mechanical design ielearning.kocw.net/contents4/document/lec/2013/chonnam/... · 2013-07-19 ·...
TRANSCRIPT
Bong-Kee Lee School of Mechanical Engineering
Chonnam National University
Mechanical Design I
3. Failure (III)
(Chap 2.12)
School of Mechanical Engineering Mechanical Design I
Fatigue Failure
피로 파손(fatigue failure or fracture)
– 최대 응력이 항복강도 이하인 반복응력에 의하여 점진적으로 파손되는 현상
• 한 점에서 미세한 균열이 발생 → 응력 집중 → 균열 전파 → 파손
• 소성변형 없이 갑자기 파손됨
School of Mechanical Engineering Mechanical Design I
Fatigue Failure
피로 파손의 예
– fatigue failure of a bolt (repeated unidirectional bending)
School of Mechanical Engineering Mechanical Design I
Fatigue Failure
피로 파손의 예
– fatigue fracture of a drive shaft
School of Mechanical Engineering Mechanical Design I
Fatigue Failure
피로 파손의 예
– fatigue fracture surface of a pin
School of Mechanical Engineering Mechanical Design I
Fatigue Failure
피로 파손의 예
– fatigue fracture surface of a forged connecting rod
School of Mechanical Engineering Mechanical Design I
Fatigue Failure
피로 파손의 예
– fatigue fracture surface due to a pure tension
School of Mechanical Engineering Mechanical Design I
Variable Loading
반복응력의 종류
2,
2
stresssteady or static
stress of range
component midrange
component amplitude
stress maximum
stress minimum
minmaxminmax
max
min
am
s
r
m
a일반반복
편진
양진
평균응력 응력진폭 (교번응력)
School of Mechanical Engineering Mechanical Design I
Stress-Life Method
피로 시험(fatigue test)
– 일정한 응력 진폭 → 시편의 파손이 일어날 때까지의 응력 반복 회수를 구함
School of Mechanical Engineering Mechanical Design I
Stress-Life Method
S-N 곡선(S-N Diagram)
– 응력 및 파손이 일어난 반복 회수의 관계
– 양진 반복응력
School of Mechanical Engineering Mechanical Design I
Stress-Life Method
피로 한도(fatigue limit)
– 내구 한도(endurance limit), 피로 강도(fatigue strength), 내구 강도(endurance strength)
– 어느 한계 값 이하의 반복 응력에서는 많은 반복을 하여도 피로 파괴가 일어나지 않는, 재료에서의 한계응력 값
School of Mechanical Engineering Mechanical Design I
Stress-Life Method
피로 한도(fatigue limit)
– 철강 등 ~ N=106
– 비철금속 ~ N=5·108
School of Mechanical Engineering Mechanical Design I
Stress-Life Method
피로 한도(fatigue limit)
– ref. Table 2-10 in the textbook
[MPa] 1400[MPa] 700
[MPa] 14005.00
ut
utut
e
School of Mechanical Engineering Mechanical Design I
Endurance Limit Modifying Factors
수정 계수(modifying factor)
– 피로 한도(강도)에 영향을 미치는 인자를 고려하여 피로 한도의 값을 수정
– 표면효과, 치수효과, 하중의 종류, 사용온도, 신뢰도, 사용환경 등
0
0
etotale
emsrtfle
C
CCCCCC
School of Mechanical Engineering Mechanical Design I
Endurance Limit Modifying Factors
표면 효과(surface finish)
– 표면 조도(surface roughness) 등에 의한 변화
– 연마된 면은 피로 한도가 증가
)( b
uta
b
utf
aSk
aC
School of Mechanical Engineering Mechanical Design I
Endurance Limit Modifying Factors
치수 효과(size)
– 형상은 같더라도 치수가 커지면 결함이 존재할 확률이 높기 때문에, 이를 보정해 주기 위한 계수
1 9.0~7.0
loading) (axial
[mm] 2545151.1
[mm] 5179.262.7/
[mm] 2505085.1
[mm] 50106.7/
[mm] 100.1
)or torsion bending section;-crosscircular h (shaft wit
157.0
107.0
19.0
068.0
bs
b
s
s
s
korC
DD
DDk
or
DDC
DDC
DC
School of Mechanical Engineering Mechanical Design I
Endurance Limit Modifying Factors
치수 효과(size)
– 부품이 회전하지 않거나 원형이 아닌 경우
• 등가 지름 ~ effective dimension
2
95.0
2/1
0766.0
rodr rectangula :808.0
rodcircular gnonrotatin :360.0
shapes) structural ng(nonrotati
e
e
e
dA
or
hbd
dd
School of Mechanical Engineering Mechanical Design I
Endurance Limit Modifying Factors
하중의 종류(loading)
– 일반적으로 피로 강도의 경우 원형 봉의 반복굽힘에 대한 강도: 회전굽힘에 의한 피로강도
– 다른 하중의 경우에 대한 보정이 요구됨
(torsion)59.0
(axial)85.0
(bending)1
1(torsion)
[MPa] 15201
[MPa] 1520923.0(axial)
1(bending)
c
l
el
el
l
k
or
C
C
C
C
School of Mechanical Engineering Mechanical Design I
Endurance Limit Modifying Factors
사용온도(temperature)
C][ 54037
10246.6105621.0
103414.0106507.09877.0
C][ 5504504500058.01
C][ 4501
41238
253
T
TT
TTS
Sk
or
TTC
TC
RT
Td
t
t
School of Mechanical Engineering Mechanical Design I
Endurance Limit Modifying Factors
신뢰도(reliability)
– 8% 표준 편차(standard deviation)
School of Mechanical Engineering Mechanical Design I
Endurance Limit Modifying Factors
기타 사용 환경
– 제조 과정
– 잔류응력
– 코팅
– 부식 피로
School of Mechanical Engineering Mechanical Design I
Stress Concentration and Notch Sensitivity
노치(notch) 효과
– 반복 하중으로 인하여 노치부분에 응력이 집중되어 크랙(crack)이 발생하여 피로한도가 작아지는 현상
– 피로 응력 집중 계수(fatigue stress concentration factor) or 노치 계수(notch factor)
0
max
0
max
specimen free-notchin stress
specimen notchedin stress maximum
fs
f
K
K
School of Mechanical Engineering Mechanical Design I
Stress Concentration and Notch Sensitivity
노치(notch) 효과
– 노치 감도 계수(notch sensitivity factor): 노치가 재료의 피로 파괴에 미치는 민감도
• geometry → Kc → material → q → Kf
11or 11
ysensitivitnotch full has material the1
allat notches y tosensitivit no has material the0
1
1or
1
1
csshearfscf
cs
fs
shear
c
f
KqKKqK
q
q
K
Kq
K
Kq
응력집중계수 피로응력집중계수
School of Mechanical Engineering Mechanical Design I
Stress Concentration and Notch Sensitivity
노치(notch) 효과
School of Mechanical Engineering Mechanical Design I
Stress Concentration and Notch Sensitivity
노치(notch) 효과
equationHardrath -Kuhn :
1
1
constantNeuber , : /1
11
equation)(Neuber
1
1
) y,sensitivit(notch
r
aq
ara
KK
K
Kq
q
cf
c
f
School of Mechanical Engineering Mechanical Design I
Fluctuating Stresses
반복응력에 대한 피로파손이론
– (I) completely reversing simple loads
– (II) fluctuating simple loads
– (III) combinations of loading modes
School of Mechanical Engineering Mechanical Design I
Fluctuating Stresses
반복응력에 대한 피로파손이론
– (I) completely reversing simple loads
→ 양진응력: S-N 곡선
2,0 minmax
am
School of Mechanical Engineering Mechanical Design I
Fluctuating Stresses
반복응력에 대한 피로파손이론
– (I) completely reversing simple loads
310, Nf
e
utNff
310,
MPa 490 MPa 1400
School of Mechanical Engineering Mechanical Design I
Fluctuating Stresses
반복응력에 대한 피로파손이론
– (I) completely reversing simple loads
b
a
b
f
e
ut
e
ut
ef
utf
b
f
aaN
fb
fa
N
fN
aN
/1/1
2
6
3
log3
1
10at
10at
relation, sBasquin' from
cNb
cNb
cN
cNN
a
a
b
a
b
a
b
f
logloglog
logloglog
loglog
constant
textbookin the or,
School of Mechanical Engineering Mechanical Design I
Fluctuating Stresses
반복응력에 대한 피로파손이론
– (I) completely reversing simple loads
• Example 2-21
fracture fatigue no30for
237186842.237185~,60for
24508614.24507~,80for
4214710.4213~,100for
45939.2,12674.0
10log50log:10
10log120log:10
loglog
MPa30,60,80,100
MPa5010;MPa12010
66
33
63
a
a
a
a
a
a
ek
N
N
N
ba
baN
baN
bNa
NN
School of Mechanical Engineering Mechanical Design I
Fluctuating Stresses
반복응력에 대한 피로파손이론
– (II) fluctuating simple loads (일반 반복응력)
• 평균응력(σm)과 교번응력(응력진폭, σa)의 합 – 평균응력: 정하중, 항복강도/극한강도 → x-축
– 교번응력: 동하중, 피로한도 → y-축
School of Mechanical Engineering Mechanical Design I
Fluctuating Stresses
반복응력에 대한 피로파손이론
– (II) fluctuating simple loads
: various criteria of failure
Yma
Y
m
e
a
u
m
e
a
u
m
e
a
Y
m
e
a
yielding-cycle-firstLanger
1line elliptic-ASME
1lineGerber
1lineGoodman (modified)
1line Soderberg
22
2
School of Mechanical Engineering Mechanical Design I
Fluctuating Stresses
반복응력에 대한 피로파손이론
– (II) fluctuating simple loads
• Example: (modified) Goodman line
초기 예하중이 없는 경우 초기 예하중이 있는 경우
σm
σa
σe
σu σY
(σm, σa)
하중선(load line)
파괴점(failure point)
σm
σa
σe
σu σY
(σm, σa)
(σ0, 0)
School of Mechanical Engineering Mechanical Design I
Fluctuating Stresses
반복응력에 대한 피로파손이론
– (II) fluctuating simple loads
: modified Goodman diagram – 헤이그 선도(Haigh diagram)
School of Mechanical Engineering Mechanical Design I
Fluctuating Stresses
반복응력에 대한 피로파손이론
– (II) fluctuating simple loads
: modified Goodman diagram – Smith diagram
School of Mechanical Engineering Mechanical Design I
Fluctuating Stresses
반복응력에 대한 피로파손이론
School of Mechanical Engineering Mechanical Design I
Fluctuating Stresses
반복응력에 대한 피로파손이론
– (III) combinations of loading modes (합성응력에 대한 피로한도 해석)
• (textbook) 112~114 (in 5th ed.)
School of Mechanical Engineering Mechanical Design I
Fluctuating Stresses
반복응력에 대한 피로파손이론
– Example 2-18
• 원형 단면 봉 – 단면적, A = 1000[mm2]
– 최대인장하중, Fmax=150[kN]; 최소인장하중, Fmin=90[kN]
– 피로응력집중계수, Kf=1.2; 평균응력집중계수, Kfm=1.0
– 피로강도수정계수, Ctotal=0.8
– 파단강도(극한강도), σu=600[N/mm2]
– 항복강도, σY=400[N/mm2]
– (양진)피로한도, σe0=300[N/mm2]
School of Mechanical Engineering Mechanical Design I
Fluctuating Stresses
반복응력에 대한 피로파손이론
– Example 2-18
School of Mechanical Engineering Mechanical Design I
Fluctuating Stresses
반복응력에 대한 피로파손이론
– Example 2-19
• 원형 단면 봉 – 최대인장하중, Fmax=25000[N]; 최소인장하중, Fmin=5000[N]
– 피로응력집중계수, Kf=1.4; 평균응력집중계수, Kfm=1.5
– 피로강도수정계수, Cl=1.0, Cf=0.9, Cm=0.9, Cr=1.0
– 파단강도(극한강도), σu=600[MPa]
– 항복강도, σY=480[MPa]
– 안전계수, S=2
(1) 무한수명을 가지기 위한 최소 지름 d
(2) 수명이 반복수 N=105 인 경우의 지름 d
School of Mechanical Engineering Mechanical Design I
Fluctuating Stresses
반복응력에 대한 피로파손이론
– 예.
• 스틸 바(bar) – 반복응력: σmax=420[MPa], σmin=-140[MPa]
– σu=560[MPa], σY=455[MPa], σe=280[MPa], f=0.9
– modified Goodman line
34335~10loglogloglog
MPa37311
9577.2,0851.0loglog
MPa504:10&MPa280:10
MPa2802
140420,MPa140
2
140420
5357.4
36
NbNabNa
babNa
fNN
f
f
u
m
f
a
u
m
e
a
ufef
am
School of Mechanical Engineering Mechanical Design I
Fluctuating Stresses
반복응력에 대한 피로파손이론
– 예.
• 복합 하중: 굽힘, 축 방향, 비틀림 – 굽힘: 양진, 최대응력 60[MPa]
– 축 방향: 일정한 압축응력 20[MPa]
– 비틀림: 편진, 0~50[MPa]
– Kf,bending=1.4, Kf,axial=1.1, Kf,torsion=2.0
– σu=400[MPa], σY=300[MPa], σe=200[MPa]
– modified Goodman line
School of Mechanical Engineering Mechanical Design I
Fluctuating Stresses
반복응력에 대한 피로파손이론
– 예.
21.1~
11
MPa6.120,MPa35.893
3stress Misesvon
MPa50,MPa50MPa25,MPa25:torsion
0,MPa220,MPa20:axial
MPa84,0MPa60,0:bending
,,
,,
2/122
2/12222/12
221
2
1
S
u
mVM
e
aVM
u
m
e
a
aVMmVMxyxxVM
xyyyxxVM
amam
amam
amam