Effects Of Nonproportional Loading Research Articles

Fatigue Failure Life of SS400 Steel under Non-Proportional Loading in High Cycle Region

This study discusses fatigue properties of low carbon steel under multiaxial non-proportional loading and an evaluation of failure life. Multiaxial fatigue tests under non-proportional loading with various stress amplitudes were carried out using a hollow cylinder specimen in low and high cycle regions at room temperature. In the test, three types of strain/stress path were employed. They are a push-pull, a reversed torsion and a combined push-pull and reversed torsion loadings in which stress amplitudes used were constant and random. This study evaluates an effect of non-proportional loading on fatigue life in the high cycle fatigue region to discuss the applicability of ΔεNP proposed by Itoh et al. on life evaluations in the high cycle region and under random loading.

OS0701 改良9Cr-1Mo鋼の高温軸ねじり低サイクル疲労試験寿命におよぼす非比例負荷の影響(OS7-1 高温・寿命,OS-7 多軸応力下における疲労損傷および疲労き裂進展1)

The in-phase and 90deg out-of-phase straining axial-torsional low-cycle fatigue tests were conducted on Mod.9Cr-1Mo steel at 823K under the PP-type strain waveform, and it was examined whether or not the equivalent plastic strain range proposed by the author and his colleagues to estimate the effect of nonproportional loading in case of SUS304 and 316LC steels can be applied to Mod.9Cr-lMo steel. As the results, it was found that the observed nonproportional loading effects were little in case of Mod.9Cr-1Mo steel and not only the proposed equivalent plastic strain range but also the von Mises plastic strain range and the Brown & Miller's equivalent shear strain amplitude. can well estimate the 90deg out-of-phase straining axial-torsional PP test lives of the material.

A new approach for failure criterion for sheet metals

The interpretation of sheet forming simulations relies on failure criteria to define the limits of metal deformation. The common requirements for these criteria across a broad range of application areas have not yet been satisfied or fully identified, and a single criterion to satisfy all needs has not been developed. Areas where existing criteria appear to be lacking are in the comprehension of the effects of non-proportional loading, general non-planar and triaxial stress loading, and process and material mechanisms that differentiate between necking and fracture. This study was mainly motivated to provide an efficient method for the analysis of necking and fracture limits for sheet metals. In this paper, a model for the necking limit is combined with a model for the fracture limit in the principal stress space by employing a stress-based forming limit curve (FLC) and the maximum shear stress (MSS) criterion. A new metal failure criterion for in-plane isotropic metals is described, based on and validated by a set of critical experiments. This criterion also takes into consideration of the stress distribution through the thickness of the sheet metal to identify the mode of failure, including localized necking prior to fracture, surface cracking, and through-thickness fracture, with or without a preceding neck. The fracture model is also applied to the openability of a food can for AA 5182. The predicted results show very good agreement with the experimentally observed data.

An improved model of 3-dimensional finite element analysis of mechanical behavior of endodontic instruments

The aim of this study was to develop a numeric method to study the mechanical behavior of an endodontic instrument during different loading paths and to demonstrate the importance of the behavior model in the finite element results. A numeric study of an endodontic instrument was carried out. At first, the geometry was meshed with a finite element code. Then, 3 among the most representative loadings in clinical use, i.e., bending, torsion, and nonproportional bending-torsion, were studied. Each of them was simulated by setting 3 different behaviors: elasticity, elastoplasticity, and an ad hoc model for the superelasticity. The simulations with nonproportional bending-torsion loading showed that the mechanical behavior of Ni-Ti shape memory alloy was strongly affected by change in the loading direction. Elastic and elastoplastic models were unable to consider this feature of Ni-Ti behavior. Only a superelastic model taking into account the effects of nonproportional loading proved to respect this crucial point. To realize valid simulations of the mechanical behavior of Ni-Ti instruments during different mechanical loading paths, it is necessary to use an ad hoc mechanical behavior model.

Effect of Nonproportional Loading on Creep-Fatigue Life of SUS304 Steel Subjected to CC-Type Combined Push-Pull Loading and Cyclic Torsion at 973K in Air

This paper investigates the applicability of the procedure proposed by one of the authors for estimating the nonproportional loading effect on PP test lives to the estimation of the creep-fatigue lives of SUS304 austenitic stainless steel subjected to nonproportionally combined push-pull and cyclic torsion under CC type strain waveform. Fully reversed strain-controlled CC tests were conducted on thin-walled tubular specimens of SUS304 steel at 973K in air under in-phase and 90deg out-of-phase straining conditions. The partitioned inelastic strain range versus life equations, Δecc versus Ncc relationships, obtained from three different proportional loading conditions, such as push-pull, cyclic torsion, and in-phase combined push-pull and cyclic torsion, are found to be correlated with one another by the multiaxiality factor. By using the multiaxiality modified Δepp versus Npp and Δecc versus Ncc relationships, the 90deg out-of-phase straining CC test lives were estimated by the proposed procedure, where the strain range partitioning was done by superposing the hysteresis loops of PP tests on those of CC tests. As the results, the estimated lives are found to agree well with the experimental lives in adopting the superposition method rather than the rapid loading method.

S0301-2-1 SUS304鋼の軸ねじり疲労における非比例負荷効果におよぼす温度とひずみ速度の影響(疲労特性に及ぼす各種因子の影響(2))

S0301-2-1 SUS304鋼の軸ねじり疲労における非比例負荷効果におよぼす温度とひずみ速度の影響(疲労特性に及ぼす各種因子の影響(2))

Fatigue life assessment for metal alloys under nonproportional low-cycle loading

A procedure for nonproportional low-cycle fatigue life assessment is proposed for various metal alloys that differ in structure. It is based on the Pisarenko-Lebedev equivalent strain and a correcting function allowing for nonproportional loading effects such as additional hardening and life reduction in the case of nonproportional strain paths. The calculated results are compared to the experimental ones reported elsewhere for steels, titanium-, nickel-, and aluminum-based alloys. A good agreement between the results is observed for all the materials and strain paths studied. The accuracy of the calculations for nonproportional loading is found to be same as in the case of proportional loading.

Effect of Multiaxial Stress State on High-Temperature Low-Cycle Fatigue Properties of SUS304 Steel

Fully reversed strain-controlled low-cycle fatigue tests, so called PP tests, were conducted on thin-walled tubular specimens of SUS304 austenitic stainless steel at 973K in air under proportional and nonproportinal loading conditions. Push-pull straining, cyclic torsion straining and in-phase straining of push-pull and cyclic torsion were selected as proportional loading, and 90deg out-of-phase straining of push-pull and cyclic torsion as nonproportional loading. Experimental data were analyzed by using both the Manson-Coffin equation and the critical plane model proposed by Brown and Miller, and the effects of the multiaxial stress state on the strain range versus life relationship were discussed. As the results, a new parameter was proposed that has a hopeful potential to estimate the effect of nonproportional loading on creep-fatigue life quantitatively based on the strain range partitioning method.

Multiaxial mixed-mode cracking – small crack initiation and propagation*

Abstract Both the fatigue crack path and fatigue life of CK45 steel and 42CrMo4 steel under various multiaxial loading paths are studied in this paper. The replica method was applied to monitor the crack initiation and small crack growth, the fractographic analyses were carried out on the fracture surface and the crack initiation angle was measured. The effects of non-proportional loading on both the crack path and fatigue life were studied, and the flattening of asperities on the crack surface due to compressive normal stress was also observed. An improved model is proposed based on correcting the strain range parameter of the ASME code approach, taking into account the additional hardening caused by the non-proportional loading path, which can improve the predictions of the fatigue lives for various non-proportional loading paths and provide an easy way to overcome the drawbacks of the current ASME code approach for non-proportional fatigue. Based on these corrected strain range parameters, a strain intensity factor range is used to correlate with the experimental results of small crack growth rates. It is concluded that the orientation of the early crack growth can be predicted well by the critical damage plane, but the fatigue life can not be predicted accurately using only the parameters on the critical plane, since the damage on all the planes contributes to fatigue damage as stated by the integral approaches.

Fatigue life prediction of type 304 stainless steel under sequential biaxial loading

Low-cycle fatigue tests are conducted on type 304 stainless steel with the loading sequence of: axial/torsional, torsional/axial, in-phase/90°-out-of-phase, and 90°-out-of-phase/in-phase. The results show that cross hardening occurs in axial/torsional loading but not in torsional/axial loading. Much additional hardening is observed under out-of-phase loading. Prior loading in sequential in-phase/out-of-phase loading (or vice versa) produces a small degree of additional hardening in stress response in the latter loading compared with pure in-phase or out-of-phase loading. The ( n 1/ N 1, n 2/ N 2) data points fall below the linear damage line in all cases. The double-linear damage rule, the damage curve approach and the plastic work model are found to give nonconservative predictions. A modified damage model is proposed, which accommodates nonproportional loading effects in sequential loading. Fatigue lives predicted based on the new model are within a factor-2 scatter band for all test conditions.

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.

A Unified Numerical Approach for Multiaxial Fatigue Limit Evaluation

A unified numerical approach to evaluate the endurance limit for general multiaxial fatigue loading, under proportional or nonproportional loading, is presented. A minimum circumscribed ellipsoid approach is proposed for computing the amplitude and mean value of the equivalent shear stress, and an efficient numerical algorithm is developed for solving the min–max problem by using a constrained optimization method. The approach is general and efficient, especially suitable for computer-aided design and optimization. With this approach, nonproportional loading effects can be taken into account, overcoming limitations of many other multiaxial fatigue criteria. Experimental results collected from the literature are compared with results predicted by the numerical approach proposed in this paper. The comparison shows that the predictions agree well with experiments for both proportional and nonproportional loading situations.

A two scale damage concept applied to fatigue

The ductile type of damage is a phenomenon now well understood. Once the fully coupled set of constitutive equations is identified, Damage Mechanics is a powerful tool to predict failure. Brittle materials do not exhibit such a damageable macroscopic behavior. Nevertheless, they still fail. On the idea that damage is localized at the microscopic scale, a scale smaller than the mesoscopic one of the Representative Volume Element (RVE), we propose a three-dimensional failure modeling for monotonic as well as for fatigue loading. We develop a two scale model of what we shall call brittle damage: at the microscopic scale, micro-cracks or micro-voids exhibit a damageable plastic-like behavior with no effect on the global (mesoscopic) elastic behavior. Microscopic failure is assumed to coincide with the RVE failure. This model turns out to represent quite well physical phenomena related to high cycle fatigue such as the mean stress effect, the nonlinear accumulation of damage, initial strain hardening or damage effect and the nonproportional loading effect for bi-axial fatigue. The model has been implemented as a post-processor computer code. A simplified identification procedure for the determination of the material properties is given.

Additional Damage of A17075-T651 under $90^{\circ}C$ Out-of phase Biaxial Loading from Crystal Structure Dependence

Accounting for the additional damages come out from non-proportional loading path effect, material damage according to crystal structure dependence was studied. Microscopic observations of damaged material by SEM(Scanning Electron Microscope) showed crystal structure dependence. Biaxial in-phase loaded specimens showed the slips of same direction, which pararell each other, but biaxial 90.deg. out-of-phase loaded specimens showed multiply crossed slips. S. H. Doong and D. F. Socie reported that wavy/planar or planar slip material showed the increase in the cyclic hardening level during non-proportional cycling. From these results, the additional hardening and non-proportional loading effects were related with slip mechanism, and the slip mechanism was related with crystal structure. In the present study, a damage mechanism which accounts for the non-proportional loading effect from crystal structure dependence was considered and applied to A17075-T651.

On plastic deformation and fatigue under multiaxial loading

This paper presents an experimental and theoretical investigation of deformation and fatigue behaviour under multiaxial random loading. The inelastic stress-strain response under complex loading paths has been predicted using an incremental plasticity model, which incorporates a memory rule to account for the variable-amplitude and non-proportional loading effects. Based on hysteresis strain-hardening behaviour and the history described by the memory effect under multiaxial loading, a mechanics-based cycle counting method has also been proposed for multiaxial random loading. The evaluation of cumulative damage by the cycle counting method combined with Miner's linear rule and a strain-path-dependent fatigue damage parameter is compared with experimental results of two metals under biaxial variable-amplitude loading.

Cyclic Behavior of Structural Steels. I: Experiments

This paper presents the nonproportional cyclic elastoplastic behavior of structural steels under biaxial loading, through a combined experimental and analytical study. In particular, the work seeks to illustrate the cyclic behavior within the yield plateau, which is an important feature of mild steel subjected to combined torsion-compression loading with proportional and nonproportional cyclic histories. A newly developed biaxial testing system used in the experiments is presented. Some important cyclic behavior of the steel within the yield plateau, such as the decrease and disappearance of the yield plateau, reduction of the elastic range, cyclic hardening, effect of nonproportional loading, and material memory are described and discussed. In a companion paper, Shen et al. carry out an analytical study by developing a new multiaxial two-surface plasticity model for structural steels. The experimental results are used to substantiate the analytical model.

Effect of non-proportional loading on creep-fatigue properties of 304 stainless steel at low strain ranges near the elastic region: Asayaman, T., Aoto, K. and Wada, Y. Nucl Eng Des (Mar. 1993) 139 (3), 299–309

This paper presents a comprehensive investigation into non-proportional multi-axial fatigue of welded components by introducing an equivalent structural stress parameter that takes into account of load-path non-proportionality in addition to plate thickness and stress state effects. This is accomplished by formulating a “moment of load path” or “MLP” based fatigue damage parameter that provides a consistent treatment of load-path non-proportionality under arbitrary multi-axial loading conditions for which cycle counting can be consistently performed by means of a previously developed path-dependent maximum range (PDMR) cycle counting procedure. To examine its broad applicability and effectiveness, non-proportional multi-axial test data obtained using different components, joint types, and loading conditions from various sources are analyzed using the newly developed equivalent stress parameter. The results show that the new equivalent stress parameter enables not only an effective consolidation of all multi-axial test data (up to about 300 tests) analyzed in this paper into a narrow band, but also the demonstrated transferability between the master S-N curve (dominated by test data under uniaxial cyclic loading conditions) adopted by the 2007 ASME Div 2 and API 579 RP/ASME FFS-1 Codes and the consolidated S-N curve dominated by severe non-proportional multi-axial cyclic loading conditions. As a result of the present development, a unified fatigue evaluation procedure based on the newly proposed effective stress parameter and a single master S-N curve can be implemented for arbitrary cyclic loading conditions regardless of stress multi-axiality or load path proportionality.

Characteristic features of the modeling of the cyclical instability of materials subjected to elastoplastic deformation. Report 2. Method of determining model parameters

A procedure is described for determining the parameters of the structural model of a cyclically unstable medium, which we had proposed earlier. The influence exerted by the number of subelements on the accuracy of description of the structural model of nonproportional-loading effects is assessed.

Nonproportional loading effects on elastic-plastic behavior based on stress resultants for thin plates of strain hardening materials

A stress resultant constitutive law in rate form is constructed for power-law hardening materials. The change of plate thickness is considered in the constitutive law. The elastic-plastic behavior of a plate element based on the stress resultant constitutive law under uniaxial combined tension and bending is determined under a limited number of nonproportional and unloading paths. The results based on the stress resultant constitutive law and the through-the-thickness integration method are compared within the context of both the small-strain and finite deformation approaches. The results indicate that the selection of the normalized equivalent stress resultant and the corresponding work-conjugate normalized equivalent generalized strain is appropriate for describing the hardening behavior in the stress resultant space. However, the hardening rule in a power law form must be modified for low hardening materials at large plastic deformation when finite deformation effects are considered.

Effect of nonproportional loading on creep-fatigue properties of 304 stainless steel at low strain ranges near the elastic region

The effect of nonproportional strain path on fatigue/creep-fatigue properties was investigated with 304 stainless steel at 550°C under strain controlled biaxial conditions. The fatigue/creep-fatigue life reduction due to nonproportional strain path occurred even at the lowest strain range investigated, that is, 0.2% for fatigue loading and 0.3% for creep-fatigue loading. The Mises-type path-dependent equivalent strain range was employed in order to evaluate the fatigue/creep-fatigue strength under nonproportional loading conditions. Stress relaxation behavior under nonproportional loading was examined. It was shown that stress relaxes proportionally toward the origin of stress plane even under nonproportional loading. Fatigue damage and creep damage were calculated based on the linear damage summation rule. Life prediction was shown to be possible within an accuracy of a factor of about 2 for nonproportional loading along with other waveforms including pure axial loading, pure torsional loading and combined proportional loading.