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Novel Method to Utilize Multi-scale Physics-based Technique for Crack Path Determination in Fiber-reinforced Composites
Navy SBIR 2016.1 - Topic N161-010 NAVAIR - Ms. Donna Attick - [email protected] Opens: January 11, 2016 - Closes: February 17, 2016 N161-010 TITLE: Novel Method to Utilize Multi-scale Physics-based Technique for Crack Path Determination in Fiber-reinforced Composites TECHNOLOGY AREA(S): Air Platform, Space Platforms ACQUISITION PROGRAM: PMA 275, V-22 Osprey OBJECTIVE: Develop an innovative technique utilizing peridynamic theory to determine crack path in fiber-reinforced composite structures. DESCRIPTION: Accurate prediction of crack growth behavior is essential in determining inspection intervals and maintenance schedules of aerospace structures where failure could lead to catastrophic consequences and loss of life. The financial costs involved when an in-service component is found to contain a defect is a major factor in the search for numerical methods to predict 3-D crack propagation. Damage initiation and subsequent propagation in fiber-reinforced composites are not understood as clearly as metals because of the presence of stiff fibers within soft matrix material causing inhomogeneity. Failure of fiber-reinforced composites involves a progressive series of events with discrete failure modes such as matrix cracking, fiber-matrix shear, fiber breakage and delamination. The presence of such failure modes result in stiffness reduction. This leads to stress redistribution in the layers and constituents. The ability to predict crack path progression in fiber-reinforced composite structures is essential in the design of new aircraft and the sustainment of legacy fleet. This effort will provide a pro-active approach in the design of next generation air vehicles as they will be constructed from lighter, stronger materials such as fiber-reinforced composites. Reliable methods to predict 3-D crack propagation will reduce maintenance inspections and life of in-service components can be extended providing huge monetary savings. Lack of predictive capability for crack propagation paths in fiber-reinforced composite structures under cyclic loading continues to prevail despite the extensive amount of research. Simulating damage initiation and subsequent global structural failure is one of the most active topics in computational mechanics. Several mathematical models and numerical methods have been developed over the years to assess various limit states such as failures due to permanent deformation, cracks, or de-cohesion/delamination in composite materials. Current numerical methods are damage based or rely on discrete cracks. They are generally computationally expensive and require a fine scale description of structural and mechanical properties. Although the existing failure criteria for isotropic materials are applied to many problems with acceptable success, there still exist challenges when predicting the evolution of an arbitrary crack shape that may be non-planar. Often these are multiple cracks exhibiting complex pattern forming within non-planar 3-D surfaces. The presence of manufacturing or service related residual stresses and the sequence of load interactions introduces additional challenges, requiring more complicated numerical techniques. Existing numerical methods for calculating fracture parameters encounter challenges due to this topological evolution. Although mature, powerful, and versatile, finite element analysis (FEA) simply fails to predict failure initiation and complex crack growth because the FEA formulation is not mathematically suitable for the simulation of failure. The standard theory of classical continuum mechanics has certain limitations when addressing crack initiation and growth in materials because partial differential equations of motion include spatial derivatives of displacement components which are not valid in the presence of displacement discontinuities such as cracks. An alternative theory, known as the peridynamic theory, is a nonlocal theory that does not require spatial derivatives and removes the obstacles concerning the prediction of crack initiation and growth in materials based on classical continuum mechanics. Peridynamic theory is formulated using integral equations as opposed to derivatives of displacement components. This feature allows crack initiation and propagation at multiple sites, with arbitrary paths inside the material, without resorting to external crack growth criteria. Peridynamic theory has the capability to handle multi-scale modeling for both length and time, and address discontinuities and non-linearity. Peridynamic theory has the potential to serve as a basic model across all scales, avoiding the difficulties inherent in multi-model coupling. In addition, peridynamic theory has the ability to efficiently link with many microscale models including molecular dynamics. There is a need for a novel physics based method to determine the crack growth and path in fiber-reinforced composite structures using peridynamic theory. The proposed computational models must underpin the true physical processes rather than empirical correlations and deal with mechanisms operating at different length scales. This capability will provide insight into crack initiation, growth in fiber-reinforced composite materials, and enable improved failure prediction and remaining useful life estimation. This effort will produce a theoretical basis, technique and tool that can be integrated into a continuum code for crack path prediction and that is computationally efficient and accurate. PHASE I: Demonstrate the feasibility of an analytical technique/method for crack path prediction in fiber-reinforced composite structures using peridynamic theory and applying this method for example case studies. Compare the results obtained from proposed peridynamic approach with available finite element or other advanced methods using benchmark problems. PHASE II: Develop and demonstrate a prototype tool utilizing the multi-scale/multi-physics based framework developed in Phase I. Demonstrate the use of tool through the analysis of a representative component of interest. Implement the proposed model in a continuum code for crack path prediction in simulated service conditions while validating with experimental data. PHASE III DUAL USE APPLICATIONS: Transition the multi-scale/multi-physics tool for use with commercially available computational tools to predict fiber-reinforced composite damage progression on Navy aircraft platforms. The results of this research will be useful in design of new aircraft as well as sustainment of in-service fleet. The software will determine the crack growth and path in fiber-reinforced composite structures and help in predicting remaining useful life. The developed technology will be integrated with existing computational software, making it commercially available to address the design and in-service maintenance issues faced by many industries besides naval applications such as space, commercial aircraft, etc. REFERENCES: 1. Silling, SA. (2000). Reformulation of Elasticity Theory for Discontinuities and Long-Range Forces. Journal of Mechanics and Physics of Solids, Vol. 48, pp. 175-209. Retrieved from http://link.springer.com/article/10.1007/s10704-013-9925-1 2. Silling, SA., Epton M., Weckner O., Xu J., & Askari, A. (2007). Peridynamics States and Constitutive Modeling. Journal of Elasticity, Vol. 88, pp. 151-184. Retrieved from http://link.springer.com/chapter/10.1007/978-3-319-00771-7_24 3. Madenci, E. & Oterkus, E. (2013). Peridynamic Theory and its Applications. Springer, New York. Retrieved from http://link.springer.com/chapter/10.1007/978-1-4614-8465-3_2 4. Kilic, B., Agwai, A. & Madenci, E., (2009). Peridynamic Theory for Progressive Damage Prediction in Centre-Cracked Composite Laminates. Composite Structures. Vol. 90, pp. 141-151. Retrieved from http://link.springer.com/article/10.2478/s13531-012-002 5. Timbrell, C., Chandwani, R., and Cook, G. (2004). State of the art in crack propagation. Journee Scientifique Les methodes de dimensionnement en fatigue, Centre de Competences Materiaux & Conception (CCM&C), Fribourg,Switzerland. 6. Seleson, P., Parks, ML., Gunzberger M., & Lehoucq, RB.(2009). Peridynamics as an Upscaling Of Molecular Dynamics. Multiscale Modeling Simulations. Society for Industrial and Applied Mathematics. Vol. 8, No. 1, pp. 204�227. KEYWORDS: Fatigue; multi-scale; crack path; fiber-reinforced composites; physics-based; Peridynamic TPOC-1: 301-342-0297 TPOC-2: 301-757-4103 Questions may also be submitted through DoD SBIR/STTR SITIS website.
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