My interests span a wide range of research challenges that lie at the interface between mechanics and other disciplines, such as materials science, geology, chemistry and structural engineering. I enjoy addressing fundamental scientific conundrums that have important implications for technology development and engineering practice. Some examples of my recent research endeavours are provided in the following sections. The numerical codes that I have developed are available for download below.
Hydrogen is famed for causing catastrophic failures in metallic components. The ductility and fracture resistance of metals are drastically reduced in the presence of hydrogen and these effects increase with material strength; a 90% reduction in fracture toughness is observed in high strength steels. However, due to the complicated multi-physics and multi-scale nature of the problem, the accurate prediction of the lifetime of engineering components undergoing hydrogen assisted fracture remains an elusive goal.
I have aimed at solving this scientific challenge by applying a mechanics rationale to identify the first-order effects governing the fracture process. Specifically, I placed my efforts in enriching continuum models to resolve the critical variables of the problem – crack tip stresses [Martínez-Pañeda & Betegón, 2015] and hydrogen concentration [Martínez-Pañeda et al., 2016] – over the critical distance at which cracking initiates, a few microns or less. Ultimately, we proposed an implicitly multi-scale model that shows an unprecedented level of agreement with experiments on various high-strength alloys and over a very wide range of applied potentials [Martínez-Pañeda et al., 2016b]. We then proceed to develop computational multi-physics models that enable fracture [Martínez-Pañeda et al., 2018] and fatigue [del Busto et al., 2017] life predictions of industrial components as a function of the material properties, the environment and the loading conditions. In addition, we have shown how early cracking puts into question the use of slow strain rate tests (SSRT) for measuring hydrogen embrittlement susceptibility [Martínez-Pañeda et al., 2020].
CRACK TIP PLASTICITY: THE ROLE OF DISLOCATION HARDENING
Macroscopic fracturing in metallic materials depends sensitively on properties that pertain to the micro and atomic scales. Continuum theories can be enriched to link scales in fracture mechanics and properly characterise material behaviour at the small scales involved in crack tip deformation.
Of utmost importance to fracture processes that take place within microns ahead of the crack is the role of plastic strain gradients in elevating crack tip stresses. Non-homogeneous plastic deformation requires extra storage of geometrically necessary dislocations (GNDs) to accommodate lattice curvature. As shown by discrete dislocation simulations, the resulting increased dislocation density promotes local strain hardening and leads to high crack tip stresses that are much larger than those predicted by conventional plasticity. Crack tip gradient hardening can be captured at the continuum level by using strain gradient plasticity theory. We develop suitable numerical frameworks to characterise crack tip stresses under small and large strains [Martínez-Pañeda and Niordson, 2016], as well as modelling crack growth resistance [Martínez-Pañeda et al., 2019]. Moreover, our theoretical and numerical analyses reveal the existence of an elastic core at the crack tip, reminiscent of dislocation free-zones, where the stresses exhibit the linear elastic singularity [Martínez-Pañeda and Fleck, 2019]. We have shown that the high crack tip stresses predicted by strain gradient plasticity provide a rational basis to understand: (1) brittle fracture in the presence of plasticity (quasi-cleavage), as observed in many material systems, such as metal-ceramic interfaces or ferritic steels at low temperatures [Martínez-Pañeda et al., 2019b]; and (2) the brittle fracture of otherwise ductile steels that have been exposed to embrittlement species [Martínez-Pañeda et al., 2016].
Another interesting research question is: how much do kinematic hardening effects affect crack growth in static/monotonic fracture? Unlike fatigue analysis, isotropic hardening has been the de facto choice for modelling crack growth resistance under static loading. Contrarily, we show that kinematic/anisotropic plastic hardening effects, so far neglected, play a fundamental role under monotonic loading due to non-proportional straining as the crack advances. Our numerical results show that fracture toughness values can easily duplicate when these kinematic hardening effects are accounted for [Martínez-Pañeda and Fleck, 2018; Juul et al., 2019]. The results could have important implications for R-curve based damage assessment.
COMPUTATIONAL FRACTURE METHODS
The past two decades have witnessed a dramatic growth in the development of computational tools for fracture mechanics, despite the challenges associated with modelling evolving discontinuities. Attention has shifted from the analysis of stationary cracks (computation of stress intensity factors and J-integral) to the modelling of crack growth and other complex features such as branching, merging or fragmentation. Our contributions can be classified into three fronts.
First, we have contributed to the success of cohesive zone models. On the one side, we developed new control algorithms that enable capturing crack growth using cohesive elements without convergence problems [Martínez-Pañeda et al. 2017] and eliminating the iterative procedure intrinsic to steady state analyses [Juul et al., 2019]. This has enabled us to compute R-curves and explore the influence of crack tip dislocation hardening and plastic dissipation [Martínez-Pañeda and Fleck, 2018; Martínez-Pañeda et al., 2019]. On the other side, we have developed Abaqus2Matlab [Papazafeiropoulos et al., 2017], a comprehensive piece of software that couples Abaqus and Matlab, enabling (for example) estimating the cohesive parameters by means of neural networks.
Second, we have contributed to the development of the eXtended Finite Element Method (X-FEM) by presenting a new X-FEM non-linear framework for elastic-plastic solids [Martínez-Pañeda et al., 2017]. The scheme is capable of capturing the stress elevation due to strain gradients by means of suitably defined asymptotic functions. In addition, it includes (i) higher order elements, (ii) a linear weighting function for the blending elements, (iii) an iterative solver for nonlinear systems and (iv) an appropriate triangular integration scheme.
Third, we have embraced the remarkable success of the phase field fracture method with relish. The phase field fracture method is a very robust tool, with sound underlying physics (based on the concepts of fracture energy and a process zone) and capable of capturing complex crack phenomena, such as crack nucleation at arbitrary sites, crack growth along complex trajectories, and branching and coalescence of multiple cracks. Our contributions lie in the development of (1) a phase field formulation for functionally graded materials [Hirshikesh et al., 2019], (2) a multi-physics deformation-diffusion-fracture framework, particularised to the case of hydrogen embrittlement [Martínez-Pañeda et al., 2018], and (3) quasi-Newton monolithic solution schemes, that reveal notable computational gains [Kristensen and Martínez-Pañeda, 2020].
SMALL SCALE TESTING METHODOLOGIES
Miniature testing devices and techniques are gaining increasing traction due to their capabilities in performing material assessment in an (almost) non-destructive manner. Among the different experimental techniques proposed, the Small Punch Test is particularly popular, as it has proven capable of reliably characterising the mechanical response when little material is available – i.e., heat-affected zones, irradiated material, etc.
We have aimed at extending the success of the Small Punch Test to the assessment of fracture properties by introducing different notched geometries, to accommodate different triaxiality conditions [Cuesta et al., 2019]. We have also presented new hybrid experimental-numerical methodologies based on the crack tip opening displacement [Martínez-Pañeda et al., 2016]. Understanding damage initiation and subsequent failure required conducting Gurson-type analyses of material failure [Martínez-Pañeda et al., 2016b]. And, more recently, we have employed the Small Punch Test to characterise additively manufactured metallic [Cuesta et al., 2019] and polymer samples [Cuesta et al., 2019]. These research achievements are being exploited commercially by the spin-off company KHIS group.
MECHANICS OF FUNCTIONALLY GRADED MATERIALS
There is an emerging interest in the analysis of the mechanical response of materials with spatially varying properties. New manufacturing technologies make it possible to engineer materials with functionally graded microstructures, so-called functionally graded materials (FGMs). The resulting spatial variation of material properties eliminates stress discontinuities at material interfaces and optimises material performance under non-uniform service conditions. For example, the performance of coatings subjected to large thermal gradients can be significantly improved by using metal-ceramic FGMs, which combine the thermal and corrosive resistance of ceramics with the mechanical strength and high tenacity of metals.
We aim at facilitating this technological disruption by presenting suitable numerical schemes to introduce the gradient in both elastic [Martínez-Pañeda, 2019] and elastic-plastic [Mathew et al., 2019] properties into a finite element framework. In addition, we have devoted efforts to model and understand the fracture of FGMs, which often constitutes the primary design criterion. The challenge lies in capturing the complex crack trajectories that arise as a consequence of the crack tip mode mixity induced by the spatial variation of material properties. We have presented new numerical solutions in the context of the X-FEM [Martínez-Pañeda & Gallego, 2015] and phase field fracture [Hirshikesh et al. 2019] methods that show a very satisfactory agreement with experimental observations.
(If using these codes for research or industrial purposes please remember to cite the associated paper.)
- FEniCS Python script for phase field fracture. Download here.
- Abaqus UEL subroutine for higher order strain gradient plasticity (Gudmundson, 2004). Download here.
- Abaqus UEL subroutine for phase field fracture and hydrogen diffusion. Download here.
- Abaqus UEL subroutine for the phase field fracture method. Download here.
- Control algorithm for convergence problems in crack propagation studies. Download Abaqus input files here.
- Matlab script with the predictive hydrogen assisted cracking model of Martínez-Pañeda, Niordson and Gangloff. Download here.
- Abaqus2Matlab: a toolbox to connect Abaqus and Matlab (see www.abaqus2matlab.com). Download here.
- Abaqus USDFLD subroutine to implement functionally graded materials. Download here.
- Matlab non-linear X-FEM code for elasticity, von Mises plasticity and mechanism-based strain gradient plasticity. Download here.
- Abaqus UEL subroutine for cohesive elements, including cyclic damage. Download here.
- Abaqus UMAT subroutine for Mechanism-based Strain Gradient (MSG) plasticity. Download here.
I had the fortune to collaborate with very bright academics and their contributions cannot be acknowledged enough. These include, among others, Norman Fleck (University of Cambridge), Vikram Deshpande (University of Cambridge), Christian Niordson (Technical University of Denmark), Covadonga Betegón (University of Oviedo), Rick Gangloff (University of Virginia), Stéphane Bordas (University of Luxembourg), Lorenzo Bardella (University of Brescia), Bob McMeeking (UCSB), Rafael Gallego (University of Granada), George Papazafeiropoulos (NTUA), Ivan Cuesta (University of Burgos), Miguel Muniz-Calvente (University of Oviedo) and Sundar Natarajan (IIT Madras).
We are grateful for the past and present support of our research by the following sponsors: the Engineering and Physical Sciences Research Council (EPSRC), the Royal Commission for the 1851 Exhibition, the Danish Hydrocarbon Research and Technology Centre (DHRTC), the University Institute of Industrial Technology of Asturias, the Spanish Ministry of Science and Innovation, the University of Oviedo, the Technical University of Denmark and Imperial College London.
Predicting structural failure in aggressive environments, University of Nottingham, 2019
Predicting damage and failure in aggressive environments, Cranfield University, 2019
Towards virtual testing in the energy sector: reliable modelling of hydrogen assisted fracture, Institution of Mechanical Engineers, 2019
Predictive modelling of hydrogen assisted cracking, University of Seville, 2019
Predictive modelling of hydrogen assisted fracture, Texas A&M, 2019
Adventures in mechanics: unravelling hydrogen embrittlement and other challenges, MIT (Massachusetts Institute of Technology), 2019
Towards Virtual Testing in Hydrogen-Rich Environments, Danish Center for Applied Mathematics and Mechanics, 2018
Predictive modeling of hydrogen assisted cracking – a Micromechanics conquest, University of Cambridge, Bio & Micromechanics Seminar Series, 2018
Strain gradient plasticity – numerical modelling and implications for fracture and hydrogen embrittlement, Queen Mary, University of London, 2018
Predictive modelling of environmentally assisted cracking – a micromechanics conquest, Carlos III University of Madrid, 2017
Mechanism-based modelling of hydrogen embrittlement, University of Virginia, 2017
Mechanism-based modeling of hydrogen assisted cracking: gradient effects, boundary conditions and cohesive zone models, NTNU Trondheim, 2017
Gradient effects in fracture and damage, IMDEA Materials, 2016
A mechanism-based framework for hydrogen assisted cracking, Technical University of Denmark, 2019
Strain gradient plasticity: numerical modelling and fracture assessment, University of Cambridge, 2016
Numerical modeling of size effects in metal plasticity, University of Granada, 2016
Modeling size effects in metal plasticity with particular emphasis on fracture, University of Luxembourg, 2015