scholarly journals Experimental Investigation of the Mechanical Behavior of Layer-Crack Specimens under Cyclic Uniaxial Compression

Symmetry ◽  
2019 ◽  
Vol 11 (4) ◽  
pp. 465
Author(s):  
Wei-yao Guo ◽  
Feng-hai Yu ◽  
Yue Qiu ◽  
Tong-bin Zhao ◽  
Yun-liang Tan
Keyword(s):  
Cyclic Loading ◽  
Energy Density ◽  
Mechanical Behavior ◽  
Elastic Energy ◽  
Peak Stress ◽  
Dissipated Energy ◽  
Strengthening Effect ◽  
Input Energy ◽  
Rock Bursts ◽  
Number Of Cycles

It is generally acknowledged that the failure of the layer-crack structure is closely related to rock bursts (a layer-crack structure means a coal or rock rib that is cut by fractures that are parallel or sub-parallel to the surface of the rib). Understanding the mechanical behavior of the layer-crack structure under cyclic loading is beneficial for rock burst mitigation. This study experimentally investigated the influence of the geometry of vertical fissure (i.e., width, length and number) on the mechanical properties of layer-crack rock specimens. The results show that the sensitivity of parameters with respect to the geometry of the fissure from strong to weak is the number, length and width. First, the peak stress under cyclic loading increases by approximately 7.82%–17.35%, thereby exerting an obvious strengthening effect. Second, the fissure geometry slightly affects the energy evolution of the layer-crack specimen, i.e., the input energy density, elastic energy density and dissipated energy density all gradually increase with the increase of the number of cycles. However, when approaching a specimen failure, the increasing rates from quick to slow are the dissipated energy, input energy and elastic energy. Third, the damage variable of the layer-crack specimen shows a concave increasing trend with the increase of the number of cycles. When the number of cycles is equal, the damage increases with the increase of the number of fissures, but it decreases with the increase of the fissure length. Fourth, AE events occur shortly before specimen failures, but rapidly increase near the specimen failures. The accumulated AE events that lead to specimen failures decrease with the increase in the number of fissures. These results can provide some basic data for the research of rock bursts related to the failures of layer-crack structures.

scholarly journals Mechanical Properties and Energy Dissipation of Sandstone under Cyclic Loading-Unloading

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Shoudong Xie ◽  
Chang Su ◽  
Ying Xu ◽  
Qianqian Wang ◽  
Jian Wang ◽  
...  
Keyword(s):  
Cyclic Loading ◽  
Energy Density ◽  
Deformation Energy ◽  
Dissipated Energy ◽  
Stress Limit ◽  
Strength Change ◽  
Upper Limits ◽  
Total Strain Energy Density ◽  
Number Of Cycles ◽  
External Loads

For the bearing rock in geotechnical engineering, it is frequently affected by external loads. This paper adopted different upper limits of stress to carry out cyclic loading-unloading on the sandstone specimens to make them in different damage degrees and analyzed the mechanical mechanism of the damaged sandstone under different stresses. Then, the strength change and energy evolution of sandstone with different damage degrees were analyzed, and the damage of the loaded sandstone was quantitatively characterized. The experimental results showed that the strength and plastic deformation of sandstone after cyclic loading-unloading with different upper-stress limits gradually decreased with the increase of the upper-stress limit. In the loading-unloading stages of cyclic loading-unloading, the elastic modulus increased with the increase of the upper-stress limit. In general, as the number of cycles increased, the total strain energy density and elastic deformation energy density gradually increased, and as the upper-stress limit increased, both of them also increased. The damage factor of sandstone after cyclic loading-unloading, which was characterized by dissipated energy, increased in an S-shape with the increase of the upper-stress limit, and the growth rate first increased and then decreased.

scholarly journals Energy Evolution Characteristics and Distribution Laws of Rock Materials under Triaxial Cyclic Loading and Unloading Compression

2017 ◽  
Vol 2017 ◽  
pp. 1-16 ◽  
Author(s):  
Mingwei Zhang ◽  
Qingbin Meng ◽  
Shengdong Liu
Keyword(s):  
Cyclic Loading ◽  
Energy Density ◽  
Elastic Energy ◽  
Confining Pressure ◽  
Dissipated Energy ◽  
Energy Evolution ◽  
Elastic Energy Density ◽  
Evolution Characteristics ◽  
Storage Limit ◽  
Confining Pressures

To explore the influence of confining pressure on the energy evolution characteristics of loaded rocks, triaxial cyclic loading-unloading experiments on sandstones were carried out under 6 kinds of confining pressures using the axial loading and circumferential deforming control modes. Total energy density, elastic energy density, and dissipated energy density absorbed by rock specimens under different confining pressures were obtained. The confining pressure effect of the evolution process and distribution law in energy accumulation and dissipation was analyzed. Energy conversion mechanism from rock deformation to failure was revealed, and energy conversion equations in different stress-strain stages were established. The method of representing the rock energy accumulation, dissipation, and release behaviors by energy storage limit density, maximum dissipated energy density, and residual elastic energy density was established. The rock showed that, with the increase of confining pressure, the characteristic energy density of rock increased in the power exponent form, and the energy storage limit density increased faster than the maximum dissipated energy density. The greater the confining pressure was, the greater the proportion of elastic energy before peak was. It is indicated that the confining pressure increased the energy inputting intensity, improved the energy accumulating efficiency, and inhibited the energy releasing degree.

Analysis the characteristic of energy and damage of coal-rock composite structure under cycle loading

2021 ◽  
Author(s):  
Tan Li ◽  
Guangbo Chen ◽  
Zhongcheng Qin ◽  
Qinghai Li
Keyword(s):  
Cyclic Loading ◽  
Elastic Energy ◽  
Composite Structure ◽  
Calculation Method ◽  
Composite Structures ◽  
Damage Variable ◽  
Dissipated Energy ◽  
Height Ratio ◽  
Coal Rock ◽  
The Stability

Abstract The stability of coal-rock composite structures is of great significance to coal mine safety production. To study the stability and deformation failure characteristics of the coal-rock composite structure, the uniaxial cyclic loading tests of the coal-rock composite structures with different coal-rock height ratios were carried out. Lithology and coal-rock height ratio play an important role in the energy dissipation of coal-rock composite structures. The higher the coal-rock height ratio, the greater the average elastic energy and dissipated energy produced per cycle of coal-rock composite structures, the smaller the total elastic energy and dissipated energy produced in the process of cyclic loading. Based on the difference of damage variables calculated by dissipative energy method and acoustic emission method, a more sensitive joint calculation method for calculating damage variable was proposed. The joint damage variable calculation method can more accurately and sensitively reflect the damage of coal-rock composite structure under cyclic loading. The macroscopic crack first appears in the coal specimen in the coal-rock composite structure, the degree of broken coal specimens in the composite structure is inversely proportional to the coal-rock height ratio. The strength and deformation characteristics of the coal-rock composite structure are mainly affected by coal sample in the composite structure.

A Macromechanical Constitutive Model of Shape Memory Alloys Under Uniaxial Cyclic Loading

2012 ◽  
Vol 28 (3) ◽  
pp. 469-477 ◽  
Author(s):  
H. Lei ◽  
B. Zhou ◽  
Z. Wang ◽  
Y. Wang
Keyword(s):  
Cyclic Loading ◽  
Constitutive Model ◽  
Shape Memory Alloys ◽  
Mechanical Behavior ◽  
Shape Memory ◽  
Hysteretic Behavior ◽  
Test Results ◽  
Model Match ◽  
Number Of Cycles ◽  
The Relationship

AbstractIn this paper, the thermomechanical behavior of shape memory alloys (SMAs) subjected to uniaxial cyclic loading is investigated. To obtain experimental data, the strain-controlled cyclic loading-unloading tests are conducted at various strain-rates and temperatures. Dislocations slip and deformation twins are considered to be the main reason that causes the unique cyclic mechanical behavior of SMAs. A new variable of shape memory residual factor was introduced, which will tend to zero with the increasing of the number of cycles. Exponential form equations are established to describe the evolution of shape memory residual factor, elastic modulus and critical stress, in which the influence of strain-rate, number of cycles and temperature are taken into account. The relationship between critical stresses and temperature is modified by considering the cycling effect. A macromechanical constitutive model was constructed to predict the cyclic mechanical behavior at constant temperature. Based on the material parameters obtained from test results, the hysteretic behavior of SMAs subjected to isothermal uniaxial cyclic loading is simulated. It is shown that the numerical results of the modified model match well with the test results.

Energy Evolution and Water Immersion-Induced Weakening Mechanism in the Sandstone Roof of Coal Mines

2021 ◽  
Author(s):  
Wenjie Liu ◽  
Ke Yang ◽  
Shuai Zhang ◽  
Zhainan Zhang ◽  
Rijie Xu
Keyword(s):  
Energy Storage ◽  
Water Content ◽  
Elastic Energy ◽  
Coal Mines ◽  
Energy Utilization ◽  
Dissipated Energy ◽  
Plastic Energy ◽  
Storage Limit ◽  
Energy Share ◽  
Number Of Cycles

Abstract The instability of underground spaces in abandoned coal mines with water-immersed rocks is one of the main hazards hindering the geothermal energy utilization and ecological restoration of post-mining areas. This study conducted graded cyclic loading-unloading tests of five groups of sandstone samples with different water contents. The evolution laws of input, elastic, dissipated, damping, and plastic energies were explored in detail, taking into account the damping effect. The normalized plastic energy was used to characterize the damage evolution of sandstone samples, which failure modes were analyzed from both macroscopic and microscopic perspectives. The X-ray diffraction technique and scanning electron microscopy were used to reveal the softening mechanism of sandstone's strength and elastic energy storage limit. The results showed that the graded cyclic loading's input, elastic, and dissipated energies increased gradually. The elastic energy share first increased and then stabilized, while dissipated energy share variation had the opposite trend. In each cycle, the input energy was primarily stored in the form of elastic energy, while the dissipated energy was mainly used to overcome the damping of sandstone. When the normalized number of cycles approached unity, the plastic energy share sharply increased, while that of the dampening energy featured an abrupt drop. Such change indicated an inevitable instability failure of the water-bearing sandstone. As the water content increased, the pore water exhibited more substantial lubrication, water-wedging, and dissolution effects on mineral particles. As a result, the latter obtained a round form, and the elastic energy storage limit of the sandstone decreased. When the water content was increased, the damage factor of sandstone after the same number of cycles increased at a relatively higher rate, and there was a transition of failure mode from brittle to ductile.

scholarly journals Mechanical Behavior of Shale Rock under Uniaxial Cyclic Loading and Unloading Condition

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Baoyun Zhao ◽  
Dongyan Liu ◽  
Ziyun Li ◽  
Wei Huang ◽  
Qian Dong
Keyword(s):  
Cyclic Loading ◽  
Mechanical Behavior ◽  
Creep Behavior ◽  
Peak Stress ◽  
Creep Model ◽  
Cycle Number ◽  
Shale Rock ◽  
Cyclic Loading And Unloading ◽  
Residual Strains ◽  
Loading And Unloading

In order to investigate the mechanical behavior of shale rock under cyclic loading and unloading condition, two kinds of incremental cyclic loading tests were conducted. Based on the result of the short-term uniaxial incremental cyclic loading test, the permanent residual strain, modulus, and damage evolution were analyzed firstly. Results showed that the relationship between the residual strains and the cycle number can be expressed by an exponential function. The deformation modulus E50 and elastic modulus ES first increased and then decreased with the peak stress under the loading condition, and both of them increased approximately linearly with the peak stress under the unloading condition. On the basis of the energy dissipation, the damage variables showed an exponential increasing with the strain at peak stress. The creep behavior of the shale rock was also analyzed. Results showed that there are obvious instantaneous strain, decay creep, and steady creep under each stress level and the specimen appears the accelerated creep stage under the 4th stress of 51.16 MPa. Based on the characteristics of the Burgers creep model, a viscoelastic-plastic creep model was proposed through viscoplastic mechanics, which agrees very well with the experimental results and can better describe the creep behavior of shale rock better than the Burgers creep model. Results can provide some mechanics reference evidence for shale gas development.

scholarly journals Experimental Investigation on the Energy Storage Characteristics of Red Sandstone in Triaxial Compression Tests with Constant Confining Pressure

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Liuliu Li ◽  
Fengqiang Gong
Keyword(s):  
Energy Density ◽  
Elastic Energy ◽  
Quadratic Function ◽  
Input Energy ◽  
Compression Tests ◽  
Red Sandstone ◽  
Elastic Energy Density ◽  
Deep Rock ◽  
Confining Pressures ◽  
Input Energy Density

The elastic energy stored in deep rock in three-dimensional stress environment is the energy source of rockburst. To investigate the energy storage characteristics of deep rock under different confining pressures, a series of triaxial single-cyclic loading-unloading compression tests were conducted on red sandstone specimens under eight confining pressures. The input energy density, elastic energy density, and dissipative energy density of the specimen in axial, circumferential, and total directions can be obtained by the area diagram integration method. The results show that the input energy density in the axial direction accounts for the largest logarithmic proportion of the total input energy density, and the relationship between all energy density parameters and unloading level can be described by quadratic function. In the axial direction, there is a linear function relationship among elastic energy density, dissipative energy density, and input energy density. In the circumferential direction, there is a quadratic function relationship among elastic energy density, dissipative energy density, and input energy density. For the total energy density parameters of the rock specimen, the relationship among elastic energy density, dissipative energy density, and input energy density conforms to the quadratic function. According to the above correlation function, the elastic energy stored in deep rock under different confining pressures can be accurately obtained, which provides a foundation for studying the mechanism of rockburst under three-dimensional unloading from the energy perspective.

scholarly journals Energy Analysis Method for Uniaxial Compression Test of Sandstone under Static and Quasi-Dynamic Loading Rates

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Zhixi Liu ◽  
Guangming Zhao ◽  
Xiangrui Meng ◽  
Ruofei Zhang ◽  
Dong Chunliang ◽  
...  
Keyword(s):  
Cyclic Loading ◽  
Uniaxial Compression ◽  
Compression Test ◽  
Elastic Energy ◽  
Loading Rate ◽  
Uniaxial Compression Test ◽  
Input Energy ◽  
Analysis Method ◽  
Compression Tests ◽  
Loading Rates

To investigate the energy evolution characteristics of sandstone under static-quasi-dynamic loading rates (1.0 × 10−3, 5.0 × 10−3, 1.0 × 10−2, 5.0 × 10−2, and 1.0 × 10−1 mm/s), the uniaxial compression tests, the uniaxial cyclic loading-unloading tests, and the uniaxial incrementally cyclic loading-unloading tests were conducted under five different loading rates. Through analysis of the elastic energy of the uniaxial cyclic loading-unloading test and the uniaxial incremental cyclic loading-unloading test, show that the impact of the loading rate and the cycle numbers on the elastic energy is less. Hence, we can deem that when the loads of the uniaxial incremental cyclic loading-unloading test and the uniaxial compression test are equal, the elastic energy of the two also equals. The energy in the uniaxial compression tests analyzed by the uniaxial incrementally cyclic loading-unloading test show that elastic energy increased linearly when the input energy increased under different loading rates. Through the linear energy storage law and the uniaxial incremental cyclic loading and unloading test, it is possible to analyze the energy in the uniaxial compression test at any loading rates. The results show that the greater the loading rate, the greater the peak elastic energy and peak input energy. But when the load is equal, the greater the loading rate, the smaller the input energy and elastic energy. Compared with traditional methods, the new energy analysis method is accurate and simple. Meanwhile, based on energy dissipation, the damage of rock during uniaxial compression tests was studied.

Mechanical Damage to the Intervertebral Disc Annulus Fibrosus Subjected to Cyclic Tensile Loading

2003 ◽  
Author(s):  
David A. Ryan ◽  
Jeffrey J. MacLean ◽  
James C. Iatridis
Keyword(s):  
Cyclic Loading ◽  
Material Properties ◽  
Annulus Fibrosus ◽  
Permanent Deformation ◽  
Mechanical Damage ◽  
Quantitative Relationship ◽  
Peak Stress ◽  
Tensile Loading ◽  
Number Of Cycles

Damage progression in the circumferential direction of the disc annulus is likely to occur in vivo in response to cyclic loading with associated degradation in tensile material properties, yet this information is not available in the literature. We hypothesize that damage of the annulus will be increased by the number of cycles and magnitude of strain applied to the tissue. Therefore, the objective of this study is to obtain a quantitative relationship between number of cycles and magnitude of tensile strain and damage on the annulus fibrosus. Damage to the annulus is assessed through measurement of permanent deformation (% elongation) and peak stress in the tissue under cyclic loading conditions.

The Qualification of BWR Steam Dryer Weldments Exposed to Cyclic Loading Using Finite Element Methods

2013 ◽  
Author(s):  
Michael R. Breach
Keyword(s):  
Finite Element ◽  
Cyclic Loading ◽  
Stress Field ◽  
Finite Element Methods ◽  
Fatigue Cracks ◽  
Failure Process ◽  
Peak Stress ◽  
Point Of View ◽  
Nominal Stress ◽  
Number Of Cycles

The qualification of welds other than full penetration groove welds exposed to cyclic loading using finite element methods requires an understanding of the basis behind classical methodologies. These methodologies usually address nominal stresses. The nominal stress (S-N) method was the first approach developed to try to understand this failure process and is still widely used in applications where the applied stress is nominally within the elastic range of the material and the number of cycles to failure is large. From this point of view, the nominal stress approach is best suited to that area of the fatigue process known as high cycle fatigue. Cracks and discontinuities will cause stress redistribution and concentrations leading to secondary and peak stresses additive to the nominal stress when referencing the S-N curves. Therefore, fundamental to the qualification of weldments of components and structures is the determination of the nominal stress field; however, this can be problematic for several reasons: • Secondary, Peak stress arising from structural discontinuities can mask the actual nominal stress field. • There may be an insufficient number of elements and/or integration points through the thickness to rely on linearization techniques, to separate the nominal stresses from the secondary and peak stresses due to the high cost of using bricks or tetrahedrons. • In complex shell structures, the nominal stress field in weldments that satisfies equilibrium against externally applied loads is not readily distinguished; this is due to the shear preponderance of mesh sensitive discontinuities. Herein, is a summary of methods to address the aforementioned problem and guidance in determining the true peak stresses and their qualification. Methods documented in ASME BPV Code Section VIII Div. 2, and various papers are compared. These methods will be used to assess existing methods that may be used in the industry. ASME BPV Code Section III Subsections NG and NB will be used as a basis to classify and qualify the weldment stresses.

Sign in / Sign up

Export Citation Format

Share Document