Dynamic cracking resistance of structural materials predicted from impact fracture of an aircraft alloy

A new approach to studying the dynamic strength properties of structural materials is demonstrated with fracture of 2024-T3 aircraft aluminum alloy. The central idea of this approach is the incubation time to failure. In [1], experimental data for dynamic fracture of this alloy were analyzed in terms of the classical fracture criterion, which is based on the principle of maximum critical stress intensity factor [2]. In [1], the dependence of the stress intensity factor limiting value (the dynamic fracture toughness K_Id, which was assumed to be a functional characteristic of the material) on the loading rate was also measured. The same experimental data were analyzed in terms of an alternative structure-time approach [3]. In this approach, the dynamic fracture toughness K_Id is considered as an estimable characteristic of the problem, so that determination of limiting loads does not require a priori knowledge of the loading-rate dependence of the dynamic fracture toughness. The incubation time to failure of the aircraft aluminum alloy is calculated. The difference in the loading-rate dependences of the dynamic fracture toughness, which is observed for various structural materials, is explained. The dynamic fracture toughness of the alloy under pulsed threshold loads is calculated.     

Quasi-brittle fracture as failure of hierarchical structure

The paper proposes a quasi-brittle fracture model based on the kinetic approach and empirical regularities such as the concentration criterion and Zhurkov’s formula for a material in the form of a nested self-similar hierarchical structure. The concentration criterion is reformulated as a failure probability condition for structural levels. The hierarchy scheme takes into account critical values of the concentration parameter. The failure probabilities of hierarchy levels are calculated as functions of time, temperature, material parameters, and loading condition. Knowing the failure probabilities of hierarchy levels allows one to evaluate the stress dynamics in a material, average failure volume, elastic energy and inelastic strain release, etc. Experimental and calculated dependences are compared.     

Time dependence of the spall strength under nanosecond loading

The problem of spall fracture is considered using an incubation time criterion. Some experimental fracture effects are discussed. The spall strength is found to depend substantially on the pulse parameters, in particular, the rate of decrease of the load. The strain-rate and time dependences of spall strength are shown to be considered as calculated characteristics rather than as functions of a material.     

Fracture mechanisms in bulk metallic glassy materials

We find that the failure of bulk metallic glassy (BMG) materials follows three modes, i.e., shear fracture with a fracture plane significantly deviating from 45 degrees to the loading direction, normal tensile fracture with a fracture plane perpendicular to the loading direction, or distensile fracture in a break or splitting mode with a fracture plane parallel to the loading direction. The actually occurring type of failure strongly depends on the applied loading mode and the microstructure of the material. Extensive evidence indicates that the Tresca fracture criterion is invalid, and for the first time, three fracture criteria are developed for isotropic materials with high strength, such as advanced BMGs or the newly developed bulk nanostructural materials.     

Temperature dependence of spall strength and the effect of anomalous melting temperatures in shock-wave loading

The effects of temperature anomalies in materials subjected to the action of shock waves are studied. The spall failure of aluminum single crystals and polycrystals at various temperatures was experimentally studied in [1]. An analysis of the experimental data for polycrystalline aluminum shows that the breaking strength only weakly changes with temperature when it increases from room temperature to 90% of the melting temperature and, then, drops sharply to zero with a further increase in the temperature. For aluminum single crystals, the effect of anomalously high temperatures was experimentally detected; i.e., their strength remained high in the state where melting was expected during tension. The criterion of incubation time of failure is used to obtain an analytical expression for the temperature dependence of the spall strength of the materials. A new melting criterion, which relates the instant of a phase transition to the melting incubation period, is introduced. This criterion allows one to naturally explain the effect of anomalously high melting temperatures detected during the pulsed action.     

Analytical and Numerical Studies of the One-Dimensional Spin Facilitated Kinetic Ising Model

The one-dimensional spin facilitated kinetic Ising model is studied analytically using the master equation and by simulations. The local state of the spins (corresponding to mobile and immobile cells) can change depending on the state of the neighbored spins, which reflects the high cooperativity inherent in glassy materials. The short-time behavior is analyzed using a Fock space representation for the master equation. The hierarchy of evolution equations for the averaged spin state and the time dependence of the spin autocorrelation function are calculated with different methods (mean-field theory, expansion in powers of the time, partial summation) and compared with numerical simulations. The long-time behavior can be obtained by mapping the one-dimensional spin facilitated kinetic Ising model onto a one-dimensional diffusion model containing birth and death processes. The resulting master equation is solved by van Kampen's size expansion, which leads to a Langevin equation with Gaussian noise. The predicted autocorrelation function and the global memory offer in the long-time limit a screened algebraic decay and a stretched exponential decay, respectively, consistent with numerical simulations.     

Structural mechanisms of fracture of nanocrystalline materials

Structural mechanisms and features of brittle and quasi-brittle fracture of nanocrystalline materials are theoretically analyzed. The role of size effects and internal stresses caused by a nonequilibrium structure during brittle trans-and intercrystallite fracture is studied. The dependence of the nanocrystalline material durability on the working stress and grain size is calculated. The conditions for certain mechanisms of plastic deformation to be operative in nanocrystalline materials are analyzed. The influence of the grain-boundary and dislocation mechanisms of plastic deformation on the conditions of nanocrack formation is studied. The dependence of the fracture toughness of nanomaterials on structure parameters is calculated.     

Possible manifestations of the quantum effect (Tunneling) in elementary events in the fracture kinetics of polymers

An elementary event in the kinetics of fracture of polymers, i.e., breaking of a stressed skeletal bond in a chain molecule, has been simulated by the decay of a loaded quantum anharmonic oscillator. The probability and the average time of expectation of the escape of a particle from the potential well in the Morse potential under the action of a tensile force have been calculated over a wide range of temperatures. It has been demonstrated that the escape of the particle occurs predominantly through the tunneling mechanism at low and medium temperatures and through a combination of the tunneling (under-barrier) and over-barrier (thermal-fluctuation) mechanisms with comparable contributions at high temperatures. The calculations have revealed that the participation of the tunneling mechanism in the kinetics of fracture of polymers manifests itself in a low-temperature athermal plateau in the temperature dependence of the breaking strength. A comparison between the calculated and experimental temperature dependences of the breaking strength for the oriented polymer polycaproamide has shown that the calculated and experimental results are in qualitative and quantitative agreement, which allows the conclusion that the tunneling mechanism can contribute to the fracture of polymers.     

Energy of a solid sphere under nonstationary oscillations

Analytical solution for spherically symmetric nonstationary oscillations of acoustic and elastic solid sphere is given. Time dependence of potential, kinetic and internal energy of a solid sphere is analyzed. The received results are of practical importance for a wide range of problems connected to testing of material dynamic strength parameters and to the problems of optimizing (minimizing) energy needed for fracture of solids.     

Statistical kinetics of rock fracture and forecasting of seismic phenomena

Based on kinetic concepts of the strength of solids and a related hierarchical model of rock fracture, physically justified criteria for the appearance of the fracture source stage of the process are formulated. A technique for forecasting the region, time, and energy of seismic phenomena is developed, and its algorithm is described. Examples of forecasts based on an analysis of seismic conditions on the Kamchatka Peninsula and SUBR company mines are given.     

The kinetics and energy balance of mechanochemical transformations

The kinetic theory of strength formulated by Zhurkov is expanded to include an energy consumption analysis of the processes of deformation and fracture of solids and their compounds. The dependence of the kinetics of the structure defect formation and of chemical reactions in the processes of deformation and fracture of solids on the energy expended is found. Experiments and calculations concerning energy yields of the defect formation, deformational mixing, and mechanochemical reactions are discussed.     

Strength evaluation of brittle ceramics with surface defects subjected to thermal shock

The thermal shock strength of a ceramic material plate with a semi-elliptical surface crack is evaluated in this paper. The thermal stress distribution at the plate without crack is expressed by a polynomial form. The calculated thermal stresses are used to obtain the thermal stress intensity factors of semi-elliptical surface cracks using the geometric functions. Variations of thermal stress intensity factor with crack depth and time are obtained. For the strength evaluation of the material, crack growth analysis is conducted. In addition, the thermal shock resistance of the ceramic material plate is evaluated by the stress-based failure criterion and the toughness-based failure criterion. The critical temperature at which crack propagation starts is obtained. Applicability of the two failure criteria in thermal shock resistance evaluation of ceramic is identified and the importance of the semi-elliptical surface defects on the thermal shock resistance behaviour of ceramic materials is justified.     

动态断裂过程的数值分析及LY-12铝的层裂

 本文从文献[1]中用于分析柱壳动态膨胀断裂过程的损伤度函数出发，将它推广到对一维应变下层裂过程的数值模拟研究。试件材料为LY-12铝，其特性方程取为含粘性的本构方程形式。数值计算结果很好地再现了实测自由面速度u_fs随时间t的变化过程，并表现出层裂强度σ_c及层裂面上的临界损伤度α_c都分别是应变率ε_c'的单调递增函数关系。σ_c~ε_c'的这种变化规律在许多文献中已屡见报道，例如可见文献[2-3]。在10⁵ s^-1~10⁶ s^-1应变率范围内，σ_c~ε_c'关系可以表示为ε_c'exp(-11.4α_c)=2 100 s^-1，这个式子可以作为一种层裂判据使用。数值计算还给出了层裂片的损伤度剖面，其形状特征与Barbee等对回收试件的细观测量结果在定性上一致。     

Plastic fracture of quasicrystals

Elasto-plastic crack solutions for some one- and two-dimensional quasicrystals have been found based on the generalized Dugdale–Barenblatt model. The size of the plastic zone and crack tip opening displacement are determined, from which a plastic fracture criterion for the materials is suggested.     

Similarity law for a homogeneous discharge in the presence of a strong field and analogues of the Stoletov constant for the pulsed regime

It is demonstrated that the similarity relationships (breakdown curves), which establish a dependence of the field strength divided by the pressure on the product of the pressure and the delay time of the breakdown, are realized upon the uniform breakdown of the gas gap in the presence of both rectangular and triangular voltage pulses, which is interesting for the physics of gas and plasma discharges, and remain valid for strong fields. The breakdown criterion is described with a two-valued curve such that the effective multiplication of electrons in gas becomes possible in the presence of both weak and strong fields and at small products of the pressure and the pulse time. An analogue of the Stoletov effect, which corresponds to a maximum in the current with respect to pressure at a given voltage pulse, is demonstrated for the pulsed discharge. The analogues of the Stoletov constant are calculated for non-self-sustained pulsed discharges in various gases. The minimum delay time of the breakdown is also determined by these constants.     

Criterion of the incubation time in the problems of pulsed fracture and electric breakdown

The problems of a pulsed strength of continuum media are considered in terms of the structural-time approach that is based on the concept of the incubation fracture time. This approach makes it possible to describe phenomena that arise under high-velocity external effects. A limiting condition that determines the instant of rupture or breakdown is proposed on the basis of the structural-time approach. A way to interpret and to determine the incubation time is proposed. A phenomenological model of an electric breakdown of solid dielectrics is formulated. Examples are considered where the structural-time approach is applied to problems of spall fracture, crack initiation, and a pulsed breakdown of dielectrics. A procedure for describing the time dependence of the electric strength (volt-second characteristic) is described in detail. The results of the calculations are found to be in good agreement with experimental data.     

Characteristics of elementary acts in the kinetics of metal fracture

Experimental studies of the fracture kinetics of polycrystalline metals have led to the problem of the barrier and activation volume of elementary fracture acts. A model is proposed where the field binding one atom to its environment in a metal is represented by equivalent bonds directed along three orthogonal axes. These bonds are described using the Morse potential, whose parameters are found from the values of the Young’s modulus and the linear thermal expansion coefficient for metals. The validity of the model is checked by comparing the results obtained with metal sublimation data. The values of the barrier and activation volume of elementary fracture acts are determined for 15 polycrystalline metals. The levels of local overstresses are estimated. The theoretical breaking strengths of the metals are calculated.     

On the theory of laser sputtering through pairing of holes in compound semiconductors

A simple kinetic model is used to explain the observed dependence of the sputtering quantum yield on the laser fluence. The mechanism of sputtering presented here involves pairing of two holes against their repulsive Coulomb barrier, which depends on the concentration of photoexcited charge carriers through Debye screening. A threshold laser fluence is obtained at a concentration of photoexcited charge carriers that suppresses the barrier sufficiently to allow the pairing of holes at the surface bonds. The bonds are broken and atoms are ejected from the surface. The temperature dependence of the threshold laser fluence is discussed. Results agree qualitatively with experiments and existing theories.On leave of absence from: Institute of Solid State Physics, Bulgarian Academy of Sciences, 72 Lenin Boulevard, BG-1784 Sofia, Bulgaria     

Role of disorder in the size scaling of material strength

We study the sample-size dependence of the strength of disordered materials with a flaw, by numerical simulations of lattice models for fracture. We find a crossover between a regime controlled by the disorder and another controlled by stress concentrations, ruled by continuum fracture mechanics. The results are formulated in terms of a scaling law involving a statistical fracture process zone. Its existence and scaling properties are revealed only by sampling over many configurations of the disorder. The scaling law is in good agreement with experimental results obtained from notched paper samples.