Peridynamic modeling of composite laminate under low-velocity impactusing energy-based criteria
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摘要: 近场动力学模拟复合材料层合板低速冲击损伤具有一定优势。本文在球型域常规态近场动力学复合材料模型基础上，建立了考虑时间步长下不同断裂混合比的能量失效判定准则，并开展了基于能量准则的复合材料层合板低速冲击近场动力学模拟。首先对复合材料低速冲击近场动力学模拟的模型刚度进行了验证，近场动力学模拟的冲击接触力、冲击速度及冲击位移与有限元结果具有较好的一致性。在此基础上，开展了复合材料低速冲击近场动力学损伤模拟，给出了冲击过程中复合材料层合板纤维断裂、基体开裂及分层损伤扩展过程。对比试验结果，近场动力学模拟的分层损伤面积和分层形状与试验结果具有较好的一致性，验证了所开展的基于能量准则的复合材料层合板低速冲击近场动力学模拟的有效性。Abstract: Peridynamic (PD) theory has been proven to be of advantages in low-velocity impact modeling of composite laminate. Based on ordinary state-based PD composite spherical-horizon model, energy-based failure criteria was established, which considered mixed-mode fracture in each time step. PD modeling of composite laminate under low-velocity impact was conducted using the established energy-based criteria. Firstly, the modeling stiffness was validated. PD modeling impact load, impact velocity and impact displacement agree well with finite element method (FEM) results. Then, PD damage modeling of composite laminate under low-velocity impact was conducted, and the fiber breakage, matrix crack and delamination damage process were illustrated. Compared with test results, PD modeling delamination area and shape are in good accordance, which validates the conducted PD modeling of composite laminate under low-velocity impact using energy-based criteria.
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Key words:
- composite /
- peridynamics /
- low-velocity impact /
- delamination damage /
- matrix crack
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图 1 近场动力学符号
Figure 1. Peridynamic notations
$ {\boldsymbol{x}}_{(k)}^{(n)} $—Material point; $ {\boldsymbol{u}}_{(k)}^{(n)} $—Deformation; $\mathcal{H}$—Horizon zone; $\delta $—Radius of horizon zone; x(j)—Bond material point; u(j)—Displacement of x(j); ξ—Bond; η'—Bond deformation
图 2 复合材料低速冲击刚度验证示意图
Figure 2. Composite low-velocity impact stiffness validation diagram
图 3 复合材料低速冲击刚度验证变形云图
Figure 3. Deformation cloud for low velocity impact of composite
uz—Displacement in z direction
图 4 复合材料低速冲击刚度验证冲击力-时间曲线
Figure 4. Low velocity impact load-time curves of composite
FEM—Finite element method; PD—Peridynamics
图 5 复合材料低速冲击刚度验证冲击速度-时间曲线
Figure 5. Low velocity impact velocity-time curves of composite
图 6 复合材料低速冲击刚度验证冲击位移-时间曲线
Figure 6. Low velocity impact displacement-time curves of composite
图 7 复合材料低速冲击损伤模拟示意图
Figure 7. Schematic diagram of low velocity impact damage simulation of composite
ux, uy, uz—Displacement in x, y, z directions
图 8 复合材料冲击损伤模拟冲击力-时间曲线
Figure 8. Low velocity impact damage modeling load-time curves of composite materials
FEM_NoDamage—Finite element method result without damage; PD_NoDamage—Peridynamic results without damage; PD_Damage—Peridynamic results with damage
图 9 复合材料低速冲击损伤模拟每一层的分层损伤随冲击时间的变化
Figure 9. Delamination variation of composite each ply under low-velocity impact with time
$\varphi_{\text {delamination }}^{(n)(n+1)}$—Delamination damage factor
图 10 复合材料低速冲击损伤模拟每一层的纤维断裂随冲击时间的变化
Figure 10. Fiber breakage variation of composite each ply under low-velocity impact with time
$ {\varphi _{{\text{fiber breakage}}}} $—Fiber breakage damage factor
图 11 复合材料低速冲击损伤模拟每一层的基体开裂随冲击时间的变化
Figure 11. Matrix crack variation of composite each ply under low-velocity impact with time
$ {\varphi _{{\text{matrix cracking}}}} $—Matrix cracking damage factor
图 12 复合材料低速冲击损伤模拟分层形状对比
Figure 12. Delamination shape comparison of composite under low-velocity impact
Legend in the figure is envelope of delamination damage factor
表 1 复合材料圆形板材料参数
Table 1. Composite circular laminate material parameters
$ {E_1}/{\text{GPa}} $ $ {E_2}/{\text{GPa}} $ $ {G_{12}}/{\text{GPa}} $ $ {\nu _{12}} $ ρ/(kg·m−3) 153 10.3 6.0 0.3 1600 Notes: $ {E_1} $, $ {E_2} $ and $ {G_{12}} $—Modulus; $ {\nu _{12}} $—Poisson's ratio; $ \rho $—Density. 
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表 2 碳纤维增强环氧树脂复合材料(T700/M21)的面内材料性能[25]
Table 2. In-plane material parameters of carbon fiber reinforced epoxy resin composite (T700/M21)[25]
ρ=1580 kg/m3 E1/
GPaE2/
GPaG12/
GPaν12 XT/
MPaXC/
MPaYT/
MPaYC/
MPa130 7.7 4.8 0.3 2080 1250 60 290 Note: XT, XC, YT and YC—Strength.
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${G_{{\text{IC}}}}/{\text{MPa}}$ ${G_{{\text{IIC}}}}/{\text{MPa}}$ $\eta $ 0.5 1.6 1.45 Notes: ${G_{{\text{IC}}}}$ and ${G_{{\text{IIC}}}}$—Fracture toughness; $\eta $—Exponent.
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