The deformation model of the DCB-sample with elastoplastic properties

The loading of a strip with a crack-like defect according to mode I is considered. In contrast to the classical representation of a crack in the form of a mathematical section, the proposed model defines a crack as a physical cut with a characteristic linear size. The mental continuation of a physical cut in a solid forms an interaction layer (IL). It is important that the stress-strain state of the layer at a finite value of the linear parameter does not introduce a singularity into the crack model. The process of elastoplastic deformation with a constant layer length is considered. We obtained a simplified analytical solution to the problem of deformation of two elastic bodies connected by a thin layer with elastoplastic properties. The dependence of the displacement and stress fields on the length and thickness of the interaction layer has been found. It is shown that, under the classical plasticity condition, the range of variation of the external load leading to a purely elastic behavior is possible only for a finite layer thickness. As the layer thickness tends to zero, as in the Dugdale model, the plasticity region is formed at an arbitrarily small external load. For small layer thicknesses, a local plasticity criterion is proposed, by using which it is possible to distinguish the intervals of the external load variations associated with elastic and plastic deformations. The local plasticity condition, determined by the critical value of the energy product, makes it possible to reflect the stage of elastic deformation at an arbitrarily small finite thickness of the interaction layer. An asymptotic dependence of the external load on the IL thickness and the reduced length of the plastic zone is obtained. At the same time, the separation of the external load into elastic and plastic components is preserved. From the analysis of the experimental data, an estimate of the elastic limit of the energy product for the AV138 adhesive was obtained.

Indentation mapping of stretched adhesive membranes

Unilateral adhesive contact between a rigid indenter and a uniformly stretched membrane of arbitrary shape is considered. The generalized Johnson–Kendall–Roberts (JKR)-type and Derjaguin– Muller–Toporov (DMT)-type models of non-axisymmetric adhesive contact are presented for short- and long-range adhesion, respectively, and the JKR–DMT transition is established in the framework of the generalized Maugis–Dugdale model. A refined method of matched asymptotic expansions is applied to construct the leading-order asymptotic model for indentation mapping of freestanding two-dimensional materials with an axisymmetric probe, using the approximate analytical solution obtained in explicit form for an infinite membrane in the limit of short-range adhesive contact with an indenter in the form of an elliptic paraboloid. The cases of a spherical indenter and a rectangular membrane are studied in detail.

Plane Contact and Adhesion of Two Elastic Solids With an Interface Groove

A systematic study is performed on the plane contact and adhesion of two elastic solids with an interface groove. The nonadhesion and Johnson–Kendall–Roberts (JKR) adhesion solutions for a typical groove shape are obtained in closed form by solving singular integral equations and using energy release rate approaches. It is found that the JKR adhesion solution depends solely on a dimensionless parameter α and the groove is predicted to be unstably flattened with no applied load when α≥0.535. Furthermore, the corresponding Maugis–Dugdale adhesion model has been revisited with three possible equilibrium states. By introducing the classical Tabor parameter μ, a complete transition between the nonadhesion and the JKR adhesion contact models is captured, which can be recovered as two limiting cases of the Maugis–Dugdale model. Depending on two nondimensional parameters α and μ, where α2 represents the ratio of the surface energy in the groove to the elastic strain energy when the grooved surface is flattened, different transition processes among three equilibrium states are characterized by one or more jumps between partial and full contact. Larger values of α and μ tend to induce more energy loss due to adhesion hysteresis. Combination values of α and μ are also suggested to design self-healing interface grooves due to adhesion.

The coupled criterion for description of fatigue fracture. Material embrittlement in pre-fracture zone

Step-wise extension of a crack in quasi-brittle materials under low-cycle loading conditions is considered. Both steady and unsteady loadings in pulsating loading mode are studied. It is proposed to use quasi-brittle fracture diagrams for bodies under cyclic loading conditions. When diagrams are plotted, both necessary and sufficient fracture criteria by Neuber-Novozhilov are used. A specific implementation is made on the base of the Leonov-Panasyuk-Dugdale model for the mode I cracks when the pre-fracture zone width coincides with the plasticity zone width near the crack tip. The condition of a step-wise crack tip extension has been derived. A crack extends only in the embrittled material of the pre-fracture zone. The number of cycles between jumps of the crack tip is calculated by the Coffin equation, when damage accumulation in material in the pre-fracture zone is taken into account. Critical fracture parameters under low-cyclic loading conditions have been obtained in a closed form. Estimates of the average rate of crack tip advance for a loading cycle at step-wise crack extension and S − N curves have been obtained.