Effect Of Initial Stress Research Articles

Non-Destructive Testing Mechanism for Pre-Stressed Steel Wire Using Acoustic Emission Monitoring.

In this paper, the guided ultrasonic wave propagation characteristics in the axisymmetric pre-stressed viscoelastic waveguide for acoustic emission (AE) monitoring, using the semi-analytical finite element (SAFE) method, is studied broadly. For the numerical investigation, a single high-strength steel wire is considered. A comprehensive and in-depth study on the AE signal’s propagation characteristics is carried out based on the SAFE method. Both undamped and damped waveguides are considered for attaining SAFE solutions and presented in a detailed manner. The SAFE method for an axisymmetric cross-section in cylindrical coordinates analyzes the two main influencing factors of steel wire in a practical scenario: Material damping and initial tension. For the effect of initial stress, the calculation shows that the initial tensile stress can increase and decrease the energy velocity and attenuation factor of most modal waves above the cut-off frequency, and the effect is linear. Some longitudinal wave modes in the high-frequency region show their potential for AE monitoring as these modes have a low attenuation factor and small external surface vibration. By considering various states of initial stress in a damped waveguide, the effect of pre-stress on the dispersion characteristics is understood in a better manner. A non-destructive testing (NDT) mechanism for pre-stressed steel wire using AE monitoring is proposed for the health monitoring of structures.

Propagation of Rayleigh wave in initially-stressed compressible hyperelastic materials

In this paper, propagation of Rayleigh surface wave in a compressible half-space solid with initial stress is discussed. The basic formulation of the problem includes the non linear theory of elasticity and theory of invariants. The equations governing infinitesimal motions superimposed on a finite deformation are used to study the combined effect of initial stress and finite deformation on wave speed. Secular equation governing the wave speed of a surface wave is presented and analyzed in detail. Various conditions are found for the existence and uniqueness of the wave speed. Furthermore, to understand the physical behavior of surface wave propagation, the theoretical results are plotted and analyzed for various numerical values of parameters involved in a prototype model. It is concluded that the surface wave speed is considerably affected by compression and tension as well as due to the stretch ratios of deformation. Moreover, for various choices of numerical values of governing parameters, the admissible numerical values of initial stress components and stretch ratios are also illustrated graphically.

Rayleigh waves in a magneto-thermoelastic anisotropic half-space

The aim of the present article is to study the propagation of Rayleigh surface waves in homogeneous transversely isotropic medium. The problem is considered under the purview of three-phase-lag model in an initially stressed magneto-thermoelastic half-space. Normal mode analysis is employed to the considered equations and eigenvalue approach is used to obtain the expressions for the displacements, stresses, and temperature. The frequency equations of Rayleigh surface waves are derived, and different cases are discussed. The effect of magnetic field and initial stress on the phase velocity and attenuation coefficient of Rayleigh waves are presented graphically.

Effect of Impedance Boundary on the Reflection of Plane Waves in Fraction-Order Thermoelasticity in an Initially Stressed Rotating Half-Space with a Magnetic Field

In this research article, the propagation of the plane waves in an initially stressed rotating magneto-thermoelastic solid half-space in the context of fractional-order derivative thermoelasticity is studied. The governing equations in the x–z plane are formulated and solved to obtain a cubic velocity equation that indicates the existence of three coupled plane waves. A reflection phenomenon for the incidence of a coupled plane wave for thermally insulated/isothermal surface is studied. The plane surface of the half-space is subjected to impedance boundary conditions, where normal and tangential tractions are proportional to the product of normal and tangential displacement components and frequency, respectively. The reflection coefficients and energy ratios of various reflected waves are computed numerically for a particular material and the effects of rotation, initial stress, magnetic field, fractional-order, and impedance parameters on the reflection coefficients and energy ratios are shown graphically.

Dispersion relation for transverse waves in pre-stressed irregular single-walled carbon nanotubes

This article studies the dispersion relation of transverse waves in an initially stresses single-walled carbon nanotube (SWCNT) with surface irregularity using Flügge shell theory. Taking into account the effects of surface irregularity and initial stresses, propagation of transverse waves is studied and dispersion curves are plotted for optical transverse waves in several figures. The effects of surface irregularity and initial stresses are confirmed by comparing obtained numerical results with those in cases of uniform and initial stress–free SWCNT. Obtained results turn out that, the increase of irregularity parameter increases the phase velocity of transverse waves, while the increase of the initial stress parameter decreases the phase velocity of transverse waves propagating in SWCNTs. To the author best knowledge, effects of surface irregularity and initial stresses on transverse waves propagation, especially propagation in single-walled carbon nanotubes, have not been done before. The previous studies were devoted to the uniform and initial stresses-free carbon nanotubes. It should be emphasized that the transverse waves propagation in pre-stressed and irregular single-walled carbon nanotubes is novel, workable, and at the beginning of the path. İn this manner, understanding the influences of surface irregularity as well as initial stresses on the phase velocity of transverse waves may serve as useful references for the applications and designs of nano oscillators and nanodevices, in which single-walled carbon nanotubes act as the most prevalent nanocomposite structural element.

Effect of vertical effective and initial static shear stresses on the liquefaction resistance of sands in cyclic direct simple shear tests

To investigate the effect of the vertical effective and initial static shear stresses on cyclic resistance under cyclic loading with principal stress rotation, a series of cyclic direct simple shear tests were conducted on loose and dense Nakdong River sands. The results revealed that the increasing vertical effective stress (σ′v0) often decreased the cyclic resistance, and the decrease was more evident for a high initial static shear ratio (α = 0.2). The degree of reduction of the correction factor Kσ predicted by recommended methods in practice mostly showed more conservative results than the measured Kσ values in this study. Increasing the initial static shear stress decreased the cyclic resistance of the loose sand. For the dense sand, the cyclic resistance either increased or decreased, depending on the combined effect of the σ′v0 and α levels. The correction factor Kα decreased minimally to 0.689 for the loose sand and rose maximally to 1.175 for the dense sand. When the relative density (Dr) increased from 40% to 80%, the increase in the cyclic resistance for a high α (=0.2) was considerably greater than that for α = 0. The cyclic response of the loose sand was due to sudden flow deformation without any apparent shear strain accumulation, regardless of the α value; while the cyclic response of the dense sand indicated plastic strain accumulation. Thus, the cyclic resistance of sand is influenced by the combined effect of Dr, σ′v0, and α, with the potential influence of principal stress rotation.

Effect of initial minimum principal stress and unloading rate on the spalling and rockburst of marble: a true triaxial experiment investigation

Hard rock often performs as brittle failures, such as cracking, spalling, and rockburst, induced by excavation in deep underground engineering. To understand the effect of the minimum principal stress and unloading rate on the spalling and rockburst of marble, unloading experiments were carried out by using true triaxial equipment combined with a high-speed camera, acoustic emission instrumentation, and scanning electron microscope. The experimental results showed that the failure process of marble specimens was more stable and less inclined to exhibit dynamic ejection with a low strain energy release per unit time under a low unloading rate. At the same time, the initial minimum principal stress controlled the marble’s failure mode by changing its mode from predominantly shear failure to shear-tension failure as the minimum principal stress decreased, similar to the spalling behaviors of surrounding rock observed in the underground tunnel. What’s more, the dynamic rockburst of the marble specimen was simulated under the condition with a high unloading rate, high initial minimum principal, and free face on the specimen. Based on these experimental investigations, a flowchart was also presented to estimate the possible failure mode of marble specimens under different initial minimum principal stress and unloading rate conditions, which would be conducive to the disaster prevention of hard rock in deep underground engineering.

Mechanical properties and failure behavior of rock with different flaw inclinations under coupled static and dynamic loads

The deep fissured rock mass is affected by coupled effects of initial ground stress and external dynamic disturbance. In order to study the effect of internal flaw on pre-stressed rock mechanical responses and failure behavior under impact loading, intact granite specimens and specimens with different flaw inclinations are tested by a modified split Hopkinson pressure bar (SHPB) and digital image correlation (DIC) method. The results show that peak strain and dynamic strength of intact specimens and specimens with different flaw angles (α) decrease with the increase of axial static pressure. The 90° flaw has weak reduction effect on peak strain, dynamic strength and combined strength, while 45° and 0° flaws have remarkable reduction effect. Specimens with 90° flaw are suffered combined shear and tensile failure under middle and low axial static pre-stresses, and suffered shear failure under high axial static pre-stresses. Specimens with 45° and 0° flaws are suffered oblique shear failure caused by pre-existing flaw under different axial static pre-stresses. Besides, based on digital image correlation method, it is found that micro-cracks before formation of macro fractures (include shear and tensile fractures) belong to tensile cracks. Tensile and shear strain localizations at pre-existing flaw tip for specimen with 45° and 0° flaws are produced much earlier than that at other positions.

A generalized strain energy function using fractional powers: Application to isotropy, transverse isotropy, orthotropy, and residual stress symmetry

In this paper, we propose a generalized strain energy density function based on invariants of stretch tensor with arbitrary exponents. We employ polynomial, logarithmic and exponential functions of these invariants to develop the strain energy functions. We also study characteristics and applications of the proposed model for isotropy, transverse isotropy, orthotropy with a special focus on initial/residual stress symmetry. The proposed invariants generalize the existing strain energy potentials constructed with invariants of Cauchy stretch. We construct generalized strain energy functions for initial stress problems using initial stress symmetries. We obtain objectivity of strain energy for initially stressed transversely isotropic solids to derive the invariants and study resulting symmetry. By extending Dunford–Taylor integration based approach and tensor diagonalization approach, we obtain stress through differentiation of anisotropic scalar invariants with respect to a tensor. These approaches are usually applicable for derivative of isotropic tensor functions with respect to tensors. Using initial stress compatibility, we derive constraint equations for material parameters by evaluating the limits of Cauchy stress in the reference configuration. In order to apply the proposed model for initial stress problems, we further investigate bending and unbending of hyperelastic structures. We study bending of a rectangle to a cylinder and unbending of a cylinder to a rectangle in presence of initial/residual stress and observe both magnifying and moderating effects of initial stress for stress distribution and flexural characteristics. Using experimental data we substantiate the proposed model for seat foam, bovine pericardium and rabbit skin which represent compressible isotropic and incompressible orthotropic materials. For demonstration, we use both polynomial and exponential functions of these invariants. Furthermore, we develop a nonlinear finite element computational model for thermo-hyperelastic structure where thermal stress represents the initial stress. We corroborate this stress–strain data with the proposed model for initial stress symmetry and observe nice agreements.

Wave Dispersion in Multilayered Reinforced Nonlocal Plates under Nonlinearly Varying Initial Stress

This paper deals with the effects of initial stress on wave propagations in small-scale plates with shape memory alloy (SMA) nanoscale wires. The initial stress is exerted on the small-scale plate along both in-plane directions. A scale-dependent model of plates is developed for taking into consideration size influences on the wave propagation. In addition, in order to take into account the effects of SMA nanoscale wires, the one-dimensional Brinson’s model is applied. A set of coupled differential equations is obtained for the non-uniformly prestressed small-scale plate with SMA nanoscale wires. An exact solution is obtained for the phase and group velocities of the prestressed small-scale system. The influences of non-uniformly distributed initial stresses as well as scale and SMA effects on the phase and group velocities are explored and discussed. It is found that initial stresses as well as the orientation and volume fraction of SMA nanoscale wires can be used as a controlling factor for the wave propagation characteristics of small-scale plates.

The effects of initial deviatoric stress on anisotropy of marine clay and strain components

This study investigated effects of initial deviatoric stress state and the orientation of their major principal stresses on the strain components and shear strength of soft marine clay. Hollow cylinder test results demonstrated that the axial and circumferential strain component magnitudes substantially depended on the initial deviatoric stress and the principal stress direction. The octahedral shear indicated the highly anisotropic microstructure of the clay, and the initial deviatoric stress significantly affected the octahedral shear strain development and influenced the anisotropic microstructure. The results can provide an experimental basis for constitutive modeling of marine clay and provide guidance for ocean engineering.

Wave propagation in an initially stressed rotating thermo-diffusive medium with two-temperature and micro-concentrations

PurposeThe purpose of this paper is to study the reflection of plane waves in an initially stressed rotating thermoelastic diffusive medium with micro-concentrations and two-temperature.Design/methodology/approachA two-dimensional model of generalized thermoelasticity is considered. The governing equations are transformed into the non-dimensional forms using the dimensionless variables. Then, potential functions are introduced for the decoupling of the waves. Further, appropriate boundary conditions are assumed to completely solve the problem. Finally, numerical computations are performed using MATLAB.FindingsThe problem is solved analytically and it is found that there exist five coupled waves in addition to an independent micro-concentration wave in the considered medium. The amplitude ratios and energy ratios of these reflected waves have also been computed numerically for a specific material.Originality/valueThe modulus values of amplitude ratios are presented graphically to exhibit the effects of angular velocity, initial stress, two-temperature, diffusion and micro-concentration parameters. The expressions of energy ratios obtained in explicit form are also depicted graphically as functions of angle of incidence. The law of conservation of energy at the free surface during reflection phenomenon is also verified.

Shear wave propagation in magneto poroelastic medium sandwiched between self-reinforced poroelastic medium and poroelastic half space

PurposeThe purpose of this paper is to investigate the effect of reinforcement, inhomogeneity and initial stress on the propagation of shear waves. The problem consists of magneto poroelastic medium sandwiched between self-reinforced medium and poroelastic half space. Using Biot’s theory of wave propagation, the frequency equation is obtained.Design/methodology/approachShear wave propagation in magneto poroelastic medium embedded between a self-reinforced medium and poroelastic half space is investigated. This particular setup is quite possible in the Earth crust. All the three media are assumed to be inhomogeneous under initial stress. The significant effects of initial stress and inhomogeneity parameters of individual media have been studied.FindingsPhase velocity is computed against wavenumber for various values of self-reinforcement, heterogeneity parameter and initial stress. Classical elasticity results are deduced as a particular case of the present study. Also in the absence of inhomogeneity and initial stress, frequency equation is discussed. Graphical representation is made to exhibit the results.Originality/valueShear wave propagation in magneto poroelastic medium embedded between a self-reinforced medium, and poroelastic half space are investigated in presence of initial stress, and inhomogeneity parameter. For heterogeneous poroelastic half space, the Whittaker’s solution is obtained. From the numerical results, it is observed that heterogeneity parameter, inhomogeneity parameter and reinforcement parameter have significant influences on the wave characteristics. In addition, frequency equation is discussed in absence of inhomogeneity and initial stress. For the validation purpose, numerical results are also computed for a particular case.

A mixed-field Timoshenko beam-column element for direct analysis of tapered I-sections members

ABSTRACT Tapered members produced by robotic fabrication techniques offer architectural and structural advantages and have the potential to become more prevalent than prismatic members. However, the conventional analysis and design methods based on simplified assumptions such as equivalent stiffness cannot be used to accurately evaluate a member's performance. To provide a reliable and practicable stability design method, a direct analysis method of tapered I sections is proposed. A mixed-field tapered beam-column element is derived for use within the modeling of structural frames. The effects of initial geometric imperfection and additional shear stress are directly considered in the element formulation. A polynomial describing the member's critical initial out-of-plumbness is adopted, and an arbitrarily located internal hinge is incorporated in the element to enhance the element's deformation capacity and capture the behaviors of the most critical section. Displacement and force interpolation matrices incorporating the shear deformation are utilized, and the Gauss quadrature method is employed to evaluate the element stiffness matrix. Finally, verification examples demonstrate that the proposed method can be used to accurately and efficiently evaluate the performance of tapered members, indicating that the element can be conveniently employed in member and frame analysis and design.

Evaluation of the effects of initial deviatoric stress and cyclic stress amplitude on liquefaction potential of loose and medium-dense sands: An energy-based method

The energy-based method is a promising tool for evaluating soil liquefaction potential. In this study, the effects of initial deviatoric stress (qs) and cyclic stress amplitude (qcyc) on soil liquefaction potential in undrained cyclic triaxial tests were evaluated using the energy-based method. The testing results indicate that the required dissipated energy for the onset of liquefaction is influenced by both qcyc and qs for a loose sand, while it is only affected by qs for a medium-dense sand. For both loose and medium-dense sands, there exists an approximately unique relationship between the residual excess pore water pressure ratio and the normalized dissipated energy (Wn) during cyclic loadings, independent of qcyc and qs. The relationship between the double-amplitude axial strain and the Wn is influenced not only by initial conditions but also by loading conditions. The evaluation of the effects of the various factors on the liquefaction potential based on the energy-based method provides insight into the liquefaction resistance for both loose and medium-dense sands.

Coupled Lamb waves propagation along the direction of non-principal symmetry axes in pre-stressed anisotropic composite lamina

Based on the linear three-dimensional elastic theory and the mechanics theory of incremental deformation, using the Legendre orthogonal polynomial expansion (LOPE) method, the wave equations of Lamb wave propagation in the non-principal symmetry axes direction of anisotropic composite lamina was firstly derived when the initial stresses were applied in the horizontal and vertical directions. Subsequently, the coupled equations of Lamb wave propagation were numerically solved. In order to verify the accuracy of the process, the dispersion curves of phase velocity in an isotropic aluminum plate and anisotropic composite lamina without loaded initial stresses were beforehand calculated by LOPE method to compare with those obtained from the commercial software of DISPERSE® and available data. Then, a series of cases referring to unidirectional fiber reinforced composite lamina were further implemented to study the effects of horizontal initial stress and vertical initial stress on the fundamental Lamb wave modes. The results show that the phase velocity of the A0 mode is more sensitive to the implementation of initial stresses compared with the S0 mode and SH0 mode. Finally, the effect of fiber orientation was illustrated in details.

Effects of initial stresses on reflection phenomenon of plane waves at the free surface of a rotating piezothermoelastic fiber-reinforced composite half-space

In this paper the impact of initial stresses on reflection characteristics of plane waves at the free surface of a rotating piezothermoelastic fiber-reinforced composite (PTFRC) half-space has been investigated. Three theories of thermoelasticity viz. Green-Lindsay, Lord-Shulman and Classical dynamical coupled theories have been used to explore the problem. The expressions of the amplitude ratios of four types of reflected waves viz. quasi-longitudinal (qP), quasi-transverse (qSV), thermal (T-mode) and electro acoustic (EA) waves have been obtained with the aid of suitable boundary conditions which exhibited their reliance on the incident angle, the properties of the rotating media and varying magnitudes of initial stresses and the impacts of the aforesaid parameters have been extensively studied and demonstrated graphically. Also, the energy ratio of the reflected waves has been derived for different values of initial stresses and it has been showed that the total energy flux at the surface attains value unity.

Wave propagation in an initially stressed magneto-thermoelastic medium with voids and microtemperatures

Present analysis is concerned with the propagation of plane waves in an initially stressed magneto-thermoelastic half-space with microtemperatures and voids. It is noticed that there exist four kinds of coupled dilatational waves in addition to shear and microtemperature waves in such type of medium. Using appropriate boundary conditions, the amplitude and energy ratios for the reflected waves have been presented in closed form when (i) a set of coupled dilatational waves is made incident and (ii) a shear wave is made incident. Amplitude ratios of various reflected waves are presented graphically to explore the effects of magnetic field, initial stress and void parameter. It is verified that there is no loss of energy at the free surface during reflection phenomena.

Disturbances in an initially stressed fiber-reinforced orthotropic thermoelastic medium due to inclined load

The present concept is related to the two-dimensional deformation in an initially stressed fiber-reinforced orthotropic thermoelastic model in the context of Green–Naghdi type III (GN III) theory as a result of the application of an inclined load. Normal and shear loads are assumed to be linear. The full expressions for the displacement components, temperature field and stresses are obtained by using normal mode technique. Comparisons are made in an orthotropic, transversely isotropic and an isotropic medium to illustrate the effects of fiber reinforcement on these physical quantities. The effects of initial stress, Green–Naghdi theories (type III and type II), inclination angle of load and time on the field variables are also considered.

Reflection of plane waves on generalized thermoelastic medium under effect of temperature dependent properties and initial stress with three-phase-lag model

The present paper investigates the reflection coefficient of thermoelastic plane waves at the free surface of an elastic half-space influenced by initial stress and temperature-dependent properties in the presence of thermal loading bounded by the three-phase-lag (3PHL) thermoelastic model. It revealed three plane waves, i.e. (thermal wave (T-wave), P-wave, and SV-wave). It provided the numerical solution and presented the effect of initial stress and temperature-dependent properties of the reflection coefficient graphically. Moreover, the paper utilized the altered reflected elastic waves because of initial stress and temperature-dependence to identify the more accurate nature of waves reflection, especially seismic waves.