PSI - Issue 28

B.W. Williams et al. / Procedia Structural Integrity 28 (2020) 1024–1038 Author name / Structural Integrity Procedia 00 (2019) 000–000

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1. Introduction Finite Element Analysis (FEA), with accurately captured material behaviour, can be used to model full-scale tank car accident scenarios. The overall objective of this work is to develop a FEA material model for TC128B that can describe the structural integrity for the entire temperature and strain-rate range resultant during an accident scenario, including fire and crash. Above 550 °C, plastic collapse due to creep deformation is expected and a high temperature material model can be used in full-scale simulations as detailed by Hantouche et al. (2018). Below about 24 °C, the material will fail by ductile or brittle fracture. Full-scale simulations have been compared to experiment side impact data of tank cars by Carolan et al. (2018) with good agreement at room temperature. The focus of this work is to develop a FEA material model that describes failure from 24 °C to -80 °C for quasi-static and dynamic strain-rates under a range of stress states. It is important to capture strain-rate sensitivity of steel in the models as the strength and ductility will be influenced by typical crash strain-rates that can approach 100 s -1 . Damage mechanics models have been used in FEA to describe fracture of metals that are subjected to a wide range of loading conditions, from the high stress triaxiality at a crack front to lower triaxiality conditions that are present during crash events. There are two parts to a typical damage model implementation in FEA. First, damage increases in the element, without a decrease in strength, until a damage initiation criterion is met. Second, the element is softened according to a damage evolution criterion and when a critical value is met the element is deleted. The Modified-Mohr Coulomb (MMC) damage model detailed by Bai and Wierzbicki (2010) in which the effective plastic strain to damage is a function of stress triaxiality and Lode angle. Paredes et al. (2016) and Paredes et al. (2018) utilized the MMC damage model to describe the fracture response of X70 and TC128 steel alloys. The damage models were calibrated using experiments, simulations, and optimization techniques. Several mechanical test geometries including notched tension, shear, biaxial and fracture geometries such as Single-Edge-Bending (SEB) and Compact Tension (CT) were considered to produce a wide range of loading conditions described by triaxiality and Lode angle. The model was valid for one temperature (room temperature) and one strain-rate (quasi-static). The current work studies whether the well calibrated damage model for TC128B detailed by Paredes et al. (2018) can be adjusted to capture influence of multiple temperatures and strain-rates, without the necessity to perform extensive experiment, simulation and optimization. Only experimental data from quasi-static uniaxial tension tests and dynamic Charpy V-Notch (CVN) fracture tests will be considered. Slight variation in the fracture behaviour due to the grade-to-grade variation between the TC128 studied by Paredes et al. (2018) and the TC128B studied in the current work is being addressed in concurrent work. At low temperature, it is typical for steel alloys to exhibit Lüders band formation leading to discontinuous yielding. Dahl et al. (2018) considered the influence of Lüders bands in FEA studies of cracks in a steel alloy used in artic applications. Models of the Crack-Tip-Opening-Displacement (CTOD) in Single-Edge-Tension (SET) specimens indicate that discontinuous yielding can lead to an increase in the crack driving force. Tu et al. (2018) also studied the influence of Lüders strain through models of SET using the Gurson damage model to simulate crack growth. It was observed that discontinuous yielding did not influence the initiation toughness but could influence the crack growth resistance behaviour of the material. These studies indicate the importance of capturing the influence of Lüders bands in the stress versus strain response of steel alloys used for FEA. Both ductile and brittle (or cleavage) fracture can be present in Charpy tests. An extensive review of mechanism and models to describe both brittle and ductile fracture is given by Pineau et al. (2016). This article details the well known Beremin (1983) model utilizing the Weibull stress to describe brittle fracture, as well as alternative brittle fracture models. The influence of stress triaxiality and Lode angle on ductile fracture is detailed as well as several damage mechanics models that can be used to capture ductile fracture. Challenges in modeling ductile to brittle transition in steels are detailed by Pineau (2008) where it is concluded that existing models are still too simplified, particularly in capturing brittle fracture when preceded by ductile fracture. An early coupled ductile-brittle damage model is detailed by Renevey et al. (1996) that captured the probabilistic nature of brittle fracture using the Beremin model but also with a probabilistic condition applied to the Gurson damage model for ductile fracture. More recently, Moattari et al. (2016) detailed a coupled model using a modified Beremin model for cleavage and a continuum damage model (specifically, the Bonora model) for ductile fracture. The model was used to predict fracture toughness ( K 1c ) values in SEB and CT specimens. Of note, is that a temperature dependence on the brittle failure stress was reported. Hojo et al. (2016) also presented a coupled cleavage (Beremin)