结构用钢材的本构模型与断裂模型研究

闫伸; 赵宪忠

doi:10.13206/j.gjgS26090145

结构用钢材的本构模型与断裂模型研究

doi: 10.13206/j.gjgS26090145

闫伸^1,2,
赵宪忠^1,2, ,

1. 同济大学土木工程学院, 上海 200092;
2. 土木工程防灾减灾全国重点实验室, 上海 200092

基金项目:

国家自然科学基金项目（52578232，52178152，51678432）。

详细信息

作者简介:
闫伸，博士，副教授，主要从事钢结构断裂失效与倒塌及钢结构加固方面的研究。

通讯作者:
赵宪忠，博士，教授，主要从事钢结构节点、钢结构连续性倒塌及结构智能设计与建造方面的研究，x.zhao@tongji.edu.cn。

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出版历程
- 收稿日期: 2026-09-01
- 网络出版日期: 2026-11-06

Constitutive and Fracture Models for Structural Steels

Yan Shen^1,2,
Zhao Xianzhong^{1,2
, ,}

1. College of Civil Engineering, Tongji University, Shanghai 200092, China;
2. State Key Laboratory of Disaster Reduction in Civil Engineering, Shanghai 200092, China

摘要

摘要: 塑性集中发展进而诱发断裂是钢结构的一种重要破坏模式，对其准确模拟需要首先建立材料全过程本构模型与考虑复杂应力状态效应的材料断裂模型。针对结构钢从屈服、强化直至断裂的全过程本构响应，讨论了真应力-真应变关系的确定方法：颈缩前可由工程应力-工程应变关系直接转换；颈缩后则提出GPN（Generalised Post Necking）模型，该模型颈缩点处连续可导、颈缩后应变硬化模量随塑性应变下降程度可控，仅采用两个参数便可描述各种牌号钢材的颈缩后强化行为；建立了模型参数的直接计算方法。在高应变率作用下，结构钢的全过程应力-应变响应呈现显著的应变率强化效应，且该强化效应随塑性应变发展而逐渐降低，据此提出了反映全过程应变率效应的SD-DIF（Strain dependent Dynamic Increase Factor）模型；该模型形式简捷，且表现出比传统应变率-塑性应变解耦型模型更高的预测精度。针对复杂应力状态下的材料断裂问题，采用应力三轴度和罗德（Lode）角参数表征材料点应力状态，揭示了两者对材料断裂应变的作用规律，建立了LMVGM（Lode angle Modified Void Growth Model）模型，以仅含3个参数的指数函数形式统一描述全应力状态空间的材料断裂轨迹面。高应变率与复杂应力状态组合下的宏观试验及微观表征表明，材料断裂特性的应变率效应与应力状态效应存在明显耦合，应变率效应的程度及变化趋势均依赖于所处的应力状态。基于此，在LMVGM模型基础上引入同时考虑应变率、应力三轴度和Lode角参数作用的断裂应变动力系数，建立了应变率-应力状态耦合的CD-LMVGM（Coupled Dynamic LMVGM）模型；该模型能准确区分拉伸状态下的正应变率效应与剪切状态下的负应变率效应，且对多种材料的断裂特性均表现出稳定的较高预测能力。
- 结构钢 /
- 全过程行为 /
- 应力-应变关系 /
- 应力状态 /
- 断裂 /
- 高速动载
Abstract: Localized plastic deformation followed by fracture is an important failure mode of steel structures， and its accurate prediction requires a full-range constitutive model together with a fracture model capable of accounting for complex stress states. Under static loading， methods for determining the true stress-true strain relationship over the full response of structural steels， from yielding and strain hardening up to fracture initiation， were systematically discussed. Before necking， the true stress-true strain relationship can be directly converted from the engineering stress-strain relationship. After necking， the Generalised Post-Necking （GPN） model was proposed， which ensures a continuously differentiable response at the onset of necking and allows the degree of reduction in the post-necking strain-hardening modulus with increasing plastic strain to be flexibly controlled. With only two parameters， it can describe the post-necking hardening behavior of various grades of steel. In addition， a direct method for determining the GPN model parameters was established. Under high strain rates， a pronounced strain-rate hardening effect was demonstrated over the full stress-strain response of structural steels， and this effect decreased as plastic strain developed. Accordingly， a Strain-Dependent Dynamic Increase Factor （SD-DIF） model was proposed. The model has a concise form and provides higher predictive accuracy than conventional models in which the strain-rate effect is decoupled from plastic strain. Regarding fracture initiation under complex stress states， stress triaxiality and the Lode angle parameter were adopted to characterize the stress state at a material point， and their effects on fracture strain were revealed. By incorporating the Lode angle effect into the Void Growth Model （VGM）， a Lode-angle Modified VGM （LMVGM） was developed， in which a three-parameter exponential formulation provides a unified description of the effects of stress triaxiality and the Lode angle parameter on fracture strain. Macroscopic tests and microstructural characterization under combined high strain rates and complex stress states revealed a pronounced coupled effect between strain rate and stress state， with both the magnitude and the trend of the strain-rate effect depending on the stress state. Based on this finding， a dynamic factor for fracture strain that simultaneously depends on strain rate， stress triaxiality， and the Lode angle parameter was introduced into the LMVGM， leading to a Coupled Dynamic LMVGM （CD-LMVGM）. The model can simultaneously capture the positive strain-rate effect under tension-dominated stress states and the negative strain-rate effect under shear-dominated stress states， while maintaining consistently high predictive accuracy for the fracture behavior of different materials.
- structural steel /
- full-range behavior /
- stress-strain relationship /
- stress state /
- fracture /
- high-speed dynamic loading

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