# tensile strenght

“Nominal” (red) and “true” (blue) stress of steel in the stress-strain diagram . (The former refers to the initial cross-section of the test object. The latter takes into account the constriction during the tensile test.) The tensile strength is the maximum of the nominal stress, here marked with 1 . Point 2 indicates the yield point, point 3 the breaking stress .

The tensile strength (in particular with respect to textiles and paper and tear strength ) is one of a plurality of strength characteristics of a material : the maximum mechanical tension that can withstand the material. It is mostly calculated from the results of the tensile test as the maximum tensile force achieved based on the original cross-section of the standardized tensile specimen : ${\ displaystyle F_ {z}}$ ${\ displaystyle A_ {0}}$

${\ displaystyle R _ {\ mathrm {m}} = {\ frac {F_ {z}} {A_ {0}}}}$

Ductile materials such as steel expand even further in the tensile test after the tensile strength is exceeded, and their cross-section is reduced. Brittle materials such as cast iron, on the other hand, break when the tensile strength is exceeded.

As symbols of the tensile strength are used: , , , , , or . ${\ displaystyle R _ {\ mathrm {m}}}$${\ displaystyle R _ {\ mathrm {Z}}}$${\ displaystyle \ sigma _ {\ mathrm {M}}}$${\ displaystyle \ sigma _ {\ mathrm {m}}}$${\ displaystyle \ sigma _ {\ mathrm {B}}}$${\ displaystyle \ beta _ {\ mathrm {Z}}}$${\ displaystyle f _ {\ mathrm {ct}}}$

The dimension of tensile strength is force per area. Frequently used units of measurement are N / mm² or MPa ( Mega pascal ). In the stress-strain diagram , the tensile strength can be read off directly as a Y-axis value at the highest point of the curve.

## Nominal and true tensile strength

A distinction is often made between the “nominal” voltage (“engineering voltage”) and the “true” voltage . ${\ displaystyle \ sigma _ {\ text {nominal}}}$${\ displaystyle \ sigma _ {\ text {true}}}$

The (nominal) stress values (tensile strength, yield point ) read from the stress-strain diagram do not correspond to the true stress in the material. This is because when calculating the nominal stress, the tensile force is related to the initial cross-section.

In the tensile test, however, the actual cross-section is smaller than the initial cross-section due to transverse contraction or constriction ; this deformation (lengthening and constriction) is an elastic - plastic deformation, i. H. for samples made of ductile materials, visible and measurable after the test. The true tensile strength does not correspond to the nominal stress in the specimen at the moment of breakage, but is higher .

Since real loads are mostly applied forces that have an absolute magnitude and are not related to the cross-sectional area, the nominal tensile strength is normally decisive when dimensioning components .

Rather, the yield point is used for dimensioning in technology. The tensile strength plays a role, for example, in production during deformation or machining . Brittle materials, on the other hand, are dimensioned according to their tensile strength, but with these materials there is no relevant necking and therefore no difference between nominal and true stress. In short: a component has long since failed technically when it reaches its tensile strength, with or without constriction.

The maximum of the true stress occurs in the constriction area of ​​the sample. Here the deformation and, if necessary, the solidification increases until it breaks.

In the instrumented tensile test, the specimen cross-section is measured continuously and the force is related to the real cross-section. Samples examined in this way show a continuous increase in the true stress until breakage (blue curve in the figure). However, the value determined in this way is only of theoretical importance.

## Tensile strength as part of the name

In the past, tensile strength was often used to characterize materials. An example of this is the designation of structural steels . Steel 52 (St52, today S355) was named after its tensile strength of 52  kp / mm² (510  N / mm² ).

Due to the harmonization of European and international standards, many steels are now referred to according to their yield strength , which from a structural point of view is a better characteristic value for the load-bearing capacity of a material.

## Sample values

material Tensile strength in
N / mm² or MPa
Glass 7-70
tin 15th
porcelain 45
Polystyrene 45 to 64
Aluminum alloys usually 200 to 450; rarely up to 640
Cast iron with flake graphite 100 to 350
human hair 200
Titanium alloys 290 to 1200
Structural steel 310 to 690
Alloyed steel 1100 to 1300
Carbon nanotubes up to 63,000

## Individual evidence

1. ^ Wolfgang Seidel: Material technology. Materials - Properties - Testing - Application. Carl Hanser Verlag, Munich 2008, ISBN 978-3-446-40789-3 , p. 16.
2. Siegfried Roebert (ed.): Systematic building materials teaching. Volume 1, VEB Verlag für Bauwesen, Berlin 1972, p. 39.
3. Dubbel - Paperback for mechanical engineering , 12th edition, part 1, p. 513
4. Standards committee in construction in DIN : DIN 1045-1. Structures made of concrete, reinforced concrete and prestressed concrete - Part 1: Dimensioning and construction. Beuth Verlag, 2008, p. 18.
5. ^ Bargel: Material science , 11th edition, p. 352.
6. ^ Bargel: Material science , 11th edition, p. 348.
7. ^ Bargel: Material science , 11th edition, p. 364
8. ^ Bargel: Material science , 11th edition, p. 430
9. ^ Ostermann: Application technology aluminum , 3rd edition, p. 768.
10. Haberhauer: Maschinenelelemente 17th edition, p. 627.
11. ^ Bargel: Material science , 11th edition, p. 343.
12. Haberhauer: Maschinenelelemente 17th edition, p. 625.
13. ^ Holzmann: Strength of Materials , 10th Edition, p. 69.