Method of determining the failure parameters of structural members with edge cracks

Materials Science - The theoretical-experimental method of determining the fracture parameters of structural members has been generalized for edge cracks on the basis of a solution for a half-plane...     

Method of determining the failure parameters of structural members with edge cracks

Conclusions The theoretical-experimental method of determining the fracture parameters of structural members has been generalized for edge cracks on the basis of a solution for a half-plane with an edge crack.The error of determining the stress-intensity factors K_I and K_II does not exceed 2–3%. In many cases, the method makes it possible to determine, with the accuracy sufficient for practice, the stresses acting along the crack-line prior to crack appearance.The results show that the polynomials (7) can be used to approximate the load function. The number of terms, retained in the expansion (7), can be selected on the basis of the criterion (8). The approximation (9) is more suitable for solving the contact problems. Using this approximation, it is possible to have on average the error of determining the SIF and restore the loads applied to the panel.To apply the method, it is sufficient to measure the relative displacement of the edges in 1–3 points at a large distance from the tip.For the cracks extending to the curvilinear boundary the accuracy of restoration of the stresses by the proposed method depends on the b/R ratio, whereas there is no such dependence for a straight boundary.Translated from Fiziko-Khimicheskaya Mekhanika Materialov, No. 6, pp. 29–35, November–December, 1992.     

Pop-in behavior induced by interaction of cracks

The linear fracture mechanics concept was used to analyze the stability of two and three colinear cracks in infinite planes. It was found that at a particular condition of the initial crack arrangement, long crack can absorb the short one stably resulting the pop-in behavior. The condition of the crack arrangement for the pop-in occurance, amount of load dropping and crack displacement increment were obtained.     

Modeling failure of heterogeneous viscoelastic solids under dynamic/impact loading due to multiple evolving cracks using a two-way coupled multiscale model

This paper presents a model for predicting damage evolution in heterogeneous viscoelastic solids under dynamic/impact loading. Some theoretical developments associated with the model have been previously reported. These are reviewed briefly, with the main focus of this paper on new developments and applications. A two-way coupled multiscale approach is employed and damage is considered in the form of multiple cracks evolving in the local (micro) scale. The objective of such a model is to develop the ability to consider energy dissipation due to both bulk dissipation and the development of multiple cracks occurring on multiple length and time scales. While predictions of these events may seem extraordinarily costly and complex, there are multiple structural applications where effective models would save considerable expense. In some applications, such as protective devices, viscoelastic materials may be preferred because of the considerable amount of energy dissipated in the bulk as well as in the fracture process. In such applications, experimentally based design methodologies are extremely costly, therefore suggesting the need for improved models. In this paper, the authors focus on the application of the newly developed multiscale model to the solution of some example problems involving dynamic and impact loading of viscoelastic heterogeneous materials with growing cracks at the local scale.     

A method to predict failure pressures of steam generator tubes with multiple through-wall cracks

This paper proposes a simple numerical method to predict burst pressures of steam generator tubes with multiple through-wall cracks, based on the stress-modified fracture strain damage model with stress reduction technique. For validation, simulated results using the proposed method are compared with 31 published experimental data of Alloy 600 plates and tubes with single or two through-wall cracks, showing that predicted loads are within 10% of experimentally-measured ones for all cases considered. Furthermore, a parametric study is performed to investigate the interaction effect of two through-wall cracks in Alloy 600 steam generator tubes under internal pressure.     

Modeling of coalescence of dispersed surface cracks. Part 2. Simulation model for multiple fracture

Abstarct A simulation model for multiple fracture has been developed that reproduces random processes of initiation, growth, and coalescence of dispersed surface cracks. The model is based on the method of statistical simulation (Monte Carlo method) and on the fracture regularities determined experimentally. The main factor responsible for fracture is found to be the coalescence of dispersed cracks, especially at the final stage, which accounts for about 30% of the total life. The ultimate state of a structure is defined by the condition according to which the length of the largest of the available damages is bigger than the calculated value of the maximum crack length.Translated from Problemy Prochnosti, No. 1, pp. 108–117, January–February, 2005.     

Analysis of cracks with multiple branches

Solutions for crack tip stress intensity factors were determined by the finite element method for a wide range of branch crack configurations. In the analysis it is assumed that the length of each branch is much smaller than the length of the main crack. For a large majority of the cases analyzed, the branch region was subject to a mode I stress state (K ₁). In the remaining cases a uniform stress field acting parallel to the main crack was imposed. For conditions where previous solutions were available, a comparison was made.     

Dynamics of anisotropic composite cantilevers weakened by multiple transverse open cracks

In this paper an exact solution methodology, based on Laplace transform technique enabling one to analyze the bending free vibration of cantilevered laminated composite beams weakened by multiple non-propagating part-through surface cracks is presented. Toward determining the local flexibility characteristics induced by the individual cracks, the concept of the massless rotational spring is applied. The governing equations of the composite beam with open cracks as used in this paper have been derived via Hamilton's variational principle in conjunction with Timoshenko's beam model. As a result, transverse shear and rotatory inertia effects are included in the model. The effects of various parameters such as the ply-angle, fiber volume fraction, crack number, position and depth on the beam free vibration are highlighted. The extensive numerical results show that the existence of multiple cracks in anisotropic composite beams affects the free vibration response in a more complex fashion than in the case of beam counterparts weakened by a single crack. It should be mentioned that to the best of the authors' knowledge, with the exception of the present study, the problem of free vibration of composite beams weakened by multiple open cracks was not yet investigated.     

Stability of arrays of multiple edge cracks

The creation and subsequent shedding of arrays of edge cracks is a natural phenomenon which occurs in heat-checked gun tubes, rapidly cooled pressure vessels and rock, dried-out mud flats, paint and concrete and in ceramic coatings and permafrost. The phenomenon covers five orders of magnitude in crack spacing and the driving mechanisms may include fast fracture, environmental cracking and fatigue crack growth. A simple model is developed which indicates that the shedding behaviour is governed by the behavior of individual cracks rather than global energy changes. The model predicts that all cracks will deepen until a crack-spacing/crack depth ratio (2h/a) of 3.0 is achieved, at which stage crack-shedding will commence. Two out of every three cracks will be shed, leading to a new (higher) crack spacing/crack depth ratio at which stage growth of all currently active cracks will be dominant. An approach based upon rapid, approximate methods for determining stress intensity provides good indications of behaviour provided near-surface stress gradients are not excessive. In cases where stress gradients are high it is shown that it is necessary to employ numerical techniques in calculating stress intensity. Two specific examples are presented, the first at very small scale (heat-check cracking in a gun tube, typical crack spacing 1 mm) and the second at very large scale (permafrost cracking, typical crack spacing 20 m). The predicted ratios for the proportion of cracks shed and for crack spacing/crack depth are in agreement with experimental evidence for gun tubes, concrete and permafrost. The ratios also appear to match experimental observations of “island delamination” in ceramic coatings and paint films.     

Predicting failure of composite structures containing cracks

The ability to predict failure loads in composite structures containing through-the-thickness cracks is a requirement in a variety of structural design circumstances. The objective of this study was to develop a practical computational technique that simulates progressive damage growth in the vicinity of the crack tip in a manner that allows the prediction of failure over a wide range of crack sizes. This was accomplished through the use of the discrete crack model with a general purpose finite element program. Calculations were performed for two different laminates with various crack sizes under tensile loading. An analysis was also performed on a section of a composite aircraft fuselage containing a crack and subjected to internal pressure loading. Reasonably good agreement was found between the calculations and the results from tests.     

Detection of multiple cracks using frequency measurements

A method for detection of multiple open cracks in a slender Euler-Bernoulli beams is presented based on frequency measurements. The method is based on the approach given by Hu and Liang [J. Franklin Inst. 330 (5) (1993) 841], transverse vibration modelling through transfer matrix method and representation of a crack by rotational spring. The beam is virtually divided into a number of segments, which can be decided by the analyst, and each of them is considered to be associated with a damage parameter. The procedure gives a linear relationship explicitly between the changes in natural frequencies of the beam and the damage parameters. These parameters are determined from the knowledge of changes in the natural frequencies. After obtaining them, each is treated in turn to exactly pinpoint the crack location in the segment and determine its size. The forward, or natural frequency determination, problems are examined in the passing. The method is approximate, but it can handle segmented beams, any boundary conditions, intermediate spring or rigid supports, etc. It eliminates the need for any symbolic computation which is envisaged by Hu and Liang [J. Franklin Inst. 330 (5) (1993) 841] to obtain mode shapes of the corresponding uncracked beams. The proposed method gives a clear insight into the whole analysis. Case studies (numerical) are presented to demonstrate the method effectiveness for two simultaneous cracks of size 10% and more of section depth. The differences between the actual and predicted crack locations and sizes are less than 10% and 15% respectively. The numbers of segments into which the beam is virtually divided limits the maximum number of cracks that can be handled. The difference in the forward problem is less than 5%.     

Sealing process induced by carbonation of localized cracks in cementitious materials

The healing of cracks plays an important role with regard to the air- and water-tightness of concrete structures and the durability of cement based materials in general. This paper aims at further characterization and better comprehension of the healing phenomenon induced by the precipitation of calcite in localized cracks. The experimental program consisted in generating a localized crack in a cement paste or concrete specimen and healing the crack created by percolation tests with carbonated water or gas (CO₂-air mixture). For tests with liquid, results show that the healing process depends on physical parameters like crack width, pressure gradient and carbonate content in the percolating fluid. For tests with gas, the supply of the crack with Ca²⁺ ions to form calcite depends on the moisture transport mode on the crack edges, conditioned by the relative humidity of the percolating gas mixture. A simplified model of the leakage rate evolution is proposed. It provides indications concerning the effect of each test parameter on the healing process and allows the experimental results to be reproduced. Application of the model to other tests from the literature shows its limits and gives guidance for future investigations.     

Cold cracks in welded joints of structural steels

The present survey is devoted to the investigation of a dangerous phenomenon (quite often observed in the process of arc welding) of the formation of hydrogen-induced cold cracks in welded joints of structural steels. We briefly analyze the existing models of the mechanism of hydrogen embrittlement. It is shown that difficulties in understanding the processes of initiation and growth of cold cracks are explained not only by the necessity of determination of the principal factors which govern the embrittling action of hydrogen but also by the absence of reliable knowledge of the microscopic mechanisms of fracture processes in metals. We suggest a new model of hydrogen embrittlement of metals with bcc lattice developed at the Paton Institute of Electric Welding. According to this model, atomic hydrogen adsorbed on the metal surface in the form of anions affects the surface energy of submicrocracks appearing in dislocation clusters in the process of deformation whose initial period of propagation obeys the classical Griffith scheme. The proposed model enables one to explain all known distinctive features of the cold cracking of welded joints and forms a groundwork for the physical simulation based the use of mathematical methods and aimed at the quantitative evaluation of the contribution of each factor to the indicated processes. Paton Institute of Electric Welding, Ukrainian Academy of Sciences, Kiev. Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 32, No. 1, pp. 53–66, January–February, 1996.     

Ductile failure of cylindrical bodies with axial cracks loaded by internal pressure

The article considers problems of finding the limit pressure leading to ductile failure of a cylinder with an axial crack. Actual formulas are obtained for a thin-walled shell and for cylinders with considerable thickness. The article shows their satisfactory agreement with the results of full-scale tests.Translated from Problemy Prochnosti, No. 2, pp. 16–20, February, 1990.