Process-induced deformation characteristics of variable stiffness composite laminates based on automatic placement technology
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摘要: 准确预测和控制变刚度结构的固化变形是合理进行变刚度设计的关键环节，复合材料结构的固化变形不仅会影响结构的刚度强度特性、同时会对结构的装配性能产生影响。基于自动铺放技术，提出面向过程的丝束-路径-面板多级三维变刚度有限元模型算法。结合Kamal自催化固化动力学模型和广义Maxwell黏弹性本构模型进行热-化学-力多场耦合分析，计算固化过程中结构内部温度场、固化度场和残余应力场的变化，最终得到变刚度层合板的固化变形特性。通过参数化分析，研究了自动铺放过程中轨迹控制参数T0、T1和覆盖法则对结构固化变形产生的影响。研究结果表明：T0=45°时，当T1<T0变刚度结构的固化变形随着T1的增大而增大，当T1>T0，变刚度结构的固化变形随着
$ {T_1}$ 的增大而减小。100%覆盖法则有效减小结构的固化变形，而0%覆盖法则使固化变形增大。本文提出的方法可以有效预测工艺参数对变刚度结构固化变形的影响。Abstract: Accurately predicting and controlling the process-induced deformation of a variable stiffness structure is a key to obtain a reasonable variable stiffness design, the process-induced deformation of a composite structure will not only affect the stiffness and strength of the structure, but also affect the assembly performance of the structure. Based on the automatic placement technology, a process-oriented tow-course-panel multi-level three-dimensional variable stiffness finite element model algorithm was proposed. Combining the Kamal autocatalytic reaction curing kinetic model and the generalized Maxwell viscoelastic constitutive model for thermo-chemical-mechanical multi-field coupling analysis, the changes in the internal temperature field, curing degree field and residual stress field of the structure during the curing process were calculated, and the curing deformation of the variable stiffness structure was finally obtained. The results show that: when T0=45°, T1<T0, the curing deformation of the variable stiffness structure increases with the increase of T1. When T1>T0, the curing deformation of the variable stiffness structure decreases with the increase of T1. The 100% coverage rule effectively reduces the curing deformation of the structure, while the 0% coverage rule increases the curing deformation. The method proposed in this paper can effectively predict the effect of process parameters on the process-induced deformation of variable stiffness structures. -
图 2 面向铺放过程的变刚度复合材料层合板三维有限元模型建模方法
Figure 2. Three-dimensional finite element model modeling method for AFP of variable stiffness composite laminates
图 3 变刚度复合材料层合板纤维角度线性变化
Figure 3. Fiber angle linear variation of variable stiffness composite laminates
T1—End fiber angle; T0—Initial fiber angle; d—Characteristic length; φ—Reference coordinate system deflection angle
图 4 变刚度复合材料层合板丝束铺放路径模型
Figure 4. Course model of variable stiffness composite laminate
A'—A point on the centerline of the fiber course; A—A point on the course centerline normal; φA'—Fiber angle at point; φA—Fiber angle at point A
图 6 变刚度复合材料层合板丝束剪切区域计算模型
Figure 6. Tow cutting area calculation model of variable stiffness composite laminates
P—A point in the course; P', P''—Lower and upper boundary of the tow where point P is located; B—Intersection of the course normal where point P is located and the lower boundary of the course; D, D', D''—P, P', P'' corresponds to the point on the lower boundary of the course in the translation direction
图 7 三维变刚度层合板有限元模型
Figure 7. Three-dimensional finite element model of variable stiffness composite laminates
图 8 本文理论模型计算AS4/3501-6复合材料层合板固化度场和温度场有效性验证
Figure 8. Validation verification of theoretical model for calculating curing degree field and temperature field of AS4/3501-6 composite laminates
图 9 本文理论模型计算AS4/3501-6复合材料层合板残余应力有效性验证
Figure 9. Verification of the validity of the theoretical model in the calculation of residual stress of AS4/3501-6 composite laminates
y—y-axis; a—Length of side
图 10 AS4/3501-6变刚度层合板对角截面的面外位移：(a) 理想模型；(b) 100%覆盖法则；(c) 0%覆盖法则(
${T_0} > {T_1}$ )Figure 10. Out-of-plane displacement of diagonal section: (a) Ideal model; (b) 100% covering rule; (c) 0% covering rule (
${T_0} > {T_1}$ ) of AS4/3501-6 variable stiffness laminates
图 11 AS4/3501-6变刚度层合板对角截面的面外位移：(a) 理想模型；(b) 100%覆盖法则；(c) 0%覆盖法则(
${T_0} < {T_1}$ )Figure 11. Out-of-plane displacement of diagonal section: (a) Ideal model; (b) 100% covering rule; (c) 0% covering rule (
${T_0} < {T_1}$ ) of AS4/3501-6 variable stiffness laminates
图 12 纤维轨迹参数对AS4/3501-6变刚度层合板固化变形影响的参数化研究
Figure 12. Parameterized study of fiber trajectory parameters and effects on curing deformation of AS4/3501-6 variable stiffness composite laminates
表 1 AS4/3501-6碳纤维/环氧树脂预浸料热化学参数[17]
Table 1. Thermochemical parameters for the AS4/3501-6 carbon/epoxy prepreg[17]
Constant Value $\rho /\left( {{\rm{kg}} \cdot {{\rm{m}}^{{\rm{ - 3}}}}} \right)$ 1578 ${c_{\rm{p}}}/\left( {{\rm{J}} \cdot {{\left( {{\rm{kg}} \cdot {\rm{K}}} \right)}^{{\rm{ - 1}}}}} \right)$ 862 ${k_x}/\left( {{\rm{W}} \cdot {{\left( {{\rm{m}} \cdot {\rm{K}}} \right)}^{{\rm{ - 1}}}}} \right)$ 12.83 ${k_y} = {k_z}/\left( {{\rm{W}} \cdot {{\left( {{\rm{m}} \cdot {\rm{K}}} \right)}^{{\rm{ - 1}}}}} \right)$ 0.4135 ${H_{\rm{T}}}/\left( {{\rm{J}} \cdot {\rm{k}}{{\rm{g}}^{{\rm{ - 1}}}}} \right)$ $198.6 \times {10^3}$ ${{{A_1}} /{{\rm{mi}}{{\rm{n}}^{{\rm{ - 1}}}}}}$ $2.101 \times {10^9}$ ${{{A_2}} /{{\rm{mi}}{{\rm{n}}^{{\rm{ - 1}}}}}}$ $ - 2.014 \times {10^9}$ ${{{A_3}} /{{\rm{mi}}{{\rm{n}}^{{\rm{ - 1}}}}}}$ $1.96 \times {10^5}$ ${{\Delta {E_1}} /{\left( {{\rm{J}} \cdot {\rm{mo}}{{\rm{l}}^{{\rm{ - 1}}}}} \right)}}$ $8.07 \times {10^4}$ ${{\Delta {E_2}} / {\left( {{\rm{J}} \cdot {\rm{mo}}{{\rm{l}}^{{\rm{ - 1}}}}} \right)}}$ $7.78 \times {10^4}$ ${{\Delta {E_3}}/ {\left( {{\rm{J}} \cdot {\rm{mo}}{{\rm{l}}^{{\rm{ - 1}}}}} \right)}}$ $5.66 \times {10^4}$ Notes: $\rho $—Density of material; Cp—Specific heat of composite; kx and ky—Heat conduction coefficient of prepreg along x direction and y direction; HT—Total heat of the curing of unit mass; A1, A2, A3—Frequency factors of autocatalysis model; $\Delta {E_1}$,$\Delta {E_2}$,$\Delta {E_3}$—Activation energy of autocatalysis model. 
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表 2 AS4/3501-6碳纤维/环氧树脂预浸料参考固化度下的松弛时间和权重因子[19]
Table 2. Relaxation times and weighting factors at the reference degree of cure of AS4/3501-6 carbon/epoxy prepreg[19]
m ${\tau _m}/\min $ ${W_m}$ 1 $2.922 \times {10^1}$ 0.059 2 $2.921 \times {10^3}$ 0.066 3 $1.824 \times {10^5}$ 0.083 4 $1.103 \times {10^7}$ 0.112 5 $2.831 \times {10^8}$ 0.154 6 $7.943 \times {10^9}$ 0.262 7 $1.953 \times {10^{11}}$ 0.184 8 $3.315 \times {10^{12}}$ 0.049 9 $4.917 \times {10^{14}}$ 0.025 Notes: ${\tau _m}$—Discrete stress relaxation time for the ${m{{\rm{th}}}}$ Maxwell element; ${W_m}$—Mass factor for the ${m{{\rm{th}}}}$ Maxwell element.
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表 3 AS4/3501-6预浸料未松弛状态下热力学参数
Table 3. Thermomechanical parameters for the unrelaxed AS4/3501-6 prepreg
Parameter Value Elastic modulus ${E_1}/{\rm{MPa}}$ 126000 Elastic modulus ${E_2} = {E_3}/{\rm{MPa}}$ 8300 Shear modulus ${G_{12}} = {G_{13}}/{\rm{MPa}}$ 4100 Shear modulus ${G_{23}}/{\rm{MPa}}$ 2800 Thermal expansion coefficient ${\alpha _1}/\left( {{\rm{1}}{{\rm{0}}^{{\rm{ - 6}}}} \cdot {}^{\circ} {{\rm{C}}^{ - 1}}} \right)$ 0.5 Thermal expansion coefficient ${\alpha _2} = {\alpha _3}/\left( {{\rm{1}}{{\rm{0}}^{{\rm{ - 6}}}} \cdot {}^{\circ}{{\rm{C}}^{ - 1}}} \right)$ $35.3$ Chemical shrinkage coefficient ${\varPhi _1}/{\rm{1}}{{\rm{0}}^{{\rm{ - 6}}}}$ −167 Chemical shrinkage coefficient ${\varPhi _2} = {\varPhi _3}/{\rm{1}}{{\rm{0}}^{{\rm{ - 6}}}}$ −8810
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