Application of continuum damage mechanics model for composites in progressive failure prediction of bolted joints
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摘要: 提出考虑层合板面内(纤维和基体失效)和层间失效的复合材料连续损伤力学模型,对螺栓接头的渐进失效行为进行预测。基于Tsai-Wu强度准则,发展可以判定复合材料面内和层间失效的强度准则。采用幂指数衰减材料退化模型模拟复合材料的损伤扩展过程。建立连续损伤力学模型用以研究0°铺层比例和螺栓直径对复合材料螺栓接头挤压性能的影响,预测结果与实验结果吻合。结果表明:0°铺层比例过高,接头发生剪切破坏,降低连接结构承载能力;增大螺栓直径,层合板损伤受到抑制,可提高复合材料螺栓接头的挤压强度。Abstract: A continuum damage mechanics model for composites, considering the intralaminar (fibre and matrix failure) and interlaminar failure, was proposed to predict the progressive damage behavior of bolted joints. Based on Tsai-Wu strength criterion, a new failure-judgement formula was developed to distinguish the intralaminar and interlaminar failure. An exponent material degradation model was introduced to simulate the damage evolution of the composite. A continuum damage mechanics model was established to analyze the effect of 0° ply ratio and bolt diameter on the bearing characteristic of the composite bolted joints. The predicted results exhibit good agreement with the experimental results. These results show that high 0° ply ratio induces the shear-out failure of the composite bolted joints, decreasing the structural bearing capability. Increasing the bolt diameter can restrain the damage of the composite laminate and improve the bearing strength of the composite bolted joints.
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Key words:
- composite /
- bolted joint /
- continuum damage mechanics model /
- progressive damage /
- strength criterion
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表 1 T800级碳纤维增强聚合物复合材料层合板铺层比例和顺序
Table 1. Ply ratios and sequences of T800 carbon fiber reinforced polymer composite laminate
Code Ply ratio/
%[0°/±45°/90°]Ply sequence A (30/60/10) [45°/0°/−45°/0°/45°/90°/−45°/0°/45°/−45°]3s B (50/40/10) [45°/0°/−45°/0°/90°/0°/45°/0°/−45°/0°]3s C (70/20/10) [45°/0°/0°/−45°/0°/0°/0°/90°/0°/0°]3s 表 2 T800级碳纤维增强聚合物复合材料力学性能[23]
Table 2. Mechanical properties of T800 carbon fiber reinforced polymer composite[23]
Elastic constant Value Strength Value E1/GPa 195 XT/MPa 3 071 E2=E3/GPa 8.58 XC/MPa 1 747 G12=G13/GPa 4.57 YT=ZT/MPa 88 G23/GPa 2.9 YC=ZC/MPa 271 ν12=ν13 0.33 S12=S13/MPa 143 v23 0.48 S23/MPa 143 Notes: Ei(i=1,2,3)—Elastic modulus in material principle directions; Gij(1≤i<j≤3)—Shear elastic modulus in material principle directions; νij(1≤i<j≤3)—Poison’s ratio in material principal directions; XT and XC—Tensile and compressive strength in fiber directions; YT and YC—Tensile and compressive strength normal to fiber directions; ZT and ZC—Tensile and compressive strength in interlaminar directions; S12 and S13—In-plane shear strength in material directions; S23—Interlaminar shear strength in material directions. 表 3 T800级碳纤维增强聚合物复合材料的断裂韧性[24]
Table 3. Fracture toughness of T800 carbon fiber reinforced polymer composite[24]
Gf/(N·mm−1) Gn/(N·mm−1) Gs/(N·mm−1) 106.3 0.28 0.79 Notes: Gf—Fracture toughness in fiber direction; Gn—Transverse normal fracture toughness; Gs—Shear fracture toughness. Property Value E/GPa 110 — — ν 0.29 — — σy/MPa 950 1 034 1 103 εp 0 0.002 0.1 Notes: E—Young’s modulus; ν—Poison’s ratio; σy—Yield stress; εp—Yield strain. 表 5 T800级碳纤维增强聚合物复合材料螺栓接头的拉伸试验矩阵
Table 5. Tensile test matrix of T800 carbon fiber reinforced polymer composite bolted joints
Specimen Ply ratio/%[0°/±45°/90°] Bolt diameter D/mm A-12.8 (30/60/10) 12.8 B-12.8 (50/40/10) 12.8 C-12.8 (70/20/10) 12.8 A-9.53 (30/60/10) 9.5 A-14.3 (30/60/10) 14.3 表 6 试验与数值结果比较(接头C-12.8)
Table 6. Comparison between experimental and numerical results (Joint configuration C-12.8)
Model Ultimate bearing strength/MPa Prediction Test Error/% This paper 967.3 935.3 3.4 Linde model 1 007 935.3 7.7 Hashin model 1 001 935.3 7.1 -
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