be carried out based on this damage parameter constructed at the fatigue critical location with the spectral method for random vibration fatigue life. The multiaxial random vibration fatigue experiment with mean stress loadings is conducted on the notched plate specimens made of 2297-T87 aviation grade aluminum alloy, and the initiation sites of the fatigue cracks as well as the experimental fatigue lives are compared with those calculated by the proposed models, where satisfactory prediction capabilities on both the fatigue crack initiation locations and fatigue lives of the models are demonstrated.

An Overview of Fatigue Testing Systems for Metals under Uniaxial and Multiaxial Random Loadings

This paper presents an overview of fatigue testing systems in high-cycle regime for metals subjected to uniaxial and multiaxial random loadings. The different testing systems are critically discussed, highlighting advantages and possible limitations. By identifying relevant features, the testing systems are classified in terms of type of machine (servo-hydraulic or shaker tables), specimen geometry and applied constraints, number of load or acceleration inputs needed to perform the test, type of loading acting on the specimen and resulting state of stress. Specimens with plate, cylindrical and more elaborated geometry are also considered as a further classification criterion. This review also discusses the relationship between the applied input and the resulting local state of stress in the specimen. Since a general criterion to classify fatigue testing systems for random loadings seems not to exist, the present review—by emphasizing analogies and differences among various layouts—may provide the reader with a guideline to classify future equipment.

An algorithm for fast critical plane search in computer‐aided engineering durability analysis under multiaxial random loadings: Application to the Carpinteri–Spagnoli–Vantadori spectral method

AbstractThis paper presents a new algorithm to implement the Carpinteri–Spagnoli–Vantadori (CSV) multiaxial fatigue criterion for random loading and to shorten the computation time. This goal is achieved after calculating the exact expressions of stress spectral moments in every rotated plane, which allow the maximum variance and expected maximum peak of normal/shear stress to be computed directly. This permits the new algorithm to determine the five rotations of the critical plane without using ‘for/end’ loops (which represent a slow numerical operation), although some information on stress signals examined is lost. Two examples are presented to demonstrate the advantages of the new algorithm in comparison with its standard version, which are particularly remarkable when considering the stress output of all finite element model nodes. The approach behind the new algorithm can be extended to other multiaxial spectral criteria that use angular rotations or direction cosines to locate the critical plane or the direction of maximum stress variance.

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.

Multiaxial high-cycle fatigue life prediction under random spectrum loadings

A multiaxial fatigue life prediction model under general multiaxial random loadings is proposed in this paper. First, a brief review for existing multiaxial fatigue models is given with a special focus is on the Liu- Mahadevan critical plane concept, which can be applied to both brittle and ductile materials. Next, the new model development based on the Liu-Mahadevan critical plane concept for random loading is presented. The key concept is to use two-steps to identify the critical plane: identify the maximum damage plane due to normal stress and calculate the critical plane orientation with respect to the maximum damage plane due to normal stress. Multiaxial rain-flow cycle counting method with mean stress correction is used to estimate the damage on the critical plane. Equivalent stress transformation is proposed to convert the multiaxial random load spectrum to an equivalent constant amplitude spectrum. The equivalent stress is then used for fatigue life predictions. The proposed model is validated with both literature and in-house testing data generated using an Al 7075-T6 alloy under various random uniaxial and multiaxial spectrums. Comparison between experimental and predicted fatigue life lives shows good agreements; thus, demonstrating efficacy of the proposed model. Finally, concluding remarks and future work based on the results obtained are discussed.

Computer‐aided durability analysis of complex structures under multiaxial random loadings through the Projection‐by‐Projection spectral method

Computer‐aided durability analysis of complex structures under multiaxial random loadings through the Projection‐by‐Projection spectral method

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 high-cycle fatigue modelling for random loading

In this paper, a multiaxial fatigue life prediction model is proposed under general multiaxial random loadings. First, a brief review for existing multiaxial fatigue models is given and special focus is on the LiuMahadevan critical plane concept, which can be applied to both brittle and ductile materials. Next, new model development based on the Liu-Mahadevan critical plane concept for random loading is presented. The key concept is to use two-steps to identify the critical plane: identify the maximum damage plane due to normal stress and calculate the critical plane orientation with respect to the maximum damage plane due to normal stress. Multiaxial rain-flow cycle counting method with mean stress correction is used to estimate the damage on the critical plane. Equivalent stress transformation is proposed to convert the multiaxial random load spectrum to an equivalent constant amplitude spectrum. The equivalent stress is used for fatigue life prediction. Following this, experimental design and testing is performed for Al 7075-T6 under various different random uniaxial and multiaxial spectrums. The developed model is validated with both literature and in-house testing data. Very good agreement is observed for the investigated material. Finally, conclusion and future work is given based on the proposed study.

The “Projection-by-Projection” (PbP) criterion for multiaxial random fatigue loadings

This work is motivated by the increasing interest towards the application of the “Projection-by-Projection” (PbP) spectral method in finite element (FE) analysis of components under multiaxial random loadings. To help users and engineers in developing their software routines, this paper presents a set of numerical case studies to be used as a guideline to implement the PbP method. The sequence of analysis steps in the method are first summarized and explained. A first numerical example is then illustrated, in which various types of biaxial random stress are applied to three materials with different tension/torsion fatigue properties. Results of each analysis step are displayed explicitly to allow a plain understanding of how the PbP method works. The examples are chosen with the purpose to show the capability of the method to take into account the effect of correlation degree among stress components, and the relationship between material and multiaxial stress in relation to the tension/torsion fatigue properties. A case study is finally discussed, in which the method is applied to a FE structural durability analysis of a simple structure subjected to random excitations. The example describes the flowchart and the program by which to implement the method through Ansys APDL software. This final example illustrates how the PbP method is an efficient tool to analyze multiaxial random stresses in complex structures.

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.

Frequency‐based analysis of random fatigue loads: Models, hypotheses, reality

AbstractSpectral methods use analytical expressions to estimate the fatigue damage in vibrating structures subjected to uniaxial or multiaxial random stresses. They exploit the random vibration theory which idealizes the random stress as a random process characterized by a power spectral density (PSD) in the frequency‐domain. The random process is hypothesized to be stationary or non‐stationary, Gaussian or non‐Gaussian, and with narrow‐band or wide‐band power spectral density. The accuracy of analytical spectral solutions depends on whether such hypotheses are fulfilled by actual random time‐histories encountered in practice. Knowing the range of applicability of each spectral method is then of utmost importance to avoid estimation errors. After a short account on the frequency‐domain description of random processes, this paper presents a brief survey on selected spectral methods for uniaxial and multiaxial random loading. It then analyzes when the hypotheses behind each spectral method are not verified in reality, with the purpose to provide recommendations for a safe use of frequency‐based methods.

Discussion on fatigue life estimation under multiaxial random loading: Comparison between time- and frequency-domain approach

In the present paper, two critical plane-based criteria proposed by Carpinteri et al. are discussed. Both criteria aim to estimate the fatigue life of smooth metallic structural components under multiaxial random loading, but one is formulated in time-domain whereas the other one in frequency-domain. Such criteria are here modified in order to improve their accuracy in terms of fatigue life estimation, and then applied to experimental fatigue data related to 18G2A structural steel tests available in the literature, performed on smooth specimens under random non-proportional bending and torsion loading.

Fatigue lifetime estimation of bearing pin of console manipulator loaded with multiaxial random loading

Fatigue lifetime estimation of load bearing parts of construction is a key factor in a design of technique used for long term operation. Complex loading in combination with complex geometry of the most loaded parts represents only one of many problems that engineers have to deal with. One of the most commonly used approaches how to deal with this problem is to use the technical standards. This approach, despite its indisputable advantages (clear and comprehensible steps of calculation), has several significant shortcomings (non-economical oversized design). In this paper we propose procedure of how to estimate fatigue lifetime of construction parts that are loaded with random operational loading. The result of proposed procedure is distribution function of fatigue lifetime which takes into account the complex geometry of the designed part and random character of the complex loading (multiaxial stress state) in a hotspot. This approach is then demonstrated on fatigue lifetime estimation of bearing pin of a console manipulator loaded by random operational loading. Loading process was obtained using set of strain gages. The measured loading process was then transformed into stress histories in critical hotspot using FEM. Method of processing the stress loading histories in critical hotspot into a form usable in combination with hypotheses for fatigue damage calculation under multiaxial stress states is presented.