Reinforcement of a thin cracked plate by a system of parallel stringers

The stress-strain state of an infinite plate with curvilinear cracks reinforced by a system of parallel stringers is investigated. The stringers are attached to the plate by riveting. It is assumed that the cracked plate with the system of stringers is in a generalized plane stress state. The boundary-value problem is reduced to a system of singular integral equations, which is solved by the method of mechanical quadratures. Numerical results are presented for a reinforced plate with a rectilinear or curvilinear crack (along a parabolic arc).Karpenko Physicomechanical Institute, Ukrainian Academy of Sciences, L'viv. Translated from Fiziko-Khimicheskaya Mekhanika Materialov, Vol. 30, No. 1, pp. 96–105, January–February, 1994.     

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.     

Growth of plasticity bands around the tip of an arbitrarily oriented crack in a semiinfinite thin plate

Summary Elastoplastic equilibrium is considered for a thin semiinfinite plate containing an arbitrarily oriented rectilinear edge crack. It is assumed that the plastic strains are localized along a narrow band arising from the crack tip. The elastoplastic treatment is then reduced to a planar treatment in the theory of elasticity with an edge kinked crack whose edges are subject to defined forces. The solution is derived by means of singular integral equations. Numerical results have been obtained for a tensile load acting at infinity for a constant pressure acting on the crack edges. An estimate is made of how the free edge of the plate affects the magnitude and orientation of the plasticity band.Translated from Fiziko-Khimicheskaya Mekhanika Materialov, No. 3, pp. 25–31, May–June, 1992.     

Planar elastoplastic behavior in a body containing cracks with plastic strain localized in thin layers

Conclusion A general approach is given for planar treatments (planar state of stress and planar strain) in the elastoplastic equilibrium of a body containing cracks when the plastic strain is localized in thin layers. The plasticity region is represented as rectilinear cracks arising from the vertex of the main crack, on which the plasticity conditions are satisfied. The elastoplastic treatment is thus reduced to a treatment in the linear theory of elasticity for a body weakened by a kinked or branched crack with unknown lengths and orientations for the side branches. The latter are derived during the solution obtained by means of singular integral equations. Numerical results have been obtained for the stretching of an infinite plate containing an arbitrarily oriented rectilinear crack. Values are given for the crack opening at the vertex and for the length and orientation angle of the plasticity band.Translated from Fiziko-Khimicheskaya Mekhanika Materialov, Vol. 27, No. 5, pp. 35–42, September–October, 1991.     

裂纹板贴补应力分析

本文采用含裂纹无限大板特殊基本解和合力边界条件,用体积力法对含裂纹金属薄板的胶贴补强问题进行应力分析。使用一满足胶贴层位移连续条件的剪切单元,把问题转化为对裂纹板和贴片的分析。由于使用的特殊基本解精确满足裂纹面自由力边界条件,避免了对裂纹尖端附近的奇异场进行离散处理,因而可以比较精确地求出裂纹尖端附近的应力分布,同时由于单位集中力引起的裂纹尖端应力强度因子可以解析得到,因而可以较准确地反映出用应力强度因子的降低来表征的贴补效果。作为贴补计算的例子,文中计算了受拉力和剪力作用时,含中心裂纹的金属裂纹板在贴补前后裂纹尖端应力强度因子的降低,给出了贴片的厚度、弹性模量和尺寸及肢贴层厚度等对贴补效果的影响。     

Cracking and mechanical-property forecasting for carburized materials in high-temperature equipment

Conclusion The deformation approach in the nonlinear mechanics of failure has been used to extend the method of equivalent states of strain to determine crack vertex opening for any propagation mechanism. The opening has been determined for transverse shear applied to a crack in a plate and to a crack from antiplanar shear on torsion in a cylindrical specimen having an external ring crack. The equivalent stress state method is simple and can be widely used in engineering.Translated from Fiziko-Khimicheskaya Mekhanika Materialov, No. 4, pp. 44–47, July–August, 1991.     

The effect of stringers and patches on the stress intensities around cracks in plates

In the present paper a method was developed to study a certain important class of mixed boundary value problems concerning the interaction between a reinforced isotropic and linearly elastic thin plate by rectilinear and curvilinear thin strip inclusions (stringers), and superimposed elastic thin sheets (patches) perfectly bonded to the plate along their peripheries, and the internal cracks existing in the plate. The method is based on the complex stress function and the singular integral equations theories. An exact expression for the complex stress function was given for the most general case. The method was applied with success to an example of a superimposed circular patch on an internal crack existing in a thin plate. The variation of the stress intensity factors at the tips of the internal crack in terms of its relative position with respect to the patch-centre, as well as, of the relative elastic properties of the patch and the plate, was determined numerically.     

Crack growth induced delamination on steel members reinforced by prestressed composite patch

ABSTRACT Prestressed composite patch bonded on cracked steel section is a promising technique to reinforce cracked details or to prevent fatigue cracking on steel structural elements. It introduces compressive stresses that produce a crack closure effect. Moreover, it modifies the crack geometry by bridging the crack faces and so reduces the stress intensity range at the crack tip. Fatigue tests were performed on notched steel plate reinforced by CFRP strips as a step toward the validation of crack patching for fatigue life extension of riveted steel bridges. A crack growth induced debonded region in the adhesive‐plate interface was observed using an optical technique. Moreover, the size of the debonded region significantly influences the efficiency of the crack repair. Debond crack total strain energy release rate is computed by the modified virtual crack closure technique (MVCCT). A parametric analysis is performed to investigate the influence of some design parameters such as the composite patch Young's modulus, the adhesive thickness and the pretension level on the adhesive‐plate interface debond.     

Stress-intensity coefficients around the vertices of cracks and rigid inclusions in strips with clamped or free boundaries

Summary Singular integral equations have been applied to the state of stress and strain in an elastic strip with edges rigidly clamped or free from stresses and which has N arbitrarily oriented defects of crack or rigid-inclusion type. A system of singular integral equations is constructed. The kernels in the equations is constructed. The kernels in the equations are expanded as series in a small parameter to derive a solution for a central crack or inclusion in a clamped strip. Graphs have been formulated relating the stress intensity coefficients around the defect vertices to the angle of orientation.The results can be used in calculating strength characteristics for composites reinforced by rigid fibers or coated with thin hard materials.Translated from Fiziko-Khimicheskaya Mekhanika Materialov, Vol. 26, No. 4, pp. 65–75, July–August, 1990.     

Line-spring model for surface cracks in a reissner plate

In this paper the line-spring model developed by Rice and Levy for a surface crack in elastic plates is reconsidered. The problem is formulated by using Reissner's plate bending theory. For the plane strain problem of a strip containing an edge crack and subjected to tension and bending new expressions for stress intensity factors are used which are valid up to a depth-to-thickness ratio of 0.8. The stress intensity factors for a semi-elliptic and a rectangular crack are calculated. Considering the simplicity of the technique and the severity of the underlying assumptions, the results compare rather well with the existing finite element solutions.     

Effect of breaks in riveted stringers on the elastic and limiting equilibrium of a cracked plate

We study the stress-strain state and limiting equilibrium of a thin cracked plate reinforced by intact and broken riveted stringers and consider two types of loading of the stringers: their ends either are loaded by forces acting at infinity or free of loads. The boundary-value problem is reduced to a system of singular integral and integral-algebraic equations whose numerical solution is obtained by the method of mechanical quadratures for a series of geometric and physical parameters of the plate, crack, stringers, and rivets. It is shown that, as rule, broken stringers weaken the reinforced cracked plate and that the effect of breaks in the stringers on the stress intensity factors in the plate and the ultimate load is significant. Karpenko Physicomechanical Institute, Ukrainian Academy of Sciences, L'viv. Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 35, No. 3, pp. 39–47 May–June, 1999.     

Elastic strain of a helical tube containing a moving inhomogeneous liquid

Flexural strain of curvilinear tubes under the action of inertial centrifugal forces of an internal flow characterized by variable velocity and density along the elastic line is considered. The elastic strain of a helical tube containing a moving liquid, rigidly restrained at its ends, is investigated.Translated from Problemy Prochnosti, No. 5, pp. 110–115, May, 1990.     

On the strain energy release rate for a cracked plate subjected to out-of-plane bending moment

For a through-the-thickness crack in an infinite plate subjected to out-of-plane uniform bending moment, the strain energy release rate is determined using the virtual crack extension and the variation of potential energy. It is shown that the strain energy release rate for the Reissner's plate approaches the classical plate solution as the ratio of plate thickness to crack size becomes infinitesimally small. By using this result, the limiting expression of the stress intensity factor can be explicitly obtained. For general problems, the modified crack closure method is shown to be an efficient tool for evaluating the strain energy release rates from which the stress intensity factor can be calculated. Both the classical plate element and the Mindlin plate element are investigated, and the applicability of the classical plate element is evaluated.Because the stress-free conditions along the crack face lead to inter-penetration of the plate, a line contact model is assumed to investigate the closure effect using Reissner plate theory. Closure at the compressive side is shown to reduce crack opening displacement and consequently the stress intensity factors. When closure is considered, the strain energy rate based on the Reissner plate theory converges to the classical plate solution. This is similar to the nonclosure case.     

Limiting state of a semiinfinite plate with edge crack in bending with tension

We solve the problem of stressed state and limiting equilibrium of a semiinfinite plate with edge crack under the action of symmetric bending with tension. In the two-dimensional case, the possibility of crack closure is taken into account by using a model of contact along a line. An algorithm for the numerical solution of the mixed problem is proposed. The diagram of limiting equilibrium of the cracked plate shows that the range of safe states enlarges if the effect of crack closure is taken into account.Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 40, No. 2, pp. 73–77, March–April, 2004.     

Solutions of multiple crack problems of a circular plate or an infinite plate containing a circular hole by using Fredholm integral equation approach

Presented is an elementary solution, which is a particular solution of the circular plate containing one crack. The solution consists of two parts and satisfies the following conditions: (i) the first part corresponds to a pair of normal and tangential concentrated forces acting at a prescribed point on both edges of a single crack; (ii) the second part corresponds to some distributed tractions along both edges of the crack; (iii) the obtained elementary solution, i.e. the sum of the first and second parts, satisfies a traction free condition on the circular boundary. Using this elementary solution and taking some undetermined density of the elementary solution along each crack, a system of Fredholm integral equations of multiple crack problems can always be obtained. The multiple crack problems of an infinite plate containing a circular hole can be solved in a similar way. Several numerical examples are given in this paper.     

Crystal plasticity analysis of stress–assisted martensitic transformation in Ti–10V–2Fe–3Al (wt.%)

A new model based on crystal–plasticity, crystallography, thermodynamics, kinetics and statistics is developed for stress–assisted martensitic transformation. The model includes the essential features of the stress–assisted martensitic transformation, such as: nuclei of progressively lower potency are activated in the course of transformation, the martensite phase appears in the form of thin plates, the parent phase exerts a higher resistance toward the growth of a plate in the thickness than in the radial direction, the average plate size decreases while the average plate aspect ratio increases with the extent of transformation, etc. The model is implemented in the commercial finite element code ABAQUS/Standard to analyze the evolution of martensite, materials texture and the resulting equivalent stress–equivalent strain curve during the stress–assisted martensitic transformation under different stress and strain states in a polycrystalline Ti–10V–2Fe–3Al (wt.%) alloy. The equivalent stress–equivalent strain curves and the volume fraction of martensite–equivalent strain curves are found to be mainly controlled by the applied stress state. Conversely, the texture observed in the transformed Ti–10V–2Fe–3Al is found to be primarily controlled by the imposed macroscopic strain state. The validity of the proposed materials constitutive model has been established by demonstrating a reasonable agreement between the model predictions and the available experimental data.     

Crack curving under mode-I loading

The whole history of failure of a rectangular panel with two symmetrical notches and a central crack subjected to a progressively increasing tension load normal to the crack plane is studied. The material of the panel exhibits substantial plastic deformation prior to fracture. An elastic-plastic analysis of the plate is first performed based on finite elements. The results of stress analysis are coupled with the strain energy density theory to determine the critical load for crack initiation and the history of stable crack growth up to the point of instability. At instability the crack runs fast through the elastic material bypassing the plastic zone near the plate boundary. The crack deviates from its initial direction and is curved even though the plate is subjected to opening-mode loading. Results for crack trajectories are given for various initial crack lengths and notch radii of the plate.Presented at Fourth Greek National Congress on Mechanics, 26–29 June 1995, held at Xanthi, Greece.     

Tension of a cylindrical bar having an infinite row of circumferential cracks

In this paper, the crack problems in the case of a cylindrical bar having a circumferential crack and a cylindrical bar having an infinite row of circumferential cracks under tension are analyzed by the body force method. The stress field for a periodic array of ring forces in an infinite body is used to solve the problems. The solution is obtained by superposing the stress fields of ring forces in order to satisfy a given boundary condition. The stress intensity factors are calculated for various geometrical conditions. The obtained values of stress intensity factor of a single circumferential crack are considered to be more reliable than the results of other paper's. As the crack becomes very shallow, the stress intensity factor of a row of circumferential cracks approaches the value corresponding to that of a row of edge cracks in a semi-infinite plate under tension. As the crack becomes very deep, it approaches the values corresponding to that of a single deep circumferential crack.     

Calculating stress intensity factors for a semi-elliptical surface crack in a heterogeneous stress field

The author proposes an equation for calculating the stress intensity factor (SIF) for a semi-elliptical surface crack for uniform, linear, and quadratic laws of variation of the load applied to its edges. The derivation of the equation is based on the well-known Newman—Raju solution for a bent plate. The distribution of the values of SIF along the crack front, obtained using the empirical equations, coincides with the results of calculations carried out using the finite element method (FEM).Translated from Problemy Prochnosti, No. 7, pp. 38–41, July, 1990.     

A two parameter driving force for fatigue crack growth analysis

A model for fatigue crack growth (FCG) analysis based on the elastic–plastic crack tip stress–strain history was proposed. The fatigue crack growth was predicted by simulating the stress–strain response in the material volume adjacent to the crack tip and estimating the accumulated fatigue damage. The fatigue crack growth was regarded as a process of successive crack re-initiation in the crack tip region. The model was developed to predict the effect of the mean stress including the influence of the applied compressive stress. A fatigue crack growth expression was derived using both the plane strain and plane stress state assumption. It was found that the FCG was controlled by a two parameter driving force in the form of: . The driving force was derived on the basis of the local stresses and strains at the crack tip using the Smith–Watson–Topper (SWT) fatigue damage parameter: D=σ_maxΔε/2.The effect of the internal (residual) stress induced by the reversed cyclic plasticity was accounted for the subsequent analysis. Experimental fatigue crack growth data sets for two aluminum alloys (7075-T6 and 2024-T351) and one steel alloy (4340) were used for the verification of the model.