John Agren is correct; J C Jai, our original questioner wanted to know the strength of the solid at the melting point, not a mix of partially solidified alloy.

With regard to the strength of the solid, many years ago I estimated the yield strength of iron at its melting point from extrapolations carried out by a number of researches of strength at high temperatures.  For solid iron at its melting point it seemed that the strength was in the range 1.5 to 6.0 MPa. I used this value to calculate the maximum stresses which could be built up in the residual liquid during the freezing of a sphere assuming an elastic/plastic model. This small strength, when integrated for its cumulative effect over the volume of the sphere led to tensile stresses in its center of up to 150 MPa. This tensile stress was experienced by the residual liquid. The study proved that liquids could not suffer sufficient stress to nucleate pores homogeneously in solidifying castings.

This estimate of strength was, however, particularly uncertain because of creep at high temperatures, causing the yield strength to be strain rate dependent. I therefore repeated this study using a creep rate relation for the strength of iron at its melting point, but achieved very similar results for the resulting stress which developed in the sphere, indicating that the effective yield stress at rates of strain experienced in small castings was around a few MPa.

The creep model give similar estimates of stress for pure Al, Cu, Ni and Fe, indicating that the effective yield stress at familiar rates of strain are fairly similar for all these metals.  Therefore if, somehow, a polycrystalline tensile test bar could be made and pulled, we should expect a yield point in this range.

However, J C Jai is not straining polycrystalline specimens. He is attempting to damage a dendrite, which is a single crystal.  It is well known that if single crystals are pulled in tension, especially if of small size, they can fail simply by slip on, perhaps, a single slip plane, or at least a single slip band, the crystal simply slides apart.

Other deformation modes include plastic bending (again a creep mode) followed by rapid reorganisation of the dislocations into subgrain boundaries or grain boundaries. A high angle grain boundary, depending on the relative energies, may be wetted by the surrounding liquid metal, with the result that the liquid penetrates the boundary and the dendrite separates into two parts. This appears to be one of the mechanisms of dendrite fragmentation during events encouraging dendrite multiplication. The mechanism has been proposed particularly for the constricted neck of some alloy dendrites, even though energy calculations indicate that the neck can not only fail by penetration of liquid along a recrystallized boundary, but at sufficient strain and strain rate may actually melt.

J C Jai observations that the dendrites do not fracture is to be expected: solids at their melting point are ductile; the nucleation and growth of a crack in a solidifying metal is energetically improbable to the point of impossibility. However, the existence of a crack entrained from the outside of the metal, in the form of an oxide bifilm, would be expected to be common. Even so, as a result of the ductility of the metal at and near its melting point, the crack, if stressed, will not be expected to propagate: it will merely open somewhat to become blunt. This behaviour is also common.

We did trials on 5N purity Al ribbons RT till 250°C. At 250°C YS was around 7 N/mm², TS approx. 19 N/mm². I would assume, at MP it's even lower.

Conference Paper High temperature behaviour and reliability of Al-Ribbon for ...

The strength of all materials falls to zero at the melting temperature (if one exists).  This also applies to all materials with a peritectic or eutectic melting - and so on.  It is almost by definition that this is the case. The activation energy for separating atoms or molecules tends to zero as Tm is approached.   Liquids have no conventional tensile strength; the cohesive strength of liquid, also called tensile, is defined differently, but at the boiling point this too is zero.

I believe that it is the viscosity which has much significance than the tensile strength. As we heat the ingot, the atoms and their plains (in the solid aluminium ingot) vibrate with higher magnitude which results in disordering of atoms, this is where we see the ingots loosing their shape and rigidity. 

Thanks for your suggestions. In general, the tensile strength of pure Al is 35 MPa. Thus, with increasing temperature, its strength will decrease, as Milke’s result.

In my experiments, we found the columnar grain (it should be noted that it is already solid) of pure Al can be fractured under an electromagnetic field, resulting an obvious grain refinement. It puzzled me a long time.

I want to know the strength of pure Al at melting temperature (solid Al at melting temperature, i.e. solid phase in the solid-liquid mixture) or a little lower than melting temperature (like 659 or 658oC). I think it should be lower than the theoretically estimated 6MPa. Just as Milke’s result, the yield strength of pure Al at 250 oC is only 7 MPa.

I want to ask whether there are some data at even higher temperature.

I agree with Darvell, that the strengh of solid pure Al tends to zero at melting temperature, but it still has a value, even though it is very low.

Another thing to keep in mind is the effect of mechanical energy. If the material is in its solid state at the melting point, mechanical loading may give the system enough additional energy to induce spontaneous melting.

Well below the melting point, if force is applied slowly, it could be considered adiabatic, however I would imagine that the degree to which this generalization is appropriate decreases as the melting point is approached.

Adding some theoretical considerations to our practical results: There are 2 components in a critical shear strength, one of them is depending on T², another one has low dependency on T. If you look to attached image, it's obvious, that in linear approach YS will be zero latest at 400°C. However, above 1/2 melting T the diffusion processes play a bigger role and 250°C is definetely above. My esimation for YS at 650°Cwill still be below 3 N/mm².

All of them concept will be fine that YS,TS  = 1/ temperature. In general, the tensile strength of pure Al is measured 28 MPa. When increased temperature at 100 °C, 14 - 16 MPa. In three times, different YS reading like 14, 15, 16 MPa.

Dear Dr. Jie, I hope " http://www.nature.com/nature/journal/v445/n7123/full/nature05426.html " this work would help you understand the mechanism.

http://www.nature.com/nature/journal/v445/n7123/full/nature05426.html

"if force is applied slowly, it could be considered adiabatic"

Sorry, no.  Allowing time for thermal equilibrium denies that.

But, to reiterate: at Tm it can have no strength - how could you make the specimen?  It could not stand up for itself, let alone be pulled.  Consider the effect of T on mean atomic separation, then the effect of that on the force-separation curve: it is flat (dF/dx = 0, also means stiffness zero) at the distance corresponding to Tm. Hence: Zero strength.  There is no work to be done for further separation, indeed energy is regained by the external system because the slope is now negative.

Thanks for your suggestions and recommended references, which helps me a lot.

Large solid columnar dendrite Al can be fractured by EM (electromagnetic) field. I thought the possible reason may be as following:

1 Remelting by Joule heat induced by EM field.

### Joule heat input is 0.2W/cm3, it is far lower than the remelting of Al solid about 8W/cm3.

2 Remelting by the warmer liquid Al transfer by the EM-induced convection

### It only can remelting the solid Al, but cannot fracture the dendrite.

3 EM-induced agitation force direct fracture the dendrite (the question I asked, which may come into existence if the strength of Al at melting or a little slower temperature is too low.)

### I think it plays a critical role in the dendrite fragmentation, with the aid of aspects 1 and 2.

4 A possible reason provided by Holycross “mechanical loading may give the system enough additional energy to induce spontaneous melting”.

### It may cause spontaneous melt, but does not fracture the trunk of large columnar grain.

5 Dendrites are bended and form a low-angle grain boundary as a result due to the convection.

### It is not the reason of my experiments.

I think that single mechanism cannot cause the fragmentation of columnar dendrite. Maybe together action of several reasons finally result in the fracture. Among, the strength of solid Al at melting temperature may be very important.

Some remarks:

1. It seems to me that the concept of yield strength is not valid at the melting temperature of a metal.

2. It seems to me that the above discussion is about binding forces at the melting temperature.

3. Supposing thermodynamical equilibrium at the melting temperature, liquid and solid coexist at the melting/solidification temperature. 

4. So, the soldification/melting heat contains information about the binding forces in the solid.

Close to the melting temperature the strength is quite low because plastic deformation by creep occurs easily. However, it is wrong to say that there would be no strength by definition. It should also be observed that the elastic constants do not approach zero at the melting temperature. Melting is a competetition between the stability of the liquid and the solid phases rather than the result of a mechanical instability.

it largely depends what phases are present at the melting point. the liquid metal has no tensile strength, as you can only have shear forces in liquids. for the solid phase you need a coherent network to have tensile forces.

Thanks for your suggestion.

Indeed, for the semi-solid of alloy, as Katgerman said, the strength of semi-solid can be measured after the formation of coherent network.

I agree with Joh that the strength is quite low because plastic deformation by creep occurs easily. The solidification time under EM field in our experment is only about several minutes. Thus, maybe the creep does not plays an important role in the fragmentation due to limited time. The role of induced Joule heat and warmer liquid together with the EM force may result in the fragmentation of Al solid during its growth process.  

However, it still is a hypothesis because the exact emperimental evidence is difficult to obtain and the behavior of Al at temperature close to melting point is hardly known.

John Agren is correct; J C Jai, our original questioner wanted to know the strength of the solid at the melting point, not a mix of partially solidified alloy.

With regard to the strength of the solid, many years ago I estimated the yield strength of iron at its melting point from extrapolations carried out by a number of researches of strength at high temperatures.  For solid iron at its melting point it seemed that the strength was in the range 1.5 to 6.0 MPa. I used this value to calculate the maximum stresses which could be built up in the residual liquid during the freezing of a sphere assuming an elastic/plastic model. This small strength, when integrated for its cumulative effect over the volume of the sphere led to tensile stresses in its center of up to 150 MPa. This tensile stress was experienced by the residual liquid. The study proved that liquids could not suffer sufficient stress to nucleate pores homogeneously in solidifying castings.

This estimate of strength was, however, particularly uncertain because of creep at high temperatures, causing the yield strength to be strain rate dependent. I therefore repeated this study using a creep rate relation for the strength of iron at its melting point, but achieved very similar results for the resulting stress which developed in the sphere, indicating that the effective yield stress at rates of strain experienced in small castings was around a few MPa.

The creep model give similar estimates of stress for pure Al, Cu, Ni and Fe, indicating that the effective yield stress at familiar rates of strain are fairly similar for all these metals.  Therefore if, somehow, a polycrystalline tensile test bar could be made and pulled, we should expect a yield point in this range.

However, J C Jai is not straining polycrystalline specimens. He is attempting to damage a dendrite, which is a single crystal.  It is well known that if single crystals are pulled in tension, especially if of small size, they can fail simply by slip on, perhaps, a single slip plane, or at least a single slip band, the crystal simply slides apart.

Other deformation modes include plastic bending (again a creep mode) followed by rapid reorganisation of the dislocations into subgrain boundaries or grain boundaries. A high angle grain boundary, depending on the relative energies, may be wetted by the surrounding liquid metal, with the result that the liquid penetrates the boundary and the dendrite separates into two parts. This appears to be one of the mechanisms of dendrite fragmentation during events encouraging dendrite multiplication. The mechanism has been proposed particularly for the constricted neck of some alloy dendrites, even though energy calculations indicate that the neck can not only fail by penetration of liquid along a recrystallized boundary, but at sufficient strain and strain rate may actually melt.

J C Jai observations that the dendrites do not fracture is to be expected: solids at their melting point are ductile; the nucleation and growth of a crack in a solidifying metal is energetically improbable to the point of impossibility. However, the existence of a crack entrained from the outside of the metal, in the form of an oxide bifilm, would be expected to be common. Even so, as a result of the ductility of the metal at and near its melting point, the crack, if stressed, will not be expected to propagate: it will merely open somewhat to become blunt. This behaviour is also common.