Periodic Reporting for period 1 - M3TiAM (Multiscale-Multiphysics Modelling of Ti alloy medical implants based on Additive Manufacturing technology)
Reporting period: 2023-02-01 to 2025-01-31
Bone is the second most transplanted tissue in the world, with a total of over four million operations using bone grafts or bone replacement materials. 5% of people who receive an implant, such as hip replacement, may require a revision surgery within 10 years, and 15% may need a revision surgery within 20 years; as a result, numerous patients will require at least one implant replacement in their lifetime. In the United States of America alone, over 635000 hip replacements and 72000 hip revision surgeries per year are expected by 2030. Common causes of such surgeries include bone fracture near the implant, implant wear, fracture, and loosening.
From a structural point of view, a limitation of most currently used metallic materials for implants (e.g. titanium alloy Ti-6Al-4V) is their Young’s modulus poorly matching that of the surrounding bones generating stress-shielding. In this context, Additive Manufacturing (AM) recently emerged as a breakthrough technology, enabling patient-customized implants based on complex scaffold materials. AM metallic implants based on titanium (Ti) alloy scaffolds can closely match the bone geometry, local properties and functionalities, allowing to reduce stress-shielding, promote angiogenesis, improve osteoconduction; leading to a remarkable increase in the patients’ quality of life. As a counterpart, AM produces parts with non-equilibrium microstructures, for instance martensitic phase in Ti-6Al-4V, and microvoids that reduce the fatigue performance. One way of tuning mechanical properties of Ti alloys is by means of post-processing heat treatments, which results in phase transformations, microstructure coarsening, and microvoid elimination. While common across a broad range of applications, heat treatments to tune the properties of metallic alloys have been relatively less explored for biomedical implants. In the meantime, theory, modelling, and simulation methods have emerged, which now afford quantitative and predictive simulations of microstructural evolution, but also the effect of different microstructures on the material properties and lifetime.
The M3TiAM project (Multiscale-Multiphysics Modelling of Ti alloy medical implants based on Additive Manufacturing technology) specifically aims at developing computational tools to predict the influence of post-processing on the microstructure and mechanical properties of scaffolds structures, in order to guide and accelerate the design of novel Ti-based implants, down to the level of microstructural design. On the long term, such tools will contribute to the making of a robust closed-loop quality control system, which could be seemingly integrated with in-process monitoring and feedback control systems.
In order to achieve this goal, the underlying specific objectives are proposed:
- Develop an efficient microscale Phase Field-Fast Fourier Transform model (PF-FFT) to predict the microstructure evolution of Ti alloys during post-processing (process-sensitive-model).
- Develop an efficient microscale Crystal Plasticity-Fast Fourier Transform model (CP-FFT) to predict the macroscopic elasto-plastic behaviours of α+β Ti alloys taking into account microstructural features (structure-sensitive-model).
- Experimental characterization of microstructure features and mechanical testing of representative additively manufactured samples, in order to validate and calibrate PF-FFT and CP-FFT models.
From a structural point of view, a limitation of most currently used metallic materials for implants (e.g. titanium alloy Ti-6Al-4V) is their Young’s modulus poorly matching that of the surrounding bones generating stress-shielding. In this context, Additive Manufacturing (AM) recently emerged as a breakthrough technology, enabling patient-customized implants based on complex scaffold materials. AM metallic implants based on titanium (Ti) alloy scaffolds can closely match the bone geometry, local properties and functionalities, allowing to reduce stress-shielding, promote angiogenesis, improve osteoconduction; leading to a remarkable increase in the patients’ quality of life. As a counterpart, AM produces parts with non-equilibrium microstructures, for instance martensitic phase in Ti-6Al-4V, and microvoids that reduce the fatigue performance. One way of tuning mechanical properties of Ti alloys is by means of post-processing heat treatments, which results in phase transformations, microstructure coarsening, and microvoid elimination. While common across a broad range of applications, heat treatments to tune the properties of metallic alloys have been relatively less explored for biomedical implants. In the meantime, theory, modelling, and simulation methods have emerged, which now afford quantitative and predictive simulations of microstructural evolution, but also the effect of different microstructures on the material properties and lifetime.
The M3TiAM project (Multiscale-Multiphysics Modelling of Ti alloy medical implants based on Additive Manufacturing technology) specifically aims at developing computational tools to predict the influence of post-processing on the microstructure and mechanical properties of scaffolds structures, in order to guide and accelerate the design of novel Ti-based implants, down to the level of microstructural design. On the long term, such tools will contribute to the making of a robust closed-loop quality control system, which could be seemingly integrated with in-process monitoring and feedback control systems.
In order to achieve this goal, the underlying specific objectives are proposed:
- Develop an efficient microscale Phase Field-Fast Fourier Transform model (PF-FFT) to predict the microstructure evolution of Ti alloys during post-processing (process-sensitive-model).
- Develop an efficient microscale Crystal Plasticity-Fast Fourier Transform model (CP-FFT) to predict the macroscopic elasto-plastic behaviours of α+β Ti alloys taking into account microstructural features (structure-sensitive-model).
- Experimental characterization of microstructure features and mechanical testing of representative additively manufactured samples, in order to validate and calibrate PF-FFT and CP-FFT models.
During the execution of M3TiAM project, the following activities were carried out:
- Development of a novel phase-field model to predict the microstructure evolution of additive manufactured Ti64 alloy parts during post heat treatments (specifically: martensite α’ decomposition into a stable or metastable α+β microstructure).
- Development of linear and non-linear solvers, based on FFT, to compute the solution of the coupled partial differential equations involved in the problem.
- Implementation of the resolution scheme in Python environment with GPU parallelization.
- Coupling the phase-field model with CalPhaD calculations (ThermoCalc software) to compute the chemical potential of alloying elements as a function of temperature.
- Development of a Matlab tool, based on MTEX package, to generate the initial condition of the phase-field model from experimental EBSD maps.
- Development of two Crystal Plasticity FFT models to predict the macroscopic elastoplastic behaviour of Ti64 additively manufactured samples with a microstructure obtained after heat treatments. Both models are based on the FFTMAD solver developed at IMDEA, in a Python environment.
- Characterization of grain microstructure, in particular SEM microscopy and EBSD maps, of as-built Ti64 samples with martensitic microstructure.
- Development of a Matlab tool, based on MTEX utility, for reconstruction of parent β grain.
- Development of heat treatment of as-built samples, under different time and temperature conditions, using a dilatometry equipment with Argon protective atmosphere to record, in-situ, the kinetics of the transformation.
- Development of a novel phase-field model to predict the microstructure evolution of additive manufactured Ti64 alloy parts during post heat treatments (specifically: martensite α’ decomposition into a stable or metastable α+β microstructure).
- Development of linear and non-linear solvers, based on FFT, to compute the solution of the coupled partial differential equations involved in the problem.
- Implementation of the resolution scheme in Python environment with GPU parallelization.
- Coupling the phase-field model with CalPhaD calculations (ThermoCalc software) to compute the chemical potential of alloying elements as a function of temperature.
- Development of a Matlab tool, based on MTEX package, to generate the initial condition of the phase-field model from experimental EBSD maps.
- Development of two Crystal Plasticity FFT models to predict the macroscopic elastoplastic behaviour of Ti64 additively manufactured samples with a microstructure obtained after heat treatments. Both models are based on the FFTMAD solver developed at IMDEA, in a Python environment.
- Characterization of grain microstructure, in particular SEM microscopy and EBSD maps, of as-built Ti64 samples with martensitic microstructure.
- Development of a Matlab tool, based on MTEX utility, for reconstruction of parent β grain.
- Development of heat treatment of as-built samples, under different time and temperature conditions, using a dilatometry equipment with Argon protective atmosphere to record, in-situ, the kinetics of the transformation.
The following results were reached:
1) Efficient new solver for phase-field simulations of microstructure evolution during solid-state phase transformations. Phase-field models for microstructure formation are among the most versatile, powerful, and consequently nowadays widespread tools to simulate complex microstructure formation and evolution. Still, their computational limitations, in terms of accessible length and time scales, is well acknowledged, thus motivating the development of advanced accelerated solvers. In this project, we developed linear and non-linear high efficiency algorithms to solve coupled partial differential equations (phase-field equations), leveraging fast Fourier transforms (FFT) and Graphics Processing Units (GPU) massive parallelization. It has allowed to reduce the computational time (by three orders of magnitude), or alternatively to increase the accuracy (also by several orders of magnitude) for a comparable computational cost. While the model was developed in the scope of martensite decomposition (α’ to α+β) in additively manufactured Ti64 alloys, the similarity of mathematical formulation makes it applicable across many areas of science and engineering (essentially to nearly any diffusion-limited phase transformation).
2) Simulation tool for the efficient exploration of heat treatments in additively manufactured Ti64 alloy. Additive manufacturing technology based on powder-bed or wire feedstock fusion, applied to part production of Ti64 alloy presents some challenges because the as-built microstructure is martensitic – i.e. a kinetically stabilized metastable α’ phase presenting a fine lath microstructure with high strength but very poor ductility, making its use limited as is. Post heat treatments are thus necessary to obtain an α+β stable microstructure, which allows to improve ductility, while potentially retaining a high strength inherited from the α’ martensite lath structure. To date, the optimization of such heat treatment (e.g. annealing time and temperature) has been performed through costly and inefficient trial-and-error experimental campaign, which could be significantly reduced (i.e. accelerated) by appropriate simulation tools, which may also give a deeper understanding of the underlying mechanisms. Most of the published model in the literature were based on mean-field equation such as Avrami, which are not capable to simulate the detailed grain morphological evolution, critical to the resulting high strength of the material. In this project, for the first time, a phase field model was developed to simulate Ti64 martensite transformation into α+β phases. This model is expected to have an important impact because extend the applicability of phase-field technique to solid state transformation in Ti alloys and provides a novel tool to explore and optimize heat treatment processes in 3D printed Ti64 alloy.
3) Microstructure-aware micromechanical model for 3D printed and post-process Ti64 alloy. Additive manufactured parts are characterized by an elongated grain morphology due to the nature of solidification (often proceeding through epitaxial growth across several deposited layers). From an experimental point of view, the effect of these grain in the anisotropic mechanical response is well acknowledged. Yet computationally efficient simulation tools to correlate microstructures and properties in such complex microstructures (e.g. ultrafine α+β) remained lacking. The mechanical model developed in this project will allow to assess the influence of elongated prior β grains on the resulting martensitic α’ and final α+β structure, and to quantify the degree of anisotropy as a function of grain distribution.
4) Industrial impact. Along the project, we establish a strategic collaboration with a strategic industrial stakeholder, which could become a main user of the developed tools. Renishaw is one of the World leaders in developing laser powder-bed fusion equipment for 3D additive manufacturing of metals. We hold several meetings with engineers at Renishaw Iberica (Renishaw Spanish branch) in order to demonstrate our capabilities and offer to help them improve their customer recommendation for postprocessing (so far established based on expert knowledge linking processing conditions to resulting properties, but without in-depth consideration of the underlying microstructure). They sent us a few printed samples, for us to characterize (in as-built and heat treated conditions). While this task also remains in progress, we are expected to pursue it beyond the scope of the project, which could lead to the accelerated optimal selection of annealing parameters to obtain strong yet tough ultra-fine α+β microstructures.
1) Efficient new solver for phase-field simulations of microstructure evolution during solid-state phase transformations. Phase-field models for microstructure formation are among the most versatile, powerful, and consequently nowadays widespread tools to simulate complex microstructure formation and evolution. Still, their computational limitations, in terms of accessible length and time scales, is well acknowledged, thus motivating the development of advanced accelerated solvers. In this project, we developed linear and non-linear high efficiency algorithms to solve coupled partial differential equations (phase-field equations), leveraging fast Fourier transforms (FFT) and Graphics Processing Units (GPU) massive parallelization. It has allowed to reduce the computational time (by three orders of magnitude), or alternatively to increase the accuracy (also by several orders of magnitude) for a comparable computational cost. While the model was developed in the scope of martensite decomposition (α’ to α+β) in additively manufactured Ti64 alloys, the similarity of mathematical formulation makes it applicable across many areas of science and engineering (essentially to nearly any diffusion-limited phase transformation).
2) Simulation tool for the efficient exploration of heat treatments in additively manufactured Ti64 alloy. Additive manufacturing technology based on powder-bed or wire feedstock fusion, applied to part production of Ti64 alloy presents some challenges because the as-built microstructure is martensitic – i.e. a kinetically stabilized metastable α’ phase presenting a fine lath microstructure with high strength but very poor ductility, making its use limited as is. Post heat treatments are thus necessary to obtain an α+β stable microstructure, which allows to improve ductility, while potentially retaining a high strength inherited from the α’ martensite lath structure. To date, the optimization of such heat treatment (e.g. annealing time and temperature) has been performed through costly and inefficient trial-and-error experimental campaign, which could be significantly reduced (i.e. accelerated) by appropriate simulation tools, which may also give a deeper understanding of the underlying mechanisms. Most of the published model in the literature were based on mean-field equation such as Avrami, which are not capable to simulate the detailed grain morphological evolution, critical to the resulting high strength of the material. In this project, for the first time, a phase field model was developed to simulate Ti64 martensite transformation into α+β phases. This model is expected to have an important impact because extend the applicability of phase-field technique to solid state transformation in Ti alloys and provides a novel tool to explore and optimize heat treatment processes in 3D printed Ti64 alloy.
3) Microstructure-aware micromechanical model for 3D printed and post-process Ti64 alloy. Additive manufactured parts are characterized by an elongated grain morphology due to the nature of solidification (often proceeding through epitaxial growth across several deposited layers). From an experimental point of view, the effect of these grain in the anisotropic mechanical response is well acknowledged. Yet computationally efficient simulation tools to correlate microstructures and properties in such complex microstructures (e.g. ultrafine α+β) remained lacking. The mechanical model developed in this project will allow to assess the influence of elongated prior β grains on the resulting martensitic α’ and final α+β structure, and to quantify the degree of anisotropy as a function of grain distribution.
4) Industrial impact. Along the project, we establish a strategic collaboration with a strategic industrial stakeholder, which could become a main user of the developed tools. Renishaw is one of the World leaders in developing laser powder-bed fusion equipment for 3D additive manufacturing of metals. We hold several meetings with engineers at Renishaw Iberica (Renishaw Spanish branch) in order to demonstrate our capabilities and offer to help them improve their customer recommendation for postprocessing (so far established based on expert knowledge linking processing conditions to resulting properties, but without in-depth consideration of the underlying microstructure). They sent us a few printed samples, for us to characterize (in as-built and heat treated conditions). While this task also remains in progress, we are expected to pursue it beyond the scope of the project, which could lead to the accelerated optimal selection of annealing parameters to obtain strong yet tough ultra-fine α+β microstructures.