Are you using Vickers?

Hi Luis! 

Do you have access to an instrumented indentator or a nanoindentator? You can obtain a lot of information of the elastic-plastic behavior of your samples with this techniques. Be aware for the formation of pile-up around the indenter (you´ll have to do some research about this because it´s a very complex phenomenon and it depends on the material under study).

In my opinion, you should not extrapolate conventional hardness measurements with elastic modulus, as you will be measuring two very different material properties. A conventional hardness measurement yields no information about the elastic properties of the material, be careful!

Good luck!!

A micro indentation machine with appropriate measurement attachments for the applied force and corresponding strain within the elastic limit, in  principle, can give some idea about the elastic property of the small material talked about.

I agree with Germán Prieto.

I would avoid mixing elastic properties with "ultimate" properties.

The elastic modulus of  7075 Aluminum alloy  is around 72 GPa.

All the modifications induced by heat treatments, cold working, precipitation hardening and so on do not affect the elastic properties.

It is true, however , that metals do exhibit a linear correlation between hardness  and tensile strength. So that you only need to measure the strength and the hardness at two points of the aging interval (for example at its extreme tails)  to find the correlation  between the two quantities. 

The slope of yield strength-Vickers hardness (in MPa) relationships is always 0.383 (please see the first publication below).  The y-intercept will change with alloy and microstructure.  The tensile strength-Vickers hardness relationship is purely empirical. For 7010, we reported an empirical equation (see the second paper below).  Good luck!

Article On the Relationship Between Vickers Hardness and Yield Stres...

Article Hardness-Strength Relationships in the Aluminum Alloy 7010

It culd be good idea to use non-destructive measurement of young modulus by impulse xcitation method e.g. You can compare values of young modulu (and shear modulus respectively) with values provided by instrumented indentation method. Impulse excitation technique is quick, simple and non-destructive.

I agree (with Prof. Murat Tiryakioglu ) that hardness can be related to yield strength as well as tensile strength. Please see that the topic on relationship between hardness and strength has been discussed earlier in RG with reference to Mg alloys: please see the link :-https://www.researchgate.net/post/What_is_the_relationship_between_hardness_and_strength_of_an_alloy_Especially_magnesium_alloys

The Review paper by W.C. Oliver and G.M. Pharr in J. Mater. Res., Vol. 19, No. 1, Jan 2004 may be useful to you, if you are interested in 'Measurement of hardness and elastic modulus by instrumented indentation'.

Dear Luis Armando Hernandez Molina,

Properties can be devided in intrinsic and extrinsic properties. Hardness and Young's modulus belong to different classes of properties. Hence, the value of hardness principally cannot be related to Young's modulus. Intrinsic properties are interrelated via the Grüneisen constant. For a more elaborated discussion of this interesting issue I refer to Materials Science in Design and Engineering:

http://www.delftacademicpress.nl/m017.php

http://www.delftacademicpress.nl/m017.php

I agree with Prof. P. Van Mourik that the properties (hardness and modulus) belong to two different classes of properties.The subject of correlating hardness and modulus has been debated since hardness is a measure of resistance to permanent plastic deformation, whereas elasticity corresponds to reversible elastic deformation. 

However, there are correlations in literature, proposed by Teter, Pugh, Gilman and Cohen. Pugh's modulus ratio (k = G/B; G is shear modulus and B is bulk modulus)  can be useful to identify the brittleness and ductility of materials. Also, such correlations between hardness and modulus (though debatable) may provide useful insight in the design and development of ultrahard/superhard materials and high-performance high-strength structural materials.

Please see:- "Intrinsic Correlation between Hardness and Elasticity in Polycrystalline Materials and Bulk Metallic Glasses", Xing-Qiu Chen, Haiyang Niu, Dianzhong Li, Yiyi Li, Condensed Matter and Materials Science 2011:- Please see the link if you have access:  http://arxiv.org/pdf/1102.4063.pdf 

I agree with Prof P. Van Mourik. The hardness and strength belong to different class of properties.  However, the empirical relationship between two properties has been found  on base of great measurments.  So it is a way to extrapolate hardness to another mechanical properties.  Why the relationship exists is needed further to study

Dear Phaniraj C

The paper http://arxiv.org/pdf/1102.4063.pdf  is very impressive as it relies on a wealth of data that fit into the model proposed. Nevertheless I dare to make some remarks and questions

1. The materials considered have covalent bonding or are Bulk Metallic Glasses. Elastic constants are in principle tensors; only in case the materials under study can be considered as isotropic, elastic constants can be taken as scalars. Can the materials studied safely be considered as isotropic?

2. In case the plastic deformation due to the Vickers indenter can be neglected,  in the paper the Vickers hardness is directly related to the shear modulus G. This means that the Vickers hardness measurement can readily be conceived as the enforcement of a brittle fracture preceded by a totally elastic deformation that can be described by the appropriate elastic constant. So, this result can hardly be considered as very surprising.

3. The Vickers indenter will enforce deformations that can be described as a combination of shear and compression. The above indicated paper strongly suggests that the factor k=G/B with B=bulk modulus reflects this combination. Large values of k represent a brittle material behaviour and a low value of k hints at a more ductile material behaviour. The k-value of the brittle diamond equals 1.2. Assuming isotropy of the materials studied and assuming that the compression part cannot be taken as the cause of the permanent Vickers indentation, this strongly suggests that the shear occurred was beyond the elastic limit, thus in contrast with the bulk modulus linked with ductility.

4. The authors explicitly point out that the approach proposed ‘may be not accurate to predict the hardness of metallic-bonding dominated materials’. Obviously this is linked with the fact that metals, which are polycrystalline, show ductility via dislocation movement. In metals, heat-treatment condition, grain size, composition (chemical and physical) influence hardness values.

 5. Given the above considerations, the answer to the original question ’Is there a way to extrapolate hardness or micro-hardness measurements to Young's modulus or another mechanical properties in Al and Al alloys?’ is:  no extrapolation to elastic constants, at least for the time being. Of course, it is well known that hardness of metals shows an empirical relation with strength.

Dear Prof. P. Van Mourik, I enjoyed reading your comments I agree with you that extrapolating hardness to Young's modulus is not correct as they are two different classes of properties. Elastic modulus is the intrinsic property related to bond strength whereas hardness is extrinsic materials response. It is known that for metals/their alloys, the heat treatment and change in microstructure does affect hardness but not the elastic modulus.  

But I have a doubt in my mind that generally the materials with higher elastic modulus display higher strength. Further, hardness and strength are related empirically. This calls for some clue that they may be related? and yet to be understood:-  this doubt is not yet clear to me and I am confused!!

Dear Phaniraj C,

'That generally the materials with higher elastic modulus display higher strength' seems intuitively so plausible. However, at least two classes of materials do not follow this intuition: metals and polymers. For ceramics in general it is observed that properties like fracture toughness and strength can be influenced by the microstructure  (cf. Physical Ceramics by Yet-Ming Chiang et al, Wiley & sons, 1997, New York, Table 5.7 and 5.8). Even for ceramics, the microstructure can play a part in improving properties like fracture toughness. At present my intuition as yours also says that, neglecting microstructurel considerations, in case of pure brittle fracture, i.e. fracture without prior plastic deformation, the chance of higher values for the fracture strength increases with higher values for Young's modulus. To study this intuition the proper assumptions must be taken into account.

Dear Prof. P. Van Mourik, I appreciate your answer and thanks. Let me admit that I do not work on this topic and to me, understanding hardness-elastic modulus correlation has been complex.

In metals, plastic deformation is usually by dislocation glide and hardness is a measure of resistance to plastic deformation. Whereas strongly bonded materials of covalent/ionic type may experience plastic deformation by microscopic fracture (by crack initiation and propagation) that is related to breaking of atomic bonds and hardness of brittle materials may be correlated to elastic modulus. 

Dear Dr. Luis Armando Hernandez Molina, the following literature may be useful to you.

(1) The Ph.D. Thesis (April 2000:- LBNL-45246) by  'Christopher Krenn' on "The ideal strength and mechanical hardness of solids". ( I have only glanced at it). Please see the link if you have access:- https://www.google.com/url?url=https://publications.lbl.gov/islandora/object/ir%253A115302/datastream/PDF/download/citation.pdf&rct=j&frm=1&q=&esrc=s&sa=U&ei=YfmUVduYCZSTuASm5ILgCA&ved=0CBwQFjAC&usg=AFQjCNE3hLiQ6wRnype180g8RVzacQmATw    (2) "MECHANICAL HARDNESS: A SEMIEMPIRICAL THEORY BASED ON SCREENED ELECTROSTATICS AND ELASTIC SHEAR", D.G. CLERC* and H.M. LEDBETTER,  J. Phys. Chem. Solids 59, 1071 (1998).

Dear Phaniraj C,

Thank you so much for your reference to the thesis 'The ideal strength and mechanical hardness of solids'. This thesis considers hardness as an intrinsic property and the ideal strength as an upper limit for the lattice in study. The distance between the materials scientist's definition of hardness (the resistance of a material to permanent indentation) and the foregoing approach seems remarkable. I am curious about the results of your study of this thesis.

Dear Prof. P. Van Mourik, Thanks for your reply. I enjoyed the discussions and was educative.

But, I do not work on this topic. Please see that I have modified my answer and added reference to a paper by D.G. CLERC and H.M. LEDBETTER, J. Phys. Chem. Solids 59, 1071 (1998). I work on creep behavior and I am not an expert in this area of hardness-elastic modulus correlations. 

Thank you all for taking one minute of your time, I have a couple of papers to read.

Mr Phaniraj, I am just an engineer, but I will begin doctorate studies in the biomaterials field soon.

Mr. Luis Armando Hernandez Molina, my best wishes to you.