Stress Concentration Coefficient Research Articles

Development model and experimental characterization of residual stress of 3D printing PLA parts with porous structure

Porous structural materials are widely adopted in medical field owing to their excellent mechanical and physical properties. The 3D printing technology offers new opportunities for the preparation of porous structures. However, during 3D printing of porous structure, continuous rapid heating and cooling cycles lead to residual stress. Severe quality defects including cracks, warpage, and deformation caused by the residual stress have remained to be a problem. In this study, a development model of residual stress with porous structure was established using fused deposition molding (FDM), and the residual stress was found to have a linear correlation with stress concentration coefficient. Samples with different pass and aperture sizes were fabricated by FDM. The residual stresses developed on the surface of samples were evaluated by Raman spectroscopy. The relationship between pore size and surface residual stress was obtained, indicating that the variation in surface residual stress is consistent with stress concentration coefficient with the increase in pore size. Based on above results, the accuracy of theoretical modeling was confirmed. This development model of residual stress has guiding paramount for 3D printing porous structures.

Disaster Control of Roof Falling in Deep Coal Mine Roadway Subjected to High Abutment Pressure

The roof falling accident is a serious threat to the lives of miners in deep coal mining, especially when the coal mine is more than 1000 meters deep. In regard to the 5306 coalface in the Tangkou coal mine, Shandong, China, the depth of coal seam is 992.8 m and the stress concentration coefficient of the roadway surrounding rock is 3.33. This leads to a serious deformation of the roadway roof, thereby producing a high risk of the roof falling disaster. In this pursuit, based on the mechanical analysis of roadway roof subjected to a high abutment pressure, the mathematical expressions of the setting load and movable column length of supports were introduced. Furthermore, the stability control mechanism of the roadway roof was analyzed and the optimized support parameters of supports are provided. The results showed that the longtime effective support of the roadway roof required the strength and deformation coupling of supports and anchored surrounding rock. The support length of the belt roadway should be at least 57.7 m, with 0-30 m away from the coalface supported by hydraulic supports and 32-57.7 m supported by single props. In addition, the maximum setting load and movable column length of hydraulic supports were 21.67 MPa and 280.3 mm and 12.44 MPa and 177.1 mm for single props, respectively. By applying the optimized support parameters of supports to the belt roadway of the 5306 coalface, the effective control of the roadway roof and the disaster control of roof falling were realized.

Experiment on Corrosion Fatigue Life of Steel Strands under the Coupling Effects of Chloride Environment and Alternating Loads

Corrosion pits will lead to local stress concentration on the surface of steel strands and even shorter fatigue life and worse mechanical properties of steel strands. In order to explore the corrosion mechanics of steel strands to predict the fatigue life, accelerated salt spray corrosion test is carried out to simulate the corrosion laws of steel strands and record the changes of the corrosion degrees during the experiment, considering the coupling effects of alternating loads and chloride environment. Besides, the impact of stress amplitudes on the corrosion degrees of steel strands is quantitatively studied by the corrosion weight loss, and corroded steel strands in experiment are graded according to the corrosion weight loss to test the mechanical properties, respectively; the results show that the corrosion weight loss and tensile strength of steel strands obey the exponential distribution, and the relationship with elongation is linear. In addition, the relationships between the stress concentration coefficient and the pit length, width, and depth are obtained; with the three-dimensional linear regression theory, the accuracy of the regression model is verified by t-value test, laying a foundation for predicting the corrosion life of the cables.

Parametric study of the stress state of beams with round holes in pure bending

A parametric study of the stress state of a rectangular cross-section beam with round holes in pure bending is performed by the finite element method implemented in the ANSYS Mechanical APDL software package. Correction coefficients were obtained for normal stresses determined by strength of materials methods. The coefficients of stress concentration during bending were determined depending on the size of the holes, as well as the distance between them. The research results obtained can be used in practical problems of designing perforated beams.

Research on Stress Analysis and Control of Surrounding Rock of Trapezoidal Roadways Based on Complex Variable Theory

Aiming at the problem of the serious deformation of the mining roadways in the trapezoidal section of the coal mine, the method of combining theoretical analysis and field application is used to study the surrounding rock control method of the trapezoidal roadways. The conformal mapping function of the trapezoidal roadways is calculated by the theory of complex change, and then from the analytical solution of the tangential stress distributed in the surrounding rock of trapezoidal roadways which is under the influence of the bidirectional unequal pressure, homogeneous, isotropic, and elastic rock mass is obtained. Research studies show that the roof‐stress distribution of the trapezoidal roadways is uniform and the confining pressure is small, while the two sidewalls and the floor are opposite. The stress distribution of the two sidewalls and the floor varies greatly, and the stress concentration factor is large. The top corner of the trapezoidal roadways is basically not affected by stress concentration, but the stress concentration coefficient at the bottom corner is relatively large, and reinforcement measures are required in the roadway support. Based on the aforementioned research results, the multisupport scheme of “bolting with wire mesh and anchor cable + W‐type steel belt + joist steel shed support + anchor cable grouting” was proposed to the surrounding rock of trapezoidal roadways with large stress caused by mining influence, thus solving the actual mining problem.

Дослідження розтягу перфорованих пластин методом скінченних елементів

The problem of axial stretching of a plate with a double-periodic system of round holes arranged in a checkerboard pattern is considered. The specified problem is reduced to elasticity second problem for one period of plate, which was solved by the finite element method. As a result, the reduced elastic characteristics of the equivalent homogeneous orthotropic plate are found. The analysis of their behavior depending on dimensionless geometrical parameters is carried out. The area of variation of the geometric parameters was divided into two subareas. The behavior of the equivalent elastic characteristics in these areas is significantly different. It turned out that the double-periodic perforated plate shows significantly anisotropic behavior. The limit values of the Poisson's ratios can reach unity and, on the other hand, may be less than the original value. Dependences of the stress concentration coefficient on dimensionless geometrical parameters are obtained too. Performed comparative analysis of the obtained results with the results known from the literature, confirmed their adequacy.

Development of a Nonlinear Dependence for Determining the Stress-Strain State of the Pipeline-Composite Bandage System

The range of applications of polymeric materials in the oil and gas industries is expanding every year. For example, at present, a number of industrial enterprises are engaged in the production of various tape polymer composite structures that are used to repair pipelines. They are widely used due to the significant advantages of polymeric materials over steel such as low costs, low weight, corrosion resistance and strength. Moreover, most of the operated pipelines are about to reach their standard service life. In the course of technical diagnostics, a significant number of defects of mechanical origin from external influences are constantly revealed. Repair work on pipelines must fully restore the bearing capacity of the site. Therefore, the use of polymer materials for pipeline repair is an important task. Here, we propose to use polymer composite bandages, which will increase the overhaul period. However, a coherent methodology for choosing a material and calculating the required thickness of this structure is not available in the literature, and, therefore, the purpose of this work was to develop such a methodology, as well as to assess the stress-strain state of pipeline-bandage systems. The method presented in this work takes into account the possible anisotropy of the shroud material in the longitudinal and transverse directions and the possibility of plastic deformation of the pipeline material in the annular direction. This work is based on the following assumptions: (a) bilinear dependence of stress on deformation for steel; (b) plastic deformations of the band material are absent; and (3) absolute adhesion between the pipeline and the band. The paper presents the analysis of the market of polymeric materials for pipeline repair, their key properties, and the minimum thickness of the band made of these materials was calculated for various values of the stress concentration coefficient.

Study on Reasonable Layout of Upper Protective Layer for Prevention Rock Burst under Coal Seam Group with Close Quarters Conditions

To study the reasonable layout of upper protective layer for the prevention rock burst under coal seam group with close quarters conditions, a panel 3203 that belong to Zhongxing Colliery is taken as a typical engineering background. By means of on‐site survey, theoretical analysis, numerical simulation, and on‐site industrial applications, the reasonable layout of upper protective layer for prevention rock burst is studied. The results show that the overall stress environment of the floor under gob of upper protective layer is good, and the overall stress environment of the floor under the upper side of gob is also good, but the overall stress environment of the floor under the lower side of gob is bad. According to numerical simulation results, an L‐shaped stress superposition area is formed in the lower end of panel 3203 under the original layout scheme conditions, and the maximum stress concentration coefficient is about 2.8 in stage I and 4.0 in stage II. A new stress superposition area is formed at the middle to lower end part of advance mining face of panel 3203 for the stage II under the optimal layout scheme conditions, and the maximum stress concentration coefficient is about 2.4; the original L‐shaped stress superposition area is gone due the transfer and release of stress, and the optimal layout scheme has a very significant effect on the prevention and control of the subsequent rock burst accidents; the monitoring results of working resistance of hydraulic supports and surrounding rock deformation indicate that the overall pressure relief of the surrounding rock in advanced segment of 3205 tailgate can be effectively realized. The study conclusions provide theoretical foundation and a new guidance for preventing rock burst with similar engineering geological conditions.

Mining‐Induced Pressure‐Relief Mechanism of Coal‐Rock Mass for Different Protective Layer Mining Modes

The protective layer mining method of the traditional deep coal seam in has been confronted with great challenges, and it is difficult for coal and gas to be extracted together. Taking the occurrence conditions of III1 mining area of Luling Coal Mine located at Huaibei, China, as engineering background, the influence law of the lithology on stress environment in front of the stope was analyzed by theoretical analysis and numerical simulations. The mining‐induced mechanical effect of coal‐rock mass was studied under different protective layer mining modes. The results showed that the peak value of the advanced abutment pressure decreased with the decrease of lithologic strength under the same mining conditions. For simulated geological conditions, the stress concentration coefficient of soft rock and coal seam protective layer mining modes was 1.9 and 1.7, respectively. Under the mining stress path of different protective layers, the ratio of axial stress increase and confining pressure unloading in secondary unloading phase were 2 : 1 and 1.5 : 1, respectively. The axial stress‐strain curves of different protective layer mining modes had similar trends, and they had a volume expansion at the end of unloading (failure stage). In addition, it revealed the pressure‐relief antireflection mechanism of the protective layer mining. Under the same confining pressure condition, the peak stress and peak strain increased with the increase of loading and unloading velocity ratio. The reduced value of the confining pressure increased, while the volume expansion decreased at failure. The results were applied to III1 mining area in soft rock protective layer mining, which created the mining way of traditional coal seam protective layer. Furthermore, the gas control technology of soft rock protective layer working face was put forward for deep coal seam with low permeability and high gas, enriching the pressure‐relief mining theory of protective layer.

Mathematical models of rock mass affected by high pressure gradients

The authors propose to solve the problems connected with high pressure gradients using a model of a linearly elastic body with a structural parameter. The closed finite difference system of equations is formulated for plain strain deformation conditions. The problem on deformation of rock mass in the vicinity of an underground opening affected by mixed-type gravity-and-tectonic stress field is solved. It is demonstrated that addition of the structure in the solution changes the value of the stress concentration coefficient.

Dual-hazard control mechanism of burst-prone and spontaneous combustion coalface considering effect of retreat speed

For longwall top coal caving coalface characterized by strong rock burst tendency and high risk of spontaneous combustion, retreat speed is one of the key factors to induce the rock burst and spontaneous combustion of residual coal in goaf. A high retreat speed may lead to violent roof activity and impact dynamic load, which aggravates the tendency of rock burst. A low retreat speed may lead to spontaneous combustion of residual coal in goaf due to long time exposure to aerobic environment. In this study, the characteristics of overburden stress distributions, energy release laws, and the evolving laws of the oxidation and temperature rising zones in the goaf under different retreat speeds are analyzed. The spontaneous combustion coefficient of residual coal Qs is defined. What is more, the dual-hazard control mechanism of rock burst and spontaneous combustion of residual coal considering effect of retreat speed is put forward. The results show that the energy release of the stope with low retreat speed is stable, while that with high retreat speed appears obvious fluctuation phenomenon. With the increase of retreat speed, the relative stress concentration coefficient increases exponentially, while the spontaneous combustion coefficient of residual coal in goaf decreases exponentially. According to the curve of retreat speed and relative stress concentration coefficient and curve of retreat speed and spontaneous combustion coefficient, the reasonable operating interval and optimal operating point of retreat speed in strong rock burst tendency and easy spontaneous combustion coal seam can be determined.

Stability Analysis and Derived Control Measures for Rock Surrounding a Roadway in a Lower Coal Seam under Concentrated Stress of a Coal Pillar

Numerical simulations have often been used in close-distance coal seam studies. However, numerical simulations can contain certain subjective and objective limitations, such as high randomness and excessively simplified models. In this study, close-distance coal seams were mechanically modeled based on the half-plane theory. An analytical solution of the floor stress distribution was derived and visualized using Mathematica software. The principal stress difference was regarded as a stability criterion for the rock surrounding the roadway. Then, the evolution laws of the floor principal stress difference under different factors that influence stability were further examined. Finally, stability control measures for the rock surrounding the roadway in the lower coal seam were proposed. The results indicated the following: (1) The principal stress difference of the floor considers the centerline of the upper coal pillar as a symmetry axis and transmits radially downward. The principal stress difference in the rock surrounding the roadway gradually decreases as the distance from the upper coal pillar increases and can be ranked in the following order: left rib > roof > right rib. (2) The minimum principal stress difference zones are located at the center of the left and right “spirals,” which are obliquely below the edge of the upper coal pillar. This is an ideal position for the lower coal seam roadway. (3) The shallowness of the roadway, a small stress concentration coefficient, high level of coal cohesion, large coal internal friction angle, and appropriate lengthening of the working face of the upper coal seam are conducive to the stability of the lower coal seam roadway. (4) Through bolt (cable) support, borehole pressure relief, and pregrouting measures, the roof-to-floor and rib-to-rib convergence of the 13313 return airway is significantly reduced, and the stability of the rock surrounding the roadway is substantially improved. This research provides a theoretical basis and field experience for stabilizing the lower coal seam roadways in close-distance coal seams.

The Influence of Metallurgical Factors on Stress Corrosion Cracking of Various Steels in an Aggressive Chloride–Sulfide Environment

The influence of metallurgical factors on stress corrosion cracking of steels of different classes in an aggressive NACE solution at 25°C is analyzed. The dependences of the stress leading to the transition from active corrosion to the mechanism of hydrogen embrittlement (critical stress) on the yield stress and the coefficient of stress concentration are plotted. The relationship between the critical stress, conditional yield stress, and overstress values is revealed. It is concluded that the loss of corrosion resistance for unalloyed steels with a yield stress below 500 MPa is caused by an increase in the hydrogen concentration during deformation of the material in a corrosive environment.

Numerical simulation research on response characteristics of surrounding rock for deep super-large section chamber under dynamic and static combined loading condition

The stability control of surrounding rock for large or super-large section chamber is a difficult technical problem in deep mining condition. Based on the in-site geological conditions of Longgu coal mine, this paper used the dynamic module of FLAC3D to study the response characteristics of deep super-large section chamber under dynamic and static combined loading condition. Results showed that under the static loading condition, the maximum vertical stress, deformation and failure range are large, where the stress concentration coefficient is 1.64. The maximum roof-to-floor and two-sides deformations are 54.6 mm and 53.1 mm, respectively. Then, under the dynamic and static combined loading condition: (1) The influence of dynamic load frequency on the two-sides is more obvious; (2) The dynamic load amplitude has the greatest influence on the stress concentration degree, and the plastic failure tends to develop to the deeper; (3) With the dynamic load source distance increase, the response of surrounding rock is gradually attenuated. On this basis, empirical equations for each dynamic load conditions were obtained by using regression analysis method, and all correlation coefficients are greater than 0.99. This research provided reference for the supporting design of deep super-large section chamber under same or similar conditions.

Research on the temporal-spatial evolution of ground pressure at short-distance coal seams

To study the temporal-spatial evolution of ground pressure at short-distance coal seams, this paper studied the displacement law of overlying strata and the temporal-spatial evolution of ground stress by analog simulation experiments. The results show when the upper coal seam is mined, overlying strata of the stope form three zones: the caved zone, the fractured zone and the bending subsidence zone. The caved zone which subsided in the largest quantity showed an irregular subsidence curve. The fractured zone where the maximum subsidence amounts are basically located in the middle of the goaf had approximately parabolic subsidence curves. The bending subsidence zone underwent the least subsidence as it was controlled by the key layer. In the coal mining process, stress concentrated in front of both the opening-off cut and the working face. When the working face advanced to 150 m, bearing stress of the opening-off cut and the working face was up to 20 MPa, with a stress concentration coefficient of 1.98. When the lower coal seam was mined, the immediate roof kept caving as the mining proceeded, with no obvious initial weighting or periodic weighting in the main roof. Only the roof stress within the mining area demonstrated greater fluctuations as the mining moved on. Pressures at the opening-off cut and the stopping line remained high in the whole process, so it is suggested to pay special attention to pressure detection during the first cut and make sure the roof is well supported for the mining of lower coal seam.

Calculation of pipeline pressure testing for the reduction of residual stress in tee joints

Oil and gas pipeline accidents most frequently occur in output places and weld joints. Increased stress in weld joints can be explained by the presence of stress concentrators and residual welding stresses. Pipeline pressure testing can reduce the value of residual welding stresses. The article considers the method of calculating coefficients of stress concentration depending on the construction, geometrical dimensions and the type of tee welding joints. The authors calculated and proved that reinforcing tee joints by means of a coupling ring increases the number of welding joints and coefficient of stress concentration. The study theoretically proves the possibility of reducing residual stresses in tee joints choosing the right mode of pipeline pressure testing and defines the limits of changes in pipeline pressure testing which ensure plastic deformation of metal in welding joints alongside the elastic deformation of the main material of the tee joint.

Effect of polymer coating on stress concentration of sheet element with a hole

The paper considers a solution to the problem of determining the stress state of a flat metal plate having a round opening moulded with a reinforced polymer coating. To obtain the solution, methods of the theory of elasticity were used, in particular, the method of complex potentials. The opening with the reinforced polymer is presented as an elastic insert placed into the plate without interference. The plate is under uniaxial tensile stresses. The calculated dependences for normal and tangential stresses are obtained. The polar coordinate system is applied. The effect of the thickness of the reinforced polymer coating on the stress concentration coefficient near the round opening is investigated. A significant decrease in the concentration coefficient with increasing coating thickness is shown.

A practical model for efficient anti-fatigue design and selection of metallic materials: II. Parameter analysis and fatigue strength improvement

In the first paper, a Y-T-F model was proposed based on the restrictions of both strength and plasticity; the corresponding applications on the fatigue strength prediction have also been discussed. In this second paper, the emphasis will be put on the issues of fatigue strength improvement. Based on the primary form of the Y-T-F model, the parameters are further analyzed and quantified, to clarify the influences of various factors on fatigue strength. Firstly, the damage capacity C is proved to be sensitive to the elastic modulus E, which could change with the alloying components and nano-scaled grain boundaries; the increase of E would lead to the increasing C, thus increase the fatigue strength. Secondly, the microstructure characteristic coefficient a, as well as the yield strength σy and tensile strength σb in the crack initiation region could be influenced by the processing mode, grain size and microstructure uniformity of materials; the change of microstructure characteristics would affect the changing tendency of tensile strength--fatigue strength relation via varying the values of a, σy and σb. Thirdly, the damage weight coefficient ω is found to be a reflection of the fatigue strength declination induced by defects; the defect dimension D, the defect shape correlated stress concentration coefficient Kt, as well as the strengthening level of matrix materials σb are all corresponding factors. Quantified correlations between the above parameters and corresponding factors are comprehensively built up, hence obtaining the influences of either a single factor or multiple factors on fatigue strength. This further developed Y-T-F model would be helpful to clarify the direction of fatigue strength improvement, and contribute to the anti-fatigue design optimization of metallic materials.

Spallation damage mechanism of prefabricated elliptical holes by different transient incident waves in sandstones

The predictability of the failure process of underground rock mass located adjacent to a cavity is a key challenge in engineering practices. Therefore, the spallation failure of prefabricated elliptical holes in different orientations under various impact pressures was studied and analyzed by Hopkinson pressure bar. The failure process of long rod red sandstone was recorded in real-time by a high-speed camera during the experiment. The experimental results indicated that spallation did not necessarily occur in all the prefabricated holes, while the impact pressure had a great influence on the spall location of a defective rock mass. Also, the prefabricated holes located closer to the free surface experienced less damage under the impact of lower pressure than the holes located farther away from the surface. In addition, a finite element software, LS-DYNA, was employed to carry out equal-scale modeling and analysis of the circumferential stress variations in elliptical holes. The simulation results showed that the amplitude and wavelength of the stress wave would greatly affect the damage of elliptical defective holes and the initial defects weakened the integrity of the rock. Furthermore, the results showed that the larger the amplitude and wavelength, the lower the stress concentration coefficient of the rock in tensile failure and the most significant damage around the hole was observed at the peak tensile stress.

Physical simulation of upper protective coal layer mining with different coal seam inclinations

AbstractProtective coal layer (PCL) mining is a preferred regional method for preventing coal and gas outbursts; stress‐relief of PCL mining is the prerequisite of pressure‐relief gas drainage. In order to study the stress‐relief effect of PCL mining on protected coal seams and determine the protection scope of PCL mining under different inclinations, this paper uses physical simulations to study the stress‐relief law and deformation characteristics of the strata during upper PCL mining with a gentle inclination (25°), an intermediate inclination (45°), and a steep inclination (65°). The results show that as the coal seam dip increases, the degree of deformation and failure of the overburden strata gradually decreases, the severe subsidence and expansion area of the overburden strata tends to gradually develop in the uphill direction of the working face, and the floor strata underlying the protective seam significantly expand toward the goaf. However, the absolute value of the upward movement of the floor strata is much smaller than that of the roof strata; and the greater the dip angle, the greater the ratio of floor displacement to roof subsidence. The stress‐relief curve of the protected layer is approximately U‐shaped. As the inclination of the coal seam increases, the stress‐relief range decreases gradually. The maximum relief‐stress and the stress release coefficient of the protected layer initially increase and then decrease. The stress concentration coefficient of the protected coal seam initially increases first and then decreases in both uphill and downhill of the working face in the PCL. As the inclination increases, the stress‐relief angle of the downhill boundary initially increases and then decreases, while the stress‐relief angle of the uphill boundary decreases gradually. Our research results provide guidance for the delimitation of the protected scope of PCLs with different dip angles.