•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.
Wetlands are the world's largest natural source of methane, a powerful greenhouse gas. The strong sensitivity of methane emissions to environmental factors such as soil temperature and moisture has ...led to concerns about potential positive feedbacks to climate change. This risk is particularly relevant at high latitudes, which have experienced pronounced warming and where thawing permafrost could potentially liberate large amounts of labile carbon over the next 100 years. However, global models disagree as to the magnitude and spatial distribution of emissions, due to uncertainties in wetland area and emissions per unit area and a scarcity of in situ observations. Recent intensive field campaigns across the West Siberian Lowland (WSL) make this an ideal region over which to assess the performance of large-scale process-based wetland models in a high-latitude environment. Here we present the results of a follow-up to the Wetland and Wetland CH4 Intercomparison of Models Project (WETCHIMP), focused on the West Siberian Lowland (WETCHIMP-WSL). We assessed 21 models and 5 inversions over this domain in terms of total CH4 emissions, simulated wetland areas, and CH4 fluxes per unit wetland area and compared these results to an intensive in situ CH4 flux data set, several wetland maps, and two satellite surface water products. We found that (a) despite the large scatter of individual estimates, 12-year mean estimates of annual total emissions over the WSL from forward models (5.34 ± 0.54 Tg CH4 yr-1), inversions (6.06 ± 1.22 Tg CH4 yr-1), and in situ observations (3.91 ± 1.29 Tg CH4 yr-1) largely agreed; (b) forward models using surface water products alone to estimate wetland areas suffered from severe biases in CH4 emissions; (c) the interannual time series of models that lacked either soil thermal physics appropriate to the high latitudes or realistic emissions from unsaturated peatlands tended to be dominated by a single environmental driver (inundation or air temperature), unlike those of inversions and more sophisticated forward models; (d) differences in biogeochemical schemes across models had relatively smaller influence over performance; and (e) multiyear or multidecade observational records are crucial for evaluating models' responses to long-term climate change.
Small lakes represent an important source of atmospheric CH4 from northern wetlands. However, spatiotemporal variations in flux magnitudes and the lack of knowledge about their main environmental ...controls contribute large uncertainty into the global CH4 budget. In this study, we measured methane fluxes from small lakes using chambers and bubble traps. Field investigations were carried out in July–August 2014 within the West Siberian middle and southern taiga zones. The average and median of measured methane chamber fluxes were 0.32 and 0.30 mgCH4 m−2 h−1 for middle taiga lakes and 8.6 and 4.1 mgCH4 m−2 h−1 for southern taiga lakes, respectively. Pronounced flux variability was found during measurements on individual lakes, between individual lakes and between zones. To analyze these differences and the influences of environmental controls, we developed a new dynamic process-based model. It shows good performance with emission rates from the southern taiga lakes and poor performance for individual lakes in the middle taiga region. The model shows that, in addition to well-known controls such as temperature, pH and lake depth, there are significant variations in the maximal methane production potential between these climatic zones. In addition, the model shows that variations in gas-filled pore space in lake sediments are capable of controlling the total methane emissions from individual lakes. The CH4 emissions exhibited distinct zonal differences not only in absolute values but also in their probability density functions: the middle taiga lake fluxes were best described by a lognormal distribution while the southern taiga lakes followed a power-law distribution. The latter suggests applicability of self-organized criticality theory for methane emissions from the southern taiga zone, which could help to explain the strong variability within individual lakes.
A physical cut model is used to describe the changes in the stress-strain state (SSS) in elastoplastic bodies weakened by cracks. The distance between the crack edges is considered to be finite in ...contrast to the mathematical cut. The interactive layer with a thickness limited by the possibility of using the hypothesis of continuity is distinguished on the physical cut extension. Distribution of stresses and strains over the layer thickness is constant and does not depend on the geometry of the boundary between the cut and the interactive layer. The relationship between stresses and strains is determined by the deformation plasticity theory. The problem of plane strain or plane stress state of an arbitrary finite body weakened by a physical cut is reduced to solving a system of two variational equations for displacement fields in the body parts adjacent to the interactive layer. The proposed approach eliminates the singularity in stress distribution in contrast to the mathematical cut model. Use of local strength criteria allows us to determine the time, point and direction of the fracture initiation. Possibilities of the proposed model are illustrated by solving the problems of determining the SSS of a rectangular body weakened by a physical cut under symmetric and antisymmetric loadings.
A comparison of two models of the behavior of the material of a thin adhesive layer and their influence on the value of the J-integral for a specific experimental sample with specified mechanical and ...geometric properties is considered. A linearly elastic model of behavior and a model that takes into account the zone of weakened bonds with a finite linear distribution of the stress field are studied. The value of the J-integral is determined via the product of the specific work of the stresses and the thickness of the adhesive layer in the area of adhesive bond breaking. It is assumed that the thickness of the adhesive is finite and small compared to the thickness of the cantilever of the DCB sample. The finiteness of the layer thickness makes it possible to determine its deformations at relatively small thicknesses and to find the corresponding energy product. The distribution of stresses in the model with a zone of weakened bonds, determined by the ultimate strength and ductility of the adhesive, introduces the determining value of the J-integral. For an adhesive with pronounced plastic properties, the result of calculating the J-integral, taking into account the finiteness of the stress state, gives a result close to the experiment in comparison with the elastic model.
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.
The effect of a hole radius in an elastic layer on a critical external load at the moment of the onset of fracture, determined by the energy criterion, is investigated. A free energy flow through an ...interaction arc is used as a fracture criterion to describe the dependence of a critical external load on a hole radius. The length of the interaction arc constructed in the vicinity of a free energy peak point is determined using a linear parameter. The introduced linear parameter for a polymethyl methacrylate layer is obtained using known experimental data. The maximum value of the linear parameter can be taken as a material constant.
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