


Vol 22, No 4 (2019)
- Year: 2019
- Articles: 10
- URL: https://journal-vniispk.ru/1029-9599/issue/view/12100
Article
Thin Homogeneous Two-Layered Plates of Cubic Crystals with Different Layer Orientation
Abstract
The paper provides a theoretical analysis of axially stretched rectangular thin plates composed of two differently oriented layers of cubic crystals. In one layer, the crystal has its principal crystallographic orientations parallel to the plate edges, and in the other, the crystal is oriented at a certain angle to the plate plane. The analysis shows that more than fifty cubic crystals with positive anisotropy can form two-layered plates whose effective Young’s modulus is greater than the moduli of both layers, which violates the well-known Voigt’s rule of mixtures. The anomalous behavior of effective Young’s modulus and Poisson’s ratios in the plates depends on the properties of their constituent crystals: the sign and value of anisotropy coefficients and Poisson’s ratio, ratio of Young’s moduli, relative orientation angle, and layer thickness ratio.



Effect of Point Defects on the Interface Strength of Joint Materials
Abstract
The paper proposes a nonequilibrium thermodynamic model of quasi-static crack growth at the interface of perfectly elastic materials which are either free of defects or contain nonequilibrium point defects like vacancies or interstitial/substitutional impurity atoms. Considering that the interface of joint materials is a point-defect adsorber from their bulk, the model establishes a crack growth criterion in terms of the defect adsorbability at the interface of two materials and at their free surfaces formed by an open crack, work of reversible interface separation dependent on the defect concentration in the materials, and crack growth rate. The criterion suggests that varying the defect concentration can provide one or another crack mode: growth or healing. The model is supported by a detailed mathematical analysis of the crack growth in the presence of nonequilibrium vacancies. Assuming that only one of the joint materials contains vacancies, the analysis gives an equation for the vacancy concentration which can change the crack mode, shows its analytical solution for two limiting concentrations, and demonstrates how the crack mode is changed as the vacancy concentration increases. The analysis is supplemented with quantitative estimates of the range of external and internal parameters (temperature, tensile stress, parameters of two joint materials, vacancy adsorbability at their interface and free surfaces) that admit of the two limiting cases in actual multilayer structures under typical operating conditions. The research results can be useful for modeling and optimizing the adhesion characteristics and assessing the service life of multilayer structures employed in modern micro- and nanoelectronics.



Direct Crystal Elastoviscoplasticity Model: An Application to the Study of Single Crystal Deformation
Abstract
This paper models the uniaxial compression of a single crystal of commercial purity aluminum, and compares the modeling results with experimental data. The problem is solved using a first-type direct model based on the finite element method. The material behavior is described by a crystal elastoviscoplasticity model that explicitly accounts for shearing on crystallographic planes. The main feature of this study is a physically sound description of the geometric nonlinearity associated with crystal lattice rotation. The modeling results show that the original homogeneous single crystal is divided into volumes with different plastic shear rate intensity and lattice orientation, which is in satisfactory agreement with experimental data.



Mathematical Modeling of Stress-Strain Evolution in the Rock Mass around a Mine Opening. Evaluation of the Steps of First Roof Caving at Different Thicknesses of the Main Roof
Abstract
Intensive mining activity has highlighted the need to study the dynamics of rock mass elements and to assess the degree of their nonequilibrium. The roof, floor, pillars, gateways, and so on are in a highly nonequilibrium state due to difficult mining conditions and high face advance rates. A good tool for predicting the mechanical behavior of the rock mass during mining is mathematical modeling, which is based on the solution of dynamic problems taking into account the nonequilibrium and nonstationary deformation and failure of rocks. In this paper, dynamic modeling has been performed within an evolutionary framework to investigate the steps of first caving in a model rock mass during face advance. All other things being equal, the thickness of the main coal seam roof is varied in the calculations. The steps of first caving are evaluated in the conditions of highly nonstationary deformation of the rock mass. The fluctuation statistics of the stress-strain parameters of the rock mass is analyzed. It is shown that the first roof caving is preceded by a fall in the slope of the amplitude-frequency curve of stress fluctuation.



On the Solution of Quasi-Static Micro- and Mesomechanical Problems in a Dynamic Formulation
Abstract
Simulations of characteristic mesoscale processes in a solid require a computational domain with a large number of structural elements (grains, inclusions, pores, etc.) and a sufficiently detailed mesh for their approximation. Reasoning that the computer power needed for such simulation increases nonlinearly with the number of structural elements, it is desirable to minimize the computational costs without loss of information and accuracy, for example, by solving quasi-static problems in a dynamic statement. Here we analyze the applicability of dynamic methods to quasi-static micro- and mesomechanical problems with explicit account of microstructure by the example of dynamic and static finite element computations of uniaxial tension for materials insensitive to strain rates. The analysis shows that the main parameter influencing the coincidence of dynamic and static solutions is the time in which the loading rate rises to its amplitude. If this rise time is longer than two travels of an elastic wave through a material, the dynamic and static problem solutions deviate by no more than 0.1% while the random access memory and the computation time needed for the static case is about ten times those for the dynamic one. Thus, explicit dynamic methods can be applied to advantage to quasi-static problems of micro- and mesomechanics.



Dynamic Strength of Heavy 90W—7Ni—3Fe Alloy Produced by Spark Plasma Sintering
Abstract
The dynamic strength of heavy 90W—7Ni—3Fe alloy (wt %) was studied on two types of specimens: formed from submicron powder by spark plasma sintering (SPS) and from coarse-grained powder with a particle size of ≈20 µm by standard liquid phase sintering (LPS). Mhe study shows that the dynamic strength of the LPS and SPS specimens ranges up to 2750 and 3150 MPa, respectively, and that the SPS projectiles at an impact velocity of 1200 m/s penetrate 60% deeper into a steel target than the LPS projectiles. The difference in the penetration depth results from different penetration mechanisms: piercing for the coarse-grained material and cratering for the fine-grained one.



Hydrogen Embrittlement of Austenitic Stainless Steels with Ultrafine-Grained Structures of Different Morphologies
Abstract
The paper studies the effect of electrolytic hydrogen charging on the plastic flow, strength properties, ductility, and fracture mechanisms in austenitic stainless steels Cr17Ni13Mo3C0.01, Cr18Ni10TiC0.12, and Cr18Ni9C0.17 with different stacking fault energies. The investigated steels are subjected to warm ABC-pressing and thermomechanical processing, including cold rolling and annealing, to produce the ultrafine-grained structure of different morphologies, such as ultrafine-grained (submicrocrystalline), misoriented grain-subgrain and mixed (grain and subgrain) structures of submicron scale. The strength properties of the steels after warm pressing and rolling with annealing exceed 3.5–6.0 times the properties of the quenched steels with coarse-grained structure. Electrolytic hydrogen charging of the studied steels with submicron-sized structure reduces the yield strength irrespective of the grain/subgrain size, structure, steel composition, and its stacking fault energy. The formation of a highly defective grain-subgrain structure with high dislocation density suppresses the effect of hydrogen embrittlement in Cr17Ni13Mo3C0.01 and Cr18Ni10TiC0.12 steels, in which no or a small volume fraction of strain-induced α′ martensite forms in tension. The tempering of the highly defective structure and the formation of a large fraction of high-angle misorientations in the stable Cr17Ni13Mo3C0.01 steel enhances the effect of hydrogen embrittlement in the specimens as compared to the specimens with a grain-subgrain structure with a high density of dislocations and low-angle boundaries. The hydrogen embrittlement effects are most pronounced in ultrafine-grained (submicrocrystalline) Cr18Ni10TiC0.12 and Cr18Ni9C0.17 steels with predominantly grain structure, which undergo induced γ→α′ phase transformation.



Two-Temperature Photothermal Interactions in a Semiconducting Material with a 3D Spherical Cavity
Abstract
In this paper, a two-temperatures photothermoelastic interactions in an infinite semiconductor medium with a spherical cavity were studied using mathematical methods. The cavity internal surface is traction free and the carrier density is photogenerated by boundary heat flux with an exponentially decaying pulse. Laplace transform techniques are used to obtain the exact solution of the problem in the transformed domain by the eigenvalue approach and the inversion of Laplace transforms has been carried numerically. Numerical computations have been also performed for a silicon-like semiconductor material.



Analytical Model for Dynamic Yield Strength of Metal
Abstract
Strain rate effect of yield strength has been a hot topic for a long time in impact mechanics over decades, and it is important to explore the physical mechanism behind this phenomenon. In this study, a one-dimensional stress bar analytical model for the dynamic yield stress of metal materials under a sinusoidal stress wave pulse is presented based on the structural-temporal failure criterion, and the corresponding numerical results accord well with previous experimental data under the high strain rate. Moreover, the dynamic yield strength can be determined by the nondimensional parameters κ and χ as well as a material parameter α. Specifically, the first nondimensional parameter κ can be determined by the ratio between the loading amplitude and quasi-static yield strength. The second nondimensional parameter χ is calculated by the ratio between the loading period and the incubation time. 0herefore, the dynamic yield strength can be essentially determined by the quasi-static material parameters, incubation time and loading parameters. The so-called strain-rate effect on the yield strength should be treated as an interaction process parameter in a dynamic loading—material system and should not be considered as an intrinsic material property anymore. additionally, this study may help researchers to determine the parameters in the numerical models including the strain rate effect of the dynamic yield surface.



Forming Limit Diagram Generation from In-Plane Uniaxial and Notch Tensile Test with Local Strain Measurement through Digital Image Correlation
Abstract
Requirement of forming limit curve appears indispensible for property check during formable sheet metal development cycle and quality control of formable sheet metal at production shop floor. In the present work, left side of the forming limit curve (uniaxial tensile to plane strain tensile) is experimentally determined from in-plane uniaxial and notch tensile test with local strain measurement through digital image correlation technique. A novel procedure has been developed to generate forming limit curve with considerably reduced experimental effort. The proposed new procedure is based on a combination of in-plane uniaxial notch tensile test with local strain measurement and modeling. The forming limit curve generated using the new procedure has been compared with the standard procedure (Nakajima test) and a good correlation has been obtained.


