Phase-field modeling of stress-induced precipitation and kinetics in engineering metals
Doktorsavhandling, 2020

The formation of brittle compounds in metals operating in corrosive environments can be a tremendous source of embrittlement for industrial structures and such phenomenon is commonly enhanced in presence of stresses. To study this type of microstructural change modeling is preferred to experiment to reduce costs and prevent undesirable environmental impacts. This thesis aims at developing an engineering approach to model stress-induced precipitation, especially near stress concentrators, e.g. crack tips, for multi-phase and polycrystalline metals, with numerical efficiency.

In this thesis, four phase-field models are developed and applied on stress-induced hydride precipitation in zirconium and titanium alloys. The energy of the system is minimized through the time-dependent Ginzburg-Landau equation, which provides insights to the kinetics of the phenomenon. In these models, the driving force for precipitation is the coupling between the applied stress and the phase transformation-induced dilatation of the system. Models 1-3 implicitly incorporate near crack-tip stress fields by using linear elastic fracture mechanics so that only the phase-field equation is solved numerically with the finite volume method, reducing the computational costs. Phase transformation is investigated for intragranular, intergranular and interphase cracks in single- and two-phase materials by considering isotropy and some degrees of anisotropy, grain/phase boundary energy, different transition orders and solid solubility limit. Model 4 allows representing anisotropy connected to lattice mismatch and the orientation of the precipitates influenced by the applied stress. The model is employed through the finite element program Abaqus, where the fully coupled thermo-mechanical solving method is applied to the coupled mechanical/phase-field problem. Hydride growth is observed to follow the near-crack tip hydrostatic stress contours and can reach a steady state for specific conditions. The relation between hydride formation kinetics and material properties, and stress relaxation are well-reflected in the results.

With the presented approaches, precipitation kinetics including different kinds of defects, multi-phase microstructures, phase/grain boundaries, order transitions and loading modes can be successfully captured with low computational costs. They could therefore contribute to the numerical efficiency of multi-scale environment-assisted embrittlement prediction schemes within commercial software serving engineering projects.

phase-field theory

finite element method


finite volume method

phase transformation


hydrogen embrittlement

linear elastic fracture mechanics

VDL (Virtual Development Laboratory), Chalmers Tvärgata 4C, Gothenburg, Sweden
Opponent: Professor Reinhart Pippan, Austrian Academy of Science, Austria


Claudio Nigro

Chalmers, Industri- och materialvetenskap, Konstruktionsmaterial

In their operating environment, metals can undergo a modification of their material properties. In specific cases, the formation of compounds, such as rust, more brittle than the rest of the material, can induce a decrease of the carrying capacities of a metallic structure. Such phenomena combined to the application of a mechanical load can lead to drastic material failures. In nuclear power plant and space rockets, some key structures are exposed to hydrogen, whose interaction with titanium or zirconium-based materials can give rise to hydrogen embrittlement through the formation of brittle hydride.

To prevent dramatic outcomes, the study of such phenomena appears clearly necessary. In order to reduce the costs and possible impacts on the environment, the means of simulation is preferred to experiment. In this thesis, mathematical models and numerical methodologies, based on modern tools, such as phase field theory, linear elastic fracture mechanics and finite element method, are developed and analyzed to investigate the formation of material compounds in metallic structures operating in specific environments and loading conditions. A particular attention is given to the formation of hydride near opening crack tips, areas of high stress concentration. The models and methods presented in this thesis allow to capture many relevant aspects with numerical efficiency.

In the future, the integration of such models and methodologies in commercial software could contribute to the increase of cost and time efficiency of engineering projects.



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Doktorsavhandlingar vid Chalmers tekniska högskola. Ny serie: 4804



VDL (Virtual Development Laboratory), Chalmers Tvärgata 4C, Gothenburg, Sweden

Opponent: Professor Reinhart Pippan, Austrian Academy of Science, Austria

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