Evolution of structural damage and macrofailure of inhomogeneous media at the supercritical stage of deformation

Abstract

The article deals with the evolution of structural damage of an inhomogeneous body as a function of the properties of the loading system whose characteristics are taken into account by supplementing the boundaryvalue problem (1), (2) with the boundary conditions of the third kind (3) and (4). of structural disruptions, and formation of a macrodefect. Increased rigidity of the loading system makes it possible to stabilize the process of damage calculation, and this leads to an increase of limit deformations. The realization of the supercritical stage of deformation, together with energy dissipation upon structural destruction is the mechanism of adaptation of an inhomogeneous body to the loading conditions.Investigations of the regularities of the failure of polymer and composite materials [1], metals [2], and rocks [3] show that macroscopic failure of these materials is preceded by complex multistage processes accompanied by the nucleation, cumulation, and localization of disperse damage with the subsequent formation of a macrodefect. In an inhomogeneous body with a certain structure we naturally fred some difference in the nature of the development of the processes of failure determined not only by strength and strain characteristics but also by imperfections in the form of discontinuities and damage. In engineering practice it was noted that there is a substantial difference in the kinetics of damage cumulation in hydraulic and pneumatic pressure vessels and pipes which cannot be explained by structural features of the material. The data of special experimental investigations of this problem show that the fracture strength depends substantially on the rigidity of the loading system (external constraint), too [4, 5].By loading system we mean the totality of solid, liquid, and/or gaseous bodies deformed as a remit of transmission of a load to the body as a whole or to some separate part of it. The replacement of one state of the material in the region under consideration by another state leads to a change of the external load in dependence on the properties and design arrangement of the loading system whose characteristics can be taken into account in the solution of boundary-vaine problems of the mechanics of inelastic deformation and structural failure by boundary conditions of the third kind formulated in [6]. On the basis of the suggested model of a structurally inhomogeneous medium [7, 8] we investigate problems of multistage processes of damage cumulation and of the influence of the properties of the loading system on the formation of conditions determining the transition from microfailure to macrofailure.The mechanical behavior of a structurally inhomogeneous body fl, bounded by the surface Off, whose scleronomic isotropic components do not change the type of elastic symmetry in the process of damage cumulation, is described under quasistatic loading by the system of differential equations in incremental form:

Structural damage accumulation and stable postcritical deformation of composite materials

“…An increase in the volume of the fiber content leads to increased rigidity of the external constraint from the side of the material directly contacting with the softened region, hereby promoting stabilization of the process of softening [12] material in the plastic zone and most part of the postcritically deformed matrix at the given moment undergo elastic unloading (in Fig. 3, the corresponding regions are marked by dots).…”

“…At sufficient rigidity of the loading system, the deformation of the work-softening material, according to the above statement, is considered to be steady. Inequality (6), which is a stffficient condition for uniqueness of the solution to the boundary problems for bodies with work-softening zones, can also be derived on the basis of the energy balance [12] Here, D is the negative tensor relating to the small increments in stresses and strains at the work-softening stage of deformation. By using the introduced characteristics of the loading system, we can generalize the extreme and variational principles.…”

“…It was shown that, for various macro-homogeneous stress-strain states, the work-softening of a heterogeneous medium resulted from the development of equilibrium dissipative processes of structural destruction. The model considered here allows for (i) registering and investigating the effect of growth of limiting deformations, which immediately precede the macrofailure, with increased stiffness coefficients included in the boundary conditions (5), (ii) separating in a natural way the equilibrium and nonequilibrium stages of deformation, and (iii) detecting the change in the mechanism and scale levels of primary damage accumulation and the local instability of the failure process [12]. i Figure 1 shows the results of pseudo-plastic deformation of the representative volume of a granular composite containing 3072 structural elements at various ratios of the hydrostatic and deviatoric components (or the first and the second invariants) of the macrostrain tensor.…”