﻿ 内聚力模型的形状对胶接结构断裂过程的影响
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 力学学报  2016, Vol. 48 Issue (5): 1088-1095  DOI: 10.6052/0459-1879-16-064 0

引用本文 [复制中英文]

[复制中文]
Zhang Jun , Jia Hong . INFLUENCE OF COHESIVE ZONE MODELS SHAPE ON ADHESIVELY BONDED JOINTS[J]. Chinese Journal of Ship Research, 2016, 48(5): 1088-1095. DOI: 10.6052/0459-1879-16-064.
[复制英文]

文章历史

2016-03-02 收稿
2016-04-18 录用
2016-04-24网络版发表

1 实验过程 1.1 粘接试件制作

 图 1 铝型材和粘接试件的尺寸 Figure 1 Configuration of specimen and aluminum extrusion dimensions
 图 2 双臂梁试件的结构尺寸 Figure 2 Configuration and dimensions of the DCB specimen
1.2 实验方案

 图 3 Arcan夹具的安装图(a),铝型材试件的夹具(b) Figure 3 Scheme of assembly of the specimen in modified Arcan fixture (a) and clamp for Aluminum extrusion (b)
 图 4 试件的引伸计安装 Figure 4 Scheme of the extensometer on the specimen
2 内聚力模型

 图 5 3种内聚力模型的拉伸-分离关系曲线 Figure 5 Schematic representation of traction-separation relationship of the cohesive zone models
2.1 抛物线型内聚力模型

 $T_n = - \dfrac{\phi _n }{\delta _{n1} }\exp \Bigg ( - \dfrac{\varDelta _n }{\delta _n } \Bigg) \Bigg\{ \dfrac{\varDelta _n }{\delta _n }\exp \left( { - \dfrac{\varDelta _\tau^2 }{\delta _{\tau 1}^2 }} \right) +$ $\dfrac{1 - q}{r - 1}\left[{1 - \exp \left( { - \dfrac{\varDelta _\tau ^2 }{\delta _{\tau 1}^2 }} \right)} \right]\left( {r - \dfrac{\Delta _n }{\delta _{n1} }} \right) \Bigg \}$ (1)
 $T_\tau = - \dfrac{\phi _n }{\delta _{n1} } 2\dfrac{\delta _{n1} }{\delta _{\tau 1} } \dfrac{\varDelta _\tau }{\delta _{\tau 1} }\left[{q + \left( {\dfrac{r - q}{r - 1}} \right)\dfrac{\varDelta _n }{\delta _{n1} }} \right]\cdot$ $\exp \left( { - \dfrac{\varDelta _n }{\delta _{n1} }} \right)\exp \left( { - \dfrac{\varDelta _\tau ^2 }{\delta _{\tau 1}^2 }} \right)$ (2)

 $\phi _{\rm n} = \sigma _{\max } \delta _{n1} {\rm e}$ (3)
 $\phi _{\tau} = \sqrt {{\rm e}/ 2} \tau _{\max } \delta _{\tau 1}$ (4)

2.2 双线型内聚力模型

 $T_n = \left\{ \!\! \begin{array}{ll} \dfrac{\sigma _{\max } }{\sigma _{n1} }\varDelta _n & \left( {\varDelta _n ≤ \delta _{n1} } \right) \\ \sigma _{\max } \dfrac{\delta _n^{\rm f} - \varDelta _n }{\delta _n^{\rm f} - \delta _{n1} } & \left( {\varDelta _n > \delta _{n1} } \right)\end{array} \right.$ (5)
 $T_\tau = \left\{ \!\! \begin{array}{ll} \dfrac{\tau _{\max } }{\delta _{\tau 1} }\varDelta _\tau & \left( {\varDelta _\tau \leq \delta _{\tau 1} } \right) \\ \tau _{\max } \dfrac{\delta _\tau ^{\rm f} - \varDelta _\tau }{\delta _\tau ^{\rm f} - \delta _{\tau 1} } & \left( {\Delta _\tau > \delta _{\tau 1} } \right) \end{array} \right.$ (6)

 $\phi _n = \dfrac{1}{2}\sigma _{\max } \delta _n^{\rm f}$ (7)
 $\phi _\tau = \dfrac{1}{2}\tau _{\max } \delta _\tau ^{\rm f}$ (8)

2.3 三线型内聚力模型

 $T_n = \left\{ \!\!\begin{array}{ll} \dfrac{\sigma _{\max } }{\sigma _{n1} }\varDelta _n & \left( {\varDelta _n ≤ \delta _{n1} } \right) \\ \sigma _{\max } & \left( {\delta _{n1} ≤ \varDelta _n ≤ \delta _{n2} } \right) \\ \dfrac{\sigma _{\max } }{\delta _n^{\rm f} - \delta _{n2} }\;(\delta _n^{\rm f} - \varDelta _n ) & \left( {\delta _{n2} ≤ \varDelta _n ≤ \delta _n^{\rm f} } \right) \\ 0 & \left( {\varDelta _n>\delta _n^{\rm f} } \right)\end{array} \right.$ (9)
 $T_\tau = \left\{ \begin{array}{ll} \dfrac{\tau _{\max } }{\sigma _{\tau 1} }\varDelta _\tau & \left( {\varDelta _\tau ≤ \delta _{\tau 1} } \right) \\ \tau _{\max } & \left( {\delta _{\tau 1} ≤ \varDelta _\tau ≤ \delta _{\tau 2} } \right) \\ \dfrac{\tau _{\max } }{\delta _\tau ^{\rm f} - \delta _{\tau 2} }\;(\delta _\tau^{\rm f} - \varDelta _\tau ) & \left( {\delta _{\tau 2} ≤ \varDelta _\tau ≤ \delta _\tau^{\rm f} } \right)\\ 0 & \left( {\varDelta _\tau>\delta _\tau^{\rm f} } \right)\end{array} \right.$ (10)

 $\phi _n = \dfrac{1}{2}\sigma _{\max } \left( {\delta _{n2} - \delta _{n1} + \delta _n^{\rm f} } \right)$ (11)
 $\phi _\tau = \dfrac{1}{2}\tau _{\max } \left( {\delta _{\tau 2} - \delta _{\tau 1} + \delta _\tau ^{\rm f} } \right)$ (12)

3 模型建立和模拟方法

4 结果与分析 4.1 脆性胶黏剂拉伸和剪切实验及数值计算

 图 6 脆性胶接试件的拉伸与剪切的应力-位移曲线 Figure 6 Typical tensile and shear stress-displacement cure of the epoxy-based adhesive bonding specimen

 图 7 3种内聚力模型计算脆性胶接试件拉伸断裂曲线 Figure 7 Predicted results for the epoxy-base adhesive tensile test using the different CZMs
 图 8 3种内聚力模型计算脆性胶接试件剪切断裂曲线 Figure 8 Predicted results for the epoxy-base adhesive shear test using the different CZMs
4.2 延展性胶黏剂拉伸和剪切实验及数值计算

 图 9 延展性胶接试件的拉伸与剪切的应力-位移曲线 Figure 9 Typical tensile and shear stress-displacement cure of the VHB$^{\rm TM}$ tape adhesive bonding specimen

 图 10 3种内聚力模型计算延展性胶接试件拉伸断裂曲线 Figure 10 Predicted results for the VHBTM tape adhesive tensile test using the different CZMs
 图 11 3种内聚力模型计算的延展性胶接试件剪切断裂曲线 Figure 11 Predicted results for the VHBTM tape adhesive shear test using the different CZMs
4.3 双臂梁试件的断裂实验及数值计算

 图 12 脆性胶接的双臂梁试件断裂实验与3种内聚力模型计算结果 Figure 12 Brittle adhesive experimental results of DCB specimen and predicted results using the different CZMs

 图 13 延展性胶接的双臂梁试件断裂实验与3种内聚力\模型计算结果 Figure 13 Experimental results of DCB specimen and predicted results using the different CZMs
5 结论