Application of cohesive elements in modeling the low-velocity impact responseand failure of fiber reinforced plastic laminates
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摘要: 纤维增强树脂基复合材料层合板（fibre reinforced plastic composites，FRP）在航空、航天、交通、造船等诸多工程中得到了日益广泛的应用，而其在冲击载荷下的响应和破坏特别是分层一直为学术界所关注。本文中对FRP层合板在冲击载荷下的响应和破坏进行数值模拟，并通过引入粘结层重点研究其分层破坏。首先，介绍一种基于改进的粘结区域方法的粘结层损伤模型；其次，详细介绍了有限元模型建模过程和建模细节；最后，对有限元模型进行验证，并分析分层损伤发生的原因。模拟结果表明，该模型不仅能准确预测FRP层合板在低速冲击载荷下的载荷-时间曲线和载荷-位移曲线，还能成功地预测其分层破坏。
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关键词:
- 纤维增强树脂基复合材料 /
- 渐进损伤本构模型 /
- 分层 /
- 粘结单元
Abstract: Fiber reinforced plastic laminates (FRP) have been widely applied in modern industries such as aeronautics, astronautics, transportation, naval architecture. The impact response and failure process of FRP laminates are a major concern in academic and engineering community. In this paper, the response and failure of FRP laminates under impact loading are numerically simulated with emphasis being placed upon delamination by cohesive elements. The paper consists of three main parts: a damage model of adhesive layer based on improved cohesive zone method is firstly described; and then followed by constructing a finite element model with some modeling details; finally, the finite element model is validated on experiments, and the reason of delamination damage is delineated. It has been demonstrated that the present model can predict not only the load-time history and the load-displacement curve but also the delamination of FRP laminates under low-velocity impact. -
图 3 将粘结单元插入实体单元示意图
Figure 3. Illustration of cohesive elements inserted in solid elements
图 4 低速冲击下CFRP层合板的有限元模型
Figure 4. Finite element model for CFRP laminates under low velocity impact
表 1 模型中用到的粘结层参数
Table 1. cohesive interface properties used in present model
材料参数 数值 材料参数 数值 材料参数 数值 $ {\tau _{n}^{\left( {\rm{s}} \right)}}$ 11 MPa $ {\tau _{s}^{\left( {\rm{s}} \right)}}$ 17 MPa $ {\tau _{t}^{\left( {\rm{s}} \right)}}$ 17 MPa $ {G_{{\rm{IC}}}}$ 0.3 N/mm[17] $ {G_{{\rm{IIC}}}}$ 0.8 N/mm[17] $ {G_{{\rm{IIIC}}}}$ 0.8 N/mm[17] $ {K_{n}^{\left( {\rm{s}} \right)}}$ 850 MPa[21] $ {K_{s}^{\left( {\rm{s}} \right)}}$ 850 MPa[21] $ {K_{t}^{\left( {\rm{s}} \right)}}$ 850 MPa[21] $ {A_{\rm{i}}}$ 2.5[22] $ {B_{\rm{i}}}$ 0.9[22] $ {C_{\rm{i}}}$ 3.7[22] $ {A_{\rm{m}}}$ 1.85[22] $ {B_{\rm{m}}}$ 0.5[22] $ {C_{\rm{m}}}$ 1.3[22] 
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表 2 Graphite/epoxy单层板的参数值
Table 2. Parameters for graphite/epoxy laminates
材料参数 数值 材料参数 数值 材料参数 数值 $ {{E}_{11}}$ 143.4 GPa[17] $ {Y_{\rm{t}}}$ 54 MPa[17] $ {{\nu }_{23}}$. 0.52[17] $ {{E}_{22}}$ 9.27 GPa[17] $ {{X}_{\rm{c}}}$ 1 650 MPa[17] $ {{\nu }_{13}},{{\nu }_{12}}$ 0.31[17] $ {{E}_{33}}$ 9.27 GPa[17] $ {{Y}_{\rm{c}}}$ 240 MPa[17] $ {{\delta }_{1}^{\left( \rm{f} \right)}},\rm{ }{{\delta }_{2}^{\left( \rm{f} \right)}}$ 5.7×10−2 mm[12] $ {G_{12}}$ 3.8 GPa[17] $ {Z_{\rm{t}}}$ 54 MPa[17] $ {\delta _7^{\left( {\rm{f}} \right)}}$ 2.7×10−2 mm[12] $ {G_{23}}$ 3.2 GPa[17] $ {Z_{\rm{c}}}$ 240 MPa[17] $ {\delta _3^{\left( {\rm{f}} \right)}},{\rm{ }}{\delta _4^{\left( {\rm{f}} \right)}}$ 7.65×10−2 mm[12] $ {G_{31}}$ 3.8 GPa[17] $ {S_{12}}$ 100 MPa[17] $ {\delta _5^{\left( {\rm{f}} \right)}}$ 5×10−3 mm[12] $ {X_{\rm{t}}}$ 2 945 MPa[17] $ {S_{31}},{S_{23}}$ 100 MPa[17] $ {\delta _6^{\left( {\rm{f}} \right)}}$ 5×10−2 mm[12]
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