Development of fatigue cracks in complex mechanical structures

The paper summarizes some theoretical and experimental activities concerned with reliability problems of mechanical structures within advanced Czechoslovakian scientific and research institutions. The aim of the paper is directed to the system concept of the fatigue damage mechanism as acting on real mechanical structures in real operational conditions or in those being simulated in laboratories. Such a concept—which has long been emphasized by Prof. A. M. Freudenthal—is based herein on the knowledge gained by studying large-scale structure failures namely in aeronautics.     

Van der Waals interactions between brittle cracks and gaseous environments

The role of van der Waals forces in crack-tip decohesion is considered for a sharp-crack system in a gaseous environment. Simplistic calculations of the interaction between a single gas molecule and the two confining walls of the crack indicate the existence of a potential well close to the tip region. Diffusing gas molecules are thereby predicted to experience a significant attraction toward the crack-tip bonds, where they become trapped in a state of interfacial physisorption. Provided diffusing molecules are not so large that they cause obstruction at the crack walls, this trapping state may constitute an important precursor to subsequent chemical steps in the overall decohesion process.     

Evaluation of the strength of structural materials with cracks under complex loading

We develop an experimental procedure and geometry of the specimens for the evaluation of the characteristics of crack growth resistance of structural materials for various macromechanisms of fracture (modes I, II, and III). We plotted diagrams of the limiting-equilibrium state of a body containing a crack (its strength) under complex proportionally increasing loading.     

A technique for studying interacting cracks of complex geometry in 2D

A method for studying brittle fracture in an infinite plate containing interacting cracks of complex shape under general loading conditions is developed and studied for accuracy and potential applications. This technique is based on superposition and dislocation theory and can be used to determine the full stress and displacement fields in a cracked body. In addition, stress intensity factors at both crack tips and wedges, created by crack kinking and branching, are calculated so that crack growth and initiation can be analyzed at these locations of possible crack propagation. Such information can then be used to study damage accumulation in structures containing a large number of interacting cracks.     

Modelling complex cracks with finite elements: a kinematically enriched constitutive model

A continuum constitutive framework with embedded cohesive interface model is presented to describe the failure of quasi-brittle materials. Both cohesive behaviour for cracking inside the fracture process zone and elastic bulk behaviour are treated at integration points making implementation straightforward. In this sense, the proposed approach is simpler than existing ones that focus on element enrichments, such as the extended finite element method, while share similarities with smeared crack models, and offers the capability to correctly model quasi-brittle failure in post-peak regime at constitutive level. In this work, the formulation is introduced, numerical algorithms described and static and dynamic fracture simulations with complex crack patterns are conducted to demonstrate the capability and advantage of the proposed approach.     

Fractal study on collective evolution of short fatigue cracks under complex stress conditions

This paper proposes a Paris-type damage model to investigate the collective evolution of short fatigue cracks based on fractal theory. On the basis of experimentally determined images, the fractal dimensions (FDs) of rounded notched specimens’ surfaces are numerically calculated by using Otsu threshold segmentation and box-counting dimension method. The results show that FDs’ evolution presents “HILL” curves’ characteristics. The transition period between FD rapid growth stage and FD constant stage takes place at about 30% of fatigue life. The good match between experimental results and FEM analyses reveals the model can describe collective damage process caused by all fatigue cracks.     

Anisotropic material with interacting arbitrarily oriented cracks. Stress intensity factors and crack-microcrack interactions

Elastic interactions of cracks arbitrarily oriented in a 2-D anisotropic matrix are analyzed. The impact of material's anisotropy on mechanics of interactions is found to be significant. The anisotropy of Young's moduli produces the strongest impact: it enhances (weakens) the interactions under a loading applied in the stiffer (softer) direction. Sensitivity to the shear modulus is somewhat lower and the impact of Poisson's ratios is small.Crack-microcrack interactions are analysed and compared with the ones in the isotropic matrix. If the main crack is normal to the stiffer direction of the matrix, the anisotropy noticeably enhances the microcrack's impact; for the crack normal to the softer direction, the influence of anisotropy is found to be insignificant.Effective molduli of anisotropic materials with arbitrarily oriented interacting cracks are derived in companion papers [26,27].     

Stress intensity factors for half-elliptical surface cracks subjected to complex crack face loadings

The disagreement in the literature on the stress intensity factors for surface cracks is considerable. It is also noted that not enough attention has been given to the behaviour of surface cracks in stress fields more complex than uniform tension and bending, although such solutions are needed for crack problems in, e.g. thermal and residual stress fields.In the present paper, stress intensity factors (Mode I) are presented for nine crack geometries in combination with six load cases. The finite element method using 20-node collapsed quarter point singular elements was employed. By a proper modelling of the problem, the number of degrees of freedom was significantly reduced and high accuracy achieved. For the cases of uniform stress and bending, the results agree very well with those of Refs. [8,10], (1–3% for most cases) except one, ($\text{a}\text{c = 0.2}$, $\text{a}\text{t = 0.75}$) for which the present results are 10–17% lower than those in [8]. (For this case other published results deviate up to ± 50%). The K-factors for the more complex loadings will be useful in analysing surface cracks in complex stress fields.     

Stress intensity factors for interacting cracks and complex crack configurations in linear elastic media

In this paper, an effective numerical method for analyzing interacting multiple cracks and complex crack configurations in infinite linear elastic media is presented. By extending Bueckner’s principle suited for a crack to a general system containing multiple interacting cracks, the original problem is divided into a homogeneous problem (the one without cracks) subjected to remote loads and a multiple-crack problem in an unloaded body with applied tractions on the crack surfaces. Thus, the results in terms of the stress intensity factors (SIFs) can be obtained by taking into account the latter problem, which is analyzed easily by means of the displacement discontinuity method with crack-tip elements proposed recently by the author. Test examples are included to illustrate that the method is very simple and effective for analyzing interacting multiple cracks and complex crack configurations in an infinite linear elastic media under remote uniform stresses. Specifically, analysis of perpendicular cracks under general in-plane loading is performed using the numerical approach and many numerical results are given in the form of tables.     

Interaction of cracks with other cracks or boundaries

Thin strips made of plexiglas and containing either two symmetric and collinear edge cracks or an edge crack close to a boundary were subjected to tension. If these strips were viewed in a coherent monochromatic light beam emitted from a He-Ne gas laser, the light reflected from the back surface of the strip deviated because of the highly strained zone surrounding the crack-tip and formed a caustic. It was previously shown [7] that the caustic is a circle, the diameter of which is directly related. to the stress intensity factor. The interaction between either symmetric cracks or a single crack and a boundary was studied by measuring the diameter and the distortion of the shape of the highly strained zones around the crack tips. A series of ratios of crack length to the minimum width of the strips were studied and the critical loads for initial of rapid fracture were determined and compared for either case.     

Numerical modeling of complex interactions between underwater shocks and composite structures

To study the complex interactions between underwater shocks and composite structures, a strongly coupled Eulerian–Lagrangian numerical solver is developed. The coupled numerical solver consists of an Eulerian fluid solver, a Lagrangian solid solver, a one-fluid cavitation model, and an interface capturing scheme. The interface capturing scheme features a fluid characteristics method and a modified ghost fluid method (MGFM). The MGFM is reformulated for fluid–solid coupling by treating simultaneously the fluid characteristics equation and the solid equation of motion to determine the interface variables, leading to a strongly coupled Eulerian–Lagrangian scheme. Various components of the numerical solver are first individually tested and validated. The strongly coupled solver is then applied to realistic shock-structure interaction problems involving composite structures. The accuracy of the coupled solver is demonstrated via comparison with numerical predictions and experimental observations available in literature. Finally, the validated coupled numerical solver is utilized to study the effectiveness of a proof-of-concept shock mitigation scheme.     

General approach for monitoring peptide-protein interactions based on graphene-peptide complex

Peptide-protein interactions have critical roles in biology. Monitoring peptide-protein interactions plays an important role in investigating molecular recognition, screening drugs, and designing biosensors. In this paper, we develop a novel fluorescent approach to monitor peptide-protein interactions based on the assembly of pyrene-labeled peptide and graphene oxide (GO). The pyrene-labeled peptide is strongly adsorbed on the surface of GO via π-π interactions and hydrophobic interactions. As a result, the proximity of the GO to the pyrene moiety effectively quenches the fluorescence of pyrene. In the presence of target protein, the competitive binding of the target protein with GO for peptide results in the restoration of fluorescence signal. This signaling mechanism makes it possible to monitor the peptide-protein interactions in a homogeneous real-time format.     

Determination of the stressed state near edge cracks in a plate containing a hole of complex shape

We propose an approach to the determination of the stressed state of plates with edge cracks near holes of complex shapes based on the method of integral equations. We find the stress intensity factors for the cracks located near holes in the form of equilateral polygons and for systems of cracks of various lengths located near circular holes.