﻿ 圆棒表面非共面双裂纹交互影响数值分析 Numerical Study of the Interaction Behavior of Two Non-Coplanar Cracks in Round Bars

Modeling and Simulation
Vol.06 No.02(2017), Article ID:20579,8 pages
10.12677/MOS.2017.62011

Numerical Study of the Interaction Behavior of Two Non-Coplanar Cracks in Round Bars

Maigefeireti, Zeya Li

College of Science, Minzu University of China, Beijing

Received: Apr. 30th, 2017; accepted: May 19th, 2017; published: May 22nd, 2017

ABSTRACT

In the present study, the interaction of two non-coplanar cracks in round bars was investigated using the superposition finite element method (s-version FEM, S-FEM). The S-FEM, in the frame of finite element method, is a global-local overlaying method. The advantage of this method is saving the effort in FE modeling for multiple cracks. The virtual crack closure method is used to crack stress intensity factors. The interactions of two static cracks were analyzed by changing the relative distance between the cracks and the crack sizes. The analyses results may provide a reference for structure damage evaluation.

Keywords:Numerical Simulation, Superposition Fem, Fatigue Crack Growth, Two Cracks

1. 引言

2. 有限元重合网格法

Figure 1. S-FEM model of a finite body with two cracks

(1)

(2)

f是外力和体力之和。刚度矩阵是对称的，

3. 计算模型以及应力强度因子计算验证

(3)

3.1. 相对距离

(a) (b)

Figure 2. (a) Two non-coplanar cracks in a round bar under bending and (b) finite element models used in the analysis

(a) (b)

Figure 3. Geometric parameters definitions for a crack in round bar

(a) (b)

Figure 4. Comparison results of Stress intensity factor between S-FEM and general FEM (a) deepest point (b) surface point

1) 只考虑水平距离时，两个裂纹在同一平面内，即H/a = 0 mm。我们考虑两种情况，第一种，两个裂纹关于圆棒的中心线对称分布，同时绕Z轴转动以改变水平间距S。第二种情况为，两个裂纹非对称分布，一个裂纹位置固定，另一个裂纹位置绕轴旋转从而改变S。第一种对称分布的情况(图5)，当两个裂纹近端距离接近于0时，交互影响达到最大值，远端A和深点C的影响也存在但是表现较小。当距离变大时，在B点和C点的影响慢慢消失，反而在远端A出现了屏蔽效应，即交互因子出现了小于1.0的情况，裂纹2对裂纹1除了有交互增强的作用外，还存在交互减弱的影响。非对称情况下(图6)，随着裂纹间距的扩大，交互增强的影响减弱并趋于常值。

2) 只考虑垂直距离时，我们计算了水平距离分别为S/s = 0.02 (图7)和S/s = 0.2 (图8)的对称分布情况。在文献 [11] 分析中指出，当H/a小于0.8时平板中的两个裂纹交互效果显著。在本研究中，我们也得到了类似的规律，如图所示临近端裂尖的增强交互效应在0 < H/a < 0.8范围内十分显著。

3.2. 裂纹尺寸

Figure 5. Interaction factor as a function of relative horizontal distance (H/a = 0)

Figure 6. Interaction factor as a function of relative horizontal distance (asymmetric distribution, H/a = 0)

Figure 7. Interaction factor as a function of the relative vertical distance (S/s = 0.02)

Figure 8. Interaction factor as a function of the relative vertical distance (S/s = 0.2)

Figure 9. Variation of interaction factor of Crack 1 with the change in the crack size of Crack 2 (a/s is fixed)

Figure 10. Variation of interaction factor of Crack 1 with the change in the crack size of Crack 2 (a is fixed)

4. 结论

Numerical Study of the Interaction Behavior of Two Non-Coplanar Cracks in Round Bars[J]. 建模与仿真, 2017, 06(02): 90-97. http://dx.doi.org/10.12677/MOS.2017.62011

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