基于Tanaka-Mura位错模型的疲劳裂纹萌生寿命预测

邓彩艳; 刘庚; 龚宝明; 刘永

doi:10.12073/j.hjxb.20200706003

基于Tanaka-Mura位错模型的疲劳裂纹萌生寿命预测

天津大学，天津，300350

基金项目: 国家自然科学基金资助项目（51875402）

详细信息

作者简介:
邓彩艳，博士，教授，博士研究生导师；主要从事焊接结构断裂、疲劳及延寿技术、焊接结构完整性的研究；Email：dengcy@tju.edu.cn.

通讯作者:
龚宝明，副教授. Email：gongbm@tju.edu.cn.

中图分类号: TG 454
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出版历程
- 收稿日期: 2020-07-05
- 网络出版日期: 2021-02-04
- 刊出日期: 2021-04-01

Fatigue crack initiation life prediction based on Tanaka-Mura dislocation model

Tianjin University, Tianjin, 300350, China

摘要

摘要: 为了准确预测材料的疲劳寿命，提高结构疲劳寿命预测精度，对ABAQUS有限元数值模拟预测试样疲劳寿命的方法进行了研究. 基于Tanaka-Mura位错理论，利用python语言对ABAQUS进行二次开发，模拟预测了S960QL马氏体钢和Ti₂AlNb钛合金接头各区域疲劳裂纹萌生寿命. 利用泰森多边形法生成了晶体特征单元建立了微观子模型，考虑了体心立方结构相互垂直的两条滑移带作为潜在的裂纹萌生位置，并对具有相同取向的多条平行滑移带都进行了模拟计算. 通过计算得到的裂纹扩展速率变化，给出了裂纹萌生阶段过渡到裂纹扩展阶段的临界点处的裂纹萌生寿命. 模拟结果表明，除焊缝柱状晶组织外裂纹萌生寿命与试验数据吻合良好.
- 疲劳 /
- 数值模拟 /
- 裂纹萌生 /
- 焊接接头
Abstract: In order to accurately predict the fatigue life of materials and improve the accuracy of structural fatigue life prediction, the method of ABAQUS finite element numerical simulation to predict the fatigue life of specimens was studied. Based on Tanaka-Mura dislocation theory, ABAQUS was redeveloped by using Python language. The fatigue crack initiation life of S960QL martensitic steel and Ti₂AlNb titanium alloy joint was simulated and predicted. The representative volume element is generated by Tyson polygon method, and the micro sub-model is established. Two perpendicular slip bands of bcc structure are considered as potential crack initiation locations, and several parallel slip bands with the same orientation are simulated. The crack initiation life at the critical point from the crack initiation stage to the crack growth stage is given by the calculated crack growth rate change. The simulation results show that the crack initiation life is in good agreement with the experimental data except the columnar crystal structure.
- fatigue /
- numerical simulation /
- crack initiation /
- welded joint

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图 1 有限元模拟模型图

Figure 1. Model of finite element simulation. (a) finite element model of martensitic steel; (b) finite element model of titanium alloy joint

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图 2 有限元模型图

Figure 2. Model of finite element simulation. (a) microstructure of Ti₂AlNb welded joint; (b) finite element model of Ti₂AlNb welded joint

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图 3 宏观模型与子模型图

Figure 3. Macro model and sub-model diagram

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图 4 子模型的边界条件设置

Figure 4. Boundary condition of sub-model

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图 5 子模型中赋予晶粒随机取向

Figure 5. Random orientation of grains in sub-model

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图 6 晶粒内的多重滑移带

Figure 6. A grain with multiple slip bands

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图 7 短裂纹与长裂纹裂纹扩展速率变化

Figure 7. Change of crack growth rate of short crack and long crack

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图 8 马氏体钢子模型的剪应力分布

Figure 8. Shear stress distribution of sub-model of martensitic steel

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图 9 钛合金接头子模型的剪应力分布

Figure 9. Shear stress distribution of sub-model of titanium alloy joint. (a) Ti₂AlNb (weld zone); (b) Ti₂AlNb (heat affected zone); (c) Ti₂AlNb (base metal zone)

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图 10 马氏体钢疲劳裂纹萌生模拟结果

Figure 10. Simulation results of fatigue crack initiation of martensitic steel. (a) N = 7 960 (10 cracks); (b) N = 48 475 (50 cracks); (c) N = 104 223 (100 cracks); (d) N = 206 300 (167 cracks)

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图 11 热影响区疲劳裂纹萌生模拟结果

Figure 11. Simulation results of fatigue crack initiation in HAZ

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图 12 裂纹数目与扩展速率关系图

Figure 12. Relationship between crack number and crack growth rate. (a) martensitic steel; (b) heat affected zone of titanium alloy joint; (c) base metal zone of titanium alloy joint

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表 1 正交各向异性弹性刚度矩阵各分量

Table 1 Components of orthotropic elastic stiffness matrix

材料	C₁₁/GPa	C₂₂/GPa	C₃₃/GPa	C₁₂/GPa	C₁₃/GPa	C₂₃/GPa	C₄₄/GPa	C₅₅/GPa	C₆₆/GPa
S960QL	233	233	233	135	135	135	118	118	118
Ti₂AlNb (HAZ)	164	164	164	70	70	70	47	47	47

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表 2 模拟所需其它参数

Table 2 Other parameters required for simulation

材料	临界分剪应力 K_crss/MPa	单位面积断裂能 W_s/(kJ·m⁻²)	泊松比 υ
S960QL	108	2	0.3
Ti₂AlNb 焊缝区	180	1.324	0.3
Ti₂AlNb 热影响区	133	2	0.3
Ti₂AlNb 母材区	170.06	2	0.3

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表 3 模拟结果与试验值对比

Table 3 Comparison between simulation results and experimental values

材料	试验值	预测值	误差
S960QL	216 000	206 300	4.49%
Ti₂AlNb (WELD)	48002	10394	78.35%
Ti₂AlNb (HAZ)	55009	55236	0.4%
Ti₂AlNb (BASE)	60007	64096	6.81%

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