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Reporting period: 2019-09-01 to 2021-08-31

Fatigue behavior of metallic alloys is controlled by the number of cycles necessary to nucleate a crack and that necessary to propagate the crack until a critical size. The former (including the propagation of very short cracks whose length is comparable to the grain size) is the dominant one in the case of high cycle fatigue and often very important in low cycle fatigue. It is also well established, from the qualitative viewpoint, that fatigue crack nucleation and the propagation is highly dependent on the microstructure (grain boundary, grain size, texture, twin, precipitates), while the quantitative influences of each microstructural feature is missing particularly in HCP metals.

The objective of the MAFMA was to understand the deformation and fracture mechanisms of Mg alloys during cyclic deformation and to establish the effect of the microstructural features on the mechanisms of fatigue crack nucleation in Mg alloys using a combination of in-situ mechanical tests and simulations at different length scales within the spirit of integrated computational materials engineering.

In summary, experimental tests showed that fatigue cracks were mainly nucleated at high-angle grain boundaries around small grains or parallel to slip bands (pyramidal or basal) and to twin interfaces in large grains. This information was integrated within a physically-based crystal plasticity model and the fatigue life of Mg alloys was predicted using computational homogenization of a representative volume element of the microstructure by means of fatigue indicator parameters which were partially based on the newly observed fatigue crack nucleation mechanisms. In addition, a coupled crystal plasticity/phase field model was developed to include in the simulations the lattice rotation associated with twinning (twinning was only included as a pseudo-slip mechanism in the crystal plasticity framework), which will provide a more realistic simulation of nucleation of fatigue cracks near twin boundaries. Finally, molecular dynamics simulations were carried out to understand the effect of precipitates on dislocation glide and twin migration. The achievement of this project will allow to design novel Mg alloys with improved fatigue resistance.
Works with clear measurable details:
1) Measure the fatigue life and cyclic stress strain curves. Fatigue tests in an extruded Mg-RE alloy and a AZ31b commercial alloy were carried out to measure the cyclic stress strain curve and the fatigue life. This information was used to determine the parameters for the crystal plasticity model to simulate the mechanical response and the fatigue indicator parameters to predict the fatigue life.
2) Determine fatigue crack initiation mechanisms. Micro-crack nucleation events were investigated by means of in situ fatigue experiments. It was found that cracks were nucleated at grain boundaries with large misorientation angle as well as along basal, prismatic and pyramidal slip traces and parallel to twin interfaces in large grains. The micro-crack length and location data will be used to develop fatigue life predication tools.
3) Develop modelling tools for magnesium alloy deformation. A CP-PF-FEM model was developed where twin migration was governed by phase field equations. The new model takes into account the explicit crystal lattice rotation caused by matrix-twin transformation.
4) Investigate the influence of precipitates on hardening. The effect of precipitates on dislocation glide and twin migration as well as the effect of grain size on twin growth rate was analyzed by means of MD simulations.

Peer-reviewed scientific journal papers using ArXiv as the repository:
A.Jamali A.Ma J. Llorca, “Influence of grain size and grain boundary misorientation on the fatigue crack initiation mechanisms of textured AZ31 Mg alloy”. Scripta Materialia, 207, 114304, 2022.
M.Zhang H. Zhang, A.Ma J.Llorca “Experimental and numerical analysis of cyclic deformation and fatigue behavior of a Mg-RE alloy”. International Journal of Plasticity. 139, 102885, 2021.

Finished drafts:
M.Zhang A.Ma J.Llorca “Modelling of twinning deformation in magnesium by CPFEM coupled with a phase field model”, ready for submission.
A.Ma G.Esteban-Manzanares J.Llorca “Atomistic simulations of precipitation hardening on twin propagation in Mg-Al-Zn alloys”, ready for submission.

International conferences:
A.Jamali M.Zhang A.Ma J.LLorca. "Experimental analysis and numerical simulation of cyclic deformation and Fatigue behavior of AZ31 Mg alloy". Virtual TMS 2021, 150th Annual Meeting and Exhibition, March 2021. (invited)
A.Jamali M.Zhang A.Ma J.LLorca. "Cyclic deformation mechanisms and fatigue life prediction of AZ31 Mg alloy". 12th International Conference on Magnesium Alloys and their Applications (Mg 2021), June 2021.
A.Ma G.Esteban-Manzanares J.Llorca “Atomistic simulations of precipitate/twin interactions in Mg-Al-Zn alloys “, 25 International Congress of Theoretical and Applied Mechanics (ICTAM), Milan (Italy), 23-28 August 2020.
G.Esteban-Manzanares I.Papadimitriou R.Alizadeh A.Ma J.LLorca. “Precipitate strengthening in Mg alloys: atomistic simulations and experimental observations”. XV International conference on Computational Plasticity COMPLAS 2019, Barcelona, Spain, September 2019. (keynote)
M.Zhang H.Zhang A.Ma J.LLorca. “Modelling and experimental analysis of fatigue of Mg-RE alloys”. EUROMAT 2019, Stockholm, Sweden, September 2019. (invited)

Possible exploitations as well as the way to exploit:
1)Application of our crystal plasticity/phase field model (based on the commercial software Abaqus) to simulate the deformation of Mg components including explicitly the lattice rotation associated within twinning.
2)The approach based on microstructure-informed fatigue indicator parameters is a significantly step forward to predict the fatigue life of available Mg alloys, taking into account the actual fatigue crack initiation mechanisms. From the experimental information of grain size and texture, representative volume elements of the microstructure can be built and used to predict the fatigue life of Mg alloys. This information can be used to design new microstructures with improved fatigue resistance.
According to the Europe police (EV5V-CT94-0375) Magnesium alloys are potential metals to be progressively introduced in structural components in many areas, especially in transport to reduce weight and achieve required CO2 reductions. As the deformation and failure mechanisms of Mg alloys are very complicated owing to basal slip, prism slip, primed slip and twinning, there lack reliable continuum level constitutive models for engineering application.
1)Progress was made for one of the most challenging open questions of Mg alloys, i.e. the influence of twin and grain boundaries on the fatigue crack nucleation and growth by using rigorously scale-bridged models and in-situ experiments.
2)The outcome of this interdisciplinary research proposal was published in high impact peer-reviewed journals and at international conferences.
3)The approach and the code developed in this proposal will improve the predictive power of Integrated Computational Materials Engineering concerning Mg alloy industry.
4)It was expected that the achievement of this project will allow to design novel Mg alloys with improved fatigue resistance.
Crystal plasticity modelling of cyclic stress-strain curves.
Slip traces and micro-cracks. Red lines for twins, green for pyramidal slip.