NONLINEAR VIBRATION FOR MODERATE THICKNESS RECTANGULAR CRACKED PLATES INCLUDING COUPLED EFFECT OF ELASTIC FOUNDATION

Based on Reissner plate theory and Hamilton variational principle, the nonlinear equations of motion were derived for the moderate thickness rectangular plates with transverse surface penetrating crack on the two-parameter foundation. Under the condition of free boundary, a set of trial functions satisfying all boundary conditions and crack＇s continuous conditions were proposed. By employing the Galerkin method and the harmonic balance method, the nonlinear vibration equations were solved and the nonlinear vibration behaviors of the plate were analyzed. In numerical computation, the effects of the different location and depth of crack, the different structural parameters of plates and the different physical parameters of foundation on the nonlinear amplitude frequency response curves of the plate were discussed.

Using Extended Finite Element Method for Computation of the Stress Intensity Factor, Crack Growth Simulation and Predicting Fatigue Crack Growth in a Slant-Cracked Plate of 6061-T651 Aluminum

The 6061-T651 aluminium alloy is one of the most common aluminium alloys for marine components and general structures. The stress intensity factor (SIF) is an important parameter for estimating the life of the cracked structure. In this paper, the stress intensity factors of a slant-cracked plate, which is made of 6061-T651 aluminum, have been calculated using extended finite element method (XFEM) and finite element method (FEM) in ABAQUS software and the results were compared with theoretical values. Numerical values obtained from these two methods were close to the theoretical values. In simulations of crack growth at different crack angles, the crack propagation angle values were closer to the theoretical values in XFEM method. Also, the accuracy and validity of fatigue crack growth curve were much closer to the theoretical graph in XFEM than the FEM. Therefore, in this paper the capabilities of XFEM were realized in analyzing issues such as cracks.

Free Vibration of Stiffened Plate with Cracked Stiffeners

In this paper,a new cracked stiffener model for the stiffener with a partthrough and open crack is proposed,considering the compatibility condition of displacements between the plate and the stiffener.Based on the first-order shear deformation theory,the free vibration of stiffened isotropic plates with cracked stiffeners are investigated for the first time.The description of the crack parameters is based on the continuous equivalent bending stiffness and equivalent depth of the cracked beam,and it takes into consideration of shear deformation,bending-extensional coupling vibration,and eccentricity between the stiffeners and the plate.The stiffened plates with single or multiple cracked stiffeners are formulated and discussed.The Ritz method with the modified characteristic functions is applied to demonstrate the effects of crack parameters(crack depth and location)coupling with the position and number of the cracked stiffeners on the vibration frequencies and modes of the stiffened plate.The validity and accuracy of the present solutions are verified through convergence studies and compared with the finite element results.

ANALYSIS OF NONLINEAR DYNAMIC RESPONSE FOR VISCOELASTIC COMPOSITE PLATE WITH TRANSVERSE MATRIX CRACKS

Based on the Schapery three-dimensional viscoelastic constitutive relationship with growing damage, a damage model with transverse matrix cracks for the unidirectional ?bre rein- forced viscoelastic composite plates is developed. By using Karman theory, the nonlinear dynamic governing equations of the viscoelastic composite plates under transverse periodic loading are es- tablished. By applying the ?nite di?erence method in spatial domain and the Newton-Newmark method in time domain, and using the iterative procedure, the integral-partial di?erential gov- erning equations are solved. Some examples are given and the results are compared with available data.

THE EVALUATION OF STRESS INTENSITY FACTORS OF PLANE CRACK FOR ORTHOTROPIC PLATE WITH EQUAL PARAMETER BY F2LFEM

In this paper, the evaluation of stress intensity factor of plane crack problems for orthotropic plate of equal-parameter is investigated using a fractal two-level finite element method （F2LFEM）. The general solution of an orthotropic crack problem is obtained by assimilating the problem with isotropic crack problem, and is employed as the global interpolation function in F2LFEM. In the neighborhood of crack tip of the crack plate, the fractal geometry concept is introduced to achieve the similar meshes having similarity ratio less than one and generate an infinitesimal mesh so that the relationship between the stiffness matrices of two adjacent layers is equal. A large number of degrees of freedom around the crack tip are transformed to a small set of generalized coordinates. Numerical examples show that this method is efficient and accurate in evaluating the stress intensity factor （SIF）.

Fracture toughness and fatigue crack growth analysis of 7050-T7451 alloy thick plate with different thicknesses

The strength, fracture toughness and fatigue crack growth resistance of 7050-T7451 aluminum alloy plate with different thicknesses （35 mm and 160 ram） were investigated by means of optical microscope, scanning electron microscope and transmission electron microscope. The results show that thicker plate has lower strength and fracture toughness but higher fatigue crack growth resistance, by comparison to the thinner plate. The drop of strength is mainly attributed to grain coarsening in the thicker plate, and the increased degree of recrystallization results in the loss of Kio However, the coarsened grains in the thicker plate make cracks deflected and closure effect enhanced due to surface roughness increased. For both of plates, in the fracture surface subjected plain strain, a transition from transgranular dimpled fracture to intergranular dimpled fracture is observed during the fracture process.

Effect of gradient temperature rolling process on promoting crack healing in Q500 heavy plates

To ensure the quality of heavy plate products as determined by ultrasonic inspection, it is necessary to effectively control defects such as cracks and shrinkage cavities in heavy plates. Generally, some defects such as large size cracks exist due to insufficient deformation in the center of traditionally rolled plates. Compared with the traditional rolling process, gradient temperature rolling(GTR) process can effectively increase deformation inside heavy plates. In this study, the effect of GTR on crack healing was analyzed through a comparison experiment with the uniform temperature rolling(UTR). The results show that the GTR process could increase the plastic strain inside the heavy plate and effectively promote the healing process of the preset cracks. The degrees of crack healing at the center and quarter thickness position of the steel plate via GTR were greater than twice those of the plate via UTR. The GTR process can significantly reduce the internal defects of heavy plates and improve the defect detection level of heavy plate products. Also, The GTR process results in the formation of new crystal grains in the crack region, which is crucial to crack healing.

Edge crack growth of mortar plate specimens under uniaxial loading tests

In this paper, a compression-to-tension conversion technique is developed by applying predominant mode I loading test, using a servo-controlled compression system. The technique is applied to thin mortar plate specimens of different widths that include a prefabricated crack on either a single side to facilitate unilateral crack propagation, or prefabricated cracks positioned on both sides asymmetrically with respect to the specimen midpoint to facilitate bilateral crack propagation under direct tensile stress with a loading rate of 0.001 mm/s. The results show that the main pathways of unilateral crack propagation governing specimen failure are fluctuated locally, but present an approximately straight line overall in the absence of pre-existing internal defects. However, the pathways of bilateral crack propagation are relatively complex, although they present similar characteristics. Analysis results suggest that bilateral crack propagation can be basically divided into three stages, i.e. a stage of linear propagation, a stage representing deviation from the other crack, and a stage where one crack approaches either the other crack or approaches the opposite edge of the specimen, and thereby forming a continuous crack through the specimen. In addition, the stressestrain curves of bilateral crack specimens do not vary significantly around the point of peak stress prior to specimen failure, which means that the specimens do not fail instantaneously.

Formation mechanism of transverse crack in repair welding for thick plate of Q345 high strength steel

Transverse cracks occur usually in repair welding for thick plate of high strength steel. It needs multiple times of repair welding. The quality of production and deliver deadline will be influenced. Therefore, it is very significant to investigate the cause and control of transverse crack in repair welding. In this paper, both ends restraint crack experiment is developed to produce delay transverse crack for high strength steel. Metallographic results show that four types of cracks are found in repair welding metal zone and heat affected zone. Large chevron transverse cracks are found in repair welding zone. Lots of micro transverse cracks are found in inter-layer repair welding metal zone, root HAZ and two ends of repair welding individually. The distribution character and formation mechanism of the transverse crack are further analyzed through hardness testing and residual stress measurement.

Mathematical Modelling and 3D FEM Analysis of the Influence of Initial Stresses on the ERR in a Band Crack’s Front in the Rectangular Orthotropic Thick Plate

This paper deals with the mathematical modelling and 3D FEM study of the energy release rate(ERR)in the band crack’s front contained in the orthotropic thick rectangular plate which is stretched or compressed initially before the loading of the crack's edge planes.The initial stretching or compressing of the plate causes uniformly distributed normal stress to appear acting in the direction which is parallel to the plane on which the band crack is located.After the appearance of the initial stress in the plate it is assumed that the crack's edge planes are loaded with additional uniformly distributed normal forces and the ERR caused with this additional loading is studied.The corresponding boundary value problem is formulated within the scope of the so-called 3D linearized theory of elasticity which allows the initial stress on the values of the ERR to be taken into consideration.Numerical results on the influence of the initial stress,anisotropy properties of the plate material,the crack’s length and its distance from the face planes of the plate on the values of the ERR,are presented and discussed.In particular,it is established that for the relatively greater length of the crack’s band,the initial stretching of the plate causes a decrease,but the initial compression causes an increase in the values of the ERR.

TRANSVERSE VIBRATION CHARACTERISTICS OF VISCOELASTIC RECTANGULAR PLATE WITH CRACK

Based on the two-dimensional viscoelastic differential constitutive relation and the thin plate theory, the differential equations of motion of the viscoelastic plate with an all-over part-through crack are established and the expression of additional rotation induced by the crack is derived. The complex eigenvalue equations of the viscoelastic plate with crack are derived by the differential quadrature method, and the 8method is used at the crack continuity conditions. Dimensionless complex frequencies of a crack viscoelastic plate with four edges simply supported, two opposite edges simply supported and other two edges clamped are calculated. The effects of the crack parameter, the aspect ratio and dimensionless delay time of the material on the transverse vibration of the viscoelastic plate are analyzed.

FSM-Monitoring of Fatigue Crack in Lattice-Stiffened Steel Plate Deck for Bridge Structures

For elucidating applicability of FSM （field signature method） on detection of fatigue crack initiation and monitoring of its propagation, a series of fatigue tests on steel plate decks （4,625 × 2,250 mm^2） stiffened in lattice-shape by longitudinal and lateral ribs was carried out by using a wheel load traveling test machine. The fatigue crack was observed by visual inspection at the weld toe between the deck plate and the longitudinal rib when the number of wheel load traveling repetition was around 210 thousands. The response of FSM-monitoring, which was the potential difference change between the sensing pins （pair）, became clear when the number of the repetition was around 190 thousands. The fatigue crack initiation could be detected by FSM considerably earlier than visual inspection. The fatigue crack propagation such as the direction could also be monitored even though the distance of the sensing pins was extended to 230 mm. On the other hand, the electric field analysis for the virgin situation without any cracks was carried out. The results of analysis indicated that 60 mm length of crack which could not be confirmed by visual inspection could be detected by FSM.

Elastic-plastic analytical solution for centric crack loaded by two pairs of point shear forces in finite plate

The near crack line analysis method was used to investigate a centric crack loaded by two pairs of point shear forces in a finite plate, and the analytical solution was obtained. The solution includes the unit normal vector of the elastic-plastic boundary near the crack line, the elastic-plastic stress fields near the crack line, the variations of the length of the plastic zone along the crack line with an external load, and the bearing capacity of a finite plate with a centric crack loaded by two pairs of point shear forces. The results are sufficiently precise near the crack line because the assumptions of small scale yielding theory have not been made and no other assumptions are taken.

Stresses due to an adhesion crack in T-shaped junction of two orthotropic plates

The general solution of stresses is derived for a T-shaped junction of two thin plates with an adhesion crack. The plates are orthotropic. A shear force is applied on the crack surface. The analysis is based on the supposition that the stresses in each plate can be approximated by a plane stress condition. The results obtained are verified by numerical calculation of FEM.

SPECIAL HIGH-ORDER BENDING CRACK TIP FINITE ELEMENT FOR THE REISSNER PLATE

Based on the crack tip field expansion of the Reissner plate, a special high order bending crack tip element is developed, and the element stiffness matrix is given in the explicit form, which is especially convenient for engineering analyses. A numerical example is presented and compared with previous results to demonstrate the efficiency and accuracy of the special element.

Numerical simulation of plate rigid restraint cracking tests based on cohesive element model

Cohesive element is developed from the Dugdal-Barenblatt model in the field of fracture mechanics. The mechanical constitutive relation of cohesive element can be artificially assumed depending on the specific applications. It has been successfully applied in the study of crystal plasticity/brittle fracture process and decohesion between delaminations. In this paper, tensile experiments of large steel plate with different length of pre-existing cracks are conducted. Based on commercial software ABAQUS, cohesive element is adopted to simulate the tensile tests, and appropriate parameter values are obtained by fitting displacement-force curves. Using these parameters, a numerical method is presented by applying cohesive element to thermo-elastic-plastic finite element method （TEP-FEM） to simulate plate rigid restraint cracking （PRRC） tests. By changing constitutive relation of cohesive element, dimensions of the model and welding conditions, the influence of welding restraint intensity and welding conditions on the crack propagation are discussed, respectively. Three types of welding cold cracking are simulated. Significant influence of welding cold cracking on resistant stress in welding line is captured by this numerical method.

Higher-order crack tip fields for functionally graded material plate with transverse shear deformation

The crack tip fields are investigated for a cracked functionally graded material （FGM） plate by Reissner＇s linear plate theory with the consideration of the transverse shear deformation generated by bending. The elastic modulus and Poisson＇s ratio of the functionally graded plates are assumed to vary continuously through the coordinate y, according to a linear law and a constant, respectively. The governing equations, i.e., the 6th-order partial differential equations with variable coefficients, are derived in the polar coordinate system based on Reissner＇s plate theory. Furthermore, the generalized displacements are treated in a separation-of-variable form, and the higher-order crack tip fields of the cracked FGM plate are obtained by the eigen-expansion method. It is found that the analytic solutions degenerate to the corresponding fields of the isotropic homogeneous plate with Reissner＇s effect when the in-homogeneity parameter approaches zero.

STRESS INTENSITY FACTORS OF A PLATE WITH TWO CRACKS EMANATING FROM AN ARBITRARY HOLE

In this paper, Muskhelishvili complex function theory and boundary collocation method are used to calculate the stress intensity factors (SIF) of a plate with two cracks emanating from an arbitrary hole. The calculated examples include a circular, elliptical, rectangular, or rhombic hole in a plate. The principle and procedure by the method is not only rather simple, but also has good accuracy. The SIF values calculated compare very favorably with the existing solutions. A t the same time,the method can be used far different finite plate with two cracks emanating from a hole with more complex geometrical and loading conditions. It is an effective unified approach for this kind of fracture problems.

Construction Technical Temperature Cracking for a and Control of Concrete Plate Type Raft Foundation

The mass fiat raft foundation Section is large and Cement is in large quantities, the temperature changes in the larger cement hydration heat of the water releasing, the temperature stress is main reason reducing cracking. According to the basement of a project of Guangzhou large slab raft foundation engineering as an example, Discussing the construction technology measures of early crack of large volume concrete of raft plate in the process of construction,. The results show that it Can effectively prevents the slab foundation structure cracking and achieves good results through controlling Concrete materials and concrete temperature Parameter such as the lifting machine temperature and the pouring temperature and the expansion joint or the whole pouring length.

NEAR CRACK LINE ELASTIC-PLASTIC ANALYSIS FOR A FINITE PLATE LOADED BY TWO PAIRS OF ANTIPLANE POINT FORCES

In this paper, the improved near crack line analysis method proposed in Refs. [1] and [2] is used to investigate a center crack loaded by two pairs of antiplane point forces in a finite plate in an elastic-perfectly plastic solid. And the analytical solutions are obtained, that is elastic-plastic stress fields near the crack line and the law that the length of the plastic zone along the crack line is varied with an external loads tr,ld the bearing capacity of a finite plate with a center crack. The results of this paper are sufficiently precise near the crack line, because the assumptions of the small scale yielding theory have not been used and no other assumptions have been taken.