Forming limit curves (FLCs), which are constructed using the limit strains at localised necking, are the most widely used tools for the evaluation of the formability of sheet metals. Fracture forming limit curves (FFLCs) are more recently developed, complementary tools for formability evaluation which are instead constructed using the limit strains at fracture. Since the formability depends strongly on forming conditions such as strain state, temperature and strain rate, models for predicting FLCs and FFLCs are essential for the optimisation and further application of hot forming processes in which these forming conditions vary significantly with both position and time. However, no model has so far been developed to predict FFLCs either alone or in conjunction with FLCs for sheet metals such as boron steel under hot stamping conditions. In this study, a set of unified viscoplastic constitutive equations for the prediction of both FLCs and FFLCs based on continuum damage mechanics (CDM) has been formulated from a set of recently developed constitutive equations for dislocation-based hardening, in combination with two novel coupled variables characterising the accumulated damage leading to localised necking and fracture. The novel variables take into account the effects of strain state, temperature and strain rate on the formability of sheet metals. The material constants in the CDM-based constitutive equations have been calibrated using experimental data comprising true stress-true strain curves and limit strains of a 22MnB5 boron steel obtained at a range of temperatures and strain rates. Investigation of the effect of varying selected parameters in the coupled damage variables on the resulting computed FLCs and FFLCs has demonstrated the flexibility of the model in enabling curves of different shapes and numerical values to be constructed. This indicates the potential of the CDM-based constitutive model for application to other materials for warm or hot stamping processes.

成形极限曲线 (FLC) 是使用局部颈缩时的极限应变构建的，是评估钣金成形性的最广泛使用的工具。断裂成形极限曲线 (FFLC) 是最近开发的，用于成形性评估的补充工具，而是使用断裂时的极限应变构建的。由于可成形性很大程度上取决于应变状态、温度和应变速率等成形条件，因此预测 FLC 和 FFLC 的模型对于热成形工艺的优化和进一步应用至关重要，其中这些成形条件随位置和时间而显着变化。然而，迄今为止，尚未开发出任何模型来单独或与 FLC 一起预测热冲压条件下的钣金（如硼钢）的 FFLC。在这项研究中，从一组最近开发的基于位错的硬化本构方程，结合两个新的耦合表征导致局部颈缩和断裂的累积损伤的变量。新变量考虑了应变状态、温度和应变速率对钣金可成形性的影响。基于 CDM 的本构方程中的材料常数已经使用实验数据进行了校准，这些数据包括在一定温度和应变率范围内获得的 22MnB5 硼钢的真实应力-真实应变曲线和极限应变。研究耦合损伤变量中不同选定参数对计算得到的 FLC 和 FFLC 的影响，证明了模型在构建不同形状和数值的曲线方面的灵活性。这表明基于 CDM 的本构模型在应用于其他材料的温烫或烫印工艺方面的潜力。