scholarly journals Indices to Determine the Reliability of Rocks under Fatigue Load Based on Strain Energy Method

2019 ◽  
Vol 9 (3) ◽  
pp. 360 ◽  
Author(s):  
Huanran Fu ◽  
Sijing Wang ◽  
Xiangjun Pei ◽  
Weichang Chen
Keyword(s):  
Elastic Modulus ◽  
Energy Density ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Total Strain ◽  
Fatigue Load ◽  
Total Strain Energy ◽  
Rock Engineering ◽  
Rock Types ◽  
Total Strain Energy Density

Rock is a complicated material which includes randomly distributed grains and cracks. The reliability of rocks under fatigue load is very important during the construction and operation of rock engineering. In this paper, we studied the deformation and failure process of red sandstone under fatigue load in a laboratory based on a new division method of strain energy types. The traditional elastic strain energy density is divided into two categories: grain strain energy density and crack strain energy density. We find that the proportion of the grain strain energy density to total strain energy density can be used as an indicator of rock yield and the proportion of the crack strain energy density to total strain energy density can be used as an indicator of rock failure. Subsequently, through extensive literature research, we found that such a phenomenon is widespread. We also find the proportion of grain strain energy density to total strain energy density when yielding is affected by rock types and elastic modulus. The proportion of crack strain energy density to total strain energy density in the pre-peak stage is stable and not affected by rock types and elastic modulus, which is about 0.04~0.13. These findings should be very helpful for rock stable state judging in rock engineering.

A Model to Predict Fatigue Life of Concrete Based on Total Strain Energy Density

2011 ◽  
Vol 99-100 ◽  
pp. 1018-1022
Author(s):  
Li Zhang ◽  
Si Chu Gong ◽  
Xu Dong Ma
Keyword(s):  
Fatigue Life ◽  
Energy Density ◽  
Fatigue Damage ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Cumulative Damage ◽  
Total Strain ◽  
Total Strain Energy ◽  
Cumulative Fatigue Damage ◽  
Total Strain Energy Density

A law on the cumulative damage is presented basing on total strain energy induced as damage parameter to calculate the cumulative damage when the specimens of concrete subjected to fatigue loading.Then the maximum of critical cumulative damage and location of production are determined basing on the equation of cumulative fatigue damage combined with experimental result through using the finite element analysis and the critical plane method in fatigue analysis.The relation equation between the standardized critical total strain energy density and stress level is obtained by considering the impact of loading level.The fatigue life of specimens can be predicted by combining the equation of cumulative fatigue damage with the relation equation of damage and stress level and the prediction results coincide with experimental results very well.

Strain Energy Approach for Axial and Torsional Fatigue Life Prediction in Aged NiCrMoV Steels

2003 ◽  
Vol 17 (08n09) ◽  
pp. 1665-1670
Author(s):  
Gee Wook Song ◽  
Jung Seob Hyun ◽  
Jeong Soo Ha
Keyword(s):  
Fatigue Life ◽  
Energy Density ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Multiaxial Fatigue ◽  
Density Model ◽  
Total Strain ◽  
Total Strain Energy ◽  
Torsional Fatigue ◽  
Total Strain Energy Density

Axial and torsional low cycle fatigue tests were performed for NiCrMoV steels serviced low-pressure turbine rotor of nuclear power plant. The results were used to evaluate multiaxial fatigue life models including Tresca, von Mises and Brown and Miller's critical plane. The fatigue life predicted by the multiaxial fatigue models didn't correspond with the experimental results in small strain range. We proposed the total strain energy density model to predict torsional fatigue life from axial fatigue data. The total strain energy density model was found to best correlate the experimental data with predictions being within a factor of 2.

A Total Strain Energy Density Theory for Cumulative Fatigue Damage

1988 ◽  
Vol 110 (1) ◽  
pp. 36-41 ◽  
Author(s):  
K. Golos ◽  
F. Ellyin
Keyword(s):  
Energy Density ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Elastic Strain Energy ◽  
Cumulative Damage ◽  
Total Strain ◽  
Pressure Vessel Steel ◽  
Total Strain Energy ◽  
Vessel Steel ◽  
Total Strain Energy Density

A unified theory based on the cyclic strain energy density criterion is presented first. It is shown that the fatigue failure in both low and high-cycle regimes, and cumulative damage and loading sequence, can all be expressed in terms of a single damage parameter. The damage criterion is based on the total strain energy density per cycle (sum of the plastic and tensile elastic strain energy). Both the crack initiation and propagation phases of the fatigue life are embodied in this approach. A systematic investigation into the cyclic, fatigue and cumulative damage behavior of the pressure vessel steel, A-516 Gr. 70, is subsequently presented. The comparison between the predicted and experimental results is found to be good.

Analysis of Multi-Stable Architectures for Morphing Structures

2020 ◽  
Author(s):  
Anil Erol ◽  
Jeffery Baur
Keyword(s):  
Energy Density ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Compressive Loading ◽  
Total Strain ◽  
Total Strain Energy ◽  
Wide Range ◽  
Unit Cells ◽  
Mechanical Logic ◽  
The Individual

Abstract The field of multi-stable structures has been steadily growing due to a wide range of potential applications including energy harvesting, MEMS, and mechanical logic. This work focuses on utilizing elastic energy trapping and snap-through phenomena of bistable unit cells to design a latticed, hierarchical multi-stable cylinder that can articulate up to 30 degrees from its center axis. The employment of bistable elements is hypothesized to reduce the total strain energy required to articulate the cylinder, and yield faster responses with the snap-through. While multi-stable cylinders exist in previous studies, there have been no previous attempts at studying different modes of deformation beyond compressive loading. Thus, the current work presents a new problem regarding the effects of bistable elements in a latticed cylinder that is carrying tensile, compressive, and shear loadings and exhibiting large displacements as the cylinder is articulated.. The total strain energy density of the articulating cylinder is investigated as a function of the heights of the unit cells, which aids in determining an ideal height for the design that minimizes the strain energy density. Results show that the strain energy of an articulating cylinder can be minimized with the use of multi-stability, and that a multi-stable cylinder can require up to three times less loads to maintain desired articulation compared to a mono-stable structure. These results will lead to future works on further optimizing the articulating cylinder by varying additional parameters like the individual heights of rows, the thicknesses of unit cell beams, the strain energy density, and the initial loading threshold for articulation. In addition, the work in this study can yield methodologies for designing arbitrarily morphing skins beyond just cylindrical geometries.

scholarly journals Effect of Heat Treatment on the Cyclic Deforming Behavior of As-Extruded ZA81M Magnesium Alloy

Metals ◽  
2022 ◽  
Vol 12 (1) ◽  
pp. 146
Author(s):  
Tianjiao Luo ◽  
Jianguang Feng ◽  
Chenye Liu ◽  
Cong Wang ◽  
Yingju Li ◽  
...  
Keyword(s):  
Heat Treatment ◽  
Fatigue Life ◽  
Magnesium Alloy ◽  
Energy Density ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Solution Treatment ◽  
Second Phase ◽  
Total Strain Energy ◽  
Total Strain Energy Density

In the present work, the effect of heat treatment on the cyclic deformation behavior of as-extruded ZA81M magnesium alloy was investigated. Two heat treatment conditions were applied to the as-extruded ZA81M alloy: a solution treatment (T4, 653 K for 40 h and quenched with 298 K water) and a solution treatment plus artificial aging (T6, 348 K for 32 h (pre-aging at low temperature) and 453 K for 8 h (the second aging) and quenched with 353 K water). The results showed that the fine second phase precipitated after the aging treatment, the tensile yield strength of the T6-treated specimens increased, and the stress amplitude of T6-treated specimens was always higher than that of T4-treated specimens. The T6-treated specimens had a higher total strain energy density and a shorter fatigue life at a strain amplitude of 0.4%, and a lower total strain energy density and a longer fatigue life at a strain amplitude of 0.8%, compared to the T4-treated specimens. All fatigue cracks of the T4 and T6 ZA81M alloy were initiated at the second phase or along the grain boundary and propagated perpendicular to the loading direction.

scholarly journals Low Cycle Fatigue Life Prediction Model of 800H Alloy Based on the Total Strain Energy Density Method

Materials ◽  
2019 ◽  
Vol 13 (1) ◽  
pp. 76 ◽  
Author(s):  
Wei Zhang ◽  
Tao Jiang ◽  
Liqiang Liu
Keyword(s):  
Prediction Model ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Life Prediction ◽  
Low Cycle Fatigue ◽  
Fatigue Life Prediction ◽  
Cycle Fatigue ◽  
Total Strain Energy ◽  
Total Strain Energy Density ◽  
Life Prediction Model

In this paper, a high-temperature low-cycle fatigue life prediction model, based on the total strain energy density method, was established. Considering the influence of the Masing and non-Masing behavior of materials on life prediction, a new life prediction model was obtained by modifying the existing prediction model. With an 800H alloy of the heat transfer tube of a steam generator as the research object, the high-temperature and low-cycle fatigue test was carried out at two temperatures. The results show that the predicted and experimental results are in good agreement, proving the validity of the life prediction model.

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