The purpose of this study is to extend the solution of the temperature fields in the weld pool to... more The purpose of this study is to extend the solution of the temperature fields in the weld pool to the transient part. In this respect, a moving heat front in a semi infinite solid with constant heat flux boundary condition is considered. Then the temperature fields in the transient period of weld pool formation are determined by Neumark's time marching method. The numerical results reveal interesting information. Finally, it is observed that results obtained in the final steps are comparable to the quasi-steady state solution.
International Journal of Mechanical Sciences, 2013
ABSTRACT The solutions of a Volterra type edge dislocation in an isotropic wedge with free–free a... more ABSTRACT The solutions of a Volterra type edge dislocation in an isotropic wedge with free–free and fixed–free boundary conditions are accomplished by means of the Mellin transformation. The same technique is employed to carry out stress analysis in a wedge under concentrated normal and shear forces. The dislocation solutions are employed as strain nuclei to derive integral equations for a wedge weakened by multiple cracks. These equations are solved numerically for dislocation density functions on the cracks which are used to determine stress intensity factors. In the special cases of quarter and half planes, the solutions agree well with those available in literature. As a new result, the interaction of an edge- and an embedded-crack with different orientations is investigated.
International Journal of Engineering Science, 1987
(') N. I. Mushelishvili, Application of integrals of Cauchy type to a class of singular integral ... more (') N. I. Mushelishvili, Application of integrals of Cauchy type to a class of singular integral equations, Travaux de l'Institut mathématique de Tbilissi (Trudy Tbilisskogo matematicheskogo instituta) vol. 10 (1941) pp. 1-44; also see pp. 161-162. (2) I. Vecoua, Integral equations with a singular kernel of Cauchy type, Travaux de l'Institut mathématique de Tbilissi (Trudy Tbilisskogo matematicheskogo instituta) vol. 10 (1941) pp.
The generalized thermoelasticity based on the Lord-Shulman (LS), Green-Lindsay (GL), and Green-Na... more The generalized thermoelasticity based on the Lord-Shulman (LS), Green-Lindsay (GL), and Green-Naghdi (GN) theories admit the second sound effect. By introducing some parameters all these theories are combined and a unified set of equations is rendered. These equations are then solved for a layer of isotropic and homogeneous material to study the thermal and mechanical wave propagations. The disturbances are generated by a sudden application of temperature to the boundary. The non-dimensionalized form of the ...
Magnetoacoustic emission (MAE) method has been tested regarding its sensitivity to the presence o... more Magnetoacoustic emission (MAE) method has been tested regarding its sensitivity to the presence of electrolytically absorbed hydrogen in low carbon steel. MAE method is based on emission of acoustic waves from the bulk of a ferromagnetic material subjected to magnetization change. The presented preliminary results from a study of the effect of electrolytically charged hydrogen on the MAE response of carbon steel clearly show that the process of hydrogen discharge and ingress into a ferromagnetic material such as steel causes a manifold increase of a MAE parameter ΣA i , which is a sum of amplitudes of impulses from the MAE signal. It is noted that there is a delay in time required, most probably, for the removal of the corrosion products from the steel surface and providing the conditions for the sufficient amount of hydrogen to be absorbed by the near-the-surface volume of the sample. The results are shortly discussed together with the issues connected to the applicability of MAE method as a NDE toll for hydrogen detection.
There is considerable interest in two-dimensional turbulent mixing layer, to name a few e.g. natu... more There is considerable interest in two-dimensional turbulent mixing layer, to name a few e.g. nature, combustion chamber, premixers of gas turbine combustor and many other technological applications. There features are the presence of large vortical structure, free turbulent characteristics, asymptotic behavior, faster growth rate. Some of the parameters that are known to affect the mixing layer behavior are investigated through the numerical models and experimental analysis during these past decades.
The dislocation-distributed technique is utilized to study the elastodynamic fracture behavior of... more The dislocation-distributed technique is utilized to study the elastodynamic fracture behavior of a graded isotropic layer with viscous damping. By investigation of the stress components due to the dislocation, the familiar Cauchy singularity is detected at the location of dislocation. Then the dislocation is utilized for the formation of cracks in the strip. The stress components of dislocation and time-harmonic antiplane point force leads to the integral equations. These equations results in the stress intensity factors (SIF) for the crack configuration in the strip.
The finite strain longitudinal free vibration of a rod is studied. Utilizing second Piola-Kirchho... more The finite strain longitudinal free vibration of a rod is studied. Utilizing second Piola-Kirchhoff stress and Green strain tensors, the equation of motion is written in terms of displacement in reference configuration. Three different types of homogenous boundary conditions may be considered for the rod, leading to three nonlinear eigenvalue problems. The series solutions with three terms satisfying the boundary
The notion of Volterra dislocation is generalized to define a quasi-static uncoupled thermo-elast... more The notion of Volterra dislocation is generalized to define a quasi-static uncoupled thermo-elastic dislocation. The solution to dislocation is obtained in a layer with a fixed and a free boundary. A layer containing multiple cracks with specified temperature at the boundary and aforementioned mechanical boundary conditions is considered. By means of the distributed dislocation technique, the dislocation solution is introduced into the layer to derive integral equations for dislocation density functions on the surfaces of cracks. These equations are Cauchy singular and are solved numerically. The solutions are employed to determine stress intensity factors (SIFs) for cracks in both cases of the impermeable and partially permeable heat flux.
ABSTRACT Stress analysis is carried out in a graded orthotropic layer containing a screw dislocat... more ABSTRACT Stress analysis is carried out in a graded orthotropic layer containing a screw dislocation undergoing time-harmonic deformation. Energy dissipation in the layer is modeled by viscous damping. The stress fields are Cauchy singular at the location of dislocation. The dislocation solution is utilized to derive integral equations for multiple interacting cracks with any location and orientation in the layer. These equations are solved numerically thereby obtaining the dislocation density function on the crack surfaces and stress intensity factors of cracks. The dependencies of stress intensity factors of cracks on the excitation frequency of applied traction and material properties of the layer are investigated. The analysis allows the determination of natural frequencies of a cracked layer. Furthermore, the interactions of two cracks having various configurations are studied.
The stress fields in an orthotropic infinite plane containing Volterra type climb and glide edge ... more The stress fields in an orthotropic infinite plane containing Volterra type climb and glide edge dislocations are derived. The dislocation solutions are utilized to formulate integral equations for dislocation density functions on the surfaces of smooth cracks. The integral equations are of Cauchy singular type and are solved for several different cases of crack configurations and arrangements. The results are used to evaluate modes I and II stress intensity factors for multiple smooth cracks.
In this paper Element Free Galerkin Method is used and applied to the stress analysis problems wh... more In this paper Element Free Galerkin Method is used and applied to the stress analysis problems where material has a tendency towards both elastoplastic and creep behavior. In doing so, following a brief description of the nonlinear constitutive formulation of elastoplastic and creep, a new technique for the numerical analysis of nonlinear problems has been constructed. The method has been examined in two different plates with and without a crack. The value of C*-integral has been used as a base for comparison of the creep results. A rather close agreement is seen between results of this work and the others.
International Journal of Solids and Structures, 2015
Stress analysis is carried out in an isotropic layer weakened by multiple cracks under time-harmo... more Stress analysis is carried out in an isotropic layer weakened by multiple cracks under time-harmonic loading. The viscous damping is used to model energy dissipation in the material. The analysis is based on the stress fields caused by climb and glide of an edge dislocation in the layer. The solution for dislocation is obtained by means of the integral transform method. Furthermore, stress analysis in the intact layer under self-equilibrating harmonic point loads is carried out. These solutions are employed to derive a set of Cauchy singular integral equations for analyzing cracks parallel/perpendicular to the layer boundary. The numerical solution of these equations yields dislocation densities on a crack surface which are used to determine dynamic stress intensity factors over a range of frequency. The natural frequencies of layers with horizontal cracks are obtained and the interaction of multiple cracks is studied.
International Journal of Solids and Structures, 1997
The antiplane deformation of an isotropic wedge with finite radius is studied in this paper. Depe... more The antiplane deformation of an isotropic wedge with finite radius is studied in this paper. Depending upon the boundary data prescribed on the circular segment of the wedge, traction or displacement, two problems are analysed. In each problem three different cases of boundary conditions on the radial edges are considered. The radial boundary data are: traction-displacement, displacement-displacement and traction-traction. The solution of governing differential equations is accomplished by means of finite Mellin transforms. The closed form solutions are obtained for displacement and stress fields in the entire domain. The geometric singularities of stress fields are identical to those cited in the literature. However, in displacement-displacement case under certain representation of boundary condition, another type of singularity has been observed.
Large numbers of creep cavities have been measured in AISI type 304 stainless steel using automat... more Large numbers of creep cavities have been measured in AISI type 304 stainless steel using automatic image analysis techniques. Among other things, the data exhibit substantial amounts of scatter, and indicate that the distribution of creep cavities may not be spatially homogeneous, even in the presence of uniform stress and temperature fields. The cavity radii appear to be. approximately distributed according to a conditional Weibull distribution. Indirect evidence is presented to support the view that the nucleation of cavities is heavily influenced by grain boundary sliding. Comparisons are drawn with the observed cavity radius distributions and the predictions of the analytical cavity growth model of Chen and Argon and a constrained cavity growth model due to Rice. It is found that the distribution predicted by the constrained growth model is considerably narrower than the experimental distribution, but that the model of Chen and Argon shows reasonable agreement with experiment.
The stress fields in an infinite plane containing Volterra type climb and glide edge dislocations... more The stress fields in an infinite plane containing Volterra type climb and glide edge dislocations under time-harmonic excitation are derived. The dislocation solutions are utilized to formulate integral equations for dislocation density functions on the surfaces of smooth cracks. The integral equations are of Cauchy singular type which are solved numerically for several different cases of crack configurations and arrangements. The results are used to evaluate modes I and II stress intensity factors for multiple smooth cracks.
International Journal of Solids and Structures, 2004
ABSTRACT Stress analysis is accomplished for an infinite isotropic wedge weakened by a screw disl... more ABSTRACT Stress analysis is accomplished for an infinite isotropic wedge weakened by a screw dislocation. Two different cases of boundary conditions, i.e., traction–displacement and traction–traction, is considered for the wedge. The Mellin transform is utilized to solve the governing differential equation. The dislocation solution is employed for the analysis of wedges containing multiple cracks under antiplane deformation. The resultant system of singular integral equations is solved numerically to determine dislocation density on the cracks surfaces. This allows the calculation of crack opening displacements and stress intensity factors. The effects of wedge angle and cracks location and orientation on the stress intensity factors of straight cracks are investigated.
ABSTRACT Based on the Timoshenko beam model the equations of motion are obtained for large deflec... more ABSTRACT Based on the Timoshenko beam model the equations of motion are obtained for large deflection of off-center impact of a column by a rigid mass via Hamilton's principle. These are a set of coupled nonlinear partial differential equations. The Newmark time integration scheme and differential quadrature method are employed to convert the equations into a set of nonlinear algebraic equations for displacement components. The equations are solved numerically and the effects of weight and velocity of the rigid mass and also off-center distance on deformation of the column are studied.
The solution of Volterra type climb and glide edge dislocations is utilized to formulate integral... more The solution of Volterra type climb and glide edge dislocations is utilized to formulate integral equations for an orthotropic homogeneous infinite plane weakened by multiple smooth cracks and/or cavities. Cavities are considered as closed curved cracks without singularity. The integral equations are of Cauchy singular type which are converted to hypersingular integral equations. These equations are then solved numerically to determine stress intensity factors for cracks and hoop stress on the cavities. The results for isotropic and orthotropic planes are compared with available solutions in literature and excellent agreement is observed. The formulation allows stress analysis of orthotropic planes with several arbitrarily oriented cracks and cavities.
The purpose of this study is to extend the solution of the temperature fields in the weld pool to... more The purpose of this study is to extend the solution of the temperature fields in the weld pool to the transient part. In this respect, a moving heat front in a semi infinite solid with constant heat flux boundary condition is considered. Then the temperature fields in the transient period of weld pool formation are determined by Neumark's time marching method. The numerical results reveal interesting information. Finally, it is observed that results obtained in the final steps are comparable to the quasi-steady state solution.
International Journal of Mechanical Sciences, 2013
ABSTRACT The solutions of a Volterra type edge dislocation in an isotropic wedge with free–free a... more ABSTRACT The solutions of a Volterra type edge dislocation in an isotropic wedge with free–free and fixed–free boundary conditions are accomplished by means of the Mellin transformation. The same technique is employed to carry out stress analysis in a wedge under concentrated normal and shear forces. The dislocation solutions are employed as strain nuclei to derive integral equations for a wedge weakened by multiple cracks. These equations are solved numerically for dislocation density functions on the cracks which are used to determine stress intensity factors. In the special cases of quarter and half planes, the solutions agree well with those available in literature. As a new result, the interaction of an edge- and an embedded-crack with different orientations is investigated.
International Journal of Engineering Science, 1987
(') N. I. Mushelishvili, Application of integrals of Cauchy type to a class of singular integral ... more (') N. I. Mushelishvili, Application of integrals of Cauchy type to a class of singular integral equations, Travaux de l'Institut mathématique de Tbilissi (Trudy Tbilisskogo matematicheskogo instituta) vol. 10 (1941) pp. 1-44; also see pp. 161-162. (2) I. Vecoua, Integral equations with a singular kernel of Cauchy type, Travaux de l'Institut mathématique de Tbilissi (Trudy Tbilisskogo matematicheskogo instituta) vol. 10 (1941) pp.
The generalized thermoelasticity based on the Lord-Shulman (LS), Green-Lindsay (GL), and Green-Na... more The generalized thermoelasticity based on the Lord-Shulman (LS), Green-Lindsay (GL), and Green-Naghdi (GN) theories admit the second sound effect. By introducing some parameters all these theories are combined and a unified set of equations is rendered. These equations are then solved for a layer of isotropic and homogeneous material to study the thermal and mechanical wave propagations. The disturbances are generated by a sudden application of temperature to the boundary. The non-dimensionalized form of the ...
Magnetoacoustic emission (MAE) method has been tested regarding its sensitivity to the presence o... more Magnetoacoustic emission (MAE) method has been tested regarding its sensitivity to the presence of electrolytically absorbed hydrogen in low carbon steel. MAE method is based on emission of acoustic waves from the bulk of a ferromagnetic material subjected to magnetization change. The presented preliminary results from a study of the effect of electrolytically charged hydrogen on the MAE response of carbon steel clearly show that the process of hydrogen discharge and ingress into a ferromagnetic material such as steel causes a manifold increase of a MAE parameter ΣA i , which is a sum of amplitudes of impulses from the MAE signal. It is noted that there is a delay in time required, most probably, for the removal of the corrosion products from the steel surface and providing the conditions for the sufficient amount of hydrogen to be absorbed by the near-the-surface volume of the sample. The results are shortly discussed together with the issues connected to the applicability of MAE method as a NDE toll for hydrogen detection.
There is considerable interest in two-dimensional turbulent mixing layer, to name a few e.g. natu... more There is considerable interest in two-dimensional turbulent mixing layer, to name a few e.g. nature, combustion chamber, premixers of gas turbine combustor and many other technological applications. There features are the presence of large vortical structure, free turbulent characteristics, asymptotic behavior, faster growth rate. Some of the parameters that are known to affect the mixing layer behavior are investigated through the numerical models and experimental analysis during these past decades.
The dislocation-distributed technique is utilized to study the elastodynamic fracture behavior of... more The dislocation-distributed technique is utilized to study the elastodynamic fracture behavior of a graded isotropic layer with viscous damping. By investigation of the stress components due to the dislocation, the familiar Cauchy singularity is detected at the location of dislocation. Then the dislocation is utilized for the formation of cracks in the strip. The stress components of dislocation and time-harmonic antiplane point force leads to the integral equations. These equations results in the stress intensity factors (SIF) for the crack configuration in the strip.
The finite strain longitudinal free vibration of a rod is studied. Utilizing second Piola-Kirchho... more The finite strain longitudinal free vibration of a rod is studied. Utilizing second Piola-Kirchhoff stress and Green strain tensors, the equation of motion is written in terms of displacement in reference configuration. Three different types of homogenous boundary conditions may be considered for the rod, leading to three nonlinear eigenvalue problems. The series solutions with three terms satisfying the boundary
The notion of Volterra dislocation is generalized to define a quasi-static uncoupled thermo-elast... more The notion of Volterra dislocation is generalized to define a quasi-static uncoupled thermo-elastic dislocation. The solution to dislocation is obtained in a layer with a fixed and a free boundary. A layer containing multiple cracks with specified temperature at the boundary and aforementioned mechanical boundary conditions is considered. By means of the distributed dislocation technique, the dislocation solution is introduced into the layer to derive integral equations for dislocation density functions on the surfaces of cracks. These equations are Cauchy singular and are solved numerically. The solutions are employed to determine stress intensity factors (SIFs) for cracks in both cases of the impermeable and partially permeable heat flux.
ABSTRACT Stress analysis is carried out in a graded orthotropic layer containing a screw dislocat... more ABSTRACT Stress analysis is carried out in a graded orthotropic layer containing a screw dislocation undergoing time-harmonic deformation. Energy dissipation in the layer is modeled by viscous damping. The stress fields are Cauchy singular at the location of dislocation. The dislocation solution is utilized to derive integral equations for multiple interacting cracks with any location and orientation in the layer. These equations are solved numerically thereby obtaining the dislocation density function on the crack surfaces and stress intensity factors of cracks. The dependencies of stress intensity factors of cracks on the excitation frequency of applied traction and material properties of the layer are investigated. The analysis allows the determination of natural frequencies of a cracked layer. Furthermore, the interactions of two cracks having various configurations are studied.
The stress fields in an orthotropic infinite plane containing Volterra type climb and glide edge ... more The stress fields in an orthotropic infinite plane containing Volterra type climb and glide edge dislocations are derived. The dislocation solutions are utilized to formulate integral equations for dislocation density functions on the surfaces of smooth cracks. The integral equations are of Cauchy singular type and are solved for several different cases of crack configurations and arrangements. The results are used to evaluate modes I and II stress intensity factors for multiple smooth cracks.
In this paper Element Free Galerkin Method is used and applied to the stress analysis problems wh... more In this paper Element Free Galerkin Method is used and applied to the stress analysis problems where material has a tendency towards both elastoplastic and creep behavior. In doing so, following a brief description of the nonlinear constitutive formulation of elastoplastic and creep, a new technique for the numerical analysis of nonlinear problems has been constructed. The method has been examined in two different plates with and without a crack. The value of C*-integral has been used as a base for comparison of the creep results. A rather close agreement is seen between results of this work and the others.
International Journal of Solids and Structures, 2015
Stress analysis is carried out in an isotropic layer weakened by multiple cracks under time-harmo... more Stress analysis is carried out in an isotropic layer weakened by multiple cracks under time-harmonic loading. The viscous damping is used to model energy dissipation in the material. The analysis is based on the stress fields caused by climb and glide of an edge dislocation in the layer. The solution for dislocation is obtained by means of the integral transform method. Furthermore, stress analysis in the intact layer under self-equilibrating harmonic point loads is carried out. These solutions are employed to derive a set of Cauchy singular integral equations for analyzing cracks parallel/perpendicular to the layer boundary. The numerical solution of these equations yields dislocation densities on a crack surface which are used to determine dynamic stress intensity factors over a range of frequency. The natural frequencies of layers with horizontal cracks are obtained and the interaction of multiple cracks is studied.
International Journal of Solids and Structures, 1997
The antiplane deformation of an isotropic wedge with finite radius is studied in this paper. Depe... more The antiplane deformation of an isotropic wedge with finite radius is studied in this paper. Depending upon the boundary data prescribed on the circular segment of the wedge, traction or displacement, two problems are analysed. In each problem three different cases of boundary conditions on the radial edges are considered. The radial boundary data are: traction-displacement, displacement-displacement and traction-traction. The solution of governing differential equations is accomplished by means of finite Mellin transforms. The closed form solutions are obtained for displacement and stress fields in the entire domain. The geometric singularities of stress fields are identical to those cited in the literature. However, in displacement-displacement case under certain representation of boundary condition, another type of singularity has been observed.
Large numbers of creep cavities have been measured in AISI type 304 stainless steel using automat... more Large numbers of creep cavities have been measured in AISI type 304 stainless steel using automatic image analysis techniques. Among other things, the data exhibit substantial amounts of scatter, and indicate that the distribution of creep cavities may not be spatially homogeneous, even in the presence of uniform stress and temperature fields. The cavity radii appear to be. approximately distributed according to a conditional Weibull distribution. Indirect evidence is presented to support the view that the nucleation of cavities is heavily influenced by grain boundary sliding. Comparisons are drawn with the observed cavity radius distributions and the predictions of the analytical cavity growth model of Chen and Argon and a constrained cavity growth model due to Rice. It is found that the distribution predicted by the constrained growth model is considerably narrower than the experimental distribution, but that the model of Chen and Argon shows reasonable agreement with experiment.
The stress fields in an infinite plane containing Volterra type climb and glide edge dislocations... more The stress fields in an infinite plane containing Volterra type climb and glide edge dislocations under time-harmonic excitation are derived. The dislocation solutions are utilized to formulate integral equations for dislocation density functions on the surfaces of smooth cracks. The integral equations are of Cauchy singular type which are solved numerically for several different cases of crack configurations and arrangements. The results are used to evaluate modes I and II stress intensity factors for multiple smooth cracks.
International Journal of Solids and Structures, 2004
ABSTRACT Stress analysis is accomplished for an infinite isotropic wedge weakened by a screw disl... more ABSTRACT Stress analysis is accomplished for an infinite isotropic wedge weakened by a screw dislocation. Two different cases of boundary conditions, i.e., traction–displacement and traction–traction, is considered for the wedge. The Mellin transform is utilized to solve the governing differential equation. The dislocation solution is employed for the analysis of wedges containing multiple cracks under antiplane deformation. The resultant system of singular integral equations is solved numerically to determine dislocation density on the cracks surfaces. This allows the calculation of crack opening displacements and stress intensity factors. The effects of wedge angle and cracks location and orientation on the stress intensity factors of straight cracks are investigated.
ABSTRACT Based on the Timoshenko beam model the equations of motion are obtained for large deflec... more ABSTRACT Based on the Timoshenko beam model the equations of motion are obtained for large deflection of off-center impact of a column by a rigid mass via Hamilton's principle. These are a set of coupled nonlinear partial differential equations. The Newmark time integration scheme and differential quadrature method are employed to convert the equations into a set of nonlinear algebraic equations for displacement components. The equations are solved numerically and the effects of weight and velocity of the rigid mass and also off-center distance on deformation of the column are studied.
The solution of Volterra type climb and glide edge dislocations is utilized to formulate integral... more The solution of Volterra type climb and glide edge dislocations is utilized to formulate integral equations for an orthotropic homogeneous infinite plane weakened by multiple smooth cracks and/or cavities. Cavities are considered as closed curved cracks without singularity. The integral equations are of Cauchy singular type which are converted to hypersingular integral equations. These equations are then solved numerically to determine stress intensity factors for cracks and hoop stress on the cavities. The results for isotropic and orthotropic planes are compared with available solutions in literature and excellent agreement is observed. The formulation allows stress analysis of orthotropic planes with several arbitrarily oriented cracks and cavities.
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