On the Ductility at Plastic Localisations in Steel Structures

Abstract

High-strength steels offer the benefit of weight, size and cost reductions in structural applications, but their use has seen limitations owing to concerns about their higher yield-to-tensile strength ratio (σ_y/σ_u) relative to lower-strength steels. A maximum limit on the σ_y/σ_u ratio is imposed as a material requirement by various steel structural design standards, product specifications and material certification rules, due to the σ_y/σ_u ratio's connection to strain hardening and the amount of plastic deformation that can be sustained without the loss of strength at locally collapsing or locally straining zones. However, the σ_y/σ_u ratio acts only as an indirect indicator of structural ductility, being one of the many factors that affect the plastic deformation capacity of a structure and whose effect and relevance vary with the structural context. This thesis hence investigates the role and applicability of the σ_y/σ_u ratio as a ductility requirement in steel design, in view of other important material and geometrical properties, with a focus on improving the assessment of ductility in steel structures, towards more efficient and confident use of steels with high σ_y/σ_u. Two mechanisms of plastic localisation that affect the structural ductility are identified as being critical to the present stipulation of σ_y/σ_u limits in design practice: local buckling in plastic hinges in stocky beams subject to bending and ultimate ductile fracture of cracked structural details.

For the plastic hinge rotation capacity of stocky beams, welded I-section high-strength steel beams are considered in this thesis, due to their widespread use in steel structures. A parametric study using a finite-element modelling approach validated by experiments in the literature, taking into account welding residual stresses, geometrical imperfections and plastic strain hardening behaviour, is performed to investigate the role of the σ_y/σ_u ratio in the plastic buckling response. Not only does the σ_y/σ_u ratio play an important role in this context, the maximum allowable σ_y/σ_u for ensuring a certain rotation capacity at a plastic hinge depends on the yield strength σ_y, the slenderness of the flange, the slenderness of the web, and the relative slenderness between the flange and web. The local ductility requirements relating to plastic hinge rotation can be made more efficient if they are made to be dependent on the σ_y, σ_y/σ_u and cross-sectional slenderness.

The maximum σ_y/σ_u ratio has also been considered to function as an indirect provision for ductility where localised tensile plastic straining is expected to occur (such as notched and cracked details). This was initially based on the concept of delaying the onset of necking instability in the structure but has subsequently come to be seen as part of a set of substitute upper-shelf toughness requirements for ensuring that the ultimate strength of structural details susceptible to cracking assumed in design can be achieved. This σ_y/σ_u requirement is implemented alongside a minimum tensile test fracture elongation (Α) and a minimum Charpy value for the avoidance of brittle fracture behaviour. However, the mechanical basis for the use of σ_y/σ_u and Α in this capacity is lacking. Recently, there has been a growing trend towards the use of minimum upper-shelf Charpy energies C_v as a better upper-shelf ductility indicator, but a clear consensus on the implications of this for the use of σ_y/σ_u and Α has yet to emerge. Furthermore, even C_v is not a direct measure of fracture toughness. The most direct way to assess the upper-shelf toughness is to perform fracture toughness tests, such as the pre-cracked single-edge notched bending tests, but these tests are deemed too costly and complicated to implement for general material certification purposes. Often, correlations between the upper-shelf notch toughness in terms of C_v and the fracture toughness in terms of the J-integral are used to estimate the material’s fracture toughness from Charpy tests. The existing correlations, however, are predominantly based on empirical findings and have not systematically considered if and how variations in the σ_y/σ_u and Α might affect the correlation between the notch toughness and the fracture toughness.

In light of this, a parametric damage-mechanics approach is used to investigate how the correlation between the notch toughness C_v from Charpy impact tests and the critical ductile fracture initiation toughness J_Q from quasi-static fracture tests is affected by changes in the fracture elongation Α, yield strength σ_y and yield-to-tensile strength ratio σ_y/σ_u obtained from tensile testing. To this end, a phenomenological rate-dependent plasticity model coupled with damage and temperature effects is developed. The validity of the modelling approach is shown by its ability to simultaneously model the tensile test, the Charpy V-notch test and the precracked single-edge notched bending test. This is demonstrated for two steels, AH36 and S690QL, capturing the force-displacement responses and the characteristic ductile fracture mechanism of slant fracture in all three tests. The applicability of simplifying assumptions used to reduce the damage model complexity while maintaining its ability to simulate the mechanical response in key tests covering an important range of stress states is exemplified. The insights gained are used to reduce the calibration effort needed for the subsequent parametric study on the correlation between material certificate data (σ_y/σ_u, Α, C_v), damage mechanics parameters and fracture toughness.

First, a correlation based on regression between the damage parameters and the mechanical properties from mill test certificates is found by calibrating the damage parameters assuming a range of material certiciate properties typical of S690Q steels. Then, the correlation between C_v and J_Q is assessed by simulating the single-edge notched bending test for the varying mill test certificate properties (σ_y/σ_u, Α, C_v), taking into account how the damage parameters change with these mechanical properties. It is seen that although varying σ_y/σ_u and Α has some effect on how the total notch energy C_v is correlated to J_Q, it does not reflect a significant effect on the ductile fracture initiation toughness but is rather associated with the fact that the C_v includes a significant portion of energy for stable ductile propagation and fracture occurring at the specimen's free surface, while J_Q primarily concerns the early, onset stage of stable ductile tunnelling behaviour at the centre of the specimen. The σ_y/σ_u and Α are seen to have an even smaller effect on the correlation between J_Q and the energy (C_vm) dissipated up to the occurrence of the peak force in the instrumented Charpy test, in comparison with the C_v--to--J_Q correlation, especially for low C_vm.

As a result of the investigation of these two key mechanisms, a shift towards more context-specific ductility criteria, accounting for the structure's failure mechanism and geometry as well as properties obtained from material testing, is recommended. Additionally, the current use of σ_y/σ_u and Α as part of a set of substitute upper-shelf toughness requirements has little basis, with σ_y/σ_u and Α showing weak correlations to ductile fracture resistance. Instead, the use of upper-shelf notch toughness parameters like C_v and C_vm, which better correlate with ductile fracture initiation toughness, is recommended as a more suitable proxy for direct fracture toughness testing. Along the way, a valuable modelling approach for damage mechanics whose relevance extends beyond the present research objectives has been demonstrated, involving a calibration process that is centred around a small number of easily accessible engineering properties and realising complex fracture simulations with reduced calibration effort.