Mechanical Behavior and Failure Mechanism of Glass Fiber Reinforced Plastics under Quasi-Static and Dynamic Compressive Loading

ZHANG Xihuang; LI Jinzhu; WU Haijun; HUANG Fenglei

doi:10.11858/gywlxb.20210734

Volume 35 Issue 6

Nov 2021

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Chinese Journal of High Pressure Physics > 2021 > 35(6): 064105.

YUAN Qin, LI Shuaiqi, ZHOU Li, HE Duanwei. Reciprocating Phase Transitions Behavior of Germanium under High Pressure[J]. Chinese Journal of High Pressure Physics, 2022, 36(5): 051104. doi: 10.11858/gywlxb.20220578

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ZHANG Xihuang, LI Jinzhu, WU Haijun, HUANG Fenglei. Mechanical Behavior and Failure Mechanism of Glass Fiber Reinforced Plastics under Quasi-Static and Dynamic Compressive Loading[J]. Chinese Journal of High Pressure Physics, 2021, 35(6): 064105. doi: 10.11858/gywlxb.20210734

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Mechanical Behavior and Failure Mechanism of Glass Fiber Reinforced Plastics under Quasi-Static and Dynamic Compressive Loading

doi: 10.11858/gywlxb.20210734

State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing 100081, China

Received Date: 08 Mar 2021
Rev Recd Date: 25 Mar 2021

Abstract

Abstract

To study the mechanical properties of glass fiber reinforced plastic composites under static and dynamic loading, compression experiments were conducted in two directions using a materials testing system (MTS) and a split Hopkinson pressure bar (SHPB). The typical damage pattern of the composites was obtained by scanning electron microscopy (SEM). The results show that the material has strong strain rate sensitivity and anisotropy. Delamination damage and interlaminar crush are the factors that caused the in-plane and out-of-plane loading damage, respectively. The microscopic analysis of the fracture shows that the degree of fiber-matrix fragmentation is higher under dynamic loading. The force between the fiber-matrix interface is stronger, which may be one reason for the difference in the dynamic and static mechanical response of the material. A compressive constitutive model with strain-rate and damage effects was developed to accurately describe the dynamic compressive stress-strain behaviors of the composite along the two perpendicular directions.
- glass fiber reinforced plastics,
- dynamic mechanical behaviors,
- strain rate effect,
- constitutive model

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TC4钛合金是一种 $\alpha + \beta$ 型中强度钛合金，具有较高的强度和较优异的塑性，在航空、航天、船舶以及兵器领域应用广泛^[1]。鸟撞问题是飞机结构在起降过程中面临的主要威胁之一。鸟撞发生时，鸟体在毫秒级时间内瞬间冲击机体结构。高速冲击产生的巨大能量将导致机身结构严重损伤，从而引发伤亡事故。因此，国际适航标准要求所有向前部件在使用前必须分析其抗鸟撞性能。

大量的研究表明，鸟体在高速冲击作用下表现出明显的流体流动飞溅特性。近年来，诸多学者针对飞机结构的抗鸟撞性能开展了大量研究工作。普遍认为，高速鸟撞冲击问题是一个应变率相关的流固耦合问题。目前结构抗鸟撞性能的数值分析方法主要有3种：拉格朗日有限元法（Lagrangian finite element）、任意拉格朗日-欧拉法（Arbitrary Lagrange-Euler，ALE）和光滑粒子流体动力学方法（Smooth particle hydro-dynamic，SPH）。采用拉格朗日有限元法分析高速鸟撞冲击时，因鸟体结构变形大，致使单元发生畸变，故拉格朗日有限元法只适合模拟低速鸟撞。SPH方法是一种基于拉格朗日技术的自适应无网格粒子法，将其与有限元方法进行耦合，可在流固耦合问题求解中展现显著的优势^[2-3]。由于SPH粒子在空间相互独立，因此SPH法比拉格朗日有限元法和ALE法更适于解决高速鸟撞冲击问题^[4]。例如：刘军等^[5]通过对比鸟撞平板叶片实验结果和SPH法及拉格朗日有限元法数值分析结果，发现SPH方法与实验结果更接近；刘富等^[6]采用SPH方法进行了2024-T3铝合金平板抗高速鸟撞冲击性能研究，得到了与实验结果相近的模拟结果；Liu等^[7]通过不同速度的平板鸟撞冲击实验和数值分析，研究了适用于不同鸟撞速度的鸟体模型；姚小虎等^[8]通过鸟撞圆弧风挡实验和数值计算，分析了风挡玻璃在鸟撞冲击过程中的损伤破坏。

本研究采用三维图像相关法（3 dimensional digital correlate，3D-DIC），分析TC4钛合金平板高速鸟撞过程中的变形场，基于SPH方法和TC4钛合金的Johnson-Cook动态损伤模型，建立TC4钛合金平板鸟撞数值模型，并将模拟结果与鸟撞实验进行对比验证。

1. 钛合金平板鸟撞实验

鸟撞实验装置由鸟弹发射系统、TC4钛合金靶板、速度测试系统、照明系统和高速摄像系统组成。实验装置如图1所示。本实验使用的鸟弹为长L = 228 mm、直径D = 114 mm的明胶弹。鸟弹由空气炮发射，利用激光测速仪记录发射速度，激光测速仪的系统误差小于0.5%。为了解析TC4钛合金靶板背面的三维变形场，在靶板背面设置两台I-SPEED 716型高速摄影机，拍摄帧率设置为10⁴帧每秒。位于靶板正面的两台SA-X型高速摄影机记录鸟弹飞行轨迹和撞击靶板时的响应，保证鸟弹垂直撞击TC4钛合金靶板。实验开始之前，进行调焦、视场校准和同步设置。将4台高速摄影机的触发开关通过BNC线引至操作间，其中用于动态3D-DIC测量的两台相机使用转接头连接，以实现同步触发。高速摄影机布局如图2所示。

图 1 实验装置示意图

Figure 1. Schematic of experimental apparatus

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图 2 高速摄影机布局

Figure 2. High speed camera arrangement

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试件材料为TC4钛合金平板，尺寸为600 mm × 600 mm × 1.6 mm。通过均匀分布的16颗M10螺栓及4.0 mm厚的夹具，将试件固定在试验工装上，夹具尺寸与螺栓分布如图3所示。

图 3 靶板尺寸

Figure 3. Size of target board

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鸟撞实验共设3个发射速度，分别为149、167和180 m/s。每组进行4次重复实验。图4显示了3种速度工况下鸟撞实验结果。图4中第1行的3幅图为平板正面高速摄影图像，可以看出：鸟弹包裹在弹托中由炮管发射，在空气阻力和实验舱入射口的作用下，鸟弹和弹托在撞击TC4钛合金平板前完全分离。弹托保证了鸟弹在发射过程中的整体形状和结构不受炮管内高压气体的破坏，弹托与鸟弹的完全分离消除了弹托对TC4平板鸟撞响应的影响。图4中第2行和第3行图像分别显示了TC4钛合金平板的正面和背面鸟撞冲击结果。发射速度为149 m/s的4次实验中，TC4钛合金平板均未发生破坏；发射速度为167 m/s的4次实验中，2次发生破坏，2次未发生破坏；而发射速度为180 m/s的4次实验中，平板均发生破坏。

图 4 149、167和180 m/s的鸟撞实验结果

Figure 4. Results of bird strike experiments at the speed of 149, 167 and 180 m/s

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图5为TC4钛合金平板破坏照片。鸟体撞击平板后产生的拉伸波向外传播，在螺栓处产生剪切作用，平板发生了剪切破坏。

图 5 TC4钛合金平板破坏照片

Figure 5. Failure of TC4 titanium alloy plate

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2. 钛合金平板鸟撞数值计算

2.1 计算模型

数值计算采用的鸟体几何模型与实验相同，为两端半球状、中间圆柱体的胶囊状柱体，长径比L/D = 2，如图6所示。鸟体模型的质量为1.8 kg。采用SPH单元模拟高速鸟撞冲击过程中的鸟体流体状飞溅，鸟体材料参数列于表1。

表 1 鸟体材料参数

Table 1. Material parameters of bird body

Density/（kg·m⁻³）	Elastic modulus/GPa	Poisson’s ratio	Yield stress/MPa	Failure strain	Tangent modulus/MPa
928	0.068	0.49	0.69	1.25	5

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图 6 鸟弹的几何尺寸

Figure 6. Geometry of bird ball

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高速鸟撞实验过程中，靶板夹具和支撑架的刚度足够大，夹具和支撑架只发生线弹性变形，因此采用钢材的线弹性本构模型描述。TC4钛合金平板在高速鸟撞冲击载荷作用下发生了大变形和损伤破坏。实验发现，TC4钛合金平板的主要破坏形式是剪切破坏，因此在数值仿真计算中需要考虑剪应力的影响。大量实验表明，钛合金材料具有拉压不对称性，需要对von Mises屈服准则进行修正。本研究将Johnson-Cook动态本构模型和Johnson-Cook损伤失效模型引入邹学韬等^[9]提出的von Mises修正本构框架中。该本构可以表征TC4钛合金在强冲击载荷作用下的塑性流动应力和损伤破坏行为。Johnson-Cook动态本构模型的表达式为

${\sigma _{\rm{s}}}{\rm{ = (}}A{\rm{ + }}B{\varepsilon ^n})(1 + C\ln {\dot \varepsilon ^*})(1 - {{T^*}^m})$

(1)

式中： ${\sigma _{\rm{s}}}$ 为塑性流动应力；A为参考应变率下的屈服应力；B和n为应变强化系数； $\varepsilon$ 为等效塑性应变；C为应变率敏感系数； ${\dot \varepsilon ^*}{\rm{ = }}\dot \varepsilon /{\dot \varepsilon _0}$ 为无量纲应变率， ${\dot \varepsilon _0}$ 为参考应变率； ${T^*}{\rm{ = (}}T - {T_{\rm{r}}})/({T_{\rm{m}}} - {T_{\rm{r}}})$ 为无量纲温度，T为温度， ${T_{\rm m}}$ 为材料熔化温度， ${T_{\rm{r}}}$ 为参考温度；m为温度软化系数。

考虑到TC4钛合金材料的拉压不对称性，引入拉压不对称因子 $G(\sigma )$ 修正von Mises屈服面，得到屈服函数为

$\phi {\rm{ = }}f(\sigma )G(\sigma ) = 1$

(2)

$f(\sigma ) = 3J/{\sigma _{\rm{s}}^2}$

(3)

$G(\sigma ) = \exp [ - c(\xi + 1)] = 1$

(4)

式中： $f(\sigma ) = 1$ 为von Mises屈服面函数； $\xi =\cos (3\theta ) = \dfrac{{27}}{2} \cdot \dfrac{{{J_3}}}{{{{(3{J_2})}^{3/2}}}}$ 为Lode参数，其中 $\theta$ 为Lode角，J₂为偏应力第二不变量，J₃为偏应力第三不变量； $c$ 为不对称系数，可以通过两种简单应力状态求解。本研究中，不对称系数 $c$ 取

$c = - 2\ln \left(\frac{{{\sigma _{\rm{s}}}}}{{\sqrt 3 {\tau _{\rm{s}}}}}\right)=- 2\ln \alpha ,\;\;\;\;\alpha=\frac{{{\sigma _{\rm{s}}}}}{{\sqrt 3 {\tau _{\rm{s}}}}}$

(5)

式中： ${\tau _{\rm{s}}}$ 为纯剪切加载的屈服应力。于是，根据相关联的流动法则，即屈服面函数等于塑性势函数 $g{\rm{(}}\sigma {\rm{)}}$ ，得到该本构的增量表达式

$\left\{ \begin{aligned} & {\rm{d}}{\sigma _{ij}} = {{{D}}_{\rm{e}}}{\rm{(d}}{\varepsilon _{ij}} - {\rm{d}}\varepsilon _{ij}^{\rm{p}}) \\ & {\rm{d}}\varepsilon _{ij}^{\rm{p}} = {\rm{d}}\lambda \dfrac{{\partial g}}{{\partial {\sigma _{ij}}}} \\ & {\rm{d}}\lambda =\dfrac{{g\left( {\sigma _{ij}^{{\rm{trail}}}} \right) + \dfrac{{\partial g}}{{\partial \dot \varepsilon }}{\rm{d}}\dot \varepsilon }}{{\dfrac{{\partial g}}{{\partial {\sigma _{ij}}}}{Y_{ij}} - \dfrac{{\partial g}}{{\partial \sigma _{{\rm{eq}}}^{\rm{p}}}}H}} \\ & {Y_{ij}} = {{{D}}_{\rm{e}}}\dfrac{3}{{{\sigma _{\rm{s}}^2}}}{\rm{exp}}\left[ {2\ln \alpha (\xi + 1)} \right]\left( {\dfrac{{\partial {J_2}}}{{\partial {\sigma _{ij}}}} + 2{J_2}\ln \alpha \dfrac{{\partial \xi }}{{\partial {\sigma _{ij}}}}} \right) \\ & H=\sqrt {\dfrac{2}{3}\dfrac{{\partial g}}{{\partial {\sigma _{ij}}}}\dfrac{{\partial g}}{{\partial {\sigma _{ij}}}}} \end{aligned} \right.$

(6)

式中：D_e为弹性矩阵， ${\rm{d}}\lambda$ 为塑性流动因子， $\varepsilon _{ij}^{\rm{p}}$ 为塑性应变， $\sigma _{ij}^{{\rm{trail}}}$ 为试探应力， $\sigma _{{\rm{eq}}}^{\rm{p}}$ 为等效塑性应力。

Johnson-Cook损伤失效模型为

${\varepsilon _{\rm{f}}}{\rm{ = [}}{D_1}{\rm{ + }}{D_2}\exp ({D_3}{\sigma ^*})](1 + {D_4}\ln {\dot \varepsilon ^*})(1 + {D_5}{T^*})$

(7)

式中： ${\varepsilon _{\rm{f}}}$ 为失效应变；D₁～D₅为材料参数； ${\sigma ^*}{\rm{ = }}p/{\sigma _{\rm{eq}}}{\rm{ }}$ ，其中p为静水压力， ${\sigma _{\rm{eq}}}$ 为等效应力。

数值计算所使用的本构模型参数列于表2^[10-11]，其中E为弹性模量，ρ为密度，μ为泊松比。

表 2 TC4钛合金材料参数^[10-11]

Table 2. Parameters of TC4 titanium alloy^[10-11]

ρ/(g·cm⁻³)	μ	T_m/K	A/MPa	B/MPa	n	C	m
4.430	0.33	1 878	1060	1090	0.884	0.0117	1.1

E/GPa	${\dot \varepsilon _{{0}}}$ /s⁻¹	D₁	D₂	D₃	D₄	D₅
135	4 × 10⁻⁴	−0.090	0.270	0.480	0.014	3.870

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TC4钛合金平板高速鸟撞的数值计算有限元模型如图7所示。TC4靶板、夹具和M10螺栓均采用C3D8R六面体八节点减缩积分单元模拟。通过建立一般接触，计算鸟体撞击TC4钛合金靶板以及螺栓和靶板之间的接触。夹具通过16颗M10螺栓固定在支架上，在数值计算中对螺栓进行固支约束。鸟体速度分别设置为149、167和180 m/s。

图 7 鸟撞数值计算模型

Figure 7. Numerical model of bird strike

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在TC4钛合金平板上选取6个具有代表意义的观测点，如图8所示，其中观测点S₁、S₂和S₃沿轴向分布，S₄、S₅和S₆沿对角线方向分布。

图 8 观测点布局

Figure 8. Distribution of observation points

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2.2 计算结果

图9为鸟撞速度为149 m/s时TC4钛合金平板的等效应力云图。鸟体撞击平板后，鸟体前端受到冲击压缩后解体并呈流体状飞溅，鸟体后端仍保持固体状态。平板受鸟体冲击后产生拉伸波，并向平板四周传播。1.66 ms时鸟体完全解体，鸟体撞击的冲击能量完全耗散，此时TC4钛合金平板的应力、应变和位移达到最大值，随后开始一定程度回弹。

图 9 149 m/s鸟撞等效应力云图

Figure 9. Equivalent stress nephograms of bird impacting with the velocity of 149 m/s

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图10为鸟撞击后TC4钛合金平板变形的数值计算结果和3D-DIC实验结果对比。图10中149 m/s和167 m/s工况下的最大位移（S_max）图像选自未破坏实验，180 m/s工况下的最大位移图像选自平板破坏飞出前（2.00 ms前）。鸟撞过程中，TC4钛合金平板的变形大，对角线方向隆起，隆起处亮度明显增大，使得平板部分区域被遮挡，同时也遮挡了高速摄影机，因此出现部分区域未追踪到变形场的问题。由图10可知，计算得到的最大位移场与实验结果吻合较好。3种工况下数值仿真和实验得到的观测点最大位移如表3所示。

表 3 TC4钛合金平板鸟撞最大位移

Table 3. Maximum displacement of titanium alloy plate impacted by a bird

Velocity/(m·s⁻¹)	Method	Maximum displacement/mm
Velocity/(m·s⁻¹)	Method	S₁	S₂	S₃	S₄	S₅	S₆
149	Sim.	65	51	36	64	55	23
149	Exp.	68	60	38	63	53	25
167	Sim.	75	60	48	76	65	27
167	Exp.	80	59	47	76	63	24
180	Sim.	119	101	63	118	103	54
180	Exp.	117	90	53	103	95	50

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图 10 TC4钛合金平板鸟撞变形结果

Figure 10. Deformation of TC4 titanium alloy plate under the bird impact

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图11为计算得到的180 m/s工况下TC4钛合金平板破坏过程中的等效塑性应变云图。从图11可以看出：0.40 ms时，位于轴线上的4颗螺栓附近开始出现裂纹；0.68 ms时，平板与夹具接触处进入塑性阶段；1.04 ms时，平板对角线和夹具接触处开始起裂，并沿着夹具边缘和对角线方向扩展；2.00 ms时，最先起裂的4颗螺栓孔处裂纹贯穿。对比可见，计算得到的螺栓孔处的损伤和破坏形式与实验结果基本一致。

图 11 180 m/s工况下计算得到的TC4钛合金平板破坏过程

Figure 11. Failure process of TC4 titanium alloy plate calculated at 180 m/s

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计算与实验得到的位移-时间曲线对比如图12所示。从图12中可以看出，计算得到的位移变化趋势及大小与实验结果基本吻合，表明本研究使用的Johnson-Cook动态本构和损伤失效模型对于模拟TC4钛合金高速鸟撞冲击问题是比较准确的。

图 12 位移-时间曲线的计算和实验结果对比

Figure 12. Comparison of calculated displacement-time curves with experimental results

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图13对比了6个观测点的应变时程曲线。数值计算得到的6个观测点应变与实验数据的整体吻合度较高。从图13中可以看出，最靠近鸟撞点的观测点S₁和S₄的等效应变在0～0.2 ms内增大，0.2～1.0 ms内保持平稳，1.0～1.4 ms再次增大，1.4 ms后再次保持不变，呈现双台阶模式。其余观测点均未表现出此双台阶模式。观测点S₁和S₂的等效应变出现双台阶的原因在于这两个点位于鸟弹半径范围之内。鸟弹撞击TC4钛合金平板瞬间，应变瞬间增大；0.2～1.0 ms内应力波向边界传递并在边界处反向，此时S₁和S₂区域内材料包裹着鸟弹运动，因此应变出现平台段；1.0 ms时，边界反射的应力波再次到达S₁和S₂区域，使得应变再次增大。

图 13 应变-时间曲线的计算与实验结果对比

Figure 13. Comparison of calculated strain-time curves with experimental results

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3. 结　论

通过3D-DIC实验和数值计算方法，研究了1.8 kg鸟体高速撞击1.6 mm厚TC4钛合金平板的动态响应和损伤破坏，得到了较精确、有效的有限元模型，并得到如下结论。

（1）1.6 mm厚的TC4钛合金在1.8 kg鸟体高速撞击下的临界破坏速度为167 m/s。撞击过程中平板内部未破坏，而螺栓和夹具处发生剪切破坏。

（2）3D-DIC测试技术能够比较准确地测定鸟撞冲击过程中TC4钛合金平板的变形场。高速冲击过程中平板的变形较大，易出现光线遮挡和反光，需要设置补充高速摄影机。

（3）实验表明，鸟撞冲击后TC4钛合金平板破坏主要为螺栓等边界处的剪切破坏。将修正的von Mises屈服准则引入Johnson-Cook动态本构和损伤模型中，在本构中同时考虑拉伸和剪切两种应力状态。该本构能够准确地模拟鸟撞平板问题。

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