High Temperature Strain of Metals and Alloys Part 2 pptx

The sensors used to measure stress and elongation of the specimen must be compact because of the relatively small distance between the axis and the slits of an X-ray goniometer for examp

10 1 Macroscopic Characteristics of Strain of Metallic Materials at High Temperatures

6 The various directions of research are somewhat separated from each other

7 The physical nature of the creep deformation behavior of industrial su-peralloys has not been investigated sufficiently Quantitative physical theories are still being worked out

I consider that the essence of the problem of the physical fundamentals of high-temperature strain consists in structural evolution under specific exter-nal conditions My approach to the problem is based on the concept that the effect of applied stresses upon the crystal lattice at high temperatures results

in distinctive structural changes and these specific changes lead to the defi-nite macroscopic behavior of a material, especially, to the strain rate and to the stress resistance

A key to the problem is the response of the structural elements of a material

In some way the situation is in accordance with the Le Chatelier rule The changes in a metallic system which take place under the influence of external conditions are directed so as to relax this influence The formation of an ordered dislocation structure is just an evolution process which tries to act against applied stresses The point is that the high temperature conditions give the possibility of supplying the dislocation rearrangement with energy and which results in the substructure formation

That is why our aim is first to investigate quantitatively and in detail the interaction of dislocations with each other, the formation of subgrains, the interactions between dislocations and particles in superalloys, and only then

to conclude a physical mechanism for the process

The nature of microscopic processes should be revealed as a result of ex-periments that enable one to observe the events on the atomic, microscopic scale, and not on the basis of the general properties of crystal lattice defects nor on the basis of mechanical tests

This approach enables us to find unequivocal and explicit expressions for the high-temperature steady-state strain rate These expressions contain sub-structural characteristics, physical material constants and external conditions The essence of this approach is defined as the physics of the processes, which are the structural background and the kinetic basis of the macroscopic defor-mation of metals and solid solutions in the interval (0.40–0.70)Tm, whereTm

is the absolute melting temperature Superalloys operate at higher tempera-tures

Thus, the planned path can be shown schematically as follows Systematic investigations of the structure of metals strained at high-temperature.⇒ The

determination of the physical mechanism of strain, which should be based upon experimental data.⇒ Calculation of the macroscopic strain rate on the

basis of this mechanism.⇒ Comparison with experiment.

This plan demands first an efficient structural investigation and detailed proofs of correctness of physical models

An in situ investigation of metals is necessary in order to address the

prob-lem of the physics of the high-temperature deformation

High Temperature Strain of Metals and Alloys, Valim Levitin (Author)

Copyright c
2006 WILEY-VCH Verlag GmbH & Co KGaA, Weinheim

ISBN: 3-527-313389-9

13

2

The Experimental Equipment and the in situ X-ray Investigation

Technique

2.1

Experimental Installation

The experimental installation for direct measurements of substructural changes

in the massive metallic specimens during deformation at high temperatures must meet the following requirements

1 The sensors used to measure stress and elongation of the specimen must

be compact because of the relatively small distance between the axis and the slits of an X-ray goniometer (for example, a typical distance may be 65 mm)

2 It is advantageous to mount a loading mechanism on the frame of the chamber in order to provide rotation of the specimen around the axis of the goniometer during its exposure to X-rays The mechanism must be able

to create a load of the order of thousands of Newtons while preserving the vacuum

3 The windows in the chamber should be arranged in such a way that they are transparent to X-rays Recording of the scattered irradiation must be pro-vided in the interval of the Bragg angles that is important for measurements Figure 2.1 shows a set-up of an experimental installation designed accord-ing to these requirements [13] A specimen 1 is fastened in holders 2 and 3

A double-shovel shaped specimen with gauge diameter 1.5 to 3.0 mm and gauge length up to 20 mm is used The lower holder 3 is fastened rigidly to the frame of the chamber The upper holder 2 can move along the axis direction Movement of the upper holder is achieved with an electric motor, a reducer and a worm-and-worm gear 5 The gear rotates on the external thread of a hollow rod 6 The speed of the holder 2 may be continuously adjusted with the electric motor One may also use different reducer gears The speed may

be varied from5 × 10 −7to3 × 10 −3s−1 Silphon 7 enables one to move the

rod relative to the chamber while preserving the vacuum

Due to the motion of the rod 6 it is possible to apply a load of up to 2000N to the specimen A special dynamometer 8–12 is used to measure the stress It

consists of a frame 8 and an electronic valve 9 (a so-called diode mechanotron) Deformation of the frame because of stress is transmitted through the screw

10 to the stem of the valve The elongation of the specimen is measured with

a clock indicator 14 with an accuracy of 0.01 mm

The chamber 18 and covers 17 have special windows 19 made of beryllium The initial beam enters and the scattered irradiation leaves through this win-dow The location and the size of the window enables one to measure angles

of2θ in the interval from 50 ◦to165◦ The Wilson packing 24 enables one to

rotate the chamber around the goniometer axis during X-ray irradiation The second cover has a window made of glass in order to measure the temperature

of the specimen with an optical pyrometer The temperature can also be mea-sured with a thermocouple fastened to the specimen The chamber 18 and covers 17 are cooled with flowing water Adjustment of the chamber relative

to the initial X-ray beam is provided by sledges 22, 23 in two perpendicular directions

The specimen 1 is heated by electrode 16 by passing an alternating cur-rent The electrode is cooled with flowing water The specified temperature is maintained with an electric circuit with an accuracy of 5K

A mechanical pump and sorption pump ensure, through the hollow rod 6,

a vacuum level in the chamber of less than1.33 × 10 −4Pa (1 × 10 −6torr).

Fig 2.1 The experimental installation for the X-ray structural investigations of metallic specimens during high-temperature tests

2.2 Measurement Procedure 15

2.2

Measurement Procedure

Polycrystal specimens of metals and alloys are investigated A method for measuring the irradiation intensity which is diffracted with separate crystals has been worked out Dependence of the X-ray intensity upon the double Bragg angle,I(2θ), is recorded.

The measurement procedure is as follows: the specimen is placed between holders in the chamber The thermocouple is fastened to the operating point

of the specimen The specimen is then adjusted relative to the initial beam; the vacuum is established in the chamber and the heating is turned on

First it is necessary to choose a number of crystals to be monitored and

to determine the exact coordinates of their reflections There are three angle values that enable one to define a reflecting position of a crystal: the rotation of the specimen with the chamber around the goniometer axis (angleω) and the

rotation of the detector of the scattered X-rays in the meridianal plane (angle

ψ) These two rotations make possible the selection of reflecting crystals when

the detector is installed in advance in the horizontal plane at the double Bragg angle2θ relative to the initial X-ray beam It is possible to obtain the maximum

of intensity as a control point by means of thorough adjustment of all three angles

The monochromatic irradiationK βof an X-ray tube is used X-ray irradi-ation is performed before loading the specimen, then straight after loading and subsequently at the regular intervals Recording of a diffraction curve usually takes from 5 to 10 min and is repeated three times

In Fig 2.2 the formation of diffracted radiation is presented Sections of the Evald sphere are shown A projection of the reflecting plane is seen as a short line segment at the center of Fig 2.2(c) A node of a so-called reciprocal lattice

is in a reflected position, i.e on the surface of the Evald sphere Three angles conform to this position: angleω of the crystal rotation and the two angles, 2θ

andψ, of the detector motion Angles ω and 2θ are measured in the equatorial

(horizontal) plane of the goniometer and angleψ in the meridianal (vertical)

plane The diffracted beam is recorded permanently with a fixed scintillation detector with a rectangular split

The dimensions of the node in the reciprocal lattice are known to be de-pendent upon the misorientation angle δ of subgrains (cells) in the metal

under examination, the divergence χ of the initial X-ray beam, the interval

between wavelengths and the crystal dimensions The divergence results in the appearance of a strokeχ, which is formed by the ends of the diffracted beam vectors This stroke is directed to the reciprocal crystal lattice vector  H

at an angleθ.

Fig 2.2 Formation of the diffracted

beam for the method of investigation:

(a) the Evald sphere;s
0and
s are unit

vectors of the initial and of the diffracted

beams, respectively;
H is the reciprocal

lattice vector; EP, MP are equatorial and

meridianal planes, respectively (b) The

reflection strip (shaded) at the intersec-tion of a node of the reciprocal lattice and the Evald sphere (c) Directions of erosion

of the reciprocal lattice node due to the divergence of the initial beamχ and to

the finite size,l, of the studied crystal.

The experimental technique that has been worked out by us enables one to study structural changes in the same crystallites of the polycrystalline spec-imens during high-temperature deformation For this purpose the angular dependence of the diffracted intensity,I(2θ), is measured.

The most typical range of conditions was chosen: temperatures in the in-terval from0.40 Tmto0.80 Tm, stresses between10−4 µ and 2×10 −3 µ, where

Tmis the melting temperature andµ is the shear modulus.

2.3 Measurements of Structural Parameters 17

2.3

Measurements of Structural Parameters

It was revealed that the high-temperature deformation does not result in a broadening of the X-ray reflections Therefore dynamic effects were used to obtain data about the material structure The multiple wave reflections from parallel crystalline planes of the same crystal lead to a reduction in the wave energy This phenomenon is called primary extinction The X-ray intensity loss depends upon the number of reflecting planes, i.e upon the subgrain size Measurements of a relation between irradiated and initial intensities make it possible to determine the dimensions of the reflecting crystal

According to the classical theory of Darvin [14] the decrease in intensity factors of irradiation due to primary extinction is given by

wheren is the number of the parallel reflecting planes in the crystal, q is the

so-called reflection power of the crystal plane

where e is the charge of an electron, m is the mass of an electron, c is the

velocity of light,N is the number of elementary cells in the unit of irradiated

volume,F is the structural amplitude and θ is the Bragg angle.

The size of a subgrain is equal to

whered is the interplane spacing in the crystal lattice.

A screening effect is also observed Internal subgrains are screened with subgrains which are situated in external layers of the material This phe-nomenon is called secondary extinction Secondary extinction results in an increase in the absorption coefficient,µ The increment of X-ray absorption

is equal togQ, where

Q =

e2

mc2

2λ3

a6|F |21 + cos22θ

where η is the mean angle of misorientation of neighboring subgrains, Q

is the reflectivity of the crystal,λ is the wavelength, a is the crystal lattice

parameter Measurements of subgrain dimensions should be performed in conditions where secondary extinction does not play a considerable part Thus,

we can write the following conditions:

Assume thatgQ = 0.1µ It follows that

nq = 2Dd



Q

whereL is the angle coefficient, which appears in Eq (2.5).

Inequalities (2.6) are satisfied whennq > 0.59.

Therefore the following inequality must also be satisfied:

Dd



µη

Consequently, interferences with a large interplane spacing d should be

chosen for measurements of subgrain sizes For example, the minimum values ofD to be measured are equal to 0.29, 0.34, 0.13µm for Ni, Fe, W,

respectively

We have used the following method to calculate the values of substructure parameters The full power of a diffracted X-ray beam, which is scattered by

a crystal, is expressed as

whereI0is the power of the initial beam,V is the crystal volume, the other

variables have been described above

Denote the intensity (power) of a beam diffracted by a crystal in the initial strainless state byIin, after high-temperature deformation byI T, after strong

deformation at room-temperature byId It follows from the general formula (2.9) that

Strong “cold” deformation of a specimen results in an increase in the den-sity of dislocations and other crystal lattice defects Under these conditions both types of extinction are suppressed, andfd = 1; gdfdQd µ Thus Id

can be expressed as

Id = I0QV

2.3 Measurements of Structural Parameters 19

We have

We may neglect the difference between values Qin and Q T because the increase in temperature influencesQ and the fraction in Eq (2.9) in opposite

directions

Measurements ofIinand Idas well as Iin andI T are performed for the

same crystallite Therefore taking the ratios in pairs we obtain the following equations for calculation:

Iin

Id =

finµ

Iin

I T = fin (µ + g T f T Q)

The order of calculation is as follows First values ofgin, g T are calculated

In order to be able to computegin, g T from Eq (2.4) one needs the values of

the anglesη These have to be found from independent measurements Then

Eq (2.13) is used to calculatefin Next one calculatesf T from Eq (2.14) and finally calculates the subgrain sizesD from Eqs (2.1) and (2.3) This method

of measurement gives a relative accuracy of 5–7%

In Fig 2.3 the distribution curves for misorientation anglesδ in the

sub-grain are presented These data were obtained by rotating the specimen around the axis of the goniometer while the detector was motionless It goes without saying that monochromatic irradiation was used

Fig 2.3 Distribution of angle misorientations of subgrains

in nickel Symbols correspond to the Gaussian distribution

Solid curves are the experimental dependences Test

temperature 1073K 1, stress 20MPa; 2, stress 14MPa

This distribution was found to be a Gaussian distribution as was verified

by means of a the so-called Kolmogorov test In Fig 2.3 the theoretical depen-dence is marked with symbols

From the fact that the distribution of misorientations conforms with the Gaussian law one may calculate the mean angle between adjacent subgrains:

The density of dislocations within subgrain walls may be estimated as [15]

2.4

Diffraction Electron Microscopy

High-resolution transmission electron microscopy (TEM) enables the direct observation of metal structure and therefore has an advantage over other methods

There are some typical difficulties one faces when using TEM: the field

of view is relatively small; the specimen must be thin enough, of the order

of 100 nm, so that it is transparent to the electron beam; it is possible to deform thin foils during preparation It is appropriate to apply both the X-ray method and TEM so that they complement each other and this combination

is particularly valuable for studying high-temperature strain

Electron waves are scattered by the thin crystal specimen The electron intensity distribution in the specimen brings about a variable brightness on the screen of the microscope The direct beam generates a so-called light-field image Deflection of the diffracted beams from the optical axis of the microscope is about 20 mrad Diffracted beams are usually absorbed with an aperture

Crystal lattice defects cause displacements of atoms from their equilib-rium positions These distorted areas scatter electron waves differently, and

a diffraction contrast can be seen on the screen of the instrument Diffracted beams also form images To study them one has to decline the illuminating system of the microscope in order to shift the image to the center of the screen, where result dark-field images are formed Thus a diffraction contrast from defects is observed if the aperture passes either the direct or the diffracted electron beam

Atomic displacements, which are parallel to a reflecting crystal plane do not contribute to the diffraction contrast but perpendicular displacements of atoms lead to a contrast image