# 胶接接头胶层切应力测试新方法Experimental Study on Shear Stress of Adhesive Joint Layer

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Adhesive joint theoretical analysis shows the uneven distribution of layer shear stress. Many theories are formed to describe this distribution. But a test method to verify its theoretical result is absent. This paper presents a new layer shear stress test method. Through testing the normal stress of lap joint specimen, equation of normal stress distribution can be fitted. And then, the distribution of shear stress in internal layer can be deduced. The test results show that the adhesive shear stress distribution is consistent with the theoretical values.

1. 引言

2. 测试方法

2.1. 测试原理

${\sigma }_{1x}=A\mathrm{cosh}\left(\lambda x\right)+B\mathrm{sinh}\left(\lambda x\right)+C$ (1)

$\tau =-\frac{\text{d}{\sigma }_{1x}}{\text{d}x}{t}_{1}=-{t}_{1}\lambda \left[A\mathrm{sinh}\left(\lambda x\right)+B\mathrm{cosh}\left(\lambda x\right)\right]$ (2)

${\lambda }^{2}=\frac{G}{t}\left(\frac{1}{{E}_{1}{t}_{1}}+\frac{1}{{E}_{2}{t}_{2}}\right)$

$A=\frac{F\left({E}_{2}{t}_{2}-{E}_{1}{t}_{1}\right)}{2{t}_{1}b\left({E}_{2}{t}_{2}+{E}_{1}{t}_{1}\right)\mathrm{cosh}\left(\lambda c\right)}$

$B=-\frac{F}{2{t}_{1}b\mathrm{sinh}\left(\lambda c\right)}$

$C=\frac{F{E}_{2}}{b\left({E}_{1}{t}_{1}+{E}_{2}{t}_{2}\right)}$

$\frac{\text{d}\sigma \left(x\right)}{\text{d}x}{t}_{1}+\tau \left(x\right)=0$ (3)

t1——盖板的厚度；

τ(x)——胶层中的切应力分布函数。

2.2. 测试方案

2.3. 测试过程

Figure 1. Shear-Lag model

Figure 2. Two-layer shear-Lag model

3. 测试结果

3.1. 盖板正应力测试结果

Table 1. Dimension of the samples

Figure 3. Position of the strain gage

Figure 4. Tension test of the samples

Table 2. The strain of the test position

Table 3. Normal stress of the test position and its theoretical result

3.2. 胶层切应力测试结果

$\tau \left(x\right)=-{t}_{1}\lambda \left[A\mathrm{sinh}\lambda x+B\mathrm{cosh}\left(\lambda x\right)\right]$ (4)

${\alpha }_{l}=\frac{{\tau }_{\mathrm{max},l}}{{\tau }_{ave}},\text{\hspace{0.17em}}\text{\hspace{0.17em}}{\alpha }_{r}=\frac{{\tau }_{\mathrm{max},r}}{{\tau }_{ave}}$ (5)

Table 4. The fitting result of normal stress distribution coefficients

Table 5. Test of the shear stress distribution and its theoretical result

Figure 5. Normal stress of the test position and its theoretical result

4. 结论

Figure 6. Shear stress of the test position and its theoretical result

 [1] Volkersen, O. (1938) The Rivet Load Distribution in Lap-Joints with Members of Constant Thickness Subjected to Tension. Luftfahrtforschung, 15, 41-47. [2] Goland, M. and Reissner, E. (1944) The Stresses in Cemented Joints. Journal of Apply Mechanic, 11, A17-A27. [3] Ojalvo, I.U. and Eidinoff, H.L. (1978) Bond Thickness upon Stresses in Single-Lap Adhesive Joints. AIAA Journal, 16, 204-211. [4] Adams, R.D. and Mallick, V. (1992) A Method for the Stress Analysis of Lap Joints. International Journal of Adhesion & Adhesives, 38, 199-217. https://doi.org/10.1080/00218469208030455 [5] Moutrille, M.P., Derrien, K., Baptiste, D., Balandraud, X. and Grédiac, M. (2009) Through-Thickness Strain Field Measurement in a Composite/Aluminum Adhesive Joint. Composites Part A, 40, 985-996. https://doi.org/10.1016/j.compositesa.2008.04.018