What is Lueder Linien
Flow figuresPhenomena that can be seen with the naked eye on the surface of solid bodies when they are subjected to mechanical stress as soon as the stress exceeds the yield point of the material.
If the surface of the stressed body is unprocessed, e.g. coated with so-called hammer blows in the case of rolling iron, the flow figures show that the hammer blow layer, because it is brittle and less deformable than the underlying metal, jumps off it and leaves bright stripes. Such are the flow figures first from Luders observed and referred to as "drop figures" . Under the action of moist air, the areas freed from the blow of the hammer rust easily, and the flow figures then usually emerge very sharply due to the rust color (see Fig. 1). If the surface of the piece was cleanly polished before the stress, the flow figures are recognizable by reflections, which result from mass particles receding against the originally flat surface, sometimes so far that the unevenness can be felt. To Ewing and Rosenhain microscopically observed the samples subjected to tension, compression and twisting, the individual parts of the grains slide in planes that are parallel to one another as the permanent shape changes begin (see Fig. 2) , . Pohlmeyer obtained very sharp flow figures by coating the machined surface of the test rods with what is known as Barff's layer before exposure by annealing in water vapor, which then cracked off during the experiment in sharply delimited disputes (see Fig. 3) . Hartmann ,  reports on vergehe of the French artillery, in which polished steel rods were allowed to tarnish slightly before the exposure at 100–2000 C. to produce the flow figures and rubbed off with a lot of sandpaper after the exposure.
Essentially, the flow figures consist of side-by-side and intersecting line systems, the shape of which depends on the type of stress both heads at the same time. The strips form an angle of slightly more than 45 "with the direction of pull (rod axis) and can usually be traced on all four surfaces around the rod. If the tensioning mechanism of the machine remains in action, the strips either widen or more or less occur at a great distance from the stripes that were created first or new stripes across them, steadily or by leaps and bounds over the entire length of the rod (see Fig. 5). The further development of the flow figures during the tensile test is, as FIGS. 6-11 show, extremely different. The reasons for this different design with the same load have not yet been researched; They are likely to be found in the uneven distribution of stresses as well as in the previous mechanical processing and heat treatment of the material and in its more or less uniform chemical composition . For example, the moiré-like flow figures in Fig. 11 show a striking resemblance to the appearance of the rod surface in Fig. 12, which was created only when working on the planing machine and is a result of an uneven chemical composition (phosphorus secretions). If the tensioning mechanism of the machine is operated at a constant, moderate speed while the flow figures are being created, i.e. the test rod is slowly stretched, the force required for this tends to be slightly less than the force when the first flow figures were produced. Sometimes it sways up and down. Their steady increase up to the maximum and breaking load only occurs again when the flow figures extend over the entire rod. With the steady increase in force, the flow figures on the polished surfaces disappear again; the surface takes on a completely rough appearance.
Hartmann  treated the smoothly polished surface of his test rods during exposure to dilute acids and observed:
1. that the same lines as in the flow figures appear before the yield point is exceeded;
2. that the number of lines increases with increasing load, but that the individual lines permanently maintain their original inclination to the direction of force and that this direction of inclination also appears in the course of the cracks and fracture surfaces;
3. That the size of the angle of inclination is peculiar to the material and, with uniform loading, is independent of the shape of the body and the speed of the stress.
Hartmann deduces from this that the external force acts on those material particles which are at a certain angle to the direction of force, and that the lines indicate the direction in which the force is imparted in the stressed material. He therefore calls them "lines of force". In their appearance, he first noticed the following law: With pure tensile stress, two straight, regular line systems are created on the surface of the flat bars, which intersect and form an angle with the direction of the forceα form, which is greater than 45 ° for metals. In the case of cylindrical tensile bars, the lines of force are helical lines, the tangents of which also form the angle α with the generatrix of the cylinder. When subjected to pressure, the lines of force only run regularly if the height or length of the test piece is almost the same as its width. Two intersecting systems of straight parallel lines then emerge on the four sides of the cube; However, their inclination to the direction of force is not greater than in the tensile test, but less than 45 °. Similarly, the outer surfaces of cylindrical pressure samples again show helical lines, regardless of whether the cylinders consist of one piece or are composed of individual disks; Logarithmic line systems are created on the circular end surfaces of the discs.The lines of force on the surface of spheres with two attached parallel pressure surfaces are intersecting spherical spirals, the tangents of which form an angle smaller than 90 ° at the intersection points. In the case of partial loading or if forces hindering the change in shape act in addition to the external force, the lines of force are not parallel, their shape then depends on the nature of the hindering forces. - Forces acting in bursts cause lines of force of the same kind as slowly acting forces; but the length of the lines decreases with the same impact work with increasing speed or decreasing duration of the impact or impact; the speed with which the force can be imparted in the material is therefore limited.
The above-mentioned influence of the forces hindering the change of shape on the type of flow patterns is clearly evident in the illustration (Fig. 13) of a rod, the width of which was graduated from one end to the other with the same thickness and which was loaded until the strongest part just began to flow . With this rod shape, the load from the narrower rod part is not transferred over its entire width to the wider one, so that the change in shape of the latter is hindered by the resistance of its parts that are not directly stressed. It can be seen from FIG. 13 that main groups of striations were created, namely 1. those inclined at approximately 45 ° to the rod axis and 2. those branching off from this and directed almost perpendicular to the rod axis. The former testify to the fact that as the flow progresses from the narrower rod part to the wider part of the rod, flow occurs first in the latter due to the shear stresses and that the strongest shear stresses emanate from the two gradation corners. The triangular part delimited by the surfaces with the greatest shear stress is, as it were, pulled out of the whole. Outside this triangle, only one line each, which also points to shear stresses, can be perceived on the right and left; all other flow figures lie within the triangle. In the latter, the material flowed first and was therefore subjected to the greatest stress. The striations, which are inclined to the rod axis, again testify to shear stresses, while the transverse striations are likely to have arisen as a result of tensile stresses when the yield point was exceeded. Since the rod lengths within the triangle grow towards the center of the rod, the tensile stresses are correspondingly lower, which explains the gradual disappearance of the transverse stripes towards the center of the rod. If one also observes that the narrower rod part at the edges only shows industrious figures over relatively short stretches, it can be explained why breaks in structural parts occur especially where there are abrupt changes in cross-section. This example shows how the position and the course of flow patterns on the surface in the operation of broken construction parts can offer indications to investigate the causes of the destruction by overexertion.
Detailed discussions about the origin of the flow figures and the supposed causes of their various courses based on the observations in the former mechanical-technical research institute in Charlottenburg can be found in the. Working from Cherry , Martens ,  and Rudeloff . Rejtö  gives a very detailed, noteworthy explanation of the causes and laws for the creation of the lines of force, in which he discusses the molecular transmission of forces and internal friction of solid bodies ,  with the considerations of Hartmann  brings into relationship.
Literature:  Lüders, About the change in the elasticity of steel-like iron and steel rods and about a molecular movement observed when bending such rods, Dingler's polyt. Journal 1860, Vol. 155, p. 18. -  Nature, May 18, 1899. -  Test results regarding the transmission of forces, structural change and displacement, Building Materials Science 1899, p. 365. -  Martens, Materials Science for den Maschinenbau, p. 67. -  Hartmann, Distribution des deformations dans les métaux soumis à des efforts, Paris 1896. -  On the origin of the lines of force on the surfaces of the stressed bodies, Building Materials Science 1898/99, Vol. 3, p. 77. -  Rudeloff, investigations into the influence of previous changes in shape on the strength properties of metals, communications from the Kgl. techn. Research institutes, 1901, I. Supplement. -  Kirsch, contributions to the study of flow, especially in iron and steel, ibid., 1888, p. 37. -  Martens, investigations with railway material, ibid., 1890, II. Supplementary booklet. -  Rejtö, A., Internal friction of solid bodies as an absolute property and the formulas of the tension and pressure diagrams derived with the help of the same, Baumaterialienkunde 1897/98, Vol. 11, p. 231. -  Kick, Fr. , On the Congress of the International Association for Materials Testing in Stockholm, ibid., Vol. 2, p. 301.
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