•The general energy product converges with the reduction in linear size at shear.•The fracture criterion includes the stress tensor hydrostatic component and the external boundary.•The influence of ...shear on the CRLD specimen is part of the general variational problem statement.•The linear size determining GEP convergence was taken for the characteristic size of the pre-fracture zone.
This article considers the influence of shear on a specimen with a crack-like defect (CRLD) as part of the general variational statement of the problem with a distinguished interactive layer. The delta-element fracture criterion is formulated as a generalized energy product (GEP), accounting for the influence of hydrostatic stress and the existence of an external boundary. The GEP convergence with a reduction of the layer thickness in the layers element is shown both in the simplified analytical solution and in the numerical solution by the finite elements method (FEM). The linear size determining the GEP convergence in the layers element is taken for the characteristic size of the finite element conjugate to the physical excision and its continuation. It is shown that, unlike the simplified analytical solution, the solution by FEM allows finding the maximum GEP outside the layer.
An equilibrium thermoelastic state of two plates connected by a thin layer is examined. The problem is reduced to a system of six second-order differential equations. Temperature deformations of a ...bimetallic plate clamped at one edge and free at the other are considered. In the case of zero thickness of the interaction layer, the law of change of the interface line and the distribution of stresses along this line are obtained. In a uniform state (pure bend), the curvature of the interface line becomes constant. For zero Poisson ratio, the temperature dependence of the curvature is obtained.
On the basis of the general variational formulation of the problem of the deformation of two bodies connected by a thin layer, a system of differential equations of equilibrium of the ...double-cantilever beam is obtained, taking into account the shear deformations of the cantilevers, both in the interface section and in the free section, taking into account also the elastoplastic properties of the layer. In this work, we use the connection representation of the
J
-integral in terms of the energy product and the energy product of dissipation. For purely elastic deformation, on the basis of the analytical solution of the system, an expression is obtained for the stress state of an extremely thin layer connecting the cantilevers, which is dependent on the material properties of both the layer and the cantilevers. The obtained expression for the elastic energy flux is compared with the known ones. The energy product at the top of the layer is found, the value of which depends only on the material properties of the consoles. With the elastoplastic behavior of the layer, the energy product of dissipation was found, which turned out to be dependent on the yield stress of the adhesive. The energy product in this case is proportional to the layer thickness. For adhesives with pronounced plastic properties, taking into account the dissipative mechanism of energy release leads to fundamental differences in the
J
-integral in comparison with the elastic calculation. The dependences of the DCB sample compliance with subcritical growth of the plastic deformation region in the adhesive are plotted.
This paper describes a study of deformation of an ideal elastoplastic adhesive layer of a sample in the form of an elastic double-cantilever beam. The
integral values are determined for a number of ...adhesives with account for all diagonal stress tensor components in the layer. It is shown that the
integral value is significantly affected by the plane problem type in the case where an elastic-plastic model of layer deformation is applied. As demonstrated in the study, compressive stresses may be present during normal fracture in the irreversible deformation region of the adhesive in a plane stressed state.
Model crack with a scalable linear parameter Glagolev, V V; Glagolev, L V; Fursaev, A A ...
Journal of physics. Conference series,
04/2019, Letnik:
1203, Številka:
1
Journal Article
Recenzirano
Odprti dostop
The cracked body strain problem is considered in a linearly elastic formulation on the basis of the interaction layer (IL) concept for loading with opening mode or shear. The stress state in the IL ...is determined on the basis of the average-thickness characteristics of the stressed and strained state (SSS). The proposed problem formulation includes the linear parameter (LP). The wedge force-to-IL thickness relation is derived proceeding from the problem's analytical solution to a beam approximation. It is shown that it is possible to use the energy product of the linear size and the increment in the layer's specific free energy as the generic criterion of destruction. The established association of the specimen size with the critical force ensures is found out to ensure the independence of the critical force from the IL thickness to a desired degree of precision. The resulting and the conventional solution for a notch in the form of mathematical cut are compared to determine the assumptions on which Griffith's criterion concurs with the EP criterion.
Finite deformation of a panel under the influence of pressure is considered. The statement of the problem in displacements with equilibrium conditions represented via true stresses in Lagrangian ...coordinates is proposed. It is proven that the initial equations are satisfied when the panel is uniformly curved during deformation. The use of the previously proposed defining relation makes it possible to determine a differential relationship of the laws of pressure and curvature with time at an arbitrary strain rate. Ideally plastic and superplastic deformations are considered. The dependences of pressure on the curvature and strain time are obtained at which superplasticity occurs. It is revealed that, in this case, the range of stable changes in the curvature does not depend on the strain rate, and the threshold stress does not affect the time it takes to reach a given curvature of the panel.
A model of a physical section that describes stress–strain states in elastic–plastic solids weakened by cracks is proposed. The problem of plane deformation and the stress state of a solid of an ...infinite size of an arbitrary geometry, weakened by a physical section, is solved. It comes down to a system of two variational equations with respect to displacement fields in the parts of the solid bordering the interaction layer. For a material whose properties are close to those of a D16T alloy, the linear parameter introduced into the crack model is estimated, and the critical conditions of solids with lateral cracks in the case of a normal detachment are determined.
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