**2. Literature survey on structural behaviour at cold (sub-zero) temperatures**

A number of studies in modelling of material behaviour for structural steels at cold (sub-zero) temperatures are available in the literature. Most of the studies dealt

### *Ultimate Compressive Strength of Steel Stiffened-Plate Structures Triggered by Brittle… DOI: http://dx.doi.org/10.5772/intechopen.97155*

with predominantly ductile behaviour of materials with the focus on how crack initiates in association with ductile fracture. Ehlers and Varsta [16] and Ehlers [17] derived the true stress versus true strain relation of ordinary steel. The effects of stress triaxiality on ductile fracture have been one of research topics [18–24]. The works of the Choung group have provided useful insights for ductile fracture behaviour of structural steels [14, 25–32].

It is recognised that structural steel behaviour is predominantly ductile at temperatures higher than the temperature of the ductile-to-brittle fracture transition, as shown in **Figure 1**. As the temperature decreases approaching cryogenic condition, the material behaves predominantly in a brittle manner with partial or no ductility [33–40]. Majzoobi et al. [41] observed that the ductile-to-brittle fracture transition of carbon steel occurs at about -80°C, and the material behaviour becomes entirely brittle at -196°C.

Although there are considerable uncertainties associated with the ductile-tobrittle fracture transition temperature (DBTT), a number of evidences for brittle fracture behaviour of steel structures at cryogenic condition have been seen in the literature, depending on the type of materials and loading conditions (e.g., quasistatic or impact), among other factors. Crushing testing of steel tubes under quasistatic loads at -60°C [42, 43] showed ductile fracture, as shown in **Figure 2**. Dropped-object impact testing of steel stiffened plate panels at -60°C [44] showed brittle fracture, as shown in **Figure 3**. Full-scale collapse testing of a steel stiffenedplate structure under axial-compressive loading showed that the ultimate strength was reached by a trigger of brittle fracture [1], as shown in **Figures 4** and **5**. At room temperature, the structures reached the ultimate strength by flexuraltorsional buckling [1], but brittle fracture triggered the global failure at cryogenic conditions [7].

Here, an attempt is made to develop new fracture criteria based on the hypothesis that crack initiates if an equivalent stress exceeds a critical value, to model the fracture phenomenon of high-strength steel (AH32) under cryogenic conditions. Existing material models for the fracture analysis is first reviewed.
