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Can some please explain why is the elastic modulus of aluminium and work hardened aluminium the same?

Is it only the same for pure metals?

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Elasticity of materials depends only on the strength of the atomic bonds. Atoms are pushed apart from each other by their negatively charged electron clouds. They are pulled closer together by the negative electrons of one atom attracting the positively charged nuclei of neighboring atoms, and vice-versa. At some distance the attractive and repulsive forces balance, and the atoms are in equilibrium. To separate the atoms (or bring them closer together) takes application of an outside force. Application of an outside force shifts atoms from their natural equilibrium positions, which is resisted by the changing electrostatic conditions. The differential resistance to differential change in position is measurable at large scales as elastic modulus.

In contrast to elastic modulus, strength depends mostly on the microstructure of a material, and not relative atomic position. Most practical metals, like aluminum, are composed of many differently-oriented crystalline grains. Where the grains meet are grain boundaries. Plastic deformation of metals occurs by slip of planes in the crystalline grains, one line of atoms at a time. The lines of atoms that are actively moving are called dislocations. The more plastic deformation, or cold work, experienced by a metal sample, the greater the density of dislocations. Dislocations eventually get blocked by grain boundaries and by each other, increasing the resistance to further plastic deformation, and this effect is measurable as an increase in strength. As the dislocation density increases, these blockages occur with greater frequency and with greater resistance, and strength increases in proportion to cold work.

If the stresses that caused plastic deformation are removed, the material retains its increase in strength. However, the atoms haven't gotten closer together or further apart from each other on average. They've only been moved around relative to one another by crystal slip and dislocation motion. Thus the elastic modulus hasn't changed as a result of cold work.

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In general hardness has very little effect on the elastic modulus of metals. Hardness and tensile strength are closely related but elasticity is a pretty much independent property.

This is somewhat counter intuitive and often causes some confusion especially in the context of tempering steel. Contrary to popular belief springs are not heat treated to make them more elastic but to improve their strength, this increases the extent to which they can deflect without deforming but not their elastic modulus ans so called 'spring temper' is a balance between ultimate strength and toughness and has no bearing on the spring constant itself.

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  • $\begingroup$ I was hesitant to answer this because I was expecting like a 7 paragraph all-encompassing write up from you. I'm glad this didn't make my answer look like peanuts haha. $\endgroup$ – JMac Jun 5 '17 at 16:10
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    $\begingroup$ I certainly wouldn't want to discourage anybody form answering questions. Often something simple and intuitively understandable answers the original posters question better than a detailed technical analysis that only peopel who know the answer already will understand ;) $\endgroup$ – Chris Johns Jun 5 '17 at 17:26
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    $\begingroup$ "better than a detailed technical analysis that only people who know the answer already will understand " And thankfully we got one of those as well. I was worried for a minute there we weren't going to have an in-depth materials analysis of it. starrise was on it. $\endgroup$ – JMac Jun 5 '17 at 20:26
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Work hardening is done to increase the strength of the material, not the stiffness.

You change the yield stress to be closer to the failure stress of the material. If I understand it correctly it also increases the elastic range and takes away from the plastic range of deformation (which seems reasonable as it requires plastic deformation to work harden in the first place).

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