Relationships governing the damage process under different loading conditions

Ботвина, Л. Р.; Oparina, I. B.; Baikov, A. A.

doi:10.1007/bf00566441

Cited by 5 publications

(5 citation statements)

References 15 publications

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“…This is indicated by data of J. G. Tchalenko [2], presented in Fig. It also follows from [3,4] that the stages of the damage process also remain the same at different scale levels. It also follows from [3,4] that the stages of the damage process also remain the same at different scale levels.…”

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confidence: 55%

“…Equation (3) has been obtained by processing experimental data and is based on an analysis of the stages of the damage process that begins with stable cumulation and growth of defects, transforms into the process of accelerated merging of pores, and ends with rapid development of the formed crack to the size of a trunk crack. However, in both cases the rate of damage cumulation is a power function of the [4]. If the range of variation of this factor is wide enough, the magnitude of the stable stage ranges from the maximum value for the given test conditions to zero [4].…”

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confidence: 97%

“…In [4] the rate of damage cumulation undeer various loading conditions is described by the power equation In [4] the rate of damage cumulation undeer various loading conditions is described by the power equation…”

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“…Every scale or structural level has a corresponding time dependence of the number and size of defects and curve of the size distribution of defects described by a power function of the form [3,9] N=AI -h (4) This function is often represented in the form of the dependence of the number of cumulated defects (N z) on their size. Every scale or structural level has a corresponding time dependence of the number and size of defects and curve of the size distribution of defects described by a power function of the form [3,9] N=AI -h (4) This function is often represented in the form of the dependence of the number of cumulated defects (N z) on their size.…”

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Analysis of the process of damage cumulation on various scale levels

1997

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It is known that the structure of the material plays a decisive role in the stage of initiation of fracture that is connected with formation of multiple pores and cracks. This stage has been studied less than the stage of development of a localized microcrack, which is described in terms of fracture mechanics. However, in order to optimize the structure of metals and alloys we should understand the laws governing the cumulation of discontinuities in the stage of the appearance of a trunk crack at various structural levels. This will allow us to relate the parameters of the structure with the characteristics of the process of cumulation of pores and microcracks and thus provide a basis for developing new materials with a high fracture resistance in the initial stage of fracture and for damage diagnostics by methods of nondestructive testing. It should be noted that analysis of damage cumulation is also of interest from the standpoint of the general laws of the fracture process in various materials, including metals, nonmetals, and rocks, because much experimental data show that these laws are similar and independent of the nature of the material and the scale level considered.Cumulation of discontinuities is studied [1-5 etc.] within the framework of the intensely developing field of damage mechanics, based on the universally acknowledged concept of vulnerability to damage introduced by L. M. Kachanov [6] and Yu. N. Rabotnov [7]. According to this concept the level of damage m is determined from the relative area of cracks or pores cumulated at the source of fracture in the specimen in the process of loading. It is assumed that at the initial moment the vulnerability to damage is equal to zero, and at the moment of failure it is equal to unity. It is difficult to evaluate the intermediate cases, but L. M. Kachanov has suggested using the following kinetic equation based, as he puts it, on the concepts of statistical physics for estimating the progress of damage:where cr is the stress, T is the temperature, and r is the time. The variables may include parameters characterizing the deformation and internal structure of the material. The solution of the suggested differential equation with respect to the rate of cumulation of defects is complicated by the dependence of the function F on numerous factors that determine the load-I A. A. Baikov Institute of Metallurgy of the Russian Academy of Sciences, Moscow, Russia; International Institute of the Theory of Earthquake Prediction and Mathematical Geophysics of the Russian Academy of Sciences, Moscow, Russia.ing conditions. For this reason, the rate of damage is described either by cumbersome semi-empirical equations relating this parameter to basic mechanical properties or by relations that determine the damage as a certain function of the relative endurance of the material. Most often the rate of cumulation of discontinuities is described by a power or exponential function of the form dm/dt -(1 -m) p (cy/cl0)" ;where p and n are dimensionless constants, k is Boltzma...

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confidence: 55%

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confidence: 97%

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confidence: 99%

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confidence: 99%

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Analysis of the process of damage cumulation on various scale levels

1997

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“…Experimental observations of advanced size level are formed by the coalescence of mesocracks of a lower level were reported. 28,29 Taking into account this fact, we can state the ontogenesis principle of multiple fracture: 30 to create a crack of some level L (m) in a volume of an intact material, the fracture process should pass through all previous stages of crack development and coalesce. In other words, before a mesocrack of an advanced level arose in a volume of an intact material, microdefects had become microcracks of the lowest level, some of which in turn coalescing with each other had transformed in mesocracks of a lower level and so on until they had created the mesocracks of the level which is previous to the level under consideration.…”

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Self-Similar Models and Size Effect of Multiple Fracture

Borodich

2001

Fractals

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Multiple fracture of polyphase quasi-brittle materials is analyzed from the standpoint of similarity methods. First, two self-similar models of development of a cloud of micro-and mesocracks in an unbounded solid are constructed. Both presented models supposed that the main part of the process zone is wedge-shaped and the process zone is bounded by an arc of a circle with the center at the main crack tip. The former model is based on the hypothesis of discontinuous self-similar character of the main crack propagation, while the latter model employs physical fractal approach. Finally, the problem of size effect for bounded models is studied. It is assumed that the main cause of the size effect is that the process zone cannot be fully developed in a bounded model of a real size construction.

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