How can a material that is very hard not be very strong?

[Mesquite-oh]

I have a steel wrench- it is very hard and it is very strong. I have a breakfast muffin- it is very soft and it is not strong. I have a drinking glass- it is very hard, but it is not very strong at all. Help me out here, how can the glass be hard, but not strong? I know that it has something to do with brittleness and elasticity, but I just can’t get my mind around how if a substance is hard, how at the same time it can be shattered.

I started thinking about this when I was looking into getting a ring made out of tungsten carbide- very hard, but at the same time not very tough? Almost impossible to scratch, but at the same time can be broken into fragments if pressure is put on it? Used in industrial drills to repeatedly and effortlessly drill into steel, but needs to be put into steel inserts because steel is tougher? Huh?

[Harmonix]

Someone correct me if i’m wrong, but i’ve always understood it like this. If something is very hard, then it doesn’t flex at all. If it doesn’t flex at all, then when something shocks it it will not distribute any of the force. When taking all that impact in a single point it will simply sheer.

[Alive_At_Both_Ends]

@Harmonix

If something is very hard, then it doesn’t flex at all.

Doesn’t flex “very much”. No material is (or can be) totally rigid.

[Harmonious_Discord]

The above is right. A little fact. A diamond is strong, but after it has once been heated to a high tempurature and cooled, becomes very brittle. It will shatter if someone trys to then cut it. Brittleness is related to the crystalization of the material.

[David_Simmons]

According to this site and several others that I turned up (Google strength of materials+hardness), strength of a given material, say steel, is directly proportional to hardness, the harder, the stronger.

The reason glass is weak compared to steel is that it’s glass and not because it’s hard.

There is a class of materials called"amorphour metals" or “metallic glass” that are both exceedingly hard and exceedingly strong.

[brewha]

[QUOTE=David Simmons]
According to this site and several others that I turned up (Google strength of materials+hardness), strength of a given material, say steel, is directly proportional to hardness, the harder, the stronger.

QUOTE]

That’s not exactly what the site is saying. As a mechanical engineering, I’ve had several classes on this subject. Strength and hardness in that context might not mean what you think that they do. Just because a material resists deformation or resists scratchs does not mean that it is strong.

You also have to take into account compressive vs tensile strength. A material like cast iron is hard and very strong in compression, but crap in tension.

For a metal to be strong, it has to be both hard and elastic. Both of these properties do not easily coexist, so you have to compromise to get the best properties for a particular application.

[David_Simmons]

[QUOTE=brewha]

@David Simmons

According to this site and several others that I turned up (Google strength of materials+hardness), strength of a given material, say steel, is directly proportional to hardness, the harder, the stronger.

QUOTE]

That’s not exactly what the site is saying. As a mechanical engineering, I’ve had several classes on this subject. Strength and hardness in that context might not mean what you think that they do. Just because a material resists deformation or resists scratchs does not mean that it is strong.

You also have to take into account compressive vs tensile strength. A material like cast iron is hard and very strong in compression, but crap in tension.

For a metal to be strong, it has to be both hard and elastic. Both of these properties do not easily coexist, so you have to compromise to get the best properties for a particular application.

Thanks for the clarifiaction.

[Quercus]

Right, as Harmonix pointed out, what we think of as ‘strong’ is really a mix of different material properties, that can conflict with each other. Something with lot of rigidity, like a ceramic, is ‘strong’ in that it won’t bend, but will in general be more brittle.

The reason steel is such a good tool is actually because it isn’t as rigid as glass. If you whack a steel wrench with something equally hard, it will bend and dent a little bit, but stay in one piece. An obsidian blade is harder and sharper than a steel one, and won’t dull as quickly, but if you whack the obsidian blade, it won’t flex or bend, so all the energy is concentrated in one small spot, probably breaking it.

A lot of the metallurgy of iron/steel is in getting the right balance of hardness and springiness for the particular application. For things like knives, they’ll even try and change the properties at different points, so that the edge is very hard to keep a sharp edge, while the back is more soft and springy, so the knife won’t break.

[David_Simmons]

For metals I’ll go back to my original statement that the harder the stronger for a given material. There is a straight line plotting hardness as the horizontal axis and tensile strength on the vertical. The line starts low at low hardness and runs upward to the right as hardness is increased. The strength-hardness values for metals fall pretty much on this line. The hardness vs. tensile strength curve is here. Scroll down to section 7, the Relation of Hardness to Other Material Properties.

Tensile strength, say, is an intrinsic characteristing of the material and depends upon the ability of the component parts of the material, crystals in the case of metals, to hold together when stressed.

Cast iron and silicon glass are both brittle and hard. Cast iron is stronger because iron crystals hold to adjacent iron crystals more strongly than do the components of glass (which is not crystaline). We need a solid state phisicist to come along and explain just why this is so.

[Spectre_of_Pithecanthropus]

@David Simmons

According to this site and several others that I turned up (Google strength of materials+hardness), strength of a given material, say steel, is directly proportional to hardness, the harder, the stronger.

The reason glass is weak compared to steel is that it’s glass and not because it’s hard.
.

I’m not sure that correlation always follows. If I remember my readings in gemology correctly, toughness can be distinguished from hardness, or scratch-resistance. Diamond is a lot tougher than glass, but not because it’s harder. Similarly, jade is much less scratch resistant than diamond, but at the same time much tougher. This is the reason those traditional Chinese carvings with all the linked rings and intricate filigree are possible.

[David_Simmons]

@Spectre of Pithecanthropus

I’m not sure that correlation always follows. If I remember my readings in gemology correctly, toughness can be distinguished from hardness, or scratch-resistance. Diamond is a lot tougher than glass, but not because it’s harder. Similarly, jade is much less scratch resistant than diamond, but at the same time much tougher. This is the reason those traditional Chinese carvings with all the linked rings and intricate filigree are possible.

The correlation doesn’t follow for different materials. That’s the whole point. The OP asked why, since glass is so much harder than steel, why isn’t it also stronger. The answer is that for different materials hardness of one compared to the other is unrelated to which one is stronger.

For metals, the correlation always follows as the curve in my previous post shows.

Toughness of materials, as I remember it, is more concerned with the ability to withstand many cycles of stress reversal.

[Fast_n_Bulbous]

@David Simmons

Cast iron and silicon glass are both brittle and hard. Cast iron is stronger because iron crystals hold to adjacent iron crystals more strongly than do the components of glass (which is not crystaline). We need a solid state phisicist to come along and explain just why this is so.

This is not entirely true. In fact the theoretical strength of silica glass is higher than that of steel, and in compression glass is extremely strong. The problem with glass is that is always has large amounts of microcracks present. These cause stress concentration within the glass causing the cracks to propagate and the glass to undergo brittle failure. Brittleness means the material won’t elastically deform (much) before failure. In fact, because cast iron contains large amounts of carbon, it too is brittle, although in this case it is because the carbon prevents slip from occuring. Brittleness is usually associated with hardness. Diamond is hard but brittle (hit a diamond with a hammer and it will shatter along cleavage planes).

As for the relationship between strength and hardness, it depends what sort of strength you are talking about. Yield strength is the stress required to permanently deform a material and Ultimate Strength is the greatest stress a material can withstand. For brittle materials these are very close or even the same. For metals there is an approximate relationship between the ultimate strength and hardness, so hardenss is often used to estimate the strength of a metal, but the yield strength can be modified by various techniques. So in fact it is very rare that a material can be hard but weak or vice versa, and usually, when this is the case, there is some specific reason.

[David_Simmons]

@Fast 'n' Bulbous

This is not entirely true. In fact the theoretical strength of silica glass is higher than that of steel, and in compression glass is extremely strong. The problem with glass is that is always has large amounts of microcracks present. These cause stress concentration within the glass causing the cracks to propagate and the glass to undergo brittle failure. Brittleness means the material won’t elastically deform (much) before failure. In fact, because cast iron contains large amounts of carbon, it too is brittle, although in this case it is because the carbon prevents slip from occuring. Brittleness is usually associated with hardness. Diamond is hard but brittle (hit a diamond with a hammer and it will shatter along cleavage planes).

True. And I’ve read that a single crystal of iron is exceedingly strong for the same reason.

I read of a technique for casting turbine blades. In the mold there was a reservoir at the bottom and it tapered to a fine hole at the top. The mold was filled with metal and then a chill applied to the bottome. The metal crystalized at the chill and the crystalization progressed upward. Just in the nature of things one crystal won the race to the hole and from then on upward the blade was a single crystal. Corrosion resistance, yield strength, ultimate strength and resistance to stress reversals were all greatly improved over previous casting methods.

As for the relationship between strength and hardness, it depends what sort of strength you are talking about. Yield strength is the stress required to permanently deform a material and Ultimate Strength is the greatest stress a material can withstand. For brittle materials these are very close or even the same. For metals there is an approximate relationship between the ultimate strength and hardness, so hardenss is often used to estimate the strength of a metal, but the yield strength can be modified by various techniques. So in fact it is very rare that a material can be hard but weak or vice versa, and usually, when this is the case, there is some specific reason.

Sure, hardness alone is a poor way to find out what the strength of anything is. The OP asked why hard materials aren’t stronger than less hard materials using the example of glass and steel.

[Hunter_Hawk]

@David Simmons

For metals I’ll go back to my original statement that the harder the stronger for a given material.

Depends on what you mean by “stronger” and “material”. Consider a file blade, for example–it’s very hard but very brittle (as I’m sure you know, files break remarkably easily). But if you anneal that file blade, it’ll get much softer but then won’t break anywhere near as easily.

Heck, there’s a sideshow trick in which the performer passes a metal bar around the audience and then breaks it by giving it a good whack upside his forehead. All you need is a bar that’s been heated and queched right to make it real brittle. (Well, that and a willingness to give yourself a good whack upside the forehead.)

[Thrasymachus]

There are three basic properties to consider for toughness. Strength, modulus, and anistropy.

Strength is the easiest to understand. Pull on a bar of “stuff” that is one inch square, and note how much force it takes until it breaks. For common steel (nails), this would be about 50,000 lbs. For high grade hardened steel it’d be around 250,000 lbs. Plastic in kid’s toys, about 5,000 lbs.

Modulus (rigidity) is pretty easy too. Do the pull-test again, but this time measure how much stretch per inch per 1000 lbs applied, and periodically release the load to see how much of the stretch is permanent.

A low modulus material will stretch farther than a high modulus one. Most hard materials do not permanently deform (yield), they just break - this is important! Glass and ceramics are in that category. Most soft materials behave almost like taffy after yielding (lengthening by tens or hundreds percent for steels and plastics).

Bear with me here, I’m just getting to the punchline now…

Energy is force x distance, so with the above two tests you can figure the strain energy or “modulus of toughness” for a material. This is energy per unit volume to break something. As you have observed, a hard material is strong - but not usually tough. When the math is done, a softer material can often absorb more energy before failing because it can stretch - even though it is “weaker” since it breaks under smaller loads.

Anisotropy makes things interesting, a lot of materials have “grain” to them or behave differently under different loadings. Concrete is pretty strong in compression, not so much at all in tension (soil is a more extreme example of the same thing - it’ll hold up a building but you can pull weeds by hand).

Manufacturing process often sows the seeds of failure - rolled or drawn metal stuff splits along the direction of rolling more easily, bent stuff tends to open cracks on the tension side (the “outside” of the bend), cast stuff usually cools unevenly and sets up funny stresses internally, scratches tend to become cracks after lots of load cycles…

Hope this wasn’t too redundant or boring.

[Sage_Rat]

I’m mostly just guessing here, so I would appreciate any corrections, but I believe that the easiest way to visualise the relative hardness/flexibility would be to look at things on the atomic level.

If you take a bunch of ball bearings and magnetize them so that they will stick together, you can form different 3D patterns with them.

You could, for instance, make a cube of them with each ball having another one placed equally each 90[sup]o[/sup] so that there would be six other bearings touching the one. Alternately, you could put them together so that there was “bubbles” where the ball bearing pattern left non-optimal holes amongst themself.

If you had a ball of each of these two configurations and press on them, the cubic version is going to have a lot less give; the one with the bubbles will squish easier.

So that’s hardness.

But the thing holding the ball bearings together at all (in our example) is magnetism. Depending on the strength of the magnetism, you will be able to stretch the ball bearings further from one another without the object tearing. With strong enough magnets, the ball bearings will just pull back to their previous positions after you have flexed the pattern.

That’s flexibility.

You could have the strongest pattern of ball bearings there is, but if the bonds holding them together is weak, it will still tear (break) easily. Some patterns may also make it so that pressure applied will become focussed along a certain plane, instead of being spread out, so even if the bonds are pretty strong, a properly placed blow may cause it to shatter.

[Tuckerfan]

@David Simmons

The correlation doesn’t follow for different materials. That’s the whole point. The OP asked why, since glass is so much harder than steel, why isn’t it also stronger. The answer is that for different materials hardness of one compared to the other is unrelated to which one is stronger.

For metals, the correlation always follows as the curve in my previous post shows.

Toughness of materials, as I remember it, is more concerned with the ability to withstand many cycles of stress reversal.

That’s not entirely correct. Some of the hardest tool steels will shatter if you drop them on a hard surface. If you mix those tool steels with a metal like cobalt, you’ll gain an amazing amount of strength. The shape of the material can also play a big role in how strong it is. Increase the cutting angle on the tool and it’ll cut through tougher materials just fine, use a flatter angle and it’ll shatter almost as soon as it encounters another piece of metal.

Pure metals are generally softer, and depending upon the alloy and tempering of the metal, you can get some pretty amazing stuff. Copper and nickel by themselves are pretty soft, throw them together, mix in just a dash of iron, and you wind up with monel, which is amazingly tough.

I’ve played with some alloys that are used for turbine blades in harsh environments that machines like butter, and I’ve dealt with stainless steel alloys that are almost impossible to machine. The secret is to pick the material which has the best properties for the job you want to do.

[Zabali_Clawbane]

Leaves are soft, yet they are also very strong. They can withstand a lot of force when the wind blows, because the leaves give and form a conical shape and thus are not ripped from the tree so long as they are living. (In the autumn is a different matter.) This is because of how they fold, different varieties fold differently. Willow is strong, it is also very flexible wood and can bend and give a lot and not break. Strength is a combination of things, one factor can be hardness, but flexibility is also useful.

[Bosda_Di_Chi_of_Tricor]

@David Simmons

There is a class of materials called"amorphour metals" or “metallic glass” that are both exceedingly hard and exceedingly strong.

<HAL*>Thank you for the link, Dave.</HAL*>

[zut]

@Hunter Hawk

Depends on what you mean by “stronger” and “material”. Consider a file blade, for example–it’s very hard but very brittle (as I’m sure you know, files break remarkably easily). But if you anneal that file blade, it’ll get much softer but then won’t break anywhere near as easily.

David is using the proper engineering definition of “strength” here: the amount of stress (or force) it takes to deform or break a material. You’re mixing in “toughness”: the amount of energy it takes to break a material. It’s unfortunate that these words also have perfectly good everyday non-engineering meanings, because they can be confusing when used in an engineering context. A material (like your file) can have high strength but low toughness, and will break remarkably easily because small cracks will cause high localized stress, which the material cannot absorb.

@David Simmons

Toughness of materials, as I remember it, is more concerned with the ability to withstand many cycles of stress reversal.

@Tuckerfan

That’s not entirely correct. Some of the hardest tool steels will shatter if you drop them on a hard surface.

Toughness of a material is its ability to store energy. That’s also tangentially related to the ability to withstand many cycles of stress reversal, in that every cycle of stress reversal causes some small deformations and cracks that reduce a material’s ability to store energy even further.

@Tuckerfan

If you mix those tool steels with a metal like cobalt, you’ll gain an amazing amount of strength. The shape of the material can also play a big role in how strong it is. Increase the cutting angle on the tool and it’ll cut through tougher materials just fine, use a flatter angle and it’ll shatter almost as soon as it encounters another piece of metal.

So far as I know, strength and toughness of steel is a function of the iron/carbon microstructure. Mixing in elements like cobalt doesn’t inherently make the steel stronger or tougher, but it does allow it to be more easily heat-treated to obtain the microstructure desired. I’m not positive about that (and I do know that some elements, like lead, will effectively decrease strength because of their presence in the microstructure), so I welcome correction.