In general, the brittleness is much more connected with the melting point of matter. That is why most of substances become deformable plastically at temperatures higher than a half of their melting point value. However, you know that some substances have no melting points, e.g. glasses and covalent crystals. There are special cases! Concerning the problem of wear resistance, be sure that in practice the correlations between the wear resistance and hardness are much more complicated than many researchers think about. For example, to intensify the surface treatment made by diamond powders the prominent specialists in jewellery production apply the special powdered mixtures of super-hard diamond with super-soft carbon black...! It seems to me that you will find some interesting things, e.g. correlations between melting points and Young's moduli, if you look through publications and presentations available on my ResearchGate account and devoted to Hetero-Modulus/Hybrid Ceramics/Composites. Good luck!

In many cases with materials you have a balance between properties. So yes it is often the case that higher strength corresponds to worse toughness/ductility.

I think there's no simple and general answer to why this happens. For example in steels we can produce different precipitate populations, those that give the best strength also increase the ductile to brittle transition temperature (lower toughness). The reason for this is the way dislocations interact with the precipitates, which we loosely understand.

I recommend you either try to understand the micromechanisms responsible for the H/E values or perform mechanical tests to optimise your paramaters for H/E and toughness

Firstly, let me specify that, as far as I am concerned, there are three principle H to E ratios, which influence the wear resistance of a material, either in bulk or coating form. These are H/E [1], H/E^2 [2] and H^3/E^2 [3]. The first ratio characterizes the resistance of the material to elastic deformation. The second ratio, which is expected to correlate well with abrasive and erosive wear, indicates material's ability to resist permanent damage. Higher H^3/E^2 ratio allows to estimate the material's ability to dissipate energy at plastic deformation during loading.

Now let me return back to your question. If we speak about hardness or Young's modulus, we should bear in mind that it characterizes the stiffness of the material, i.e. its ability to resist elastic deformation. However, toughness is the property of material, which relates to its ability to withstand plastic deformation. Thus it is rather incorrect to estimate a material's toughness by its H/E ratio, probably, the H^3/E^2 ratio would suit this purpose best. However, I should also specify that wear resistance of a material depends on many variables, and toughness of a material should be taken into account basically then, when impact loads are present under wear conditions.

Thirdly, let me concern your question about high H/E values and brittleness. Generally, high H/E value would mean that the numerical value of hardness is much higher than the numerical value of Young's modulus. In its turn, this would mean that despite it is hard to make material change its shape, if it is done, the material will break down at once. Hard materials, which are unable to withstand deformation, are usually brittle (for example, glass).

Please receive my apologies for the long explanation. Hopefully, that was clear enough.

[1] L.O. Affonso. Machinery Failure Analysis Handbook - Sustain Your Operations and Maximize Uptime. Gulf Publishing Company, USA, 2006.

[2] D.L. Joslin, W.C . Oliver. A new method for analysing data from continuous depth-sensing microindentation tests. Journal of Materials Research, 1990, 5, (1), 123-126.

[3] T.Y. Tsui, G.M. Pharr, W.C. Oliver, C.S. Bhatia, R.L. White, S. Anders, A. Anders, I.G. Brown. Nanoindentation and nanoscratching of hard carbon coatings for magnetic discs. MRS Proceedings, 383-447.

The definition "...toughness is the property of material, which relates to its ability to withstand plastic deformation..." is absolutely wrong!

Fracture toughness Kc:

Kc = (EGcr)1/2 for plane stress and

Kc = [EGcr / (1 – ν2)]1/2 for plane strain replaced surface energy

Fracture occurs when KI ≥ Kc; for the special case of plane

strain deformation, Kc becomes KIc and is considered a

material property, as the subscript I arises because of the

different ways of loading a material (it refers to Mode I, please see my lectures on "Ceramics, Glasses & Composite Materials" available on my ResearchGate account https://www.researchgate.net/publication/275271377_Ceramic_Materials_Science_Engineering_Part_3_-_Physical_Properties)

Gcr = πσf2L / 2E, where Gcr is the critical strain

energy release rate and σf is the brittle fracture

stress; Gcr (also fracture energy) is the rate of

strain energy release by growth of the crack

Toughness, or fracture toughness, or critical stress intensity factor KIc is a

measure of material resistance to crack propagation: for

ceramics KIc is in region 1-12, as e.g. for Al 25-50 MPa·m1/2.

Indeed, except the formation of new surfaces, the energy absorption

mechanisms could be, e.g. plastic deformation in ductile stuffs, fibre pull-out in composites etc.

Research Ceramic Materials Science & Engineering (Part 3 - Physical Properties)

I wish I would have expressed myself in a more clear way. I bore in mind that toughness was the material's ability to withstand deformation without cracking / fracture. The term 'plastic deformation' refers to, actually, to a certain case of the absorption of the energy of deformation, as prof. Shabalin carried out. Let me thank him for driving my attention to this.

By the way, I should correct myself and specify that hardness can't be a merit of stiffness. Please receive my sincere apologies for these mistakes.

Could I also suggest a couple of articles, where the relation between hardness and fracture toughness to wear of materials is analyzed?

1. P. Kulu, R. Veinthal, M. Saarna, R. Tarbe. Surface fatigue processes at impact wear of powder materials. Wear, 2007, 263, 463-471.

2. P. Kulu, I. Hussainova, R. Veinthal. Solid particle erosion of thermal sprayed coatings. Wear, 258, 2005, 488-496.

P. S. As far as I can see, the remaining part of my fist answer is correct.

Additionally, I would like to remind that brittleness and ductility are not the only alternatives to each other, as we can design the multiphase/composite materials, which are neither brittle, nor ductile. The nature gives us woody materials with similar characteristics. However, for high-temperature technical applications it was necessary to create a special class of composites - hetero-modulus ceramics mentioned by me above. The relative physico-chemical inertness of basal covalent carbon (or boron nitride) graphene sheets, dispersed in a high-modulus and super-hard ceramic matrix, provides the specific interface (interphase boundary) in these materials, which results in their inherent ability to absorb and dissipate the elastic energy released during crack propagation and their capability to blunt and divert a propagating crack. In my opinion, the discovery and development of hetero-modulus ceramics (or also known as high-E - low-E composites, where E is Young's modulus) is one of the greatest achievements of materials engineering design in the last half-century. Unfortunately, most of researchers are aware of only one practical method to fight against the brittleness of ceramics; this is to add to ceramics a ductile metal for the preparation of so-called cermets (or hard alloys). The cermets were first designed more than a century ago and cannot be applied in the extreme conditions. I hope that next decade hetero-modulus ceramics will be spread from defence, aerospace and nuclear industries to the civil engineering productions.

https://www.researchgate.net/publication/282706236_Nanotechnological_Advances_in_the_Hetero-Structural_Materials_Design_of_Ceramics_Presentation

https://www.researchgate.net/publication/267331197_Thermal_Shock_Resistance_of_Hetero-Modulus_Ceramics

https://www.researchgate.net/publication/233646590_Physicomechanical_properties_of_ultrahigh_temperature_heteromodulus_ceramics_based_on_group_4_transition_metal_carbides

https://www.researchgate.net/publication/274037746_Hetero-Modulus_Ceramic_Composites_for_High-Temperature_Application_Review

Conference Paper Nanotechnological Advances in the Hetero-Structural Material...

Chapter Thermal Shock Resistance of Hetero-Modulus Ceramics

Article Physicomechanical properties of ultrahigh temperature hetero...

Conference Paper Hetero-Modulus Ceramic Composites for High-Temperature Appli...

These parameters are ony indicative . You can compare two similar materails in terms of H/E... But fracture toughness depends on a lot of mico and macrostructural properties.

Thank you Dr. Shabalin, Dr. Ranganathan and Dr. Surzhenkov for the valuable insights.

Please, you can check my article to find some interpretation of these ratios:

Chapter Introduction of the Ratio of the Hardness to the Reduced Ela...

All the best, Giuseppe

Please, How do I calculate the H/E and H3/E2 ratios in contact mechanics?

Knowing that I have the values of Young's modulus and hardness.

Best regards