Integrated study of damage after overloads in single crystals

Lead Research Organisation: Cranfield University
Department Name: Sch of Aerospace, Transport & Manufact


Damage prognosis in metals is a grand challenge that engineers have faced for centuries. The complexity of this problem arises from the interaction of damage mechanisms at multiple scales. For example, a force applied far from a microscopic imperfection can promote the production of defects at the atomic scale. In between, mesoscale attributes (e.g., heterogeneous dislocation density, grain morphology, texture) regulate the exchange of damage across micro- and macro-scales.
Most modelling approaches do not explicitly consider all these length scales and they rely on phenomenological correlations between empirical formulations and macroscopic experiments. This approach is reliable for predictions within the testing conditions of the experiments used for calibration, but the uncertainty is unbound outside these conditions. This lack of predicting power is problematic in critical applications in which the mechanical response should be guaranteed for a large number of working conditions, much larger than the typical experiments required for material certification.
To mitigate modelling uncertainty, leading scientists [1-3] have proposed multiscale approaches validated at various length scales. A key value added by these approaches relies on the lower dependence of damage on loading conditions at smaller scales (e.g., the strength of the interaction between two dislocations is unnafected). Dislocation structures (e.g., cells and persistent slip bands (PSBs)) lay on the verge of sensitivity to loading conditions.
Much research [4] has shown that mesoscale structures (e.g., 1 micron in size) control the stress-strain response under fatigue loading. After an overload, the response depends on the changes of the mesoscale structures and on the crystallographic orientation. A key attribute is that only a few dislocation structures are thermodynamically stable and the same structures arise on myriads of metals. Hence, we argue that the stress-strain response of various single- and poly-crystals after an unknown loading sequence can be bound by models that probe all possible stable structures. Moreover, we hypothesize that the transient behaviour after unexpected events can be reproduced with a parameterized transition between stable structures.
This research proposes to mitigate the uncertainty of assessing overloads by integrating mesoscale mechanical tests and computational modelling. In terms of experimental effort, we will manufacture mesoscale single crystal specimens using Cranfield University proprietary Mesoscale Machining Platform. We will measure the stress-strain response of FCC single- and poly-crystalline specimens of various sizes (50 to 500 microns) after overloads with different intensity and patterns. Additionally, we will characterize mesoscale dislocation structures after overloads in order to identify the evolution of the structures and their morphology at the mesoscale.
In terms of modelling, we will exercise the crystal plasticity model recently developed by the PI [5], which is the state of the art in constitutive models for cyclic loading and has been extensively validated with single- and poly-crystal data for Ni, Cu, and stainless steel. We will propose a physics-based evolution of structures to explain and bind the stress-strain response of single- and poly-crystals after overloads. We will match overload scenarios with their mesoscale structures to predict independently the mechanical response. Finally, we will quantify the role of overloads on microstructurally small fatigue cracks by comparing the crystallographic Fatemi-Socie fatigue indicator parameter (FIP).

[1]Bo, Jiang, Dunne. J. Mech. Phys. Sol. 106 (2017):15-33.
[2]Sweeney, Vorster, Leen, et al. J. Mech. Phys. of Sol. 61 5 (2013):1224-40.
[3]Zhu, Basoalto, Warnken, and Reed. Acta Mat. 60, 12 (2012):4888-4900.
[4]Li, Li, Wang, Zhang, Prog. Mater. Sci. 56 (2011):328-377.
[5]Castelluccio, McDowell, Int. J. Plast. 98 (2017) 1-26.

Planned Impact

The fundamental understanding seek by this research aims to mitigate the uncertainty in assessing the mechanical response of a component under cyclic loading after an overload. Hence, we have the potential to influence the design and servicing of critical components across applications in which the expected fatigue life should be quantified a prior with limited experimental validation.

One specific beneficiary is the through-life servicing of components in the aerospace industry. Our work will reduce excessive conservatism by modelling the damage of components under unexpected loading excursions without the need for additional experimental testing. Certainly, our integrated approach will validate physical mechanisms that bind the stress-strain response upon overloads and quantify worst case scenario. We envision our work impacting from the conceptual engineering of a component up to the real time assessment of fit-for-service by reducing unnecessary safety coefficients and reducing manufacturing and operating costs. Eventually, lessons learned from these critical components will be transferred to less critical applications and benefit other areas.

Secondly, this research will leverage on safety assessments of stainless steel cladding in components affected by hydrogen, for example in the nuclear industry. Our ongoing research program on hydrogen embrittlement has identified that atomistic rather mesoscale mechanisms are responsible for the effects of hydrogen in FCC metals. Hence, by assessing the role of mesoscale structures plus our current understanding of hydrogen effects at the atomic level, we will be able to predict the response of hydrogen-charged metals upon overloads.

In addition, our research will also support the innovation of engineering alloys designed for specific application in which the effect of overloads must be considered a prior without experimental validation. This new paradigm not only improves performance and reduces cost, but also provides new means to envision systems that were unimaginable a few years ago. However, it requires a computational strategy that estimates the mechanical response of materials prior to manufacturing. Hence, our objectives are strategically aligned to nurture this incipient 4.0 industry in the UK and support the link between fundamental physics and engineering applications.

Finally, our research has potential to contribute to safety assessments in metallic components across applications and regulations. Current approaches to predict the safety of components is based on correlating experimental results with model parameters. However, this strategy carries a large uncertainty when the prediction is outside the boundaries of the experimental set used for calibrating. The hypothesis investigated in this program will allow to perform robust safety assessments that avoid correlations at the macroscopic level and make use of parameterizations of mesoscale structures.


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Ashraf F (2022) On the similitude relation for dislocation wall thickness under cyclic deformation in Materials Science and Engineering: A

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Dindarlou S (2022) Substructure-sensitive crystal plasticity with material-invariant parameters in International Journal of Plasticity

Description We managed to manufacture sub-millimiter samples from large grains that are single crystals.

We managed to run mechanical tests with sub-millimiter samples and the results show so unexpected size dependence. Further analysis and additional testing demonstrated that the results can be replicated, but it is not clear the rational for our observations. Publications are under development with one manuscript ready to be resubmitted after being rejected.

In parallel to experiments, we have developed a multiscale computational model with impressive predictive capabilities. We have one paper accepted and another on the point of being accepted after a positive first review. Both papers on high impact factor journals (above 5)
Exploitation Route These sub-millimiter samples enable to test single crystals from alloys, which cannot be regularly machines.

The information about size effects can help in the design of more robust/efficient small scale devises.
Sectors Aerospace, Defence and Marine,Manufacturing, including Industrial Biotechology

Description Our work has influenced various partners around the world. In particular, the nuclear navy labs in the United States is reproducing our strategy and following the path laid out from this research. We have also reached out to Goodfellow company with the intent to make available single crystals to the market manufactured as per the results of this grant.
First Year Of Impact 2021
Sector Aerospace, Defence and Marine
Impact Types Economic

Description Support to British Standard Institute committee on Fracture
Geographic Reach Multiple continents/international 
Policy Influence Type Participation in a advisory committee
Impact Understanding the deformation across scale support the advancements of standards to measure mechanical properties and enhance structural integrity and economic success. The support of the BSI committee is link to understanding the uncertainty of measurements and their lack of evaluation on the standards.
Description Impact Acceleration Grant - Internal Support from EPSRC through Cranfield University
Amount £16,500 (GBP)
Organisation Cranfield University 
Sector Academic/University
Country United Kingdom
Start 05/2020 
End 06/2022
Description Collaboration with Clement Keller 
Organisation National Institute of Applied Sciences of Rouen
Country France 
Sector Academic/University 
PI Contribution Create single crystal samples for microscopy analysis/
Collaborator Contribution Perfom EBSD and ECCI analysis to characterise the deformation of single crystals.
Impact Joint conference presentation
Start Year 2019
Description Collaboration with IMDEA, Spain 
Organisation Madrid Institute for Advanced Studies of Materials
Country Spain 
Sector Academic/University 
PI Contribution Prepare samples for testing
Collaborator Contribution Perform simulations to compare with experiments
Impact Still under development.
Start Year 2020
Description Prof Indradev Samajdar 
Organisation Indian Institute of Technology Bombay
Country India 
Sector Academic/University 
PI Contribution We developed the approach to test mechanical properties at mesoscale
Collaborator Contribution Collaboration to create large crystals for engineering materials. They will help us create large crystals from alloys that can be cut and tested
Impact Process materials that will be subsequently tested by us.
Start Year 2022
Description Support the collaboration with Nuclear Navy Lab, US 
Organisation Bechtel
Country United States 
Sector Private 
PI Contribution Some of the experimental capabilities developed in this program are being tested for a collaboration with US researchers.
Collaborator Contribution The researchers in the US are performing continuum dislocation dynamics simulations and they want to calibrate the results with our experimental data.
Impact This is ongoing. COVID has severely impacted our progress.
Start Year 2020
Description TMS conf presentation 20201 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Postgraduate students
Results and Impact We present in March 2021 the experimental developments in this project.
Year(s) Of Engagement Activity 2021