Stress State Of Material Research Articles

Statistical Errors in X-Ray Triaxial Stress Analysis by Cos α Method

Currently, the sin2ψ method is established as an effective technique as how to measure the residual stress state of metal materials non-destructively by X-ray diffraction. In recent years, new X-ray stress measurements with two-dimensional detector are developed and spreading in the world. There is the cosα method as one of the new techniques. However, the research about the statistical errors in the method continues. The measurement theory of the cos α method is reviewed on the triaxial stress state. The triaxial stress analysis by the method is examined and discussed from a viewpoint of the derived errors for the determination.

Mathematical Modeling of Boundary Stress State of Orthotropic Material

In the paper, the mathematical model for determination of stress and deformation fields inside and at the elastic region boundary of deformation of orthotropic materials under the biaxial loadings is developed. Within the proposed model, a mathematical model for determination of the material transition boundary from elastic into non-elastic deformation region is developed and a system of nonlinear equations for calculation of the values of its parameters is obtained. By using the continuous method of solution continuation with respect to the best parameter and Runge-Kutta method, the demarcation curves of absolutely elastic and non-elastic deformation regions for the pine tree are constructed. The analysis of the obtained curves is carried out and on its base it is shown that the proposed model, in contrast to the known mechanical theories of strength, makes possible to determine and substantiate the ultimate stress states of materials whose asymmetry coefficients of the boundaries of proportionality in some anisotropy directions are greater, and in others less than one.

On the Specific Features of Using the Phenomenon of Acoustoelasticity When Testing the Stress State of Anisotropic Material of Technical Objects at Subzero Temperatures

On the Specific Features of Using the Phenomenon of Acoustoelasticity When Testing the Stress State of Anisotropic Material of Technical Objects at Subzero Temperatures

INVESTIGATION OF STRESS-STRAIN STATE OF “RESTORATION & TOOTH” SYSTEM IN WEDGE-SHAPED DEFECTS BY COMPUTED MODELING METHOD

The aim of this research is to study the influence of size and location of wedge-shaped defects of teeth on stress and strain state of restorative material on the basis of biomechanical analysis. Materials and methods: Biomechanical analysis of the stress-strain state was performed on a jaw bone fragment with canine and premolar inclusion. Results: Tangential stress increase both in the adhesive layer and in restorative material with depth and width (medial-distal size) of restored wedge-shaped defects of teeth,. The most unfavorable loading on a tooth is a joint action of vertical and horizontal loading in lingual- vestibular or vestibular-lingual direction, depending on localization of the restored wedge-shaped defects of teeth. The formation of retention grooves in wedge-shaped defects of teeth reduces the value of the maximum tangential stress in the adhesive layer of restorative material to 25% and extends the longevity of restorations. Conclusions: The difference in maximal values of tangential stress increases in adhesive layer of restorative material with or without retention grooves with increasing depth of defect. Thus, it is advisable to form retention grooves in cases of wedge-shaped teeth defects that exceed 1.5 mm. In case of restoration of subgingival wedge-shaped defects of teeth of small height it is recommended to create one retention groove on the gingival or incisal planes of a carious cavity due to significant inconveniences, and sometimes impossibility of formation of traditionally located retention grooves.

Justification of vibrating hopper hole parameters during fine grained bulk material unloading

Purpose. The leakage process of the fine grained bulk material (BM) from the unloading hopper is considered. As known the BM behaviour during the unloading process is directly related to the material stress state (active or passive) inside the hopper, which depends on the physical and mechanical bulk material properties, as well as hopper geometric parameters. At the boundary of the transition from the cylindrical part to the conical part of the unloading hopper hole, the horizontal stresses that precede the leakage of the material increase sharply. The use of vibration reduces horizontal stresses in the hopper and thus improves the bulk product fluidity. Also, the use of vibration reduces the probability of the free-fall arch formation over the outlet. Therefore, the present paper is aimed at developing the mathematical model of the fine grained bulk material flow under the vibration action from the conical hopper hole. Methodology. It is used one of the methods of studying the BM behavior, namely the analysis of the stress state of the conditionally stationary (pseudo-stationary) layer of the product and the force balance equation in the free-fall arch is made for further study of the geometric parameters of the unloading hole. Findings. In this paper, the mathematical model of the BM behavior in the conical hopper hole is developed. Since the most determining factor influencing the hopper productivity is the outlet diameter, so based on the developed model, it is established relationships that allow determining all parameters that affect the diameter. Graphical dependences are obtained, which allow to estimate the influence of the angle inclination of the hopper hole walls on the value of the hopper outlet size at active and passive stress states. The dependence of the diameter of the unloading hopper hole on the BM properties is also established. The BM properties directly affect the initial shear resistance of the material. The influence of vibration on the unloading hole geometry is presented. Originality. The pseudo-immobile layer of bulk product is considered in the developed mathematical model, and it is investigated how vibration affects the BM behavior in this layer. Practical value. The practical value of this paper lies in the possibility of further mathematical modeling of the influence of the BM properties, hopper geometric dimensions and vibration on the product behavior in the material leakage process from the hopper. The results of the studies, presented in the form of graphs, can be used during the vibrating hopper design and the selection of rational modes of hopper operation.

An algorithm for finding and adding boundary conditions with the aim of solving the contact problem in computational mechanics

Computer simulations based on numerical methods applied to the equilibrium equations of Newtonian mechanics have significant impact in many industries, because they provide cheaper development of products. Using computer simulations, it is possible to investigate behavior of product parts and assemblies under different boundary conditions, loads and applied materials, which significantly reduces the number of real expensive experiments. A large number of simulations can be conducted in order to optimize the geometry, materials, product price, etc. or to confirm that the product satisfies technical and safety requirements. By discretization of equilibrium equations, it is possible to simulate only continuous models, i.e. models whose all parts are physically connected. But a problem that occurs very often is mechanical contact between two or more independent mechanical parts. In case the parts are not physically connected, it is necessary to provide an additional boundary condition using a contact algorithm so that the independent parts would be aware of each other. Because of that, the contact problem between deformable moving bodies is always an interesting topic in computational mechanics and mechanical engineering in general. The problem that initiated the development of the contact algorithm presented in this paper is the possibility of numerical simulation of mechanical tests performed during the development of medical stents with the aim to provide a look inside, to show the state of stress or strain in material of the stent.During the implementation of the contact algorithm, two problems arise: 1. finding contact surfaces between different elastic bodies and 2. preventing the penetration of one body into another body by additional boundary condition. This paper presents the implementation of a contact algorithm by finding boundary surface nodes of a deformable body that have penetrated the boundary surface elements of another deformable bodies, and adding boundary conditions that reverse the penetrated nodes to the body boundary. The algorithm is implemented within the in-house software package for finite element analysis. The software is written in Fortran, which is another challenge, given that Fortran does not have as powerful geometry libraries as other modern programming languages do. The main reason for this was compatibility with existing finite element code and facilitated implementation of future parallelization with the aim of reducing computing time.

Numerical simulation of deformation and fracture of metal-matrix composites with considering residual stresses

Thermomechanical behavior of metal-matrix composite materials is investigated. Boron carbide B4C and high-strength aluminum alloy 6061-T6 are used as strengthening particle and matrix materials, respectively. Microstructure of the metal-matrix composite takes into account the complex shape of particles explicitly. Isotropic elastoplastic and elastic-brittle models were used to simulate the mechanical response of the aluminum matrix and ceramic particles, respectively. To investigate the crack initiation and propagation in ceramic particles, a Huber type fracture criterion was chosen that takes into account the type of the local stress state in ceramic materials: bulk tension or compression. The composite material with a single particle of both the really observed in the experiment and ideally round shapes is considered. The influence of the residual thermal stresses arising during cooling of the composite material from the temperature of aluminum recrystallization to the room temperature on the character of plastic strain localization in the aluminum matrix and fracture of carbide particles and on the macroscopic strength of the composite under external tension or compression is studied numerically. Two-dimensional dynamic boundary value problems in the plane-stress and plane-strain formulations were solved numerically by the finite element method using the Explicit module of the Abaqus software package. VUMAT subroutine procedures incorporating the constitutive models were developed and integrated into the Abaqus solver. Based on the results of the numerical simulation, it was concluded that the residual thermal stresses arising during cooling lead to the change in the mechanism of the particle fracture from in-particle cracking to debonding and increase the strength of the composite subjected to tension after the cooling.

Standardization to evaluate the lasting capacity of rubberized asphalt mixtures with different testing approaches

Under the action of traffic load, the stress and failure state of pavement structure and materials are complex and diverse. Moreover, pavement materials are multi-phase, multi-component, and multi-scale mixtures. Their mechanical properties have significant differences in tension behavior, compression characteristics, and correlations with stress states. In view of the above problems, different testing approaches were carried out in this paper. A suitable yield criterion for rubberized asphalt mixtures was proposed. Then, the strength yield surface was determined under different loading rates. Based on the fatigue test results, the concept of fatigue stress ratio was further proposed. The relationship between the rubberized asphalt mixtures fatigue life and the fatigue stress ratio was established. The results showed that the yield criterion covers the impact of the loading rates and tensile-compression strength difference on the rubberized asphalt mixtures’ mechanical behavior. The strength yield surface's shape is elliptical in the σm-σe stress space and expands outward as the loading rate increases. This paper unified the fatigue equations under different testing approaches. The established fatigue equations reflect the viscoelastic characteristics and strength characteristics of materials. The study effectively solves the difficult problem of fatigue equation selection in the structural design of asphalt rubber pavement.

Anisotropic stress state and small strain stiffness in granular materials: RC experiments and DEM simulations

The paper combines experimental and numerical analyses to study the relation between small strain stiffness and micro-structure of an idealized granular material under isotropic and anisotropic stress conditions. Results from the resonant column device on glass ballotini show that the relation between the maximum shear modulus and anisotropic stress components strongly depends on the applied stress path. Discrete element simulations (DEM) are performed to investigate the material behaviour along isotropic compression, triaxial compression and constant hbox {K}_0 deformation. The DEM analysis reveals that each stress path is associated with a characteristic evolution of the coordination number, i.e., the average number of contacts per particle. In turn, the maximum shear modulus is found to be a direct function of the coordination number. In order to include the micro-structure interpretation in the analytical description, a modified version of Hardin’s relation is proposed as a function of coordination number, void ratio and mean pressure.

Solving equations of 3D elasticity for orthotropic bodies

A mathematical model of the three-dimensional orthotropic body was used. A technique has been developed for integrating equilibrium equations in displacements that describe the stress state of orthotropic materials. We find the solution of equilibrium equations in displacements for orthotropic bodies. The expression of displacements, strains and stresses is obtained through the introduced displacement function, which satisfies the sixth-order equation for partial derivatives. We develop the algorithm of the analytical and numerical solutions of boundary value problem for orthotropic rectangular prism. Solution of boundary value problems is reduced to minimize a generalized quadratic form.

Effect of Pulse Current on Residual Stresses in AMg6 Aluminum Alloy in Electrodynamic Treatment

The development of energy-efficient methods of controlling the stress state of metallic materials and welded joints is topical for modern production. One of such methods is electrodynamic treatment (EDT). It is based on the passage of electric current pulses (ECP) through the metal, time-synchronized with an impact load initiated by electrodynamic forces. In this case, an electrodynamic deformation process and a process of formation of elastic strain waves occur simultaneously in the material being treated; they are defined as “electrodynamic impact”, the result of which is a local stress relaxation in the metal. The developed mathematical model of the formation of stress and strain fields during EDT, which is based on the motion of an elastoplastic medium, does not take into account the effect of ECPs on dynamic relaxation processes. A computational and experimental assessment of the effect of ECPs, which is based on the experimental assessment of the stress state and microindentation of AMg6 aluminum alloy plates after EDT without and with the passage of ECPs through the metal being treated, has been performed by the mathematical modeling of the EDT process taking into account microindentation results. The passage of ECPs contributes to an increase in tensile plastic strains and hence to an increase in residual compressive stresses (provided that the specimens to be treated are rigidly fixed). The reliability of the procedure has been confirmed by the results of evaluating the distribution of residual welding stresses in AMg6 alloy butt joints after EDT.

3D Dynamic Elastoplastic Constitutive Model of Concrete within the Framework of Rate-Dependent Consistency Condition

In this paper, the proposed yield function is the function of stress, hardening parameter, and strain rate. To fully describe the stress state and strain rate condition of material during dynamic loading, a new coordinate system, which is composed of a stress axis and strain rate axis, is employed to present the proposed rate-dependent yield surface. The strain rate is regarded as a variable in applying the consistency condition. The rate-dependent consistency is satisfied strictly during the whole dynamic loading. The nonassociated flow rule is employed to describe the dilatancy behavior of concrete. The loading–unloading criterion based on Ilyushin’s postulate is developed into the rate-dependent loading–unloading criterion that can consider reasonably the change of elastic domain caused by strain rate. Furthermore, a three-dimensional (3D) dynamic elastoplastic model of concrete is established within the framework of the rate-dependent consistency condition. Under the dynamic uniaxial compression loading condition, the model characteristics related to rate-dependent consistency condition are discussed and analyzed. Five sets of dynamic experiment results of concrete are employed to evaluate the performance of the model.

Modelling of Impulse Load Influence on the Stress State of Foam Materials with Positive and Negative Poisson’s Ratio

Abstract The influence of impulse load applied for different duration on the distribution of normalised dynamic radial stresses in positive and negative Poisson’s ratio medium was investigated in this study. For solving the non-stationary problem in the case of plane deformation for structurally inhomogeneous materials, the model of Cosserat continuum was applied. This model enables accounting for the influence of shear-rotation deformation of micro-particles of the medium. In the framework of Cosserat elasticity, on applying the Fourier transforms for time variable and developing the boundary integral equation method, solving of the non-stationary problem reduces to the system of singular integral equations, where the components that determine the influence of shear-rotation deformations are selected. The numerical calculations were performed for the foam medium with positive and negative Poisson’s ratio for different values of time duration of impulse. Developed approach can be used to predict the mechanical behaviour of foam auxetic materials obtained at different values of a volumetric compression ratio under the action of time variable load based on analysis of the distribution of radial stresses in foam medium.

The 2-axis stress component decoupling of {100} c-Si by using oblique backscattering micro-Raman spectroscopy

With the application of strain engineering in microelectronics, complex stress states are introduced into advanced semiconductor devices. However, there is still a lack of effective metrology for the decoupling analysis of the complex stress states in semiconductor materials. This paper presents an investigation on the 2-axis stress component decoupling of {100} monocrystalline silicon (c-Si) by using oblique backscattering micro-Raman spectroscopy. A spectral-mechanical model was established, and two practicable methods for actual stress decoupling analyses were proposed. The verification experiments demonstrated the correctness and applicability of the methods proposed in this paper.

Investigation of Welded Joints Made of Construction Steel by the Barkhausen Noise Method

Steel weld seams are characterized by heterogeneity of their microstructure. Microstructure affects the nature of the distribution, sign and magnitude of residual stresses. In combination with unfavorable factors (low temperature, metal hypoductility and an unsuccessful joint form) residual stresses lead to a decrease of load carrying capacity of a whole structure. In a weld seam residual stresses are distributed in a complex way and can affect the build quality of heavy section welded structures. Monitoring of residual stresses remains a big problem. Residual stresses in welds are often evaluated only by modeling. Unfortunately, all mathematical models describe the stress state of the welded material with low accuracy. Simple quality control, the results of which can be easy interpreted, is necessary. Welded joints made by manual arc welding and by automatic submerged arc welding were investigated. Butt seams of steel sheets of different thickness have been welded. Steel was low-carbon and low-alloyed. It is often used in welded structures for various purposes, including construction, and for pipelines manufacture. The temperature range of welded structures operation is very large – from-70 to 450С. The authors studied the structure of butt weld seams by the Barkhausen noise method, which is interesting as it represents an alternative to the known methods, which characterizes the structure and stress state of material. The relationship between the weld microstructure and magnetic noise is shown. Studies have allowed us to establish the relationship between the structure and magnetic properties and to evaluate the feasibility of applying the Barkhausen noise method to welded structures.

Numerical modeling of scale effects for circular cylinder in the theory of thermoelastic materials with voids

This article is relevant, as changes during the external loading may affect the stress state of the materials. The aim of this paper is to consider the numerical modeling of heating for circular cylinders in the frame of the theory of elastic materials with voids. A numerical solution is build using COMSOL Multiphysics software, where the implementation of the considered theory is realized based on the direct equation-definition approach. Constitutive relations were written in General form partial differential equation module. A matrix form of the equations for the two-dimensional case was used. Scale effects arising in considered problems are discussed. The classical solution is the particular case of the considered theory, when the coupling number tends to asero, i.e. when the micro-dilatation effects are small and do not affect the material's stress state. The limiting case in the case of the small value of the coupling number is the classical thermoelasticity solution.

Локальное напряженное состояние материалов с ГПУ решеткой и пластические зоны под поверхностью изломов

Локальное напряженное состояние материалов с ГПУ решеткой и пластические зоны под поверхностью изломов

Особенности процессов деформирования монокристаллического никелида титана при действии импульса всестороннего сжатия

Using the example of single-crystal titanium nickelide, the importance of taking into account the volume compressibility anisotropy when calculating the processes of elastoplastic deformation in materials with cubic symmetry of elastic properties is shown. It is shown that the process of uniform volumetric deformation corresponds to the process of non-uniform stress state for materials with cubic symmetry of properties for some orientations of the calculated coordinate system relative to the directions of the main crystallographic axes. The index surface of volume compressibility (or the reciprocal of it - the compression modulus) has a non-spherical shape and is a function of Euler angles. This is shown for the first time by solving a model problem - determining the stress and strain states of a spherical body made of single-crystal titanium nickelide under the action of a comprehensive compression pulse. In the general case of orienting the calculated coordinate system relative to the directions of the main crystallographic axes, an initially spherical body of single-crystal titanium nickelide is deformed into a biaxial ellipsoid under the influence of a comprehensive compression pulse.

Mathematical modeling of area boundary of biaxial absolutely elastic states of wood

In the paper, the mathematical model for determination of the region boundary of biaxial elastic states of orthotropic materials is synthesized and the system of nonlinear algebraic equations for identification of its parameters is obtained. Using the continuous method of solution continuation concerning the best parameter and the Runge-Kutta method, the demarcation curves of absolutely elastic and non-elastic deformation regions for pine trees are depicted. The analysis of the obtained curves is carried out and on its base, it is shown that the proposed model makes possible to determine and substantiate the ultimate stress states of materials whose the asymmetry coefficients of the boundaries of proportionality in some anisotropy directions are greater, and in others less than one.

Dislocation behavior in nickel and iron during laser shock-induced plastic deformation

Laser shock peening is one of the most effective surface strengthening techniques, which uses laser shock-induced plastic deformation to optimize surface stress state and microstructures of target material. In this paper, dislocation dynamics simulation was used to investigate laser shock induced ultra-high strain rate plastic deformation of face-centered cubic (FCC) nickel and body-centered cubic (BCC) iron. Molecular dynamics was employed to calculate dislocation mobility. Based on the obtained dislocation mobility coefficient, dislocation dynamics models of nickel and iron were established. Results show that the velocity of dislocation motion increases as temperature decreases. Under ultra-high strain rate deformation, dislocation density of nickel increases while dislocation density of iron decreases as temperature rises. Moreover, iron exhibits thermal softening while nickel exhibits thermal hardening under laser shock loading. Plastic deformation dominated by dislocations is sensitive to loading direction, depending on the Schmidt factor of the slip system. The ultra-high strain rate induced by laser shock can effectively increase dislocation density by promoting dislocation multiplication and suppressing dislocation annihilation.