SEMI-ELLIPTIC SURFACE CRACK IN AN ELASTIC SOLID WITH FINITE SIZE UNDER IMPACT LOADING

In this paper a semi-elliptic surface crack problem in an elastic solid of finite size under impact loading is investigated. An analysis is performed by means of fracture dynamics and the finite element method, and a three-dimensional finite element program is developed to compute the dynamic stress intensity factor. The results reveal that the effects of the solid＇s boundary surface, crack surface, material inertia and stress wave interactions play significant roles in dynamic fracture.

A theoretical model of semi-elliptic surface crack growth

A theoretical model of semi-elliptic surface crack growth based on the low cycle strain damage accumulation near the crack tip along the cracking direction and the Newman-Raju formula is developed. The crack is regarded as a sharp notch with a small curvature radius and the process zone is assumed to be the size of cyclic plastic zone. The modified Hutchinson, Rice and Rosengren （HRR） formulations are used in the presented study. Assuming that the shape of surface crack front is controlled by two critical points： the deepest point and the surface point. The theoretical model is applied to semi-elliptic surface cracked A1 7075-T6 alloy plate under cyclic loading, and five different initial crack shapes are discussed in present study. Good agreement between experimental and theoretical results is obtained.

STOCHASTIC PROPAGATION OF SEMI-ELLIPTICAL SURFACE CRACK

The semi-elliptical surface crack growth of structural components with uncertain material resistance under random loading is studied by using the stochastic averaging principle.The FPK equation governing the transition probability density function of crack lengths is derived.The analytical solution of the FPK equation for the case of that the equations for the crack growth in the surface and depth directions are uncoupled is obtained.The effects of the parameters of the stress process and of the material property on the behavior of semi-elliptical fatigue crack growth of the components with deterministic resistance to crack growth in the stationary Gaussian stress process are examined.The comparison of the analytical result with digital simulation shows the effectiveness of the present method.

Evaluation of the Formula of Stress Intensity Factor K_1 for Semi-Elliptical Surface Crack

The stress intensity factor (SIF) of the semi elliptical surface crack in the finite body under extensional stress is sclculated by using the FEM software ANSYS release 5.5. The correction factor M f of SIF at different point along the front of the crack is determined.The relation between M f and the semi elliptical shape a/c , the relative crack depth a/b , the variation of angle θ , the relative crack width 2c/w and the relative height width ratio h/w are calculated respectively. Finally the application range and the modification of the engineering formula about SIF is proposed.

Weight Function Method for Stress Intensity Factor of Internal Surface Semi-elliptical Crack in Elliptical Holes

The hatches for inspecting are usually designed with elliptical holes in airplane structures, so computation of the stress intensity factor of three dimensional crack at elliptical holes is pivotal for damage tolerance analysis of these structures. In this paper, weight function is derived for a two dimensional through cracks at elliptical holes by applying a compounding method. Stress intensity factor formulas for an internal surface semi-elliptical crack in elliptical holes are obtained wing the three dimensional weight function method. Stress intensity factors for an internal surface semi-elliptical crack in elliptical holes under remote tension are computed. At the same time, research on how radius of curvature for elliptical holes affect stress intensity factors was conducted. Stress intensity factors decrease when radius of curvature increases. Some results and conclusions which are of practical value are given.

Effect of particle size of single-crystalline hierarchical ZSM-5 on its surface mass transfer in n-heptane catalytic cracking

Single-crystalline hierarchical ZSM-5 zeolites with different particle sizes(namely 100,140,and 200 nm)were successfully prepared by adjusting the amount of tetrapropylammonium hydroxide(TPAOH),and investigated in n-heptane catalytic cracking reaction.Diffusional measurements by zero-length column(ZLC)method showed that the apparent diffusivities of n-heptane decreased with the reduction of particle size,indicating the existence of surface barriers.Moreover,with the decrease of particle size,the additional diffusion path length increased,which meant the influence of surface barriers became more apparent.Despite the change of surface barriers,the intracrystalline diffusion still dominated the overall diffusion.Catalytic performance showed that the zeolite with smaller particle size had better stability.

Fatigue crack propagation of 7050 aluminum alloy FSW joints after surface peening

The surface composite modification of the 7050 aluminum alloy friction stir-welded joints was performed by shot peening(SP)/multiple rotation rolling(MRR)and MRR/SP,and the fatigue performance of the nugget zone(NZ)was investigated.The results demonstrated that the fatigue life of SP/MRR samples is longer than that of MRR/SP.On the plane 150μm below the surface.The grains with high angle grain boundary account for 71.5%and 34.3%for MRR/SP and SP/MRR samples,respectively.The crack propagation path of the MRR/SP is transgranular and intergranular,and it is intergranular for the MRR/SP.Multitudinous fatigue striations and some voids appeared at the fracture during the stable crack propagation stage.However,fatigue striations for SP/MRR are with smaller spacing,fewer holes,and smaller size under SP/MRR compared with fatigue fracture of MRR/SP.The differences in fatigue properties and fracture characteristics of the NZ are related to the microstructure after the two combined surface modifications.

Surface motion of a semi-elliptical hill for incident plane SH waves

A closed-form analytical solution of surface motion of a semi-elliptical cylindrical hill for incident plane SH waves is presented. Although some previous analytical work had already dealt with hill topography of semi-circular and shallow circular, our work aims at calculating surface motion of very prolate hill for high incident frequency, and explaining the special vibrating is checked by boundary conditions, numerical results for and some conclusions are obtained. properties of very prolate hill. Accuracy of the solution surface motion of oblate and prolate hills are calculated,

Formation and control of the surface defect in hypo-peritectic steel during continuous casting:A review

Hypo-peritectic steels are widely used in various industrial fields because of their high strength,high toughness,high processability,high weldability,and low material cost.However,surface defects are liable to occur during continuous casting,which includes depression,longitudinal cracks,deep oscillation marks,and severe level fluctuation with slag entrapment.The high-efficiency production of hypo-peritectic steels by continuous casting is still a great challenge due to the limited understanding of the mechanism of peritectic solidification.This work reviews the definition and classification of hypo-peritectic steels and introduces the formation tendency of common surface defects related to peritectic solidification.New achievements in the mechanism of peritectic reaction and transformation have been listed.Finally,countermeasures to avoiding surface defects of hypo-peritectic steels duiring continuous casting are summarized.Enlightening certain points in the continuous casting of hypo-peritectic steels and the development of new techniques to overcome the present problems will be a great aid to researchers.

Structural Surface Crack Monitoring Method Based on Electrical Potential Technique and Modern Surface Technology

Crack monitoring plays a great role in modern structural health monitoring, however, most of the conventional crack inspections have disadvantages in terms of the accuracy, expense, reliability, durability and level of instrumentation required. Thus, development of a simple and reliable crack inspection technique that allows continuous monitoring has been desired. In this paper, electrical potential technique and modern surface technology are employed together to develop a new structural surface crack monitoring method. A special crack monitoring coating sensor based on electrical potential technique was deposited on the hot spot of the structure by modern surface technology. The sensor consists of three layers： the isolated layer, the sensing layer and the protective layer. The isolated layer is prepared by anodic oxidation technology, the sensing layer is made of ion plated copper, and the protective layer is made of silicone. The thickness of each layer is at micrometer magnitude. The electrical conductivity of the sensor is very stable, and the fatigue performance of the specimen with or without coating sensor is nearly unchanged. The crack monitoring experiment result shows that there are two sudden rises of the coating sensor electrical potential values, corresponding to different stages of the crack initiation and propagation. Since the width of the surface coating sensor is only 0.5 mm, this crack monitoring sensor can detect the propagation of cracks less than 0.5 mm long. The method proposed takes the simplicity of electrical potential technique and can monitor surface crack of nearly all kinds of structures precisely. The results of this paper may form the basis of a new crack monitoring system.

Study on magnetic memory signals of medium carbon steel specimens with surface crack precut during loading process

Static tensile test and tensile-tensile fatigue test of medium carbon steel sheet specimens with surface crack precut were performed on MTS810 hydraulic testing machine to clear the meaning of the point of Hp(y) value zero. Magnetic memory signals were measured during the test process. The results show that only one point of Hp(y) zero value exists in all measured magnetic signal curves during the loading process, which should be a sign of intersection of positive-negative magnetic poles after magnetic ordered state appears and does not indicate the position of surface crack precut. The analysis shows that the surface crack precut can not interrupt the magnetic ordered state occurred during the test completely, hence its Hp(y) value is not zero. However, the crack extending to a penetrated defect at the instant of specimen′s fracture leads to the discontinuance of magnetic ordered state.

Selection of Judging Indicators for Surface Morphology of Soil Crack under Different Development Degrees in Yuanmou Arid-Hot Valley Region

Quantification of complicated surface morphology of soil crack is a prerequisite and key to soil crack study. This paper takes soil crack quads in Yuanmou arid-hot valley region as examples, selecting several morphological indicators, and analyzes the soil crack＇s morphological features under various development degrees. By statistic analysis, three quantitative indicators for surface morphology are selected, namely soil crack area density, area weighted mean fractal dimension and connectivity index R, which can not only express the development intensity of soil cracks, but also effectively describe its morphological complexity and connectivity. The research results set a good base for the establishment of soil crack assessment system in Yuanmou arid-hot valley region.

Longitudinal surface cracks of thin slabs

Based on the production practice of medium carbon thin slabs in the CSP plant,the reasons and influencing factors for the formation of longitudinal cracks were investigated,and some industrial measures were taken to eliminate the cracks.The results show that the efficient solutions to reduce longitudinal cracks are improving the performance of the mold powder,stabilizing the mold heat flux,and maintaining a proper taper of the mold during casting.Proper pouring temperature and secondary cooling also play important roles in preventing longitudinal surface cracks.

Surface Morphology of Soil Cracks in Yuanmou Dry-hot Valley Region,Southwest China

Surface morphology of soil cracks is one of the important factors influencing the water evaporation rate in cracked soil in Yuanmou Dry-hot Valley Region,Southwest China. Quantitative study of the complicated surface morphology of soil cracks is a prerequisite for further studies of soil-cracking mechanisms. The present paper establishes a quantitative indicator system by application of concepts and methods originating from Fractal Geometry and Network Analysis. These indicators can effectively express the complicated features of soil-crack network structure. Furthermore,a series of values related to soil-crack morphology was obtained by image processing on field photos of soil-crack quads,and gradation criteria for the degree of development of soil cracks were determined. Finally,the changes in values of the morphological indicators under different degrees of development were analyzed in detail. Our results indicate that (1) the degree of development of soil cracks can be divided into five grades,i.e.,feeble development,slight development,medium development,intensive development and extremely intensive development; (2) the values of the indicators change predictably with increasing degree of development of soil cracks. The area density (Dc) increases,and both the area-weighted mean ratio of crack area to perimeter (AWMARP),which reflects the intensity of cracking,and the index r,which is related to the connectivity of a soil crack,grow uniformly (albeit with different forms). AWMRAP increases at a geometric rate while r shows logarithm-mic growth,indicating a gradual increase in theconnectivity of a soil crack. Nevertheless,the area-weighted mean of soil-crack fractal dimension (AWMFRAC) shows a decreasing trend,indicating a gradual decline in the complexity of cracks as area density increases.

Coupling control on pillar stress concentration and surface cracks in shallow multi-seam mining

In order to ensure safe mining and reduce surface damage in shallow multi-seam mining,the failure characteristics of interburden strata with different coal pillars offset distances between pillars in the upper and lower seams,the distribution characteristics of stress concentration in coal pillars,and the development characteristics of stratum cracks and subsidence were investigated by physical and UDEC2D simulation.Meanwhile,the effect of different coal pillar offset distances on stress concentration of coal pillar and development of stratum cracks were studied.Based on those results,a formula for safe mining and reducing surface damage was established,which provided a theoretical basis for safe and environmentally friendly mining in shallow multi-seam.According to the results,the optimal coal pillar offset distance(the side to side horizontal distance of the upper and lower coal pillars)between the upper and lower coal seams was developed to reduce the stress concentration of coal pillars and surface damage.The results of this study have been applied in Ningtiaota coal mine and have achieved good results in safe and environmentally friendly mining.

Free torsional vibration of cracked nanobeams incorporating surface energy effects

This paper investigates surface energy effects, including the surface shear modulus, the surface stress, and the surface density, on the free torsional vibration of nanobeams with a circumferential crack and various boundary conditions. To formulate the problem, the surface elasticity theory is used. The cracked nanobeam is modeled by dividing it into two parts connected by a torsional linear spring in which its stiffness is related to the crack severity. Governing equations and corresponding boundary conditions are derived with the aid of Hamilton＇s principle. Then, natural frequencies are obtained analytically, and the influence of the crack severity and position, the surface energy, the boundary conditions, the mode number, and the dimensions of nanobeam on the free torsional vibration of nanobeams is studied in detail. Results of the present study reveal that the surface energy has completely different effects on the free torsionl vibration of cracked nanobeams compared with its effects on the free transverse vibration of cracked nanobeams.

Fractal characteristics of surface crack evolution in the process of gas-containing coal extrusion

In this paper, simulated experiment device of coal and gas outburst was employed to perform the experiment on gas-containing coal extrusion. In the experiment, coal surface cracks were observed with a high-speed camera and then the images were processed by sketch. Based on the above description, the paper studied the fractal dimension values from different positions of coal surface as well as their changing laws with time. The results show that there is a growing parabola trend of crack dimension value in the process of coal extrusion. Accordingly, we drew the conclusion that extruded coal crack evolution is a process of fractal dimension value increase. On the basis of fractal dimension values taken from different parts of coal masses, a fractal dimension of the contour map was drawn. Thus, it is clear that the contour map involves different crack fractal dimension values from different positions. To be specific, where there are complicated force and violent movement in coal mass, there are higher fractal dimension values, i.e., the further the middle of observation surface is from the exit of coal mass, and the lower the fractal dimension value is. In line with fractal geometry and energy theory of coal and gas outburst, this study presents the relation between fractal dimension and energy in the process of extruding. In conclusion, the evolution of crack fractal dimension value can signify that of energy, which has laid a solid foundation for the quantification research on the mechanism of gas-containing coal extrusion.

Effects of surface roughness on bending properties of rolled AZ31 alloy

This study investigated the effects of mechanical-polishing-induced surface roughness and the direction of polishing lines on the bending properties of a rolled AZ31 alloy.To this end,three-point bending tests were performed on one sample without polishing lines(SS sample)and two samples with polishing lines—one in which the polishing lines were parallel to the rolling direction(RS-RD sample)and the other in which they were parallel to the transverse direction(RS-TD sample).In all three samples,macrocracks were formed in the width direction on the outer surface,where tensile stress was predominantly generated in the longitudinal direction.However,the macrocracks formed in the SS sample were curved because of the merging of uniformly formed fine microcracks,whereas those formed in the RS-TD sample were linear owing to the formation of relatively coarse microcracks along the polishing lines.The bendability of the samples was in the order of SS>RS-RD>RS-TD,and their limiting bending depths were 4.8,4.6,and 4.4 mm,respectively.In the presence of mechanical-polishing-induced surface roughness,polishing lines perpendicular to the direction of the major stress(i.e.,tensile stress along the longitudinal direction)resulted in a greater degree of stress concentration on the outer surface of the bending specimen.This higher stress concentration promoted the formation of undesirable{10–11}contraction and{10–11}–{10–12}double twins—which typically act as crack initiation sites—and thereby facilitated crack generation and propagation.Consequently,the surface roughness caused premature fracture during bending deformation,which,in turn,caused deterioration of the bendability of the rolled Mg alloy.

Monte-Carlo Simulation of Surface Crack Growth Rate for Offshore Structural Steel E36-Z35

The Monte- Carlo method is used to simulate the surface fatigue crack growth rate for offshore structural steel E36-Z35, and to determine the distributions and relevance of the parameters in the Paris equation. By this method, the time and cost of fatigue crack propagation testing can be reduced. The application of the method is demonstrated by use of four sets of fatigue crack propagation data for offshore structural steel E36-Z35. A comparison of the test data with the theoretical prediction for surface crack growth rate shows the application of the simulation method to the fatigue crack propagation tests is successful.

METHOD FOR CALCULATION AND SIMULATION ON PROPAGATION OF SURFACE CRACK ON SPHERICAL VESSELS MADE OF STEELS

To avoid leaking or bursing by crack on surface of preddure vessels made of streels,a method for analyzing the principle of propagation of a surface crack is established,and used on a spherical vessel with program calculation and simulation,the program is written in QBASIC and the reaults are provided and discussed.