Effect of Temp on yield stress and fracture toughness

[50Cent]

Homework Statement

I am given the trends for yield stress and fracture toughness as functions of temperature for steel. I need to explain the trends

Homework Equations

none

The Attempt at a Solution

I am guessing the yield stress is the stress that the material can withstand before it starts to deform plastically. So that infers that the steel is more elastic at lower temperatues. I can't explain the reasoning for this. Any ideas?

 

[Mapes]

Both graphs can be explained by the same temperature-dependent mechanism. How does plastic deformation occur? Why does a material fracture suddenly, rather than plastically deform?

 

[50Cent]

Both graphs can be explained by the same temperature-dependent mechanism. How does plastic deformation occur? Why does a material fracture suddenly, rather than plastically deform?

Hi,
Thanks for the reply. What is the temperature-dependent mechanism? I've been looking through a few books and searching google for hours but can't find any difinitive answers. Perhaps my searches arent specific enough.

i found this text though online
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The most significant factor which is determined by the temperature is the mobility of the structural defects such as grain boundaries, point vacancies, line and screw dislocations, stacking faults and twins in both crystalline and non-crystalline solids. The movement or displacement of such mobile defects is thermally activated, and thus limited by the rate of atomic diffusion.
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is that what i need to look at? the mobility of grain boundaries at different temperatures?

Plastic deformation involves the breaking of atomic bonds by the movement of dislocations as far as i know. And a material will fracture suddenly if it has a low youngs modulus, and is a brittle material.

 

[Mapes]

Excellent. Agreed that plastic deformation in metals is generally caused by dislocation motion, which is enabled and accelerated at higher temperatures due to thermally activated processes.

Now the link to fracture mechanics: what does it mean to be brittle? Why would a material fracture suddenly instead of deforming through dislocation motion?

 

[50Cent]

Excellent. Agreed that plastic deformation in metals is generally caused by dislocation motion, which is enabled and accelerated at higher temperatures due to thermally activated processes.

Now the link to fracture mechanics: what does it mean to be brittle? Why would a material fracture suddenly instead of deforming through dislocation motion?

Ok Thanks,
So the material has a low yield stress at higher temperature, because the disocations are easier to move? When you say thermally activated processes, what do you mean by that?

A brittle fracture fails by rapid crack propagation, as is normally perpendicular to the applied stress. As i understand it, there are two main types of brittle fracture,
transgranular (through the grain boudaries)
intergranular (along grain boundaries)

Found this also, seems relevant (key points bolded):
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The first and foremost factor is temperature. Basically, at higher temperatures the yield strength is lowered and the fracture is more ductile in nature. On the opposite end, at lower temperatures the yield strength is greater and the fracture is more brittle in nature. This relationship with temperature has to do with atom vibrations. As temperature increases, the atoms in the material vibrate with greater frequency and amplitude. This increased vibration allows the atoms under stress to slip to new places in the material ( i.e. break bonds and form new ones with other atoms in the material). This slippage of atoms is seen on the outside of the material as plastic deformation, a common feature of ductile fracture.
When temperature decreases however, the exact opposite is true. Atom vibration decreases, and the atoms do not want to slip to new locations in the material. So when the stress on the material becomes high enough, the atoms just break their bonds and do not form new ones. This decrease in slippage causes little plastic deformation before fracture. Thus, we have a brittle type fracture.
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So at higher temperatures the atoms can slip more easily and make the material easier to deform? Also resulting in less brittle fracture?

 

[Mapes]

Yes. At lower temperatures, dislocations are less likely to move, and the yield strength of metals increases. But this means that at crack tips, the plastic deformation mechanism that would blunt the tip and ease the stress concentration is less likely to occur. The "plastic zone" is smaller.

A material will fracture when the energy penalty of forming more surface area is lower than the penalty of pushing dislocations through the material. When an increasing load continues to add strain energy to a material with limited possibilities for dislocation movement (e.g., a cold material), it eventually becomes energetically favorable to ease the load by fracturing. Does this make sense?

(By "thermally activated," I mean any process with an activation, or energy, barrier, such as the breaking and reforming of atomic bonds that occurs with dislocation movement.)

 

[50Cent]

Yes. At lower temperatures, dislocations are less likely to move, and the yield strength of metals increases. But this means that at crack tips, the plastic deformation mechanism that would blunt the tip and ease the stress concentration is less likely to occur. The "plastic zone" is smaller.

A material will fracture when the energy penalty of forming more surface area is lower than the penalty of pushing dislocations through the material. When an increasing load continues to add strain energy to a material with limited possibilities for dislocation movement (e.g., a cold material), it eventually becomes energetically favorable to ease the load by fracturing. Does this make sense?

(By "thermally activated," I mean any process with an activation, or energy, barrier, such as the breaking and reforming of atomic bonds that occurs with dislocation movement.)

Ahh i see. Yes i understand that. I can explain the yield graph very well now, thanks for your help. Really Appreciate it.

Finally for the fracture toughness graph. Do i apply the same information about dislocations being less likely to move at lower temp?

Or is it because at low temp the plastic zone is smaller so the material can absorb less enegery before fracture. Also what causes the sudden jump at 0 deg celsius? there must be something that enables the fracture toughness to more than double over the last 50 degrees on the graph?

 

[Mapes]

Finally for the fracture toughness graph. Do i apply the same information about dislocations being less likely to move at lower temp?

Yes, my last comment was meant to address the fracture toughness trend. Dislocation movement absorbs energy. If you think about the work you do when plastically deforming a material (force x displacement), that energy is stored in the creation and movement of immense numbers of dislocations.

Also what causes the sudden jump at 0 deg celsius? there must be something that enables the fracture toughness to more than double over the last 50 degrees on the graph?

Well, there are no error bars, so it's not clear how accurate the values are. But a thermally activated process would be expected to respond exponentially to temperature, so I suppose it's not surprising if the rate of fracture toughness improvement increases with temperature.

 

[50Cent]

ahh right. I think that's the question sorted then :) Again thank you very much, you've helped me out a great deal!

Appreciate it :D

 

[Mapes]

You're welcome.