Dynamic Stress Concentration Factor Research Articles

Scattering of Out-of-Plane Line Source Load by Shallow-Embedded Circular Lining Structure and Crack in Half Space

In this paper, we study the problems of scattering of out-of-plane line source load by half-space shallow-embedded circular lining structure and a crack in the field of linearly elastic dynamic mechanics. This is an essential solution to the displacement field for the elastic space possessing shallow-embedded circular lining structure and a crack while bearing out-of-plane harmonic line source load at arbitrary point. The wave function of scattering of shallow-embedded circular lining structure impacted by incident steady SH-wave is constructed based on the symmetry of SH-wave scattering and the method of multi-polar coordinates system. Then a crack is made out using the method of “crack-division”. Thus expressions of displacement and stress are established when shallow-embedded circular lining structure and a crack are both in existent. Finally, with two different dimensionless parameters, numerical results of scattering of out-of-plane line source load by half-space shallow-embedded circular lining structure and a crack are obtained and numerical examples are provided to show the influence of wave number ratio, shear modulus ratio, thickness ratio and the ratio of distance between the center of the different cavity and ground surface and the radius of the circular lining structure upon the dynamic stress concentration factor(DSCF) and dynamic stress intensity factor(DSIF) at crack tip.

Non-destructive Detection of a Circular Cavity in a Finite Functionally Graded Material Layer Using Anti-plane Shear Waves

A semi-analytical method is proposed to investigate the non-destructive detection of a circular cavity buried in a functionally graded material layer bonded to homogeneous materials, and the multiple scattering effect of shear waves is described accurately. The image method is used to satisfy the traction free boundary condition at the edge of the functionally graded material layer. The analytical solutions of wave fields are expressed by employing wave function expansion method, and the expanded mode coefficients are determined by satisfying the boundary conditions at the edge and around the cavity. The analytical and numerical solutions of dynamic stress concentration factors around the cavity are presented. The effects of the position of the cavity in the material layer, the incident wave number, and the properties of the two phases of materials on the dynamic stress concentration factors are analyzed. Analyses show that when the buried depth of the cavity and the thickness of the layer are relatively small, the properties of the two phases of materials have great effect on the distribution of dynamic stress around the cavity. In the region of higher frequency, the effects of the position of the cavity and the properties of the two phases of materials on the maximum dynamic stress are greater.

Dynamic stress from a subsurface cylindrical inclusion in a functionally graded material layer under anti-plane shear waves

The multiple scattering of shear waves and dynamic stress resulting from a subsurface cylindrical inclusion in a functionally graded material (FGM) layer bonded to homogeneous materials are investigated, and the analytical solution of this problem is derived. Image method is used to satisfy the traction free boundary condition of the FGM layer. The analytical solutions of wave fields around the actual and image inclusions are expressed by employing wave functions expansion method, and the expanded mode coefficients are determined by satisfying the continuous boundary conditions around the inclusions. Through the numerical solutions of dynamic stress concentration factors (DSCFs) around the inclusion, the effects of the position of the inclusion in the material layer, the properties of the inclusion, and the properties of the two phases of composites on the DSCFs are analyzed. Analyses show that when the cylindrical inclusion is stiffer than the two phases of FGMs, the dynamic stress around the inclusion increases greatly. When the distance between the surface of the structure and the inclusion is smaller, the effect of the properties of the inclusion becomes greater. When the cylindrical inclusion is softer than the two phases of FGMs, the maximum dynamic stress shows little difference; however, the variation of the distribution of the dynamic stress around the inclusion is greater.

Dynamic stress from a subsurface cavity in a semi-infinite functionally graded piezoelectric/piezomagnetic material

In this paper, an analytical method is applied to investigate the multiple scattering of anti-plane shear waves and dynamic stress around a subsurface cavity in a semi-infinite functionally graded piezoelectric/piezomagnetic composite. The analytical solutions of wave field, electric field and magnetic field are expressed by employing wave function expansion method and the expanded mode coefficients are determined by satisfying the boundary conditions of the cavity. Image method is used to satisfy the free boundary conditions of the semi-infinite structure. According to the analytical expressions of this problem, the numerical solutions of the dynamic stress concentration factor around the cavity are presented. The effects of the piezoelectric and piezomagnetic properties, the buried depth of the cavity, the incident wave number and the nonhomogeneous parameter of materials on the dynamic stress around the cavity are graphically illustrated. Analyses show that the piezoelectric and piezomagnetic properties have great effect on the dynamic stress in the region of intermediate frequency and the effect increases with increasing nonhomogeneous parameter. The effects of the nonhomogeneous parameter of materials on the dynamic stress and electric field are examined. Comparisons with other existing models are also presented.

Dynamic Stress Concentration of Circular Cavity and Double Linear Cracks in Elastic Medium

Sacttering of SH-wave of combined deffectiveness which included single circular cavity and double linear cracks in elastic medium was investigated in detail. Analytic solution of this problem was obtained by Green’s Function method and idea of crack-division at actual position of crack at two times. There were two key steps of this method. First step was to employ a special Green’s Function which was a fundamental solution of displacement field for an elastic space with a cavity in it subjected to out-of-plane harmonic line source force at any point at first. The sceond step was crack-division which was artificially to produce a crack by apllying opposite shear stress caused by incident SH-wave. Distribution of dynamic stress concentration factor (DSCF) at edge of cavity was studied by numerical analysis. Distribution Curves of DSCF of three models were plotted by numerical method in polar coordinate system. Three models were one circular cavity and without crack, one circular cavity and single crack and single circular cavity double cracks. The results were compared and discussed in different incident angle of SH-wave.Conclusion was that the interaction among SH-wave, single cavity and double crack was obvious. Dynamic stress concentration factor varied with angle and distance between cavity and crack.

Antiplane Harmonic Elastodynamic Stress Analysis of an Infinite Wedge With a Circular Cavity

In this paper, the antiplane harmonic dynamics stress of an infinite isotropic wedge with a circular cavity is analyzed for the first time by using a novel method with Green’s function, complex functions, and multipolar coordinates. A basic solution for the displacement field of an elastic half-space containing a circular cavity subjected to antiplane harmonic point force is employed as the Green’s function. Based on the Green’s function, the infinite wedge problem is equivalently transformed into the problem of a half-space divided by a semi-infinite traction free line. The equivalent problem is solved numerically to determine the dynamic stress field in the wedge at different apex angles and cavity locations. We show that the wedge angle, cavity location, and incident angle and frequency of the external load have significant effect on the dynamic stress of the cavity surface. The dynamic stress concentration factor on the cavity surface becomes singular when the cavity is close to the boundary of the wedge.

Effect of test frequency on fatigue strength of low carbon steel

ABSTRACTUltrasonic fatigue tests (test frequency: 20 kHz) and conventional tension–compression fatigue tests (10 Hz) have been conducted on annealed and 10% pre‐strained specimens of 0.13% carbon steel. Small holes were introduced on the specimen surface to investigate the effect of test frequency on small crack growth. The dynamic stress concentration factor and the stress intensity factor under ultrasonic fatigue tests were checked to be almost the same as those of conventional tension–compression fatigue tests. However, the fatigue properties were dependent on the test frequency. Ultrasonic fatigue tests showed longer fatigue life and lower fatigue crack growth rate for the annealed and 10% pre‐strained specimens. Slip bands were scarce in the neighbourhood of cracks under ultrasonic fatigue tests, while many slip bands were observed in a wide area around the crack under conventional fatigue tests. In order to explain the effect of test frequency on fatigue strength, dynamic compression tests with Split Hopkinson bars were carried out. The stress level increases substantially with the strain rate. Thus, the increase in fatigue strength might be, to a large extent, due to a reduction in crack tip cyclic plasticity during ultrasonic fatigue tests.

Dynamic stress from a cylindrical inclusion buried in a functionally graded piezoelectric material layer under electro-elastic waves

This paper presents a theoretical method to investigate the multiple scattering of electro-elastic waves and dynamic stress around a subsurface cylindrical inclusion in a functionally graded piezoelectric material layer bonded to homogeneous piezoelectric materials. The analytical solutions of wave fields are expressed by employing wave function expansion method, and the expanded mode coefficients are determined by satisfying the boundary conditions around the inclusion. The image method is used to satisfy the mechanical and electrically short conditions at the free surface of the structure. Through the numerical solutions of dynamic stress concentration factors around the inclusion, it is found that when the cylindrical inclusion possesses higher rigidity and greater piezoelectric constant than the two phases of functionally graded materials, the dynamic stress around the inclusion increases greatly. When the distance between the surface of the structure and the inclusion is smaller, the effect of the properties of the inclusion becomes greater. When the cylindrical inclusion possesses lower rigidity and smaller piezoelectric constant than the two phases of functionally graded materials, the maximum dynamic stress shows little difference; however, the variation of the distribution of the dynamic stress around the inclusion is greater. The effect of the properties of the inclusion on the dynamic stress around the inclusion is greater than that on the electric field. The effects of wave frequency on the dynamic stress and electric field are also examined.

Dynamic anti-plane interaction between an impermeable crack and a circular cavity in an infinite piezoelectric medium

Wave propagation in an infinite elastic piezoelectric medium with a circular cavity and an impermeable crack subjected to steady-state anti-plane shearing was studied based on Green’s function and the crack-division technique. Theoretical solutions were derived for the whole elastic displacement and electric potential field in the interaction between the circular cavity and the impermeable crack. Expressions were obtained on the dynamic stress concentration factor (DSCF) at the cavity’s edge, the dynamic stress intensity factor (DSIF) and the dynamic electric displacement intensity factor (DEDIF) at the crack tip. Numerical solutions were performed and plotted with different incident wave numbers, parameters of piezoelectric materials and geometries of the structure. Finally, some of the calculation results were compared with the case of dynamic anti-plane interaction of a permeable crack and a circular cavity in an infinite piezoelectric medium. This paper can provide a valuable reference for the design of piezoelectric actuators and sensors widely used in marine structures.

Multiple scattering of flexural waves from a cylindrical inclusion in a semi-infinite thin plate

In this paper, image method and wave function expansion method are applied to investigate the multiple scattering of flexural waves and dynamic stress concentration from a cylindrical inclusion in a semi-infinite thin plate, and the analytical solution of this problem is obtained. The semi-infinite plate with roller-supported boundary is considered, and the image method is used to satisfy the boundary condition. The addition theorem for Bessel functions is employed to accomplish the translation of wave fields between different local coordinate systems. As an example, the numerical results of dynamic stress concentration factors around the inclusion are graphically presented and analyzed. Analysis shows that the angular distribution of the dynamic stress around the inclusion shows great difference when the distance between the inclusion and the semi-infinite edge is different. The effects of the elastic modulus, density, Poisson's ratio, and the thickness of the inclusion on the shadow side of the inclusion are greater when the distance between inclusion and the semi-infinite edge is small. In the region of lower frequency, the effects of the elastic modulus, density, Poisson's ratio, and the thickness of the inclusion on the dynamic stress are little. Comparisons with other existing models are also discussed.

Dynamic Anti-Plane Behaviors of a Semi-Infinite Piezoelectric Medium with a Circular Cavity and a Crack near the Surface

Dynamic interaction is investigated theoretically between a circular cavity and a crack near the surface in a semi-infinite piezoelectric medium subjected to time-harmonic incident anti-plane shearing in this paper. The formulations are based on the method of complex variable and Green’s function. Dynamic stress concentration factors at the edge of the circular cavity and dynamic stress intensity factors at the crack tip are obtained by solving boundary value problems with the method of orthogonal function expansion. The calculating results are plotted to show how the frequencies and the orientation of incident wave, piezoelectric characteristic parameters of the material and the structural geometries influence upon the dynamic stress concentration factor (DSCF) and dynamic stress intensity factor (DSIF).

Multiple scattering of electro-elastic waves from a buried cavity in a functionally graded piezoelectric material layer

This paper presents a theoretical method to investigate the multiple scattering of electro-elastic waves and the dynamic stress around a buried cavity in a functionally graded piezoelectric material layer bonded to a homogeneous piezoelectric material. The analytical solutions of wave fields are expressed by employing wave function expansion method, and the expanded mode coefficients are determined by satisfying the boundary conditions around the cavity. The image method is used to satisfy the mechanical and electrically short conditions at the free surface of the structure. According to the analytical expression of this problem, the numerical solutions of the dynamic stress concentration factor around the cavity are presented. The effects of the piezoelectric property, the position of the cavity in the layer, the incident wave number and the material properties on the dynamic stress around the cavity are analyzed. Analyses show that the piezoelectric property has great effect on the dynamic stress in the region of higher frequencies, and the effect increases with the decrease of the thickness of FGPM layer. If the material properties of the homogeneous piezoelectric material are greater than those at the surface of the structure, the dynamic stress resulting from the piezoelectric property is greater. The effect material properties at the two boundaries of FGPM layer on the distribution of dynamic stress around the cavity is also examined.

Scattering of SH-wave from interface cylindrical elastic inclusion with a semicircular disconnected curve

Scattering of SH wave from an interface cylindrical elastic inclusion with a semicircular disconnected curve is investigated. The solution of dynamic stress concentration factor is given using the Green’s function and the method of complex variable functions. First, the space is divided into upper and lower parts along the interface. In the lower half space, a suitable Green’s function for the problem is constructed. It is an essential solution of the displacement field for an elastic half space with a semi-cylindrical hill of cylindrical elastic inclusion while bearing out-plane harmonic line source load at the horizontal surface. Thus, the semicircular disconnected curve can be constructed when the two parts are bonded and continuous on the interface loading the undetermined anti-plane forces on the horizontal surfaces. Also, the expressions of displacement and stress fields are obtained in this situation. Finally, examples and results of dynamic stress concentration factor are given. Influences of the cylindrical inclusion and the difference parameters of the two mediators are discussed.

Dynamic stress of a circular cavity buried in a semi-infinite functionally graded piezoelectric material subjected to shear waves

The paper presents a theoretical method to investigate the multiple scattering of shear waves and dynamic stress around a circular cavity in a semi-infinite functionally graded piezoelectric material. The analytical solutions of wave fields are expressed by employing wave function expansion method and the expanded mode coefficients are determined by satisfying the boundary conditions of the cavity. Image method is used to satisfy the free boundary condition of the semi-infinite structure. According to the analytical expression of this problem, the numerical solutions of the dynamic stress concentration factor around the cavity are presented. The effects of the piezoelectric property, the buried depth of the cavity, the incident wave number and the nonhomogeneous parameter of materials on the dynamic stress around the cavity are analyzed. Analyses show that the piezoelectric property has great effect on the dynamic stress in the region of intermediate frequency and the effect increases with increasing wave number. When the nonhomogeneous parameter of materials is less than zero, it has less influence on the maximum dynamic stress around the cavity; however, it has greater influence on the distribution of the dynamic stress around the cavity. When the nonhomogeneous parameter of materials is greater than zero, it has greater influence on both the maximum dynamic stress and the distribution of dynamic stress around the cavity, especially in the case that the buried depth is comparatively small.

Multiple scattering of shear waves and dynamic stress from a circular cavity buried in a semi-infinite slab of functionally graded materials

Based on the theory of elastodynamics and employing image method, the multiple scattering and dynamic stress in a semi-infinite slab of functionally graded materials with a circular cavity are investigated. The analytical solution of this problem is derived, and the numerical solutions of the dynamic stress concentration factor around the cavity are also presented. The effects of the distance between the cavity and the boundaries of the semi-infinite slab, the incident wave number and the non-homogeneity parameter of materials on the dynamic stress concentration factors are analyzed. Analyses show that the dynamic stress around the cavity increases with increasing non-homogeneity parameter of materials and incident wave number. The boundaries of the semi-infinite slab have great effect on both the maximum dynamic stress and the distribution of dynamic stress around the circular cavity, and the effect increases with increasing incident wave number.

Dynamic Anti-Plane Behavior of the Interaction Between a Crack and a Circular Cavity in a Piezoelectric Medium

In this paper, the dynamic interaction is investigated theoretically between a crack and a circular cavity in an infinite piezoelectric medium under time-harmonic incident anti-plane shearing. The formulations are based on the method of complex variable and Green’s function. The resulting dynamic stress intensity factors at the crack’s tip and dynamic stress concentration factors at the cavity’s edge are obtained with crack-division technique. Numerical results are plotted to show how the frequencies of incident wave, the piezoelectric characteristic parameters of the material and the geometry of the crack and the circular cavity influence upon the dynamic stress intensity factors and dynamic stress concentration factors.

Scattering of elastic waves and dynamic stress in two-particle reinforced composite system

Based on the theory of elastodynamics, applying the addition theorem for spherical Bessel functions, the multiple scattering of elastic waves and dynamic stress in two-particle reinforced composite system is investigated, and the analytical expressions of wave fields in each medium are presented. According to the continuous boundary conditions around the spherical particles, the expansion mode coefficients are determined and the analytical expression of dynamic stress concentration factor in different local coordinate systems is obtained. As an example, the variation of dynamic stress concentration factor around the interface between the particles and the matrix under different parameters is analyzed. Analyses show that when the frequency is different, the effect of the particle center-to-center distance on the dynamic stress varies greatly. Only when the distance is greater than a certain number, the effect can be ignored. When the distance is different, the effect of material properties of the particles and the matrix on the dynamic stress is also examined.

Dynamic Stress of a Circular Cavity Buried in a Semi-Infinite Functionally Graded Material Subjected to Shear Waves

The multiple scattering of shear waves and dynamic stress in a semi-infinite functionally graded material with a circular cavity is investigated, and the analytical solution of this problem is derived. The analytical solutions of wave fields are expressed by employing the wave function expansion method, and the expanded mode coefficients are determined by satisfying the boundary condition of the cavity. The image method is used to satisfy the traction-free boundary condition of the material structure. As an example, the numerical solution of the dynamic stress concentration factors around the cavity is also presented. The effects of the buried depth of the cavity, the incident wave number, and the nonhomogeneity parameter of materials on the dynamic stress concentration factors are analyzed. Analyses show that when the nonhomogeneity parameter of materials is <0, it has less influence on the maximum dynamic stress around the cavity; however, it has greater influence on the distribution of dynamic stress around the cavity. When the nonhomogeneity parameter of materials is >0, it has greater influence on both the maximum dynamic stress and the distribution of dynamic stress around the cavity, especially in the case that the buried depth is comparatively small.

Photoelastic simulation of the stress wave field around a tunnel in an anisotropic rock mass subject to shock load

The stress wave field around a tunnel in an anisotropic medium subject to shock load is analyzed using the dynamic photoelastic method. The influence of various factors on the distribution and magnitude of boundary stresses around the tunnel are studied by simulating the deformation process. The time dependence of the dynamic stress concentration factor on the tunnel walls is established

Dynamic Stress Resulting from a Plane Compressional Wave in Two-particle Reinforced Composites

In this paper, based on the theory of elastodynamics, the multiple scattering of elastic waves and dynamic stress in multiparticle reinforced composites is investigated, and the analytical solution of this problem is obtained. By using the wave function expansion method, the expressions of total wave fields in each medium are presented. The addition theorem of spherical Bessel functions is employed to accomplish the translation for different local coordinate systems. According to the continuous boundary conditions around the particles, the expanded mode coefficients are determined. As an example, the variation of dynamic stress concentration factors at the interface between the particles and the matrix under different parameters is analyzed. It can be seen from the results that when the incident frequency is different, the effect of the distance between the centers of the particles on the dynamic stress varies greatly. Only when the distance is greater than a certain number can its effect be ignored. When the distance is fixed, the effect of material properties on dynamic stress is also examined.