Vibrodiagnostic parameters of fatigue damage in rectangular plates. Part 2. Straight cracks of constant depth

The paper discusses the results of analytical determination of vibrodiagnostic parameters of fatigue damage in the form of Mode I straight cracks of constant depth in a rectangular homogeneous uniform-thickness plate with various plate fastening conditions and vibration modes. It is demonstrated that, in the range of the relative crack depth up to 0.3, the parameter of distortion of vibration monoharmonicity in the 2nd-order superharmonic resonant mode is one-two orders of magnitude higher than the value of a relative change of the plates natural frequency.Translated from Problemy Prochnosti, No. 1, pp. 43–59, January–February, 2005.     

Approximate analytical determination of vibrodiagnostic parameters of a cracked elastic body under subharmonic resonance. Part 1. Weak resonance

The paper discusses an approximate analytical method for the calculation of vibrodiagnostic parameters of an elastic body with a closing crack, which is modeled by an elastic system with a single degree of freedom at a bilinear asymmetric characteristic of the restoring force, in the region of a weak 1/2-order subharmonic resonance. __________ Translated from Problemy Prochnosti, No. 2, pp. 26–40, March–April, 2008.     

Bending of a plate containing a periodic system of collinear cracks with regard for the contact of crack lips

We study the process of bending of a plate weakened by a periodic system of collinear cracks with regard for the contact of crack lips. The stress-strain state of the plate is found by the method of solution of the problems of linear conjugation from the theory of functions of complex variable. It is shown that if the crack lips are in contact over a part of the thickness of the plate, then the intensity factors of forces decrease and the intensity factors of moments increase as compared with the case of contact of the crack lips along the line of intersection with the surface. __________ Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 44, No. 2, pp. 46–52, March–April, 2008.     

Approximate Analytical Determination of Vibrodiagnostic Parameters of Non-Linearity of Elastic Bodies Due to the Presence of a Closing Crack. Part 1. Available and Proposed Methods of Solution

The paper discusses the available analytical methods and the results of investigation of vibrations of elastic bodies with a bilinear asymmetric characteristic of restoring force that simulates the behavior of a local discontinuity in a material in the form of a closing fatigue crack. An approximate analytical method is put forward for the determination of vibrodiagnostic parameters of the vibration process of the nonlinear system under study in the range of weak superharmonic resonances.     

Approximate analytical determination of vibrodiagnostic parameters of a cracked elastic body under subharmonic resonance. Part 2. Strong resonance

Using the approach proposed in Part 1, an approximate calculation of vibration parameters is made for an elastic body with a closing crack, in the region of a strong 1/2-order subharmonic resonance with the lower-harmonic amplitude of free vibration spectrum larger than the main amplitude of forced vibrations. __________ Translated from Problemy Prochnosti, No. 3, pp. 5–16, May–June, 2008.     

Coplanar perturbation of a crack lying on the mid-plane of a plate

Several groups have studied experimentally the deformation of the front of mode I cracks propagating quasistatically along the interface between bonded plates. The theoretical interpretation of such experiments has always been based up to now on a formula of Rice (ASME J Appl Mech 52:571–579, 1985); this formula provides the first-order variation of the local mode I stress intensity factor resulting from some small, but otherwise arbitrary coplanar perturbation of the front of a semi-infinite crack in an infinite body. To be applicable to bonded plates, this formula requires that the characteristic distance of variation of this perturbation in the direction of the crack front be small compared to all other characteristic dimensions of the problem, and first of all the thickness of the plates. This condition is unfortunately frequently violated in practice. The purpose of this paper is therefore to provide a more exact formula for the variation of the local stress intensity factor, for the specific cracked geometry and boundary conditions used in experiments; this should allow for more accurate theoretical interpretations. This is done in two steps. The first one consists in adapting Rice’s (ASME J Appl Mech 52:571–579, 1985) treatment, applicable to the extreme case of plates of infinite thickness, to the other extreme one of plates of infinitesimal thickness, using the standard Love-Kirchhoff plate theory. An interesting outcome of the analysis is that the distance from the crack front to the boundary of the plate acts as a “cutoff length”, in the sense that when the distance between two points on the crack front gets larger than it, the influence of the crack advance at the first point upon the stress intensity factor at the second diminishes quickly; the plate thickness, however, plays no similar role. The second step consists in supplementing the theoretical expressions applicable to extreme values of the plate thickness with finite element computations providing results for intermediate values. These computations lead to the definition of a simple, approximate but accurate “interpolation formula” for the variation of the local stress intensity factor, applicable to plates of arbitrary thickness.     

The influence of porosity on the fatigue crack growth behavior of Ti–6Al–4V laser welds

The effect of porosity––a common welding defect––on the fatigue crack growth rate (FCGR) in Ti–6Al–4V laser welds was investigated. The experimental results reveal that porosity was present in partial penetration welds over a narrow fusion zone (FZ) with martensite structure. The FCGR of the FZ was lower than that of the base plate. The fracture surface morphology of weld metal was much rougher as compared to that of the base plate. Randomly oriented martensite in the FZ led to local cleavage fracture along a preferred plane, thus, altering the crack growth direction significantly out of the primary crack plane. The zigzag crack path in the FZ resulted in a reduced FCGR at a given ΔK compared to the base plate. Besides, the porous weld showed a serration on the crack growth curve, and behaved the similar crack growth characteristics as the defect free one. SEM fractography revealed that the deflection of crack path around porosity together with local notch blunting as the crack tip pierced into porosity, balanced the increased FCGR for the occurrence of instant crack advance as the crack front reached the porosity at a low stress ratio. In contrast, the serration and drop in FCGR occurred sparingly at a high stress ratio as the crack front met the porosity.     

Field of residual stresses in a coating with crack

We consider an object with coating deposited on its plane surface. The coating is subjected to the action of known uniform uniaxial tensile residual stresses. We analyze the field of residual stresses formed in the coating as a result of the formation of a long flat crack perpendicular both to the direction of action of tensile stresses and to the surface of the coating. The problem is studied in the two-dimensional statement. The stress field is investigated in the sections perpendicular both to the crack plane and to the surface of the coating. Two cases are analyzed, namely, the case of a through crack (through the entire thickness of the coating) and the case of a nonthrough crack with plastic zone on its continuation. The performed numerical analysis enables us to estimate the possibility of subsequent fracture of the coating after crack initiation. __________ Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 42, No. 2, pp. 80–88, March–April, 2006.     

A finite-element model for the study of vibration of a beam with a closing crack

We present a finite-element model to be used in a study of vibration of a beam with a closing crack. Some special features of numerical solution and methods for its fast realization are discussed. The results of experimental verification of the model are provided. __________ Translated from Problemy Prochnosti, No. 5, pp. 114–120, September–October, 2008.     

Approximate Analytical Determination of Vibrodiagnostic Parameters of Non-Linearity of Elastic Bodies Due to the Presence of a Closing Crack. Part 2. Determination of Diagnostic Parameters in Principal and 2-nd Order Superharmonic Resonances

Using the constitutive equations derived by the author, variously approximated analytical expressions have been obtained for the determination of principal- and superharmonic-resonance vibrodiagnostic parameters of fatigue damage in the form of a Mode I closing crack in an elastic body. The reliability of the analytical solution is assessed by comparing the calculated and the numerical solution results.     

Hardness properties and microscopic investigation of crack–crystal interaction in SiO<Subscript>2</Subscript>–MgO–Al<Subscript>2</Subscript>O<Subscript>3</Subscript>–K<Subscript>2</Subscript>O–B<Subscript>2</Subscript>O<Subscript>3</Subscript>–F glass ceramic system

In view of the potential engineering applications requiring machinability and wear resistance, the present work focuses to evaluate hardness property and to understand the damage behavior of some selected glass–ceramics having different crystal morphologies with SiO₂–MgO–Al₂O₃–K₂O–B₂O₃–F composition, using static micro-indentation tests as well as dynamic scratch tests, respectively. Vickers hardness of up to 5.5 GPa has been measured in glass–ceramics containing plate like mica crystals. Scratch tests at a high load of 50 N in artificial saliva were carried out in order to simulate the crack–microstructure interaction during real-time abrasion wear and machining operation. The experimental observations indicate that the novel “spherulitic-dendritic” shaped crystals, similar to the plate like crystals, have the potential to hinder the scratching induced crack propagation. In particular, such potential of the ‘spherulitic-dendritic’ crystals become more effective due to the larger interfacial area with the glass matrix as well as the dendritic structure of each mica plate, which helps in crack deflection and crack blunting, to a larger extent. While modest damage tolerant behavior is observed in case of ‘spherulitic-dendritic’ crystal containing material, severe brittle fracture of plate like crystals were noted, when both were scratched at 50 N load.     

Dynamic response of interfacial finite cracks in orthotropic materials subjected to concentrated loads

A cohesive zone model has been proposed to model crack growth with a part-through process zone in a thin solid. With the solid being modeled in Kirchhoff’s plate theory, the crack with a relatively long, inclined front is modeled as a line discontinuity with a finite cohesive zone within the plate. A cohesive force law is adopted to capture the effect of residual strength and residual rigidity of a plate cross-section gradually cracking through the thickness. It is derived by a plane-strain elasticity analysis of a cross section normal to the part-through crack. It is then applied in the plate formulation of a line crack to simulate its propagation within the plate plane. This model essentially resolves the originally three-dimensional crack problem in two hierarchical steps, i.e., in the thickness and in the in-plane directions. In the present study, the bending case is considered. A boundary element method is applied to numerically derive the cohesive force law and simulate the crack growth in a thin titanium-alloy plate. The computational efficiency of the model is demonstrated. The plate is shown to fracture in a nominally brittle or ductile manner depending on its thickness.     

Effect of a riveted wide patch on stresses in a cracked plate

We study the stress-strain state and limiting equilibrium of a thin plate with curvilinear cracks reinforced by a wide patch. The patch is arbitrarily located relative to the cracks and attached to the plate with elastic rivets. The boundary-value problem is reduced to a system of singular integral and integro-algebraic equations and this system is solved by the method of mechanical quadratures. Numerical analysis is performed for the case of a plate with one curvilinear or rectilinear crack reinforced by an elliptic patch. The stress intensity factors formed in this reinforced cracked plate and ultimate loads are determined for various geometric and physical parameters of the plate, crack, patch, and rivets. Karpenko Physicomechanical Institute, Ukrainian Academy of Sciences, L'viv. Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 34, No. 1, pp. 37–46, January–February, 1998.     

On the Effect of Plate Thickness on Post-Overload Fatigue Crack Growth

Plate thickness can have a profound effect on fatigue crack growth following theapplication of an overload cycle. A modified strip-yield model is presented for determining the effects of plate thickness based on the mechanism of plasticity-induced crack closure and first-order plate theory. This approach eliminates the need for any empirical or fitting parameters. Comparisons are made with experimental data for the case of a single tensile overload applied under otherwise constant. ΔK loading. The theoretical crack growthpredictions are found to be in good agreement with the experimental data.     

Correlation of a plastic zone length near the tip of a mode I crack in an orthotropic material with anisotropy parameters

We derived equations that relate the length of a plastic zone near a mode I crack tip in a plate made of an orthotropic material with yield strength levels in the direction of the anisotropy axes. The case of crack orientation along one of the anisotropy axes is examined, with the latter being determined by the strain hardening of a material at the stage preceding the crack nucleation. The growth of yield strength along the axes lying in the plane of the plate is shown to result in smaller sizes of the plastic zone. An increase in yield strength in the direction of the normal to the above plane leads to an increase in its length. Ukrainian Regional Research and Design Institute of Civil Engineering, Kiev, Ukraine. Translated from Problemy Prochnosti, No. 4, pp. 32–37, July–August, 1999.     

Stress intensity solutions for cracked plates by the dual boundary method

We describe the application of the dual boundary element method for the determination of stress intensity factors in plate bending problems. The loadings considered include internal pressure, and also combined bending and tension. Mixed mode stress intensity factors are evaluated by a crack surface displacement extrapolation technique and the J-integral technique. The boundary element results for the case studies considered in the paper have been compared with either analytical or finite element results and in all cases good agreement has been achieved. __________ Translated from Problemy Prochnosti, No. 5, pp. 81–93, September–October, 2007.     

Thermomechanical behavior of a plate composed of layers with different transparencies under the action of thermal radiation

We study the thermal and mechanical processes running in a two-layer plate (in the case of perfect mechanical contact between the opaque and semitransparent layers) caused by the thermal radiation of a heated plane surface parallel to the composite plate and located on the side of the opaque layer. The contact boundary-value problem of heat conduction is reduced to an equivalent system of three nonlinear Volterra-type equations solved by the method of successive approximations. The dependences of the distributions of temperature and stresses in the plate on the ratio of thicknesses of the layers are investigated. It is shown that the influence of the thermal radiation of the opaque layer on the computed temperature in the plate is significant at temperatures higher than 530°K. As the thickness of the semitransparent layer decreases for a fixed thickness of the opaque layer, the temperature gradient across the thickness of the semitransparent layer sharply increases. The maximum tensile stresses in the plate may appear in the opaque or semitransparent layer depending on the ratio of the their thicknesses. For certain thicknesses of the semitransparent layer, they can attain the maximum permissible values. __________ Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 43, No. 6, pp. 17–26, November–December, 2007.     

Analyses of infinite pairs of surface cracks in elastic plates

Stress intensity factors and crack opening displacements are presented for infinite pairs of surface cracks in plates subjected to remote tension by using the three dimensional weight function method developed in [7,8]. A wide range of configuration parameters is considered. The results compare very well with double edge cracks as crack aspect ratio tends to zero; with collinear cracks as it tends to infinity; with a pair of surface cracks in a wide plate when the ratio of crack length to plate width is small; and with a single surface crack in large plates when both the ratios of crack length to plate width and crack depth to plate thickness are small. Also illustrated is the significant difference between a single surface crack and the surface cracks in pairs when the ratio of crack depth to plate thickness is large.     

On determination of the natural frequency of transverse and longitudinal vibrations of a cracked beam. Part 1. analytical approach

We consider a perfectly elastic cantilever beam with a crack. The influence of the crack depth and location on the vibration mode of the beam is simulated by a local change in the cross section. This problem is solved by the Rayleigh method. Fairly simple formulas for the determination of the natural frequency of the first mode of bending and longitudinal vibrations of a cantilever beam with an open and closing crack are derived. Institute for Problems of Strength, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Problemy Prochnosti, No. 2, pp. 35–44, March–April, 1999.     

Limiting equilibrium of a spherical shell nonuniform across the thickness and containing a surface crack

The problem of limiting equilibrium of an elastoplastic spherical shell nonuniform across the thickness and containing a surface crack is reduced to a system of singular integral equations. The algorithm of numerical solution of this system takes into account the conditions of plasticity of thin shells and the conditions of boundedness of stresses in the vicinity of the crack. The influence of internal pressure and the mechanical parameters of functionally inhomogeneous material on the opening displacement of the surface crack and the length of plastic strips on its continuation is investigated. __________ Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 43, No. 3, pp. 5–11, May–June, 2007.