Dear all, I came across one problem. we measure the bulk modulus of certain material like pure metal and alloys via tensile test. As the progress of nanoindentation technique, we can get it from different phase inside one alloy conveniently. Thus, there comes the problem whether the anisotropic characteristics of crystalline affects the bulk modulus we measure from nanoindentation or not. I mean suppose we made the indents on the plane (111) in certain single crystal material, then will there be significant differences between it and the that on (100) plane? Besides, can we use this value instead of the one given by macro test on the same material? What are the factors?
In addition to the useful answers given by Grzegorz and Soud, let me comment on your question. It is about bulk modulus (or compression modulus). In suitable cases, you can get an estimate of Youngs modulus as mentioned before. In order to calculate the bulk modulus, poisson ratio is required. In general, there are two independent elastic constants for isotropic materials, and between 3 and 21 for single crystals depending on crystal symmetry. It seems to be hopeless to solve this on the basis of indentation even for isotropic material. To get the elastic properties of crystalline materials, let me suggest another strategy. The full set of single crystal elastic properties of almost any known phases are tabulated in data collections, such as Landolt-Börnstein. Calculate the desired bulk moduli of the phases from single crystal elastic constants using elasticity theory and suitable averaging procedures (Voigt, Reuss, Hashin-Shtrikman etc.). To identify tha phases your material is composed of, I suggest to use other methods such as X-ray diffraction or analytic TEM. I guess you wish to avoid such methods (perhaps you have no access), but nanoindentation is not a suitable replacement except perhaps for very special cases. Even if I have not directly answered your question, I hope this will contribute to your background.
Frank
I am not an expert but:
-what do you measure during tensile test is Young's modulus (E), and in nanoindentation indentation modulus (EIT) in general E ~ EIT but not always
-pushing indenter into different single crystals you will get different deformation response, with deformation a feature called "pile up" occurs and changes the contact area between tip and material
-in my opinion nanoindentation is better for showing differences between orientation more than giving exact values of modulus. I suppose it is not easy to show differences of cubic BCC or FCC phases but for hexagonal HCP should be easier due to higher anisotropy.
-for ceramic HCP materials I suggest you to read some papers of: Tamas Csanadi et al.https://www.researchgate.net/profile/Tamas_Csanadi He studied anisotropy by nanoindentation.
-for multiphase samples sometimes it is best method to determine properties of particular phase
-
Hi Wang, so if your material phase is itself highly anisotropic, obviously the nanoindentation results will be different for different orientation. As, the elastic and plastic anisotropy comes into play when a grain or crystal is oriented in a certain direction, the indentation will face different atomic distribution and will cause different reduced youngs modulus, thus youngs modulus.
On the other hand, if your actual material has many grains, overall behavior becomes isotropic and the average values of a good number of indentations in the same phase should give you a statistically reliable value. So, if you want to explore certain phase in a material, use nanoindentation and do a good number of indentations in one phase. You should then have an average value of the modulus by analyzing all indentations in a certain phase. If your grain size is in nm range, creating an indentation in one grain is almost impossible (if you are very lucky, you may have one/two indents!!!!).
Hope it helps. Please shoot a question if you have any.
Happy Researching!!
In addition to the useful answers given by Grzegorz and Soud, let me comment on your question. It is about bulk modulus (or compression modulus). In suitable cases, you can get an estimate of Youngs modulus as mentioned before. In order to calculate the bulk modulus, poisson ratio is required. In general, there are two independent elastic constants for isotropic materials, and between 3 and 21 for single crystals depending on crystal symmetry. It seems to be hopeless to solve this on the basis of indentation even for isotropic material. To get the elastic properties of crystalline materials, let me suggest another strategy. The full set of single crystal elastic properties of almost any known phases are tabulated in data collections, such as Landolt-Börnstein. Calculate the desired bulk moduli of the phases from single crystal elastic constants using elasticity theory and suitable averaging procedures (Voigt, Reuss, Hashin-Shtrikman etc.). To identify tha phases your material is composed of, I suggest to use other methods such as X-ray diffraction or analytic TEM. I guess you wish to avoid such methods (perhaps you have no access), but nanoindentation is not a suitable replacement except perhaps for very special cases. Even if I have not directly answered your question, I hope this will contribute to your background.
Frank
Hi,Grzegorz , Thanks for your reply. As we all know, the reduced modulus is calculated based on the contact stiffness during unloading period. The appearance of pile-up or sink-in would lead to deviation of the contact area, which we employ to calculate both modulus and hardness. So this method (nanoindentation) suffers from it more or less no matter which kind of crystal we make the indents (unless we know certain crystal or plane is more sensitive to pile-up or sink-in ). In fact, I'm quite curious about the difference between the modulus from different crystal plane in bcc or hcp. Do you have any ideas about this? Thank you so much!
Hi Soud, thank you for your suggestion. Now I have one question. I have a sample with bcc polycrystal structure, if I want to get the hardness via nanoindentation, I just need to make a good number of indents over this sample then get the average of the hardness values from different test sites. But I' m wondering whether it's reasonable to do that in this way. Does the average value represent the hardness of the bulk modulus of this material? Does the hardness from different orientation (due to different atom distribution or sth.) have additivity or not?
Hello Frank,thank you for your comments and suggestions. You mentioned two points I want to know more clear.
1. with the full set of elastic properties data from single crystal, how can we estimate the bulk modulus of certain material like alloys? There are two factors we need to take into consideration if the alloy consist of two phases. First one is compositional difference between the studied phase and the corresponding single crystal. Would it affect the modulus on the condition of they have the same crystal orientation (and indents on the same crystal plane the direction). The second one is what's the averaging procedure. I wonder whether the hardness from different oriented crystal of same phase and composition has an additivity or not. Can we add them together directly and get the average value?
2. As you have mentioned, the poisson ratio is a necessary value for the calculation of bulk modulus. However, it seems to me that the available value of poisson ratio of different phase or materials is rather limited. Do you know where we can get find some useful values?
Thank you so much for the suggestions above again!
Chuanyun
Hello Chuanyun,
thank you for your interest. Your questions are both interesting and important. I try to answer. First, let me provide the reference of an old but famous textbook: Clarence M. Zener, Elasticity and Anelasticity of Metals, The University of Chicago Press, 1948. Perhaps you can find it in a library. A more recent useful textbook is Andrew Briggs, Acoustic Microscopy, Clarendon Press, Oxford 1992. As on your question 1, let me distinguish two cases.
Case A: The grain size and interparticle spacing are much smaller than the size of the indent, so that the indented area covers many grains and many second phase particles. Then a reasonable strategy is as follows:
- Look for the tabulated single-crystal elastic constants of the matrix phase. A difference in composition between your application and the tabulated case inside the solubility limit should not cause serious deviations of the elastic constants. A difference in composition beyond the solubility limit will lead to the formation of new phases in thermal equilibrium. Then one has to take into account these phases.
- Calculate the orientational average of the elastic constants in terms of modulus of compression, shear modulus, Youngs modulus and Poisson ratio (two of them are independent, the remaining two can be derived from the first two). As the elastic properties are a fourth-rank tensor, one can only calculate upper and lower bounds of the elastic constants (Voigt bounds and Reuss bounds). Take the average of Voigt and Reuss bound, so called Hill average. Only in the case of the bulk modulus Voigt bound, Reuss bound and Hill average agree.
- Repeat the same for the particle phase.
- At this point, it is interesting to note that the bulk modulus, per definition (isotropic compression), does not depend on orientation, meaning that the averaging procedure is trivial. However, for the next step to go, bulk modulus B alone is not sufficient, you need a second elastic constant, e.g. shear modulus G, for which the averaging procedure is far from being trivial.
- Now you have to calculate the average elastic constants, B and G, for a composite material composed of two phases, 1 and 2, volume fractions f1 and f2, elastic constants B1, B2 and, G1, G2. Again, calculate upper and lower bounds and take the average in order to finally get the bulk modulus of the whole macroscopic system.
Case B: The indented area is much smaller than both the grain size and particle size. Then you can place indents inside the matrix grain and even inside the second-phase particles. The elastic response of the indenter will then generally be dependent on orientation of the grain or particle (although the bulk modulus is independent of it).
Let me attach an own old report and source text of three Pascal programs (readable with editors), each in German, but might be helpful. It is not possible for me to translate it now.
As on your question 2, Poisson ratios of some materials are tabulated in the textbook by Briggs (see above). For other cases you have to search the internet, or take single crystal elastic constants from the Landolt-Börnstein collection and apply the cumbersome averaging procedure.
Best reagards,
Frank
Hi Wang, I would suggest you to combine both Nanoindentation and EBSD to see what are you getting in terms of orientation effect. If there is none, then you could conclude that the material is isotropic. And, would you be able to tell me the average grain size.?
If the material is itself isotropic, then averaging is statistically good idea. However, if you find any orientation effect on your hardness values, then surely its not a good idea. In fact then it would be an interesting thing and I would prefer to analyze the effect of different orientation on the hardness and observe the data.
Shoot me questions if you have any.
how to calculate hardness and youngs modulus for bulk material using nano indentation
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