NDT.net • July 2004 • Vol. 9 No.07

The Defective Structure of Plastically Deformed Constructional Steel 12X18X10T

Paiziev A.A. and Knyazev E.V.
Arifov Institute of Electronics, Academy of Sciences of the Republic
of Uzbekistan, Tashkent, Uzbekistan
Fax: 998-71-162-87-67, e-mail: paiziev@glb.net

Corresponding Author Contact:
Email: paiziev@glb.net


The defective structure of plastically deformed constructional steel 12X18X10X by a method electron-positron annihilation is investigated. The spectra of angular distribution of annihilation photons are measured for steel with a various degree of plastic deformation from 3 % up to 19.5 %. It is shown, that at plastic deformation defects of dislocation type are generated basically. With use capture model of positrons on defects dislocation type dependences of concentration of dislocations on deformation are received. It is shown, that all range of deformations can be divided into three areas where dependence of annihilation parameters on deformation has linear character.

Key words: Steel, plastic deformation, defects, dislocation, positron annihilation.


The positron method has already been successfully used to study the structure and dynamics of lattice defects in metals and alloys [1, 2]. Plastic deformation produces dislocations and vacancy. In single crystals the deformation is simple and produces dislocations but in polycrystalline samples the deformation becomes complex due to the various interactions between dislocations and the grain boundaries [ 3 ]. In plastic deformed metals and alloys the positrons are captured mainly by dislocations (with density rd) and by vacancy (with concentration Cv). Other imperfections of a crystal lattice, for example, interstitial atom?, packing defects and grain boundaries as capture centers of positrons can be neglected [ 2 ]. During deformation the interaction of dislocations can lead to rise the formation of jogs and point defects [ 4 ]. At increase of deformation the concentration of point defects is increased, which, merging in the area of a defects sink on boundaries of grains and form complexes of vacancies and dislocations .

The next increase of deformation results to formation micro pores. The further increase in deformation results to formation of cracks and destruction of a material. An existing quality testing methods of deformed steels are basically limited such methods as radiography [ 5 ] and method of acoustic emission [ 6 ]. However spatial resolution of these methods is limited by the sizes of micro cracks and micro porous. The method of electron-positron annihilation (EPA) is sensitive in respect of defects as dislocations and vacancies at an initial stage of defectiveness development of a material during plastic deformation. Sensitivity of EPA method in respect of vacancy concentration is found out at ~10-7 vacancies per atom and reaches a maximum at 1.5·10-5 vacancies per atom and disappears (reaches saturation) at 10-3 vacancies per atom. Concerning dislocations the sensitivity of EPA method is shown only at their density 108 sm of length per 1 sm2. Approximately at density of 5·1011 sm / cm3 saturation [ 2 ] is reached.

The density of dislocations may be determined with the help of EPA method on mono crystal and also polycrystalline samples with weak or even strongly expressed texture. However, not enough attention was given heterogeneity of distribution of dislocations, for example in cold-rolled samples [ 2 ]. In work [ 7 ] monocrystals of copper subjected deformations by a stretching in a direction [100] and received density of dislocations 1·108-6·109 sm/sm3. In [ 8 ] positron life time and Doppler broadening annihilation line shape measurements have been made to study the recovery behavior of Zn deformed at room temperature.

In [ 9 ] noted that defects like vacancy clusters and dislocation loops may be created by deformation as well as by irradiation of austenitic stainless steel AISI 316 (specification of the American Iron and Steel Institute) with energetic particles. In work [ 6 ] is shown, that change of crystal structure austenite in thin sheet stainless steel at a stretching occurs in four stages. It is marked, that between a square of amplitude of signals of acoustic emission and change of martensite concentration deformation there is not magnitude relation.

In the present work cited the measurement data of angular distribution of annihilation photons (ADAP) in stainless constructional steel samples 12X18X10T (specification of the Russian State Standard Board) is described.


2.1 Objects and technique of researches
The 12X18X10X specimens were prepared from commercially available alloy material. The composition (atomic %) of this alloy is: C 0.1%, Cr 17.0-19.0%, Ni 9.1-11.0%, and Ti 0.2%. Steel specimen of dimension 6 mm diameter tubules have been chosen for experiment. The specimens were cut from steel tubule length ~10 mm. Before starting the experiment they were polished, etched with alcohol and one sample annealed in order to avoid defects precipitation. One set of samples (6 samples) were subjected to consecutive deformations (2%, 3.05%, 4.3%, 6.2%, 10.6%, and 19.4%) at room temperature. Angular distribution of annihilation photons (ADAP) measurements have been made to study the nature and properties of deformation induced defects. The radioactive source 22Na is used with activity 20µCi. The annihilation photons are detected by scintillation counters shielded from direct view of the source by lead collimators. The coincident (< 10psec) counting rate from the two detectors is measured as a function of the displacement of one detector. ADAP spectra measured at room temperature after deformation and annealing in pointwise-linear geometry with angular resolution 1 mrad [ 2 ]. Statistical errors of measurements correspondent up to ~104 counting out in maximum of ADAP experimental spectra. For the analysis the changing of the ADAP spectrum around a maximum (S-parameter) and characteristic R and W-parameters are determined as relation of differences of the areas under part of the ADAP spectrums in the maximum both "tail" for perfect and defective samples.

2.2 Capture model of positrons on defects.
If suppose that the positrons are captured by defects of the same type (dislocations), time variation of relative number of positrons in perfect crystalline areas np(t) and in defect ones nd(t) may be described by next system of coupled differential equations [ 2 ]:


with initial conditions nd(0)=0, nP(0)=1, µdCd- capture rate of positrons on defects. After thermalization the positrons may be annihilate in the area of perfect lattice (p) with rate lp or capture by defects (d) with rate µdCd. On defects the positrons annihilate with rate lp. Solution of equation (1) is:


Decay rate L1 (L1=tp-1, lp= tp-1) and L2 = ld=td-1 and is characteristic for defect type. Using the equations (2) we can determine capture rate of positrons µdCd and absolute concentration of defects Cd. The positron fraction captured and annihilated on defects is:


Measurable parameter F is essentially different for positron annihilation in the perfect (Fp) and disturbed (F) areas . Such parameters are mean life time of positrons and parameters of shape ADAP spectra. (H, S, W). Using the equation (3) we can get F-parameter as:


As we can see from (4) dependence F on Cd have S -like shape.


The results of the positron annihilation experiments for annealed sample and deformed for difference stage of plastic deformation are shown in Figure 1. The Full Width at Half Maximum (FWHM) of ADAP spectra showed as up triangle figures. Analysis of ADAP spectra exhibits monotone decreasing of FWHM. Approximation FWHM on the difference areas along deformation axis by straight line let us to pick out three areas of plastic deformations differing by slope ratio:

FWHM= -As+B          (5)

Fig 1: FWHM of ADAP spectra and H-parameter in depend of deformation for steel 12X18X10T

Here s signed as degree of deformation (%). On the first section (0.0-3.7%) rate of change FWHM for percent elongation ~1% is 0.273 mrad/%. On the next stage (3.7%-11.2%) the slope ratio is essentially decreased (0.087 mrad/%). The third stage (>11.2%) characterized

Method I stage, % II stage, % III stage, % IV stage, %
Acoustic 0.0-2.22.2-10.210.0-28>30
Electron-positron annihilation 0.0-3.73.7-11.2 >11.2-
A=DG/Ds, mrad/% 0.273 0.087 0.010-
Table 1: Stages of plastic deformations of stainless steel specimens determined by method ADAP and method acoustic emission [ 6 ]

by more smaller falling rate of FWHM parameter (0.01 mrad/%). As we can see the maximal sensitivity of FWHM parameter is observed on the first stage plastic deformation (0.0-3.7%). The total area of sensitivity for FWHM parameter spread up to 10.0%. In the tabl.I boundary of difference stage of plastic deformation is shown. Simultaneously this boundaries compared with acoustic emission data [ 6 ]. The first stage characterizes the interval of microplastic deformation. Just here relevant data is limited. In particular it is known [ 2 ], that in the area of microplastic deformation the features of single dislocations is showed what may be investigated by electron-positron annihilation method. In initial deformation stage especially visible over patching of acoustic emission parameters is observed and spread this stage is estimated up to 2.0% (see Tabl. I). The second stage is characterized most powerful change of austenite crystalline structure and size this stage is 7-8% according to ADAP spectra and acoustic emission data (see Tabl.I) .

Let's estimate sensitivity of shape-parameters of EPA spectra in respect to defects concentration in researched samples. For this purpose we use capture model of positrons on the centers of dislocation type. In the literature is marked that the primary form of defects in deformed steels are dislocations [9]. In particular to it indicate an invariability of the ratio S and W parameters of ADAP spectra. On the Fig. 2 dependence of S-parameter on deformation in steel 10X18H10T and also the ratio S/W is showed.

Fig 2: Shape parameter of ADAP spectra (S-parameter) and ratio S/W depending on deformation.

Apparently from fig. 2 the S-parameter has the form of a curve with saturation in the area of deformations about 8-10 %. It indicates that at such deformations all positrons are captured on defects and annihilated on bound states. Other argument for the benefit of dislocation nature of defects is fact, that return of the form of ADAP curve occurs only at temperature intensive primary recrystallization, that in opinion of authors [2] is connected to presence of dislocations. Vacancies which arise during plastic deformation are healed in time Furthermore the bonding energy of a positron with a dislocation is essentially greater the bound energy of positron with vacancy.

On Fig. 1 and 2 dependences S-and H-parameters are resulted depending on a degree of deformation according to expression (4). At calculation we shall accept for capture rate of positrons on dislocation cross section s =pro2 with radius of a dislocation core ro which it is accepted equal to average value of a lattice constant of steel a=3.58A [2]. Taking into account that for thermalised positron velocity vt=(3kT/m)1/2 =3.45·107sm/s. Then for life time of positron in a perfect area of sample we have t3=l-1=-1=187ps [ 2 ]. In result using experimental curve H (s) (Fig.1) and the formula (4) it is possible to determine correlation between density of dislocations r (sm-2) and a degree of deformation of a sample s (%). Correlation of deformation with concentration of dislocations (curve 1) and part of positrons captured on defects (curve 2) is shown on Fig.3

Fig 3: Correlation between deformation degree and dislocation density for steel 10X18X10T and depending the part of positrons captured on defects.

As we can see from Fig. 3, a sensitivity limit of annihilation parameters regard to density of dislocations makes 107-108 sm-2. The greatest sensitivity of a method is reached at density of dislocations 109-1010 sm-2 when all positrons are trapped on dislocations.


  1. In deformed stainless steel specimens 10X18X10T there are defects of dislocation type.
  2. There is linear dependence between concentration of dislocation and deformation degree.
  3. According to positron data the whole range of deformation may be divide to three areas. The first stage connected with origin point defects (mono vacancy and linear dislocation), second stage connected with formation of complexes vacancy and dislocations and tertiary stage connected with origin micro porous and micro cracks.
  4. At the every stage of plastic deformation is observing linear depending positron annihilation parameters on deformation degree. Present results agree with acoustic emission data.
  5. From experimental ADAP spectra (H-parameter) concentration of linear dislocations is determined for difference deformation degree. For linear dislocation maximal sensitivity of H-parameter determined about 5·1010 sm-2.


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