Multiaxial Loading Paths Research Articles

A modified energy-based model for low-cycle fatigue life prediction under multiaxial irregular loading

This work provides a damage accumulation algorithm to calculate low cycle fatigue life under multiaxial irregular loading path, using an intuitively constructed energy-based parameter which combines both cyclic plastic work and non-proportional (NP) hardening effect. The cumulative fatigue damage is calculated according to actual shape of the loading path, which is different from the traditional damage accumulation models that consider block sequence effect. The effectiveness of this proposed damage accumulation algorithm has been validated by experimental results of 316L stainless steel under nine regular loading paths and nine irregular multiaxial loading paths.

Low-cycle multiaxial fatigue behavior and life prediction of Q235B steel welded material

Low-cycle torsional and multiaxial fatigue experiments are carried out for thin-walled Q235B steel welded specimens under both in-phase and 90° out-of-phase loading paths. A remarkable non-proportional additional hardening effect exists in the Q235B steel welded material under the 90° out-of-phase loading paths. A new energy-based fatigue parameter is proposed that incorporates the shear strain energy on the weighted critical plane and the normal strain energy on both the weighted critical plane and orthogonal plane. The proposed energy-based fatigue parameter provides a superior ability to make life prediction for the Q235B steel welded material under the torsional and multiaxial loading paths.

In situ tension-tension strain path changes of cold-rolled Mg AZ31B

The mechanical behavior of cold-rolled Mg AZ31B is studied during in-plane multiaxial loading and tension-tension strain path changes performed on cruciform samples using in situ neutron diffraction and EBSD. The results are compared with uniaxial tension loading of dogbone-shaped samples measured with in situ neutron diffraction and acoustic emission. The activity of slip and twinning mechanisms and the active twin variants are discussed for the different strain paths. It is shown that initial strains of 4–5% cause a strengthened yield stress during reload for strain path change angles of 90 and 135°. The strengthening is primarily due to dislocation accumulation during the initial load impeding dislocation motion during the reload. The twinning observed during the prestrain activates complex multivariant secondary twinning which may also contribute to the strengthening in the reload.

Corrected stress field intensity approach based on averaging superior limit of intrinsic damage dissipation work

Corrected stress field intensity obtained by averaging the superior limit of intrinsic damage dissipation work in critical domain, which considers thoroughly thermodynamic consistency within irreversible thermodynamic framework, was proposed for predictions of high-cycle fatigue endurance limits. Simultaneously, the effects of mean stress, additional hardening behavior related to non-proportional loading paths and stress gradients on multiaxial high-cycle fatigue are taken into account in the proposed approach. The approach is an extension of the general stress field intensity. For a better comparison, existing multiaxial high-cycle fatigue criteria were employed to predict the endurance limits of different metallic materials subjected to different multiaxial loading paths, and it is shown that present proposal performs better from statistical value of error indexes, which make the proposed approach of corrected stress field intensity and its associated concepts provide a new conception to predict endurance limits of multiaxial high-cycle fatigue with high accuracy.

Cyclic plasticity modeling of nickel-based superalloy Inconel 718 under multi-axial thermo-mechanical fatigue loading conditions

High temperature components work mainly under thermo-mechanical loading conditions. Recent investigations reveal significant effects of the thermo-mechanical coupling on material behavior. In the present work, extensive experiments are performed for nickel-based superalloy Inconel 718 under both isothermal and thermo-mechanical loading conditions. Within the framework of the Ohno-Wang cyclic plasticity, a modified constitutive model is suggested to describe cyclic hardening/softening, non-proportional hardening, non-masing effects observed in the experiments. The implicit integration algorithm is developed and implemented into a commercial finite element code. Comparison between experiments and computations confirms that the suggested model can predict the cyclic plastic behavior under most different varying temperatures and multi-axial loading paths reasonably.

Evaluation of fatigue damage model of CDM by different proportional and non-proportional strain controlled loading paths

Fatigue damage models based on the continuum damage mechanics have been proposed to predict fatigue life of specimens under uniaxial and multiaxial loadings. In this research the fatigue damage model of Chaboche is used to predict the fatigue life under different proportional and non-proportional strain controlled loadings paths. The nonlinear kinematic hardening model of Chaboche is used and it is coupled by nonlinear fatigue damage model. S-N curves of 7075-T6 and 6061-T6 alloys are modeled by applying the fatigue damage model of Chaboche. Constants of the models are determined from S-N curves of two different stress ratios and cyclic uniaxial tests. Ten different loading paths are considered and modeled. Modeling of the multiaxial loading paths is carried out by the obtained constants. Fatigue life is predicted and compared with the experimental results. The experimental and numerical results consist of high and low cycle fatigue tests. Maximum stress in each cyclic strain loops are also obtained by the present models and compared with the experimental results. The present research evaluates the capabilities of the used fatigue damage model.

Multiaxial Fatigue Crack Orientation and Early Growth Investigation Considering the Nonproportional Loading

The paper presents a comprehensive investigation of fatigue cracking behaviors under various nonproportional multiaxial cycle loading paths based on the critical plane approach. The maximum normal and shear stress/strain fields are presented to analyze the crack orientation and early growth directions in polar diagrams. The experimental observed crack paths and directions were compared with maximum strain loci of each angle to determine multiaxial fatigue failure mode. The results show that crack orientation and growth paths appear in the maximum shear and normal strain plane, respectively. Likelihood cracking regions of various loading paths are predicted according the determined failure mode. Besides, nonproportionality factor is introduced to characterize the degree of multiaxiality on these loading paths.

Investigation on the Anisotropic Transformation Surfaces of Super-Elastic NiTi Shape Memory Alloys Under Multiaxial Cyclic Loading Conditions

The cyclic transformation behaviors of polycrystalline super-elastic NiTi shape memory alloys (SMAs) under multiaxial loading paths with different angles between axial and torsional loading orientations were experimentally investigated. The experimental results showed that the start stresses of forward and reverse transformations decreased with the increase in the number of cycles and exhibit obvious anisotropic evolutions. The start stresses of forward and reverse transformations in the tensile and torsional directions did not satisfy the von Mises criterion. The shape of transformation surface during the forward and reverse transformations evolved with the increase in the number of cycles. Then, new cyclic anisotropic transformation surfaces were established by introducing an anisotropic tensor into the von Mises equivalent stress based on a typical transformation criterion related to $$J_2 $$ and $$J_3 $$ . Moreover, the evolution equations of material parameters used in the proposed transformation surfaces were established to describe the subsequent evolutions of transformation surfaces. Finally, the start stresses of forward and reverse transformations predicted using the proposed transformation surfaces were compared with the experimental results. It shows that the proposed transformation surfaces can reasonably describe the start stresses of forward and reverse transformations, which are helpful for establishing a three-dimensional cyclic constitutive model to describe the cyclic transformation behaviors of super-elastic NiTi SMAs.

Experimental validation of shape memory material model implemented in commercial finite element software under multiaxial loading

Shape memory alloys are used in ever-increasing numbers of applications, such as implants made of porous shape memory alloys, where the material is subjected to complex loading conditions with various loading paths. Finite element simulation of such parts requires utilizing a constitutive model that is able to capture the multiaxial and path-dependent behavior of shape memory alloys. The main objective of this article is to investigate the accuracy of the constitutive model implemented in current commercial finite element software such as Ansys in predicting the shape memory alloys mechanical response under different multiaxial loading paths. To this end, several isothermal tests were conducted on thin-walled NiTi tubes with uniaxial, as well as multiaxial, path-varying loadings. The performance of the material model within Ansys was then investigated by finite element modeling of the sample tubes and performing simulations of the tests. Comparing the finite element results with experimental data, it was observed that while this model provided a close prediction of the uniaxial tensile superelastic response, it was not able to reproduce the multiaxial and path-dependent behavior of the shape memory alloy samples with sufficient accuracy. A brief discussion of the reasons behind the inaccuracy of the current model and potentially promising models for future investigation are provided.

Evaluation of different techniques in estimating orientation of crack initiation planes and fatigue lifetime under complex multiaxial loading paths

In the present investigation, the accuracy of two methods, i.e., the Shear Strain-Maximum Variance Method (γ-MVM) and the Maximum Damage Method (MDM), in predicting the orientation of the crack initiation planes was checked by considering several results taken from the literature and generated by testing five different metallic materials under complex multiaxial loading. The γ-MVM postulates that the critical plane is that material plane containing the direction experiencing the maximum variance of the resolved shear strain. In contrast, the MDM defines the critical plane as that material plane on which the accumulated damage reaches its maximum value. In the present investigation, the MDM was applied in conjunction with Fatemi-Socie’s (FS) multiaxial fatigue criterion, Bannantine-Socie’s (BS) cycle counting method, and Miner’s linear rule. The validation exercise being performed demonstrated that both the γ-MVM and the MDM were capable of accurately predicting the orientation of the crack initiation planes in the selected metals. Subsequently, the reliability of three different design methodologies suitable for estimating fatigue lifetime of metals subjected to variable amplitude multiaxial loading was assessed quantitatively by using a number of experimental results taken from the literature. In more detail, Methodology A was based on the MDM applied along with the FS criterion, the BS cycle counting method, and Miner’s rule. Methodology B made use of the γ-MVM, the FS criterion, the BS cycle counting method, and Miner’s linear rule. Finally, Methodology C involved the γ-MVM, the Modified Manson Coffin Curve Method (MMCCM), the classical Rain-Flow cycle counting method, and Miner’s linear rule. According to this systematic validation exercise, the usage of these three design procedures was seen to result in satisfactory predictions, with the estimates falling within an error band of three.

Effects of peak stress and stress amplitude on multiaxial transformation ratchetting and fatigue life of superelastic NiTi SMA micro-tubes: Experiments and life-prediction model

Multiaxial whole-life transformation ratchetting and fatigue failure of superelastic NiTi SMA micro-tubes are observed in the non-proportionally multiaxial stress-controlled cyclic tests at the human-body temperature (310K) under five different multiaxial loading paths. The effects of the axial peak stress and stress amplitude on the transformation ratchetting and fatigue life are addressed. It is found that the super-elastic NiTi SMA micro-tubes sustain more significant path-dependent fatigue failure in the multiaxial cyclic tests with lower axial peak stress and stress amplitude, while the fatigue lives of the NiTi micro-tubes under different loading paths are gradually converged with the increasing axial peak stress and stress amplitude. Based on the experimental findings, a fatigue failure model is proposed to predict the multiaxial fatigue life of the super-elastic NiTi SMA micro-tubes by considering the initial/saturated dissipation energy and the non-proportionality of the loading paths. It is shown that the predicted multiaxial fatigue lives agree with the experimental ones fairly well.

A continuum damage model for multi-axial low cycle fatigue of porous sintered metals based on the critical plane concept

Experimental investigations reveal very different damage mechanisms in porous sintered metals from those of conventional dense materials. Interactions between the inherent porosity and heterogeneous matrix result in complicated deformation behavior and fatigue damage processes. In the present work, the damage evolution in the sintered metal under multi-axial cyclic loading conditions is studied experimentally and computationally. The total damage is divided into the stress-related elastic damage, the plastic damage induced by the plastic deformations and the fatigue damage driven by cyclic loading. To predict the cyclic deformation behavior as well as the fatigue damage evolution, a nonlinear fatigue damage model coupled with the critical plane concept is proposed, embedded into the Ohno–Wang cyclic plasticity and implemented into the FEM software ABAQUS based on an implicit integration algorithm. The proposed damage model is computationally and experimentally verified under multi-axial cyclic loading paths with different strain amplitudes. A good agreement between experimental and computational results shows that the present model is able to describe cyclic mechanical behavior and fatigue damage of porous metals.

Non-proportionally multiaxial cyclic deformation of AZ31 magnesium alloy: Experimental observations

The non-proportionally multiaxial cyclic deformation of extruded AZ31 magnesium alloy with a hexagonal close-packed (HCP) crystal structure is investigated at room temperature by performing the strain- and stress-controlled axial-torsional cyclic tests with different loading paths and using thin-walled tubular specimens. The cyclic hardening/softening and multiaxial ratchetting of the AZ31 alloy are discussed. The AZ31 alloy shows significant cyclic hardening in both axial and torsional stress-strain responses. An additional softening occurs in the axial response, while an additional hardening presents in the torsional one under the multiaxial (i.e., combined axial-torsional) cyclic loading conditions. The multiaxial ratchetting mainly occurs in the direction of non-zero mean stress, and the ratchetting strain greatly depends on the shapes of multiaxial loading paths. The traditional equivalent stress-strain responses cannot reasonably characterize the multiaxial cyclic ones of the AZ31 alloy, since different mechanisms of plastic deformation are involved in the axial and torsional deformations. The axial and torsional stress-strain responses should be discussed separately.

Thermo-mechanically coupled cyclic elasto-viscoplastic constitutive model of metals: Theory and application

Thermo-mechanically coupled cyclic deformations often occur in metallic components subjected to cyclic loading. A framework of thermo-mechanically coupled elasto-plasticity (including rate-independent or rate-dependent plasticity) is first presented in this work based on the thermodynamic laws and logarithmic stress rate. Then, a specific thermo-mechanically coupled elasto-viscoplastic constitutive model is constructed from the framework to describe the thermo-mechanically coupled cyclic deformation of 316L stainless steel by using combined nonlinear isotropic and kinematic hardening rules and considering the internal thermal production. The nonlinear kinematic hardening rule is extended from that originally proposed by Abdel-Karim and Ohno (2000) and Ohno and Abdel-Karim (2000) for small deformation; and a cyclic hardening-softening-hardening feature observed in the cyclic test of the steel is reflected by using a nonlinear isotropic hardening rule consisting of several component equations. The strain amplitude dependence of cyclic hardening is considered by introducing a memory surface of plastic strain proposed by Chaboche et al. (1979), and the additional hardening effect caused by the non-proportional multiaxial cyclic loading path is involved by using the non-proportionality parameter defined by Tanaka (1994). Furthermore, the proposed constitutive model is implemented into a finite element code (e.g., ABAQUS) by combining the user subroutines UMAT and UMATHT. Finally, the proposed model is verified by comparing the predictions with the experimental results of 316L stainless steel. It is shown that the predictions agree well with the corresponding experimental ones.

A structural stress‐based critical plane method for multiaxial fatigue life estimation in welded joints

AbstractThis paper aims at proposing a new fatigue life estimation model that is preferably adapted to welded joints subjected to multiaxial loading. First, a mesh‐size insensitive structural stress is defined that enables to characterize the stress concentration effect appropriately. Second, the multiaxial stress state and loading path influence are taken into account in the lifetime prediction model by adopting a suitable critical plane method, originally proposed by Carpinteri and co‐authors. Experimental verification is conducted for a given welded joint geometry under different loading conditions, including uniaxial, torsional and multiaxial loads. The reliability and effectiveness of the new method are validated through substantive fatigue testing data.

Ratcheting of 304 Stainless Steel Alloys subjected to Stress‐Controlled and mixed Stress‐ and Strain‐Controlled Conditions evaluated by Kinematic Hardening Rules

AbstractThe present study predicts ratcheting response of SS304 tubular stainless steel samples using kinematic hardening rules of Ohno–Wang (O–W), Chen‐Jiao‐Kim (C–J–K) and a newly modified hardening rule under various stress‐controlled, and combined stress‐ and strain‐controlled histories. The O–W hardening rule was developed based on the critical state of dynamic recovery of backstress. The C–J–K hardening rule further developed the O–W rule to include the effect of non‐proportionality in ratcheting assessment of materials. The modified rule involved terms , and in the dynamic recovery of the Ahmadzadeh–Varvani (A–V) model to respectively track different directions under multiaxial loading, account for non‐proportionality and prevent plastic shakedown of ratcheting data over multiaxial stress cycles.The O–W model persistently overestimated ratcheting strain over the multiaxial loading paths. The C–J–K model further lowered this overprediction and improved the predicted ratcheting curves. The predicted ratcheting curves based on the modified model closely agreed with experimental data under various loading paths.

Ratcheting assessment of steel samples under various non-proportional loading paths by means of kinematic hardening rules

Abstract The present study predicts ratcheting response of 1045 and 1Cr18Ni9Ti tubular steel samples using nonlinear kinematic hardening rules of Ohno-Wang (O–W), Jiang–Sehitoglu (J–S), McDowell, Chen–Jiao–Kim (C–J–K) and newly modified model based on the hardening rule of Ahmadzadeh–Varvani (A–V) under various multiaxial loading histories. The modified hardening rule with less complexity holds components of backstress unity vector a ¯ / a ¯ and the normal vector to the yield surface n ¯ in its dynamic recovery to encounter non-proportionality. The components in the Macaulay brackets d e ¯ p ⋅ a ¯ / a ¯ possessing different directions enable the hardening rule to track different directions under multiaxial stress cycles. Coefficient γ2 controls the ratcheting rate and is regulated by term 2 − n ¯ . a ¯ / a ¯ to further lower the ratcheting strain curve. Term n ¯ . a ¯ / a ¯ 1 / 2 in the dynamic recovery prevents ratcheting plastic shakedown as stress cycles progress. The O–W, J–S and McDowell models persistently overestimated ratcheting curves in 1045 and 1Cr18Ni9Ti steel alloys for various multiaxial loading paths. Chen–Jiao–Kim modified the O–W model and possessed lower ratcheting results as compared with those predicted by other hardening rules. The predicted ratcheting curves through the modified model closely agreed with experimental data obtained under various multiaxial loading paths.

Non-proportional multiaxial whole-life transformation ratchetting and fatigue failure of super-elastic NiTi shape memory alloy micro-tubes

Experimental observations are performed to investigate the non-proportional multiaxial whole-life transformation ratchetting and fatigue failure of superelastic NiTi SMA micro-tubes in stress-controlled loadings at human-body temperature (310K). The effects of axial mean stress and stress hold on the whole-life transformation ratchetting and fatigue life are investigated with uniaxial, torsional and five different multiaxial loading paths. The results show that the stress holds on the upper or lower transformation plateaus will both promote forward and reverse transformation, and lead to shorter fatigue life. The multiaxial fatigue lives of NiTi shape memory alloy depend significantly on loading paths and applied stress levels.

Shortcuts in multiple dimensions: the multiaxial racetrack filter

Filtering techniques have been proposed for multiaxial load histories, usually aiming to filter out non-reversals, i.e. sampling points that do not constitute a reversal in any of its stress or strain components. However, the path between two reversals is needed to evaluate the equivalent stress or strain associated with each event. Filtering out too many points in such path would almost certainly result in lower equivalent stresses or strains than expected. To avoid such issues, it is important to consider how a measured multiaxial loading path deviates from its course using some metric, such as the von Mises stress or strain. In this work, a multiaxial version of the racetrack filter is proposed, which is able to perform efficient filtering even for 6D nonproportional histories. In the Multiaxial Racetrack algorithm, the stress or strain history is represented in a 6D space, only requiring from the user a desired scalar filtering amplitude r. For uniaxial histories, the proposed algorithm exactly reproduces the classic racetrack filter. The efficiency of the proposed Multiaxial Racetrack filter is qualitatively verified from a tension-torsion history example, showing the reduction in the number of data points for larger filter amplitudes r. The procedure can efficiently filter out non-damaging events but preserving the overall multiaxial path shape and multiaxial reversion points, which usually do not coincide with the reversion points of individual stress or strain components.

Effect of mean stress on multiaxial ratcheting life: A simplified life prediction model based on average equivalent stress amplitude

This article proposes a model to predict uniaxial and multiaxial ratcheting life by addressing the three primary parameters that influence failure life: fatigue damage, ratcheting damage and the multiaxial loading path. These three factors are addressed in the present model by (a) the stress amplitude for fatigue damage, (b) mean stress-dependent Goodman equation for ratcheting damage and (c) an inherent weight factor based on average equivalent stress to account for the multiaxial loading. The proposed model requires only two material constants which can be easily determined from uniaxial symmetric stress-controlled fatigue tests. Experimental ratcheting life data collected from the literature for 1025 and 42CrMo steel under multiaxial proportional and nonproportional constant amplitude loading ratcheting with triangular sinusoidal and trapezoidal waveform (i.e. linear, rhombic, circular, elliptical and square stress paths) have shown good agreement with the proposed model.