Elementary Crack Research Articles

Digital image correlation analyses of masonry infilled frame: Uncertainty-based mesh refinement and damage quantification

Masonry walls are subjected to cyclic lateral loads to study damage caused by earthquakes. Imaging techniques are useful to quantify crack networks in such tests, where preferential locations for their initiation are not present. However, detecting small cracks in large structures is challenging. It is shown that finite element (FE)-based digital image correlation (DIC) can detect and quantify cracks by combining optical and mechanical information of a cyclic shear experiment performed on a full-size masonry wall. Pixel-wise gray-level residuals and elementary crack opening displacement fields are the key quantities of the proposed framework. Detection criteria based on standard uncertainties guided the application of new DIC strategies (i.e., mechanical regularization, mesh adaption, and damage). Two damage regimes were quantified. Zigzagged cracks were first formed, for which their opening displacements were on average less than 0.5 mm with very limited damage. They were followed by sliding shear cracks, whose mean opening displacements varied between 1 and 3 mm, and damage developed in a more gradual and extended way. Such rich full-field data set may be used for validating damage models up to full-scale simulations.

Insights into fracture behavior of Ni-based superalloy single crystals: An atomistic investigation

Comprehending the plastic deformation and failure mechanisms in Ni-based superalloys is vital to enhance their intrinsic ductility. In view of this, the present work intends to illustrate the complex deformation mechanisms ensued during tensile deformation of pre-cracked Ni-Ni3Al single crystals using atomistic simulations. Simulations of fracture, thermodynamic continuum treatments of crack initiation and detailed calculations of crack propagation toughness are performed synergistically to analyze the competition between dislocation emission and cleavage. This competition is evaluated under Mode-I loading for 18 different pre-cracked configurations (three different crack lengths, three phase orientations and two phases) in totality. Our results demonstrate that dislocation as well as twin plasticity eventuate and the competition between the two plastic modes depends on the crystallographic orientation of the abutting phases. Higher initial crack lengths can otherwise lead to cleavage like propagation in the material; however this does not imply inferior ductility of the system as long as the phase boundary lies in the path of advancing crack. Changes in configurations in terms of pre-cracked phase or initial crack lengths can engender appreciable differences in the elementary crack tip phenomena. The numerical computations of crack propagation toughness are compared favorably well with the available experiments in the literature. The calculated variations in overall toughness of the material are discussed and analyzed in light of the observed deformation landscapes.

Root rotations and root displacements in bimaterial layers and thin films

An elasticity technique to derive compliance coefficients describing crack tip root rotations and displacements in end-loaded, bimaterial, isotropic and orthotropic layers has been recently proposed in Ustinov and Massabò (Int. J. Solids Struct., 2022). The coefficients define the boundary conditions which account for the near tip deformations when using beam (plate) theories to describe the detached layers. The coefficients, collected into 6x6 compliance matrices, relate crack tip kinematic variables describing relative displacements and rotations between the detached and intact parts, and six elementary crack tip loadings, which combine to describe general end loadings. The steps necessary to use the coefficients in the solution of statically determined problems, when the forces acting on the layer are known through equilibrium, is presented here with reference to classical fracture mechanics specimens.

Fracture Mechanics Solutions for Interfacial Cracks between Compressible Thin Layers and Substrates

The decohesion of coatings, thin films, or layers used to protect or strengthen technological and structural components causes the loss of their functions. In this paper, analytical, computational, and semi-analytical 2D solutions are derived for the energy release rate and mode-mixity phase angle of an edge-delamination crack between a thin layer and an infinitely deep substrate. The thin layer is subjected to general edge loading: axial and shear forces and bending moment. The solutions are presented in terms of elementary crack tip loads and apply to a wide range of material combinations, with a large mismatch of the elastic constants (isotropic materials with Dundurs’ parameters − 1 ≤ α ≤ 1 and − 0.4 ≤ β ≤ 0.4 ). Results show that for stiff layers over soft substrates ( α → 1 ), the effects of material compressibility are weak, and the assumption of substrate incompressibility is accurate; for other combinations, including soft layers over stiff substrates ( α → − 1 ), the effects may be relevant and problem specific. The solutions are applicable to edge- and buckling-delamination of thin layers bonded to thick substrates, to mixed-mode fracture characterization test methods, and as benchmark cases.

Macroscopic probabilistic cracking approach for the numerical modelling of fluid leakage in concrete

The article presents a numerical finite element study of fluid leakage in concrete. Concrete cracking is numerically modelled in the framework of a macroscopic probabilistic approach. Material heterogeneity and the re- lated mechanical effects are taken into account by defining the elementary mechanical properties according to spatially uncorrelated random fields. Each finite element is consid- ered as representative of a volume of heterogeneous ma- terial, whose mechanical behaviour depends on its own volume. The parameters of the statistical distributions defining the elementary mechanical properties thus vary over the computational mesh element-by-element. A weak hydro-mechanical coupling assumption is introduced to represent the influence of cracking on the variation of transfer properties: it is assumed that the mechanical cracking of a finite element induces a loss of isotropy of its own permeability tensor. At the elementary level, an ex- perimentally enhanced parallel plates model is used to re- late the local crack permeability to the elementary crack aperture. A Monte Carlo-like approach allows to statisti- cally validate the numerical method. The self-consistency of the proposed modelling strategy is finally explored through the numerical simulation of the hydro-mechanical splitting test, recently proposed by authors to evaluate the real-time evolution of the transfer properties of a concrete sample under loading.

On the relationship of the cumulative jump model for random fatigue to empirical data

The cumulative jump model, consisting of a random sum of random increments, has previously been proposed, in a general format, to model the fatigue crack growth process. In this paper the cumulative jump process for random fatigue is used to model the constant-load amplitude Virkler fatigue crack growth data. It is shown, through the proper choice of the intensity function of the underlying birth process, that the mean crack growth behavior of the model may be specified to match any desired functional form. This assures reasonable agreement with experiments. For fatigue crack growth the intensity function is characterized by a constant and a random variable (this makes the underlying birth process a so-called doubly stochastic counting process). For the case of the `simplified' jump model (constant elementary crack increments), the constant and the random variable characterizing the intensity function may be estimated by matching approximate formulae for the mean and the variance of the model with the data. Simulations of the jump model show trajectories which behave qualitatively like the data and yield distribution functions for the crack length which match well the data.

A non-local stress and strain energy release rate mixed mode fracture initiation and propagation criteria

A non-local stress condition for crack initiation and propagation in brittle materials is presented. This condition is expressed in terms of normal and tangential traction components acting on a physical plane segment (damage zone) of specified length. Next, a non-local strain energy release rate criterion is proposed. This condition is based on the assumption that initiation or propagation of cracking occurs when the maximal value of the function of opening and sliding energy release rates reaches a critical value. The value of energy release rates is determined for finite elementary crack growth. Mixed mode conditions are considered, for which both the critical load value and the crack orientation are predicted from the non-local stress and energy criteria, which are applicable to both regular and singular stress concentrations. The effect of non-singular second order term ( T σ -stress) on the crack propagation is discussed.

CURVILINEAR RANDOM FATIGUE CRACK GROWTH: EFFECTS OF OVERLOADS

Abstract— In the paper a previously proposed stochastic description for curvilinear fatigue crack growth is extended and adopted to the characterization of crack retardation due to overloads. The model has the form of a cumulative process with random elementary crack increments and random angles of the crack deflection. The basic statistical characteristics of the model‐process are related to fracture mechanics and to the parameters known from traditional experimental predictions.

Computer-aided quantifier elimination in crack problems under constraints for the stress intensity factors

It is suggested that crack problems under constraints, concerning the values of the parameters involved, be studied by the method of quantifier elimination in such a way that quantifier-free formulae can be derived assuring the validity of a restriction about the stress intensity factors (usually that such a factor does not exceed a critical value) for all possible values of the parameters under the applicable constraints. This permits safe conclusions about the possible fracture of a cracked specimen (under constraints on the parameters involved) for every set of values of the geometry/loading/fracture parameters. The elementary crack problem of a single straight crack in an infinite plane isotropic elastic medium is used as the vehicle for the illustration of the present approach and the related quantifier-free formula is easily derived. A simple case of a periodic array of cracks is also considered in brief. The classical algebraic tools of resultants and Sturm's sequences (together with Sturm's theorem) as well as the computer algebra system Maple V have been used in the present computations. More general results, with the help of Collins' famous cylindrical algebraic decomposition method, in more complicated crack problems, can also be obtained.

Cumulative jump-correlated model for random fatigue

The paper is concerned with stochastic modelling of fatigue crack growth under random loading and other uncertainties. It constitutes an extension of the paper by Sobcyk and Trȩbicki ( Engng Fracture Mech. 34, 477–493, 1989) to the more general situation where the elementary crack's increments are mutually correlated random variables. In order to account for a possible correlation between the elementary increments the Morgenstern model for the joint probability distribution is adopted and the moments of the crack's size are evaluated. Then use of the maximum entropy principle leads to the approximate probability distribution of the crack's size. Numerical calculations for real data illustrate the effect of the correlation in crack's increments on statistics of the crack's size and show the features analogous to these observed in existing experimental data.

Mixed mode fracture of concrete

Strain-softening and strain-localization in cementitious and ceramic materials can be described by using a cohesive crack model, with closing forces at the crack tip, which represent plasticity, inclusion interlocking, fibre bridging and any kind of non-linear behaviour. In the present paper, the cohesive crack model is extended to mixed mode propagation and an experimental confirmation is provided by testing four-point shear specimens of concrete. A constant crack mouth sliding displacement rate is imposed, so that is is possible to control and detect the snap-back load vs deflection branches. The behaviour of the larger specimens is found to be the brittler. On the other hand, the brittleness in the numerical simulations is controlled through the crack length, which is certainly a monotonic increasing function during the irreversible fracture process. The experimental load vs deflection diagrams as well as the experimental fracture trajectories are captured satisfactorily by the numerical model. The mixed mode fracture energy results tend to be of the same order of magnitude as the Mode I fracture energy ℷF, each elementary crack growth step being produced by an opening mechanism along the curvilinear trajectory. This is particularly true for the larger specimens, where energy dissipation due to friction and interlocking is negligible if compared with the energy dissipated by separation.

SINGULAR FUNCTIONS SUITED TO ANALYZE A FINITE VALUE OF STRESS CONCENTRATION NEAR THE END OF A CRACK TRAVERSING A PLATE

In this paper two singular stress functions suited to analyze crack problems of plates are presented. One of them is a stress function of two-dimensional problems which creates a crack opening displacement due to normal loads applied along the crack (mode 1) in an infinite plate. The other is the same function as that but due to shear loads along the crack (mode 2). The Authors define these two functions as elementary crack function with opening of unit length. Super-posing these functions with different length of elementary crack opening, the stress concentrations due to many cracks contained in the infinite plate can be analyzed numerically with good accuracy. The characteristics of this method is that the stress softening zones at both end of the crack can be constructed where either crack opening displacements or stress concentrations with finite magnitude appear.

Fatigue oxidation interaction in a superalloy—application to life prediction in high temperature low cycle fatigue

A study of the interaction between fatigue and oxidation has been carried out in the case of a cast cobalt base superalloy MARM 509 tested in laboratory air at 900 °C. The influence of fatigue cycling on oxidation of this alloy has been studied by quantitative metallography on polished specimens exposed to air in a furnace and on strain-cycled low-cycle fatigue specimens. The oxidation kinetics were determined by thickness measurements for matrix oxidation and by oxidized depth measurements for the preferential oxidation of MC carbides. In both cases the oxidation kinetics were found to be dramatically enhanced by cycling for the matrix oxidation according to a linear relationship with plastic strain amplitude and less dramatically for carbides according to an exponential relationship with the maximum cyclic stress. From these observations a damage equation which describes fatigue damage as a crack growth process has been proposed: the elementary crack advance is a summation of a mechanical contribution due to the fatigue process itself which is described by Tomkins’ equation and of an oxidation contribution which has been evaluated from metallographic measurements. Integration of this crack growth equation gives predicted fatigue lives which are in good agreement with experimental results within a factor of two.