Plastic Collapse Behavior and Remaining Life Assessment of Statically Indeterminate Cracked Beam ¾ Using the Limit Analysis Technique Sung-Po Liu Department of Mechanical Engineering, Ching Yun University, Jung-Li, Taiwan 320, R.O.C. Abstract This paper develops an analytical model for the plastic collapse of a statically indeterminate rectangular beam containing a crack. Limit analysis, elastic-plastic fracture mechanics, compliance, and J-integral concepts are used to study J IC and dJ/da, which influence the crack propagation in this study. The relations among the plastic hinge, applied load, linear displacement, rotational angle, and crack growth lead to a better understanding of the problem. The LBB (Leak-Before-Break) characteristic of the statically indeterminate rectangular beam is valid if the crack propagates before plastic collapse. Unstable ductile fractures occur when the crack propagates before plastic collapse or when dJ/da is smaller than the minimum critical value. The life span of the crack extension to collapse can be computed by the 4 th order of the Runge-Kutta method. The information provided in this study can be applied to safe and reliable design structures. These analyses and design strategies developed in this paper are useful for the safety performance of a structural beam under crack deformation. Key Words: Elastic-Plastic Fracture Mechanics, Crack Propagation Resistance, Crack Growth, Statically Indeterminate Beam, Leak-Before-Break 1. Introduction Most research in the past twenty years has dealt with forces, displacements, buckling, torsion, etc. in structural mechanics; the deformation analysis was considered a boundary value problem [1-3]. The principles of virtual work, energy, and limit analysis of plastic structures helped solve many other problems in structural engineer- ing. The study of this field became exciting, particularly since Van den Broeck proposed the limit-design theory [4]. The limit-design theory is valuable for its framework structure. However, the traditional research of limit- strength analysis had not been applied to the cracked sys- tem, which means there was no consideration of fracture mechanics. This type of research is urgent for the stati- cally indeterminate framework structure. Based on the reports of previously published litera- ture, the relationship between plastic-collapse load and plastic-collapse displacement by combines the limit an- alysis theory and the elastic-plastic fracture mechanics that can be applied to the constrained condition of opti- mization by minimizing the crack extension resistance dJ/da [5]. As a result, this paper proposed an innovative method to analyze and evaluate the loading status and plastic collapse behavior of statically indeterminate framework structures containing a crack. The present model and analysis deals with three considerations that must be noticed and solved: (1) The structure and support can generate some degree of deformation in machines and structures relating to energy conversion. These structures naturally be- come statically indeterminate framework. It is neces- sary to understand the mechanism of plastic be- havior, of collapse, and the interactive influence of each member in order to evaluate the true safety mar- gin and create a design based on the Leak-Before- Journal of Applied Science and Engineering, Vol. 15, No. 4, pp. 333-342 (2012) 333 *Corresponding author. E-mail: [email protected]
Plastic Collapse Behavior and Remaining Life Assessment of Statically Indeterminate Cracked Beam Using the Limit Analysis Technique
Jun 24, 2023
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