Comments

In reply to Phase field modelling of fracture and fatigue in Shape Memory Alloys

Dear Cheikh,

Thanks for your interest. The phase field method is used to model the cracking. It is a phase field fracture method. The martensite-austenite transformation is taken care of using averaged internal variables, as you say. One could use a two-field phase field approach but this is not the purpose of our work. Our aim was to present the first phase field formulation for fracture (and fatigue) in SMAs.

Best,
Emilio Martínez Pañeda

• Log in or register to post comments

In reply to Phase field modelling of fracture and fatigue in Shape Memory Alloys

Nice work, but it looks more phenomenological with averaged internal variables than PFM with order parameters. 

• Log in or register to post comments

In reply to New results on shock mitigation of MC gels to appear in JMPS

the authors thank prof. P. Sharma, the JMPS editor who handled our paper with utmost efficiency and courtesy

• Log in or register to post comments

In reply to Dear Zhigang,

Since we are in the business of advertising codes, let me also pitch in mef90/vDef, the open source parallel implementation that I have used for almost all of my work in the field in the last 25 years or so.

Blaise

• Log in or register to post comments

In reply to Dear Per,

Dear Per, Emilio, and others,

The 2001 paper is a bit dated now. Our 2008 long article / book "The variational approach to fracture" (DOI: 10.1007/s10659-007-9107-3), although also dated by today's standard, provides a good view of the foundations and theory of a field that is about 25 years old, even though many have discovered it recently.

Blaise

• Log in or register to post comments

In reply to Postdoctoral Research Fellowship at the University of Udine in Phase-Field modelling of fracture

The position is now formally open for applications. The deadline is 16th November 2020 2pm (CET).

Apply online here:

http://web.uniud.it/ateneo/normativa/albo_ufficiale/886%20-%202020

For informal enquires: enrico.salvati@uniud.it

• Log in or register to post comments

In reply to Dear Emilio,

Dear Per,

Thank you for your kind reply. In addition to the 1998 paper by Francfort and Marigo I would recommend the 2000 work by Bourdin, Francfort and Marigo ("Numerical experiments in revisited brittle fracture"), where details of the phase field framework, including Gamma convergence and the Ambrosio and Tortorelli functional, are introduced. 

Regarding our recent paper on phase field fracture (and fatigue) of Shape Memory Alloys; an internal variable - the martensite volume fraction - is used to determine which regions correspond to martensite, austenite or the transformation region. 

I agree with your statement, the fracture energy-related length scale only plays a role if incorporated into the model. In that sense, I was thinking of the role of the phase field length scale (which can be tought as proportional to this fracture energy-related length scale) versus other models that include such a fracture length scale: cohesive zone models, non-local continuum damage models, etc. 

Kind regards,
Emilio Martínez-Pañeda

• Log in or register to post comments

In reply to Two funded PhD positions at the University of Western Ontario, Canada.

No comment

• Log in or register to post comments

In reply to Dear Zhigang,

Dear Emilio,

Thanks for the well-informed comment. I appreciate your mentioning of Oscar Lopez-Pamies's blog. From there I learned about the 1998 paper by Francfort and Marigo. When we wrote our first paper on the subject in 2011 we thought we were first but that was soon revised. I didn't know about the early Francfort and Marigo paper until now, though. 

I like your papers and not the least the most recent "just accepted", where you use phase field modelling to understand the evolving concentration of martensite and the propagation of cracks. If I understand it correctly the martensite/austenite composite is treated as homogeneous, but I guess it wouldn't be a big theoretical step to include a third phase to separate the martensite and austenite phases. I guess the numerical treatment will provide some challenges.

You are right regarding the material length scale connected to the fracture toughness. With the stress level at which the fracture processes operates, the toughness gives a characteristic length, but it doesn't help until it is allowed to play a role in the model. If the fracture processes are referred to a point, a sharp crack tip, I don't think the crack can penetrate an interface to a stiffer material. The required remote load becomes unlimited for any non-zero fracture toughness. A somewhat paradoxical result. 

The phase-field model has a length scale, given by the square root ratio of a molecular mobility coefficient vs. a coefficient defining the energy barrier of a surface energy potential. The length scales with the thickness of the transition region between the phases. The square root product of the mentioned two coefficients gives the surface energy.  

Replacing the crack tip stress singularity with a cohesive zone, or a box model, allows the crack to penetrate the interface to a stiffer material. I know from own experience that phase field models of corrosion pitting, does the trick. Also we see that the blur crack tip in the present paper works. I could not find any comments in the present paper regarding the expected decrease of the crack energy release rate or necessity to increase the remote load to maintain a constant crack growth rate. If there were a dip of the crack tip driving force versus the remote load it would give a possible comparison with the length scale L, as defined by you.

Best regards, Per

• Log in or register to post comments

In reply to PhD position in computational mechanics (focus elastodynamics)

Hello,

There is a PhD position in the general area of discontinuous Galerkin methods for elastodynamics (dispersive media) and / or Radiative Transfer Equation (RTE). The graduate research assistantship (GRA) position is for the University of Tennessee Space Institute (UTSI) which is a part of University of Tennessee Knoxville (UTK). The student will be located in Knoxville. Some important points are:

The student should have a strong background and interest in all or most of the following areas:

1.Computer programming: Proficiency in C++ programming is highly valued. 

2.Computational solid and/or electromagnetics (preferable).

3.Mathematics: familiarity with elastodynamics and in general hyperbolic and elliptic PDEs.

Interested applicants should send an email to rabedi@utk.edu, directly describing their background in the four areas mentioned above and attaching their CV / resume.  Note that due to COVID19 complications, preference may be given to students who are either in the US or can get the visa relatively quickly.

For a general overview of the research projects in my group you can refer to http://rezaabedi.info and  http://tinyurl.com/sdgyoutube/.

Reza

• Log in or register to post comments

In reply to PhD position in computational mechanics (focus elastodynamics)

Hello,

There is a PhD position in the general area of discontinuous Galerkin methods for elastodynamics (dispersive media) and / or Radiative Transfer Equation (RTE). The graduate research assistantship (GRA) position is for the University of Tennessee Space Institute (UTSI) which is a part of University of Tennessee Knoxville (UTK). The student will be located in Knoxville. Some important points are:

The student should have a strong background and interest in all or most of the following areas:

1.Computer programming: Proficiency in C++ programming is highly valued. 

2.Computational solid and/or electromagnetics (preferable).

3.Mathematics: familiarity with elastodynamics and in general hyperbolic and elliptic PDEs.

Interested applicants should send an email to rabedi@utk.edu, directly describing their background in the four areas mentioned above and attaching their CV / resume.  Note that due to COVID19 complications, preference may be given to students who are either in the US or can get the visa relatively quickly.

For a general overview of the research projects in my group you can refer to http://rezaabedi.info and  http://tinyurl.com/sdgyoutube/.

Reza

»

• rabedi's blog

 


• 909 reads

• Log in or register to post comments

In reply to Discussion of fracture paper #27 - Phase-field modelling of cracks and interfaces

Dear Zhigang,

Yes, you can find ESIS on Twitter: @ESIS_web

Dear Per,

It is remarkable how phase field methods can revolutionise many areas, including fracture mechanics but also others such as corrosion modelling - as you have pioneeringly demonstrated. Its ability to (naturally) predict features such as crack deflection and branching make it a very suitable technique to gain insight into problems such the case of a crack impinging on an interface. There have been a number of papers using phase field to gain complementary insight to that of He and Hutchinson [1-3].

In my group, we have also embraced this success with relish, and tried to contribute to the community. For example, by extending phase field formulations to deal with fracture in hydrogen-embrittled solids [4-6], functionally graded materials [7] and shape memory alloys [8].  

Some aspects of the formulation might require further research. There has been some discussion on the lack of a explicit connection with the material strength and the implications for crack nucleation - an interesting paper by Oscar Lopez-Pamies was posted in iMechanica recently (https://imechanica.org/node/24284). 

Regarding your question (implications of the length scale), I would argue that all fracture/damage models that are based on a toughness or critical energy release rate have embedded a material length scale: L~GcE/sigma_c^2=Kic^2/sigma_c^2. Analogous to what Rice calls the material's characteristic length or Zhigang refers to as the fractocohesive length. I found the paper by Tanné et al. a nice piece of work in the subject [9].

Best,

Emilio Martínez-Pañeda

PS: If someone is interested in playing around with the method, I have released all my phase field codes for Abaqus and FEniCS, including phase field fatigue [10]: https://www.imperial.ac.uk/mechanics-materials/codes/

[1] https://www.sciencedirect.com/science/article/pii/S0045782516317066
[2] https://www.sciencedirect.com/science/article/pii/S0045782518305772
[3] https://www.sciencedirect.com/science/article/pii/S0045782519300192
[4] https://www.sciencedirect.com/science/article/pii/S0045782518303529
[5] https://www.sciencedirect.com/science/article/pii/S0010938X19316464
[6] https://www.sciencedirect.com/science/article/pii/S0022509620303276 
[7] https://www.sciencedirect.com/science/article/pii/S135983681930229X
[8] https://arxiv.org/pdf/2010.04390.pdf (just accepted in CMAME)
[9] https://www.sciencedirect.com/science/article/pii/S0022509617306543
[10] https://www.sciencedirect.com/science/article/pii/S0167844219305580

• Log in or register to post comments

In reply to Discussion of fracture paper #27 - Phase-field modelling of cracks and interfaces

I have tweeted a link to these ESIS entires on fracture: https://twitter.com/zhigangsuo/status/1319060444758376453. Does ESIS have a twitter account?

As an experiment, I have tweeted a thread called

One Hundred Years of Toughness

https://twitter.com/zhigangsuo/status/1290570290657996800

• Log in or register to post comments

In reply to The Mechanochemistry Discussions

Thank you for the news! Looking forward to them!

• Log in or register to post comments

In reply to The Mechanochemistry Discussions

Thank you so much for the information!

• Log in or register to post comments

In reply to MicroStructPy: Generation of statistically representative microstructures with direct grain geometry control

Thank you for sharing the code. A quick question that can this code generate periodic mesh on the RVE boundaries?

• Log in or register to post comments

In reply to The Mechanochemistry Discussions

Can't wait to attend, but I have to do it asynchronous as it conflicts with my class time. 

• Log in or register to post comments

In reply to The Mechanochemistry Discussions

Cool. Thanks for sharing this series.

• Log in or register to post comments

In reply to Interlocking topologies

Thank you Nitesh! I just got time to go through the video. The video your suggested is very helpful especially on the generation of 3D interlocked topologies. Although I did not invovle too much on this research topic, Prof. Francois Barthelat's group is working quite a lot on the fabrication and mechanics of topologically interlocked structures (by Aram Bahmani, Ahmed Dalaq and Mohammad Mirkhalaf Valashani). I think Prof. Krishnamurthy is exploring more types of toplogies than we are but we are exploring different techniques to fabricate toplogically interlocked materials. There might be some collaboration opportunites.

• Log in or register to post comments

In reply to Journal Club for October 2020: Toughening Transparent Ceramics with Bio-inspired Architectures

Great work! 

I cannot resist to suggest you to watch this talk by Prof. Krishnamurthy, where he talks about technique to generate various interlocking topologies (Video link). I think it might be helpful, not sure. I am not familiar with either of the research areas, however, this appears to me as a connecting link. 

-Nitesh

• Log in or register to post comments