Ultimate strength of cracked plate elements under axial compression or tension
Introduction
Steel structures such as ships, offshore platforms and land-based structures are prone to suffer various types of damage as they get older. Corrosion and fatigue cracking may be the two most important types of damage in aging structures. Clearly, in such cases the structures that started out being adequate may become marginal later in life or even reach the catastrophic failure state.
It is of crucial importance to estimate the residual strength of damaged structures for many reasons. For instance, it is essential to seek rational standards for structural integrity of aging structures without economic penalties with respect to the repair and maintenance costs incurred over the lifetime cycle of the structure, while risk or reliability assessment scheme is normally applied for that purpose.
Within the scheme of the ultimate limit state based risk or reliability assessment for aging structures, closed-form expressions for predicting the ultimate strength of structural members taking account of the effect of structural damages are required. In the present paper, a relevant theoretical model for predicting the ultimate strength [16] of a steel plate element under axial compression or tension, where cracking damage is treated as a parameter of influence, is studied.
Under the action of repeated loading, fatigue cracks may be initiated in the stress concentration areas of the structure. Initial defects or cracks may also be formed in the structure by inappropriate fabrication procedure and may conceivably remain undetected over time. In addition to propagation under repeated cyclic loading, cracks may also grow in an unstable way under monotonically increasing extreme loads, a circumstance which eventually can lead to catastrophic failure of the structure. This possibility is of course usually tempered by the ductility of the material involved, and also by the presence of reduced stress intensity regions in a complex structure that may serve as crack arresters even in an otherwise monolithic structure.
For residual strength assessment of aging steel structures under extreme loads as well as under fluctuating loads, it is thus often necessary to take into account a known or premised crack as a parameter of influence. In the rare situation when the structure has been weakened by large cracks or large scale plasticity associated with cracks, resulting in a decrease of structural stiffness, large deformations are likely to develop [1].
Fig. 1 shows a schematic representation of the nonlinear behavior of cracked steel structures under monotonic loading. It is noted that for similar structures the stiffness and ultimate strength of cracked structures is smaller than those of uncracked structures.
A large number of studies on the fatigue fracture and ultimate limit load of cracked steel plates under cyclic loading have been previously undertaken in the literature, but there are a few contributions to the ultimate strength behavior of cracked plates under monotonic loading [2], [3], [4], [5], [6], [7], [8], [9], [10]. Furthermore, the prime concern of these previous studies is limited to the study on the behavior of the cracked structure under tensile loading or to the estimation of elastic buckling strength. To the author's knowledge, there are a few systematic contributions to the elastic–plastic large deflection behavior of cracked steel plates under axial tension/compression [11], each of which is a primary load component in ships, offshore structures and other steel structures.
The aim of the present study is to obtain insights into the ultimate strength behavior of ductile structures given one or more cracks, and to be able to indicate how to use such knowledge within the current framework of ultimate strength calculation for a complex structural system.
In this regard, the objectives of the present study are (i) to investigate the ultimate strength reduction characteristics of a steel plate with fatigue cracking and under monotonically applied axial tension/compression, and (ii) to develop theoretical models for predicting the ultimate strength of plate elements with fatigue cracking and under axial tension or compression.
It is to be noted, however, that the present study does not aim to address fracture related critical crack length considerations. Procedures exist for undertaking critical crack length estimates for a given level of tensile loading using fracture mechanics [1], [12].
A series of the ultimate strength tests on cracked steel plate structures under axial tension or compression are carried out varying the crack sizes and locations. A series of ANSYS [13] elastic–plastic large deflection finite element analyses are also carried out on cracked steel plates under axial tension or compression. Based on the experimental and numerical results obtained, relevant design formulae for the ultimate strength of cracked plates are developed.
Section snippets
Structural idealization of cracked steel plates
Fig. 2 shows a steel plate element bounded by support members in a continuous stiffened plate structure subjected to axial loads. The x-axis of the plate is in any one reference direction and the y-axis is in the direction normal to the x direction. The plate length and breadth are denoted by a and b, respectively. The plate thickness is t.
The material of plates used in steel plated structures such as ships and offshore structures is normally either mild steel or high tensile steel, with yield
Theoretical model to predict the plate ultimate tensile strength
To predict the ultimate tensile strength of a steel plate with premised cracking, it is sometimes considered that the plate may reach the ultimate strength if the stress intensity factor for the so-called Mode I crack deformation exceeds a critical value [1], [12], namelywhere KI is the stress intensity factor for the so called Mode I deformation which unfolds the crack, KIc is the critical value of KI at which the onset of unstable crack propagation occurs. While KI is theoretically
Theoretical model to predict the plate ultimate compressive strength
While a crack in a panel under axial compressive loading may close and buckling may then occur, it is also possible that some lateral deflection may take place either because of initial deformations or additional local out-of-plane loading. After buckling, lateral deformation is a near certainty. In such cases with lateral deformation, the crack can affect (reduce) the panel collapse strength as out-of-plane deformation increases. It may, therefore, be pessimistically assumed that the effect of
Concluding remarks
In the present study, the ultimate strength reduction characteristics of a steel cracked plate subjected to axial tension/compression have been investigated both experimentally and numerically. Based on the results developed from the present study, the following conclusions can be drawn:
- (1)
It is evident that the fatigue cracking damage reduces the ultimate strength of a steel plate significantly.
- (2)
A possibly simpler and intuitive model is studied to predict the ultimate strength of a cracked plate
Acknowledgements
The present study was undertaken with support from the American Bureau of Shipping and the 2002 Korea Sea Grant Program of the Korea Ministry of Maritime Affairs and Fisheries. The authors are pleased to acknowledge their support. The effort of Dr Bong Ju Kim regarding ANSYS computations is appreciated.
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