# 基于极限载荷与断裂强度的5A06铝合金焊接缺陷安全性评定的数值方法研究Numerical Method Study on Safety Assessment of Welding Defects of 5A06 Aluminum Alloy Based on Ultimate Load and Fracture Strength

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In this paper, a numerical method for assessment the safety of 5A06 aluminum alloy strip with welded defects is established. First, the quantitative relationship between the limit stress and the length of the crack is established by the limit load analysis method, and then the failure assessment curve (FAC) can be obtained. For the 130 mm thick 5A06 Aluminum Alloy butt welding plate, welding residual stress distribution and residual stress intensity factor are obtained by SINTAP, and the stress intensity factor of the working load is calculated by the virtual crack closure tech-nique (VCCT method), then the 5A06 Aluminum Alloy failure assessment diagram (FAD) is estab-lished. The numerical method proposed in this paper can be used to evaluate the safety of the bearing capacity under the condition of a given defect. On the contrary, under the given external load conditions, the limitation of the defect can be determined.

1. 引言

2. 失效评估曲线(FAC)的数值确定方法

2.1. 材料5A06铝合金力学性能参数

5A06铝合金板的应力应变曲线如图1所示 [26] ，相关的力学性能参数如表1所示。

2.2. 有限元模型

Figure 1. Real stress-strain curve of 5A06 aluminum alloy

Table 1. Mechanical properties of 5A06 aluminum alloy

Figure 2. 3D model of 5A06 aluminum alloy plate with penetrating crack

Figure 3. Meshing of two dimensional model with central crack

3. 失效评估曲线(FAC)

3.1. 带裂纹5A06铝合金板确定极限应力σNC

$\frac{{\sigma }_{NC}}{{\sigma }_{0}}=0.43+0.4{e}^{20c/W}+0.18{e}^{66.7c/W}$ (1)

3.2. FAC的确定方法

Figure 4. Load-end tress and maximum strain curve with different crack lengths

Table 2. Ultimate stress σ N C with different cracks

Figure 5. The relationship between the limit stress ratio and the dimensionless crack length

${\sigma }_{NC}^{\infty }={\sigma }_{NC}Y$ (2)

$Y=\sqrt{\mathrm{sec}\left(\frac{\pi c}{W}\right)}$ (3)

${K}_{Q}\equiv {\sigma }_{NC}^{\infty }\sqrt{\pi c}$ (4)

${K}_{Q}={K}_{IFM}\left[1-{\delta }_{aci}\left(\frac{{\sigma }_{NC}^{\infty }}{{\sigma }_{0}}\right)\right]\sqrt{1-{\left(\frac{{\sigma }_{NC}^{\infty }}{{\sigma }_{0}}\right)}^{2}}$ (5)

${K}_{Q}=47\left[1-0.2102\left(\frac{{\sigma }_{NC}^{\infty }}{{\sigma }_{0}}\right)\right]\sqrt{1-{\left(\frac{{\sigma }_{NC}^{\infty }}{{\sigma }_{0}}\right)}^{2}}$ (6)

Table 3. Fitting value of fracture parameters K I F M and δ a c i of 5A06 aluminum alloy

Figure 6. Failure assessment curve (FAC) obtained by fitting data points

4.1. 失效评估点(FAP)

$\frac{{\sigma }_{NC}^{\infty }}{{\sigma }_{0}}=\frac{{\sigma }_{app}+{\sigma }_{res}}{{\sigma }_{0}}$ (7)

${K}_{tot}={K}_{app}+{K}_{res}$ (8)

4.1.1. 残余应力的分布与Kres的计算方法

$a=\frac{2c}{2}$$b=\frac{{W}_{1}}{2}$

$a\le b$ 时，

${K}_{res}={\sigma }_{yw}\sqrt{\pi a}$ (9)

$b 时，

${K}_{res}={\sigma }_{yw}\sqrt{\pi a}\left(2/\pi \right)\left\{\left(2/\pi \right)-\frac{\left[{\left({a}^{2}-{b}^{2}\right)}^{1/2}-b\pi /2+b{\mathrm{sin}}^{-1}\left(b/a\right)\right]}{\left({y}_{0}-b\right)}\right\}$ (10)

$a>{y}_{0}$ 时，

${K}_{res}={\sigma }_{yw}\sqrt{\pi a}\left(2/\pi \right)\left\{{\mathrm{sin}}^{-1}\left(b/a\right)-\frac{\left[{\left({a}^{2}-{b}^{2}\right)}^{1/2}-{\left({a}^{2}-{b}^{2}\right)}^{1/2}-b{\mathrm{sin}}^{-1}\left({y}_{0}/a\right)+b{\mathrm{sin}}^{-1}\left(b/a\right)\right]}{\left({y}_{0}-b\right)}\right\}$ (11)

Figure 7. Longitudinal welding residual stress distribution diagram

4.1.2. Kapp的计算方法

$W=\frac{1}{2}{\int }_{0}^{\Delta c}u\left(r\right)\sigma \left(r-\Delta c\right)dr$ (12)

$G=\underset{\Delta c\to o}{\mathrm{lim}}\frac{W}{\Delta c}=\underset{\Delta c\to o}{\mathrm{lim}}\frac{1}{2\Delta c}{\int }_{0}^{\Delta c}u\left(r\right)\sigma \left(\Delta c-r\right)\text{d}r$ (13)

Figure 8. Diagrammatic sketch of a plate with a central crack defect

Figure 9. Virtual crack closure model

${K}_{app}\text{=}\sqrt{G\text{E}}$ (14)

4.1.3. 5A06铝合金板焊接残余应力分布与Kres的计算

4.1.4. 5A06铝合金板在不同工况下应力强度因子Kapp的计算

Figure 10. The model of crack extension is Δc

Figure 11. Residual stress distribution of 5A06 aluminum alloy

5. 结果与讨论

Table 4. Stress intensity factors under different working conditions

Figure 12. The relationship between the residual stress intensity factor and the half crack length

Table 5. Fracture parameters of 5A06 aluminum alloy with residual stress and working load (40 MPa)

Table 6. Fracture parameters of 5A06 aluminum alloy with residual stress and working load (80 MPa and 120 MPa)

Figure 13. Failure assessment diagram of 5A06 aluminum alloy

NOTES



*通讯作者。

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