Journal articles: 'Multiaxial'

1

Kosaka, Rui, Fumio Ogawa, Takamoto Itoh, and Masao Sakane. "Creep Damage Evaluation using Uniaxial Miniature Specimens for Multiaxially Damaged Components." MATEC Web of Conferences 300 (2019): 07003. http://dx.doi.org/10.1051/matecconf/201930007003.

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This study discusses a method of evaluating multiaxial creep damage for high temperature components subjected to multiaxial creep damage utilizing a miniature creep testing. A new model of the damage evaluation is proposed based on a linear creep damage accumulation and von Mises equivalent stress being a measure of multiaxial creep damage. The model clearly indicates that conventional creep damage evaluation methods utilizing a unidirectional miniature creep testing give an unconservative estimate in some cases for multiaxially creep damaged components. To verify the appropriateness of the proposed model, multiaxial creep tests were performed using cruciform specimens of a Mod.9Cr-1Mo steel. Miniature specimens in two directions were machined from a pre-damaged cruciform specimen and the uniaxial creep rupture lifetimes of the miniature specimens demonstrate the validity of the proposed model.

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Wang, C. H., and M. W. Brown. "Life Prediction Techniques for Variable Amplitude Multiaxial Fatigue—Part 1: Theories." Journal of Engineering Materials and Technology 118, no. 3 (July 1, 1996): 367–70. http://dx.doi.org/10.1115/1.2806821.

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Fatigue life prediction under multiaxis random loading is an extremely complex and intractable topic; only a few methods have been proposed in the literature. In addition, experimental results under multiaxis random loading are also scarce. In part one of this two-part paper, a multiaxial non-proportional cycle counting method and fatigue damage calculation procedure are proposed, which is compared with one published damage-searching method. Both theories are based on critical plane concepts, one being an extension of the local strain approach for uniaxial variable amplitude loading and the other employing a new counting algorithm for multiaxis random loading. In principle, these two methods can be considered as bounding solutions for fatigue damage accumulation under multiaxis random loading.

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Ozdemir, Huseyin, and Kadir Bilisik. "Off-Axis Flexural Properties of Multiaxis 3D Basalt Fiber Preform/Cementitious Concretes: Experimental Study." Materials 14, no. 11 (May 21, 2021): 2713. http://dx.doi.org/10.3390/ma14112713.

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Multiaxis three-dimensional (3D) continuous basalt fiber/cementitious concretes were manufactured. The novelty of the study was that the non-interlace preform structures were multiaxially created by placing all continious filamentary bundles in the in-plane direction of the preform via developed flat winding-molding method to improve the fracture toughness of the concrete composite. Principle and off-axis flexural properties of multiaxis three-dimensional (3D) continuous basalt fiber/cementitious concretes were experimentally studied. It was identified that the principle and off-axis flexural load-bearing, flexural strength and the toughness properties of the multiaxis 3D basalt concrete were extraordinarily affected by the continuous basalt filament bundle orientations and placement in the pristine concrete. The principle and off-axis flexural strength and energy absorption performance of the uniaxial (B-1D-(0°)), biaxial ((B-2D-(0°), B-2D-(90°) and B-2D-(+45°)), and multiaxial (B-4D-(0°), B-4D-(+45°) and B-4D-(−45°)) concrete composites were considerably greater compared to those of pristine concrete. Fractured four directional basalt concretes had regional breakages of the brittle cementitious matrix and broom-like damage features on the filaments, fiber-matrix debonding, intrafilament bundle splitting, and minor filament entanglement. Multiaxis 3D basalt concrete, particularly in the B-4D structure, controlled the crack phenomena and it was recognized as a more damage-tolerant material than the neat concrete.

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Lu, Fucong, Kun Zhang, Yuhang Hou, and Zhiwen Wu. "Investigation on Temperature-Dependent Multiaxial Ratchetting of Polycarbonate by a Novel Experimental Method." Advances in Materials Science and Engineering 2022 (May 13, 2022): 1–9. http://dx.doi.org/10.1155/2022/6577569.

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A novel method to heat the multiaxial hollow thin-wall specimen was proposed, where its gauge length section can be heated by the liquid (i.e., water) filled inside the specimen instead of the closed furnace. This method realizes the direct measurement of multiaxial strain on the surface of specimen at different temperatures by the noncontact digital image correlation. By utilizing the proposed method, the multiaxial stress-control cyclic tests were performed to investigate the multiaxial ratchetting of polycarbonate (PC) at different temperatures. It is found that the multiaxial ratchetting of PC depends greatly on the test temperatures and the multiaxial ratchetting strain increases with increasing the test temperature. The temperature-dependent multiaxial ratchetting is also influenced by valley stresses. The unrecoverable part of deformation in the multiaxial ratchetting strain increases with increasing temperature.

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Wang, Lei, Wu Zhen Li, and Tian Zhong Sui. "Review of Multiaxial Fatigue Life Prediction Technology under Complex Loading." Advanced Materials Research 118-120 (June 2010): 283–88. http://dx.doi.org/10.4028/www.scientific.net/amr.118-120.283.

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The research on multiaxial fatigue life prediction methods is reviewed in the present paper from two aspects of experiment and theory. It is pointed out that the reasonable methods of the critical plane determining, multiaxial cycle counting and multiaxial fatigue damage parameter fixing are necessary if the fatigue life prediction models established under the multiaxial constant amplitude loading were applied to the life prediction of the complex multiaxial load. The shortcomings of existing researches are discussed. In the aspect of experiment, it is devoid of the multiaxial fatigue test that the loading components acted with different frequencies, and in the aspect of theory, the additional hardening effect of the multiaxial out-of-frequency loading is not considered. Both in the theoretical research and practical engineering applications, the problem of the out-of-frequency multiaxial loading is a pressing issue.

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Shirafuji, Nakao, Kenji Shimomizuki, Masao Sakane, and Masateru Ohnami. "Tension-Torsion Multiaxial Low Cycle Fatigue of Mar-M247LC Directionally Solidified Superalloy at Elevated Temperature." Journal of Engineering Materials and Technology 120, no. 1 (January 1, 1998): 57–63. http://dx.doi.org/10.1115/1.2806838.

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This paper studies the high temperature multiaxial low cycle fatigue of Mar-M247LC directionally solidified superalloy. Tension-torsion multiaxial low cycle fatigue tests were carried out using Mar-M247LC tubular specimens at 1173K in air. Several multiaxial strain and stress parameters were applied to the experimental data to examine the suitability of the parameters. All the multiaxial strain parameters proposed so far could not successfully correlate the multiaxial low cycle fatigue data of the directionally solidified superalloy, but the maximum principal stress and the equivalent stress based on crack opening displacement could correlate the data within a small scatter. This paper proposes a new multiaxial strain parameter which takes account of the anisotropy of elastic constant of directionally solidified superalloys. The proposed strain parameter correlates the multiaxial low cycle fatigue data within a factor of two scatter band. This paper also describes the crack mode and cyclic constitutive relation of the superalloy in connection with the anisotropy of the elastic constant.

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Bercelli, Lorenzo, Cédric Doudard, and Sylvain Moyne. "Taking into account the non-proportional loading effect on high cycle fatigue life predictions obtained by invariant-based approaches." MATEC Web of Conferences 300 (2019): 12003. http://dx.doi.org/10.1051/matecconf/201930012003.

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Industrial structures are often subjected to multiaxial fatigue loadings. If the multiple stress signals are not synced the loading is said to be non-proportional. Most of the multiaxial fatigue criteria give highly inaccurate lifetime predictions when used in the case of such loadings. The scalar equivalent stress defined by the criteria does not take into account the non-proportional nature of the multiaxial loading and leads to non-conservative predictions. Moreover a multiaxial fatigue criterion can only be applied on a stress cycle which has no clear definition when multiple unsynced signals are to be considered. This study addresses these issues by proposing a correction of an invariant based multiaxial fatigue criterion through the definition of a non-proportional degree indicator. A definition of multiaxial cycle is also given based on the Wang-Brown method. Finally a complete chain of invariant based lifetime prediction for non-proportional multiaxial fatigue is validated.

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Zhao, Er Nian, and Wei Lian Qu. "Multiaxial Fatigue Life Prediction of Metallic Materials Based on Critical Plane Method under Non-Proportional Loading." Key Engineering Materials 730 (February 2017): 516–20. http://dx.doi.org/10.4028/www.scientific.net/kem.730.516.

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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.

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9

Stouffer, D. C., V. G. Ramaswamy, J. H. Laflen, R. H. Van Stone, and R. Williams. "A Constitutive Model for the Inelastic Multiaxial Response of Rene’ 80 at 871C and 982C." Journal of Engineering Materials and Technology 112, no. 2 (April 1, 1990): 241–46. http://dx.doi.org/10.1115/1.2903315.

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This paper contains an extension of the uniaxial state variable constitutive model of Ramaswamy et al. (1988) to the case of multiaxial loading. The correlation between uniaxial and multiaxial loading conditions is achieved through the assumptions of material isotropy and conservation of inelastic volume. The multiaxial extension is based only on the material parameters evaluated from uniaxial loading. The research is accompanied by a multiaxial experimental program to evaluate the response of Rene’ 80 at 871°C and 982° C. Experiments in the program include torsion, proportional axial and torsion, and nonproportional loading. It was shown experimentally that there is no extra hardening from the multiaxial loading than results from uniaxial loading. Further, it is shown that the multiaxial model is successful in predicting the experimental results using only the parameters determined from the uniaxial experiments.

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10

Hiyoshi, Noritake, and Yoshihisa Iriyama. "Development of Tension-Torsion Multiaxial Creep Testing Apparatus for Heat Resisting Steel." MATEC Web of Conferences 159 (2018): 02015. http://dx.doi.org/10.1051/matecconf/201815902015.

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This paper describes development of a combined tensiontorsion multiaxial creep testing apparatus for heat resisting steel. It is essential for high temperature component designing to investigate creep rupture life and creep properties of heat resisting steel. Although high temperature structural components undergo multiaxial stress damage due to complex loading situation or shape discontinuity of the actual structure, there is no commercial testing apparatus which can conduct a creep testing under multiaxial stress conditions. In this study, we developed a combined tension-torsion multiaxial creep testing apparatus which can apply multiaxial stress to a hollow cylinder type testing specimen with 6 kN axial load and 12 Nm torsional load at high temperatures. Since the testing apparatus also has measuring devices for axial and shear displacements of the specimen, relationship curve between testing time and equivalent strain under multiaxial stress conditions of type 304 stainless steel is also discussed.

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11

Kang, Tae Jin, and Cheol Kim. "Mechanical and Impact Properties of Composite Laminates Reinforced with Kevlar Multiaxial Warp Knit Fabrics." Engineering Plastics 5, no. 4 (January 1997): 147823919700500. http://dx.doi.org/10.1177/147823919700500403.

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The mechanical and impact properties of multiaxial warp knit fabric reinforced composite laminates have been studied. Kevlar® fibre was used to fabricate the multiaxial warp knit structure for unidirectional reinforcing as well as stitching yarns. Tensile, flexural, short beam shear, and impact properties have been compared with those of woven laminated composites. The results showed that increased interlaminar shear strength is the main characteristic feature of the multiaxial warp knit composite compared with plain woven laminates. The interlaminar shear strength of multiaxial warp knit composites showed up to 52% increase compared with that of woven laminates composites. Also the delamination was retarded due to the increase in interlaminar shear strength of the multiaxial warp knit composites. It is shown that the through-the-thickness reinforcing loops resist any delamination. The tensile strength of the multiaxial warp knit composites increased by about 5–12% compared with the theoretical values computed from classical lamination theory. It is generally accepted that impact induced delamination area increases with the increase in the total absorbed impact energy in collisions with foreign objects. But the multiaxial warp knit composites showed that the total absorbed impact energy decreased with the increase in through-the-thickness reinforcement fibres. The multiaxial warp knit composites showed reduced vertical deformations compared with woven laminates, as the reinforcing loop density increased.

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12

Kang, Tae Jin, and Cheol Kim. "Mechanical and Impact Properties of Composite Laminates Reinforced with Kevlar Multiaxial Warp Knit Fabrics." Polymers and Polymer Composites 5, no. 4 (January 1997): 265–72. http://dx.doi.org/10.1177/096739119700500403.

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The mechanical and impact properties of multiaxial warp knit fabric reinforced composite laminates have been studied. Kevlar® fibre was used to fabricate the multiaxial warp knit structure for unidirectional reinforcing as well as stitching yarns. Tensile, flexural, short beam shear, and impact properties have been compared with those of woven laminated composites. The results showed that increased interlaminar shear strength is the main characteristic feature of the multiaxial warp knit composite compared with plain woven laminates. The interlaminar shear strength of multiaxial warp knit composites showed up to 52% increase compared with that of woven laminates composites. Also the delamination was retarded due to the increase in interlaminar shear strength of the multiaxial warp knit composites. It is shown that the through-the-thickness reinforcing loops resist any delamination. The tensile strength of the multiaxial warp knit composites increased by about 5–12% compared with the theoretical values computed from classical lamination theory. It is generally accepted that impact induced delamination area increases with the increase in the total absorbed impact energy in collisions with foreign objects. But the multiaxial warp knit composites showed that the total absorbed impact energy decreased with the increase in through-the-thickness reinforcement fibres. The multiaxial warp knit composites showed reduced vertical deformations compared with woven laminates, as the reinforcing loop density increased.

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13

Shang, De Guang, Guo Qin Sun, Jing Deng, and Chu Liang Yan. "Multiaxial Fatigue Damage Models." Key Engineering Materials 324-325 (November 2006): 747–50. http://dx.doi.org/10.4028/www.scientific.net/kem.324-325.747.

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Two multiaxial damage parameters are proposed in this paper. The proposed fatigue damage parameters do not include any weight constants, which can be used under either multiaxial proportional loading or non-proportional loading. On the basis of the research on the critical plane approach for the tension-torsion thin tubular multiaxial fatigue specimens, two multiaxial fatigue damage models are proposed by combining the maximum shear strain and the normal strain excursion between adjacent turning points of the maximum shear strain on the critical plane. The proposed multiaxial fatigue damage models are used to predict the fatigue lives of the tension-torsion thin tube, and the results show that a good agreement is demonstrated with experimental data.

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Poisson, J. L., S. Méo, F. Lacroix, G. Berton, and N. Ranganathan. "MULTIAXIAL FATIGUE CRITERIA APPLIED TO A POLYCHLOROPRENE RUBBER." Rubber Chemistry and Technology 85, no. 1 (March 1, 2012): 80–91. http://dx.doi.org/10.5254/1.3672431.

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Abstract Due to their interesting mechanical behavior and their diversity, rubber materials are more and more used in industry. Indeed, formulating a multiaxial fatigue criterion to predict fatigue lives of rubber components constitutes an important objective to conceive rubber products. An experimental campaign is developed here to study the multiaxial fatigue behavior of polychloroprene rubber. To reproduce multiaxial solicitations, combined tension–torsion tests were carried out on a dumbbell-type specimen (an axisymmetric rubber part bonded to metal parts with a reduced section at mid-height), with several values of phase angles between tension and torsion. A constitutive model is needed to calculate multiaxial fatigue criteria, and then analyze fatigue results. A large strain viscoelastic model, based on the tension–torsion kinematics, is then used to determine the material's stress–strain law. Dissipated energy density is introduced as a multiaxial fatigue criterion, and compared with those usually used in the literature. A multiaxial Haigh diagram is then built to observe the influence of Rd-ratio (ratio of the axial displacement's minimum to the axial displacement's maximum) on the multiaxial fatigue lives of polychloroprene rubber.

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Lu, Chun, Jiliang Mo, Ruixue Sun, Yuanke Wu, and Zhiyong Fan. "Investigation into Multiaxial Character of Thermomechanical Fatigue Damage on High-Speed Railway Brake Disc." Vehicles 3, no. 2 (June 1, 2021): 287–99. http://dx.doi.org/10.3390/vehicles3020018.

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The multiaxial character of high-speed railway brake disc thermomechanical fatigue damage is studied in this work. Although the amplitudes and distributions of temperature, strain and stress are similar with uniform and rotating loading methods, the multiaxial behavior and out-of-phase failure status can only be revealed by the latter one. With the help of a multiaxial fatigue model, fatigue damage evaluation and fatigue life prediction are implemented, the contribution of a uniaxial fatigue parameter, multiaxial fatigue parameter and out-of-phase failure parameter to the total damage is discussed, and it is found that using the amplitude and distribution of temperature, stress and strain for fatigue evaluation will lead to an underestimation of brake disc thermomechanical fatigue damage. The results indicate that the brake disc thermomechanical fatigue damage belongs to a type of multiaxial fatigue. Using a uniaxial fatigue parameter causes around 14% underestimation of fatigue damage, while employing a multiaxial fatigue parameter without the consideration of out-of-phase failure will lead to an underestimation of about 5%. This work explains the importance of studying the thermomechanical fatigue damage of the brake disc from the perspective of multiaxial fatigue.

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Margetin, Matus, and Dominik Biro. "Performance of chosen multiaxial cycle counting method under non-proportional multiaxial variable loading." MATEC Web of Conferences 165 (2018): 16008. http://dx.doi.org/10.1051/matecconf/201816516008.

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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.

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Gao, Ganggang, Jianhui Liu, Xuebin Lu, and Rong Zhang. "A damage-based method to predict crack initiation lifetime of high-strength steel under proportional bending-torsional loadings." Advances in Mechanical Engineering 14, no. 8 (August 2022): 168781322211184. http://dx.doi.org/10.1177/16878132221118479.

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The fatigue life of specimen consists of crack initiation and crack propagation life. As the fracture toughness of high strength steel is low, the specimen will fail soon once crack appears. Therefore, the crack initiation life of high strength steel is considered to be its whole life. Based on the evolution of material fatigue damage and the critical plane method commonly used in multiaxial fatigue strength theory, a crack initiation life prediction method for multiaxial specimens is proposed in this paper. Firstly, a uniaxial nonlinear fatigue damage evolution equation is proposed based on the principles of thermodynamics and continuous damage mechanics. Then, a theoretical calculation method for determining the critical plane under multiaxial load is proposed, and the specific calculation process is given. After the critical plane is determined, the multiaxial fatigue damage parameter is constructed from the normal strain amplitude and shear strain amplitude on the critical plane, and a multiaxial nonlinear fatigue damage evolution equation is proposed by replacing the uniaxial damage parameter using the multiaxial damage parameter. Finally, the crack initiation life of fatigue specimens is predicted by using the proposed multiaxial nonlinear fatigue damage evolution equation, and the multiaxial fatigue tests of Q690D steel under different bending-torsion ratios and different amplitudes are validated. The comparison results show that the prediction error of the proposed method is within the two-fold dispersion band and better than that of Manson-Coffin method.

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Sidorina, A. I. "MULTIAXIAL CARBON FABRICS IN THE PRODUCTS OF AVIATION TECHNOLOGY (review)." Aviation Materials and Technologies, no. 3 (2021): 105–16. http://dx.doi.org/10.18577/2713-0193-2021-0-3-105-116.

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The article considers the main advantages and disadvantages of application of multiaxial fabrics as reinforcing fillers for composite materials with a polymer matrix, and specifies the most common processing technologies of multiaxial fabrics into a composite material. The paper provides the information about the use of carbon multiaxial fabrics in the manufacture of structures for aircraft products by the example of the production of the Airbus A380 rear bulkhead and of the Airbus A400M upper cargo door. Brief characteristics of the world’s leading manufacturers of carbon fiber multiaxial fabrics for aircraft products are given.

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Wang, Lei, Tian Zhong Sui, and Qiu Cheng Tian. "Life Prediction and Verification under Multiaxial Fatigue Loading." Applied Mechanics and Materials 365-366 (August 2013): 991–94. http://dx.doi.org/10.4028/www.scientific.net/amm.365-366.991.

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The strain change characteristics of multiaxial fatigue are analyzed under the condition of the combined tension and torsion loading for thin-tube specimen. Based on the principle of multiaxial critical plane approach, a multiaxial fatigue damage parameter is established, which takes account of the effect of not only the maximum shear strain amplitude and normal strain amplitude on the critical plane but also the parameter of non-proportionality. The non-proportionality is the function of loading parameters which is closely contact with the strain change characteristics of multiaxial fatigue and it can indicate the whole material damage. The experiments under the tension-torsion proportional and non-proportional loading were conducted to verify the multiaxial fatigue life model proposed in this paper. The life prediction has a good correlation with the experimental results.

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Liu, Jianhui, Xin Lv, Yaobing Wei, Xuemei Pan, Yifan Jin, and Youliang Wang. "A novel model for low-cycle multiaxial fatigue life prediction based on the critical plane-damage parameter." Science Progress 103, no. 3 (July 2020): 003685042093622. http://dx.doi.org/10.1177/0036850420936220.

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Multiaxial fatigue of the components is a very complex behavior. This analyzes the multiaxial fatigue failure mechanism, reviews and compares the advantages and disadvantages of the classic model. The fatigue failure mechanism and fatigue life under multiaxial loading are derived through theoretical analysis and formulas, and finally verified with the results of multiaxial fatigue tests. The model of multiaxial fatigue life for low-cycle fatigue life prediction model not only improves the prediction accuracy of the classic model, but also considers the effects of non-proportional additional hardening phenomena and fatigue failure modes. The model is proved to be effective in low-cycle fatigue life prediction under different loading paths and types for different materials. Compared with the other three classical models, the proposed model has higher life prediction accuracy and good engineering applicability.

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Margetin, Matus, and Dominik Biro. "Multiaxial cycle counting method for non-proportional multiaxial variable loading signals based on modified maximal shear stress." MATEC Web of Conferences 300 (2019): 17003. http://dx.doi.org/10.1051/matecconf/201930017003.

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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.

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Amjadi, Mohammadreza, and Ali Fatemi. "Multiaxial Fatigue Behavior of High-Density Polyethylene (HDPE) Including Notch Effect: Experiments and Modeling." MATEC Web of Conferences 300 (2019): 05001. http://dx.doi.org/10.1051/matecconf/201930005001.

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High-Density Polyethylene (HDPE) is used in many industries with many applications from automotive industry to biomedical implants. It can be manufactured using different processing techniques including compression molding, injection molding, and blow molding. Multiaxial loading and non-proportionality between different loading sources are inevitable in many applications. It is shown that the common multiaxial fatigue criteria such as von Mises equivalent stress are not able to correlate the multiaxial fatigue data. In this study, multiaxial fatigue behavior of neat HDPE is investigated using hollow tubular specimens through experimental fatigue tests. Axial, torsion, and combined in phase and out-of-phase axial-torsion fatigue tests were conducted. Stress concentration effect on multiaxial fatigue behavior was also studied. Experimental results and analytical models used to account for the aforementioned effects are presented and discussed in this paper.

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Williams, Janet B. W., Howard H. Goldman, Alan Gruenberg, Juan E. Mezzich, and Andrew E. Skodol. "The Multiaxial System." Psychiatric Services 41, no. 11 (November 1990): 1181–82. http://dx.doi.org/10.1176/ps.41.11.1181.

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Ahn, Byong‐Ho, Raymond Carroll, Kenneth Fertig, Michele S. Sapuppo, Howard L. Watson, and Marc S. Weinberg. "Multiaxial vibration sensor." Journal of the Acoustical Society of America 77, no. 5 (May 1985): 1978. http://dx.doi.org/10.1121/1.391785.

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Mezzich, J. E. "On Developing a Psychiatric Multiaxial Schema for ICD-10." British Journal of Psychiatry 152, S1 (May 1988): 38–43. http://dx.doi.org/10.1192/s0007125000295603.

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As work proceeds on the development of the Tenth Revision of the International Classification of Diseases (ICD-10) widespread interest has been expressed in the preparation of a multiaxial diagnostic schema for psychiatric patients. In consideration of this task, the present paper briefly notes pertinent international experience on multiaxial diagnosis, the discernible purposes of this approach, design requirements, and a specific multiaxial proposal.

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Li, Bochuan, Chao Jiang, Xu Han, and Yuan Li. "The prediction of multiaxial fatigue probabilistic stress–life curve by using fuzzy theory." Artificial Intelligence for Engineering Design, Analysis and Manufacturing 31, no. 2 (May 2017): 199–206. http://dx.doi.org/10.1017/s0890060417000087.

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AbstractThe fuzziness of the traditional multiaxial fatigue prediction model is discussed and the fuzzy theory is applied into fatigue reliability analysis. The fuzzy linear regression analysis method is used to determine the fuzzy coefficients in the multiaxial stress–life equation under a small sample condition, and the corresponding multiaxial fatigue probabilistic stress–life curve is calculated with different confidence levels.

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Mao, Xue Ping, Yang Yu, Chao Li, Sai Dong Huang, Hong Xu, and Yong Zhong Ni. "Study on Creep Behaviors of T92 Steel under Multiaxial Stress State." Advanced Materials Research 860-863 (December 2013): 774–79. http://dx.doi.org/10.4028/www.scientific.net/amr.860-863.774.

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Creep tests for smooth specimens and notched specimens of T92 steel were carried out to study the effect of multiaxial stress state on creep rupture behaviors at 650°C. Creep rupture life was estimated by representative stress at multiaxial state of stress, the failure behavior of multiaxial creep was analyzed, and Kachanov creep damage formula was used to analyze the experimental data. The results show that the notch strengthens rupture life, multiaxial rupture behavior is controlled by mixed parameters, the creep ductility of the smooth and notched specimen decreases with rupture time, and damage factors of the smooth specimen and notched specimen are similar according to Kachanov formula.

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Wang, Lei, Tian Zhong Sui, Hang Zhao, and En Guo Men. "Probabilistic Model of the Multiaxial Low-Cycle Fatigue Life Prediction." Advanced Materials Research 479-481 (February 2012): 2135–40. http://dx.doi.org/10.4028/www.scientific.net/amr.479-481.2135.

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First, several widely used models of the multiaxial low-cycle fatigue life prediction based on the critical plane approach were presented in this paper, and the predicted results of these models for a medium carbon steel under the condition of multiaxial low-cycle fatigue loading were compared. Second, the stochastic expressions and probability density function curves of the fatigue performance parameters were obtained by probabilistic analysis of the medium carbon steel fatigue data. Finally, the probabilistic model of the multiaxial fatigue life prediction was simulated by Monte Carlo Method, which should provide a basis for the reliability analysis of engineering components subjected to the multiaxial complex loads.

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Machado, Pedro Vinícius Sousa, Lucas Carneiro Araújo, Marcos Venicius Soares, and José Alexander Araújo. "The use of a modified critical plane model to assess multiaxial fatigue of steels with nonmetallic inclusions." MATEC Web of Conferences 300 (2019): 16005. http://dx.doi.org/10.1051/matecconf/201930016005.

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The goal of this research is to investigate the detrimental effect of non-metallic inclusions on the fatigue strength of the AISI 4140 steel under multiaxial loading conditions. In order to do so, a multiaxial fatigue model based on the critical plane approach is coupled with Murakami’s √area model. The proposed adaptation is very easy to calibrate and can also account for the higher probability of existing a fatal small defect as the volume of stresses material increases. Experimental multiaxial fatigue data were generated and compared with the estimates provided by the adapted multiaxial fatigue model and with its original version. The errors found are not higher than 10%.

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Wu, Zhirong, Ying Pan, Hang Lei, Shuaiqiang Wang, and Lei Fang. "Fatigue Crack Growth Behavior and Failure Mechanism of Nickel-Based Alloy GH4169 under Biaxial Load Based on Fatigue Test of Cruciform Specimen." Metals 13, no. 3 (March 14, 2023): 588. http://dx.doi.org/10.3390/met13030588.

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Due to the complex geometry and various cyclic loads, aeroengine components are often in a multiaxial complex stress state during service. Multiaxial fatigue is a major cause of many air accidents. It is of great significance to study the fatigue failure mechanism of aeronautical materials. This paper carries out biaxial fatigue tests on cruciform specimens and uses the surface replication method to record the initiation and propagation process of crack. Based on these fatigue tests, this paper studies the multiaxial fatigue characteristics of nickel-based alloy GH4169 for aeroengines and analyzes the fatigue crack growth behavior and failure mechanism of nickel-based alloys under a complex multiaxial stress state.

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Kawai, M. "Anisotropic size effect law for notched strength of unidirectional carbon/epoxy laminates – Part 1: Formulation." Journal of Composite Materials 51, no. 5 (July 28, 2016): 593–602. http://dx.doi.org/10.1177/0021998316651481.

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A multiaxial quasi-brittle failure criterion for notched orthotropic composites is developed with an emphasis on establishment of an analytical formula to predict their anisotropic notched strength for any notch size under any multiaxial proportional loading. It is formulated by replacing the principal unnotched strengths with the principal notched strengths in the framework of the Tsai–Hill static failure criterion for orthotropic composites. The effects of notch size and specimen width on the principal notched strengths are described by means of the Suo-Ho-Gong model that can consider notch ductile-to-brittle transition. From the proposed multiaxial quasi-brittle failure criterion, an analytical formula is derived to predict the notched strength of finite orthotropic composite plates under multiaxial proportional loading at any angle with the principal directions of material anisotropy. The notched strength prediction formula involves a generalized notch sensitivity parameter that can be defined for any multiaxial state of stress. The multiaxial notch sensitivity parameter allows uniquely defining an intrinsic equivalent mode-I fracture toughness that is independent of notch size as well as of specimen width for any multiaxial proportional loading. Furthermore, an anisotropic size effect law for apparent equivalent mode-I fracture toughness that considers not only the effect of notch size but also the effect of specimen width is derived from the failure criterion. Finally, a quasi-brittle failure criterion for notched interface is briefly discussed as a particular case of the proposed quasi-brittle failure criterion for notched orthotropic composites.

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Wang, Lei, Tian Zhong Sui, Yu Ma, and Yan Sun. "Determination of the Critical Plane under the Multiaxial Complex Loading." Advanced Materials Research 544 (June 2012): 182–87. http://dx.doi.org/10.4028/www.scientific.net/amr.544.182.

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Engineering components and structures in service are generally subjected to the multiaxial complex loads. The approach of critical plane has been widely accepted by most researchers as the best method in the multiaxial fatigue research field. It can be used well in the constant multiaxial fatigue loads, but not in the complex loads. Basis on analyzing characteristics of shear strain on material planes, the concept of weight-averaged maximum shear strain plane is proposed. A procedure is presented to determine the critical plane under multiaxial random loading. The angle values of the planes that experience peak values of maximum shear strains are averaged by employing the weight function, which is assumed to take into account the main factors of influencing the fatigue behavior, e.g. fatigue damage. The proposed algorithm is applied to the multiaxial in- and out-of-phase experiments to assess the correlation between the weight-averaged maximum shear strain direction and the position of the experimental fatigue crack initiation plane.

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Riess, Christian, Martin Obermayr, and Michael Vormwald. "The contrast of simplicity and accuracy in modeling multiaxial notch fatigue." MATEC Web of Conferences 300 (2019): 13003. http://dx.doi.org/10.1051/matecconf/201930013003.

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The fatigue assessment of notches under multiaxial and non-proportional service loading is challenging. Simple models (e.g. local strain approach based on normal stress and strain) are of poor quality for this general case of stress states and ductile material behavior. Advanced approaches show high accuracy, but require additional material testing and calibration. From an engineering point of view, deviations are tolerable to a certain extent. This contribution introduces two approaches for modeling multiaxial notch fatigue which are easy to apply. The first approach is an extension of the classical local strain approach. The second approach implements a simplified multiaxial notch approximation which enables the use of the extended short crack model in practical applications. A large database with experiments on notched components under multiaxial stresses is set up and used to validate the proposed algorithms. Results show the eﬀectiveness of both approaches for ductile steels. Both approaches can be useful for engineers who are faced to multiaxial fatigue of notched components.

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Li, Jiejie, Jie Li, Yangheng Chen, and Jian Chen. "Strengthening Modulus and Softening Strength of Nanoporous Gold in Multiaxial Tension: Insights from Molecular Dynamics." Nanomaterials 12, no. 24 (December 8, 2022): 4381. http://dx.doi.org/10.3390/nano12244381.

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The functionalized applications of nanoporous metals place clear requirements on their basic mechanical properties, yet there is a lack of research on the mechanical response under multiaxial loading conditions. In this work, the mechanical behaviors of nanoporous gold under multiaxial tension are investigated via molecular dynamics simulations. The mechanical properties under different loading conditions are compared and the microstructure evolution is analyzed to clarify the deformation mechanisms of nanoporous gold in biaxial and triaxial tension. It is found that the modulus of nanoporous gold in multiaxial tension is strengthened and the strength is softened compared to uniaxial tension. The failure of nanoporous gold in multiaxial tension is dominated by the progressive yielding, necking, and rupture of ligaments along the multiple uniaxial loading directions. The dislocation activity under multiaxial loads is more intense and more prone to plastic deformation, ultimately resulting in lower strength and smaller failure strain. The findings provide more insight into the understanding of the deformation mechanisms of nanoporous metals under complex stress states.

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Li, Shan, and Yongxiang Zhao. "High-Cycle Fatigue Behavior of D2 Wheel Steel under Uniaxial and Multiaxial Loading Conditions for Potential Applications in the Railway Industry." Crystals 13, no. 7 (July 22, 2023): 1146. http://dx.doi.org/10.3390/cryst13071146.

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This study investigates the fatigue damage evolution mechanisms of D2 wheel steel under high-cycle uniaxial and multiaxial loading conditions, with a focus on determining the fatigue crack growth threshold (FCGT). Uniaxial and multiaxial FCGT tests were performed on pre-cracked D2 wheel steel specimens subjected to high-frequency cyclic loading at stress ratios (R) of 0.1. The results indicate that the FCGT for D2 wheel steel under uniaxial loading conditions ranges between 8–9 MPa.m0.5, while under multiaxial loading conditions, it ranges between 6–9 MPa.m0.5. Scanning electron microscopy analysis revealed differences in the crack propagation mechanisms between the uniaxial and multiaxial tests, with cracks deviating from their path and following the microstructure in the uniaxial tests, and cracks propagating along planes of weakness in the multiaxial tests. These findings provide insights into the high-cycle fatigue behavior of D2 wheel steel under different loading conditions for potential applications in the railway industry.

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Wei, Haoyang, Jie Chen, Patricio Carrion, Anahita Imanian, Nima Shamsaei, Nagaraja Iyyer, and Yongming Liu. "Multiaxial high-cycle fatigue modelling for random loading." MATEC Web of Conferences 300 (2019): 12005. http://dx.doi.org/10.1051/matecconf/201930012005.

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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.

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Paradisi, Francesco, Anna Sofia Delussu, Stefano Brunelli, Marco Iosa, Roberto Pellegrini, Daniele Zenardi, and Marco Traballesi. "The Conventional Non-Articulated SACH or a Multiaxial Prosthetic Foot for Hypomobile Transtibial Amputees? A Clinical Comparison on Mobility, Balance, and Quality of Life." Scientific World Journal 2015 (2015): 1–10. http://dx.doi.org/10.1155/2015/261801.

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The effects of a non-articulated SACH and a multiaxial foot-ankle mechanism on the performance of low-activity users are of great interest for practitioners in amputee rehabilitation. The aim of this study is to compare these two prosthetic feet and assess possible improvements introduced by the increased degrees of freedom provided by the multiaxial foot. For this purpose, a group of 20 hypomobile transtibial amputees (TTAs) had their usual SACH replaced with a multiaxial foot. Participants’ functional mobility, involving ambulatory skills in overground level walking, ramps, and stairs, was evaluated by performing Six-Minute Walking Test (6MWT), Locomotor Capability Index-5 (LCI-5), Hill Assessment Index (HAI), and Stair Assessment Index (SAI). Balance performances were assessed using Berg Balance Scale (BBS) and analysing upper body accelerations during gait. Moreover, the Prosthesis Evaluation Questionnaire (PEQ) was performed to indicate the prosthesis-related quality of life. Results showed that participants walked faster using the multiaxial foot(p<0.05)maintaining the same upright gait stability. Significant improvements with the multiaxial foot were also observed in BBS, LCI-5, and SAI times and 4 of 9 subscales of the PEQ. Our findings demonstrate that a multiaxial foot represents a considerable alternative solution with respect to the conventional SACH in the prosthetic prescription for hypomobile TTAs.

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Zheng, Shan Suo, Wen Yong Li, Qing Lin Tao, and Yu Fan. "A Multiaxial Damage Statistic Constitutive Model for Concrete." Applied Mechanics and Materials 166-169 (May 2012): 56–59. http://dx.doi.org/10.4028/www.scientific.net/amm.166-169.56.

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In order to apply the uniaxial damage evolution equation that established with the variable of strain to the multiaxial damage quantitative analysis, this paper bases on the Hsieh-Tang-Chen four-parameter failure criterion and adopts the way of making the triaxial equivalent strain combining with the uniaxial damage evolution equation to analyze and deduce the uniaxial damage evolution equation of SRHSHPC, and which is expanded to multiaxial condition as well. A function considered triaxial stress state and a related correction value are suggested, then, improving the damage evolution equation from triaxial to multiaxial form, finally proposing the multiaxial damage statistic constitutive equation for concrete, taking numerical simulation with the complete decoupling method and the result shows that the model is effective.

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Wang, Xiao-Wei, De-Guang Shang, Yu-Juan Sun, and Xiao-Dong Liu. "Algorithms for multiaxial cycle counting method and fatigue life prediction based on the weight function critical plane under random loading." International Journal of Damage Mechanics 28, no. 9 (February 18, 2019): 1367–92. http://dx.doi.org/10.1177/1056789519831051.

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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.

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Yang, Xianjie, Yan Luo, and Qing Gao. "Constitutive Modeling on Time-Dependent Deformation Behavior of 96.5Sn-3.5Ag Solder Alloy Under Cyclic Multiaxial Straining." Journal of Electronic Packaging 129, no. 1 (May 18, 2006): 41–47. http://dx.doi.org/10.1115/1.2429708.

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Based on the time dependent multiaxial deformation behavior of 96.5Sn-3.5Ag solder alloy, a constitutive model is proposed which considers the nonproportional multiaxial cyclic deformation properties. In the back stress evolution equations of this model, the nonproportionality which affects the back stress evolution rate is introduced. The approach for the determination of model parameters is proposed. The model is used to describe the time-dependent cyclic deformation behavior of 96.5Sn-3.5Ag solder alloy under cross, rectangular, rhombic, and double-triangular tensile–torsion multiaxial strain paths at different strain rates with different dwell time. The comparison between the predicted and experimental results demonstrates that the model can satisfactorily describe the time-dependent multiaxial cyclic deformation behavior under complicated nonproportional cyclic straining.

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Papuga, Jan, Eva Cízová, and Aleksander Karolczuk. "Validating the Methods to Process the Stress Path in Multiaxial High-Cycle Fatigue Criteria." Materials 14, no. 1 (January 4, 2021): 206. http://dx.doi.org/10.3390/ma14010206.

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The paper discusses one of the key features in the multiaxial fatigue strength evaluation—the procedure in which the stress path is analyzed to provide relevant measures of parameters required by multiaxial criteria. The selection of this procedure affects the complete equivalent stress derived for any multiaxial load combinations. Three major concepts—the minimum circumscribed circle, minimum circumscribed ellipse, and moment of inertia methods—are described. Analytical solutions of their evaluation for multiaxial stress state with components described by harmonic functions are provided. The concepts are validated on available experimental data when included into six different multiaxial fatigue strength criteria. The results show that the moment of inertia results in too conservative results. Differences between both methods of circumscribed entities are much smaller. There are indications however that the minimum circumscribed ellipse solution works better for critical plane criteria and for the criteria based on stress tensor transformation into the Ilyushin deviatoric space. On the other hand, the minimum circumscribed ellipse solution tends to shift integral criteria to the conservative side.

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42

Garcia, Martin, Claudio A. Pereira Baptista, and Alain Nussbaumer. "Multiaxial fatigue study on steel transversal attachments under constant amplitude proportional and non-proportional loadings." MATEC Web of Conferences 165 (2018): 16007. http://dx.doi.org/10.1051/matecconf/201816516007.

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In this study, the multiaxial fatigue strength of full-scale transversal attachment is assessed and compared to original experimental results and others found in the literature. Mild strength S235JR steel is used and an exploratory investigation on the use of high strength S690QL steel and the effect of non-proportional loading is presented. The study focuses on non-load carrying fillet welds as commonly used in bridge design and more generally between main girders and struts. The experimental program includes 33 uniaxial and multiaxial fatigue tests and was partially carried out on a new multiaxial setup that allows proportional and non-proportional tests in a typical welded detail. The fatigue life is then compared with estimations obtained from local approaches with the help of 3D finite element models. The multiaxial fatigue life assessment with some of the well-known local approaches is shown to be suited to the analysis under multiaxial stress states. The accuracy of each models and approaches is compared to the experimental values considering all the previously cited parameters.

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Hornberger, Troy A., Dustin D. Armstrong, Timothy J. Koh, Thomas J. Burkholder, and Karyn A. Esser. "Intracellular signaling specificity in response to uniaxial vs. multiaxial stretch: implications for mechanotransduction." American Journal of Physiology-Cell Physiology 288, no. 1 (January 2005): C185—C194. http://dx.doi.org/10.1152/ajpcell.00207.2004.

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Several lines of evidence suggest that muscle cells can distinguish between specific mechanical stimuli. To test this concept, we subjected C2C12 myotubes to cyclic uniaxial or multiaxial stretch. Both types of stretch induced an increase in extracellular signal-regulated kinase (ERK) and protein kinase B (PKB/Akt) phosphorylation, but only multiaxial stretch induced ribosomal S6 kinase (p70S6k) phosphorylation. Further results demonstrated that the signaling events specific to multiaxial stretch (p70S6k phosphorylation) were elicited by forces delivered through the elastic culture membrane and were not due to greater surface area deformations or localized regions of large tensile strain. Experiments performed using medium that was conditioned by multiaxial stretched myotubes indicated that a release of paracrine factors was not sufficient for the induction of signaling to p70S6k. Furthermore, incubation with gadolinium(III) chloride (500 μM), genistein (250 μM), PD-98059 (250 μM), bisindolylmaleimide I (20 μM), or LY-294002 (100 μM ) did not block the multiaxial stretch-induced signaling to p70S6k. However, disrupting the actin cytoskeleton with cytochalasin D did block the multiaxial signaling to p70S6k, with no effect on signaling to PKB/Akt. These results demonstrate that specific types of mechanical stretch activate distinct signaling pathways, and we propose that this occurs through direct mechanosensory-mechanotransduction mechanisms and not through previously defined growth factor/receptor binding pathways.

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Yin, Xiang, De-Guang Shang, Gang Zhang, Dao-Hang Li, Hang Zhang, Cheng Qian, Shuai Zhou, and Guo-Cheng Hao. "Thermal-mechanical fatigue life prediction considering fatigue-creep interaction effects." Journal of Physics: Conference Series 2569, no. 1 (August 1, 2023): 012074. http://dx.doi.org/10.1088/1742-6596/2569/1/012074.

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Abstract This study proposed a multiaxial variable temperature and amplitude damage assessment model to predict the variable temperature and amplitude fatigue life of high-temperature alloys, which are often subjected to varying multiaxial mechanical and temperature loads. To validate the proposed model, seven variable temperature and amplitude fatigue tests were conducted on GH4169 nickel-based high-temperature alloy. The proposed model shows good accuracy and reliability in predicting the lifetime of high-temperature alloy components under multiaxial mechanical and temperature loads.

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Wang, Xiao-Ming, Hao Li, Zheng-Nan Yin, and Heng Xiao. "MULTIAXIAL STRAIN ENERGY FUNCTIONS OF RUBBERLIKE MATERIALS: AN EXPLICIT APPROACH BASED ON POLYNOMIAL INTERPOLATION." Rubber Chemistry and Technology 87, no. 1 (March 1, 2014): 168–83. http://dx.doi.org/10.5254/rct.13.86960.

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ABSTRACT We propose an explicit approach to obtaining multiaxial strain energy functions for incompressible, isotropic rubberlike materials undergoing large deformations. Via polynomial interpolation, we first obtain two one-dimensional strain energy functions separately from uniaxial data and shear data, and then, from these two, we obtain a multiaxial strain energy function by means of direct procedures based on well-designed logarithmic invariants. This multiaxial strain energy function exactly fits any given data from four benchmark tests, including uniaxial and equibiaxial extension, simple shear, plane–strain extension, and so forth. Furthermore, its predictions for biaxial stretch tests provide good accord with test data. The proposed approach is explicit in a sense without involving the usual procedures both in deriving forms of the multiaxial strain energy function and in estimating a number of unknown parameters.

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Kallmeyer, Alan R., Ahmo Krgo, and Peter Kurath. "Evaluation of Multiaxial Fatigue Life Prediction Methodologies for Ti-6Al-4V." Journal of Engineering Materials and Technology 124, no. 2 (March 26, 2002): 229–37. http://dx.doi.org/10.1115/1.1446075.

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Many critical engineering components are routinely subjected to cyclic multiaxial stress states, which may include non-proportional loading and multidimensional mean stresses. Existing multiaxial fatigue models are examined to determine their suitability at estimating fatigue damage in Ti-6Al-4V under complex, multiaxial loading, with an emphasis on long-life conditions. Both proportional and non-proportional strain-controlled tension/torsion experiments were conducted on solid specimens. Several multiaxial fatigue damage parameters are evaluated based on their ability to correlate the biaxial fatigue data and uniaxial fatigue data with tensile mean stresses (R>−1) to a fully-reversed (R=−1) uniaxial baseline. Both equivalent stress-based models and critical plane approaches are evaluated. Only one equivalent stress model and two critical plane models showed promise for the range of loadings and material considered.

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Humphrey, J. D., and F. C. P. Yin. "On Constitutive Relations and Finite Deformations of Passive Cardiac Tissue: I. A Pseudostrain-Energy Function." Journal of Biomechanical Engineering 109, no. 4 (November 1, 1987): 298–304. http://dx.doi.org/10.1115/1.3138684.

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A three-dimensional constitutive relation for passive cardiac tissue is formulated in terms of a structurally motivated pseudostrain-energy function, W, while the mathematical simplicity of phenomenological approaches is preserved. A specific functional form of W is proposed on the basis of limited structural information and multiaxial experimental data. The material parameters are determined in a least-squared sense from both uniaxial and biaxial data. Our results suggest that (1) multiaxially-loaded cardiac tissue is nearly transversely-isotropic with respect to local muscle fiber directions, at least for a limited range of strain histories, (2) material parameters determined from uniaxial papillary muscle data result in gross underestimates of the stresses in multiaxially-loaded specimens, and (3) material parameters determined from equibiaxial tests predict the behavior of the tissue under various nonequibiaxial stretching protocols reasonably well.

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Hao, Meng-Fei, Shun-Peng Zhu, and Ding Liao. "New strain energy-based critical plane approach for multiaxial fatigue life prediction." Journal of Strain Analysis for Engineering Design 54, no. 5-6 (July 2019): 310–19. http://dx.doi.org/10.1177/0309324719873251.

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Based on critical plane approach, this article develops a new damage parameter through combing the equivalent strain energy aspect for multiaxial fatigue analysis, which includes no additional fitted parameters and overcomes the deficiency of using only equivalent stress/strain criterion separately under multiaxial loadings. Then, experimental data of GH4169, TC4, Al 7050-T7451 alloys under different loading conditions are applied for model validation and comparison with other four models. Results indicate that the proposed damage parameter yields better multiaxial fatigue life predictions than others.

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Bayraktar, Harun H., Atul Gupta, Ron Y. Kwon, Panayiotis Papadopoulos, and Tony M. Keaveny. "The Modified Super-Ellipsoid Yield Criterion for Human Trabecular Bone." Journal of Biomechanical Engineering 126, no. 6 (December 1, 2004): 677–84. http://dx.doi.org/10.1115/1.1763177.

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Despite the importance of multiaxial failure of trabecular bone in many biomechanical applications, to date no complete multiaxial failure criterion for human trabecular bone has been developed. By using experimentally validated nonlinear high-resolution, micro-mechanical finite-element models as a surrogate for multiaxial loading experiments, we determined the three-dimensional normal strain yield surface and all combinations of the two-dimensional normal-shear strain yield envelope. High-resolution finite-element models of three human femoral neck trabecular bone specimens obtained through micro-computed tomography were used. In total, 889 multiaxial-loading cases were analyzed, requiring over 41,000 CPU hours on parallel supercomputers. Our results indicated that the multiaxial yield behavior of trabecular bone in strain space was homogeneous across the specimens and nearly isotropic. Analysis of stress-strain curves along each axis in the 3-D normal strain space indicated uncoupled yield behavior, whereas substantial coupling was seen for normal-shear loading. A modified super-ellipsoid surface with only four parameters fit the normal strain yield data very well with an arithmetic error±SD less than −0.04±5.1%. Furthermore, the principal strains associated with normal-shear loading showed excellent agreement with the yield surface obtained for normal strain loading (arithmetic error±SD<2.5±6.5%). We conclude that the four-parameter “Modified Super-Ellipsoid” yield surface presented here describes the multiaxial failure behavior of human femoral neck trabecular bone very well.

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Gao, Tianrun, Jianping Jing, Changmin Chen, Jiqing Cong, Jianzhao Li, and Shiyu Cao. "A practical nonlinear damage accumulation method to predict the life and crack propagation of blade subjected to multilevel cyclic fatigue loads." Journal of Strain Analysis for Engineering Design 55, no. 3-4 (February 12, 2020): 86–98. http://dx.doi.org/10.1177/0309324719900598.

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An accurate life prediction is important to the design of a high-speed rotary blade subjected to multilevel cyclic loads. The widely used Miner’s rule and uniaxial stress prediction method always deviate from actual life of the blade. A prediction method based on Chaboche’s nonlinear damage evolution model is utilized to predict the multilevel cyclic fatigue life of a compressor blade subjected to start-up centrifugal force and working aerodynamic force. Chaboche’s model is verified by comparing with experimental data of different materials. The blade life predicted by Chaboche’s rule and Miner’s rule are compared, and it is found that Miner’s rule might overestimate the blade life under the typical loading spectrum of start-up centrifugal force and working aerodynamic force. To study the impact of multiaxial stress state on the blade life, the life predicted by uniaxial stress method is compared to that predicted by multiaxial stress method, and it demonstrates that the multiaxial stress state of the blade should not be neglected. Finally, the crack propagation of the blade under multiaxial fatigue loads is simulated successfully by element deletion technique, which is conducted by translating Chaboche’s multiaxial model into a user defined UMAT program in ABAQUS. The predicted crack propagation life is compared with that predicted by an approximate Paris law method plate model. This research proves that the method to predict the blade life subjected to multilevel cyclic loads based on multiaxial Chaboche’s model could provide a valuable reference for engineering blade fatigue design.

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Journal articles on the topic 'Multiaxial'

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