Fracture features of anisotropic materials at different impact velocities

Krivosheina, M. N.; Kobenko, S. V.; Tuch, E. V.; Кашин, О. А.; Лотков, А. И.; Khon, Yu. A.

doi:10.1080/17797179.2017.1393733

Cited by 8 publications

(6 citation statements)

References 18 publications

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“…In our simulation, we analyse the deformation of a single-crystal target (VZhM8 alloy) loaded by an aluminium impactor with an initial velocity of 600 m/s. The contact surface of the impactor and target is assigned a friction-free sliding boundary condition (Figure 7(a)) [32,33]. The impactor thickness is 1 mm, and the target thickness is 2 mm.…”

Section: Deformation Of a Shock-loaded Targetmentioning

confidence: 99%

Mathematical simulation of elastoplastic deformation in cubic materials with an account of anisotropic bulk compressibility

Krivosheina

Tuch

2021

Mathematics and Mechanics of Solids

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It was shown for the first time that when modelling the deformation of materials with cubic symmetry (at full stress), the rotation of the computational axes leads to the identification of anisotropic volumetric compressibility. Loading of the materials with cubic symmetry of properties in the directions not coincided with the main directions (for example, 011) allows one to detect 75% cases of the auxetic single crystals (i.e. with negative Poisson’s ratio). In these cases, the negative volumetric compressibility has anisotropy, in contrast to the volumetric compressibility calculated along the crystallographic axes for cubic materials. Anisotropy of the volumetric compressibility leads to anisotropy of velocities of propagation of body waves. This paper considers several elastoplastic problems for a cubic material with different orientations of a coordinate system about its crystallographic axes. The behaviour of such a material under dynamic loads is modelled with an account of anisotropic bulk compressibility to provide the same anisotropy of bulk wave velocities in the elastic and plastic ranges and a uniform pressure function at the elastic-to-plastic strain transition. For each orientation of the coordinate system and respective planes, different values at the indicatrices of elastic constants are specified, and this specifies different deformation processes in cubic materials. Such an effect is demonstrated by solving three problems in three-dimensional (3D) statements approximating the following processes: (1) one-dimensional elastoplastic deformation in a thin target impacted by a thin plate; (2) uniform compression in a spherical body under pulsed hydrostatic pressure; and (3) 3D elastoplastic deformation in a cylindrical body striking a rigid target in view of anisotropic bulk compressibility. The problems were solved numerically using original programs based on the finite element method modified by GR Johnson for impact problems. Solving problems in a 3D formulation makes it possible to take into account the dependences of the direction of the elastic and plastic characteristics of the material, as well as the velocities of propagation of elastic and plastic waves from that direction. The simulation results suggest that for cubic materials, changing the orientation of two coordinate axes in a plane changes the strains along all three axes, including those perpendicular to this plane. It is concluded that anisotropic bulk compressibility in cubic materials should be allowed for by mathematical models of their elastic and plastic deformation. We demonstrate that the orientation of a computational coordinate system for cubic materials should be in those directions in which their deformation is analysed in each particular case.

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Section: Deformation Of a Shock-loaded Targetmentioning

confidence: 99%

Mathematical simulation of elastoplastic deformation in cubic materials with an account of anisotropic bulk compressibility

Krivosheina

Tuch

2021

Mathematics and Mechanics of Solids

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“…where C i jkl are the components of the elastic constant tensor in the calculated coordinate system. The calculations were carried out using a mathematical model that includes the decomposition of the total stress tensor into the deviator part and the "anisotropic" hydrostatic stress [21]:…”

Section: Mathematical Statement Of the Problemmentioning

confidence: 99%

“…From the solution of the problem of shock loading of the cylinder along the [011] direction the reason of this asymmetry is clear. In the study of the deformation processes for the three cases of loading of the cylinders against a rigid wall and shock loading targets carried out nu-merically by the dynamic finite element method using original programs [20,21]. The aim of the work is to study the processes of elastic-plastic deformation in materials characterized by cubic symmetry of mechanical properties under dynamic loads.…”

Section: Introductionmentioning

confidence: 99%

Features of the processes of elastic deformation in cubic crystals

Strebkova¹,

Krivosheina²,

Mayer³

2019

MathMon

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The processes of elastoplastic deformation in single-crystal alloys characterized by cubic symmetry of properties are investigated. Using the heat-resistant single-crystal alloy VZhM8 used to create gas turbine engine blades by directional crystallization as an example, the dependences of deformation processes on the orientation of loading directions with respect to crystallographic axes are shown. Significant anisotropy of mechanical properties, including the presence of negative Poisson's ratios, in heat-resistant nickel alloys is maintained up to a temperature of 1150 • C. Therefore, over the entire range of operating temperatures, the propagation velocities of elastic and plastic waves in single-crystal heat-resistant nickel alloys depend on the propagation direction. On the example of a VZhM8 single-crystal alloy under dynamic loading in a three-dimensional formulation, the differences in the processes of deformation realized in a single crystal under loading along the [011], [111] and [001] axes are investigated.

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“…where υ i are the velocity vector components; i, j = 1,2,3. The total stress tensor is decomposed into deviatoric stress and anisotropic hydrostatic stress [20]:…”

Section: Mathematical Model For Elastoplastic Deformation In Anisotro...mentioning

confidence: 99%

“…The simulation was performed using original software. The 3D finite element simulation for uniformly compressed Zn single crystals was performed using original software and formulations reported elsewhere [20].…”

Section: Problem Statements For Shock-loaded Transversally Isotropic ...mentioning

confidence: 99%

Propagation of longitudinal and bulk waves in shock-loaded transversally isotropic single crystals

Николаевна

Viktorovich

Владимировна

et al. 2019

Materials Science and Technology

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The paper is present 3D numerical simulation data on elastoplastic deformation in auxetic single crystals with account of anisotropic pressure. The use of anisotropic pressure allows us to demonstrate the absence of shock wave splitting into an elastic precursor and a plastic wave in a Zn single crystal in the loading direction [0001]. This effect in Zn single crystals is observed in full-scale experiments at any loading rate in the [0001] direction. It is shown that anisotropic pressure should be entered into mathematical models of materials whose elastic properties are characterised by five and more independent elastic constants and hence by bulk compression anisotropy. The use of isotropic pressure in simulating the deformation of such materials leads to nonphysical results.

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Fracture features of anisotropic materials at different impact velocities

Cited by 8 publications

References 18 publications

Mathematical simulation of elastoplastic deformation in cubic materials with an account of anisotropic bulk compressibility

Mathematical simulation of elastoplastic deformation in cubic materials with an account of anisotropic bulk compressibility

Features of the processes of elastic deformation in cubic crystals

Propagation of longitudinal and bulk waves in shock-loaded transversally isotropic single crystals

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