Journal articles: 'Linear damage rule (LDR)'

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Jin, O., H. Lee, and S. Mall. "Investigation Into Cumulative Damage Rules to Predict Fretting Fatigue Life of Ti-6Al-4V Under Two-Level Block Loading Condition1." Journal of Engineering Materials and Technology 125, no. 3 (July 1, 2003): 315–23. http://dx.doi.org/10.1115/1.1590998.

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The effects of variable amplitude loading on fretting fatigue behavior of titanium alloy, Ti-6Al-4V were examined. Fretting fatigue tests were carried out under constant stress amplitude and three different two-level block loading conditions: high-low (Hi-Lo), low-high (Lo-Hi), and repeated block of high and low stress amplitudes. The damage fractions and fretting fatigue lives were estimated by linear and non-linear cumulative damage rules. Damage curve analysis (DCA) and double linear damage rule (DLDR) were capable to account for the loading order effects in Hi-Lo and Lo-Hi loadings. In addition, the predictions by DCA and DLDR were better than that by linear damage rule (LDR). Besides its simplicity of implementation, LDR was also capable of estimating failure lives reasonably well. Repeated two-level block loading resulted in shorter lives and lower fretting fatigue limit compared to those under constant amplitude loading. The degree of reduction in fretting fatigue lives and fatigue strength depended on the ratio of cycles at lower stress amplitude to that at higher stress amplitude. Fracture surface of specimens subjected to Hi-Lo and repeated block loading showed the clear evidence of change in stress amplitude of applied load. Especially, the repeated two-level block loading resulted in characteristic markers which reflected change in crack growth rates corresponding to different stress amplitudes.

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Santecchia, E., A. M. S. Hamouda, F. Musharavati, E. Zalnezhad, M. Cabibbo, M. El Mehtedi, and S. Spigarelli. "A Review on Fatigue Life Prediction Methods for Metals." Advances in Materials Science and Engineering 2016 (2016): 1–26. http://dx.doi.org/10.1155/2016/9573524.

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Metallic materials are extensively used in engineering structures and fatigue failure is one of the most common failure modes of metal structures. Fatigue phenomena occur when a material is subjected to fluctuating stresses and strains, which lead to failure due to damage accumulation. Different methods, including the Palmgren-Miner linear damage rule- (LDR-) based, multiaxial and variable amplitude loading, stochastic-based, energy-based, and continuum damage mechanics methods, forecast fatigue life. This paper reviews fatigue life prediction techniques for metallic materials. An ideal fatigue life prediction model should include the main features of those already established methods, and its implementation in simulation systems could help engineers and scientists in different applications. In conclusion, LDR-based, multiaxial and variable amplitude loading, stochastic-based, continuum damage mechanics, and energy-based methods are easy, realistic, microstructure dependent, well timed, and damage connected, respectively, for the ideal prediction model.

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Song, Zi Yuan. "Influence of Load Interaction between Creep and TMF on the Life of Single Crystal Nickel-based Superalloy." Materials Science Forum 1027 (April 2021): 99–106. http://dx.doi.org/10.4028/www.scientific.net/msf.1027.99.

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Experimental investigation on the influence of load interaction on the life of Single Crystal Nickel-based Superalloy is conducted. Three kinds of load spectrums considering single and coupled failure mode are designed. Life tests are carried out under creep, thermo-mechanical fatigue (TMF), and creep-TMF interaction loading. The test results show that test lives, under the creep-TMF interaction loading, are lower than the life predictions given by the linear damage accumulation (LDA) rule, indicating that the load coupling can accelerate the damage evolution process. The microstructure of fractured specimens shows that under the creep-TMF interaction loading, rafting cause more dislocations to accumulate in the at γ/γ′ phase boundary, which could be the evidence of life decrease.

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Jin, Dan, Jian Hua Wu, and Xu Chen. "Fatigue Damage and Life Prediction under Sequential Biaxial Loading." Key Engineering Materials 324-325 (November 2006): 255–58. http://dx.doi.org/10.4028/www.scientific.net/kem.324-325.255.

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Fatigue tests are conducted on 304 stainless steel and 45C steel under fully reversed strain control conditions with two different loading modes. 45C steel exhibits cyclic softening under each phase loading. While for 304 stainless steel, much additional hardening is observed in out-of-phase loading. The damage values for failure of 45C steel is similar to the previous research, however, 304 stainless steel is not. Fatigue life is predicted based on the linear damage rule, the double linear damage rule, and the plastic work model of Morrow. The damage value is different in the same loading mode for the two materials according to linear damage rule.

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Lambert, R. G. "Plastic Work Interaction Damage Rule Applied to Narrow-Band Gaussian Random Stress Situations." Journal of Pressure Vessel Technology 110, no. 1 (February 1, 1988): 88–90. http://dx.doi.org/10.1115/1.3265573.

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Fatigue life estimates that use a structural material’s constant amplitude stress life data values and a linear cumulative damage rule are always nonconservative for stress histories containing numerous subcycles and only a few large-amplitude cycles. Conservative fatigue life estimates were previously achieved by others with a plastic work interaction damage rule using the material’s overstrain fatigue life parameter values. Verification fatigue tests were run on laboratory specimens of 1020 steel using four selected variable amplitude stress wave form profiles. This paper extends the application of the plastic work interaction damage rule to narrowband Gaussian random stress situations. The derived stress life mathematical expression is of a power law form. The predicted fatigue life is more accurate than that predicted using a conventional linear damage rule.

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Blacha, Łukasz. "Non-Linear Probabilistic Modification of Miner’s Rule for Damage Accumulation." Materials 14, no. 23 (November 30, 2021): 7335. http://dx.doi.org/10.3390/ma14237335.

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A non-linear modification to Miner’s rule for damage accumulation is proposed to reduce the scatter between experimental fatigue life and fatigue life predicted according to the original Miner’s sum. Based on P-s-n probability distribution and design s-n curves, the modification satisfies the assumption of equality between the mean damage degree (at the critical level) and fatigue life random variables, which is not covered in the original formulation. The adopted formulation shows the discrepancies between the fatigue lives predicted according to the design s-n curves and the estimated probability distribution. It also proves that it is inappropriate to apply a normal distribution to fatigue life analysis and that the model becomes non-linear only for non-normal distributions. The predictions according to the established model were compared to the predictions obtained with Miner’s rule.

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Altus, Eli. "Fatigue, Fractals, and a Modified Miner’s Rule." Journal of Applied Mechanics 58, no. 1 (March 1, 1991): 37–42. http://dx.doi.org/10.1115/1.2897176.

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A Mechano Chemical Fatigue Model (MCFM) was recently developed. Two basic features of the model are studied here: (a) the fractal (self-similarity under magnification) property of the damage function, which is predicted by the model and (b) how it leads to a “Modified Miner’s Rule” (MMR), where the fatigue response is dependent on the loading order. Based on the simplest (basic) case of the model, the damage function is dependent on a single parameter when a Weibull strength distribution for the microscale elements (chains) is used. the MCFM proposes a rational explanation to a linear fatigue failure envelope for a two level (High-Low, Low-High) stress loading while the damage law is nonlinear. This is in contrast to the regular Miner Rule, where the damage progression is assumed linear. Applying multilevel cyclic loading the model shows a “fading memory“ response for a monotonically increasing stress. While for a decreasing stress steps there is an intermediate delay stage for which a constant damage rate is found. The microscopic basis of the MCFM enables a clear and direct physical interpretation of the macro behavior as related to the microscale damage mechanisms.

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Zhu, Hong Bing, Bo Xia, and Yao Zhao. "RC Beam Bridge’s Fatigue Cumulative Damage Rule Research." Advanced Materials Research 787 (September 2013): 829–32. http://dx.doi.org/10.4028/www.scientific.net/amr.787.829.

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Fatigue damage is the RC beam bridge is facing a big problem, for the RC beam bridge fatigue tests and fatigue cumulative damage theory research is very meaningful. Summarizes the research achievements of the RC beam bridge fatigue test, from constant amplitude fatigue, luffing fatigue and stochastic fatigue, etc, are discussed in this paper. Analyses the existing linear, nonlinear and probability fatigue cumulative damage theory and its applicable conditions, advantages and disadvantages. RC fatigue tests were discussed and the problems that exist in the fatigue cumulative damage theory research.

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Fallah-Mehdipour, E., O. Bozorg Haddad, and M. A. Mariño. "Developing reservoir operational decision rule by genetic programming." Journal of Hydroinformatics 15, no. 1 (July 30, 2012): 103–19. http://dx.doi.org/10.2166/hydro.2012.140.

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The reservoir operational decision rule is an equation that can balance reservoir system parameters in each period by considering previous experiences of the system. That equation includes variables such as inflow, volume storage and released water from the reservoir that are commonly related to each other by some constant coefficients in predefined linear and nonlinear patterns. Although optimization tools have been extensively applied to develop an optimal operational decision rule, only optimal constant coefficients have been derived and the operational patterns are assumed to be fixed in that operational rule curve. Genetic programming (GP) is an evolutionary algorithm (EA), based on genetic algorithm (GA), which is capable of calculating an operational rule curve by considering optimal operational undefined patterns. In this paper, GP is used to extract optimal operational decision rules in two case studies by meeting downstream water demands and hydropower energy generation. The extracted rules are compared with common linear and nonlinear decision rules, LDR and NLDR, determined by a software package for interactive general optimization (LINGO) and GA. The GP rule improves the objective functions in the training and testing data sets by 2.48 and 8.53%, respectively, compared to the best rule by LINGO and GA in supplying downstream demand. Similarly, the hydropower energy generation improves by 48.03 and 44.21% in the training and testing data sets, respectively. Results show that the obtained objective function value is enhanced significantly for both the training and testing data using GP. They also indicate that the proposed rule, based on GP, is effective in determining optimal rule curves for reservoirs.

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Dias, João Paulo, Stephen Ekwaro-Osire, Americo Cunha, Shweta Dabetwar, Abraham Nispel, Fisseha M. Alemayehu, and Haileyesus B. Endeshaw. "Parametric probabilistic approach for cumulative fatigue damage using double linear damage rule considering limited data." International Journal of Fatigue 127 (October 2019): 246–58. http://dx.doi.org/10.1016/j.ijfatigue.2019.06.011.

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Depue, Tracy K., Patrick C. Kennedy, and Steven A. Rutledge. "Performance of the Hail Differential Reflectivity (HDR) Polarimetric Radar Hail Indicator." Journal of Applied Meteorology and Climatology 46, no. 8 (August 1, 2007): 1290–301. http://dx.doi.org/10.1175/jam2529.1.

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Abstract A series of poststorm surveys were conducted in the wake of hailstorms observed by the Colorado State University–University of Chicago–Illinois State Water Survey (CSU-CHILL) S-Band polarimetric radar. Information on hail characteristics (maximum diameter, building damage, apparent hailstone density, etc.) was solicited from the general-public storm observers that were contacted during the surveys; the locations of their observations were determined using GPS equipment. Low-elevation angle radar measurements of reflectivity, differential reflectivity ZDR, and linear depolarization ratio (LDR) were interpolated to the ground-observer locations. Relationships between the hail differential reflectivity parameter HDR and the observer-reported hail characteristics were examined. It was found that HDR thresholds of 21 and 30 dB were reasonably successful (critical success index values of ∼0.77) in respectively identifying regions where large (>19 mm in diameter) and structurally damaging hail were observed. The LDR characteristics in the observed hail areas were also examined. Because of sensitivities to variations in the hailstone bulk ice density, degree of surface wetness, and shape irregularities, the basic correlation between LDR magnitude and hail diameter was poor. However, when the reported hail diameters exceeded ∼25 mm, LDR levels below ∼−24 dB were uncommon.

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Stigh, U. "Continuum Damage Mechanics and the Life-Fraction Rule." Journal of Applied Mechanics 73, no. 4 (October 24, 2005): 702–4. http://dx.doi.org/10.1115/1.2150502.

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This paper gives a short review of two different methods for life prediction at high temperature; namely continuum damage mechanics (CDM) and the linear life-fraction rule (LFR). It is well known that the class of CDM theories with a separable evolution law gives a life prediction in accordance with the LFR. However, it appears to be an open question if this is a necessary condition. It is here shown that in order for a CDM theory to comply with the LFR it must have a separable evolution law. That is, if we can assume that a material follows the LFR, it is necessary to chose a separable evolution law for this material. The reverse is also true, to get a life-fraction different from unity, we must chose a nonseparable evolution law.

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Ren, Huilong, Xiaoying Zhuang, and Timon Rabczuk. "A new peridynamic formulation with shear deformation for elastic solid." Journal of Micromechanics and Molecular Physics 01, no. 02 (July 2016): 1650009. http://dx.doi.org/10.1142/s2424913016500090.

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We propose a new peridynamic formulation with shear deformation for linear elastic solid. The key idea lies in subtracting the rigid body rotation part from the total deformation. Based on the strain energy equivalence between classic local model and non-local model, the bond force vector is derived. A new damage rule of maximal deviatoric bond strain for elastic brittle fracture is proposed in order to account for both the tensile damage and shear damage. 2D and 3D numerical examples are tested to verify the accuracy of the current peridynamics. The new damage rule is applied to simulate the propagation of Mode I, II and III cracks.

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YAMAUCHI, Masafumi, Toshihide IGARI, Toshiro MATSUBARA, and Katsuya SETOGUCHI. "Creep-fatigue life prediction for modified 9Cr-1Mo steel by linear damage rule." Journal of the Society of Materials Science, Japan 39, no. 442 (1990): 965–69. http://dx.doi.org/10.2472/jsms.39.965.

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Djebli, Abdelkader, Mostefa Bendouba, and Aid Abdelkarim. "Fatigue Life Prediction under Variable Loading Based a Non-Linear Energy Model." International Journal of Engineering Research in Africa 22 (February 2016): 14–21. http://dx.doi.org/10.4028/www.scientific.net/jera.22.14.

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A method of fatigue damage accumulation based upon application of energy parameters of the fatigue process is proposed in the paper. Using this model is simple, it has no parameter to be determined, it requires only the knowledge of the curve W–N (W: strain energy density N: number of cycles at failure) determined from the experimental Wöhler curve. To examine the performance of nonlinear models proposed in the estimation of fatigue damage and fatigue life of components under random loading, a batch of specimens made of 6082 T6 aluminium alloy has been studied and some of the results are reported in the present paper. The paper describes an algorithm and suggests a fatigue cumulative damage model, especially when random loading is considered. This work contains the results of uni-axial random load fatigue tests with different mean and amplitude values performed on 6082 T6 aluminium alloy specimens. The proposed model has been formulated to take into account the damage evolution at different load levels and it allows the effect of the loading sequence to be included by means of a recurrence formula derived for multilevel loading, considering complex load sequences. It is concluded that a ‘damaged stress interaction damage rule’ proposed here allows a better fatigue damage prediction than the widely used Palmgren–Miner rule, and a formula derived in random fatigue could be used to predict the fatigue damage and fatigue lifetime very easily. The results obtained by the model are compared with the experimental results and those calculated by the most fatigue damage model used in fatigue (Miner’s model). The comparison shows that the proposed model, presents a good estimation of the experimental results. Moreover, the error is minimized in comparison to the Miner’s model.

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Wang, Huili, Sifeng Qin, and Yunjie Wang. "Nonlinear cumulative damage model and application to bridge fatigue life evaluation." Advances in Structural Engineering 21, no. 9 (December 21, 2017): 1402–8. http://dx.doi.org/10.1177/1369433217746344.

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Fatigue is a damage accumulation process in which material property deteriorates continuously. Fatigue life prediction issues are important for safety. This article aims to develop a nonlinear cumulative damage model. A fatigue damage model based on the continuum damage mechanics is addressed and applied to bridge fatigue life evaluation. First, the bridge nonlinear cumulative damage model based on damage mechanics is propounded and equivalent effective stress range is given. Then, the effects of the main parameter in the model are analyzed. Finally, Xinghai Bay Bridge is taken as a case study. The results indicate that the damage is increased with the material parameter [Formula: see text] reduced. [Formula: see text] is a material parameter depending on stress amplitude and without physical meaning. If [Formula: see text], the effect of [Formula: see text] is negligible. If [Formula: see text], nonlinear cumulative damage model degrades into Miner’s rule and effect of [Formula: see text] to structural damage is maximum. The cumulative damage curve calculated by the nonlinear cumulative damage model is nonlinear, with a low cumulative rate initially but a very high cumulative rate at the end of the design life, whereas the Miner’s rule is linear. The nonlinear cumulative damage model can reflect actual damage process, while Miner’s rule is pessimistic.

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Zuluaga-Ramírez, Pablo, Malte Frövel, Álvaro Arconada, Tomás Belenguer, and Félix Salazar. "Evaluation of the Fatigue Linear Damage Accumulation Rule for Aeronautical CFRP Using Artificial Neural Networks." Advanced Materials Research 1016 (August 2014): 8–13. http://dx.doi.org/10.4028/www.scientific.net/amr.1016.8.

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New optimized aerospace structures use composite materials for critical components and subsystems which make essential the knowledge of their fatigue properties. In the present work, the conventional methodology based on linear damage accumulation rules, applied to determine the fatigue life of structures subjected to spectral loads was evaluated for an aeronautical Carbon Fiber Reinforced Epoxy composite material. A test program has been performed to obtain the classical S-N curves at different stress ratios. Constant life diagrams, CLDs, where determined by means of Artificial Neural Networks due to the absence of consistent models for composites. A series of coupons have been tested until failure with a modified version of the standard FALSTAFF load sequence and were compared to the theoretical damage index calculated based on the conventional linear damage accumulation rule. The obtained results show non-conservative predictions.

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Huang, Heyuan, Meiying Zhao, Xiaopeng Wan, and Chi Hou. "A Composite Bolted Joints Non-Linear Stiffness Model and its Application." Xibei Gongye Daxue Xuebao/Journal of Northwestern Polytechnical University 36, no. 1 (February 2018): 66–73. http://dx.doi.org/10.1051/jnwpu/20183610066.

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The paper presents a nonlinear stiffness model on the bearing damage and bolt-load distribution rule of composite bolted joints. Based on the experimental stress-strain curves of composite single-bolted joints, the bearing damage process of structures can be divided into:linear non-damage stage; nonlinear damage propagation stage and linear degeneration stage. In this paper, the composite bolted joints are represented by a system of springs in which the static friction effects between laminates are considered in the linear stage, the non-linear interlaminate shear behavior and the nonlinear damage function for composite are defined and failure behavior based on the energy abortion principle is simulated in the linear degeneration stage. At last, the multi-fasters spring model is analyzed by importing the single-faster spring model.Comparing with the experimental data of multi-fasters shows the numerical result is in good agreement with experimental curves and has little error on the bolt-load distribution, which satisfies to the requirements in the engineering.

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Lambert, Ronald. "Case Histories of Selection Criteria for Random Vibration Screening." Journal of the IEST 28, no. 1 (January 1, 1985): 19–25. http://dx.doi.org/10.17764/jiet.1.28.1.n64535155p85767p.

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This paper describes the criteria for selecting the random vibration screening level and duration such that defects are uncovered without consuming significant useful life prior to service use. Miner's Linear Damage Rule is used as the basis for the derived damage expressions. Three real-world case histories are included to demonstrate the application of these criteria.

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Cai, Fu Hai, Xin Wang, and Fu Ling Zhao. "A New Fatigue Life Calculation Method Based on Non-Linear Cumulative Damage Theory." Applied Mechanics and Materials 423-426 (September 2013): 2116–22. http://dx.doi.org/10.4028/www.scientific.net/amm.423-426.2116.

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Operating characteristics of small and medium tonnage lattice boom crane which withstand fatigue loads was analyzed in this paper. It showed that the lattice boom crane utilization level is in the overlap zone of low cycle fatigue and high cycle fatigue. There may be some plastic deformation in the structure. So the total damage calculated by the Palmgren-Miner rule had a large scatter. Typical operating conditions was analyzed that K-type welded joints of the boom is under axial load and in-plane bending loads. Several critical areas of K-type welded joints were determined by ANSYS finite element calculation software where the stress amplitude was larger on the single side of the lattice boom. A new stress spectrum acquisition method based on the “measured+statistics+compare+simulation” integrated strategy of crane K-type welded joints was proposed. Based on a simplified Huffman non-linear cumulative damage theory, fatigue life of crane K-type welded Joints were calculated based on the strain parameters. They were compared with Palmgren-Miner rule and together with fracture mechanics method. Results showed that although they were all conservative compared with test results, the new method can be applied easily in for engineering applications because it only need amplitude constant amplitude fatigue strain-life data.

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Zou, Hua, Qiang Li, and Shou Guang Sun. "Nonlinear Cumulative Fatigue Damage Model." Advanced Materials Research 328-330 (September 2011): 1440–44. http://dx.doi.org/10.4028/www.scientific.net/amr.328-330.1440.

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Cumulative fatigue damage is an important consideration in determining the fatigue life of structures. A cumulative linear damage rule cannot provide a reasonable explanation for cumulative fatigue damage, but a damage curve method based on nonlinear cumulative fatigue damage model can give a reasonable explanation. In this paper, a specific mathematical model is put forward, which is based on the damage curve method. In the model, miner formula is modified properly and an exponent formula is give out to fit the damage accumulate. According to a two-step fatigue test of aluminum–alloy welded joint, the comparison between the calculated results and the testing results is less than 5%. It shows that the model is reasonable and accuracy.

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Gao, Meng Qi, Ping Ying Wang, and He Ping Ding. "Analysis on the Fatigue Life of Asphalt Pavement under Traffic Flow Loads." Applied Mechanics and Materials 361-363 (August 2013): 1727–34. http://dx.doi.org/10.4028/www.scientific.net/amm.361-363.1727.

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To study the fatigue life of asphalt pavement under traffic loads, a 3-D finite element analysis (FEA) Visio-elastic road model was established on the layered theory with ANSYS software. The fatigue damage was calculated with the maximum horizontal tensile strain of asphalt layer bottom based on the fatigue fracture mechanics, when single axis went across. Then the fatigue life was obtained after the fatigue damage occurred in some degree by the Miners linear cumulative damage rule. The results show that it taken 3.4 years when the damage area reached 10% of wheel path area, and 4.5years when reached 45%; while the calculated result was 5.5 years by axial-load conversion method. The analysis shows that the fatigue life of asphalt pavement calculated by fatigue fracture mechanics rule has more significance in practice.

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Wei, T. X., Z. Zhang, Z. Yang, Y. Sheng, and R. P. Wang. "Optical damage and the third-order nonlinearity in GeGaS glasses." Chalcogenide Letters 19, no. 9 (September 25, 2022): 627–35. http://dx.doi.org/10.15251/cl.2022.199.627.

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We have measured optical properties of GexGa4S96-x (x=22.5, 27, 30, 33.3 and 36) glasses including optical bandgap Eg, hardness, linear and nonlinear refractive index and laser damage threshold. We found that, both Eg and laser damage threshold exhibit maximum values in Ge30Ga4S66 glass, linear refractive index increases with increasing Ge content, but nonlinear refractive index has a minimum in Ge30Ga4S66, and their correlation can be well described by the Miller’s rule. We conclude that, Ge30Ga4S66 glass with chemically stoichiometric composition might be ideal for the chalcogenide-based optical amplifiers since it has reasonable optical nonlinearity, and high figure of merit (FOM) and laser damage threshold.

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Nakada, Masayuki, Junji Noda, and Yasushi Miyano. "Fatigue Life Prediction of CFRP Laminates under Variable Stress Amplitude and Frequency." Key Engineering Materials 334-335 (March 2007): 445–48. http://dx.doi.org/10.4028/www.scientific.net/kem.334-335.445.

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This paper is concerned with the fatigue life prediction of CFRP laminates under variable cyclic loading using the linear cumulative damage (LCD) rule with statistical approach. Three-point bending fatigue tests for plain-woven CFRP laminates were carried out undervarious cyclic loading with constant and variable stress amplitude and frequency. As results, the applicability of LCD rule to the flexural fatigue life was confirmed for this CFRP laminates.

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Lin, Hong, Hamid Nayeb-Hashemi, and Charles A. Berg. "Cumulative Damage Behavior of Anisotropic Al-6061-T6 as a Function of Axial-Torsional Loading Mode Sequence." Journal of Engineering Materials and Technology 116, no. 1 (January 1, 1994): 27–34. http://dx.doi.org/10.1115/1.2904252.

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Two types of low cycle fatigue tests were conducted along two principal orthotropic directions of an orthotropic Al-6061-T6 plate in strain control at room temperature: (1) reference fatigue tests under three loading conditions: push-pull, torsion, and combined push-pull/torsion in-phase; (2) sequential fatigue tests in which different sequences of push-pull and torsion were performed. Fatigue cracking behavior was observed during all of the fatigue tests. Shear cracking dominated the damage of the material. Anisotropic constitutive relations of the material were used in the evaluation of several multiaxial fatigue damage models. The predictive capabilities of these models were assessed based on the results of reference fatigue tests. The damage accumulation behavior of the material was found to depend on the sequence of the loading mode. For the sequence of torsion then push-pull, the damage summation was greater than unity. However, for the sequence of push-pull then torsion, the damage accumulation was near unity as predicted by the linear damage rule. A nonlinear damage accumulation rule could represent the results of the sequential fatigue tests.

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Huang, Ding, Li, Zhou, and Huang. "A Modified Model for Nonlinear Fatigue Damage Accumulation of Turbine Disc Considering the Load Interaction Effect." Metals 9, no. 9 (August 22, 2019): 919. http://dx.doi.org/10.3390/met9090919.

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Fatigue damage accumulation theory is one of the core contents in structure fatigue strength design and life prediction. Among them, the nonlinear damage model can overcome the shortcomings of the linear damage model, which takes the loading sequence effect into account. Besides, the loading interaction cannot be ignored for its profound influence in damage accumulation behavior. In the paper, some commonly-used methods of the linear and nonlinear fatigue damage accumulation theory are investigated. In particular, a modified nonlinear fatigue damage accumulation model which considers the effects of loading sequences as well as loading interactions on fatigue life is developed, and a load interaction parameter is obtained by analyzing damage models which assumes that the load logarithm ratio between adjacent stress levels can characterize this phenomenon. Finally, the modified model is employed to predict the fatigue life of high pressure turbine disc. Moreover, comparison is made between the experimental data as well as the predicted lives using the Miner’s rule, the Ye’s model, and the modified model.

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Lei, Liang, Shi Xingang, Cui Yunhua, Wang Lefan, and Yan Xiangcheng. "A new fatigue damage model for pavement concrete beams bearing multi-level bending loads." PLOS ONE 16, no. 8 (August 5, 2021): e0255048. http://dx.doi.org/10.1371/journal.pone.0255048.

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MTS-810 material testing machine and acoustic emission signal analyzer were adopted to explore the mechanical behavior of concrete beams broken by the static load and the nonlinear cumulative damage law of concrete beams broken by fatigue bending from single-stage loading. Then, by introducing the Ramesh Talreja’s Damage Criterion, the damage rule of single-stage loading was extended to the damage accumulation rule under multi-stage loading, and the results were verified by the results of two-stage and three-stage fatigue loading tests. Two main conclusions are achieved: first, affected by four-point bending load, the fatigue life of the concrete specimen is in line with the law of the two-parameter Weibull distribution, namely the higher the stress level is, the shorter the fatigue life is. Second, an obvious nonlinear relationship was discovered in the damage of concrete. The model deduced in this paper and the Palmgren-Miner linear damage accumulation model were adopted to compare the test results of flexural fatigue under single, two and three stage loads. The calculation results of this model were more reliable.

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Pollycove, Myron, and Ludwig E. Feinendegen. "Low-dose radioimmuno-therapy of cancer." Human & Experimental Toxicology 27, no. 2 (February 2008): 169–75. http://dx.doi.org/10.1177/0960327107083411.

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Four decades of genomic, cellular, animal and human data have shown that low-dose ionizing radiation stimulates positive genomic and cellular responses associated with effective cancer prevention and therapy and increased life span of mammals and humans. 1—8 Nevertheless, this data is questioned because it seems to contradict the well demonstrated linear relation between ionizing radiation dose and damage to DNA without providing a clear mechanistic explanation of how low-dose radiation could produce such beneficial effects. This apparent contradiction is dispelled by current radiobiology that now includes DNA damage both from ionizing radiation and from endogenous metabolic free radicals, and coupled with the biological response to low-dose radiation. Acceptance of current radiobiology would invalidate long established recommendations and regulations of worldwide radiation safety organizations and so destroy the basis of the very expensive existing system of regulation and remediation. More importantly, current radiobiology would facilitate urgently needed clinical trials of low dose radiation (LDR) cancer therapy.

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Hectors, Kris, and Wim De Waele. "Cumulative Damage and Life Prediction Models for High-Cycle Fatigue of Metals: A Review." Metals 11, no. 2 (January 22, 2021): 204. http://dx.doi.org/10.3390/met11020204.

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Fatigue design of engineering structures is typically based on lifetime calculation using a cumulative damage law. The linear damage rule by Miner is the universal standard for fatigue design even though numerous experimental studies have shown its deficiencies and possible non-conservative outcomes. In an effort to overcome these deficiencies, many nonlinear cumulative damage models and life prediction models have been developed since; however, none of them have found wide acceptance. This review article aims to provide a comprehensive overview of the state-of-the art in cumulative damage and lifetime prediction models for endurance based high-cycle fatigue design of metal structures.

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Wang, Yanju, Xinhao Wang, Yanfeng Yang, Xiang Lan, Zhao Zhang, and Heng Li. "Study on Creep-Fatigue Mechanical Behavior and Life Prediction of Ti2AlNb-Based Alloy." Materials 15, no. 18 (September 8, 2022): 6238. http://dx.doi.org/10.3390/ma15186238.

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Low-cycle fatigue, creep and creep-fatigue tests of Ti2AlNb-based alloy were carried out at 550 °C. Compared with low-cycle fatigue, a creep-fatigue hysteresis loop has larger area and smaller average stress. The introduction of creep damage will greatly reduce the cycle life, and change the fatigue crack initiation point and failure mechanism. Based on the linear damage accumulation rule, the fatigue damage and creep damage were described by the life fraction method and the time fraction method, respectively, and the creep-fatigue life of the Ti2AlNb-based alloy is predicted within an error band of ±2 times.

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31

Patil, Navendu, Pradeep Mahadevan, and Anindya Chatterjee. "A constructive empirical theory for metal fatigue under block cyclic loading." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 464, no. 2093 (February 5, 2008): 1161–79. http://dx.doi.org/10.1098/rspa.2007.0109.

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Much modern engineering design work uses S – N curves and empirical applications thereof. In industry, currently popular methods for predicting fatigue life under complex loading use ad hoc cycle counting algorithms along with Miner's rule, in spite of its known weaknesses. Many ad hoc alternatives to Miner's rule have been proposed, each with limited experimental justification. Of these, Manson's double linear damage rule (DLDR) is widely considered to be good. In this paper, we bring a new perspective to empirical, as opposed to mechanistic, fatigue damage evolution models. It is first assumed, with reasonable justification, that there is a scalar, abstract, damage variable ϕ , whose evolution under cyclic loading satisfies , where a and m are unknown functions of load parameters. One main contribution of the paper lies in deducing what the functions a and m must be in order to obtain consistency with fatigue data in handbooks. A small correction to this basic power law model is then developed. The final explicit model initially has 10 unknown fitted parameters, but these are brought down to three unknowns; the accompanying discussion is the other main contribution of the paper. Finally, comparison with Manson's and other data suggests that, with two fitted parameters, our model works as well as the DLDR and much better than Miner's rule. For other parameter choices, our model reduces to Miner's rule. We conclude with speculation about ways in which the model might be extended beyond the scope of the DLDR.

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32

Chen, Xian Min, and Hong Na Dui. "Probabilistic Modeling of Fatigue Damage Accumulation under Spectrum Loading." Applied Mechanics and Materials 684 (October 2014): 169–75. http://dx.doi.org/10.4028/www.scientific.net/amm.684.169.

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A probabilistic methodology for modeling fatigue damage accumulation and fatigue life under variable amplitude loading is proposed in this paper. With probabilistic modifications, the calculative consistency between fatigue damage and life is achieved in the model and the load sequence effects are properly accounted for variable amplitude loading. This damage model overcomes the inherent deficiencies in the linear damage accumulation rule but still preserves its simplicity for engineering application. With Monte Carlo sampling method, numerical verification of this model is conducted under two-level spectrum loading. The predicted probabilistic distributions of fatigue life are validated by the fatigue tests on Al-alloy straight lugs.

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Nozaki, Mineo, Masao Sakane, Yutaka Tsukada, and Hideo Nishimura. "Creep-Fatigue Life Evaluation for Sn-3.5Ag Solder." Journal of Engineering Materials and Technology 128, no. 2 (May 11, 2005): 142–50. http://dx.doi.org/10.1115/1.2172273.

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This paper studies the creep-fatigue life evaluation of Sn-3.5Ag solder under push-pull loading using fast-fast, fast-slow, slow-fast, slow-slow, and strain-hold strain waves. Extensive creep-fatigue data were generated using these strain waves and the applicability of four conventional creep-fatigue damage rules, the linear damage rule, the frequency modified fatigue life, the ductility exhaustion model, and the strain range partitioning method, was examined. No conventional damage rules evaluated creep-fatigue lives accurately. Only the grain boundary sliding model, developed recently for solders, predicted creep-fatigue lives with a small scatter.

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34

OTA, Yutaro, Keiji KUBUSHIRO, and Yasuhiro YAMAZAKI. "The Life Assessment by Linear Cumulative Damage Rule for Cold Dwell Fatigue of Ti-6Al-4V." Journal of the Society of Materials Science, Japan 70, no. 1 (January 15, 2021): 35–40. http://dx.doi.org/10.2472/jsms.70.35.

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35

Franke, L. "A non-linear fatigue damage rule with an exponent based on a crack growth boundary condition." International Journal of Fatigue 21, no. 8 (September 1999): 761–67. http://dx.doi.org/10.1016/s0142-1123(99)00045-6.

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36

Kobayashi, Yukiyoshi, Toshihisa Ohtsuka, Yoshinobu Kishimoto, and Kei Hadame. "OS15F098 Prediction of Fatigue Crack Growth Life Considered Crack Closure Behavior to Linear Cumulative Damage Rule." Abstracts of ATEM : International Conference on Advanced Technology in Experimental Mechanics : Asian Conference on Experimental Mechanics 2011.10 (2011): _OS15F098——_OS15F098—. http://dx.doi.org/10.1299/jsmeatem.2011.10._os15f098-.

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37

ORLIK, JULIA. "HOMOGENIZATION OF STRENGTH, FATIGUE AND CREEP DURABILITY OF COMPOSITES WITH NEAR PERIODIC STRUCTURE." Mathematical Models and Methods in Applied Sciences 15, no. 09 (September 2005): 1329–47. http://dx.doi.org/10.1142/s0218202505000807.

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Asymptotic homogenization technique and two-scale convergence is used for analysis of macro-strength, fatigue and creep durability of composites with a periodic structure. The linear damage accumulation rule is employed in the phenomenological micro-durability conditions (for each component of the composite) under varying cyclic or creep loading. Both local and nonlocal strength and durability conditions are analyzed. The strong convergence of the strength and fatigue and creep damage measures as the structure period tends to zero is proved and their limiting values are estimated.

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38

Yang, Yuqi, Longbin Liu, and Shaozhe Ding. "Fatigue Damage Characteristics and Morphology of Fiber Braided Laminated Flexible Composites." Journal of Physics: Conference Series 2361, no. 1 (October 1, 2022): 012005. http://dx.doi.org/10.1088/1742-6596/2361/1/012005.

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In this paper, the fatigue damage evolution law and damage failure mode of flexible braided thin film composites are studied by stress fatigue damage test and scanning electron microscopy morphology test of uniaxial 45° off-axis sample. The results show that the failure mode of the specimens with 45°off-axis angle is characterized by fatigue damage of both the matrix and the functional film and the fracture of the fiber bundle has little influence. In addition, the pattern fatigue stress and fatigue life data of the fatigue test of viscose matrix and functional film under different fatigue loads have the rule of linear equation, which has predictive significance on the safety of aircraft.

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Topoliński, Tomasz, Artur Cichański, Adam Mazurkiewicz, and Krzysztof Nowicki. "Applying a Stepwise Load for Calculation of the S-N Curve for Trabecular Bone Based on the Linear Hypothesis for Fatigue Damage Accumulation." Materials Science Forum 726 (August 2012): 39–42. http://dx.doi.org/10.4028/www.scientific.net/msf.726.39.

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In this work were presented calculated fatigue curves based on fatigue tests of trabecular bone under stepwise load with the application of a linear hypothesis accumulation of fatigue damage. The investigation was performed on 61 cylindrical bone samples obtained from the neck of different femur heads. The bone sample fatigue tests were carried out under compression with stepwise increases of the applied load. The fatigue calculation assumed the Palmgren-Miner (P-M) linear hypothesis accumulation of fatigue damage and the associated modified formulae. The obtained mean fatigue curves were based on the modified stress σ/E0 (E0 – initial stiffnes) for the assumed rule-determined slope or y-intercept. The highest agreement with the literature was obtained for Σn/N=10.

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40

Palma, E. S., and E. S. dos Santos. "Fatigue damage analysis in an automobile stabilizer bar." Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering 216, no. 11 (November 1, 2002): 865–71. http://dx.doi.org/10.1243/095440702321031414.

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An analysis of fatigue damage in a stabilizer bar in the front suspension (McPherson) of a passenger car was performed. A cumulative fatigue damage theory (linear damage rule) together with experimental and analytical techniques of stress analysis are used to determine the fatigue damage imposed on the stabilizer bar, under both laboratory and actual conditions. Finite element models of the stabilizer bars were used to determine the local stresses at critical regions. These stresses were then measured in the laboratory, by using strain gauges bonded on the material. The assessments of fatigue damage of the stabilizer bar under actual conditions were performed with a component mounted on a vehicle, which was driven over different road surfaces and at different velocities. The results of both experiment types are correlated and discussed.

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Rambabu, D. V., V. R. Ranganath, U. Ramamurty, and A. Chatterjee. "Variable stress ratio in cumulative fatigue damage: Experiments and comparison of three models." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 224, no. 2 (February 1, 2010): 271–82. http://dx.doi.org/10.1243/09544062jmes1579.

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We use the results of new fatigue experiments conducted with variable load levels as well as variable stress ratios to critically assess three (two old and one relatively new) cumulative fatigue damage models. Such models are usually tested using multiple blocks of periodic loading with differing amplitudes. However, available data pertain to zero-mean loading, and do not investigate the role of the variable stress ratio ( Smin/ Smax). Here, we present experimental results for variable stress ratios. Two specimen geometries and two materials (Al 2014 and Al 2024) are tested. Manson's double linear damage rule (DLDR) gives the highest accuracy in predicting the experimental outcome, even in the presence of variable stress ratios, whereas predictions of the newer model (‘a constructive empirical theory for metal fatigue under block cyclic loading’, Proc. R. Soc. A, 2008, 464, 1161–1179) are slightly inferior. The widely used Miner's rule is least accurate in terms of prediction. The merits and drawbacks of these models, in light of the experimental results, are as follows. The DLDR, though accurate, has minor scientific inconsistencies and no clear generalization. The constructive model has possible generalizability and more appealing scientific consistency, but presently has poorer accuracy. Miner's rule, though least accurate, lies within the constructive approach for special parameter values. The DLDR can guide the new (constructive) approach through new parameter fitting criteria.

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Marechal, David, Nicolas Saintier, Thierry Palin-Luc, and François Nadal. "High-Cycle Fatigue Behaviour of Pure Tantalum under Multiaxial and Variable Amplitude Loadings." Advanced Materials Research 891-892 (March 2014): 1341–46. http://dx.doi.org/10.4028/www.scientific.net/amr.891-892.1341.

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Due to its specific mechanical properties, tantalum is often used in strength-demanding military applications. High-cycle fatigue (HCF) behaviour of pure tantalum, however, has been rarely reported and the mechanisms at stake to account for deformation under cyclic loadings are still badly understood. This paper aims at better understanding the fatigue behaviour of tantalum and at clarifying the mechanisms of damage formation encountered under such loadings. HCF experiments performed at room temperature on commercially-pure tantalum are presented. Mean stress effects were investigated in the aim of clarifying the interaction between fatigue and creep. Fracture mechanisms were observed to vary from intergranular to transgranular depending on applied stress amplitude and mean stress. Damage mechanisms were investigated under tension and torsion. Results are analyzed in the light of existing fatigue criteria, the limitations of which are discussed. Finally, complex sequential loadings, representative of in-service loadings, were applied to tantalum smooth specimens. The contribution of each loading sequence to the overall damage was quantified and analyzed in terms of linear or non-linear cumulative damage rule.

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43

Ota, Yutaro, Keiji Kubushiro, and Yasuhiro Yamazaki. "The life evaluation by linear cumulative damage rule for cold dwell fatigue of Ti‐6Al‐4V alloy." Fatigue & Fracture of Engineering Materials & Structures 45, no. 1 (October 28, 2021): 259–69. http://dx.doi.org/10.1111/ffe.13597.

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44

Noda, Junji, Masayuki Nakada, and Yasushi Miyano. "Fatigue Life Prediction under Variable Cyclic Loading Based on Statistical Linear Cumulative Damage Rule for CFRP Laminates." Journal of Reinforced Plastics and Composites 26, no. 7 (May 2007): 665–80. http://dx.doi.org/10.1177/0731684407075577.

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45

Zhu, Shun-Peng, Hong-Zhong Huang, and Zhong-Lai Wang. "Fatigue Life Estimation Considering Damaging and Strengthening of Low amplitude Loads under Different Load Sequences Using Fuzzy Sets Approach." International Journal of Damage Mechanics 20, no. 6 (January 20, 2011): 876–99. http://dx.doi.org/10.1177/1056789510397077.

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In this study, based on the Miner rule, a new linear damage accumulation rule is proposed to consider the strengthening and damaging of low amplitude loads with different sequences using fuzzy sets theory. This model improves the application of the traditional Miner rule, by considering not only the damaging and strengthening of low amplitude loads, but also the load sequence effects. To apply the proposed model, the law of selecting membership functions for different load spectra is found, and different membership functions are investigated to show the important influence on estimating fatigue life. Applicability of the method is validated by comparing with the experimental data. It is also found that the predicted fatigue life by the proposed method is more accurate and reliable than that by the traditional ones.

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Gan, Jin, Di Sun, Hui Deng, Zhou Wang, Xiaoli Wang, Li Yao, and Weiguo Wu. "Fatigue Characteristic of Designed T-Type Specimen under Two-Step Repeating Variable Amplitude Load with Low-Amplitude Load below the Fatigue Limit." Journal of Marine Science and Engineering 9, no. 2 (January 20, 2021): 107. http://dx.doi.org/10.3390/jmse9020107.

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In order to investigate the non-linear fatigue cumulative damage of joints in ocean structural parts, one type of low carbon steel Q345D was employed to prepare designed T-type specimens, and a series of fatigue experiments were carried out on the specimens under two-step repeating variable amplitude loading condition. The chosen high cyclic loads were larger than the constant amplitude fatigue limit (CAFL) and the chosen low cyclic loads were below the CAFL. Firstly, the S-N curve of designed T-type specimen was obtained via different constant amplitude fatigue tests. Then, a series of two-step repeating variable load were carried out on designed T-type specimens with the aim of calculating the cumulative damage of specimen under the variable fatigue load. The discussions about non-linear fatigue cumulative damage of designed T-type specimens and the interaction effect between the high and low amplitude loadings on the fatigue life were carried out, and some meaningful conclusions were obtained according to the series of fatigue tests. The results show that fatigue cumulative damage of designed T-type specimens calculated based on Miner’s rule ranges from 0.513 to 1.756. Under the same cycle ratio, the cumulative damage increases with the increase of high cyclic stress, and at the same stress ratio, the cumulative damage increases linearly with the increase of cycle ratio. Based on the non-linear damage evaluation method, it is found that the load interaction effect between high and low stress loads exhibits different damage or strengthening effects with the change of stress ratio and cycle ratio.

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47

Zhang, Hai Wei, Yu Ting He, Li Ming Wu, Hua Ding, and Qing Shao. "Life Degeneration Rule on 2A12 Aluminium Alloy with Corrosion and Fatigue Experiment." Applied Mechanics and Materials 80-81 (July 2011): 27–31. http://dx.doi.org/10.4028/www.scientific.net/amm.80-81.27.

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2A12 specimens are selected in pre-corrosion fatigue test to get the ground corrosion effect coefficient, namely C(t) curve. Then, combining with Miner linear cumulative damage theory, theoretical fatigue life model is established based on the simulated corrosion-fatigue interactive process. Compared with actual corrosion-fatigue interactive test, theoretical life in short interactive periods is almost same, but actual life is higher in long interactive periods. Afterwards, a modified model based on C(t) curve at different interactive periods is established. The calculation shows that the modified results are in good agreement with the corrosion-fatigue interactive test.

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48

Yun, Kyong-Ku, Dong-Ho Kim, Won-Kyong Jeong, and Chimoon Won. "Comparative Study of Cumulative Damage to Pavement Concrete under Splitting Tensile, Variable Amplitude Fatigue Loadings." Transportation Research Record: Journal of the Transportation Research Board 1914, no. 1 (January 2005): 24–33. http://dx.doi.org/10.1177/0361198105191400104.

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The purpose of this study was to compare the cumulative damage to pavement concrete under splitting tensile, variable amplitude fatigue loadings by splitting tensile and flexural tensile tests. The cumulative damage theories adapted in this study included the linear damage theory, the nonlinear damage theory, and the equivalent damage theory. The results were as follows. The sums of the cumulative damage were greater by the flexural tensile test than by the splitting tensile test, even though the difference between them was small in each load case. The sums of the cumulative damage at higher stress levels showed values farther from one than those at lower stress levels. This suggested that Miner's rule might be applied to plain concrete with little error, provided that the stress level remained low. The cumulative damage obtained by the nonlinear damage theory was closer to one than that obtained by the linear damage theory in all load cases except one. This indicated that nonlinear cumulative damage could consider the effects of the magnitude and the sequence of variable amplitude fatigue loadings. The theoretical results calculated from the equivalent damage theory were similar to the experimental results except in one case, even though the equivalent damage theory was simple. The results obtained by the splitting tensile test were equivalent to or better than those obtained by the flexural tensile test for application to the equivalent damage theory. Thus, the splitting tensile test and the equivalent damage theory could be used to estimate the damage and the remaining life of pavement concrete under variable amplitude fatigue loadings.

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Petaś, Michał, Krzysztof Mróz, and Krzysztof Doliński. "DAMAGE MODELING IN GRADED LAYER SYSTEM." Acta Mechanica et Automatica 7, no. 2 (June 1, 2013): 99–106. http://dx.doi.org/10.2478/ama-2013-0018.

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Abstract The simplified approach to the modelling of low cycle fatigue (LCF) of functionally graded materials (FGM) based on the continuum mechanics is presented. The fatigue damage model takes into account the mechanical part of the load and a constant service temperature. The concept of FGM as a particle-reinforced metal-matrix composite with gradual change of the reinforcement fraction is used. The FGM is considered as a material consisting of homogeneous layers containing different volume fractions of the reinforcement. The variation of the reinforcement fraction changes the material properties for each layer. The different material properties are obtained according to modified rule of mixture. Since the fatigue damage of metal matrix composites is strongly influenced by the inelastic deformation of the metallic matrix, the constitutive equations of LCF damage model are taken into consideration. The combined isotropic/ kinematic hardening model with linear behaviour of isotropic and kinematic parts of hardening is adopted. The damage scalar parameter is associated with the plastic energy dissipation which is used to update the material properties. The fatigue damage model presented in this paper is applied to the fatigue damage analysis of the cooling channel of thruster used in space shuttles and rockets.

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Sakane, Masao, Masateru Ohnami, Teruyoshi Awaya, and Nakao Shirafuji. "Frequency and Hold-Time Effects on Low Cycle Fatigue Life of Notched Specimens at Elevated Temperature." Journal of Engineering Materials and Technology 111, no. 1 (January 1, 1989): 54–60. http://dx.doi.org/10.1115/1.3226433.

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This paper describes the frequency and hold-time effects on high temperature low cycle fatigue for round notched specimens. Unnotched and notched specimens having different elastic stress concentration factors were fatigued under triangular and trapezoidal stress waves at frequencies ranging from 5 Hz to 0.0001 Hz at 873 K. The three specific fracture characteristics were observed: cycle dependent, time dependent, and cycle-time dependent. The respective notch sensitivity occurred in the respective fracture regime. The fatigue life of notched specimens was predicted from the elastic-plastic-creep cyclic FEM analysis using the linear damage rule and the strain range partitioning rule. Both the life prediction methods predicted the creep-fatigue life within almost a factor of two scatter band.

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Journal articles on the topic 'Linear damage rule (LDR)'

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