فهرست مطالب rahmatollah ghajar

This research aims to experimentally investigate the energy absorption of thin-walled lattice tubes with a square section. The walls of the thin-walled tube are made in the form of a lattice with three types of cells: re-entrant auxetic, semi-re-entrant, and conventional honeycomb structures, and the material of the specimens is considered 304 stainless steels. All three types of lattice cells are produced by the rotary laser cutting method on a conventional tube and are axially compressed by a universal test machine under quasi-static loading at a 5 mm/min velocity. The test evaluation parameters are initial maximum force, mean crushing force, crushing force efficiency, energy absorption, and specific energy absorption. The results show that the thin-walled tube with the re-entrant auxetic structure has more specific energy absorption than the other two structures. The specific energy absorption of this structure is 25% higher than the conventional honeycomb structure. The semi-re-entrant structure has more energy absorption and mean crushing force than the other structures. The crushing force efficiency in the conventional honeycomb structure is higher than that of the other two structures, which has a value of 85%.

In this article, the determination of the mechanical properties of a micro-cellular auxetic structure is investigated. This lattice structure consists of hexagonal cells, whose cell-wall dimensions are on a micro-scale. First, using modified strain gradient theory (MSGT) and energy method, the mechanical properties of the micro-cellular auxetic structure are analytically obtained. Then for validation, Young's modulus of a micro-cellular auxetic structure is derived by tensile test and compared with theoretical results. The comparison of analytical and experimental results shows good agreement. A nanosecond laser cutting machine is used to fabricate the microcellular auxetic structure, and the ISO 6892-1 standard is used to perform tensile tests. The results show that the modified strain gradient theory plays an important role in determining the mechanical properties of micro-cellular auxetic structures. In some cases, the results of this theory are more than 100% different from the classical theory. In addition, it can be seen that by changing the dimensional parameters of the micro-cells, the mechanical properties of the auxetic structure can be tunable. For example, by reducing the magnitude of the angle of the cell wall, Young's modulus in the X 1  direction increases, and Young's modulus in the X 2  direction and the shear modulus of the structure decrease

Once a composite laminate is subjected to quasi-static tensile or fatigue loading, some damage modes initiate and propagate in the laminate. The first damage mode is the matrix crack that forms in the layers with an angle to the loading direction. Although not leading to breakage, these cracks reduce the equivalent mechanical properties of the composite laminate. In this paper, a new nonlinear analytical model is presented and used to predict the stiffness degradation of the cross-ply composite laminates. For this purpose, a new third-order polynomial function is proposed as the Helmholtz free energy of the composite, and the appropriate equations are derived. A microscopic experimental test is designed and accompanied by the analytical model to investigate the damage progression in a glass/epoxy cross-ply laminate. Also, finite-element micromechanical models with periodic boundary conditions (PBC) are proposed and used to determine the damage constants. The model is validated against the 3D micromechanical models and the quasi-static uniaxial loading-unloading experimental tests. The validation shows a very good agreement between the model and the experiments.

In this article, elastoplastic properties of polymeric nanocomposites embedded with carbon nanotubes (CNTs) are explored with emphasis on the meso-scale phenomena. To this end, a combination of finite element method and micromechanics is implemented. Accordingly, at first, considering the non-bonded nature of nanotube/polymer interactions, a multiscale finite element method is employed to replace the matrix, CNT, and polymer atoms neighboring it with a perfectly bonded equivalent nanofiller. Subsequently, nanocomposite stress-strain curves are extracted based on the mean field homogenization approach. Using this model, the effects of CNTs orientation and their agglomeration on the mechanical behavior of nanocomposite samples are thoroughly studied. Moreover, it is found that to have an efficient reinforcing effect, the CNT length should be greater than 10 nm. On the other hand, it can be concluded that there is an optimum value of this parameter (i.e. 300 nm) above which, there is no any extra stiffening effect. Furthermore, regarding the CNTs agglomeration, it is revealed that although, theoretical investigations show that increasing CNT volume fraction(VF) leads to an increase in the stiffness, occurring this phenomenon can have a deteriorative role in terms of influencing the mechanical behavior of these nanocomposites at higher VFs.

In this research, the effect of agglomeration and dispersion of the Carbon nanotubes (CNTs) on the viscoelastic properties of CNT-reinforced polymeric nanocomposites is investigated, parametrically. The effective properties of the nanocomposite are obtained by Mori-Tanaka micromechanical approach, assuming completely random oriented CNTs. Considering spherical shaped inclusions for CNTs agglomerated region, two parameters are presented and applied to Mori-Tanaka micromechanical method to model the agglomeration and dispersion of the CNTs. The polymeric matrix is assumed to be viscoelastic. The viscoelastic properties of polymer matrix are simulated by standard linear solid model with three structural parameters. Due to time-dependency of constitutive equation of the matrix, direct using of the micromechanical method is not possible. Hence, the constitutive equations of the matrix are transferred to the Laplace domain and algebraic form the mentioned equations are inserted to the Mori-Tanaka relations. To verify the model, predicted results of that are compared with available experimental data for CNT reinforced polymeric nanocomposites. Investigation of agglomeration parameters shows that the overall properties of the composite can be improved by decreasing agglomeration of the CNTs.

Static and dynamic stress intensity factors are important parameters in the fracture behavior of the cracked bodies. In the present study the displacement correlation technique (DCT) is presented to calculate static and dynamic stress intensity factors of functionally graded materials (FGMs). The displacement field is obtained using finite element method (FEM) and ABAQUS software. To consider the variation of material properties, a subroutine is prepared in the UMAT subroutine of the software. Eight-node singularity elements are used in the FEM. As ABAQUS software is not able to calculate stress intensity factors of FGMs, so a MATLAB code is developed to obtain these factors. By analyzing an example under dynamic load, dynamic fracture behavior of orthotropic FGMs and effect of non-homogeneity parameter are investigated for two cases of material properties variation directions which are perpendicular to each other. To verify presented method, a center crack in a plate of homogeneous and FGM materials are analyzed under static and dynamic loads, the results are compared with data of literatures. The results show that, if the material properties vary parallel to the crack direction, the mode I dynamic stress intensity factor at the crack tip located in the stiffer part increases with increasing of non-homogeneity parameter, while for variation in the normal direction to the crack, this factor first increases and then decreases.

A family of rotating disks used in Iranian turbine and compressor industry is investigated. Mechanical and thermal loads due to working condition would lead to the crack initiation in the inner surface of the disk. The aim of this paper is the development of the two-dimensional weight function for the rotating disks containing semi-elliptical longitudinal cracks. The general form of the two-dimensional weight function is related to the proposed weight functions for embedded cracked domain in literature. In order to determine the unknown coefficient of the weight function, the reference stress intensity factors for cracked geometry subjected to reference loads are calculated. The analysis indicated that the results are independent of the number of terms in proposed weight function expansion. Extracting the weight function for disks with from 90 to 420 mm thickness enables one to predict the stress intensity factor for cracks in the structure subjected to arbitrary loading. The stress intensity factor for each point on the crack front subjecting to one or two dimensional loads would be calculated using the derived weight function. The results reveal that the increasing of the height to thickness ratio in rotating disks leads to the increase of the stress intensity factor for high depth ratio crack ones. Results show that the configuration of the disk sections affects the stress intensity factors of the same aspect ratio cracks in the structures. The comparison of the results obtained from the weight function method and those obtained with FEM are in good agreement.

In this paper, the effect of nonhomogeneous parameter in orthotropic Functionally Graded Material(FGM) in a cracked layer is investigated. It is assumed that the mechanical and thermal properties of material are dependent on x-coordinate (collinear with crack surfaces) in exponential form. The problem is solved for internal and edge crack in two way, integral equations and generalized differential quadrature method. Thermal loading is in a way that temperature distribution in the layer is uniform. Because of variation in mechanical and thermal properties, stress distribution due to this loading is not uniform. In the solution of problem with integral equations method, first, thermo-elasticity problem with no cracks and then isothermal crack problem are separately solved. Afterward with these solutions, the main problem will be solved. In order to solve isothermal crack problem, after conversion and simplifying the equations in orthotropic material, Navier's equations will be solved with the Fourier. Numerical solution of the problem is the generalized differential quadrature element method that is being presented for verification of the results of the integral equations for a specific state in the diagram format. Also the effect of temperature on intensity factor with various values of nonhomogeneous parameter is investigated.

This paper concerns the effect of auxiliary fields and distance of contours from the crack tip on the accuracy of stress intensity factors of Functionally Graded Materials (FGMs), using the interaction integral method. In the first step, defining auxiliary fields of displacement, strain, and stress appropriately, the interaction integral is derived which is independent of derivatives of properties of the materials. Actual and auxiliary fields of displacement, strain and stress are used to compute the interaction integral. Actual fields are obtained by isoparametric finite element method, while auxiliary fields are constructed by use of the crack tip properties on the basis of William’s solution. These auxiliary fields are not appropriate, except near the crack tip. Therefore, different non-equilibrium and incompatibility formulations are used to consider the changes in non-homogeneous material. Considering the changes in FGMs as an exponential function, the results will be obtained from these formulations and are compared with others recorded in the literature. Furthermore, considering different contours, the effect of distance of contours from the crack tip on the stress intensity factors of FGMs is examined. The results confirm that the solutions using the incompatibility and constant constitutive tensor are more accurate. In contrast the non-equilibrium method is not proper for contours which are placed far away from the crack tip and presents less accuracy.

In this study, the analysis of transient thermoelastic response of a functionally graded (FG) non-axisymmetric viscoelastic cylinder is presented. The material properties are assumed to be time- dependent and radially and circumferentially non-homogeneous. The finite element (FE) formulations of the thermoelastic problem are obtained using the virtual work method and all the coupling terms are considered. According to material dependencies and nonlinearity of the constitutive equation, an iterative-based FE solution is suggested in order to solve thermo-elastic equations. The effects of material in homogeneities on the time-dependent response of mechanical and thermal components are investigated. From the results of this study, it is concluded that, using appropriate material inhomogeneities can improve the magnitudes of stress components, especially shear stress.

Most of the studies done in low velocity impact of plates only involve plate’s response to centric impact and usually have been done in no-preload condition. In this study، nonlinear numerical elasticity analysis of eccentric low-velocity impact of rectangular sandwich plate with composite face sheets subjected to biaxial preloads، and the effect of indenter energy، the stiffness of core، the thickness of core، geometry of indenter and the existence of epoxy layers in the connection between core and face sheets on impact response are investigated. In this regard، impact 3D simulation in ABAQUS rather than approximate plate theories is utilized for extracting impact responses based on the three-dimensional theory of elasticity. Numerical results are compared with experimental data presented in other references and the numerical model is verified. The analysis results showed that the contact force increased due to the reduction of overall plate movement in the cases of eccentric impact and biaxial tension preloads، which result in augmentation of damage.

Offshore platforms are exposed to random cyclic loads imposed on the structure by natural phenomena including waves, sea currents, wind and etc, so fatigue analysis of these structures is one of the most important design steps. Hot spot method is one of the most common techniques for evaluating of the fatigue life of offshore platforms. In this approach, the stress adjacent to the weld is estimated by extrapolation from the stress distribution approaching the weld, as obtained by finite element method or perhaps from strain measurements on the surface. In order to calculate the fatigue life of Amir Kabir semi-submersible drilling platform, first a model of platform is created. Then according to the environmental conditions of the Caspian sea, hydrodynamic forces exerted on the platform are calculated. The simulated hydrodynamic forces are then applied to the platform structure for calculating the stress and strain fields in the whole structure. It is found that the intersection of column and pontoon is the critical section of the platform and hence the fatigue life of the structure is predicted in terms of conditions of this location.

Elliptical subsurface cracks are one of the probable types of cracks that occur in engineering structures, especially under rolling contact fatigue. Due to the non-symmetrical geometry, coupling of the fracture modes occurs in an elliptical subsurface crack and the crack under shear loading will experience all fracture modes. This paper investigates the coupling of the fracture modes of elliptical subsurface cracks under uniform shear loadings in two directions. First, a three-dimensional parametric finite element model of a crack in an infinite space has been developed and validated. Then, by moving the crack close to surface, mixed mode stress intensity factors (SIFs) have been calculated for cracks with aspect ratios of 0.2-1.0 and ratios of crack depth to crack length of 0.05-1.0. Based on the results, coupling of the fracture modes occur considerably when the crack depth becomes less than crack length. By decreasing of the crack depth from infinite to 0.05, shear SIFs and KImax/KIImax ratio increase at least up to 65% and 90%, respectively. Six equations for SIFs of the subsurface cracks under uniform shear loadings in two directions have been obtained by fitting to the finite element results. These equations can be used efficiently in high accurate calculation of the SIFs for subsurface cracks with any aspect ratio and depth under uniform shear loading with any direction.

In this paper, dynamic analysis of doubly curved composite shells under low velocity impact is studied analytically. The governing equations based on the first-order deformation theory (FSDT) are derived for simply supported boundary conditions. The contact force history is predicted using two models of complete and improved spring-mass. Considering the displacement components as the doubly Fourier series, equations of motion shell and impactor are solved analytically. By writing code in Matlab softwar, using Galerkin method, the dynamic response of shell is obtained.0 In this investigation, the effect of geometrical parameters, such as curvature changes, aspect ratio (curvature length ratio), fiber orientation, mass and velocity of impactor, with constant impact energy, on the impact response of shell is determined by two models.

To investigate, understanding and predicting dynamic fracture behavior of a cracked body, dynamic stress intensity factors (DSIFs) are important parameters. In the present work interaction integral method is presented to compute static and dynamic stress intensity factors for three-dimensional cracks contained in the functionally graded materials (FGMs), and is implemented in conjunction with the finite element method (FEM). By a suitable definition of the auxiliary fields, the interaction integral method which is not related to derivatives of material properties can be obtained. For the sake of comparison, center, edge and elliptical cracks in homogeneous and functionally graded materials under static and dynamic loading are considered. Then material gradation is introduced in an exponential form in the two directions in and normal to the crack plane. Then the influence of the graded modulus of elasticity on static and dynamic stress intensity factors is investigated. It has been shown that, material gradation has considerable reduce influence on DSIFs of functionally graded material in comparison with homogenous material. While, static stress intensity factors can decrease or increase, depend on the direction of gradation material property.

Elliptical subsurface cracks are one of the probable types of cracks that occur in engineering structures. Due to the non-symmetrical geometry with respect to the crack surface, coupling of the fracture modes occurs in an elliptical subsurface crack and so, the crack under normal loading will experience all fracture modes. Mode III caused by the coupling effect under normal loading is negligible whereas mode II is significant. In this paper, mixed mode two dimensional weight functions of the elliptical subsurface cracks parallel to the surface are derived for aspect ratios of αlpha=0.2, 0.4, 0.6, 0.8, 1.0 and ratios of crack depth to crack length of Betta=0.05, 0.06, 0.08, 0.1, 0.14, 0.2, 0.3, 0.5, 1.0. Mixed mode stress intensity factors under uniform normal loading are used as reference stress intensity factors. By curve fitting on the calculated weight functions coefficients, the derived weight functions are able to be used for any αlpha and Betta. To verify the weight functions, the stress intensity factors of all points of the crack front are calculated under linear, elliptic paraboloid and trigonometric paraboloid stress distributions and compared to the finite element results. Comparison of the results shows high accuracy with mean relative error less than 7%. Using derived weight functions, mixed mode stress intensity factors of the subsurface elliptical crack can be determined for any αlpha and Betta and under any normal stress distributions.

In this research, low velocity impact tests have been carried out on laminated composite plates to investigate the impactor shape and temperature effect on the dynamic behavior and material damage. The woven E glass/ epoxy laminates were manufactured. The studies have been done on plate with dimensions of 120 mm× 120 mm× 3 mm, impactor with 1.4 m/s incident velocity and 7 kg mass. Specimens have been impacted by using steel flat, hemispherical, ogival and conical impactors, all 12.7 mm in diameter. The specimens impacted by the conical impactor absorbed most energy because of local penetration. The flat impactor caused the highest peak force and lowest contact duration as expected. The force history of the impactor, projectile displacement and absorbed energy of different impactor shapes has been measured and compared with each other. The temperatures were in the range of room temperature to 150 °C. The parameters including maximum contact force, projectile displacement and the absorbed energy of different temperature have been investigated. Maximum contact force decreased with increasing of temperature, and deflection of impactor increased with increasing of temperature.

In this study، the first mode of stress intensity factor of semi-elliptical circumferential crack in the outer surface of a cylinder with radius to thickness ratio of 30، is investigated. The cylinder is applied in semi-submersible drilling platforms. First، the stress field of the cylinder under thermal and mechanical loads is extracted based on semi couple thermo-elastic equations. Then، the weight functions are derived for deepest and surface points using three reference loads results. Explicit expressions of stress intensity factors for surface and deepest points are presented using thermo-elastic stress field and the weight functions of the cracked cylinder. The results obtained by proposed weight functions and those obtained by finite element method and those presented in the literatures have a good accuracy. The interaction effects of thermal and mechanical loads on the stress intensity factors are studied. The results show that with increasing load ratio، the dimensionless stress intensity factors of deepest and surface points، decrease and increase، respectively.

The autofrettaged thick-walled tube containing semi-elliptical crack is investigated. To study the variation of stress intensity factor on crack front، at first، two dimensional weight function is extracted. Stress intensity factor of all points on crack front can be calculate using proposed weight function، also، the complicated loading on crack faces including the loads due to axial gradient pressure in short cylinder and open-end tubes can be considered. Results show that، opposite of the cylinder subjected to uniform pressure، in pipes under gradient pressure، the maximum stress intensity factor are not necessarily on deepest point and surface points. The maximum stress intensity factor occurs on non-surface points in autofrettaged tubes. The results obtained from two dimensional weight function method have a good accuracy with the results obtained from finite element method. Prediction of fatigue crack configuration using two dimensional weight function can be more accurate than those obtained from one dimensional weight function.

In this study، repeated low velocity impacts on aluminum plate are investigated experimentally and numerically. In order to investigate the failure mechanism، Lemitre''s model of the continuum damage mechanics is used. Numerical simulation is carried out employing a Vumat subroutine in Abaqus FE package. Repeated impacts are performed on the plate with the same level of energy. Plastic deformation is observed on the plate in the first impact. During the subsequent impacts and prior to crack initiation، the effect of strain hardening on the aluminum plate is observed. After crack initiation، the stiffness of the structure decreases. As the impacts continue، stiffness further decreases and the damage area increases، finally perforation and penetration appear on the plate. Also، the present model is validated by the experimental results. Comparison of numerical with experimental results shows a good agreement for the force-time and force-displacement histories.

X-100 steel is one of the most recently developed materials for production of gas transportation pipelines. This material is severely anisotropic. Smooth and notched round bars with different notch radius and flat notched specimens with different notch radius and notch depth in tension are tested to characterize the failure of this material under quasi-static loading condition.Triaxiality factor that embodies the effect of mean stress and Lode angle are the parameters that affect the failure. Lode angle is a recently introduced parameter in the fracture of ductile materials and contains the effect of third invariant of deviatoric stress tensor. The load-displacement curves and pictures taken by 2 photo camera are used to study the effects of anisotropy, triaxiality factor and Lode angle on the failure of this material. Finally an experimental failure criterion is developed to model the failure of this material. In this failure criterion, strain at fracture initiation is a function of X and TF. Models that take into account the effect of Lode angle, Triaxiality factor and anisotropy in plasticity and damage are the current state of the art in the research of ductile materials.

In the last decade, decrease of the wear rate, increase in the axel load, and the velocity of the trains have changed the main damage mechanism of railway wheels from wear to rolling contact fatigue (RCF). RCF may lead to surface and subsurface cracks. The interaction between wear and RCF, removes the surface cracks, but the subsurface crack propagate gradually, and may lead to deeper and more dangerous fractures. In this study, by considering an elliptical subsurface crack, the lifetime of an Iranian railway system wheel has been predicted using FEM, and under RCF condition. To this end, a 3D model of a cracked R7T wheel with 920mm diameter in contact with UIC60 rail has been prepared and analyzed in Abaqus FEM software. The histories of the stress intensity factors of the subsurface crack have been extracted in one cycle wheel rolling. Then, equivalent stress intensity factors have been calculated using Tanaka and Liu-Mahadevan models. Finally, wheel lifetime has been predicted by Walker relation. This paper provides a local criterion of critical crack length and crack growth lifetime that is essential for frequent inspections of railroad wheel.

Engineers have a range of methods to estimate the fatigue life under multiaxial conditions. Each of these predictive methods is generally subjected to restrictions, related to the inherent simplified assumptions. The objective of this paper is to evaluate the validity of commonly used multiaxial fatigue criteria for different multiaxial loading conditions. The best criterion is identified through comparative analysis. The assessment is based on the experimental research findings of the SAE notched shaft, which is used as a benchmark [1]. The relative performance of three of existing multiaxial fatigue theories based on the strain criteria and the critical plane approaches are investigated. There is not any fixed strain life criterion that can predict the fatigue life best for different loading. Among all the critical plane models considered, Fatemi and Socie model [2] gives best fatigue life prediction for both multiaxial in phase and 90° out of phase loading cases.

During the offshore drilling operations by drillships or semisubmersible vessels the drillstring in its first drilljoint to the Kelly suffers bending due to float vessel roll or pitch. The cyclic bending stress at any point along the drillstring, is a function of the roll or pitch angle, Kelly position in bushing, and hookload. The cumulative fatigue damage of the drillpipe due to cyclic stresses near the drillpipe connection to Kelly has been calculated in this paper. The effects of the cyclic stress amplitude variation are also taken into account. Then five multiaxial fatigue models are evaluated under variable amplitude loading (similar to drillpipe loading) conditions. Comparing the results of the five models predictions by the muliaxial fatigue tests experimental data under variable amplitude axial-torsional loading, show that the combined critical plane and energy models predict the fatigue life better than the others. It works much better for variable amplitude loading than the existing models.