复合材料层压板冲击后压缩强度拟合模型

doi:10.16183/j.cnki.jsjtu.2020.360

摘要/Abstract

摘要：

碳纤维增强的环氧树脂复合材料广泛地应用于飞机的主要承力结构,其冲击后压缩强度是损伤容限评估的重要内容.目前工程上主要利用大量试验获取冲击后压缩强度,对此需要开发一套简便的数学模型以描述冲击后压缩强度规律.提出一种全新的用于拟合复合材料层压板冲击后压缩强度数据的数学模型.采用该模型和初始模型参数,可以将不同冲击能量下的冲击后压缩强度数据转化为某一等效无损伤压缩强度数据,进而采用极大似然估计法对其进行正态分布拟合,得到正态分布的标准差.重复以上步骤,直至获得标准差的极小值,即可确定冲击后压缩强度数据拟合模型参数的最佳估计值.为了进一步表明该模型的适用性,进行不同厚度、铺层比例和材料类型的冲击后压缩试验,并采用该模型拟合试验数据.结果表明该模型对不同厚度、铺层比例和材料类型的冲击后压缩试验数据均具有较好的适用性.

关键词: 复合材料, 层压板, 冲击损伤, 压缩强度, 拟合模型, 极大似然估计

Abstract:

Carbon fiber-reinforced epoxy composites are widely used in the primary structure of aircraft, the compressive strength of which after impact is an important part in the evaluation of damage tolerance. At present, it mainly relies on a large number of tests to obtain compressive strength after impact in the engineering project. Therefore, it is necessary to develop a simple mathematical model to describe the compressive strength law after impact. A novel mathematical model for fitting compressive strength data of composite laminate after impact was proposed. Using the mathematical model and the initial model parameters, the compressive strength data after impact at different impact energy could be converted into some equivalent undamaged compressive strength data. Then, these equivalent undamaged compressive strength data were normally fitted using the maximum-likelihood estimate (MLE) method to obtain the standard deviation of normal distribution. The above steps was repeated until the minimum estimator of standard deviation was obtained. Hence, the best estimators of parameters for the mathematical model were determined. In order to further demonstrate the applicability of the mathematical model, post-impact compressive strength tests including different thicknesses, layup proportion, and material types were conducted, and the experimental data were fitted with the model. The results indicate that the mathematical model has a good applicability to the compressive strength test data after impact including different thicknesses, layup proportions, and material types.

Key words: composite, laminate, impact damage, compressive strength, fitting model, maximum-likelihood estimate (MLE)

中图分类号:

TB332

管清宇, 夏品奇, 郑晓玲, 吴光辉. 复合材料层压板冲击后压缩强度拟合模型[J]. 上海交通大学学报, 2021, 55(11): 1459-1466.

GUAN Qingyu, XIA Pinqi, ZHENG Xiaoling, WU Guanghui. Fitting Model to Compressive Strength of Composite Laminate After Impact[J]. Journal of Shanghai Jiao Tong University, 2021, 55(11): 1459-1466.

图/表 14

图1

表1

图2

图3

图4

图5

图6

表2

M21/IMA材料L0铺层的损伤投影面积

E/J	$A - d$ /mm²	C_V/%
无损伤	—	—
20	390	6.4
30	697	11
40	936	8.1
50	1203	12

表2

表3

M21/IMA材料L0铺层的冲击后压缩强度数据

$A - d$ / mm²	ε_CAI×10⁶
$A - d$ / mm²	1	2	3	4	5	6
1	11754	10804	11895	12522	11489	10047
390	4655	5013	5179	4443	4571	4701
697	3730	3697	3996	4019	3442	4057
936	3451	3536	3573	3674	3743	3144
1203	3268	3212	3165	2981	3285	3493

表3

图7

图8

表4

模型参数

材料类型	铺层代码	$α^$	$β^$	$μ^$	$σ^$	B
M21/IMA	L1	0.0158	0.3581	11862	899	0.8305
	L2	0.0186	0.3870	10653	814	0.8271
X850/IM+	L0	0.0235	0.3716	9450	758	0.8159

表4

图9

图10

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材料类型	铺层代码	铺层顺序	铺层比例(0/±45/90)	名义厚度/mm	E/J
M21/IMA	L0	[45/0/-45/90]_2S	25/50/25	2.992	无损伤、20、30、 40、50
	L1	[45/0/-45/90]_3S	25/50/25	4.448
	L2	[45/0/-45/90/45/0/-45/0/90/0]_S	40/40/20	3.740
X850/IM+	L0	[45/0/-45/90]_2S	25/50/25	2.992