Crashworthiness and accidental loading simulations of steel maritime structures are often performed using shell elements that might not capture the correct strain and stress localizations post-necking. This work assesses the dominant strain states appearing in such simulations. Moreover, the difference between practical shell simulations and solid simulations is analyzed by applying both elements to several realistic representative blast and impact scenarios with different material models. Strain patterns were then observed and compared between solids and shells. Generalized plane strain deformation dominated all cases where it was either imposed by geometric boundaries or transitioned to them post-necking initiation. Shells were incapable of capturing necking and strain localization reflected by solids within the plate. Results were closer for strain localization at geometric boundaries, but indicative of the role geometric details can play. Shells captured strains due to bending efficiently, but those due to membrane stresses were only captured up to necking initiation.

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.

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 C_v, 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 σ_y and the yield-to-tensile strength ratio σ_y/σ_u 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 σ_y /σ_u 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 C_v and fracture toughness, which have not taken the effect of variations in A and σ_y/σ_u into account, should be reconsidered in light of these effects.

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.

Cohesive zone and eXtended Finite Element Modeling (xFEM) are promising methods for modeling the propagation of a crack using coarse meshes and hence saving considerable computational time. The Traction Separation Law (TSL) that is needed for such techniques is, however, mostly derived a posteriori using experiments. This prevents its widespread utilization in structures without high costs. For example, in the modeling of a compact tension test, the TSL is known to evolve as the crack grows. Qualitative physical explanations have been offered for this phenomenon. Necking ahead of the crack tip is thought to have a large effect on crack propagation, while the necking behavior in any given element is influenced by both the state of stress acting on it and the structural boundaries around it. However, a method to account for those explanations a priori in the TSL doesn’t exist. Here, TSLs are developed for the elements along the known crack path in a middle crack tension test and implemented as a damage model in Abaqus. They are derived solely from the material properties and the element dimensions, thus excluding the need for inverse engineering based on experiments. This paves the way for more general applications of traction separation laws within the maritime and offshore industry.

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.

Rotary forming is a promising technique for high-volume, low-cost production of fuel cell components such as bipolar plates, but it needs to be better characterized for this application. In this paper, die design parameters in rotary forming of ultra-thin stainless steel 316 L sheets 100 μm thick are evaluated to explore how channels perpendicular and parallel to the rolling direction are affected by critical forming process parameters, namely depth of deformation, die corner radius, and friction coefficient. Channels are formed experimentally, and the results are used to verify the 2D and 3D simulations. The process is analysed in terms of die movement path and forming. Stress, strain, formed shape, and thickness are compared for the two main forming directions. Results showed that channels formed parallel to the rolling direction experience more plastic deformation and conform better to the prescribed geometry in terms of channel and flatness angles.

High strength steels are widely used for structural applications, where a combination of excellent strength and ductile-to-brittle transition (DBT) properties are required. However, such a combination of high strength and toughness can be deteriorated in the heat affected zone (HAZ) after welding. This work aims to develop a relationship between microstructure and cleavage fracture in the most brittle areas of welded S690 high strength structures: coarse-grained and intercritically reheated coarse-grained HAZ (CGHAZ and ICCGHAZ). Gleeble thermal simulations were performed to generate three microstructures: CGHAZ and ICCGHAZ at 750 and 800 °C intercritical peak temperatures. Their microstructures were characterised, and the tensile and fracture properties were investigated at − 40 °C, where cleavage is dominant. Results show that despite the larger area fraction of martensite-austenite (M-A) constituents in ICCGHAZ 750 °C, the CGHAZ is the zone with the lowest fracture toughness. Although M-A constituents are responsible for triggering fracture, their small size (less than 1 μm) results in local stress that is insufficient for fracture. Crack propagation is found to be the crucial fracture step. Consequently, the harder auto-tempered matrix of CGHAZ leads to the lowest fracture toughness. The main crack propagates transgranularly, along {100} and {110} planes, and neither the necklace structure at prior austenite grain boundaries of ICCGHAZs nor M-A constituents are observed as preferential sites for crack growth. The fracture profile shows that prior austenite grain boundaries and other high-angle grain boundaries (e.g., packet and block) with different neighbouring Bain axes can effectively divert the cleavage crack. Moreover, M − A constituents with internal sub-structures, which have high kernel average misorientation and high-angle boundaries, are observed to deflect and arrest the secondary cracks. As a result, multiple pop-ins in load-displacement curves during bending tests are observed for the investigated HAZs.

Study of the cleavage behavior of heat treated S690 steel by a microstructure-based approach combined with finite element analysis is present in this paper. Cleavage simulations of steels subjected to heat treatments that cause grain refinement or simulate heat affected zones are performed, and are compared with experiments. It is found that the experimental improvement of toughness from grain refinement is 80% of what would be expected based on the model. The 20% difference is due to the lower number fraction of high-angle misorientation boundaries. It is also found that the resistance to micro-crack propagation is more effective in heat affected zones, which can be explained by the residual compressive stress in martensite-austenite constituents. This research assesses the balance between microstructural parameters for controlling cleavage toughness.

Multi-barrier cleavage models consider cleavage fracture which is characterized by a series of microscale events. One of the challenges for multi-barrier cleavage models is the strong variations of cleavage parameters across different types of steels. The source and magnitude of the variations have not been studied systematically. In the current paper, cleavage parameters corresponding to fracture initiation at a hard particle and crack propagation overcoming grain boundaries are determined for three bainitic steels, a martensitic steel, and a ferritic steel, using a recently proposed model. It is found that the particle fracture parameter depends on particle morphology and composition, while the grain boundary cleavage parameter depends on the hierarchical grain structure. The determined values of cleavage parameters present a high degree of consistency among the five different steels, which allows the further application on microstructure design to control macroscopic toughness.

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.

The through-thickness heterogeneous microstructure of thick-section high strength steels is responsible for the significant scatter of properties along the thickness. In this study, in order to identify the critical microstructural features in the fracture behaviour and allow for design optimisation and prediction of structural failure, the through-thickness microstructure of thick-section steels was extensively characterised and quantified. For this purpose, samples were extracted from the top quarter and middle thickness positions, and a combination of techniques including chemical composition analysis, dilatometry, and microscopy was used. The hardness variation through the thickness was analysed via micro-Vickers measurements and the local hardness variation in the middle section was studied via nanoindentation. The middle section presented larger prior austenite grain (PAG) sizes and larger sizes and area fraction of inclusions than the top section. Additionally, cubic inclusions were observed distributed as clusters in the middle, sometimes decorating PAG boundaries. Defects associated with the cubic inclusions or the interface between the matrix and the circular and cubic inclusions were observed in the mid-thickness. Moreover, the middle section presented long interfaces with the most significant hardness gradients due to the presence of hard centreline segregation bands. Hence, the microstructural and nanoindentation analyses indicated the middle section as the most likely area to have the lowest fracture toughness and, therefore, the most unfavourable section for fracture performance of the investigated S690QL high strength steel. The detrimental effect of the middle section was confirmed via CTOD tests where the middle presents lower fracture toughness than the top section.

The properties of reinforcing steel must comply with the fundamental assumptions underlying structural codes of practice on which verifications of structural behaviour are based. This is of predominant importance not only for design but also for assessment, where demand of deformation capacity of Reinforced Concrete (RC) is often considered implicitly. Yet, the actual deformation capacity directly depends on the mechanical properties and condition of reinforcing steel. Experimental results indicate that corrosion significantly reduces ductility, yield strength and ultimate tensile strength of reinforcement. It is however unclear which extent of corrosion may actually lead to a decrease of ultimate strain of the reinforcing steel below the minimum requirements following from the deformation capacity demands and how to consider such situations in the assessment of structures. The majority of information about the effects of corrosion on the mechanical properties of reinforcing steel is obtained from modern, ductile steel that has been corroded under an accelerated process, rather than under a more realistic long-term exposure. Moreover, experimental studies are fragmentary in scope and therefore often do not consistently consider important aspects such as the type of reinforcement steel and the morphology of the corrosion defect. Consequently, regression models developed to capture the effect of corrosion on reduction of the material properties of reinforcing steel, which are based on the empirical results, are usually characterised by large uncertainties. Given the lack of systematic consideration of the factors governing the reduction of the mechanical properties, such models tend to oversimplify the phenomena and are only to a limited extent suitable for the assessment of the structural safety of corroded structures. In this paper, governing factors for the reduction of mechanical properties of reinforcing steel due to pitting corrosion are investigated by an analytical model, accounting for the morphology of the corrosion defect and essential steel properties. Validation of the model shows good agreement with detailed FEA and experimental data.

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 σ_nom/σ_y.

Thick section S690 QT steel is modelled with a modified multibarrier model that is based on the weakest-link mechanism. Segregation bands are modelled as discrete layers which have different grain size, yield properties, and local fracture parameters from outside of the bands. The results show that embrittlement from segregation bands can only be adequately reflected if the inhomogeneities of the fracture parameters are accounted for. The present methodology quantitively captures the cooperation of complex microstructural features in cleavage and can facilitate the trade-off between the effects of various microstructural parameters in toughness control.

The failure assessment line (FAL) describes the interaction between plastic failure and fracture of flawed steel components subjected to tension or bending. This paper quantifies the model uncertainty of the FAL as provided in the internationally used British Standard BS 7910:2019 by comparing the assessment with the actual failure load of 82 wide plate and 4 tubular joint tests. In line with findings of others, it is demonstrated that the accuracy of the assessment is significantly improved if the crack tip constraint is considered in the assessment. Irrespective of this crack tip constraint consideration, a non-negligible number of wide plate tests has a lower failure load than the one predicted by the FAL in BS 7910:2019, if based on three fracture toughness tests. A penalty or safety margin on the FAL is advocated to compensate for this. It appears advantageous to base the assessment on the average instead of the minimum of three equivalent fracture mechanics tests together with an associated (quantified) safety margin.

For structural assessment and optimal design of thick-section high-strength steels in applications under harsh service conditions, it is essential to understand the cleavage fracture micromechanisms. In this study, we assess the effects of through-thickness microstructure of an 80-mm-thick quenched and tempered S690 high-strength steel, notch orientation, and crack tip constraint in cleavage nucleation and propagation via sub-sized crack tip opening displacement (CTOD) testing at −100 °C. The notch was placed parallel and perpendicular to the rolling direction, and the crack tip constraint was analysed by varying the a/W ratio: 0.5, 0.25, and 0.1. The notch orientation does not play a role, and the material is considered isotropic in-plane. Nb-rich inclusions were observed to act as the weak microstructural link in the steel, triggering fracture in specimens with the lowest CTOD values. While shallow-cracked specimens from the top section present larger critical CTOD values than deep-cracked ones due to stress relief ahead of the crack tip, the constraint does not have a significant influence in the middle due to the very detrimental microstructure in the presence of Nb-rich inclusions. Some specimens show areas of intergranular fracture due to the combined effect of C, Cr, Mn, Ni, and P segregation along with precipitation of Nb-rich inclusions clusters on the grain boundaries. Several crack deflections at high-angle grain boundaries were observed where the neighbouring sub-structure has different Bain axes.

Macroscale cleavage fracture toughness of high strength steels is strongly related to the fracture of hard microstructural inclusions. Therefore, an accurate determination of the local stress on these inclusions based on the matrix stress is necessary for the statistical modelling of macroscale cleavage fracture. This paper presents analytical equations to quantitatively estimate the stress of the microstructural inclusions from the far-field stress of the matrix. The analytical equations account for the inclusion shape, the inclusion orientation, the far-field stress state and matrix material properties. Finite element modelling of a representative volume element containing a hard inclusion shows that the equations provide an accurate representation of the local stress state. The equations are implemented into a multi-barrier model and compared with CTOD experiments with two different levels of constraint.