Vladimir Bratov

Energy balance in the crack growth initiation under pulsed-load conditions

1. ENERGY APPROACHTO THE FRACTURE PROBLEMThe classical approach to fracture mechanics goingback to Griffith is based on the statement that a crackpropagates if this process leads to a decrease in the totalenergy e of a system. For a plate of unit thickness, thecrack-growth conditions can be written as . (1) Griffith initially interpreted the quantity 2 γ as thesurface energy, because it represented the specific work(per unit area) expended to form a new surface. Irwinand Orowan showed that this quantity should be inter-preted as the total work (including the plastic one) inthe fracture zone. This work can be taken as the resis-tance to a certain dissipative process proceeding in asmall region near the crack tip. The study of this char-acteristic includes the determination of its physical ori-gin (different for different classes of materials) and itsmeasurement.For the fracture near the crack tip loaded by mode I,criterion (1) is equivalent to the criterion for the criticalstress-intensity factor K

Energy-based analysis of ultrasonically assisted turning

The process of ultrasonically-assisted turning (UAT) is a superposition of vibration of a cutting tool on its standard movement in conventional turning (CT). The former technique has several advantages compared with the latter, one of the main being a significant decrease in the level of cutting forces. I n this paper the effects observed in UAT are analysed employing ideas of dynamic fracture mechanics. The active stage of loading duration depends heavily on ultrasonic frequency and the cutting speed; he application of the fracture criterion based on the notion of incubation time makes it possible to calculate a dependence of this duration on its threshold amplitude. An estimation of energy, necessary to create a threshold pulse in the materi al, is made by solving the contact Hertz problem. The obtained time dependence of energy has a marked minimum. Thus, the existence of energy-efficient loading duration is demonstrated. This ex plains the decrease in the cutting force resulting from supe rimposed ultrasonic vibration. The obtained results are in agreement with experiments on ultrasonic assisted machining of aluminium and Inconel 718 alloy.

Simulation of dynamic crack propagation under quasi-static loading

It is known that, within the framework of linear fracture mechanics (LFM) under quasistatic loading, the mechanicalstress field in the vicinity of the tip of a symmetrically loaded crack represented by a mathe� matical linear cut is determined by stressintensity factor (SIF) KI for the first loading mode, the corre� sponding critical value of which is found experimen� tally. The criterion of the critical intensity factor widely used in engineering practice was extended in many works also to the dynamicfracture case (1, 2):

Grain Refinement Kinetics in a Low Alloyed Cu-Cr-Zr Alloy Subjected to Large Strain Deformation

This paper investigates the microstructural evolution and grain refinement kinetics of a solution-treated Cu–0.1Cr–0.06Zr alloy during equal channel angular pressing (ECAP) at a temperature of 673 K via route BC. The microstructural change during plastic deformation was accompanied by the formation of the microband and an increase in the misorientations of strain-induced subboundaries. We argue that continuous dynamic recrystallization refined the initially coarse grains, and discuss the dynamic recrystallization kinetics in terms of grain/subgrain boundary triple junction evolution. A modified Johnson–Mehl–Avrami–Kolmogorov relationship with a strain exponent of about 1.49 is used to express the strain dependence of the triple junctions of high-angle boundaries. Severe plastic deformation by ECAP led to substantial strengthening of the Cu–0.1Cr–0.06Zr alloy. The yield strength increased from 60 MPa in the initial state to 445 MPa after a total strain level of 12.

Structural-temporal theory of fracture as a multiscale process

The paper reports on a structural-temporal approach to analysis of multiscale fracture of solids. A practical procedure is proposed for estimating the strength characteristics of material on one scale from test data on another scale.

On steady-state moving load problems for an elastic half-space

The steady-state regime of a moving load on an elastic half-plane is addressed. It is shown that the solution can be expressed through a single harmonic function, similarly to the known eigensolution for surface Rayleigh wave, thus reducing a vector problem in linear elasticity to a scalar one for the Laplace equation. Examples of steadily moving vertical force and punch are investigated, illustrating the proposed approach.

Multiscale Fracture Model for Quasi-Brittle Materials

Fracture of quasi-brittle heterogeneous materials is steered by processes at several different scale levels. These processes can progress independently or affect each other. In order to model fracture of such materials one should account for all rupture processes contributing to overall fracture process. This paper is presenting structural-temporal approach for analysis of multiscale nature of brittle fracture. Notion of spatial-temporal cell for different scale levels is introduced. Problem of experimental determination of a fixed scale level is discussed. Possible interconnections of this scale level with higher and lower scale levels are discussed. It is shown that this can give a possibility to predict fracture on a higher (real) scale level having experimental data obtained on a lower (laboratory) scale. This possibility is of extreme importance for many applications where the possibility to evaluate material strength properties on real structure scale level does not exist (ex. geological objects, big concrete structures, trunk pipelines, etc.).

A Criterion for Detonation Initiation in Gas Mixtures

Constructing critical conditions for detonation initiation is one of the basic aspects in the theoretical description of pulsed-detonation processes and of the passage from rapid consumption (deflagration) to detonation. Presently, in the majority of cases, approaches based on the concept of detonation critical energy are used [1–4]. Many experimental studies are also devoted to the analysis of the detonation initiation under the action of the electric discharge in gas media. For example, in the experiments described in [1], the detonation initiation in the stoichiometric hydrogen–oxygen mixture under the action of the electric discharge was investigated.

Numerical implementation of the incubation time fracture criterion

The paper is discussing problems connected with embedment of the incubation time criterion for brittle fracture into finite element computational schemes. Incubation time fracture criterion is reviewed; practical questions of its numerical implementation are extensively discussed. Several examples of how the incubation time fracture criterion can be used as fracture condition in finite element computations are given. The examples include simulations of dynamic crack propagation and arrest, impact crater formation (i.e. fracture in initially intact media), spall fracture in plates. Applicability of the approach to model initiation, development and arrest of dynamic fracture is claimed.

Simulation of Dynamic Crack Propagation under QuasiStatic Loading

Simulation of dynamic crack growth under quasistatic loading was performed using finite element method with embedded incubation time fracture criterion [. Experimental data, used for comparison was taken from [. ANSYS finite element software package was used in order to receive FEM solutions. The fracture criterion was implemented as an external procedure written in C++. The developed model is not using and trimming parameters. Only initial experimental conditions and material properties measured in separate experiments are used. Received dependencies for crack velocities as a function of time closely follow those observed in experiments by J.Finberg. Simulation results provide a possibility to conclude that the incubation time approach is an effective method to predict fracture initiation as well as crack propagation at various loading rates. Dependencies of an instant crack velocity on the current level of stress intensity factor received in this work for quasistatic loads and in [ for high-rate loads is discussed and compared to those experimentally observed by K. Ravi-Chandar and W.G. Knauss [ and J. Finberg [.