When I look at the yield of one material then you find more than one yield for different thickness.

why the yield changes with changing the thickness. is there an equation to prove this ?

  • $\begingroup$ Where have you seen this? $\endgroup$
    – JMac
    Aug 23, 2017 at 19:59
  • $\begingroup$ For example here steelconstruction.info/Steel_material_properties Go down to Strength > Yield strength > Hot rolled steels $\endgroup$
    – Adam Joe
    Aug 23, 2017 at 20:48
  • 1
    $\begingroup$ It says right in the article. "For hot rolled carbon steels, the number quoted in the designation is the value of yield strength for material up to 16 mm thick. Designers should note that yield strength reduces with increasing plate or section thickness (thinner material is worked more than thick material and working increases the strength)." The reason is due to the manufacturing process for that type of steel. $\endgroup$
    – JMac
    Aug 23, 2017 at 20:54
  • $\begingroup$ if you draw out strands of metal then the drawing process eliminates many of the dislocations in the laticce of the steel. Many working processes also reduce dislocations. So material properties are much dependent on manufacturing processes less dislocations higher strength. $\endgroup$
    – joojaa
    Aug 23, 2017 at 21:23
  • $\begingroup$ Otherwise known as "cold work". Or for hot rolled, thinner section tend to have finer grain which slightly increases yield. $\endgroup$ Aug 23, 2017 at 21:30

2 Answers 2


No there is no equation for it, as it is caused by the processing differences of the different sizes and has nothing to do with the size of the material.

  • Smaller bars are subject to more work to get them down to the required size as they start out from the same size billet as the larger bars.
  • Smaller bars also take less time heat up during heat treatments, so the effects and/or heat treatment are slightly different. (see comment by starrise)

The values in the standards are also not the strength of the material you buy, they are miniumum (and sometimes maximum) values. It can be that a larger diameter bar exceeds the minimum strength of a smaller diameter bar.

The size of the bar can have an effect for materials with a large grain structure when if the bar is only a few grains wide you can have a phenomenon called grain size effect. The other condition I know of where it can happen is with surface treated or coated parts. The same depth of a surface treatment (e.g. carburizing) will have a higher surface to bulk material ratio in smaller bars.

  • $\begingroup$ I might add that thicker sections take longer for the core to cool, potentially resulting in grain growth there, reducing strength. Other coarsening mechanisms also occur resulting in coarser pearlite, coarser precipitates, etc. If the material is quenched, the desired quenched microstructure may not be available through thickness due to the slower cooling rates. Search "grain growth", "microstructural coarsening" and "jominy hardenability" for more info. $\endgroup$ Nov 22, 2018 at 15:01
  • $\begingroup$ Good point, that's what I meant by the effects/heat treaments being different but explaining it is better. $\endgroup$
    – Kagekiba
    Nov 22, 2018 at 15:12
  • $\begingroup$ The question was about structural carbon steels , not heat-treated steel. $\endgroup$ Nov 22, 2018 at 15:47

The different mechanical properties for different sheet thicknesses has to do with grain refinement of the material during the rolling process. The following figures show what is happening to the old grain structure.

enter image description here

The new elongated grain are the results of cold working. It is possible through annealing to form new grains (with no bias in direction).

The effects of cold working on Strength, Hardness and Ductility can be seen in the following image enter image description here


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