在 SimSolid 中执行的缝焊疲劳是基于应力的线性化和 Volvo 方法,然后预测疲劳损伤和寿命。线性化应力能够将贯穿厚度的弹性应力场分解为等效的膜应力和弯曲应力。
这种方法确定了弯曲对总应力的贡献,并由此确定焊缝本质上是刚性的还是柔性的。该方法通常需要两条 S-N 曲线。一种是以弯曲应力为主的弯曲 S-N 曲线,另一种是以膜应力为主的膜 S-N 曲线。根据弯曲程度在弯曲和膜 SN 曲线之间进行内插。
在焊趾处标记预计或可能的失效(疲劳裂纹)位置。这些是将评估疲劳损伤的位置。
Figure 1. 角焊缝横截面显示可能的失效位置
焊缝应力计算
SimSolid 中的缝焊疲劳损伤计算使用应力线性化方法(链接至
SimSolid 线性化应力文件)和与该应力相关的弯曲率,在相关位置使用结构应力。线性化应力在沿应力线性化段的局部坐标系中获得。局部坐标系以段的起始点和结束点为基础,如
图 2 所示。系统的 X 轴沿着从入口点到出口点的段。其他两个轴的计算方法如下:
如果局部 X 轴不平行于全局 Y 轴:(1)
Z
l
o
c
a
l
=
X
l
o
c
a
l
*
Y
g
l
o
b
a
l
Y
l
o
c
a
l
=
Z
l
o
c
a
l
*
X
l
o
c
a
l
MathType@MTEF@5@5@+=
feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9
vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x
fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaacaWGAb
WaaSbaaSqaaiaadYgacaWGVbGaam4yaiaadggacaWGSbaabeaakiab
g2da9iaadIfadaWgaaWcbaGaamiBaiaad+gacaWGJbGaamyyaiaadY
gaaeqaaOGaaiOkaiaadMfadaWgaaWcbaGaam4zaiaadYgacaWGVbGa
amOyaiaadggacaWGSbaabeaaaOqaaiaadMfadaWgaaWcbaGaamiBai
aad+gacaWGJbGaamyyaiaadYgaaeqaaOGaeyypa0JaamOwamaaBaaa
leaacaWGSbGaam4BaiaadogacaWGHbGaamiBaaqabaGccaGGQaGaam
iwamaaBaaaleaacaWGSbGaam4BaiaadogacaWGHbGaamiBaaqabaaa
aaa@5C93@
如果局部 X 轴平行于全局 Y 轴:如果局部 X 轴沿着正的全局 Y 轴,则局部 Y 轴 (
Y
l
o
c
a
l
MathType@MTEF@5@5@+=
feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9
vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x
fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamywamaaBa
aaleaacaWGSbGaam4BaiaadogacaWGHbGaamiBaaqabaaaaa@3BA1@
) 是负的全局 X 轴,反之亦然。
(2)
Z
l
o
c
a
l
=
X
l
o
c
a
l
*
Y
l
o
c
a
l
MathType@MTEF@5@5@+=
feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9
vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x
fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOwamaaBa
aaleaacaWGSbGaam4BaiaadogacaWGHbGaamiBaaqabaGccqGH9aqp
caWGybWaaSbaaSqaaiaadYgacaWGVbGaam4yaiaadggacaWGSbaabe
aakiaacQcacaWGzbWaaSbaaSqaaiaadYgacaWGVbGaam4yaiaadgga
caWGSbaabeaaaaa@48C5@
Figure 2.
根据上述提取的应力值,采用数值积分的方法计算出入口点和出口点的平均膜应力张量加上末端弯曲应力张量。
(3)
σ
i
m
=
1
T
∫
−
T
/
2
T
/
2
σ
i
d
x
MathType@MTEF@5@5@+=
feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9
vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x
fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Wdm3aa0
baaSqaaiaadMgaaeaacaWGTbaaaOGaeyypa0ZaaSaaaeaacaaIXaaa
baGaamivaaaadaWdbaqaamaaDaaaleaacqGHsislcaWGubGaai4lai
aaikdaaeaacaWGubGaai4laiaaikdaaaGccqaHdpWCdaWgaaWcbaGa
amyAaaqabaGccaWGKbGaamiEaaWcbeqab0Gaey4kIipaaaa@48F3@
(4)
σ
i
S
b
=
−
6
T
2
∫
−
T
/
2
T
/
2
σ
i
x
d
x
MathType@MTEF@5@5@+=
feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9
vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x
fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Wdm3aa0
baaSqaaiaadMgacaWGtbaabaGaamOyaaaakiabg2da9iabgkHiTmaa
laaabaGaaGOnaaqaaiaadsfadaahaaWcbeqaaiaaikdaaaaaaOWaa8
qaaeaadaqhaaWcbaGaeyOeI0Iaamivaiaac+cacaaIYaaabaGaamiv
aiaac+cacaaIYaaaaOGaeq4Wdm3aaSbaaSqaaiaadMgaaeqaaOGaam
iEaiaadsgacaWG4baaleqabeqdcqGHRiI8aaaa@4CA2@
(5)
σ
i
E
b
=
−
σ
i
S
b
MathType@MTEF@5@5@+=
feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9
vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x
fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Wdm3aa0
baaSqaaiaadMgacaWGfbaabaGaamOyaaaakiabg2da9iabgkHiTiab
eo8aZnaaDaaaleaacaWGPbGaam4uaaqaaiaadkgaaaaaaa@411C@
其中,
σ
i
m
MathType@MTEF@5@5@+=
feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9
vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x
fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Wdm3aa0
baaSqaaiaadMgaaeaacaWGTbaaaaaa@39C3@
等于
i
t
h
MathType@MTEF@5@5@+=
feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9
vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x
fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyAamaaCa
aaleqabaGaamiDaiaadIgaaaaaaa@38F4@
膜应力的第 i 个分量。
σ
i
MathType@MTEF@5@5@+=
feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9
vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x
fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Wdm3aaS
baaSqaaiaadMgaaeqaaaaa@38D0@
等于
i
t
h
MathType@MTEF@5@5@+=
feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9
vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x
fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyAamaaCa
aaleqabaGaamiDaiaadIgaaaaaaa@38F4@
提取应力值的第 i 个分量。
σ
i
S
b
MathType@MTEF@5@5@+=
feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9
vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x
fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Wdm3aa0
baaSqaaiaadMgacaWGtbaabaGaamOyaaaaaaa@3A90@
等于
i
t
h
MathType@MTEF@5@5@+=
feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9
vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x
fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyAamaaCa
aaleqabaGaamiDaiaadIgaaaaaaa@38F4@
入口弯曲应力的第 i 个分量。
σ
i
E
b
MathType@MTEF@5@5@+=
feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9
vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x
fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Wdm3aa0
baaSqaaiaadMgacaWGfbaabaGaamOyaaaaaaa@3A82@
等于
i
t
h
MathType@MTEF@5@5@+=
feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9
vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x
fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyAamaaCa
aaleqabaGaamiDaiaadIgaaaaaaa@38F4@
出口弯曲应力的第 i 个分量。
L
MathType@MTEF@5@5@+=
feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9
vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x
fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamitaaaa@36C4@
等于
i
t
h
MathType@MTEF@5@5@+=
feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9
vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x
fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyAamaaCa
aaleqabaGaamiDaiaadIgaaaaaaa@38F4@
应力线性化段的第 i 个长度。
x
MathType@MTEF@5@5@+=
feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9
vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x
fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiEaaaa@36F0@
等于某一点沿段的位置。
用于缝焊损伤参数的应力量是膜应力和弯曲应力之和。
Figure 3.
因此,顶面和底面的应力由以下等式得出:
(6)
σ
t
o
p
=
σ
i
m
+
σ
i
S
b
MathType@MTEF@5@5@+=
feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9
vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x
fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Wdm3aaS
baaSqaaiaadshacaWGVbGaamiCaaqabaGccqGH9aqpcqaHdpWCdaqh
aaWcbaGaamyAaaqaaiaad2gaaaGccqGHRaWkcqaHdpWCdaqhaaWcba
GaamyAaiaadofaaeaacaWGIbaaaaaa@452D@
(7)
σ
b o t t o m
=
σ
i
m
−
σ
i S
b
( since
σ
i E
b
= −
σ
i S
b
)
MathType@MTEF@5@5@+=
feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9
vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x
fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Wdm3aaS
baaSqaaiaadkgacaWGVbGaamiDaiaadshacaWGVbGaamyBaaqabaGc
cqGH9aqpcqaHdpWCdaqhaaWcbaGaamyAaaqaaiaad2gaaaGccqGHsi
slcqaHdpWCdaqhaaWcbaGaamyAaiaadofaaeaacaWGIbaaaOGaaiik
aiaabohacaqGPbGaaeOBaiaabogacaqGLbGaaeiiaiabeo8aZnaaDa
aaleaacaWGPbGaamyraaqaaiaadkgaaaGccqGH9aqpcqGHsislcqaH
dpWCdaqhaaWcbaGaamyAaiaadofaaeaacaWGIbaaaOGaaiykaaaa@59E3@
Note: 因此,缝焊分析引擎中使用的计算方法同样适用于从实体或薄壳体模型计算的应力。这将生成与薄壳体模型相同形式的顶面和底面应力。
Figure 4.
弯曲比 (r)
实验表明,根据 M. Fermér、M Andréasson 和 B Frodin 提出的方法,需要两种类型的 SN 曲线来进行缝焊疲劳分析。根据实验室测试,绘制了两条 SN 曲线(
图 5 )。上面的曲线是在最大应力由弯曲力矩控制的试验中获得的,下面的曲线是在最大应力由膜力控制的试验中获得的。
Figure 5.
上下两条曲线分别称为弯曲 S-N 曲线和膜 S-N 曲线。建议当膜应力在单元中占主导地位时使用膜 S-N 曲线,当弯曲应力占主导地位时使用弯曲 S-N 曲线。根据弯曲优势程度,可以在两条曲线之间进行内插。
(8)
r
=
σ
i
b
σ
i
b
+
σ
i
m
MathType@MTEF@5@5@+=
feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9
vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x
fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOCaiabg2
da9maalaaabaWaaqWaaeaacqaHdpWCdaqhaaWcbaGaamyAaaqaaiaa
dkgaaaaakiaawEa7caGLiWoaaeaadaabdaqaaiabeo8aZnaaDaaale
aacaWGPbaabaGaamOyaaaaaOGaay5bSlaawIa7aiabgUcaRmaaemaa
baGaeq4Wdm3aa0baaSqaaiaadMgaaeaacaWGTbaaaaGccaGLhWUaay
jcSdaaaaaa@4DC0@
其中,
σ
i
b
MathType@MTEF@5@5@+=
feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9
vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x
fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Wdm3aa0
baaSqaaiaadMgaaeaacaWGIbaaaaaa@39B8@
最大弯曲应力等于
6
T
2
∫
−
T
/
2
T
/
2
σ
i
x
d
x
MathType@MTEF@5@5@+=
feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9
vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x
fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaca
aI2aaabaGaamivamaaCaaaleqabaGaaGOmaaaaaaGcdaWdbaqaamaa
DaaaleaacqGHsislcaWGubGaai4laiaaikdaaeaacaWGubGaai4lai
aaikdaaaaabeqab0Gaey4kIipakiabeo8aZnaaBaaaleaacaWGPbaa
beaakiaadIhacaWGKbGaamiEaaaa@45FD@
。
σ
i
m
MathType@MTEF@5@5@+=
feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9
vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x
fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Wdm3aa0
baaSqaaiaadMgaaeaacaWGTbaaaaaa@39C3@
是最大膜应力,等于
1
T
∫
−
T
/
2
T
/
2
σ
i
d
x
MathType@MTEF@5@5@+=
feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9
vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x
fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaca
aIXaaabaGaamivaaaadaWdbaqaamaaDaaaleaacqGHsislcaWGubGa
ai4laiaaikdaaeaacaWGubGaai4laiaaikdaaaaabeqab0Gaey4kIi
pakiabeo8aZnaaBaaaleaacaWGPbaabeaakiaadsgacaWG4baaaa@4408@
平均弯曲比,
(
r
b
A
V
G
)
MathType@MTEF@5@5@+=
feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9
vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x
fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaiikaiaadk
hadaqhaaWcbaGaamOyaaqaaiaadgeacaWGwbGaam4raaaakiaacMca aaa@3BCE@
,定义为:
(9)
(
r
b
A
V
G
)
=
∑
i
=
1
n
(
r
σ
T
O
P
2
∑
i
=
1
n
σ
T
O
P
2
MathType@MTEF@5@5@+=
feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9
vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x
fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaiikaiaadk
hadaqhaaWcbaGaamOyaaqaaiaadgeacaWGwbGaam4raaaakiaacMca
cqGH9aqpdaWcaaqaaiabggHiLpaaDaaaleaacaWGPbGaeyypa0JaaG
ymaaqaaiaad6gaaaGccaGGOaGaamOCamaadmaabaGaeq4Wdm3aa0ba
aSqaaiaadsfacaWGpbGaamiuaaqaaiaaikdaaaaakiaawUfacaGLDb
aaaeaacqGHris5daqhaaWcbaGaamyAaiabg2da9iaaigdaaeaacaWG
UbaaaOWaamWaaeaacqaHdpWCdaqhaaWcbaGaamivaiaad+eacaWGqb
aabaGaaGOmaaaaaOGaay5waiaaw2faaaaaaaa@57D5@
其中,
σ
T
O
P
2
MathType@MTEF@5@5@+=
feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9
vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x
fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Wdm3aa0
baaSqaaiaadsfacaWGpbGaamiuaaqaaiaaikdaaaaaaa@3B21@
是计算损伤时顶面(即焊趾)最大应力的平方。
r
MathType@MTEF@5@5@+=
feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9
vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x
fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOCaaaa@36EA@
是弯曲比。
它是加载时间关系中所有点的弯曲率的加权平均值。
内插因子 (IF) 现在定义为:
(10)
IF
=
0.0
when
0.0
≤
r
b
A
V
G
≤
r
b
T
H
R
MathType@MTEF@5@5@+=
feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9
vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x
fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaeysaiaabA
eacqGH9aqpcaaIWaGaaiOlaiaaicdacaqGGaGaae4DaiaabIgacaqG
LbGaaeOBaiaabccacaaIWaGaaiOlaiaaicdacqGHKjYOcaWGYbWaa0
baaSqaaiaadkgaaeaacaWGbbGaamOvaiaadEeaaaGccqGHKjYOcaWG
YbWaa0baaSqaaiaadkgaaeaacaWGubGaamisaiaadkfaaaaaaa@4E52@
(11)
IF
=
r
b
A
V
G
−
r
b
T
H
R
1
−
r
b
T
H
R
when
r
b
T
H
R
<
r
b
A
V
G
≤
1.0
MathType@MTEF@5@5@+=
feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9
vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x
fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaeysaiaabA
eacqGH9aqpdaWcaaqaaiaadkhadaqhaaWcbaGaamOyaaqaaiaadgea
caWGwbGaam4raaaakiabgkHiTiaadkhadaqhaaWcbaGaamOyaaqaai
aadsfacaWGibGaamOuaaaaaOqaaiaaigdacqGHsislcaWGYbWaa0ba
aSqaaiaadkgaaeaacaWGubGaamisaiaadkfaaaaaaOGaaeiiaiaabE
hacaqGObGaaeyzaiaab6gacaqGGaGaamOCamaaDaaaleaacaWGIbaa
baGaamivaiaadIeacaWGsbaaaOGaeyipaWJaamOCamaaDaaaleaaca
WGIbaabaGaamyqaiaadAfacaWGhbaaaOGaeyizImQaaGymaiaac6ca
caaIWaaaaa@5BD1@
r
b
T
H
R
MathType@MTEF@5@5@+=
feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9
vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x
fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOCamaaDa
aaleaacaWGIbaabaGaamivaiaadIeacaWGsbaaaaaa@3A7B@
值由疲劳求解设置中的弯曲率阈值定义。默认情况下,该值设置为 0.5。如果平均弯曲率 (
r
b
A V G
MathType@MTEF@5@5@+=
feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9
vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x
fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOCamaaDa
aaleaacaWGIbaabaGaamyqaiaadAfacaWGhbaaaaaa@3A6B@
) 小于或等于弯曲率阈值 (
r
b
T H R
MathType@MTEF@5@5@+=
feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9
vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x
fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOCamaaDa
aaleaacaWGIbaabaGaamivaiaadIeacaWGsbaaaaaa@3A7B@
),则使用膜 S-N 曲线来评估损伤。如果平均弯曲比大于弯曲比阈值,则使用在膜 S-N 曲线和弯曲 S-N 曲线之间内插的 S-N 曲线。
膜曲线与弯曲 S-N 曲线之间的内插
Figure 6.
线性内插法,如
图 6 所示,使用内插系数 (IF) 的值。对于内插曲线,疲劳强度系数值 (SRI1) 的计算如下:
(12)
SRI1interpolated = SRI1membrane +
(SRI1bending – SRI1membrane ) ∙ IF
这定义了 1 个周期的应力水平。
(13)
Nc1interpolated =
10(log 10 Nc1 membrane +
(log 10
Nc1 bending
– log 10 (Nc1 membrane ) ∙IF))
(14)
S1interpolated = S1membrane + (S1bending –
S1membrane ) ∙ IF
这定义了 Nc1
interpolated 个周期的应力水平。这两个点定义了曲线的第一部分,最多 Nc1
interpolated 个周期。最后一部分通过寻找第三个点来定义,如下所示。对于刚性和柔性曲线,寿命值被定义为 Nc1 值的 10 倍。由此可以计算出 S2
bending 和 S2
membrane 。由此,我们可以进行内插,得到定义曲线高周部分的 S2
interpolated 。
(15)
S2interpolated = S2membrane + (S2bending –
S2membrane ). IF
厚度
或者,可以基于零件的厚度 t 施加厚度(尺寸效应校正)。运行方式如下:
如果
t ≤
T
r e f
MathType@MTEF@5@5@+=
feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9
vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x
fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiDaiabgs
MiJkaadsfadaWgaaWcbaGaamOCaiaadwgacaWGMbaabeaaaaa@3C72@
,则无效应(可以在疲劳求解设置中指定参考厚度或阈值)。
疲劳强度由
T
r
e
f
t
n
MathType@MTEF@5@5@+=
feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9
vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x
fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaeWaaeaada
WcaaqaaiaadsfadaWgaaWcbaGaamOCaiaadwgacaWGMbaabeaaaOqa
aiaadshaaaaacaGLOaGaayzkaaWaaWbaaSqabeaacaWGUbaaaaaa@3D80@
因子降低,其中 n 是厚度指数,如果
t
>
T
r
e
f
MathType@MTEF@5@5@+=
feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9
vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x
fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiDaiabg6
da+iaadsfadaWgaaWcbaGaamOCaiaadwgacaWGMbaabeaaaaa@3BC5@
,在所有生命周期(用作增加压力的因子)。
平均应力修正
支持对缝焊疲劳进行 FKM 平均应力修正。应力敏感性可通过平均应力修正字段在疲劳求解设置对话框中定义。可以通过缝焊疲劳求解设置对话框启用缝焊疲劳的平均应力修正。
据 FKM 准则,根据应力比 (R=SMIN/Smax) 值将 Haigh 图表分为四个区域。然后使用修正后的值选择损害和寿命计算阶段的 SN 曲线。
下面的 FKM 方程说明了修正应力振幅的计算过程 (
S
e
A
MathType@MTEF@5@5@+=
feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9
vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x
fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4uamaaDa
aaleaacaWGLbaabaGaamyqaaaaaaa@38A8@
)。损害计算中使用的实际应力值是修正的应力振幅(即
2
⋅
S
e
A
MathType@MTEF@5@5@+=
feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9
vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x
fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaGOmaiabgw
SixlaadofadaqhaaWcbaGaamyzaaqaaiaadgeaaaaaaa@3BAE@
)。这些公式适用于所输入的 SN 曲线。
区域 1 (R>1.0 ):
S
e
A
=
S
a
(
1
−
M
)
MathType@MTEF@5@5@+=
feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9
vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x
fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4uamaaDa
aaleaacaWGLbaabaGaamyqaaaakiabg2da9iaadofadaWgaaWcbaGa
amyyaaqabaGccaGGOaGaaGymaiabgkHiTiaad2eacaGGPaaaaa@3F7F@
区域 2 (
−
∞
≤
R
≤
0.0
MathType@MTEF@5@5@+=
feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9
vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x
fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyOeI0Iaey
OhIuQaeyizImQaamOuaiabgsMiJkaaicdacaGGUaGaaGimaaaa@3EB8@
):
S
e
A
=
S
a
+
M
*
S
m
MathType@MTEF@5@5@+=
feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9
vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x
fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4uamaaDa
aaleaacaWGLbaabaGaamyqaaaakiabg2da9iaadofadaWgaaWcbaGa
amyyaaqabaGccqGHRaWkcaWGnbGaaiOkaiaadofadaWgaaWcbaGaam
yBaaqabaaaaa@4004@
区域 3 (0.0<R<0.5 ):
S
e
A
=
(
1
+
M
)
S
a
+
(
M
/
3
)
*
S
m
1
+
M
/
3
MathType@MTEF@5@5@+=
feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9
vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x
fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4uamaaDa
aaleaacaWGLbaabaGaamyqaaaakiabg2da9iaacIcacaaIXaGaey4k
aSIaamytaiaacMcadaWcaaqaaiaadofadaWgaaWcbaGaamyyaaqaba
GccqGHRaWkcaGGOaGaamytaiaac+cacaaIZaGaaiykaiaacQcacaWG
tbWaaSbaaSqaaiaad2gaaeqaaaGcbaGaaGymaiabgUcaRiaad2eaca
GGVaGaaG4maaaaaaa@4A8E@
区域 4 (
R
≥
0.5
MathType@MTEF@5@5@+=
feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9
vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x
fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOuaiabgw
MiZkaaicdacaGGUaGaaGynaaaa@3ABB@
):
S
e
A
=
3
S
a
(
1
+
M
)
2
3
+
M
MathType@MTEF@5@5@+=
feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9
vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x
fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4uamaaDa
aaleaacaWGLbaabaGaamyqaaaakiabg2da9maalaaabaGaaG4maiaa
dofadaWgaaWcbaGaamyyaaqabaGccaGGOaGaaGymaiabgUcaRiaad2
eacaGGPaWaaWbaaSqabeaacaaIYaaaaaGcbaGaaG4maiabgUcaRiaa
d2eaaaaaaa@43A5@
其中,
S
e
A
MathType@MTEF@5@5@+=
feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9
vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x
fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4uamaaDa
aaleaacaWGLbaabaGaamyqaaaaaaa@38A8@
是平均应力校正后的应力振幅(耐久应力)。
S
m
MathType@MTEF@5@5@+=
feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9
vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x
fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4uamaaBa
aaleaacaWGTbaabeaaaaa@37E9@
是应力振幅,M 是平均应力敏感性。
Figure 7.