Abstract
Much research has been done on the fracture of ship hulls due to collision or grounding; especially over the past two decades, where emphasis has been on advancing relevant nonlinear finite element analysis techniques. These simulations typically involve prediction of hull fracture/rupture, and may be validated against laboratory or field trials experiments ranging in complexity from uniaxial tensile tests to large-scale grillage fracture. Generally, validation efforts ignore the sliding motion of the “struck object;” with the notable exception of Rodd [8], who mounted 1/5th scale hull side-shell modules to a sled and impacted them against a cone-shaped “rock” composed of steel. For the case of steady-state plate cutting, which is typical of stranding, grounding, and oblique collision events, the sliding motion is intrinsic to the nature of the structural response (i.e. without sliding motion, there is no plate cutting), and is captured by existing analysis tools.
There has been, however, comparatively little focus (except [1], [5], [6], and [7]) on the case of sliding hull loads resulting from grounding on a soft/wide bottom, or due to hull impact with ice. Both scenarios do not implicitly assume that fracture occurs, and the development of the hull structural response from initial impact to the (potential) point of fracture is of great interest. Typically, these scenarios – particularly impacts with ice features – are simplified to exclude tangential load motion. [1] and [6] predicted numerically that this simplification is unrealistic and unconservative, and [7] confirmed these predictions experimentally.
Numerically, the development of fracture due to sliding loads depends on the damage history from the sliding load, the fracture model chosen, and the method of implementation of that fracture model. Quinton [7], using laboratory experiments, showed that nonlinear hull response due to sliding loads (without fracture) exhibits a significantly reduced hull capacity when compared with stationary loads of similar magnitude. This “capacity loss” increased with increasing plastic damage on the trailing side of the sliding load (i.e. increasing damage history). Regarding the fracture model, it is presently common in nonlinear finite element analysis to assume that the ductile fracture of steel (aluminum and some other marine materials) occurs at some equivalent strain that is: 1. a constant (i.e. a point), 2. a function of stress triaxiality (i.e. a line) [3], or 3. a function of stress triaxiality and Lode parameter (i.e. a surface) [2]. Additionally, considering temperature and/or strain-rate effects changes the point, line or surface (as appropriate to the fracture model). Implementation of a fracture model in finite element simulations is non-trivial, and numerous methods are available (e.g. the GISSMO model, the cohesive element approach [4], and the phenomenological approach (e.g. [9]). The application of these approaches to sliding induced fracture, however, is well beyond the scope of this paper; which instead focuses on the development of (i.e. changes in) stress triaxiality and Lode parameter in plates and frames subject to sliding loads; and hence the development of the point of onset of fracture based on the initial choice of fracture model.
REFERENCES
[1] Alsos, Hagbart S. "Ship Grounding - Analysis of Ductile Fracture, Bottom Damage and Hull Girder Response." PhD Norwegian University of Science and Technology (NTNU), 2008.
[2] Bai, Yuanli, and Tomasz Wierzbicki. "A New Model of Metal Plasticity and Fracture with Pressure and Lode Dependence." International Journal of Plasticity 24.6 (2008).
[3] Bao, Yingbin, and Tomasz Wierzbicki. "On Fracture Locus in the Equivalent Strain and Stress Triaxiality Space." International Journal of Mechanical Sciences 46.1 (2004).
[4] Cirak, Fehmi, Michael Ortiz, and Anna Pandolfi. "A Cohesive Approach to Thin-Shell Fracture and Fragmentation." Computer Methods in Applied Mechanics and Engineering 194.21–24 (2005).
[5] Hong, L., and J. Amdahl. "Rapid Assessment of Ship Grounding Over Large Contact Surfaces." Ships and Offshore Structures 7.1 (2012).
[6] Quinton, B. W. T. "Progressive Damage to a Ship’s Structure due to Ice Loading." Master of Engineering Memorial University of Newfoundland, 2008. Print.St. John's, Newfoundland.
[7] Quinton, B. W. T. "Experimental and Numerical Investigation of Moving Loads on Hull Structures." PhD Memorial University of Newfoundland, 2015. St. John's, NL.
[8] Rodd, James L. "Large Scale Tanker Grounding Experiments". Proceedings of the Sixth (1996) International Offshore and Polar Engineering Conference. May 26-31, 1996, Los Angeles.
[9] Woelke, Pawel B., and Najib N. Abboud. "Modeling Fracture in Large Scale Shell Structures." Journal of the Mechanics and Physics of Solids 60.12 (2012).
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Sliding Loads and their Effect on the Stress Triaxiality and Lode Parameter Responses of Plates and Frames 
