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浙江大学学报(工学版)  2022, Vol. 56 Issue (9): 1750-1760    DOI: 10.3785/j.issn.1008-973X.2022.09.008
土木工程、交通工程     
模拟准脆性材料热开裂的热力耦合格构离散单元法
陈凌霄(),田文祥,马刚,程勇刚*(),王桥,周伟
武汉大学 水资源与水电工程科学国家重点实验室,湖北 武汉 430072
Thermal-mechanical coupled lattice discrete element method for simulating thermal cracking of quasi-brittle materials
Ling-xiao CHEN(),Wen-xiang TIAN,Gang MA,Yong-gang CHENG*(),Qiao WANG,Wei ZHOU
State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan 430072, China
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摘要:

针对准脆性材料的热传导与热开裂问题,基于格构离散单元法(LDEM)提出新的热力耦合数值模型. 通过格构离散体系与连续体传热过程的等效换算,结合格构单元的线膨胀公式,在LDEM中实现温度传导与裂纹扩展的数值模拟. 以平板的热传导与热弹性应力问题、由温度梯度与热失配引起的开裂问题为例,验证所提模型. 将所提模型应用于细观混凝土温度?应力试验的数值模拟中. 结果表明,LDEM热力耦合模型能够有效模拟准脆性材料的热传导过程、在温度影响下的裂纹萌生与扩展,是研究准脆性材料热开裂过程与机理的有力工具.

关键词: 格构离散单元法(LDEM)热力耦合热传导热开裂准脆性材料    
Abstract:

A new thermal-mechanical coupled numerical model was proposed based on the lattice discrete element method (LDEM), aiming at the heat conduction and thermal cracking of quasi-brittle materials. In LDEM, in order to simulate the numerical test of the temperature conduction and crack propagation, the equivalent conversion of the heat transfer process between the lattice discrete system and the continuum was carried out, combined with the linear expansion formula of the lattice element. Taking the heat conduction and thermoelastic stress of the plate, and the cracking caused by the temperature gradient and thermal mismatch as examples, the model was verified. In addition, the model was applied to the numerical simulation of the meso-level concrete temperature-stress test. Results show that the LDEM thermal-mechanical coupling model can simulate the heat conduction process of quasi-brittle materials, as well as the crack initiation and propagation under the influence of temperature effectively, which provides a powerful tool for studying the thermal cracking process and mechanism of quasi-brittle materials.

Key words: lattice discrete element method (LDEM)    thermal-mechanical coupling    heat conduction    thermal cracking    quasi-brittle materials
收稿日期: 2021-09-15 出版日期: 2022-09-28
CLC:  TV 315  
基金资助: 国家自然科学基金资助项目(51879206,51979207,U2040223)
通讯作者: 程勇刚     E-mail: chenlingxiao@whu.edu.cn;chengyg@whu.edu.cn
作者简介: 陈凌霄(1997—),男,硕士生,从事水工结构与材料数值仿真研究. orcid.org/0000-0003-4374-0204. E-mail: chenlingxiao@whu.edu.cn
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引用本文:

陈凌霄,田文祥,马刚,程勇刚,王桥,周伟. 模拟准脆性材料热开裂的热力耦合格构离散单元法[J]. 浙江大学学报(工学版), 2022, 56(9): 1750-1760.

Ling-xiao CHEN,Wen-xiang TIAN,Gang MA,Yong-gang CHENG,Qiao WANG,Wei ZHOU. Thermal-mechanical coupled lattice discrete element method for simulating thermal cracking of quasi-brittle materials. Journal of ZheJiang University (Engineering Science), 2022, 56(9): 1750-1760.

链接本文:

https://www.zjujournals.com/eng/CN/10.3785/j.issn.1008-973X.2022.09.008        https://www.zjujournals.com/eng/CN/Y2022/V56/I9/1750

图 1  格构离散元法的离散模式与基本结构
图 2  格构离散单元法网格划分与裂缝模拟平面示意图
图 3  连续体与基本模块的等效平行截面
图 4  荷载−应变的双线性本构模型
图 5  不同时刻平板温度和应力的LDEM解与解析解对比
图 6  不同网格尺寸下平板的温度分布对比
图 7  不同网格尺寸平板温度与应力的LDEM解与解析解对比
图 8  平板温度分布的有限元解与LDEM解对比
图 9  不同时刻平板温度与应力的LDEM解与解析解对比
图 10  钢筋混凝土材料不均匀性热开裂试验
参数 数值
混凝土保护层
bra
钢筋内芯
ra
半径/m b=0.15 a=0.03
厚度 h/m 0.002 0.002
弹性模量 E/GPa 20 40
泊松比 μ 0.2 0.3
密度 ρ/(kg·m?3) 2300 7850
抗拉强度 ft/MPa 3 235
断裂能 Gf/(N·m?1) 100
线膨胀系数 α/ K?1 7.00×10?6 2.20×10?5
初始温度 θ0/℃ 0 0
温升幅度 Δθ /℃ 100 100
表 1  钢筋混凝土热力学参数
图 11  混凝土环向应力LDEM解与解析解对比
图 12  钢筋混凝土不同温升时刻的裂纹形态
参数 数值 参数 数值
弹性模量 E/GPa 69 比热 c/ (J·kg?1·K?1) 920
泊松比 μ 0.25 线膨胀系数 α/K?1 1×10?5
密度 ρ/(kg·m?3) 2600 初始温度 θ0/℃ 20
抗拉强度 ft/MPa 9 边界温度 θc/℃ 20
断裂能 Gf/(N·m?1) 500 中心孔温度 θh/℃ 20~200
导热系数 k/(W·m?1·K?1) 1.2
表 2  花岗岩热力学参数
图 13  花岗岩在不同温升时刻的温度分布及裂纹形态
图 14  花岗岩热开裂物理试验与数值模拟结果
图 15  不同骨料体积分数的混凝土细观模型
参数 数值
砂浆基质 骨料 界面过渡区
弹性模量 E/GPa 4 50 2.4
泊松比 μ 0.20 0.16 0.20
密度 ρ/(kg·m?3) 2440 2620 2440
抗拉强度 ft/MPa 2.06 20.00 1.24
断裂能 Gf/(N·m?1) 60 500 40
导热系数 k//(W·m?1·K?1) 1.106 2.440 0.940
线膨胀系数 α/K?1 1.2×10?5 0.5×10?5 1.2×10?5
比热 c/ (J·kg?1·K?1) 762.3 719.8 762.3
表 3  混凝土各细观组分热力学参数
图 16  不同骨料体积分数试件温度与变形分布
图 17  混凝土试件在骨料体积分数不同时的收缩对比
图 18  混凝土试件在骨料体积分数不同时的约束应力对比
图 19  不同骨料体积分数试件的开裂模式
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