Andrei Kotousov

Three-dimensional stress constraint in an elastic plate with a notch

Abstract This paper presents analytical solutions for the three-dimensional stress distribution around typical stress concentrators in an isotropic plate of arbitrary thickness. Based on the assumption of a generalised plane-strain theory, which assumes that the through-the-thickness extensional strain is uniform in the thickness direction, an exact three-dimensional solution has been obtained for an annulus subjected to arbitrary loading along its edges. Emphasis has been placed on the through-the-thickness stress constraint, which is a pre-requisite to analysing the effect of plate thickness on the elastic–plastic deformation at a notch root. Important results are presented on the effects of the plate thickness and Poissons ratio on the in-plane stress concentration factor and the out-of-plane stress constraint factor. By extending the theoretical method to a plate with a non-circular notch, an approximate solution has been obtained for the through-the-thickness constraint factor in a plate with a V-shaped notch having a circular tip. The present solutions have been shown to correlate well with numerical results obtained using the finite element method.

On Scale Effect in Plates Weakened by Rounded V-Notches and Subjected to In-Plane Shear Loading

It is now well-known that in plate problems with through-the-thickness cracks in-plane shear and anti-plane loadings generate coupled three-dimensional fracture modes. The dominance domain and intensity of the singular states associated with these 3D fracture modes are functions of the intensity of the primary loading (KII and KIII) and Poisson’s ratio. A similar situation takes place for V-shaped notches. However, for geometrically similar notch geometries subjected the same nominal stress the intensity of the coupled modes is also a function of the plate thickness. Despite this almost all 3D effects are currently ignored in industrial standards and fracture assessment codes. Recent theoretical and numerical studies have demonstrated that in many practical situations the intensities of the coupled fracture modes for cracks and sharp notches are not negligible and can influence fracture conditions. The current paper extends this conclusion to rounded notches. By using the finite element modelling it is demonstrated that the intensity of the stress states associated with the coupled fracture modes in a sufficiently thick plate weakened by a rounded notch can exceed the magnitude of stresses due to the primary loading. This means that the coupled modes can dominate the stress state in the vicinity of the notch root and be primary responsible for fracture initiation.

Three-dimensional solutions for transversally isotropic composite plates

By adopting Kane and Mindlins assumption that the through-the-thickness extensional strain is uniform through the plate thickness, a generalised plane-strain theory is developed for transversely isotropic plates. The three-dimensional governing equations are successfully reduced to two coupled equations in the two-dimensional space. With the new theory, explicit solutions of the three-dimensional stresses, especially the through-the-thickness component, around a circular hole and a circular inclusion are derived.

Experimental apparatus for thermal shock fatigue investigations

Abstract An experimental rig developed for investigating crack growth in pressure vessels and piping equipment is described. The rig allows full scale modeling of cyclic thermal shock conditions that occur in operating thermal power station pressure equipment. It has the ability to apply a primary steady state mechanical load and to control the quenching environment allowing the study of the effect of welds and stress concentrators under conditions that simulate operational loadings. These results can be used for lifetime assessment. Preliminary results from the test rig analysing the effect of primary load on crack initiation and growth are presented and discussed briefly. A comparison with prediction methods from the ASME Boiler and Pressure Vessel Code is made. It is concluded that the primary load has little or no effect on crack initiation times, however it significantly affects the crack growth rate.

Elementary mathematical theory of thermal stresses and fracture during welding and cutting

Abstract In many technological processes involving the cutting or welding of thin plates there is local thermal heating or cooling at the tip of the cut. Under particular conditions the cut may be considered as a semi-infinite crack and the thermal source as a point heat source. For cutting processes the cut is behind the moving thermal source and for welding the cut is ahead of the moving thermal source. For most processes the value of the thermal source is positive (e.g. lasers, electron beam cutting, welding and others). In this paper the authors investigate analytically the stress distribution induced by a point thermal source moving with a constant velocity in an infinite plate. The stress intensity factor due to the point thermal source at the tip of the cut is calculated. It is shown that for both welding and cutting in the case of a thermal heat source the stress intensity factors will be negative, which means that the thermal field induced by the point thermal heat source will tend to close the surfaces of the cut in the vicinity of the tip. The opposite situation occurs when the cut tip is cooled by the thermal source. In this case there are positive values for the stress intensity factors and the thermal stresses may lead to brittle fracture ahead of the cut. As an example, the application of the theory under development to the uncontrolled fracture phenomenon during the thermal beam cutting of brittle materials is considered in detail. A fracture criterion for this process is obtained, which enables choosing the manufacturing parameters of the process in order to avoid the possibility of uncontrolled fracture.

A strip yield model for two collinear cracks in plates of arbitrary thickness

As two cracks grow and approach each other under fatigue loading, a deleterious interaction between them can considerably affect the crack growth rate, making theoretical evaluations and experimental data from a single isolated crack case considerably inaccurate. The aim of the present study is to investigate the interaction between two collinear cracks of equal length, taking into account the plate’s thickness effect, which was demonstrated to have a large effect on fatigue crack growth in the case of a single crack. The obtained solution to the problem is based on the Dugdale strip yield model and the distributed dislocation technique. In addition, a fundamental solution for an edge dislocation in a finite thickness plate is utilised. The present solution shows a very good agreement with previously published results for some limiting cases. The obtained results confirm a significant dependence of the interaction and stress intensity factors on the plate thickness, which can dramatically affect the plastic collapse conditions as well as fatigue crack growth rates.

Eccentricity correction for the evaluation of fracture toughness from cylindrical notched test small specimens

Abstract This paper presents the latest results of an extensive research program started in 1985 on the cylindrical notched test (CNT) specimen that evaluates fracture toughness. Specimen geometry is the cheapest methodology in manufacturing, which can produce values for fracture toughness and is also smaller than the standard compact tension test (CT) specimen. The CNT specimen has many advantages and can be used in many applications that are not possible with standard CT specimens. Requirements for the minimum diameter of the CNT specimen are discussed and compared with the similar requirements for the CT specimen. As was reported earlier, however, a major problem in CNT specimen testing is that only a very small part of all samples has the pure co-circular geometry after pre-cracking which is suitable for analytical consideration. The present paper discusses an approximate analytical approach which was developed to estimate the fracture toughness from specimens with an eccentrically displaced ligament. This approach is suitable for the calculation of the stress intensity factor for many eccentrically and externally cracked bodies. It has been validated by comparison with FE results and known analytical solutions. The testing procedure and the analytical approach presented agree well with independent CT specimen testing results.

Analysis of interfacial fracture in dental restorations

OBJECTIVES To provide a brief summary of the background theory of interfacial fracture mechanics and develop an analytical framework that identifies the critical factors for the analysis of the initiation and propagation of adhesion failure in composite restorations. METHODS A conceptual framework utilizing interfacial fracture mechanics and Toyas solution for a partially delaminated circular inclusion in an elastic matrix, which can be applied (with caution) to approximate polymer curing induced cracking about composite resins for class 1 cavity restorations. RESULTS The findings indicate that: (1) most traditional shear tests are not appropriate for the analysis of the interfacial failure initiation; (2) material properties of the restorative and tooth material have a strong influence on the energy realize rate; (3) there is a strong size effect; and (4) interfacial failure once initiated is characterized by unstable propagation along the interface almost completely encircling the composite. SIGNIFICANCE The work is important for the analysis of the reliability of composite class I restorations and provides an adequate interpretation of recent adhesion debonding experimental results utilizing tubular geometry of specimens. The approach clearly identifies the critical parameters including; curing strain, material modulii, size and interfacial strain energy release rate for reliable development of advanced restorative materials.

A new passive defect detection technique based on the principle of strain compatibility

This paper discusses the development of a new passive technique of on-line damage detection based on the most fundamental concept in continuum mechanics: strain compatibility. The main feature of this technique is its invariance to changing operating conditions. The technique is quite general and can be applied to structures made of isotropic or anisotropic materials and structural components experiencing elastic or plastic deformations. A few practical situations, involving the development of crack damage in plate structures, are considered to demonstrate the feasibility of this crack detection technique, as well as its potential for many practical applications. Future work will focus on the experimental validation of the technique.

A brief review of recent three-dimensional studies of brittle fracture

Abstract3D crack problems are area where a further intensive research is required. 3D solutions can shed more light on fracture and fatigue phenomena, provide a more accurate evaluation of strength and fatigue life or justify the application of the classical solutions of plane theories of elasticity. These, in fact, are approximate theories even when the governing equations of these theories are solved exactly. The current paper aims to provide a brief summary of the latest investigations of 3D effects associated with crack geometries and brittle fracture. In particular, we present an overview of the coupled fracture modes and 3D vertex singularities, which are currently largely ignored in experimental and theoretical studies. We also describe a recently developed experimental method for the evaluation of the stress intensity factors. This review is concerned with the situation generally described in the literature as small scale plasticity. Large plastic deformations and other non-linear effects are beyond the scope of this article.