Interaction of delaminations and matrix cracks in a CFRP plate, Part II: Simulation using an enriched shell finite element model
Introduction
The state-of-the-art in aerospace structural design, when using composite materials, is to rely heavily on testing for certification [2], [3], [4]. The ability to simulate progressive damage in composite materials can reduce the need for expensive testing and could thereby reduce the cost of using composite laminate materials in aerospace structures. Reliable and robust numerical damage simulation tools are not available for composite laminates as they are for legacy materials such as aluminum or steel. The damage simulation tools that do exist are generally expensive, often to a prohibitive level, because of the time and expertise required for their use. Furthermore, existing tools cannot always simulate progressive damage problems of the complexity and extent found in real scenarios. If reliable and affordable damage simulation tools were available for composites, certain tests could be replaced with simulations, resulting in cheaper, lighter, and overall more efficient composite structures [5], [6], [7]. Additionally, an efficient simulation tool may allow for better component design early in the design process and prevent costly redesigns.
While there are examples dating back to the 1970s and 1980s [8], [9], numerical simulation of damage in composites did not begin in earnest until computational advances enabled the widespread use of the finite element method. In the 1990s, numerical techniques for damage simulation began to be implemented into finite element models [10], [11], [12]. Since then, progressive damage simulation in laminates has advanced considerably, due partially to advances in computational technology, but also due to advances in numerical simulation methods. The Virtual Crack Closure Technique (VCCT), which is used to predict energy release rate at a crack tip, is one such method [13]. VCCT is computationally efficient and does not suffer from mesh refinement requirements and convergence difficulties associated with cohesive zone (CZ) models [14], a commonly used alternative method. However, predicting damage initiation is not an inherent capability of VCCT, so, unlike CZ models, an initial crack is required.
Simulating a progressive damage process often requires the consideration of interacting transverse matrix cracks and delaminations. Many state-of-the-art models are combinations of several simulation techniques, including continuum damage mechanics (CDM), the eXtended Finite Element Method (XFEM), VCCT, and CZ [15], [16], [17], [18], [19], [20], [21], [22]. These models, usually necessitating a 3D high-fidelity mesh with at least one element per ply in the thickness direction, can be useful and accurate in some cases, but often the complexity of a real damage scenario, which may consist of dozens of delaminations and matrix cracks, exceeds their capabilities. Additionally, the time and user expertise required for these types of simulations often is only available in research or academic settings.
Use of shell element models may offer an alternative. Shell elements have long been used by industry and have proven to be a cost effective analysis tool, albeit, for problems less complex than laminate damage simulation. Use of shell element models for laminate damage simulation, however, introduces a number of challenges, including prediction and representation of transverse matrix cracks and delaminations at multiple interfaces. Previously, use of shell elements for progressive damage simulation has consisted of either a global-local approach [23], where the actual damage simulation takes place in a high mesh fidelity region attached to an otherwise lower mesh fidelity model; or by stacking layers of shell elements to form a laminate [24], [25], [26], [27], [28].
Ideally, in terms of computational efficiency, ease of use, and predictive utility, a thin laminate plate would be modeled as a single layer of shell elements in which delaminations could form and propagate at any location in the layup. This type of approach can be thought of as having adaptive fidelity, in that the model is defined initially in low-fidelity (one shell element thick) and remains in this state everywhere, except where delamination occurs and multiple mesh layers are required. This requirement, dictated by a damage prediction criterion, may change and be updated throughout an analysis solution procedure as damage grows.
Simulation models based on shell elements that use adaptive fidelity have been proposed and studied only recently. Larsson presented a shell element in 2004 [29] which treats delamination as a discontinuity in the displacement field in a shell formulation and uses a CZ to predict growth. Similarly, Brouzoulis et al. [30], [31], [32] have developed a shell element that uses XFEM and CZs to simulate growth of multiple delaminations and transverse matrix cracks in a shell element. Their work is ongoing, but while showing promise, has not yet advanced to the point of being able to simulate a realistic progressive damage problem of the extent and complexity found in real scenarios.
McElroy presented the formulation of an adaptive fidelity shell (AFS) model for use in progressive damage simulation [33], [34]. The model was verified for mixed mode delamination simulation and validated experimentally using a delamination-migration test. The goal of this paper is to present validation of the AFS model for damage scenarios of a higher complexity level than previously considered. A biaxial-bending test will be utilized to this end. The test was presented by McElroy et al. in Part I of this two-part paper series, in which a damage process consisting of multiple delaminations interacting via transverse matrix cracks occurs in a carbon fiber reinforced polymer specimen [1]. In addition to validation of the AFS model, a high mesh fidelity (HF) simulation of the same test is performed to provide insight as to the improvement in efficiency of the shell model, compared to a typical existing state-of-the-art technique.
Section snippets
Adaptive fidelity shell model
The AFS element is designed to offer a progressive damage simulation tool that is significantly more efficient than existing alternatives. The efficiency is improved because: (1) the runtime is greatly reduced by use of a composite shell element instead of a high-fidelity 3D mesh to represent a laminate of multiple plies differing in orientation and (2) the inherent simplicity of the model allows for a faster model definition and verification procedure by the user.
A thorough description of the
High mesh fidelity model
The high mesh fidelity (HF) model was used in this study as an example of a typical state-of-the-art HF approach so that the efficiency offered by the AFS model compared to an existing state-of-the-art technique could be evaluated. The HF model utilizes a previously developed CDM technique [44] combined with a physically-based damage initiation method that is implemented in volumetric elements as a user defined material subroutine (UMAT) in Abaqus 6.14/Standard. Following initiation,
Biaxial-bending test summary
An experiment, inspired by Canturri et al., [45], was designed to create a progressive damage process in a carbon fiber reinforced polymer (CFRP) specimen that consists of 2–3 delaminations growing at different interfaces and interacting with one another via transverse matrix cracks. The specimens, square in shape and containing a quarter circle Polytetrafluoroethylene (PTFE) insert in one corner, were clamped on the two edges opposite the insert. A displacement-controlled quasi-static
Numerical simulations
Experimental results from the tests presented previously by McElroy et al. in Part I of this paper [1] are compared to results from the AFS and high mesh fidelity numerical simulations. Each model uses the same geometry, load conditions, and material properties for carbon epoxy system IM7/8552 [1]. The material properties, strength properties, and damage parameters used in the simulations were obtained from Camanho [46] and are shown in Table 1. The specimen geometry was designed to limit the
Conclusion
An enriched shell element model was used to efficiently simulate a progressive damage process in a composite laminate.The numerical results were compared to an experiment which was designed to create 2–3 delaminations occurring at different interfaces and interacting via matrix cracks in a laminate. The enriched shell model, referred to as the adaptive fidelity shell (AFS) model, is based on use of the Floating Node Method and the Virtual Crack Closure Technique. Overall, the AFS model was
Acknowledgments
The research was funded by and performed at NASA Langley Research Center and Swerea SICOMP. The authors would like to thank Dr. Robin Olsson, Dr. Nelson de Carvalho, Dr. Erik Saether, and Dr. T. Kevin O’Brien for their advice and consultation concerning this body of work.
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