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# How to characterize the interface?

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Recently, I am interested in the interface between two different masses. But, I don’t know how to characterize the interface between them, especially the adhesive strength and the mechanics model. By the way, I remember I have known the spring model of the interface, but I can’t find any papers about it. Is there any suggestions? Thank you!

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## Comments

## Interface Fracture using cohesive model

Dear Yinglee,

May be cohesive model would be something you are interested in. By two different masses, do you mean two different materials or point masses (atoms)? (at which length scale you want to work in?)

Are the two materials elastic or elasto-plastic (EP)?

You can have a look at the following two papers, in this we studied bicrystal interface fracture using cohesive modelling approach. One of the material was Alumina (elastic) and other was Niobium single crystalline material (EP).

A. Siddiq, S. Schmauder, Y. Huang, Fracture of bicrystal metal/ceramic interfaces: A study via the mechanism-based strain gradient crystal plasticity theory.

International Journal of Plasticity, 23 (4), 665-689, 2007.A. Siddiq, S. Schmauder, Interface fracture analyses of a bicrystal specimen using cohesive modelling approach.

Modelling Simul. Mater. Sci. Engng.14(6), 1015-1030, 2006.The first of the paper is more about length scale stuff in crystal plasticity theory while second paper is about the interface fracture analysis of niobium/alumina bicrystal interfaces. We have shown that using a cohesive modelling approach, two independent parameters (out of the three) are required and one can validate the simulations with the experiments by varying any of the two.

Please let me know if you need any clarification. Also, if you find it interested :))then you can download my PhD thesis, which is available online.

Best Regards,

Amir

## interface fracture

Dear Amir,

I am very interested in your work on interface fracture. Where can I download your PhD thesis mentioned above?

Thanks a lot.

## Interesting!

Dear Amir

Thank you! What I am interested in is the interfaces of nano crystals. Maybe the second paper you referred is what I want. By the way, I can’t find your Ph.D thesis online. Could you please give me a URL?

Lee

## ABAQUS+spring for interface

These papers are using ABAQUS+spring to study interface. They are very simple but efficient. Minimum math required , not senstitive to FEA mesh size, clear physical meaning, no singular nor collapse element required, no convergence trouble encountered. Try it.

1. Xie D and Biggers, Jr. SB, Progressive crack growth analysis using interface element based on the virtual crack closure technique,

Finite Elements in Analysis and Design, 42(2006): 977-984. (Science Direct Top 25 Hottest Articles, #4, Apr-Jun, 2006, #11, Jul-Sep, 2006)2. Xie D and Waas AM, Discrete cohesive zone model for mixed-mode fracture using finite element analysis,

Engineering Fracture Mechanics, 73(2006): 1783-1796. (Science Direct Top 25 Hottest Articles, #2, Apr-Jun, 2006, #8, Jul-Sep, 2006)3. Xie D, Waas AM, Shahwan KW, Schroeder JA and Boeman RG, Computation of strain energy release rate for kinking cracks based on virtual crack closure technique,

CMES:Computer Modeling in Engineering & Sciences, 6(2004): 515-524.If you want some analytical solutions, this paper is the best one from my view:

J.W. Hutchinson and Z. Suo, Mixed-mode cracking in layered materials, Advances in Applied Mechanics 29, 63-191 (1992).

Good Luck!

## I like the spring model.

Thank you very much, VCCT-DCZM. As you say, the spring model is easy to handle both from theory and FEM. So, I'd like to try the spring model firstly.

## Without going to the details

Without going to the details in your papers, I'm suspicious of the mesh dependence. It's well known that the mesh resolution should resolve the cohesive length (not the length in the spring or the cohesive elements). In other words, one should have enough elements to resolve the bridging zone. Another difficulty I suspect for spring model in Abaqus is that you probably can only run "soft" spring. You might get snap-through instability for "hard" spring. Please refer to a simple paper for reference:

Y.F. Gao, A.F. Bower, "A simple technique for avoiding convergence problems in finite element simulations of crack nucleation and growth on cohesive interfaces."Modelling and Simulation in Materials Science and Engineering12, 453-463, 2004http://web.utk.edu/~ygao7/publication.htm, paper #7

## URL of my thesis

Dear Prof. Tan and YingLee,

My thesis can be downloaded from the following link:

http://elib.uni-stuttgart.de/opus/volltexte/2006/2735/

If there are any problems in downloading then please let me know and I will send a pdf version of it.

Best Regards,

Amir

## some comments on cohesive zone

It seems to me that many people are interesting in simulating interface and fracture at small scale. Cohesive zone is good, but it is phenomenological. The connection from atomistic traction-separation to the traction-separation at macroscopic length scale requires the knowledge of bulk behavior surrounding the interface.

Another difficulty is the cohesive zone model for a real Griffith crack (corresponding to a nucleation event) is difficult because it is instriniscally unstable. Most cohesive zone simulations in literature, to my understanidng, are actually approaching the Dugdale limit. This difficutly can be avoided by using the following paper:

Y.F. Gao, A.F. Bower, "A simple technique for avoiding convergence problems in finite element simulations of crack nucleation and growth on cohesive interfaces."

Modelling and Simulation in Materials Science and Engineering12, 453-463, 2004## After reading your paper

I suspect it of any practical usage for strucutal level analysis, however, it looks beautiful.

Let me ask you a simple question: if an engineer wants to perform a FEA analysis on the debonding of stringers from a section of fuselage, will he be able to use your approach with so dense mesh to match the cohesive zone? No way!

I also disgree with your comments of "phenomenlogical". Actually, all the theory of solid mechanics are phenomenlogical! Only deformation (displacement) is measurable, all others (force, stress, constituitive law...) are just concepts that human being had developed to explain what they saw.

For cohesive zone model, of course you can sugget some paramters from small level and publish tons of papers by changing this, that, blah, blah. But when performing structural level analysis, who cares what's happenig at atomic level. Engineers only want those measurable at structural level (or called calibration).

My point is that, which method is good, highly depends on what level of problem YingLee is going to sovle. Only he knows exactly what his problem is and, therefore, let him make a choice.

## Only deformation (displacement) is measurable

I agree with your statement that:

All the theory of solid mechanics are phenomenlogical! Only deformation (displacement) is measurable, all others (force, stress, constituitive law...) are just concepts that human being had developed to explain what they saw.I also realized that: experimentally, stresses cannot be measured directly.

http://imechanica.org/node/993

## We share the same point of view on this

Henry,

I read your blog and we do share the same view on this. Similar to your saying, the strain is measured and stress is computed through equations and force is measured through the load cell, in wich a circuit bridge of strain gauges is embeded.

So only strain (deformation) is measured.

To my understanding, Hooke's law, the simplest version of constituitive law is phenomenlogical. It is NOT a derived math equation. Rather, it was drawn from experimental observation. I'm wondering why some people in solid mechanics are so actively deriving this from atomic level. Is this useful or does it make sense? Or simply dig money and publish papers. It (like Young's modulus in Hooke's law) can be easily measured. I'm puzzled. I could be wrong.

## atomistic binding relation and universal macroscopic cohesive ..

I totally agree about the following comment:

"The connection from atomistic traction-separation to the traction-separation at macroscopic length scale requires the knowledge of bulk behavior surrounding the interface."I must add that one must also consider the fact, "What is the minimum length scale, the theory works for (macroscopic theories, crystal plasticity stuff, SGCP, discrete dislocation stuff, etc.). I remember one of the talks of Prof. Huang where he explaind it explicitly about the minimum length scales each of these plasticity theory can be used.

And then based on the used theory, comes the question at what scale the cohesive model used is valid. There is one paper from Prof. Ortiz's group, where they have made an effort to correlate the atomistic binding relation and universal macroscopic cohesive behaviour.

A discrete mechanics approach to dislocation dynamics in BCC crystals

Journal of the Mechanics and Physics of Solids,Volume 55, Issue 3,March 2007,Pages 615-647A. Ramasubramaniam, M.P. Ariza and M. Ortiz

Best Regards,

Aamir

BTW: Now a days, I am working on the other side of the story. Its about solid state bonding of alloys using ultrasonic consolidation process developed at Solidica.

## atomistic binding relation (the actual reference)

Apologies for the previous referenct, the correct reference is:

Coarse-graining and renormalization of atomistic binding relations and universal macroscopic cohesive behavior

Journal of the Mechanics and Physics of Solids,Volume 50, Issue 8,August 2002,Pages 1727-1741O. Nguyen and M. Ortiz

Best

Amir