Special features of dynamic fracture of brittle materials in the mode of ultimate fracture velocities

Based on the model of spherical cavity expansion in brittle materials, which involves the concept of ultimate fracture velocities, we consider a stress-strain state in the elastic precursor zone and in the region of material broken by radial cracks. We have noted the mechanical effects of dynamic overload and fracture retardation, which arise within this model. Institute of Problems of Materials Science, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Problemy Prochnosti, No. 2, pp. 20–26, March–April, 2000.     

Analysis of the aluminum alloy resistance to the penetration of a steel rod at impact velocities of up to 500 m/s

The penetration of a steel rod into aluminum alloy plates of various thicknesses is examined. The resistance to penetration at its initial stages prior to the rod fracture is found to be determined by the dynamic strength of the plate material, its viscous component (proportional to the plastic strain rate) prevailing at impact velocities of up to 500 m/s. The depth of penetration varies with the velocity and is conditioned by wave processes in the plate, their scale being dependent on its thickness. Institute for Problems of Strength, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Problemy Prochnosti, No. 5, pp. 106–110, September–October, 1998.     

Standardization of the strength of metals under conditions of low-temperature instability of plastic deformation and the action of strong magnetic fields

We propose an approach to determination of allowable stresses by a static-strength criterion for materials of structures that operate at very low temperatures (T≤20 K). This approach takes into account the qualitative change in the nature of deformation of the material, which has a significant effect on the mechanical characteristics and the specific work of deformation. The choice of critical stresses for these conditions is substantiated. The calculations are performed by introducing corrections for low-temperature hardening of the material in the presence of the intermittent-flow effect. We discuss the possibility of taking into account the influence of strong magnetic fields on the magnitude of allowable stresses. Institute of Problems of Strength, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Problemy Prochnosti, No. 5, pp. 42–52, September–October, 1999.     

Investigation of the effect of surface treatment on the cyclic strength characteristics of nickel alloy by the acoustic emission method

Using the acoustic emission method, we study deformation processes in a plastic structural material with different technological inheritance properties under static and cyclic loading condition. The dependence of the total acoustic emission on applied stresses is shown to contain a special point characterizing the moment of change in the stress-strain state of the surface layer of the material. We derive relationships for the evaluation of fatigue limits of structural materials by acoustic emission inspection results. Zaporozh'e State Technical University, Zaporozh'e, Ukraine. Translated from Problemy Prochnosti, No. 3, pp. 139–145, May–June, 1999.     

Large-strain dynamic cavity expansion in a granular material

The dynamic problem of the symmetric expansion of a cylindrical or spherical cavity in a granular medium is considered. The constitutive behaviour of the material is governed by a hypoplasticity relation for granular soils capable of describing both monotonic and cyclic deformation. The problem is solved numerically by a finite-difference technique. A nonreflecting boundary condition used at the outer boundary of the computational domain makes it possible to model a continuous multi-cycle loading on the cavity wall. The solution is illustrated by numerical examples. Possible geomechanical applications to the modelling of the vibratory compaction and penetration in granular soils are discussed.     

有限柱形空腔膨胀理论及其应用

为研究有限平面尺寸金属厚靶侵彻问题,提出了有限柱形空腔膨胀理论.考虑侧面自由边界,将理想弹塑性材料的空腔膨胀过程分为弹塑性阶段和塑性阶段,得到了空腔壁径向压力的解析解.基于Tate磨蚀杆模型,应用有限柱形空腔膨胀理论计算靶的侵彻阻力,建立了长杆弹侵彻有限直径圆柱形金属厚靶工程模型.与现有文献试验比较表明,文中工程模型计算的侵彻深度与弹道试验结果吻合较好.     

Large-strain dynamic cavity expansion in a granular material

The dynamic problem of the symmetric expansion of a cylindrical or spherical cavity in a granular medium is considered. The constitutive behaviour of the material is governed by a hypoplasticity relation for granular soils capable of describing both monotonic and cyclic deformation. The problem is solved numerically by a finite-difference technique. A nonreflecting boundary condition used at the outer boundary of the computational domain makes it possible to model a continuous multi-cycle loading on the cavity wall. The solution is illustrated by numerical examples. Possible geomechanical applications to the modelling of the vibratory compaction and penetration in granular soils are discussed.     

A numerical study of the cavity expansion process and its application to long-rod penetration mechanics

The paper describes a series of 2D numerical simulations which followed the cavity expansion process in an elasto- plastic solid. The results from these simulations, in terms of cavity wall motion as a function of the applied pressures inside the cavity, highlighted several issues concerning cavity expansion process and the terminal ballistics of both rigid and eroding long rods. These issues include the form of the relation between the dynamic radial stress on the cavity wall and its velocity, which can be written in a simple, normalized form, at least for the materials we simulated here. Also, the difference between target resistance to the penetration of rigid and eroding-rod penetration, was quantified with a series of simulations in which the pressures in the cavity were applied on an angular section, rather than on its whole surface. Finally, we explored the inherent differences between spherical and cylindrical cavity expansion processes, which can be helpful for analytical models of the penetration of rigid rods with different nose shapes.     

Efficiency of the method of spectral vibrodiagnostics for fatigue damage of structural elements. Part 2. Bending vibrations, analytical solution

We discuss the possibility of efficient application of the harmonic analysis of strain cycles formed in an elastic rod in the process of natural or resonance vibrations to the evaluation of the degree of fatigue damage. Fatigue damage is simulated by discontinuities of the material resulting in different values of the modulus of elasticity in the processes of tension and compression. In determining the potential strain energy of a rod in the presence of a crack on the basis of linear fracture mechanics, this model enables us to deduce expressions for relative changes in the stiffness of the rod in the presence of edge and surface cracks. By using the asymptotic method of nonlinear mechanics, we find the second approximation to the solution of the differential equation of vibrations of the rod whose nonlinearity is explained by the effect of “breathing” of the discontinuity formed in the material. It is shown that the discontinuity of the material caused by fatigue damage is responsible both for changes in the natural frequency of vibrations of the rod and for significant contributions of the constant component and even harmonics to the spectrum of strain cycles in the rod. The values of the constant component and the amplitudes of even harmonics (mainly of the second one) may serve as an efficient parameter for the detection of fatigue damage to materials. Institute for Problems of Strength, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Problemy Prochnosti, No. 6, pp. 9–22, November–December, 1998.     

Concept of Ultimate Fracture-Front Velocity in Cylindrical Cavity Expansion in a Brittle Material

Expansion of a cylindrical cavity in a brittle material is analyzed on the basis of the concept of the ultimate velocity of the fracture front. The boundary problems have been solved for the material regions of various states. The expansion pressure of a cylindrical cavity as a function of the expansion velocity in a ceramic material is given and compared to that of a spherical cavity.     

Exact solution of flow theory problems with isotropic-kinematic hardening. Part 2. Setting of the deformation trajectory in the spaces of total and plastic strains

For an arbitrary isotropic and linear kinematic hardening and loading paths given in the form of arbitrary multisection polygonal lines in the five-dimensional deviatoric space of total strains, we have studied analytically an initially isotropic elastoplastic material with von Mises yielding and the associated flow rule. The solutions obtained are valid for arbitrary relationships that govern the variation of the spherical component of the stress tensor. For arbitrary isotropic and kinematic hardening, we have also obtained an analytical solution to an elastoplastic problem for an arbitrary deformation trajectory given in the deviatoria space of plastic strains Institute of Problems of Strength, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Problemy Prochnosti, No. 1, pp. 62–71, January–February, 2000     

Determination of the energy of electroplastic deformation of metals

On the basis of the well-known mechanism of electroplastic deformation, we suggest a method for determination of the fraction of energy of pulses of the electric current directly spent on the work of plastic deformation. The experimental data presented in the work confirm the validity of the proposed approach. The present work was partially financially supported by the International Science Foundation and the Ukrainian Government (Grant UBW 200). Institute for Problems of Strength, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Problemy Prochnosti, No. 4, pp. 38–43, July–August, 1997.     

On the hydrodynamic theory of long-rod penetration

The hydrodynamic theory of long-rod penetration is reexamined by applying the modified Bernoulli equation to the forces acting on both sides of the moving rod-target interface. Using a ratio of 2 for the effective cross sectional areas of the mushroomed and rigid parts of the rod, it is shown that analytical expressions can be used to calculate the resistance to target penetration. The analytical expression used to calculate this resistance is the cylindrical cavity expansion, which yields resistance values of 3–4 times the compressive yield strength of the target material. Calculations based on our model show good agreement with experimental data, for steel and tungsten long rods penetrating various steel targets.     

Influence of the dynamic behavior of materials on the penetration of long rods at elevated velocities. Discussion

We present a brief survey of the influence of the dynamic behavior of materials on the stationary penetration of long rods into thick plates at elevated velocities. Our attention is mainly focused on the analysis of the influence of the resistance of the material to plastic flow, strain rate, temperature effects, compressibility, and the boundaries of interacting bodies on the process of penetration. We also formulate basic directions of subsequent investigations. Institute for Problems of Strength, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Problemy Prochnosti, No. 4, pp. 39–51, July–August, 1998.     

On the hardening effect of plasma-deposited coatings

We studied the influence of plasma-deposited titanium-nitride coatings on the characteristics of short-term static strength of the matrix material. In the process of deposition of these coatings, we observed an increase in the conventional yield limit and ultimate strength of the material accompanied by a decrease in the characteristics of plasticity. Institute of Problems of Strength, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Problemy Prochnosti, No. 6, pp. 123–126, November–December, 1999.     

Dynamic cylindrical cavity expansion in an incompressible elastoplastic medium

Summary Self-similar dynamic expansion of a pressurized circular cylindrical cavity, embedded in an infinite elastoplastic incompressible medium, is here investigated with the large strain J₂ flow theory. Assuming steady-state conditions, thus bypassing the initial loading history, it is shown that plane-strain fields are sustained with no diverging logarithmic stress appearing in the remote elastic field. Yet, even in the absence of remotely applied stress, the appearance of small stresses at infinity is unavoidable. The present solution is exact but limited to relatively low cavity expansion velocities. A closed form expression is given for the cavitation pressure with elastic/perfectly-plastic response. A fairly general result is derived for the cavitation pressure in hardening media with a definite yield point and in linear-hardening solids as a special case. Contact is made with earlier results of quasi-static cavity expansion along with a comparison to the self-similar dynamic expansion of a spherical cavity in an incompressible Mises solid. Upper and lower bounds for penetration depth tests are suggested by using the present cylindrical cavitation model and the incompressible spherical cavitation model.     

Estimation of the cyclic life of 15KhMl and 20KhMl steels under nonisothermal conditions

The effect of nonisothermal loading on the deformation and fracture of structural steels was studied. The fracture mode of the material was shown to be determined by the peak and mean cycle stresses under isothermal conditions and by the cycle asymmetry under nonisothermal conditions. Institute for Problems of Strength, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Problemy Prochnosti, No. 3, pp. 22–27, May–June, 1998.     

Exact solution of problems of flow theory with isotropic-kinematic hardening. Part 1. Setting the loading trajectory in the space of stresses

For an arbitrary isotropic and linear kinematic hardening and loading paths given in the form of arbitrary multisection polygonal lines in the five-dimensional deviator space of stresses, we studied analytically an initially isotropic elastoplastic von Mises material and the associated flow rule. The solutions obtained are valid for arbitrary relationships governing the variation of the spherical component of the stress tensor. Explicit solutions are obtained for several important cases of material behavior. Institute of Problems of Strength, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Problemy Prochnosti, No. 6, pp. 81–92, November–December, 1999.     

Fundamental solutions of cavitation in porous solids: a comparative study

The expansion of internally pressurized cavities, embedded in infinite bodies, in spherical and cylindrical (plane strain and plane stress) configurations, is investigated within the framework of finite plasticity. Material response is modeled by the Gurson theory for porous solids and includes strain hardening. Numerical results, obtained under the assumption of nearly universal loading histories, reveal limit cavitation states for all three deformation patterns. Cavitation is identified with asymptotic levels of the specific cavitation energy, which is highest for the spherical cavity and smallest for plane stress (plate) holes. The influence of material porosity is assessed in context of weight optimization of protective plates. A limited comparison with experimental data for porous titanium plate perforation reveals close prediction of ballistic limit velocity.     

Energy partitioning and microstructural observations related to perforation of titanium and steel targets

This paper presents an analysis of two target materials and the associated energetics related to the initial penetration into the target and perforation as the penetrator exits the target. Impact tests were conducted for tungsten alloy rods striking rolled homogeneous armor (RHA) and titanium alloy plates. Rod impact velocities were nominal 1,500 and 2,000 m/s. Target thicknesses were chosen so that the rods would overmatch the targets and lose some 200 m/s during penetration. The tests utilized flash x-rays to determine rod residual lengths and velocities and target plug features to include thicknesses and velocities. From these observables, experimental determination of the corresponding kinetic energies (KEs) and estimates for the fracture energies were obtained. Also, in each case, target material adjacent to penetration channel walls was examined by optical and electron microscopy and x-ray diffraction to gain further insight into deformation processes (cavity expansion) during penetration. The analytic penetration model gave results that were in good agreement with the experimental observables. In addition, it was observed that the RHA follows traditional plastic flow of cavity expansion while titanium alloy shows deformation features that deviate significantly. The paper discusses possible causes for these differences.