低速冲击下复合材料层合板损伤预测模型评估

李峰忠; 金士杰; 张新垚; 罗忠兵

低速冲击下复合材料层合板损伤预测模型评估

大连理工大学　无损检测研究所, 大连116024

基金项目: 国家自然科学基金(52375527；52275520)

详细信息

通讯作者:
罗忠兵，博士，副教授，博士生导师，研究方向为材料损伤及其无损检测与评价　E-mail: zhbluo@dlut.edu.cn

中图分类号: V258；TB55；TB332
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- 被引次数: 0
出版历程
- 收稿日期: 2024-06-27
- 修回日期: 2024-08-02
- 录用日期: 2024-08-10
- 网络出版日期: 2024-08-31

Assessment of damage prediction models for composite laminates under low-velocity impact

NDT & E Laboratory, Dalian University of Technology, Dalian 116024, China

Funds: National Natural Science Foundation of China (52375527 and 52275520).

摘要

摘要: 针对碳纤维复合材料层合板低速冲击损伤的预测问题，采用数值模拟方法从结构外部力学响应、内部损伤状态两个方面，探讨三种损伤起始准则和三种演化方法对其影响。建立了分析层合板冲击问题的三维有限元模型，设计了包含起始判定、渐进演化及本构关系的损伤计算流程。研究了冲击过程损伤面积定量演变，为阐释损伤机制提供新视角。结合实验数据对冲击损伤数值模型进行了验证，并对不同起始准则、演化方法的预测能力进行了评价探讨。结果表明，数值预测与实验测试的动态力学响应曲线吻合度较高，证明该数值模型能够准确预测低速冲击损伤。同时发现起始准则与演化方法的结合对损伤模型预测性能十分关键，Hashin-Strain准则结合线性等效应变方法(Hashin-Strain-E1)和Puck准则结合指数型等效位移方法(Puck-E3)最优。然而，当Hashin-Strain准则结合线性或指数型等效位移方法时(Hashin-Strain-E2/E3)，会由于刚度退化严重而引发穿透性损伤。研究成果为复合材料层合板低速冲击损伤预测与评估提供参考和借鉴。
- 复合材料 /
- 低速冲击 /
- 起始准则 /
- 演化方法 /
- 损伤预测
Abstract: For the prediction of low-velocity impact damage in carbon fiber composite laminates, this study examined the influence of three damage initiation criteria and three evolution methods from structural overall mechanical response and internal damage state. To facilitate our investigation, a three-dimensional finite element model analyzing the impact behavior of laminate was established. Subsequently, a damage calculation process encompassing initiation determination, progressive evolution, and constitutive relationship was designed. Additionally, the quantitative evolution of damage area during impact was studied, which provided a new perspective for elucidating the damage mechanism. Based on experimental data, the accuracy of numerical simulation was verified. Then the prediction capabilities of different initiation criteria and evolution methods were evaluated and discussed. The results show that the numerical prediction agrees well with the experiment in dynamic mechanical response curve. This proves the numerical model can accurately predict the impact damage. Meanwhile, it has been found that the combination of initiation criteria and evolution methods significantly impacts the predictive efficacy of damage models. The pairing of the Hashin-Strain criterion with the linear equivalent strain method (Hashin-strain-E1) and the Puck criterion with the exponential equivalent displacement method (Puck-E3) yields optimal results. However, coupling the Hashin-Strain criterion with either the linear or exponential equivalent displacement method (Hashin-strain-E2/E3) can lead to penetrating damage due to severe degradation in stiffness. These research findings offer valuable insights into predicting low-velocity impact damage in composite laminates.
- Keywords: laminate /
- low-speed impact /
- initiation criterion /
- evolution method /
- damage prediction

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图 1 Puck准则中横向压缩载荷下塑性断裂行为

Figure 1. Damage fracture under transverse compression for Puck criterion

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图 2 渐进演化方法中应力、损伤变量与位移的关系

Figure 2. Relationship between stress, damage variables and displacement in progressive evolution methods

$ {\delta }_{\mathrm{e}\mathrm{q},i} $ and $ {\sigma }_{\mathrm{e}\mathrm{q},i} $ are equivalent displacement and stress; $ {\delta }_{\mathrm{e}\mathrm{q},i}^{\mathrm{i}\mathrm{n}\mathrm{i}\mathrm{t}\mathrm{i}\mathrm{a}\mathrm{l}} $ and $ {\sigma }_{\mathrm{e}\mathrm{q},i}^{\mathrm{i}\mathrm{n}\mathrm{i}\mathrm{t}\mathrm{i}\mathrm{a}\mathrm{l}} $ are initiation equivalent displacement and stress. $ {\delta }_{\mathrm{e}\mathrm{q},i}^{\mathrm{f}\mathrm{i}\mathrm{n}\mathrm{a}\mathrm{l}} $ is failure equivalent displacement. $ {d}_{i} $ is damage state variable. $ {G}_{i} $ is fracture energy

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图 3 层间单元混合型双线性牵引-分离本构关系

Figure 3. Constitutive relation of the mixed-model bilinear traction-separation for cohesive element

$ {\delta }_{\mathrm{m}}^{\mathrm{i}\mathrm{n}\mathrm{i}\mathrm{t}\mathrm{i}\mathrm{a}\mathrm{l}} $ and $ {\delta }_{\mathrm{m}}^{\mathrm{f}\mathrm{i}\mathrm{n}\mathrm{a}\mathrm{l}} $ are initiation and failure equivalent displacement. Model Ⅰ, Ⅱ/Ⅲ are the failure model in out-of-plane direction and in-plane transverse direction. N, S and T are the strength in three directions

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图 4 低速冲击损伤有限元模型

Figure 4. Low-velocity impact finite element model

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图 5 层合板低速冲击数值模拟流程

Figure 5. Numerical simulation flowchart of low-velocity impact for the laminate

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图 6 层合板动态力学响应和数值模拟指标验证

Figure 6. Dynamic mechanical response and index verification of the numerical simulation for the laminate

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图 7 层合板损伤面积动态表征

Figure 7. Dynamic characterization of damage area for the laminate

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图 8 冲击过程中层合板动态力学响应

Figure 8. Dynamic mechanical response during impact progress for the laminate

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图 9 层合板损伤面积动态表征

Figure 9. Dynamic characterization of damage area for the laminate

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图 10 不同损伤起始准则结合E1演化方法预测的层合板内部损伤形貌

Figure 10. Damage morphology within the laminate predicted by different initiation criteria combined with E1 evolution method

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表 1 不同损伤模式下的等效位移和等效应力

Table 1. Equivalent displacement and equivalent stress for different damage modes

Modes	Equivalent displacement	Equivalent stress
ft	$ \delta _{{\mathrm{eq,ft}}}^{} = {l^{\mathrm{c}}} \cdot \sqrt {{{\left\langle {{\varepsilon _{11}}} \right\rangle }^2} + {{\left( {{\varepsilon _{12}}} \right)}^2} + {{\left( {{\varepsilon _{13}}} \right)}^2}} $	$ \sigma _{{\mathrm{eq,ft}}}^{} = {l^{\mathrm{c}}} \cdot \dfrac{{\left\langle {{\sigma _{11}}} \right\rangle \left\langle {{\varepsilon _{11}}} \right\rangle + {\sigma _{12}}{\varepsilon _{12}} + {\sigma _{13}}{\varepsilon _{13}}}}{{\delta _{{\mathrm{eq,ft}}}^{}}} $
fc	$ \delta _{{\mathrm{eq,fc}}}^{} = {l^{\mathrm{c}}} \cdot \left\langle { - {\varepsilon _{11}}} \right\rangle $	$ \sigma _{{\mathrm{eq,fc}}}^{} = {l^{\mathrm{c}}} \cdot \dfrac{{\left\langle { - {\sigma _{11}}} \right\rangle \left\langle { - {\varepsilon _{11}}} \right\rangle }}{{\delta _{{\mathrm{eq,fc}}}^{}}} $
mt	$ \delta _{{\mathrm{eq,mt}}}^{} = {l^{\mathrm{c}}} \cdot \sqrt {{{\left\langle {{\varepsilon _{22}}} \right\rangle }^2} + {{\left\langle {{\varepsilon _{33}}} \right\rangle }^2} + {{\left( {{\varepsilon _{12}}} \right)}^2} + {{\left( {{\varepsilon _{23}}} \right)}^2} + {{\left( {{\varepsilon _{13}}} \right)}^2}} $	$ \sigma _{{\mathrm{eq,mt}}}^{} = {l^{\mathrm{c}}} \cdot \dfrac{{\left\langle {{\sigma _{22}}} \right\rangle \left\langle {{\varepsilon _{22}}} \right\rangle + \left\langle {{\sigma _{33}}} \right\rangle \left\langle {{\varepsilon _{33}}} \right\rangle + {\sigma _{12}}{\varepsilon _{12}} + {\sigma _{13}}{\varepsilon _{13}} + {\sigma _{23}}{\varepsilon _{23}}}}{{\delta _{{\mathrm{eq,mt}}}^{}}} $
mc	$ \delta _{{\mathrm{eq,mc}}}^{} = {l^{\mathrm{c}}} \cdot \sqrt {{{\left\langle { - {\varepsilon _{22}}} \right\rangle }^2} + {{\left\langle { - {\varepsilon _{33}}} \right\rangle }^2} + {{\left( {{\varepsilon _{12}}} \right)}^2} + {{\left( {{\varepsilon _{23}}} \right)}^2} + {{\left( {{\varepsilon _{13}}} \right)}^2}} $	$ \sigma _{{\mathrm{eq,mc}}}^{} = {l^{\mathrm{c}}} \cdot \dfrac{{\left\langle { - {\sigma _{22}}} \right\rangle \left\langle { - {\varepsilon _{22}}} \right\rangle + \left\langle { - {\sigma _{33}}} \right\rangle \left\langle { - {\varepsilon _{33}}} \right\rangle + {\sigma _{12}}{\varepsilon _{12}} + {\sigma _{13}}{\varepsilon _{13}} + {\sigma _{23}}{\varepsilon _{23}}}}{{\delta _{{\mathrm{eq,mc}}}^{}}} $
Notes: < > is Macaulay bracket. $ {\sigma }_{\mathrm{e}\mathrm{q},i} $ and $ {\delta }_{\mathrm{e}\mathrm{q},i} $ is equivalent stress and displacement, where i= ft, fc, mt and mc damage model. $ {l}^{\mathrm{c}} $ is the characteristic length of element.

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表 2 T700 GC/M21单向板和界面材料参数

Table 2. Material parameters of unidirectional laminate and interlayer for T700 GC/M21 composite

Laminate properties
Density/(kg·m⁻³)	1600
Young’s modulus/GPa	E₁₁ = 130; E₂₂ = E₃₃ = 7.7; G₁₂ = G₁₃ = 4.8; G₂₃ = 3.8
Poisson’s ratio	ν₁₂ = ν₁₃ = 0.33; ν₂₃ = 0.35
Strength/MPa	X_T = 2080; X_C =1250; Y_T = 60; Y_C =140; S₁₂ = S₁₃ = S₂₃ = 110
Fracture energy/(N·mm⁻¹)	G_ft = 133; G_fc = 40; G_mt = 0.6 N; G_mc = 2.1
Interlayer properties
Elastic modulus/GPa	E = 5
Strength/MPa	N = S = T = 30
Fracture energy/(N·mm⁻¹)	G_IC = 0.6; G_IIC = 2.1
Power exponent η	1.45

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表 3 预测模型能力指标评价

Table 3. Index evaluation for the capability of prediction model

		Peak force/kN	Max. displacement/mm	Impact time/ms	Absorbed energy/J
Experiment		8.65	5.11	3.60	13.00
Hashin-Stress	E1	10.50(+21.4%)	4.72(−7.6%)	3.24(−10%	8.66(−33.4%)
Hashin-Strain		8.84(+2.2%)	4.97(−2.7%)	3.70(+2.8%>)	10.03(−22.8%)
Puck		11.44(+32.3%)	4.64(−9.2%)	3.11(−13.6%)	8.08(−37.8%)
Hashin-Stress	E2	8.74(+1.0%)	4.91(−3.9%)	3.70(2.8%)	11.00(−15.4%)
Hashin-Strain		—	—	—	—
Puck		8.62(−0.3%)	4.93(−3.5%)	3.50(−2.8%)	9.44(−27.4%)
Hashin-Stress	E3	9.40(+8.7%)	4.96(−2.9%)	3.70(+2.8%)	10.60(−18.5%)
Hashin-Strain		—	—	—	—
Puck		7.85(−9.2%)	5.09(−0.4%)	3.70(+2.8%)	9.44(−27.4%)

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