Glide track
In materials science , traces of sliding are traces on metal surfaces that are visible with a microscope and which can be evaluated to assess the permanent plastic deformations of a component caused by overstressing.
description
In many areas of technology there are machines and systems whose components are exposed to high and extremely high mechanical loads during operation. In power plants, it is particularly those components in which the operating medium (water or steam) has high temperatures and the associated high pressures, such as pipelines and pressure vessels. Mechanical stresses due to locally different thermal expansion of the material are to be expected, especially when starting and stopping. All of these stresses are computationally recorded during the construction of such machines and systems and dimensioned in such a way that dangerous breaks do not occur during operation. Particular attention is paid to stresses that are repeated more or less regularly and can ultimately lead to material fatigue. The calculations are based on characteristic values of the materials, which are determined beforehand on test specimens with specific testing machines. A prerequisite is that the material used in the machines and systems has the same properties as in the test specimens used to determine the characteristic values and that these properties do not change over many years during operation. However, there is no such thing as absolute security, and regular checks are carried out at the most endangered parts of the components, through which damage to the components can be detected as early as possible. Local or extensive excesses of the elastic limit can lead to such damage, which can be the cause of plastic deformation of the components. The methods used are primarily visual inspection (visual inspection) and the search for possible cracks using ultrasound and eddy current methods . A supplement through microscopic examination with transportable incident light microscopes or impression techniques for surface examination of sliding marks in the laboratory is conceivable, because highly stressed components made of polycrystalline metallic materials record their own load history which ultimately leads to material fatigue. The traces of sliding (sliding steps and rows of etching pits) that can be detected on the surface of components using metallography are the signs to be examined here.
Slip steps arise where the slip planes activated during plastic deformation intersect the surface of the component. Rows of etch pits mark the points of intersection of the sliding dislocations with the surface. In the case of mechanically processed component surfaces, the escape of the sliding processes on the surface is hindered. However, the rows of etch pits can be developed after the machining layer has been removed by electrolytic polishing .
The azimuthal directional distribution of the glide tracks is of particular importance, the regularities of which can be revealed by a probability analysis. A distribution gap is symmetrical to the direction of the main stress. While it is relatively easy to create sliding tracks as sliding steps, sliding lines or sliding bands on the surface of single crystals where the sliding planes cut during plastic deformation and to observe them with the incident light microscope (especially with oblique illumination), this is the case with metallic ones Construction materials are by no means taken for granted. With the usual surface processing by turning , milling , filing or grinding , a deformation layer is created close to the surface, which hinders the sliding process controlled by crystal geometry. On the surface of conventional tensile specimens, in the vicinity of hardness indentations or in the vicinity of the fracture surface of impact bending specimens, one observes only an additional peculiar roughening of the surface, which is sometimes referred to as the "orange peel effect". This effect can be understood as a consequence of the mutual twisting of the crystallites lying under the processing layer. Lateral deflections of grinding marks can indicate plastic deformations that have taken place under the processing layer, as in Figure 1.Subsequent removal of the processing layer by electrolytic polishing and subsequent etching results in direct evidence of sliding marks as rows of etching pits as in Figure 2.
In order to be able to observe the sliding phenomena on the surface, samples with an electrolytically or chemically polished surface are used. For this reason, when testing austenitic chromium-nickel-titanium steel samples, some of the samples were electrolytically polished with an electrolyte made of perchloric acid and acetic acid in an aqueous solution before the mechanical stress.
Figure 3 shows the area around an impression for the Vickers hardness test (30 kp) on the previously electrolytically polished surface of a sample made of the steel X8CrNiTi18.10. Relatively evenly distributed sliding steps can be seen, which form parallel groups within the individual grains, the direction of which changes when the grain and twin boundaries pass. Because of the apparently low height of most of the sliding steps, their contrast is very weak. In picture 4 the same place as in picture 3 is shown after the surface has been carefully etched (for a few seconds) with "V2A stain". The slip track contrast is much stronger. The sliding tracks are marked by rows of etching pits. The individual etching pits can be shown separately at particularly favorable locations. As can be seen in Figure 5 with the highest possible light microscopic magnification (original 2000: 1), the etching pits are apparently pointed and mark the intersection points of individual dislocations. This corresponds to the experience of the author from an earlier work on the plasticity of organic molecular crystals of low symmetry.
Probability analysis for the directional distribution of sliding tracks
The probability analysis can first be carried out for a fixed orientation angle Φ of the normal of activated slip planes and then extended to the orientation angle itself as a function of the loading geometry.
Probability distribution of the directions of slip tracks with a fixed orientation angle Φ of the slip plane normal
The problem is investigated in a fixed sample coordinate system X, Y, Z (Fig. 6). Let X be oriented perpendicular to the sample surface and Z parallel to the load direction (unit vector k ). In a randomly selected grain of the polycrystalline sample with an isotropic grain orientation distribution, a plastic deformation in a sliding system with the sliding plane (hkl) g (the normal unit vector of the sliding plane be n ) and the sliding direction (uvw] g (unit vector g ) may have taken place in the surface (YZ plane) of the sample sliding tracks parallel to the track Sp of the sliding plane and thus perpendicular to the projection of the normal vector n in the YZ plane. If one uses φ z and φ x to determine the azimuths of n with respect to the rotation around the Z or . X-axis, then at the same time φ x = angle (Sp, Y). Let Φ = angle ( n , k ) be the orientation angle of the slip plane normal. The relationship between φ z and φ x can be found with the help of the information in Figure 6 is easy if one takes into account that φ x is also the angle between the projection of n into the YZ plane and the Z axis.
(1) sin φ z = tanφ x / tanΦ or tanφ x = sinφ z tanΦ
The amount of φ x cannot be greater than the orientation angle Φ. This limit value is reached when the normal vector of the slip plane n lies in the sample surface with φ z = + π / 2. If there is an upper limit value for Φ in connection with the loading geometry, there is a distribution gap for φ x symmetrically around the loading direction k . This distribution gap enables the main load direction to be determined independently from the directional distribution of the sliding tracks.
The random distribution of the orientation of the individual crystallites in the polycrystalline material can be simulated by allowing all possible orientations of n in three-dimensional space that do not lead to duplication of the orientation distribution of the slip steps. The reflection of n on the YZ plane parallel to the sample surface leads to identical positions of the sliding tracks. This means that only the half-space pointing to the positive X-axis has to be taken into account. The sample surface is the plane of symmetry for the problem. Reflection of n on the XZ plane leads to a change in sign of φ x and thus not to a doubling. Reflection of n on the XY plane leads to the mirroring of the directional distribution and thus to doubling. The possibility of variation for the orientation of n is thus limited to the front upper quarter of the space.
If the orientation angle Φ is fixed, the angle φ z is definitely between -π / 2 and + π / 2. The probability P (φ z ) for this is equal to 1. The size of the variation interval is π. With isotropic grain orientation distribution (but also with fiber texture with Z as the fiber axis), all values of φ z are equally probable, and the total probability 1 is evenly divided over the variation interval of φ z with width π, so that one has for the probability density related to φ z p (φ x ) gets:
(2) p (φ z ) = dP (φ z ) / dφ z = const. = 1 / π = 1/180 o
For the probability density (see: probability density function ) p (φ x ), using (1) results:
(3) p (φ x ) = dP (φ x ) / dφ x = dP (φ z ) / dφ x = [dP (φ z ) / dφ z ]. (Dφ z / dφ x ) = (1 / π ) .arcsin (tan φ x / tanΦ)
The probability P (φ x ) i that the angle φ x is encountered in a certain interval φ xi .. φ xi + 1 is equal to the probability P (φ z ) i that φ z is found in the according to relation (1 ) assigned interval. The following applies:
(4) P (φ xi .. φ xi + 1 ) = [p (φ xi + 1 ) - p (φ xi )] (φ xi + 1 - φ xi )
Stress geometry and orientation angle Φ
To derive the boundary conditions for the orientation angle Φ of the normal of activated slip planes, the probability P (g) is introduced that, in the event of an external load due to the tensile or compressive stress σ z, a randomly picked grain in the polycrystalline sample with an isotropic grain orientation distribution will be in an orientation favorable for sliding so that at least one sliding system is activated in this grain. A sliding system is activated as soon as the shear stress τ acting on it reaches or exceeds a certain limit value τ g related to the yield point of the material . The geometric relationships according to Figure 7 is
σz = Fz/Ao und τ = Fg /A. Mit A = Ao/cosΦ und Fg = Φz.cosλ ergibt sich:
(5) τ = s z cosΦcosλ = σ z .s > τ g
as a sliding condition. Here s = cosΦcosλ is the orientation factor introduced by Schmid and Boas. The slip condition (5) can be transformed into a purely geometric condition for the orientation factor:
(6) s > τ g / σ z = s min
The geometric meaning of the sliding condition in the form of relation (6) can be seen in a coordinate system X ', Y', Z 'firmly connected to the sliding system on the unit sphere represented therein with the polar coordinates ϑ' and φ 'in the stereographic projection of Bild 8 illustrate. For X '// g , Z' // n , ϑ '= Φ and φ' = φ n (azimuth of k with respect to rotation about n) one obtains: cos l = sinΦcos φ n , so that taking into account the relationship
sinΦcosΦ = (1/2) sin2Φ the slip condition (6) is given a new form (7):
(7) s = (1/2) cos φ n sin2Φ> s min
With the equals sign in front of s min one obtains the implicit representation of a closed curve on the unit sphere F (φ n , F) = s min . The sliding condition is fulfilled for all points in the area W g bounded by this closed curve . If the load direction k for a certain grain falls in the area Ω g , the sliding condition (5) is fulfilled for this grain and the relevant sliding system is activated. In explicit form, the function describing the boundary curve of Ω g after solving equation (7) for φ n reads as follows:
(8) cosφ n = 2s min / sin2Φ or φ n = arccos (2s min / sin2Φ)
Due to the symmetrical equality of n with - n and g with - g , it is safe to find the direction of k in the quarter sphere shown in Figure 8 with the solid angle π; the probability for this is equal to 1. The probability that with isotropic grain orientation, i. H. if there is no texture, the load direction k falls into the area Ω g and thus sliding occurs, then P (g) = Ω g / π.
Figure 8 shows the boundary curves of for various values of s min .
Extreme values of Φ result for the orientation of the load direction k in the X'-Z 'plane with φ n = 0 from equation (8):
(9) Φ min = arc sin2s min / 2 and Φ max = π / 2 - Φ min
The gap in the distribution of the sliding tracks around the load direction is 2 Breite min . From their presence, the load direction can be determined independently from the directional distribution of the sliding tracks.
The probability density for the occurrence of a certain orientation angle Φ with a grain orientation that is favorable for sliding within Ω g is along the meridian with φ n = 0 proportional to the arc length 2φ n sinΦ on the relevant circle of latitude. This results in:
(10) p (Φ g ) s = 2arccos (2s min / sinΦ) / π
The index s indicates the specified level of stress.
Probability distribution for the orientation of the sliding tracks for a given load
The probability distribution of the directions of sliding tracks at a given load is the probability that two mutually dependent events will occur simultaneously, that the sliding system in question will be activated and the sliding tracks fall within a specific azimuth interval. The individual probabilities (or their densities) according to equations (4) and (10) are multiplied with one another according to the “as well as” rule and then integrated according to the orientation angle Φ. The calculated result is shown in Figure 9 for a distribution over φ x intervals with a width of 5 o . Because of the symmetry with regard to the sign, the representation is limited to positive values of φ x . The individual curves were calculated for the displayed values of s min .
- The probabilities calculated for interval widths Dφ z = 5 o have a flat minimum at φ x = 0 with a height (2.78%) that is independent of the stress parameter s min .
- There is a gap for φ z > F max (s min ), the position of which can be used to independently determine the direction of an external load.
- With increasing stress (decreasing parameter s min ) the maximum becomes flatter and shifts towards smaller azimuth values.
Influence of the crystal structure symmetry
The influence of the crystal structure symmetry was examined in more detail for the face-centered cubic structure (kfz) - at the same time the cubic closest packing of spheres. In this there are 12 symmetrically equivalent sliding systems. The sliding plane lies in the most closely packed surfaces of the form (111), the sliding direction parallel to the closely packed grid lines of the form [01-1].
The result is the finding that with increasing load in the individual crystal grains, different sliding systems are activated one after the other, so that multiple sliding occurs (practically observed up to triple sliding e.g. in Figure 4 below). The multiple glide has no influence on the directional distribution of the sliding tracks if the different groups of sliding tracks in the individual crystal grains are counted separately.
Comparison with experimental results
Figure 8 shows the result of a first test of the theory by comparing it with the distributions obtained by measuring the azimuths of sets of slip tracks on the surface of flat specimens made of Cr-Ni-Ti steel after a tensile swell test. In the first case (Fig. 8a) the surface had been polished and etched with 5 cycles (s zmax = 433 Mpa) before the load ; the accumulated plastic elongation was 10%. In the second case (Fig. 8b) the surface was only mechanically polished. 5 cycles with s zmax = 501 MPa resulted in an accumulated elongation of 36 0 / 0 . The directional distribution was determined by two independent observers with a sample size of more than 700 sets of sliding tracks (x) and more than 400 sets (o).
With the lower load (Fig. 8a) there is a satisfactory agreement with the probability distribution for s min between 0.273 and 0.350. In the second observation (o), the distribution gap in the vicinity of φ z = 90 ° turned out to be not completely empty. This is presumably due to the mistaking of twin boundaries for slip marks on the etched surface. In the case of greater stress (Fig. 8b), there was a strong deviation from the theoretical probability distributions (compare with the curve calculated for s min = 0.350: ---). The gap for φ z > 80 o , which is completely free of sliding track azimuths, was significantly narrower than expected, the maximum shifted to larger azimuths and the minimum significantly lowered. An explanation for these deviations can be found in the texture development that already becomes clear at the high accumulated elongation (36 % ), which apparently increases the inclination of the slip planes after the start of deformation and thus changes the directional distribution of the slip tracks. If one assumes - in a very simplified way - that the orientation angle Φ has increased uniformly by the amount δΦ = 10 o and accordingly uses P (φ xj ) Φ + δΦ instead of P (φ xj ) j Φ in relation (13) , one obtains the curve drawn through in Figure 8b, which adapts itself to the experimentally determined distribution significantly better than the probability distribution calculated for isotropic grain orientation.
Bid 9 shows the result of the independent determination of the load direction (not recorded during preparation) using a two-stage carbon footprint from the surface of an alternate bending specimen by direct angle measurement with a transparent conveyor and ruler on the observation window of the electron microscope (TEM). The angles were measured with the screen inclined at 45 ° (i.e. parallel to the window). The preliminary 0-direction of the angle measurement was the direction of the horizontal tilt axis of the screen; Figure 9 shows the azimuths φ x ' corrected for the inclination of the screen . The sample size was 119. A directional value marked by (x) in the otherwise empty distribution gap relates to the mean orientation of a zigzag-shaped sliding track, as was shown by checking at a higher magnification. The classification was carried out by rounding to azimuth values divisible by 5. There are two options for determining the direction of the load (Z-axis): 1. The Z-direction is assigned to the mean of the azimuths delimiting the gap (165.5 o or −13.5 o and 38 o ), which means q '= 12.25 o leads, or 2. The Y direction is assigned to the mean of the connected azimuths (97 o ), which leads to φ x ' = 7 o for the Z axis. The difference of about 5 o in this case corresponds to the class width and can be viewed as an uncertainty in determining the load direction, which appears surprisingly small in view of the small sample size. The shadow direction resulting from the vapor deposition with C + Pt had an azimuth of 109.6 °. It is possible, but unfortunately not recorded, that the shadow direction was chosen transverse to the sample axis.
In Figure 10, the frequency distribution of the sliding track azimuths is initially entered separately for the first (x) and for the second (o) possibility of determining the Z direction and then for the respective mean value (- - o - -) of both. In this case, too, there is the best agreement with the calculated probability distribution for s min = 0.350. with a clear tendency to increase in the interval of φ x between 0 o and 10 o in addition to a widening of the distribution gap. This tendency corresponds to the influence of the compression on the orientation angle Φ.
Individual evidence
- ↑ see picture 1
- ↑ see Figure 2: Evidence of slip marks
- ↑ HHW Preuss: On the basics of a microscopic analysis of mechanical component overstressing via the directional distribution of sliding tracks . In: Wiss. Reports from the Technical University of Zittau . tape 914 , no. 16 . Zittau 1988, p. 11-18 .
- ^ Heinz HW Preuss: Probability Analysis of the Azimuthal Distribution of Glide Traces on the Surface of Plastically Deformed Polycrystalline Metals . In: Cryst. Res. Technol. tape 21 , no. 3 , 1987, pp. 241-250 .
- ↑ Heinz HW Preuß 1977, Freiberg research booklet B 204, 1978: Trikline TCNQ complex salts as a model body for investigating crystal plasticity with low symmetry, dissertation B (habilitation thesis) . In: Freiberg research booklet 1978 . B 204. Leipzig 1977.