I have performed quasi-static compression on Al open cell foam for 5 different relative densities. The stress-strain curve indicated decrease of yield strength with increasing relative density which is quite understood. However, the elastic modulus was opposite. It decreased with increasing rel. density. What can be the possible reason ? How can I relate stiffness and toughness from the curve. ?
Dear Bhasker Soni ,
As far as I can read I notice a decrease of yield strength with increasing relative density and a decrease of the elastic modulus with increasing relative density. So, according to the formulation of your question, both properties show parallel behaviour.
Dear Mr. Soni,
could you please help me, where do I find the curve you are referring to?
Besides, I agree with Dr. Van Mourik's comment, your initial question describes identical behaviour for both yield strength and elastic modulus, namely decrease at increasing relative density (which sounds strange to me, as I would expect increase with increasing relative density).
So in the end, it is not clear what you are actually observing, and thus where you see the problem.
Could you please re-formulate your question?
Best regards,
Dirk Lehmhus
@P. Van Mourik and Dirk Lehmhus :My doubt is as discussed below:
1) I think that for the yield strength/stress (Ys) for porous material will be less than its bulk counterpart. For example if the (Ys) of bulk metal is 100 MPa. If I increase the porosity in metal (i.e. relative density is decreasing), then I suppose that the Ys will be lower in porous metal than its bulk counterpart.
2) Should the elastic modulus increase or decrease with porosity ?
In a first approximation I would suggest that an Al foam can be conisdered as a composite. Hence the rule of mixtures would apply to Al foams. For a brief introduction to modelling mechanical properties of composites I would refer to Section 4.6 of Materials Science in Design and Engineering (see attached link).
http://www.delftacademicpress.nl/m017.php
Dear Mr. Soni,
thanks for your comment. However, I am still not sure whether I understand correctly what you actually observed. Regarding your individual points:
1) Yes, in all foams you would expect the yield strength go down if density goes down (which means that porosity moves up). This is the case in open and closed cell metal foams. The only exception I can think of are syntactic metal foams: Here, you can actually achieve an increase in specific compressive strength (note, this is not absolute compressive strenght, but compressive strength divided by density) with increasing porosity. You can find an example of this behaviour here:
https://www.researchgate.net/publication/264351461_Quasi-static_and_high_strain_rates_compressive_response_of_iron_and_Invar_matrix_syntactic_foams
2) Just like yield strength, it should decrease.
Both trends you can also see in the following publication on closed cell aluminum foams, which sums up a larger test programme we did a few years ago:
https://www.researchgate.net/publication/236329880_AlSi7_metallic_foams-_Aspects_of_material_modelling_for_crash_analysis
In case you are interested in the full texts, please send a request, and I'll provide them.
Best regards,
Dirk Lehmhus
Article Quasi-static and high strain rates compressive response of i...
Article AlSi7 metallic foams- Aspects of material modelling for crash analysis
As an aside, what seems surprising in your original question,
"Why was there decrease in elastic modulus under quasi-static compression of Al foams with increase in relative density?"
is that here you suggest you saw the opposite of what would be expected, a decrease in elastic modulus at increasing relative density (which equals decreasing porosity).
Is that a misunderstanding, or is it indeed some experimental observation? If so, for what kind of foam?
@Dirk Lehmhus: What I observed was an increase in elastic modulus with increasing porosity for 6061-T6 foam.
Sounds strange indeed. You should check for scatter and the statistical significance of the decrease, maybe. Besides, how did you measure the elastic modulus, and how much difference between porosities are we actually talking about? Could it be just an effect of the statistical variations in foam propertis you sometimes have?
As an aside, I had some publications on 6061-T6 foams & heat treatment of foams, too, some time ago. Maybe you find those interesting, too:
https://www.researchgate.net/publication/222416166_Properties_of_heat-treated_aluminium_foams
https://www.researchgate.net/publication/40827567_Adaptation_of_aluminium_foam_properties_by_means_of_precipitation_hardening
These two even have full texts available on Researchgate.
Best regards,
Dirk Lehmhus
Article Properties of heat-treated aluminium foams
Article Adaptation of aluminium foam properties by means of precipit...
Dear Bhasker Soni,
You observed:
1. a decrease in elastic modulus under quasi-static compression of Al foams with increase in relative density.
2. an increase in elastic modulus (under quasi-static compression) with increasing porosity for 6061-T6 foam.
Statements 1. and 2. do not necessarily need to be identical. So, my first question would be: does the above effects proceed in the same range of values of either relative density or porosity and Young's modulus? Another question that might be invoked is that the ultimate processes leading to fracture under quasi-static compression might depend on porosity, i.e. relative density. The third question regards whether or not the measured porosity as obtained from microscopical (?) measurements can reliably be linked to relative density.
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