本文建立了一种针对5A06铝合金带焊接缺陷平板的安全性评定的数值方法。首先采用极限载荷分析法建立了极限应力和裂纹长度的定量关系,从而获得失效评估曲线(FAC)。对130 mm厚的5A06铝合金对接焊接平板,采用SINTAP标准获得焊接残余应力分布和残余应力强度因子,并用虚拟裂纹闭合技术(VCCT法)计算工作载荷作用下的应力强度因子,建立了5A06铝合金失效评估图(FAD)。论文提出的数值方法能够对给定缺陷条件下的承载能力进行安全性评定;相反,在给定外载荷条件下,对缺陷的容纳限值进行确定。
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.
采用含中央穿透型裂纹平板确定5A06铝合金极限应力 σ N C 和FAC,矩形板的尺寸长为200 mm,宽为160 mm,半裂纹长度分别取为4 mm,8 mm,12 mm,16 mm,20 mm。采用有限元方法计算获得的加载端应力(图3中的P)与最大应变的关系曲线如图4所示。极限应力 σ N C 的确定方式为:求出载荷—应变曲线的弹性斜率,然后作出五倍弹性斜率直线,极限应力 σ N C 定义为两线相交处的应力值 [27] 。采用以上方法确定的5A06铝合金不同裂纹长度下的极限应力 σ N C 如表2所示。通过表2的数据,获得无因次极限应力比 σ N C / σ 0 与裂纹长度与板宽比 2 c / W 的关系曲线如图5所示,通过数据拟合,得到其函数关系式为:
σ N C σ 0 = 0.43 + 0.4 e 20 c / W + 0.18 e 66.7 c / W (1)
式中: σ 0 为不带裂纹的极限应力, σ N C 为带裂纹的极限应力,c为半裂纹长度,W为板的宽度。
3.2. FAC的确定方法
根据上节的公式(1),由极限载荷分析法得到平板在特定裂纹长度下的极限应力 σ N C ;通过公式(3)获得有限宽板修正因子,利用公式(2)换算得到无限宽板下的极限载荷 σ N C ∞ 。利用几组不同裂纹下的极限载荷 σ N C ∞ 和无缺陷存在下板的极限载荷 σ 0 ,代入基于固有缺陷模型 [28] 得到的FAC关系式(5),拟合获得常数 δ a c i 和 K I F M ,即可确定出FAC。
图4. 不同裂纹长度对应的加载端应力与最大应变曲线
Ultimate stress σ N C with different crack
W(mm)
c(mm)
σ N C (MPa)
σ 0 (MPa)
2c/W
σ N C / σ 0
160
4
245
345
0.05
0.71
160
8
205
345
0.10
0.59
160
12
185
345
0.15
0.54
160
16
170
345
0.20
0.49
160
20
158
345
0.25
0.47
表2. 不同裂纹下的极限应力 σ N C
图5. 极限应力比与无量纲裂纹长度的关系曲线
σ N C ∞ = σ N C Y (2)
Y = sec ( π c W ) (3)
K Q ≡ σ N C ∞ π c (4)
K Q = K I F M [ 1 − δ a c i ( σ N C ∞ σ 0 ) ] 1 − ( σ N C ∞ σ 0 ) 2 (5)
根据文 [29] ,裂纹长度与板宽之比2c/W > 0.086时,材料的破坏主要由塑性极限载荷控制;当2c/W ≤ 0.086时,材料的破坏主要由断裂准则控制。故本文使用极限载荷分析获得FAC曲线时,将2c/W控制在0.025以下以保证其合理性。通过式(1)得到不同裂纹长度下的极限载荷 σ N C 后,使用公式(2)与公式(3)转换为无限宽板的极限载荷值 σ N C ∞ ,再通过公式(4)计算得到对应的应力强度因子 K Q ,最后利用公式(5)拟合曲线可得到断裂参数 K I F M 与 δ a c i 如表3所示。获得的FAC曲线的函数关系式为:
K Q = 47 [ 1 − 0.2102 ( σ N C ∞ σ 0 ) ] 1 − ( σ N C ∞ σ 0 ) 2 (6)
其中: σ a p p 为施加的工作应力; σ r e s 为残余应力; K a p p 为工作应力下的应力强度因子; K r e s 为残余应力强度因子。
4.1.1. 残余应力的分布与Kres的计算方法
根据SINTAP规范 [30] ,对于平板焊接,纵向简化后的残余应力沿焊缝对称分布,简化后构件沿纵向的焊接残余应力分布如图7所示,其中 σ y w 表示材料屈服强度; σ r e s 表示焊接残余应力; W 1 表示焊缝宽度; y 0 表示残余应力沿纵向分布的尺寸:
根据图7的残余应力分布图,可计算直板存在不同长度的中央穿透型裂纹(图8所示)下的焊接残余应力强度因子 K r e s ,具体公式如下 [30] :
令 a = 2 c 2 , b = W 1 2 ;
当 a ≤ b 时,
K r e s = σ y w π a (9)
当 b < a ≤ y 0 时,
K r e s = σ y w π a ( 2 / π ) { ( 2 / π ) − [ ( a 2 − b 2 ) 1 / 2 − b π / 2 + b sin − 1 ( b / a ) ] ( y 0 − b ) } (10)
当 a > y 0 时,
K r e s = σ y w π a ( 2 / π ) { sin − 1 ( b / a ) − [ ( a 2 − b 2 ) 1 / 2 − ( a 2 − b 2 ) 1 / 2 − b sin − 1 ( y 0 / a ) + b sin − 1 ( b / a ) ] ( y 0 − b ) } (11)
图7.平板纵向的焊接残余应力分布图
4.1.2. Kapp的计算方法
采用数值方法计算评估点裂纹应力强度因子 K a p p ,首先计算裂纹尖端的应力应变场,相应的有限元模型参见图3所示,对于断裂参数的计算方法选用精度可靠,且对有限元网格尺寸大小不敏感的虚拟裂纹闭合技术(VCCT) [31] [32] 。该方法假定裂纹扩展Δc引起的系统势能改变(减小)等于闭合裂纹至原来长度所作的功,其表达式如下:
G = lim Δ c → o W Δ c = lim Δ c → o 1 2 Δ c ∫ 0 Δ c u ( r ) σ ( Δ c − r ) d r (13)
要将图9中的裂纹闭合达到图10所示状态所需的功 W = F u / 2 ,其中 F 是图10中 i 的节点力,u是图10中 i 和 i ′ 之间的距离。从而,我们可以根据方程(14)得到应力强度因子 K a p p 。
图8. 平板含中央裂纹缺陷示意图
图9. 虚拟裂纹闭合模型
K a p p = G E (14)
式中:G为能量释放率,E为材料的弹性模量
4.1.3. 5A06铝合金板焊接残余应力分布与Kres的计算
已知5A06铝合金材料的屈服强度 σ y w 为175 MPa,焊缝宽度W1 = 6 mm,利用图7可获得5A06铝合金材料残余应力场的分布(图11所示),使用公式(9),(10)和(11)可算得不同裂纹长度2c下的 K r e s ,并获得 K r e s 与裂纹长度c关系曲线(图13所示)。
4.1.4. 5A06铝合金板在不同工况下应力强度因子Kapp的计算
采用有限元法计算了5A06铝合金板不同工作应力 σ a p p 作用下裂纹前沿的应力与应变场,再使用VCCT法计算裂纹前沿的应力强度因子 K a p p 。表4列出了不同裂纹长度,不同工作载荷下裂纹前沿应力强度因子。
图10. 裂纹扩展Δc的模型
图11. 5A06铝合金材料焊接残余应力分布示意图
4.2. 5A06铝合金含中央穿透型裂纹安全性评估(FAD)
利用SINTAP提供的焊接残余应力 σ r e s (图11所示)和对应焊接残余应力 σ r e s 的应力强度因子 K r e s (图12所示),通过表4、式(7)和式(8)可计算得到评估点的参数(如表5和表6所示),结合图6的失效评估曲线FAC,作出不同长度的穿透型裂纹的焊接平板的FAD如图13所示。
颜虹州,曾祥国,帅茂兵,李玉斌,陈华燕. 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[J]. 材料科学, 2017, 07(09): 791-804. http://dx.doi.org/10.12677/MS.2017.79103
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