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Innovative Multi-scale/Multi-physics based Tool for Predicting Fatigue Crack Initiation and Propagation in Aircraft Structural Components using Phase Field Model Technique


TECHNOLOGY AREA(S): Air Platform, Space Platforms

ACQUISITION PROGRAM: PMA-299, H60 Helicopter Program

OBJECTIVE: Develop innovative Phase Field Model (PFM) within numerical framework of Isogeometric Analysis (IGA) for metallic materials subjected to fatigue loading to predict 3D crack topology under complex service loading situations.

DESCRIPTION: Fatigue cracks initiate and grow in complex stress fields in aircraft components subjected to service loadings, exhibiting the 3D nature of the problem. There are no consistent and apparent criteria for many aspects of fatigue crack growth spanning from micro to macro levels. Simulations of a fatigue crack, embedded within a grain or across several grains, require estimates of crack front behavior and an algorithm for growth considering crack size, shape, microstructure and grain boundaries. The challenges associated with modeling fatigue cracks growth stems from the inherent complexity of interaction between material’s microstructure and cracks, whether transgranular or intergranular type cracks. One of the main challenges is the numerical modeling of evolution of discontinuities such as cracks in the continuum medium. Although numerical approaches such as Finite Element Method (FEM) and Boundary Element Method (BEM) and their variants exist to evaluate crack propagation, they need complex re-meshing operations and have other difficulties in studying cracks at microstructural level. Therefore, a model that can appropriately address the underlying mechanisms of crack initiation, propagation, and its interaction with material’s microstructure such as grain boundaries is highly desirable.

Recently, the phase field method has emerged as a powerful method to simulate crack propagation. The method automatically regularizes stress singularities by introducing a smoothly varying scalar field that distinguishes between “intact” and “broken” phases of the material and can also be interpreted as a phenomenological measure of damage. The phase field model is formulated as coupled dynamical equations for the phase and displacement fields that are derived variationally from an energy function with both elastic strain and surface energy contributions. Phase field equations incorporate both the short scale physics of materials failure and macroscopic elasticity. In addition, these equations can be simulated on parallel computer architecture to describe geometrically complex dynamical phenomenon such as crack nucleation, crack kinking and branching, and crack front segmentation in three dimensions. One of the main advantages of PFM is that there are no ad hoc rules or conditions needed to determine crack nucleation, propagation, or bifurcation. Another advantage is that the solution from the PFM method can be obtained by finite element and isogeometric analysis (IGA) discretization methods which make it more appealing from the modeling perspective. Isogeometric analysis provides an efficient, smooth basis for computation. Once the problem is recast in terms of isogeometric analysis framework, the additional smoothness requirements are met with minimal computational cost.

As such, computational models are desired for fatigue crack nucleation and propagation that alleviates the complexity of re-meshing and can track the crack tip in complex microstructures, while at the same time can be efficiently implemented in an efficient computational framework. The phase field model technique in conjunction with isogeometric analysis that utilizes the geometric model, can provide the solution which does not require any criteria for crack initiation and propagation under random spectrum loading including environmental effects.

Phase field model development will be required in order to link spatial and temporal evolution of complex crack patterns to the external applied load by utilizing finite element and iso-geometric analysis (IGA) discretization methods. Starting with an initial 2D analysis, the PFM model has to describe the complex phenomena of 3D crack evolution at a microscale as well as the final fracture at the macroscale. The proposed PFM model may include an appropriate plasticity model to study load interactions occurring in complicated loading situations such as variable amplitude loading. Finite element based numerical implementations of the PFM crack propagation under dynamic loading is desirable. Furthermore, the application of PFM to dynamic ductile fracture needs to be further explored, addressing the limitations and assumptions and enhancements as needed.

Collaboration with an original equipment manufacturer (OEM) in all phases is encouraged, but not required, to assist in defining aircraft integration and commercialization requirements.

PHASE I: Determine the feasibility to develop a PFM modeling technique based on finite element and isogeometric analysis (IGA) discretization methods to model complex 3D crack patterns under service loading at micro scale as well as the final fracture at the macroscale. Develop guidelines for defining the free energy function in terms of the order parameter, elastic and plastic strains, etc., to be used in the PFM. Show the capability of the PFM model in modeling crack interaction with material’s microstructure such as grain boundary.

PHASE II: Based on Phase I effort the small business will continue to address and develop the PFM modeling capability in a systematic way to move from a qualitative visualization to a quantitative assessment. Show how the PFM model can predict 3D crack nucleation, propagation, branching and interaction under complex load spectrum. Test and validate the model by closely following crack propagation test data set for complex loading.

PHASE III DUAL USE APPLICATIONS: Integrate the developed fatigue crack initiation and propagation analysis package into processes at the FRC’s, and potentially work in conjunction with the original equipment manufacturers for analysis of repairs and new designs. Methods and techniques developed can be folded into commercial software package for broad use in a wide variety of industrial applications in estimating the life of a variety of safety critical structures.


    • Miehe, C., Hofacker, M., Welschinger, M. (2010). A phase field model for rate-independent crack propagation: Robust algorithmic implementation based on operator splits. Computer Methods in Applied Mechanics and Engineering 199 2765-2778.


    • Miehe, C., Hofacker, M., Welschinger, M. (2010). A phase field model for rate-independent crack propagation: Robust algorithmic implementation based on operator splits. Computer Methods in Applied Mechanics and Engineering 199 2765-2778.


    • Borden, M.J., Hughes, T.J.R., Landis, C.M., Verhoosel, C.V. A higher-order phase-field model for brittle fracture: Formulation and analysis within the isogeometric analysis framework. Computer Methods in Applied Mechanics and Engineering 273 (2014) 100–118.


  • Oshima, K., Takaki, T., Muramatsu, M. Development of multi-phase-field crack model to express crack propagation in polycrystal. APCOM & ISCM, 11-14th December (2013) Singapore.

KEYWORDS: Crack Growth; Multi Scale Modeling; Isogeometric; Phase Field Method; Crack Initiation; Finite Element Analysis

  • TPOC-1: 301-342-0297
  • TPOC-2: 301-757-2427

Questions may also be submitted through DoD SBIR/STTR SITIS website.

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