Table Of ContentSpringer Theses
Recognizing Outstanding Ph.D. Research
Emilio Martínez Pañeda
Strain Gradient
Plasticity-Based
Modeling of Damage
and Fracture
Springer Theses
Recognizing Outstanding Ph.D. Research
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í ñ
Emilio Mart nez Pa eda
Strain Gradient
Plasticity-Based Modeling
of Damage and Fracture
Doctoral Thesis accepted by
University of Oviedo, Oviedo, Spain
123
Author Supervisor
Dr. Emilio MartínezPañeda Prof. Covadonga Betegón
Department ofConstruction Department ofConstruction
andManufacturing Engineering andManufacturing Engineering
University of Oviedo University of Oviedo
Gijón Gijón
Spain Spain
ISSN 2190-5053 ISSN 2190-5061 (electronic)
SpringerTheses
ISBN978-3-319-63383-1 ISBN978-3-319-63384-8 (eBook)
DOI 10.1007/978-3-319-63384-8
LibraryofCongressControlNumber:2017946657
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All men by nature desire to know.
—Aristotle
It would have been virtually impossible,
indeed, to have achieved any success with the
idea of the Autogiro unless I had been able to
calculate its basic design by mathematics
before I began to build it. Success by mere
experiment would have been as unlikely as
the successful construction of a cantilever
bridge without any previous engineering
experience.
—Juan de la Cierva
I am, and ever will be, a white-socks,
pocket-protector, nerdy engineer—born
under the second law of thermodynamics,
steeped in the steam tables, in love with
free-body diagrams, transformed by Laplace,
and propelled by compressible flow.
—Neil Armstrong
’
Supervisor s Foreword
A wide array of micron scale experiments has revealed strong size-dependent
strengthening,allofthemshowingasimilartrend:thesmallerthesize,thestronger
the response. The classic theory of plasticity does not cater for this size effect. In
brief,itcanbearguedthatatthemicronscale,plasticitytheoryshouldbemodified
incorporating a length scale.
Thestraingradientplasticitytheoryisanextensionoftheconventionalplasticity
theory that explains the size effect by considering that stresses are controlled not
only by strains but also by strain gradients. The underlying idea is that material
hardening is controlled by the total density of dislocations, part of which derives
fromthegradientofstrain. Thesedislocationsbegintoplayadominantrole inthe
deformation of metallic material at the micron scale. Strain gradient plasticity
modelsdonotonlyrationalizesizeeffectsbutalsohelptounderstandwhathappens
atthe tip ofa crack ina fracture situation,wherehugestraingradients are present.
Inthepresentthesis,thestraingradienttheoryhasbeenconsideredtoobtainthe
stressandstrainfieldsatthetipofacrack.Forthefirsttime,theinfluenceofstrain
gradientsoncracktipmechanicswithinafinitestrainframeworkhasbeenassessed,
revealinghighstresselevations(relativetoconventionalplasticity)asaresultofthe
increaseddislocationdensityandthecontributionofthestraingradientstothework
hardening.Moreover,theseimportantresultswereincorporatedintheformulations
of different micromechanics damage and fracture models, showing their relevance
topredictcrackinginmetallicmaterials.Implicationsforboth,cleavageandductile
crack propagation, were established.
This research will have particularly strong implications in hydrogen-assisted
cracking, a pervasive problem in the energy industry, as the strain gradients affect
not only the stresses but also the hydrogen concentration at the crack tip. The
underlying physics is that the strain gradient effects raise the tensile stress levels
near the tip which, in turn, make it easier for the hydrogen to diffuse through the
atomiclattice.Infact,theinitialmotivationofthethesiswasabetterunderstanding
ofhydrogeneffectsontoughnessandfatiguefractureofhighandmediumstrength
steels used in the transport and storage of pressurized hydrogen, in the frame of a
research project financed by the Spanish Ministry of Science and Innovation.
vii
viii Supervisor’sForeword
For the aforementioned reasons, I am honored to write the foreword for
Dr. Emilio Martínez Pañeda Ph.D. thesis. In my view, the thesis is an outstanding
example of how to establish engineering criteria based on rigorous and solid
mathematical models. The work has been already very well received within the
academic community, with Dr. Martínez Pañeda being invited to deliver several
talks at international conferences and research institutions. In fact, some of the
fieldworkforthethesishasbeendevelopedattheUniversityofCambridge,andthe
Technical University of Denmark, besides the University of Oviedo.
Dr.MartínezPañedahasbeenanoutstandingstudentandanaturalscientistwith
a strong international vocation. From my academic point of view, Emilio’s
knowledge and expertise in the field of solid mechanics are impressive.
Furthermore, his initiative and willingness to work are remarkable and he has the
required skills and capacity to become a research leader in our field. Currently,
Dr. Martínez Pañeda is working as a Postdoctoral Researcher at the Technical
UniversityofDenmark,andIknowforsurethathewillhavealongandsuccessful
career. I hope that Dr. Martínez Pañeda will eventually work in Spain because it
will mean that we are able to value our brightest researchers and offer them the
recognition and conditions they deserve.
Gijón, Spain Prof. Covadonga Betegón
July 2017
Publications
Parts of this thesis have been published in the following articles:
Martínez-Pañeda, E., Natarajan, S., Bordas, S., 2016. Gradient plasticity crack tip
characterization by means of the extended finite element method. Computational
Mechanics 59, 831–842.
Martínez-Pañeda, E., Niordson, C.F., Gangloff, R.P., 2016. Strain gradient
plasticity-based modeling of hydrogen environment assisted cracking. Acta
Materialia 117, 321–332.
Martínez-Pañeda, E., Niordson, C.F., Bardella, L., 2016. A finite element
framework for distortion gradient plasticity with applications to bending of thin
foils. International Journal of Solids and Structures 96, 288–299.
Martínez-Pañeda, E., del Busto, S., Niordson, C.F., Betegón, C., 2016. Strain
gradient plasticity modeling of hydrogen diffusion to the crack tip. International
Journal of Hydrogen Energy 41, 10265–10274.
Martínez-Pañeda, E., Niordson, C.F., 2016. On fracture in finite strain gradient
plasticity. International Journal of Plasticity 80, 154–167.
Martínez-Pañeda, E., Betegón, C., 2015. Modeling damage and fracture within
strain-gradient plasticity. International Journal of Solids and Structures 59,
208–215.
ix
Acknowledgements
First and foremost, I wish to express my gratitude to my supervisor, Prof.
Covadonga Betegón, for her unconditional support, endless forbearance, constant
backing, and friendship. She has played an essential role in the success of this
thesis. I am also very grateful to all faculty members, administrative staff, and
laboratory technicians of the Continuum Mechanics and Structures section of the
UniversityofOviedofortheirhelpandencouragingremarks.Particularly,Iwould
like to thank Prof. Cristina Rodrguez, for always having her office doors open to
me, and Prof. Alfonso Fernández-Canteli, for being a role model. Feedback and
advice from faculty members from other sections, like Dr. Inés Peñuelas and Dr.
Roco Fernandez (Mechanical Engineering) or Dr. Inés Pariente and Prof. Javier
Belzunce (Materials Science), is also very much acknowledged. The working
atmosphere has been amazing, and I would like to thank all my young colleagues
who have played a key role in this. From the veterans (Dr. Pelayo Fernández, Dr.
Carlos López-Colina and Dr. Marta García) to the newcomers; with special grati-
tude to my friends from the VIP room (Dr. Tomás García, Miguel Muñiz and
Susana del Busto) for all the interesting discussions that we had.
My research stays in several universities across Europe have given me the
opportunity to learn from very bright scientists; their valuable advice cannot be
acknowledged enough. The Technical University of Denmark (DTU), which I had
the fortune of visiting on three occasions, has always been a second home for me.
I will never forget the kindness and politeness of all the members of the Solid
Mechanics section. Among the many friendships established, I must undoubtedly
highlight the one with my host, Prof. Christian Niordson; he has been a great
scientificmentortowhomIwillbeeternallygrateful.Myresearch careerhasbeen
also particularly influenced by Prof. Stéphane Bordas and his very active group at
the Universities of Cardiff and Luxembourg. It was a magnificent experience to
learn from him and his coworkers, and I look forward to continuing collaborating
foryearstocome.Andlast,butcertainlynotleast,mythree-monthresearchstayat
Cambridge University was strongly rewarding, having the opportunity to conduct
research under the guidance of Prof. Norman Fleck and Prof. Vikram Deshpande,
xi
