NONLINEAR PROBLEM OF FRACTURE MECHANICS OF AN INTERFACE CRACK SUBJECTED TO SHEAR WAVE

Solution for the problem for an interface crack under the action of a harmonic shear wave in normal direction is presented. The contact of the crack faces is put into consideration. The problem is solved by the boundary integral equations method, the vector components in the boundary integral equations are presented by Fourier series. The unilateral Signorini boundary conditions are involved to prevent the interpenetration of the crack faces and the emergence of tensile forces in the contact zone. Amonton-Coulomb Friction Law included allows to put into consideration relative resting of the crack opposite faces or their relative motion when one crack face is slipping or sliding across another face. The contact boundary restrictions are implemented using the iterative correction algorithm. The mathematical model adequacy is checked by comparing with classical model solution for statics problems that takes into account the crack faces contact. Numerical researches of friction influence on the displacement and contact forces distribution, size of contact zone are carried out. Influence of the faces contact and value of the friction coefficient on the distribution of stress intensity coefficients of normal rupture and transverse shear, which are the parameters of the biomaterial fracture, are presented and analyzed. It is shown that the nature of change in the distribution of the stress intensity coefficients for the conditions of tensile and shear waves is fundamentally different. It is concluded that it is possible to extend the approach proposed to the problems of three-dimensional fracture mechanics for composites with interfacial cracks at arbitrary dynamic loading.

Inverse problem for cracked inhomogeneous Kirchhoff–Love plate with two hinged rigid inclusions

We consider a family of variational problems on the equilibrium of a composite Kirchhoff–Love plate containing two flat rectilinear rigid inclusions, which are connected in a hinged manner. It is assumed that both inclusions are delaminated from an elastic matrix, thus forming an interfacial crack between the inclusions and the surrounding elastic media. Displacement boundary conditions of an inequality type are set on the crack faces that ensure a mutual nonpenetration of opposite crack faces. The problems of the family depend on a parameter specifying the coordinate of a connection point of the inclusions. For the considered family of problems, we formulate a new inverse problem of finding unknown coordinates of a hinge joint point. The continuity of solutions of the problems on this parameter is proved. The solvability of this inverse problem has been established. Using a passage to the limit, a qualitative connection between the problems for plates with flat and bulk hinged inclusions is shown.

Transition from sub-Rayleigh anticrack to supershear crack propagation in snow avalanches

Snow slab avalanches are released following anticrack propagation in highly porous weak snow layers buried below cohesive slabs. The volumetric collapse of the weak layer leads to the closure of crack faces followed by the onset of frictional contact. Here on the basis of snow fracture experiments, full-scale avalanche measurements, and numerical simulations, we report the existence of a transition from sub-Rayleigh anticrack to supershear crack propagation involving the Burridge-Andrews mechanism. Remarkably, this transition occurs even if the shear-to-normal stress ratio is lower than the static friction coefficient as a result of the loss of frictional resistance during collapse. This finding represents a new paradigm in our understanding of snow slab avalanches presenting fundamental similarities with strike-slip earthquakes.

Differences in Wear and Material Integrity of NAO and Low-Steel Brake Pads under Severe Conditions

In this study, through severe reduced-scale braking tests, we investigate the wear and integrity of organic matrix brake pads against gray cast iron (GCI) discs. Two prototype pad materials are designed with the aim of representing a typical non-metal NAO and a low-steel (LS) formulation. The worn surfaces are observed with SEM. The toughness of the pad materials is tested at the raw state and after a heat treatment. During braking, the LS-GCI disc configuration produces heavy wear. The friction parts both keep their macroscopic integrity and wear appears to be homogeneous. The LS pad is mostly covered by a layer of solid oxidized steel. The NAO-GCI disc configuration wears dramatically and cannot reach the end of the test program. The NAO pad suffers many deep cracks. Compacted third body plateaus are scarce and the corresponding disc surface appears to be very heterogeneous. The pad materials both show similar strength at the raw state and similar weakening after heat treatment. However, the NAO material is much more brittle than the LS material in both states, which seems to favor the growth of cracks. The observations of crack faces suggest that long steel fibers in the LS material palliate the brittleness of the matrix, even after heat damage.

A mode I crack with multiple islands of ideal contact between the crack faces: An asymptotic model

The problem of a mode I crack having multiple contacts between the crack faces is considered. In the case of small contact islands of arbitrary shapes, which are arbitrarily located inside the crack, the first-order asymptotic model for the crack opening displacement is constructed using the method of matched asymptotic expansions. The case of a penny-shaped crack has been studied in detail. A scaling hypothesis for the compliance reduction factor is formulated.

Crack Propagation Analysis of Compression Loaded Rolling Elements

The problem of crack propagation from internal defects in thermoplastic cylindrical bearing elements is addressed in this paper. The crack propagation in these elements takes place under mixed-mode conditions—i.e., all three possible loading modes (tensile opening mode I and shear opening modes II and III) of the crack are combined together. Moreover, their mutual relation changes during the rotation of the element. The dependency of the stress intensity factors on the crack length was described by general parametric equations. The model was then modified by adding a void to simulate the presence of a manufacturing defect. It was found that the influence of the void on the stress intensity factor values is quite high, but it fades with crack propagating further from the void. The effect of the friction between the crack faces was find negligible on stress intensity factor values. The results presented in this paper can be directly used for the calculation of bearing elements lifetime without complicated finite element simulations.

Study of the progressive failure of concrete by phase field modeling and experiments

In this research, experiments and numerical simulations are employed to research the failure process of concrete. Fracture experiments on three-point bending (TPB) concrete beams with a prefabricated edge notch at the middle of the beam bottom are performed using a modified rigid testing instrument. The characteristics of the crack and section are analyzed, including the crack tensile opening displacement, crack length and width, and crack faces characteristics. Also, the full curves of the force-crack tensile opening displacement (CMOD) and force-deflection of the TPB beams with the prefabricated edge notch after breakage are obtained. The phase field (PF) damage model is applied to the mixed-mode and mode-I failure processes of concrete structures through the ABAQUS subroutine user defined element (UEL). The crack path and the full curves of force-CMOD and force-deflection obtained by numerical calculations are consistent with the experimental results and the calculated results of other researchers. The influences of the mesh sizes, initial lengths, and notched depths on the TPB beam of concrete are also analyzed.

NONLINEAR PROBLEM OF INTERFACE CRACK BEHAVIOR UNDER THE ACTION OF SHEARING WAVE

Solution of the problem for an interface crack under the action of a harmonic shear wave is presented. It is shown that the same problems solutions of other authors were performed without taking into account the crack faces contact, and results obtained indicate the interpenetration of the faces, that is not possible. Thus, it is proved that the problem is nonlinear because the positions and sizes of the contact zone are unknown and variable during the loading. The solution is obtained by the boundary integral equations method taking into account the contact interaction of the crack faces: using the Somigliana dynamic identity and the boundary equations arising from them, the transition from the two-dimensional problem to the equivalent problem at the boundaries of the domain is realized; the vector components in the boundary integral equations are presented by Fourier series, to prevent the interpenetration of the crack faces and the emergence of tensile forces in the contact zone the Signorini unilateral constraints are involved. The numerical solution is performed by the method of boundary elements with constant approximation of the problem parameters on an element. Numerical researches of the shear wave frequency influence onto the crack faces and adjoining surface displacements, opening and extent of crack faces contact zone are carried out. The quantitative difference between the maximum tangential and normal components of adhesion line and the crack faces displacements is shown. It is shown that the position and length of the contact area change during the load period, and the magnitudes of the contact forces vary along the crack length.

Mutual influence of the faces contact area and the pre-fracture zone near the tip of the interfacial crack

BACKGROUND: Under plane strain conditions, a crack model was developed on a plane interface between two different materials, which assumes the existence near its tip of the faces contact area and a narrow lateral pre-fracture zone in a less crack-resistant material of the composite compound. The pre-fracture zone is modeled by the line of normal displacement rupture, on which the normal stress is equal to the tensile strength of the material. Assuming that the dimensions of the pre-fracture zone and the contact zone have the same order of magnitude and are significantly smaller than the crack length, the problem is reduced to the vector Wiener–Hopf equation. METHODS: An approximate method for solving the vector Wiener–Hopf equation was developed, which was used to obtain the equations for determining the sizes of the pre-fracture zone and the contact faces area. The pre-fracture zone orientation was determined from the condition of the potential energy maximum accumulated in the zone. Numerical calculations of the indicated parameters and analysis of their dependences on the configuration and module of external load are executed. RESULTS: A significant mutual influence of the pre-fracture zone and crack faces contact on their sizes and orientation of the zone was revealed.