Dear Colleague
It is known that ahead of a crack subject to static or fatigue loading microcracking and damage makes the material soften (of smaller elastic modulus) but also its strength degrades (in composite materials, there are so called “wearout models” which associate strength reduction exactly to the reduction of modulus).
Now, based on a paper under review on V-notch and cracks with radially graded materials, which you can find at https://www.researchgate.net/publication/381316809 and also here attached, I have obtained that the grading makes stress singularity possibly disappear which would seem to be beneficial for the crack. Hence, the concentration largely reduces. But I certainly can imagine that this effect is mild in most (at least man-made) materials, because we all know that cracks propagate and that microcracks are certainly not likely to make the crack arrest! Of course, there are techniques which in maintenance of some structures, do drill “holes” near the apex of the crack to make them arrest, and this is loosely also like elastic grading the material.
Materials which may be intelligent may be bone, see paper below, but I am not particularly expert in the field, and I don’t know if its mechanisms are able to stop cracks during fatigue, and if this is due to some mechanism similar to what I am describing. But of course the solution in Nature is interesting, and could be an inspiration for new man-made materials!
I was talking with some colleagues about intelligent materials which release some gels to stop cracks --- this is not exactly my idea, but instead we need to invent something that reverses the process, namely if the damage is in a form which reduces modulus as I describe in the paper and yet the material degradation effect is minor with respect to this singularity reduction, then this is a potentially very big innovation!
Are you interested to discuss further, and perhaps we can talk sometimes online on TEAMS or ZOOM?
Regards,
Prof. Michele Ciavarella
Professor of Mechanical Design.
MC lab @ Dept "of excellence" of Mechanics, Mathematics and Management. Email: [email protected] Phone: +39-080-5963670, mob.+39 3342204656
Humboldt Fellow, Technical University Hamburg
RG, imechanica, Linkedin , CV
Bone and its adaptation to mechanical loading: a review
S J Mellon [email protected] and K E TannerView all authors and affiliations
Volume 57, Issue 5
https://doi.org/10.1179/1743280412Y.0000000008
Abstract
Bone is a remarkable living material that comes in two forms with different porosities and different macrostructure, but with the same highly organised microstructure and nanostructure. As bone accumulates damage, it is removed and replaced. When the mechanical demands on bone increase the bone mass increases, while reductions in the loading leads to the removal of bone, thus bone can be considered a ‘smart material’. The ongoing replacement of old bone tissue by new bone tissue is called remodelling. Bone formation, repair and remodelling is controlled and produced by four types of cell, namely osteoblasts, osteoclasts, osteocytes and bone lining cells. Bone remodelling is regulated by signals to these cells generated by mechanical loading. Exactly how loads are transferred into bone, how the bone cells sense these loads and how the signals are translated into bone formation or removal is unknown. In this review, the structure of bone and the cells responsible for maintaining bone are described. The mechanisms that cause bone to adapt to mechanical loading have been investigated. The methods that have been employed in attempts to determine this mechanism are considered.
Ciao Mike,
Interesting discussion. Out of curiosity, as a non-expert in fracture mechanics: would auxetic properties help in what you mention? I can imagine that if two points tend to be pulled apart, the material would expand, would that somehow help ?
Alessandro
Its more complicated than that ! Fracture in auxetic materials has been studied but l doubt poisson effect can do much. The issue is also how to compare what with what. Its obvious materials have different resistance to fracture or fatigue ane that csn be improved with some tratments
A very specific and technical question!
In the context of fracture mechanics, the elastic modulus changes ahead of a crack tip can indeed affect the propagation of the crack. The elastic modulus is a measure of a material's stiffness, and changes in it can influence the stress distribution around the crack tip.
In general, it is challenging to completely stop cracks from propagating due to elastic modulus changes alone. However, researchers have explored various strategies to slow down or arrest crack growth by:
1. Modifying the material's microstructure or composition to enhance its toughness and resistance to crack growth.
2. Applying external stimuli, such as temperature or stress, to alter the material's elastic properties and reduce crack growth.
3. Introducing artificial defects or micro-cracks to redistribute the stress field and hinder crack propagation.
Some techniques used to achieve this include:
- Gradient materials with tailored elastic properties
- Transformation toughening
- Crack bridging or blunting
- Micro-crack toughening
These approaches are often used in combination with other fracture mitigation strategies, such as crack arrestors or reinforcement materials.
Keep in mind that the effectiveness of these methods depends on the specific material, loading conditions, and crack geometry. If you're interested in exploring this topic further, I recommend consulting relevant research papers and experts in the field of fracture mechanics!
thank you very much Prakash Sen , do you have any reference for your comment - Gradient materials with tailored elastic properties???
You can check Michele Ciavarella the following publications to see if it could help:
1. Ritchie, Robert O. "Toughening materials: enhancing resistance to fracture." Philosophical Transactions of the Royal Society A 379.2203 (2021): 20200437.
2.Article Numerical Analysis of Crack-Tip Fields in Functionally Grade...
Hi, Prof. Ciavarella,
Thank you for bringing our attention to this very interesting topic. It was reported that contrast in the elastic properties can lead to enhancement of fracture toughness in heterogeneous materials (Hossain, M., Hsueh, C.-J., Bourdin, B., and Bhattacharya, K. (2014). Effective toughness of heterogeneous media. J. Mech. Phys. Solids, 71:320–348.). This enhancement is probably a result of two distinct phenomena: fluctuations in stress leading to regions where the stress intensity at the crack is considerably smaller than that of the macroscopically applied value, and renucleation when crack tip reach a compliant to stiff interface. I think this paper is somewhat relevant to the question you raised: variation in elastic modulus could enhance fracture toughness. I really hope this would become another means to enhance toughness.
Regards,
Fenglin Guo
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