Dynamic Stress Concentration Research Articles

Dynamic effects of a single fiber break in unidirectional glass fiber-reinforced polymer composites: Effects of matrix plasticity

In a unidirectional composite under static tensile loading, breaking of a fiber is shown to be a locally dynamic process, leading to stress concentrations in the matrix and neighboring fibers and debonding of the interface, which can propagate at high speed over long distances. In our previous work, a fiber break within a two-dimensional fiber array embedded in elastic epoxy matrix (with cohesive interface) was modeled to quantify the effects of these dynamic stresses. The results indicated that the elastic limit of the polymer matrix can be exceeded. In this study, the effects of matrix plasticity on dynamic stress concentrations due to a single fiber break are investigated. For the range of matrix yield stresses considered, the dynamic stress concentrations are significantly higher than corresponding values predicted by a quasi-static model with a pre-broken fiber. Based on the ratio of shear yield strength of the matrix and mode II peak traction of the interface cohesive law, two distinct regimes of damage are shown to exist. Only matrix yielding occurs when this ratio is less than 1.0, while both interfacial debonding and matrix yielding occur when it is greater than 1.0. At higher fiber break strengths, where the elastic matrix model predicts unstable interfacial debonding, reduction in matrix yield strength leads to a transition to stable debonding and arrest. Reducing the matrix yield strength also leads to a lowering of the peak dynamic stress concentrations in adjacent fibers, while spreading the stress concentrations over a larger volume of the composite microstructure.

Numerical analysis on dynamic stress and vibration for tubular joints of welded steel pipes under axial loads

Reported researches rarely focus on dynamic stress concentration factors (SCF) of tubular joints between the chord and brace, where the chord is a square pipe, and the brace is a circular pipe. Tubular joints between a square pipe and circular pipe are widely applied in spatial structures as a support structure. Therefore, tubular joints of welded steel pipes under axial loads were studied numerically for determination of dynamic stress concentration factors (SCF). Finite element models were setup for a total of 165 tubular joints with various configurations, obtaining dynamic stress distributions of each model along the joint. Dynamic stress concentration factors on the brace and the chord were extracted respectively. Relations between sizes of dynamic stress concentration factors between the joint and structural parameters were discussed. The computational model was finally validated by the experimental test. The experimental curve was basically consistent with the finite element at the elastic stage of loading, indicating that the computational model at the elastic stage was very accurate. The paper mainly studied dynamic stress distribution of the tubular joint of welded steel pipes under an excitation load at the elastic stage, so the finite element model could be used to replace experimental test. SCF was 180° symmetric under different parameters. This angle was located at the crown point of tubular joints, while the welded steel pipe structure was a symmetric structure relative to the longitudinal plane. In addition, the chord and brace had SCF peaks at the angles of 90° and 270° because the two points were located at the saddle point of the tubular joints. Under angles of 0° and 180°, the SCF had obvious valley values because the two points were located at crown points of tubular joints. Finally, the vibration performance of the tubular joint was also analyzed. Vibration displacement could be reduced obviously through reinforcement of tubular joints with the collar plates. Axial pre-tensile forces would increase vibration displacement on top and bottom positions of the chord pipe. This paper can provide an important reference for the improvement of the dynamic stress concentration of joints of welded steel pipes.

Dynamic response of pre-stressed rock with a circular cavity subject to transient loading

Scientists have attempted to investigate deep underground rock failure. A key challenge to study underground rock failure is the difficulty to survey its process. Therefore, a large number of important and insightful laboratory investigations of underground rock failure experiments are conducted. In this paper, an experimental method is proposed to explore dynamic failure process of pre-stressed rock specimen with a circular hole. The failure process of a rock specimen under different initial static stress coupled with dynamic loading is clearly illustrated by a high speed camera. The experimental results indicated that high static pre-stress coupled with dynamic loading induces rock debris to be ejected at the surrounding circular hole; however, lower static pre-stress coupled dynamic loading cannot induce rock failure. The dynamic stress concentration surrounding the circular hole by transient wave incidence was further demonstrated at the condition of half-sine wave loading. In this condition, the results demonstrated that combined action of static and dynamic stress concentrations induces the primary fractures of rock specimen.

Elastic wave scattering and stress concentration in a finite anisotropic solid with nano-cavities

The paper deals with numerical evaluation of the scattered wave and dynamic stress concentration fields in a finite anisotropic solid containing multiple nano-cavities. 2D plane-strain state and in-plane wave motion are assumed. The proposed mechanical model combines classical elastodynamic theory for the bulk general anisotropic solid and the Gurtin–Murdoch theory of surface elasticity assuming localized constitutive equation for the infinitely thin interface between the cavity and the matrix. The developed computational methodology is based on the following: (a) displacement boundary integral equations along existing boundaries using the analytically derived through Radon transform fundamental solution of the equation of motion of the bulk anisotropic solid; (b) non-classical boundary conditions of the Gurtin–Murdoch model along the interface between the matrix and cavities taking into consideration a jump in the stresses as one moves from the bulk material to the cavity due to the presence of surface elasticity; and (c) elastic-viscoelastic correspondence principle. The accuracy of the developed software is proven by comparisons of the obtained results solved by boundary element method and finite element method. A detailed parametric study reveals the sensitivity of the wave field to different key factors such as size, number and configuration of the cavities, surface and bulk material properties.

The method of fundamental solution for elastic wave scattering and dynamic stress concentration in a fluid-saturated poroelastic layered half-plane

A meshless method based on the method of fundamental solution (MFS) is developed to solve elastic-wave scattering and dynamic stress concentration in a fluid-saturated poroelastic layered half-plane, by utilizing the line sources of cylindrical PI, PII, and SV waves in a poroelastic layered half-plane. The numerical accuracy and stability of the MFS is verified by examining the boundary conditions and comparison with other methods. Subsequently, the amplification effects on displacement, surface hoop stress and fluid pore pressure around a cavity in a three-layered poroelastic half-plane are investigated. Numerical results indicate that the scattering characteristics strongly depend on parameters including the incident frequency and angle, soil-layer porosity and boundary drainage condition. The amplification effects of a cavity in the poroelastic layered half-plane appear to be more significant than the corresponding case of a homogenous half-plane. The amplitude of the fluid pore pressure on the surface of the cavity is amplified up to five times that of the free field, which also considerably aggravates the dynamic stress concentration around the cavity.

Dynamic Stress Concentration at the Boundary of an Incision at the Plate Under the Action of Weak Shock Waves

Abstract This paper proposes the novel technique for analysis of dynamic stress state of multi-connected infinite plates under the action of weak shock waves. For solution of the problem it uses the integral and discrete Fourier transforms. Calculation of transformed dynamic stresses at the incisions of plates is held using the boundary-integral equation method and the theory of complex variable functions. The numerical implementation of the developed algorithm is based on the method of mechanical quadratures and collocation technique. For calculation of originals of the dynamic stresses it uses modified discrete Fourier transform. The algorithm is effective in the analysis of the dynamic stress state of defective plates.

Scattering of shear waves by a cylindrical inclusion in an anisotropic half space

Based on the complex function method and a multipolar coordinate system, scattering of shear waves by a cylindrical inclusion in an anisotropic (orthotropic) half space is studied. In order to find the solution of shear waves, the governing equation is transferred into its normalized form. Then, the scattering wave in the half space and the standing wave in the inclusion are deduced. Different incident wave angles and anisotropies are considered to obtain the reflected wave. Then, the unknown coefficients in scattering wave and standing wave are found by utilizing the continuous condition at the boundary of the inclusion. Subsequently, the dynamic stress concentration factor (DSCF) around the inclusion is calculated and analyzed. The results demonstrate that the distribution of the DSCF is influenced by the anisotropy of the half space, and the value of the DSCF is mainly affected by the wave numbers ratio and the shear modulus ratio.

Modified dynamic stress concentration factor for twin tunnels using a novel approach of FEM-scattering

The frequent failure of newly built tunnels under earthquake loading has led to a broader range of research into assessing the effect of seismic waves on tunnels. Numerous researchers have worked on twin tunnels and the effect of wave scattering due to vibration of harmonic waves to date. As for the near-field wave scattering and range of the recording of the acceleration of the ground during an earthquake. However, little research has been conducted on a comprehensive scale. This study attempted to examine the scattering in Si-o-seh Pol Bridge, a monument in Isfahan city, using the Hankel’s function of the first and second kinds for near-field earthquakes (Northridge, Tabas and Kobe). All of scattering analysis were done through FESCAM code that designed and developed in MATLAB software as a toolbox by authors of this paper. The historic bridge of Si-o-seh Pol Bridge and its neighboring twin tunnels for subway were selected as a case study. The first kind of Hankel’s function was considered as a supplementary parameter to the seismic analysis using finite element method procedure. The amount of dynamic scattering of twin tunnels subjected seismic loads considered as extra strain and stress around tunnels using Hankel’s function results. The results between two cases with and without considering scattering waves of tunnels show that the mean horizontal displacement and the mean vertical displacement of Si-o-seh Pol Bridge can be increased about 28.8% and 30.11% respectively. The results of statistical analysis with Mann-Whitney test show that there is no significant difference between the seismic performance of Si-o-seh Pol Bridge with and without consideration of the scattering effect of the tunnels (P-Value=0.6>0.05). However, the results of this study versus the past studies reflect the fact that horizontal and vertical displacements when involving the tunnel are 34.10% increase and −48.51% decline, respectively. This means that the twin tunnels are effective in displacement of the adjacent monument from the engineering perspective.

A complex function method of SH wave scattering in inhomogeneous medium

The complex function method is applied in the solution of the scattering problem for an irregularly shaped boundary in an infinite inhomogeneous elastic medium, which is deduced from the scattering problem in a homogeneous one. The potential function of the scattering wave which is generated by the irregularly boundary is obtained by applying the complex function method in the inhomogeneous medium. The reduced Helmholtz equation with variable coefficients is solved by separation of variables. Then, the potential function is expressed as the complex domain functions series. By truncating a set of infinite algebraic equations, the coefficient of the series are determined. In order to verify the validity of this method, the wave equation in a inhomogeneous medium is degenerated to the equation with constant coefficients. The domain function is discussed. The dynamic stress concentration factor around an elliptical cavity is calculated in an exponentially inhomogeneous medium.

Scattering of plane P1 waves and dynamic stress concentration by a lined tunnel in a fluid-saturated poroelastic half-space

The scattering of plane fast compressional waves (P1 waves) by a lined tunnel shallowly embedded in a poroelastic half-space is solved by indirect boundary integration equation method for a poroelastic half space. The displacement amplification on ground surface, dynamic stress concentration within the tunnel, and pore pressure fluctuation on the interface are investigated in the frequency domain, and are also compared with the results of the corresponding unlined cavity. Numerical results illustrate that the scattering of plane P1 waves around the tunnel strongly depends on the porosity of the surrounding medium, frequency and angle of the incident wave, tunnel depth. Significant amplification effect on the surface ground motion and the hoop stress in the tunnel is observed in the case of high-porosity surrounding-rock and undrained interface.

Mechanism of rock burst induced by fault slip in an island coal panel and hazard assessment using seismic tomography: a case study from Xuzhuang colliery, Xuzhou, China

Rock burst hazards induced by fault slip frequently occur in underground mining and threaten the safety of miners. In this paper, the structures of overlying strata, mechanism of fault slip, and rock burst pre-warning using seismic tomography were investigated in LW7192, a specific island longwall panel in Xuzhuang Colliery. The results show that an asymmetrical “T” structure of overlying strata is formed during LW7192 retreat, and the long hanging length of overlying key strata is maintained due to the short panel width. By analysing a modified fault sliding model, it is found that the time interval between two fault slips has a positive correlation with the energy released therein. The rock burst that occurred in LW7192 has the longest time interval between events compared with other high-energy tremors near the fault, and enormous elastic energies released by fault slip as a form of dynamic load. The superposition of dynamic loads and high stress concentration of the coal-rock mass contributes to the rock burst in LW7192. For forecasting rock burst hazards, seismic tomography was used and the results show that the velocity anomaly regions correspond well with the area of both strong tremors and the rock burst. Ultimately, large-diameter boreholes, directional hydraulic fracturing boreholes, and floor distressing boreholes were taken in the rock burst area, and the pressure relief is proved effective by seismic tomography assessment.

Scattering of out-plane wave by a circular cavity near the right-angle interface in the exponentially inhomogeneous media

By applying the theory of complex function and the image principle, this paper investigate the dynamic stress of wave propagation problems in an exponentially inhomogeneous right-angle plane with a circular cavity. The density is assumed to be an exponential change along x-axis, and the shear modulus is constant. Due to the inhomogeneity, the coefficient of the Helmholtz equation is a variable. Based on the theory of complex function, Helmholtz equation is transformed with a general conformal transformation method. By using the image principle, the right-angle plane is first mirrored as the half-space in order to find the expressions of the incident wave and the reflected wave. Then, the half-space is mapped into the finite one for solving the scattering problem of the wave. In order to verify the validity of this method, wave equation in inhomogeneous media is degenerated to the equation with constant coefficients. By truncating a set of infinite algebraic equations, the coefficient of the series is determined. The expression of scattering wave is given by the traction-free boundary condition. The displacements and stress fields are proposed. Dynamic stress concentration factor (DSCF) around circular cavity is calculated in exponentially inhomogeneous media.

Scattering of SH wave by a semi-cylindrical salient near vertical interface in the bi-material half space

With the aid of the Green function method and image method, the problem of scattering of SH-wave by a semi-cylindrical salient near vertical interface in bi-material half-space is considered to obtain its steady state response. Firstly, by the means of the image method, Green function which is the essential solution of displacement field is constructed to satisfy the stress-free condition on the horizontal boundary in a right-angle space including a semi-cylindrical salient and bearing a harmonic out-of-plane line source force at any point on the vertical boundary. Secondly, the bi-material is separated into two parts along the vertical interface, then unknown anti-plane forces are applied on the vertical interface, and according to the continuity condition, the first kind of Fredholm integral equations is established to determine unknown anti-plane forces by “the conjunction method”, then the integral equations are reduced to the linear algebraic equations by effective truncation. Finally, the dynamic stress concentration factor (DSCF) around the edge of semi-cylindrical salient is calculated, and the influences of incident wave number, incident angle, effect of interface and different combination of material parameters, etc. on DSCF are discussed.

General three-dimensional scattering and dynamic stress concentration of Lamb-like waves in a spherical shell with a spherical inclusion

Three-dimensional scattering and dynamic stress concentration of Lamb-like waves around a spherical inclusion (inhomogeneity and a cavity) in a thick spherical shell are investigated theoretically and numerically. Two spherical coordinates, located at the spherical shell center and the inclusion center, are established to express the incident and scattered wave potential functions. By a kind of addition formulas, all the potential functions can be transformed into the same coordinate, then the analytical solution of the displacements and stresses are derived, and all the undetermined coefficients are solved by satisfying the boundary condition and the interface condition. In order to describe the 3-D stresses concentration, multiple DSCFs are employed and the 3-D distributions are depicted. The results reveal the influences of inclusion material and the cavity on the distributions of DSCFs, and the influence of incident wave frequency and inclusion position are also calculated. This research is expected to provide theoretical understanding on dynamic analysis and mechanical properties evaluation of the spherical shells.

The influence of different pre-formed holes on the dynamic response of square plates under air-blast loading

Abstract Studying the blast response of plates with pre-formed holes under blast loading serves as a significant method to decouple dynamic response of plates with pre-formed holes under combined blast and fragment loading. Based on material test system (MTS) and Split Hopkinson tension bar (SHTB), the mechanical properties of experimental steel under different strain rates were obtained. Then, the experiments on the responses of plates with square, diamond and circular holes under air-blast loading were carried out and the failure modes of plates with diamond holes were derived. Later, the deformation curves of target plate were obtained by laser reverse forming technique. Next, a constitutive model program considering strain rate, stress status and temperature effect was adopted to carry out numerical simulation calculation, which verified the accuracy of this numerical simulation. Finally, discussions were carried out on the damage level at places where cracks might form, the dynamic stress concentration coefficient and stress status change, and then the influence which pre-formed holes have on the failure mode was analyzed. The results of this study show that: (1) A fortran vectorized user-material subroutine (VUMAT) program considering strain rate, stress status and temperature effect can effectively predict the dynamic response of metallic materials; (2) the shape of pre-formed holes affects the damage level, dynamic stress concentration coefficient and stress status. Besides, failure occurs more easily in plates with diamond pre-formed holes; (3) pre-formed holes have an obvious influence on the failure modes of plates under different blast distance.

Scattering of SH-Wave by a Circular Inclusion Near the Interfacial Cracks in the Piezoelectric Bi-Material Half-Space

AbstractWith the aid of the Green's function method and complex function method, the scattering problem of SH-wave by a circular inclusion near the two symmetrically permeable interfacial cracks in the piezoelectric bi-material half -space is considered to obtain the steady state response. Firstly, by means of the image method, the essential function of Green's function is constructed, which satisfies the stress free and electric insulation conditions on the horizontal boundaries in a right-angle space including a circular inclusion and bearing a harmonic out-plane line source force on the vertical boundary. Secondly, the bi-material media is divided into two parts along the vertical boundary. According to continuity condition, the first kind of Fredholm integral equations containing undetermined anti-plane forces are established by “the conjunction method” and “the crack-division technology”, then the integral equations are reduced to the algebraic equations including finite items by effective truncation. Finally, the dynamic stress concentration factor around the edge of circular inclusion and dynamic stress intensity factor at the crack tip are calculated, then the influences of the frequency of incident wave, the length of crack, the position of the crack, the position of circular inclusion, etc. on the dynamic stress concentration factor and dynamic stress intensity factor are discussed.

The relationship study between texture vibrating plate dynamic wettability and elastic wave scattering

An experimental investigation of wetting behavior of liquid droplet on texture vibrating substrate and the theoretical calculations of elastic wave scattering with two holes which based on the elastodynamics, employing complex functions are investigated to study the relationship between texture vibrating plate dynamic wettability and elastic wave scattering. Experimental results show the dynamic behavior of droplet was unstable. In 0 to π/2 cycle, droplet appeared the waveform with front steep and rear gentle along the flow direction. In π/2 to π cycle, droplet appeared slightly periodic oscillation and accompanied by a certain ripple. Based on the dynamic wetting phenomenon in a single cycle, the influence of elastic wave scattering on wetting property are analyzed. Analysis has shown that the stress concentration is caused by complex elastic wave scattering. The more concentrated the stress, the more concentrated the elastic wave energy. Compared with the single hole, the variations of dynamic stress concentration factors for two holes are complex due to the influence of interaction between two holes. Droplet emerge movement is response to the local vibration. The vibration spread in elastic plate at a time of strain, this elastic force cause droplet displacement and vibration, and accompanied with energy transfer.

Dynamic Stress Concentrations in Infinite Plates with a Circular Cutout Based on Refined Theory

In this paper, based on the refined dynamic equations of plate bending vibration, the wave function expansion method is employed to investigate the elastic wave scattering and dynamic stress concentrations in infinite plates with a circular cutout. By applying the orthogonal function expansion method, the problem is reduced into solving a set of infinite algebraic equations. Then, by using the series truncation method, the above infinite algebraic equations reduce to the finite algebraic equations. As examples, the numerical results of dynamic moment concentration factor (DMCF) in infinite plates with one circular cutout under free boundary conditions subjected to an incident flexural wave are presented, and then the influences of the parameters including incident wavenumber, thickness of plates and frequency on the dynamic moment distributions are also analysed. The analyses indicate that the wave type of scattering waves around the circular cutout converts into the propagating wave from the attenuating wave when the cutoff frequency calculated by this study is 0.861 and the DMCFs vary remarkably nearby the cutoff frequency. This phenomenon is more prominent in thick plates.

Scattering of SH Wave by a Cylindrical Inclusion and a Semi-Cylindrical Hollow Near Vertical Interface Crack in the Bi-Material Half Space

AbstractWith the aid of the Green's function method and complex function method, the scattering problem of SH-wave by a cylindrical inclusion and a semi-cylindrical hollow in the bi-material half space is considered to obtain the steady state response. Firstly, by the means of the image method, the essential solution of displacement field as well as Green's function is constructed which satisfies the stress free on the horizontal boundary in a right-angle space including a cylindrical inclusion and a semi-cylindrical hollow and bearing a harmonic out-plane line source force at any point on the vertical boundary. Secondly, the bi-material half space is divided into two parts along the vertical interface, and the first kind of Fredholm integral equations containing undetermined anti-plane forces at the linking section is established by “the conjunction method” and “the crack-division method”, the integral equations are reduced to the algebraic equations consisting of finite items by effective truncation. Finally, dynamic stress concentration factor around the edge of cylindrical inclusion and dynamic stress intensity factor at crack tip are calculated, and the influences of effect of interface and different combination of material parameters, etc. on dynamic stress concentration factor and dynamic stress intensity factor are discussed.

Dynamic effects of single fiber break in unidirectional glass fiber-reinforced composites

In a unidirectional composite under static tensile loading, breaking of a fiber is shown to be a locally dynamic process that leads to stress concentrations in the interface, matrix and neighboring fibers that can propagate at high speed over long distances. To gain better understanding of this event, a fiber-level finite element model of a two-dimensional array of S2-glass fibers embedded in an elastic epoxy matrix with interfacial cohesive traction law is developed. The brittle fiber fracture results in release of stored strain energy as a compressive stress wave that propagates along the length of the broken fiber at speeds approaching the axial wave-speed in the fiber (6 km/s). This wave induces an axial tensile wave with a dynamic tensile stress concentration in adjacent fibers that diminishes with distance. Moreover, dynamic interfacial failure is predicted where debonding initiates, propagates and arrests at longer distances than predicted by models that assume quasi-static fiber breakage. In the case of higher strength fibers breaks, unstable debond growth is predicted. A stability criterion to define the threshold fiber break strength is derived based on an energy balance between the release of fiber elastic energy and energy absorption associated with interfacial debonding. A contour map of peak dynamic stress concentrations is generated at various break stresses to quantify the zone-of-influence of dynamic failure. The dynamic results are shown to envelop a much larger volume of the microstructure than the quasi-static results. The implications of dynamic fiber fracture on damage evolution in the composite are discussed.