W.J. Wong
Please Note
9 records found
1
Requirements on the yield-to-tensile strength ratio σy/σu, fracture elongation A and the Charpy energy Cv are used together as part of an indirect method of ensuring sufficient ductility at localised areas of stress and strain concentration in the design of steel structures. Recent studies have found that these indirect requirements could be inadequate in certain situations involving cracks or manufacturing defects. Furthermore, requirements on the σy/σu which are enforced regardless of the structural context and other material properties may unnecessarily constrain the use of steels which nonetheless have high strength, fracture toughness and ductility. In contrast to the σy/σu, A, and Cv, a more direct measurement of a structure’s ability to resist fracture is given by fracture toughness testing, such as J-integral testing, but this is less frequently used, because these tests are significantly costlier than tension and Charpy tests. More often, Charpy tests are performed and correlations between upper-shelf Cv and J values are used to estimate the fracture toughness of the material. However, the existing correlations are predominantly based on empirical findings and have not systematically accounted for the effect of variations in the σy/σu, which has been shown in recent studies to affect the fracture toughness. Using a previously validated coupled damage-mechanics model with rate- and temperature-dependent plasticity and damage softening, this paper investigates the correlation between Cv and JQ (the critical J) numerically, including how it is affected by other material certificate properties such as the σy/σu and A. 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 for a large database of these steels. Then, the correlation between Cv and JQ is assessed by simulating the single-edge-notch bending test for a range of varying mill test certificate properties, taking into account how the damage parameters vary with these mechanical properties. The results are analysed to give better insight into how the notch toughness correlates to the fracture toughness, taking the σy/σu and A into account. It is seen that although varying σy/σu and A has some effect on how the total notch energy Cv is correlated to JQ, it does not reflect a significant effect on the ductile fracture initiation toughness but is rather associated with the fact that the Cv includes a significant portion of energy for stable ductile propagation and fracture occurring at the specimen’s free surface, while JQ primarily concerns the onset stage of stable ductile tunnelling behaviour at the centre of the specimen. The σy/σu and A are seen to have an even smaller effect on the correlation between JQ and the energy (Cvm) dissipated up to the occurrence of the peak force in the instrumented Charpy test, in comparison with the Cv–to–JQ correlation, especially for low Cvm.
Empirically derived Charpy energy to fracture toughness (J-integral) correlations are often used to estimate the fracture toughness of steels from Charpy tests due to the higher testing costs and time associated with direct fracture toughness tests, but analytical insight into these correlations is lacking. Accounting for differences in the strain rates and stress states in these tests to simulate the correct response in both while keeping model complexity and calibration effort manageable presents an obstacle to a numerical approach for this problem. This paper hence establishes a modelling and calibration approach that could be used to contribute mechanics-based insight into the correlations between the Charpy energy, J-integral, yield-to-tensile strength ratio and tensile test fracture elongation. A phenomenological rate-dependent plasticity model coupled with damage and temperature effects is developed by implementing the strain-based modified Mohr–Coulomb damage-softening model with Johnson–Cook thermal softening in a thermodynamically consistent Cowper–Symonds viscoplasticity model. The validity of the modelling framework 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. Accounting for thermal softening due to adiabatic heating proves to be important for the accurate simulation of ductile Charpy tests involving high impact energies. Capitalising on weak triaxiality dependence in the middle-to-high triaxiality ranges in the given materials and adopting a triaxiality-independent assumption is found to be effective for reducing the damage model complexity while maintaining its ability to simulate the mechanical response in key tests covering an important range of stress states. The importance of the role of the Lode angle in ductile fracture modelling in weakly triaxiality-dependent regimes is further substantiated. Key similarities in the fracture behaviour of the Charpy and single-edge notched bending tests are identified: they span a similar range of stress states over a large range of their response despite the initial notched versus cracked difference—an insight that could be used to reduce the calibration effort of damage mechanics models for these tests, assuming that the key differentiating factors of rate-dependence and adiabatic heating are correctly accounted for.
On the Ductility at Plastic Localisations in Steel Structures
New Insight from Routine Mechanical Test Properties
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 σy/σu ratio in the plastic buckling response. Not only does the σy/σu ratio play an important role in this context, the maximum allowable σy/σu for ensuring a certain rotation capacity at a plastic hinge depends on the yield strength σy, 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 σy, σy/σu and cross-sectional slenderness.
The maximum σy/σu 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 σy/σu 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 σy/σu and Α in this capacity is lacking. Recently, there has been a growing trend towards the use of minimum upper-shelf Charpy energies Cv as a better upper-shelf ductility indicator, but a clear consensus on the implications of this for the use of σy/σu and Α has yet to emerge. Furthermore, even Cv 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 Cv 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 σy/σu 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 Cv from Charpy impact tests and the critical ductile fracture initiation toughness JQ from quasi-static fracture tests is affected by changes in the fracture elongation Α, yield strength σy and yield-to-tensile strength ratio σy/σu 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 (σy/σu, Α, Cv), 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 Cv and JQ is assessed by simulating the single-edge notched bending test for the varying mill test certificate properties (σy/σu, Α, Cv), taking into account how the damage parameters change with these mechanical properties. It is seen that although varying σy/σu and Α has some effect on how the total notch energy Cv is correlated to JQ, it does not reflect a significant effect on the ductile fracture initiation toughness but is rather associated with the fact that the Cv includes a significant portion of energy for stable ductile propagation and fracture occurring at the specimen's free surface, while JQ primarily concerns the early, onset stage of stable ductile tunnelling behaviour at the centre of the specimen. The σy/σu and Α are seen to have an even smaller effect on the correlation between JQ and the energy (Cvm) dissipated up to the occurrence of the peak force in the instrumented Charpy test, in comparison with the Cv--to--JQ correlation, especially for low Cvm.
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 σy/σu and Α as part of a set of substitute upper-shelf toughness requirements has little basis, with σy/σu and Α showing weak correlations to ductile fracture resistance. Instead, the use of upper-shelf notch toughness parameters like Cv and Cvm, 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. ...
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 σy/σu ratio in the plastic buckling response. Not only does the σy/σu ratio play an important role in this context, the maximum allowable σy/σu for ensuring a certain rotation capacity at a plastic hinge depends on the yield strength σy, 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 σy, σy/σu and cross-sectional slenderness.
The maximum σy/σu 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 σy/σu 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 σy/σu and Α in this capacity is lacking. Recently, there has been a growing trend towards the use of minimum upper-shelf Charpy energies Cv as a better upper-shelf ductility indicator, but a clear consensus on the implications of this for the use of σy/σu and Α has yet to emerge. Furthermore, even Cv 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 Cv 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 σy/σu 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 Cv from Charpy impact tests and the critical ductile fracture initiation toughness JQ from quasi-static fracture tests is affected by changes in the fracture elongation Α, yield strength σy and yield-to-tensile strength ratio σy/σu 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 (σy/σu, Α, Cv), 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 Cv and JQ is assessed by simulating the single-edge notched bending test for the varying mill test certificate properties (σy/σu, Α, Cv), taking into account how the damage parameters change with these mechanical properties. It is seen that although varying σy/σu and Α has some effect on how the total notch energy Cv is correlated to JQ, it does not reflect a significant effect on the ductile fracture initiation toughness but is rather associated with the fact that the Cv includes a significant portion of energy for stable ductile propagation and fracture occurring at the specimen's free surface, while JQ primarily concerns the early, onset stage of stable ductile tunnelling behaviour at the centre of the specimen. The σy/σu and Α are seen to have an even smaller effect on the correlation between JQ and the energy (Cvm) dissipated up to the occurrence of the peak force in the instrumented Charpy test, in comparison with the Cv--to--JQ correlation, especially for low Cvm.
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 σy/σu and Α as part of a set of substitute upper-shelf toughness requirements has little basis, with σy/σu and Α showing weak correlations to ductile fracture resistance. Instead, the use of upper-shelf notch toughness parameters like Cv and Cvm, 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.
Calibration of ductile damage models typically involves significant experimental and reverse engineering effort, due to their stress-state dependent nature. Having access to the calibrated damage parameters for a range of materials could enable finite-element analyses of the fracture performance of the different materials in a structural detail and aid in material selection based on specific criteria such as the ductility or the toughness of the detail. By performing a parametric study and regression analysis using a previously validated rate-and temperature-dependent damage-plasticity model, considering steels with a yield strength between 730 MPa and 850 MPa, this paper presents correlations between easily available material certificate properties and calibrated damage model parameters, developed for the purpose of modelling the standardised single-edge notched bending (SENB) crack-tip opening displacement (CTOD) fracture toughness test. First, the correlations provide a tool for quickly estimating the calibrated parameters for the type of material considered in the study, so that damage mechanics modelling can be used in subsequent parametric investigations and design considerations concerning SENB fracture toughness testing. Second, the correlations give insight into the trends and relative importance of the plasticity and damage parameters in relation to the variations in engineering properties from the widely used tensile test and Charpy test, which are the fracture elongation A and Charpy energy Cv, respectively. By relating the properties obtained from these tests, which involve known stress states at key locations in the test specimens, to the strains in stress-state-dependent damage initiation locus, physical insight is obtained regarding the role of the normalised damage parameters, which are the damage initiation strains. Such information is useful both for understanding how plasticity parameters are related to fracture toughness and for the future calibration of similar materials. Finally, it is found that parametrically varying the yield strength σy and the yield-to-tensile strength ratio σy/σu simultaneously according to observed empirical trends has a small effect on the correlations between notch toughness and damage initiation strains when compared to the significantly larger effect of A. Since the damage initiation strains are directly correlated to the fracture behaviour, the σy /σu ratio’s small influence suggests that it might not be a good choice as a lo cal ductility indicator for a material in terms of ductile fracture, although it is so used in practice, a point which remains to be ascertained through further study of fracture toughness testing and simulation in light of the present findings. By the same token, the existing correlations between Cv and fracture toughness, which have not taken the effect of variations in A and σy/σu into account, should be reconsidered in light of these effects.
Ductile fracture in steels relevant to the offshore and maritime industry is often characterized by the occurrence of slant fracture, which is the development of fracture surfaces that are slanted relative to the original surface of the material. The modeling of this phenomenon is important for describing ductility and fracture toughness accurately in ductile fracture simulations. This work uses a consistency model for viscoplasticity with damage softening within a strain-based framework to investigate the effect of variations in strain hardening and Lode dependence on the slant fracture area and impact energy in Charpy tests. The model is first calibrated to uniaxial tensile, single-edge-notched-bending fracture toughness and instrumented Charpy tests performed on an S690QL steel, and then a parametric study varying the strain hardening and the Lode-dependence is performed. It is seen that an increase in the yield-to-tensile-strength ratio (equivalent to a decrease in the strain hardening exponent) leads to a decrease in the impact energy and negligible difference in the percentage slant fracture area when the damage and rate parameters are kept constant. It is found that the Charpy impact energy is not sensitive to the maximum strains in the fracture strain locus and is mainly affected by the minimum strains in the locus. Finally, the rate-dependent consistency plasticity model with a strain-based damage-softening formulation is capable of simulating slant fracture behavior even in cases where the fracture initiation strain is stress-state-independent and constant.
This article describes a dataset used to calibrate a finite element model of a thick circular hollow section (CHS) with varying d/t (diameter to thickness) ratio under cyclic loading which may be used as a computational model validation benchmark by researchers working on similar problems in structural and mechanical engineering. The test data consists of seven cold-formed S335J2H steel CHS tube specimens tested to buckling failure in low-cycle fatigue under a three-point bending arrangement, instrumented with discrete strain gauges, displacement transducers and string potentiometers together with continuous surface deformation fields obtained by two pairs of digital image correlation (DIC) cameras. ‘Half-cycle’ material data from the uniaxial tensile testing of dog-bone coupons is also provided. Comparisons between measured and simulated entities such as midspan forces, moments, displacements and mean curvatures can be obtained with MATLAB processing scripts. Complete ABAQUS model input files are also provided to aid in benchmarking.
High-strength steel beams are known to have less plastic rotation capacity than beams with lower yield strengths. This has been related to the decreased strain-hardening ability of high-strength steels, and various rules and standards for steel structures stipulate maximum limits on the allowable yield-to-tensile strength ratio ((Formula presented.)), which indirectly acts as a measure of strain hardening. While the literature suggests that there is an interdependence between strain hardening ability, yield strength, cross-sectional slenderness and rotation capacity, the presently prescribed limits on (Formula presented.) (e.g. 0.91, 0.94, 0.95) are typically constant for a given material regardless of the other parameters mentioned. This computational study hence investigates how the rotation capacity is simultaneously dependent on yield strength, strain hardening ability and cross-sectional slenderness, and how each parameter affects the relationship between the others. The results show that, with the geometrical aspect kept constant through the use of normalised slenderness parameters, a higher yield strength leads to higher rotation capacity for a given (Formula presented.), while the well-known decrease of rotation capacity with higher (Formula presented.) is confirmed. This suggests the possibility of more efficient use of high-strength steels with high (Formula presented.) when the interdependence of all the variables are accounted for. The results also suggest the importance of accounting for the relative slendernesses of the web and the flange and whether the buckling behaviour is web- or flange-dominated, since a switch between a web- and flange- dominated buckling response could lead to a reverse in the trend between the rotation capacity and the overall cross-sectional slenderness.
Application of high-strength steels in the maritime and offshore industry is currently limited by rules governing the ratio of the yield to tensile strength (the Y/T ratio). To better understand the physical basis for these rules, the nature and extent of the plastic stress/strain field in the vicinity of a stress concentration (a circular hole) in a structure made from high-strength steel are analyzed. This is done through analytical models of the stress field and the extent of plasticity in the vicinity of a hole based on classical methods. These analytical methods are validated through FEA models that are in turn validated by published experimental data. This paper concludes that a high Y/T ratio leads to a lower plastic SCF and a higher local strain in the vicinity of a hole. The extent of the plastic zone is not affected by different values of Y/T ratio for different values of σnom/σy.
Upper limits on the ratio of the yield strength to the tensile strength (σy/σu ratio) and lower limits on the fracture elongation εf are present in various offshore, maritime and civil engineering rules, standards and specifications for steel structures as a provision for the minimum material ductility and toughness which ensures sufficient structural ductility. In other instances, the design yield stress to be adopted in strength calculations is reduced from its nominal value if the σy/σu ratio exceeds a certain limit. Such requirements deter the use of high strength steels (nominal σy higher than 690 MPa), which inherently have a high σy/σu ratio. To guide subsequent efforts towards optimised and scientifically grounded σy/σu limits and wider application of high strength steels, this paper first presents an overview of the current provisions in engineering practice relating to the σy/σu ratio and structural ductility, and it then discusses the key underlying failure mechanisms to which these ductility requirements are relevant: tensile strain localization, yielding and localization precipitated by stress concentrations, localization of plastic bending hinges and ductile fracture. The reasoning behind the current provisions, the findings of previous research concerning the requirements, and the key potential areas for future research are highlighted.