Energy dissipation and storage in iron under plastic deformation (experimental study and numerical simulation)

The work is devoted to the experimental and numerical investigation of thermodynamic aspects ofthe plastic deformation in Armco iron. Dissipation and stored energies was calculated from processedexperimental data of the surface temperature obtained by infrared thermography. An original mathematicalmodel describing the process of mesoscopic defects accumulation was used for numerical simulation of thequasistatic loading of iron samples and for calculation of theoretical value of the stored energy. Experimentaland modeled values of the stored energy are in a good agreement

Energy dissipation and storage in iron under plastic deformation (experimental study and numerical simulation)

The work is devoted to the experimental and numerical investigation of thermodynamic aspects of the plastic deformation in Armco iron. Dissipation and stored energies was calculated from processed experimental data of the surface temperature obtained by infrared thermography. An original mathematical model describing the process of mesoscopic defects accumulation was used for numerical simulation of the quasistatic loading of iron samples and for calculation of theoretical value of the stored energy. Experimental and modeled values of the stored energy are in a good agreement

Theoretical Approach for Developing the Thermographic Method in Ultrasonic Fatigue

AbstractIn the last years, several approaches were developed in literature for predicting the fatigue strength of different kinds of materials. One approach is the Thermographic Method, based on the thermographic technique. This study is devoted to the development of a theoretical approach for modeling of surface and undersurface fatigue crack initiation and temperature evolution during ultrasonic fatigue test. The proposed model is based on the statistical description of mesodefect ensemble and describes an energy balance in materials (including power of energy dissipation) under cyclic loading. The model allows us to simulate the damage to fracture transition and corresponding temperature evolution in critical cross section of a sample tested in very high cyclic fatigue regime

Combined lock-in thermography and heat flow measurements for analysing heat dissipation during fatigue crack propagation

During fatigue crack propagation experiments with constant force as well as constant stress intensity lock in thermography and heat flow measurements with a new developed peltier sensor have been performed. With lock in thermography space resolved measurements are possible and the evaluation allows to distinguish between elastic and dissipated energies. The specimens have to be coated with black paint to enhance the emissivity. The thickness of the coating influences the results and therefore quantitative measurements are problematic. The heat flow measurements are easy to perform and provide quantitative results but only integral in an area given by the used peltier element. To get comparable results the values measured with thermography were summarized in an area equivalent to that of the peltier element. The experiments with constant force show a good agreement between the thermography and the heat flow measurements. In case of the experiments with a constant stress intensity some differences become visible. Whereas the thermography measurements show a linear decrease of the signal with rising crack length, the heat flow measurements show a clearly nonlinear dependency. Obviously the measured energies in thermography and peltier based heat flow measurement are not comparable

MODEL OF GEOMEDIA CONTAINING DEFECTS: COLLECTIVE EFFECTS OF DEFECTS EVOLUTION DURING FORMATION OF POTENTIAL EARTHQUAKE FOCI

This paper describes the statistical thermo-dynamical evolution of an ensemble of defects in the geomedium in the field of externally applied stresses. The authors introduce ‘tensor structural’ variables associated with two specific types of defects, fractures and localized shear faults (Fig. 1). Based on the procedure for averaging of the structural variables by statistical ensembles of defects, a self-consistency equation is developed; it determines the dependence of the macroscopic tensor of defects-induced strain on values of external stresses, the original pattern and interaction of defects. In the dimensionless case, the equation contains only the parameter of structural scaling, i.e. the ratio of specific structural scales, including the size of defects and an average distance between the defects.The self-consistency equation yields three typical responds of the geomedium containing defects to the increasing external stress (Fig. 2). The responses are determined from values of the structural scaling parameter. The concept of non-equilibrium free energy for a medium containing defects, given similar to the Ginzburg-Landau decomposition, allowed to construct evolutionary equations for the introduced parameters of order (deformation due to defects, and the structural scaling parameter) and to explore their solutions (Fig. 3).It is shown that the first response corresponds to stable quasi-plastic deformation of the geomedium, which occurs in regularly located areas characterized by the absence of collective orientation effects. Reducing the structural scaling parameter leads to the second response characterized by the occurrence of an area of meta-stability in the behavior of the medium containing defects, when, at a certain critical stress, the orientation transition takes place in the ensemble of interacting defects, which is accompanied by an abrupt increase of deformation (Fig. 2). Under the given observation/averaging scale, this transition is manifested by localized cataclastic deformation (i.e. a set of weak earthquakes), which migrates in space at a velocity several orders of magnitude lower than the speed of sound, as a ‘slow’ deformation wave (Fig. 3). Further reduction of the structural scaling parameter leads to degeneracy of the orientation meta-stability and formation of localized dissipative defect structures in the medium. Once the critical stress is reached, such structures develop in the blow-up regime, i.e. the mode of avalanche-unstable growth of defects in the localized area that is shrinking eventually. At the scale of observation, this process is manifested as brittle fracturing that causes formation of a deformation zone, which size is proportional to the scale of observation, and corresponds to occurrence of a strong earthquake.On the basis of the proposed model showing the behavior of the geomedium containing defects in the field of external stresses, it is possible to describe main ways of stress relaxation in the rock massives – brittle large-scale destruction and cataclastic deformation as consequences of the collective behavior of defects, which is determined by the structural scaling parameter.Results of this study may prove useful for estimation of critical stresses and assessment of the geomedium status in seismically active regions and be viewed as model representations of the physical hypothesis about the uniform nature of deve­lopment of discontinuities/defects in a wide range of spatial scales

Experimental study of heat dissipation at the crack tip during fatigue crack propagation

This work is devoted to the development of an experimental method for studying the energy balance during cyclic deformation and fracture. The studies were conducted on 304 stainless steel AISE and titanium alloy OT4-0 samples. The investigation of the fatigue crack propagation was carried out on flat samples with different geometries and types of stress concentrators. The heat flux sensor was developed based on the Seebeck effect. This sensor was used for measuring the heat dissipation power in the examined samples during the fatigue tests. The measurements showed that the rate of fatigue crack growth depends on the heat flux at the crack tip

On the use of the Theory of Critical Distances to estimate the dynamic strength of notched 6063-T5 aluminium alloy

In this paper the so-called Theory of Critical Distances is reformulated to make it suitable for estimating the strength of notched metals subjected to dynamic loading. The TCD takes as its starting point the assumption that engineering materials’ strength can accurately be predicted by directly post-processing the entire linear-elastic stress field acting on the material in the vicinity of the stress concentrator being assessed. In order to extend the used of the TCD to situations involving dynamic loading, the hypothesis is formed that the required critical distance (which is treated as a material property) varies as the loading rate increases. The accuracy and reliability of this novel reformulation of the TCD was checked against a number of experimental results generated by testing notched cylindrical bars of Al6063-T5. This validation exercise allowed us to prove that the TCD (applied in the form of the Point, Line, and Area Method) is capable of estimates falling within an error interval of ±20%. This result is very promising especially in light of the fact that such a design method can be used in situations of practical interest without the need for explicitly modelling the non-linear stress vs. strain dynamic behaviour of metals

A comparison of the two approaches of the theory of critical distances based on linear-elastic and elasto-plastic analyses

The problem of determining the strength of engineering structures, considering the effects of the non-local fracture in the area of stress concentrators is a great scientific and industrial interest. This work is aimed on modification of the classical theory of critical distance that is known as a method of failure prediction based on linear-elastic analysis in case of elasto-plastic material behaviour to improve the accuracy of estimation of lifetime of notched components. Accounting plasticity has been implemented with the use of the Simplified Johnson-Cook model. Mechanical tests were carried out using a 300 kN electromechanical testing machine Shimadzu AG-X Plus. The cylindrical un-notched specimens and specimens with stress concentrators of titanium alloy Grade2 were tested under tensile loading with different grippers travel speed, which ensured several orders of strain rate. The results of elasto-plastic analyses of stress distributions near a wide variety of notches are presented. The results showed that the use of the modification of the TCD based on elasto-plastic analysis gives us estimates falling within an error interval of ±5-10%, that more accurate predictions than the linear elastic TCD solution. The use of an improved description of the stress-strain state at the notch tip allows introducing the critical distances as a material parameter

МОДЕЛЬ ГЕОСРЕДЫ С ДЕФЕКТАМИ: КОЛЛЕКТИВНЫЕ ЭФФЕКТЫ РАЗВИТИЯ НЕСПЛОШНОСТЕЙ ПРИ ФОРМИРОВАНИИ ПОТЕНЦИАЛЬНЫХ ОЧАГОВ ЗЕМЛЕТРЯСЕНИЙ

This paper describes the statistical thermo-dynamical evolution of an ensemble of defects in the geomedium in the field of externally applied stresses. The authors introduce ‘tensor structural’ variables associated with two specific types of defects, fractures and localized shear faults (Fig. 1). Based on the procedure for averaging of the structural variables by statistical ensembles of defects, a self-consistency equation is developed; it determines the dependence of the macroscopic tensor of defects-induced strain on values of external stresses, the original pattern and interaction of defects. In the dimensionless case, the equation contains only the parameter of structural scaling, i.e. the ratio of specific structural scales, including the size of defects and an average distance between the defects.The self-consistency equation yields three typical responds of the geomedium containing defects to the increasing external stress (Fig. 2). The responses are determined from values of the structural scaling parameter. The concept of non-equilibrium free energy for a medium containing defects, given similar to the Ginzburg-Landau decomposition, allowed to construct evolutionary equations for the introduced parameters of order (deformation due to defects, and the structural scaling parameter) and to explore their solutions (Fig. 3).It is shown that the first response corresponds to stable quasi-plastic deformation of the geomedium, which occurs in regularly located areas characterized by the absence of collective orientation effects. Reducing the structural scaling parameter leads to the second response characterized by the occurrence of an area of meta-stability in the behavior of the medium containing defects, when, at a certain critical stress, the orientation transition takes place in the ensemble of interacting defects, which is accompanied by an abrupt increase of deformation (Fig. 2). Under the given observation/averaging scale, this transition is manifested by localized cataclastic deformation (i.e. a set of weak earthquakes), which migrates in space at a velocity several orders of magnitude lower than the speed of sound, as a ‘slow’ deformation wave (Fig. 3). Further reduction of the structural scaling parameter leads to degeneracy of the orientation meta-stability and formation of localized dissipative defect structures in the medium. Once the critical stress is reached, such structures develop in the blow-up regime, i.e. the mode of avalanche-unstable growth of defects in the localized area that is shrinking eventually. At the scale of observation, this process is manifested as brittle fracturing that causes formation of a deformation zone, which size is proportional to the scale of observation, and corresponds to occurrence of a strong earthquake.On the basis of the proposed model showing the behavior of the geomedium containing defects in the field of external stresses, it is possible to describe main ways of stress relaxation in the rock massives – brittle large-scale destruction and cataclastic deformation as consequences of the collective behavior of defects, which is determined by the structural scaling parameter.Results of this study may prove useful for estimation of critical stresses and assessment of the geomedium status in seismically active regions and be viewed as model representations of the physical hypothesis about the uniform nature of deve­lopment of discontinuities/defects in a wide range of spatial scales. В работе описана статистико-термодинамическая эволюция ансамбля дефектов в геосреде в поле внешнего приложенного напряжения. Авторами вводятся тензорные  структурные переменные, ассоциированные с двумя характерными типами дефектов: трещинами и локализованными сдвигами (рис. 1). Процедура осреднения структурных переменных по статистическому ансамблю дефектов позволила получить уравнение самосогласования, определяющее зависимость макроскопического тензора деформации, индуцированной дефектами, от величины внешних напряжений, исходной структуры и взаимодействия дефектов, которое в безразмерном случае содержит только один параметр – параметр структурного скейлинга. Параметр структурного скейлинга определяется отношением характерных структурных масштабов: размером дефектов и средним расстоянием между дефектами.В результате решения уравнения самосогласования получено три характерных реакции геосреды с дефектами на рост внешнего напряжения (рис. 2), которые определяются величиной параметра структурного скейлинга. Формулировка неравновесной свободной энергии для среды с дефектами в форме, аналогичной разложению Гинзбурга-Ландау, позволила записать эволюционные уравнения для введенных параметров порядка (деформации, обусловленной дефектами, и параметра структурного скейлинга) и исследовать их собственные  решения (рис. 3).Показано, что первая реакция соответствует устойчивому квазипластическому деформированию среды, локализованному в регулярно расположенных пространственных областях, характеризующихся отсутствием коллективных ориентационных эффектов. Уменьшение параметра структурного скейлинга приводит ко второй реакции, которая характеризуется появлением области метастабильности в поведении среды с дефектами, когда при некотором критическом напряжении происходит ориентационный переход в ансамбле взаимодействующих дефектов, сопровождающийся резким скачком деформации (рис. 2). При этом на масштабе наблюдения (осреднения) этот переход проявляется в виде локализованной катакластической деформации (множества слабых землетрясений), мигрирующей по пространству со скоростью, на порядки меньшей скорости звука – «медленной» деформационной волны (рис. 3). Дальнейшее уменьшение параметра структурного скейлинга приводит к вырождению ориентационной метастабильности и формированию в среде локализованных диссипативных дефектных структур, которые при достижении критического напряжения развиваются в режиме с обострением – режиме лавинно-неустойчивого роста дефектов в локализованной пространственной области, уменьшающейся с течением времени. На масштабе наблюдения этот процесс проявляется в виде хрупкого разрушения с формированием зоны разрушения, соизмеримой с самим масштабом наблюдения, и соответствует появлению сильного землетрясения.Таким образом, построенная модель поведения геосреды с дефектами в поле внешних напряжений позволяет описать основные способы релаксации напряжений массивами горных пород: хрупкое крупномасштабное разрушение и катакластическое деформирование, которые являются следствиями коллективного поведения дефектов, определяемого величиной параметра структурного скейлинга.Полученные результаты могут быть полезны для оценки критических напряжений и состояний геосреды в сейсмоактивных районах, а также могут рассматриваться как модельные представления физической гипотезы о единстве природы развития несплошностей (дефектов) на широком спектре пространственных масштабов