Differential Energy Criterion of Brittle Fracture as a Criterion for Wood’s Transition to the Plastic Deformation Stage

Abstract

An experimental study and modeling of the behavior of wood during compression along the fibers was carried out. The nonlinear analytical dependence of the load on the strain was considered. Attention was focused on the post-peak stage of deformation in order to determine the load and displacement at which the transition to the stage of plastic deformation occurs. The work was aimed at substantiating the application of the energy criterion of brittle fracture as a criterion for the transition to the stage of plastic deformation. To achieve this goal, methods of mathematical modeling and analysis of test results were used. As an upshot, a simple and practical procedure was developed to predict the transition point to the above stage of plastic deformation. The simulation results were consistent with laboratory tests of samples and fragments of structures. The practical significance of this criterion lies in its possible use as an additional tool for analyzing the condition of some wooden structures. Energy criteria, including the one mentioned above, belong to fairly universal criteria. Accordingly, the research methodology can be adapted to analyze the behavior of, for example, composites under other types of loads in further studies.

Modeling of trabecular bone transition into plastic deformation stage under uniaxial compression

“…Brittle fracture realized at small strains, but the process of plastic deformation continues after brittle fracture (with known limitations). Therefore, the brittle fracture criterion can used as a criterion for the transition of trabecular bone to the plastic deformation stage, which shown by the example of wood in [19]. The justification for this criterion given in [20].…”

Monotonic and cyclic load of pine wood under uniaxial compression: experiments and modeling

“…Predicting the moment of transition to the post-peak stage of plastic deformation is necessary for efficient utilization of wood (Figures 5 and 6). To predict the transition to this stage, the differential criterion of brittle fracture, discussed earlier [17,18], can be used. However, this criterion is an approximation; therefore, given the high variability of wood properties, multiple criteria should be used to reduce errors.…”

“…In order to obtain an approximate solution, we assumed (at the level of hypothesis) that the transition to the plastic state means almost complete exhaustion of elastic properties and, accordingly, brittle failure of elastic elements, after which deformation of plastic elements of the damaged composite (if such elements exist) continues. Consequently, from the physical point of view, some criterion of brittle fracture can be regarded as a criterion for the transition of an elasticplastic material from the elastic stage to the plastic deformation stage [17,18]. Undoubtedly, this brief description corresponds to an idealized simplified model, since in real natural composites (which includes wood) elastic and plastic elements interact and deform together [2], with an increase in the impact on the composite accompanied by a decrease in the share of elastic deformations and, accordingly, an increase in the share of plastic deformations (Figures 1 and 5).…”

“…This means that at each of these points the tangent stiffness 𝑆 = 𝑑𝐹 𝑑𝑢 reaches an extreme (Figure 6). The characteristic points and lines on the load-displacement curve are: peak point (1); inflection points (2 and 3); tangents 4 and 5 are drawn through points 2 and 3, respectively; a line 6 is drawn through the point of intersection of line 4 with the abscissa axis, the tangent of the angle of inclination of which is twice less than the tangent of the angle of inclination of tangent 4 [18]; the point of intersection of line 6 with the postpeak branch of the load-displacement curve (7) and point 3 determine, respectively, the upper and lower estimates of the load, at which the transition of the specimen into the plastic stage of deformation is possible; the fragment of the post-peak branch (dotted line) does not exist in practice (Figure 5), because at point 7 (or 3) the specimen transitions to the plastic deformation stage [17], which is modelled by line 8 or 9, respectively. After passing point 3, the tangential stiffness decreases in absolute value and tends to zero, so point 3 can be considered as an indicator of the composite's transition to the plastic deformation stage.…”

Information model of green building research in the Arctic: methodological aspects

“…The buildings are provided with power supply, lighting, heating and ventilation systems. Physical models allow for a large number of diverse studies [9] to verify the developed criteria for green construction in the Arctic. The research is carried out in real-world operating conditions of modular buildings and allows comparing the results for two northern territories of Russia.…”