I have reviewed some books about fracture mechanics, but I cannot explain microstructure damage with engineering fracture mechanics theory, such as fatigue damage of metals with micro-defects. Is there any outstanding work in this field? If so, can you share it with me? Greatly appreciate your answer and providing good practices in engineering.
Many thanks!
Good question.
Indeed, classical engineering fracture mechanics does not consider the role of microstructure on damage initiation and evolution.
When you aim to reconcile these two fields I find it helpful to go back to the original works of Griffith.
In his basic consideration he derives a fracture criterion from the trade-off between the elastic energy that gets stored inside a homogeneous material (without any microstructure for the moment) upon mechanical loading and the free surface energy that has to be provided when a crack opens up.
The lesson that can be learned here with respect to your question is that this energetic principle can be nicely generalized and cast into a functional form.
This means that you can construct a (free) energy functional, which includes the elastic energy, the plastic energy (for instance the energy that is stored through the statistically accumulated and the geometrically necessary dislocations for instance or some other analogue / mean-field formulation for the inelastic portion of the stored deformation energy), and the surface energy.
The specific relation to the microstructure comes from the fact that for instance the surface energy for a cohesion process inside the grain interior is different from that at a triple point or at the grain boundary for instance, which means that such general energy balance formulations can be rendered microstructure dependent and then be solved specifically (microstructure-dependent) for a local integration point that carries a certain MS ingredient.
And when thinking even beyond this, all these microstructure features such as the dislocation-related parameters or interfacial energy values etc can of course depend on the chemical decoration and partitioning values.
We have made good experience with casting these contributions for instance in a generalized Ginzburg-Landau formalism.
This can then be solved in principle by phase field simulations and can be also coupled with crystal plasticity mechanics etc.
Good luck
PS
Here are some reference suggestions where we outlined this:
Computer Methods in Applied Mechanics and Engineering
Volume 312, 1 December 2016, Pages 167-185
A phase field model for damage in elasto-viscoplastic materials
(Article A phase field model for damage in elasto-viscoplastic materials
)Journal of the Mechanics and Physics of Solids
Volume 99, February 2017, Pages 19-34
Elasto-viscoplastic phase field modelling of anisotropic cleavage fracture
(https://www.sciencedirect.com/science/article/abs/pii/S0022509616304513)
Computational Materials Science
Volume 158, 15 February 2019, Pages 420-478
(Article DAMASK – The Düsseldorf Advanced Material Simulation Kit for...
)
Recently, we got some spatially and crystallographic orientation resolved damage information in a commercial Al alloy. See our paper: Crystallographic orientation and spatially resolved damage in a dispersion-hardened Al alloy , DOI: 10.1016/j.actamat.2020.03.049 . Actually, our currently ongoing work continuously prove the conclusions in the paper and we further obtained some new and exciting results. The plastic deformation induced damage may relate to the Taylor factors of grains and the damage distribution can be characterized by using some novel experimental technique.
A lot was said, can be said and has still to be clarified and reported regarding this topic. It’s fascinating how the atomic bonding, atomic movements, their imperfect packing in the crystal, the presence of multiple interfaces, surfaces, grain orientations and elastic and plastic anisotropy etc. impact the first stages of our failure process: the crack initiation and the microstructure-sensitive crack growth. Regarding the latter I can also recommend the following review:
Article Mechanisms of fatigue crack growth – a critical digest of th...
Best regards,
René
Dear Gang,
What instrument you have used for photography of damage cross sections?
Combination of X-ray nano-computed tomography technology(three-dimensional defect analysis by micro-computed tomography), HRTEM(precipitation and mirco size effects), ESEM(fracture hairline cracks) and micro-scale cohesive zone model can investigate microstructural damage evaluation. Model Simulation results can demonstrate that microcracks and damage mechanics by porosity, atomic movements, orientations in the grain due to texture of materials, imperfections in crystal, damage due to thermal treatments etc. in the regions the multi reason for degradation of materials mechanical properties.
Ashish
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