7-fracture mechanics 弹塑性力学讲义 英文版 教学课件
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3．Damage：Fracture is one of the three forms of metals failure. (the other two forms are wearing and corrosion)
4 ． Fracture mechanics ： It’s an important branch of solid mechanics, investigating the phenomenon, the laws and the conditions from loading to fracture of the materials.
which are artificially introduced to describe the intensity of the stress field around the crack tips. By using these factors, the problem of solving the stress fields and displacements is simplified as just seeking for Ki (i=Ⅰ,Ⅱ,Ⅲ) . Unit： Ki (i=Ⅰ,Ⅱ,Ⅲ) ——[force]×[length]-3/2 =[N]×[m]-3/2
Including linear elastic fracture mechanics and elasto-plastic fracture mechanics. Griffithi brittle fracture mechanics was developed，while tenacious fracture mechanics and damage mechanics of metals are developing.
Elementary fracture mechanics
8.4 The plastic area at the tip of crack Ⅰ
With the above results and Mises yielding criterion, the plastic area at the tip of crack Ⅰcan be obtained.
Thickness of the sample
Elementary fracture mechanics
8.7 KIC——plane strain fracture toughness (平面应变断裂韧度)
KI = KIC（ fracture criterion for crackⅠ)
KITC hies
a material constant, independent thickness of the sample should be
of the geometry of the testing sample. large enough to guarantee that the the
crack tip is in a state of plane strain.
Elementary fracture mechanics
8.6 fracture criterion (断裂准则)
K i K ic (i I,II,III)
——fracture tenacity/toughness (断裂韧度），describing the resistance of crack propagating, determined by test（plane stress crack and plane strain
x y
1
2
2
x2yx2y
x y
2
2
2
x2yx2y
12 2 23 2 31 2 2 s 2
r21 Ks12co22s13si2n2 (for plane stress crack )
r2 1 K s 1 2 122co 22s4 3si2n (for plane strain crack )
And the width of the plastic area is
2
r0
1
2
K1
s
Leabharlann Baidu
(for plane stress crack )
r0
122
2
Ks1
2
(for plane strain crack )
Obviously, the width of the plastic area in plane stress state is much larger
Plastic passivation
Stress relaxation at the tip of crackⅠ
Elementary fracture mechanics
8.5 stress intensity factors (应力强度因子)
stress intensity factors
Discussion: ① Ki (i=Ⅰ,Ⅱ,Ⅲ) are independent of co-ordinate. They are parameters to describe
Elementary fracture mechanics (断裂力学基础）
8.1 Introduction （概述）
1．Definition of fracture：It is the process including formation and propagation of the macro-cracks and the fracture of the loaded piece
In plane stress state
In mediate state
In plane strain state
big enough to enhance Kic; When the thickness of the sample is
big enough, the crack tip will be in a state of plane strain. When the crack line moves, its plastic area is relatively small enough to decrease Kic KⅠc (plane strain fracture tenacity, 平面应变断裂韧度);
the intensity of the stress field around the crack tips
② Ki (i=Ⅰ,Ⅱ,Ⅲ) are close-related with the form, the size and the direction of the
cracks;
③ Ki (i=Ⅰ,Ⅱ,Ⅲ) are correlated with the value of the loading and the loading form ④ Ki (i=Ⅰ,Ⅱ,Ⅲ) are interrelated with the properties of the loaded material The physical meaning of Ki (i=Ⅰ,Ⅱ,Ⅲ) : They are mechanical parameters
The often used testing samples are shown as following:
(Details will be learned in another course Mechanical Properties of Materials
and Measurement and in a post-graduate course Damage and Fracture of Materials)
crack）.
When the thickness of the sample is small enough, the crack tip will be in a state of plane stress. When the crack line moves, its plastic area is relatively
than that in plane strain state.
And the plastic yielding of the material may result in stress relaxation at the tip of the crack.
The shape and size of the plastic area at the tip of crack Ⅰ
micro-cracks nucleation→propagation→macro-cracks formingdamage mechanics(损伤力学）
macro-cracks growing→propagation→metals fracture fracture mechanics（断裂力学）
2．Classification：tenacious fracture and brittle fracture (plastic deformation is more than or less than 5% before fracture) ; over-load fracture (the loading force is more than its strength b) and fatigue fracture (the loading force is much less than its yielding strength s, but in many cycles; about 85% cases are fatigue fracture)
4 ． Fracture mechanics ： It’s an important branch of solid mechanics, investigating the phenomenon, the laws and the conditions from loading to fracture of the materials.
which are artificially introduced to describe the intensity of the stress field around the crack tips. By using these factors, the problem of solving the stress fields and displacements is simplified as just seeking for Ki (i=Ⅰ,Ⅱ,Ⅲ) . Unit： Ki (i=Ⅰ,Ⅱ,Ⅲ) ——[force]×[length]-3/2 =[N]×[m]-3/2
Including linear elastic fracture mechanics and elasto-plastic fracture mechanics. Griffithi brittle fracture mechanics was developed，while tenacious fracture mechanics and damage mechanics of metals are developing.
Elementary fracture mechanics
8.4 The plastic area at the tip of crack Ⅰ
With the above results and Mises yielding criterion, the plastic area at the tip of crack Ⅰcan be obtained.
Thickness of the sample
Elementary fracture mechanics
8.7 KIC——plane strain fracture toughness (平面应变断裂韧度)
KI = KIC（ fracture criterion for crackⅠ)
KITC hies
a material constant, independent thickness of the sample should be
of the geometry of the testing sample. large enough to guarantee that the the
crack tip is in a state of plane strain.
Elementary fracture mechanics
8.6 fracture criterion (断裂准则)
K i K ic (i I,II,III)
——fracture tenacity/toughness (断裂韧度），describing the resistance of crack propagating, determined by test（plane stress crack and plane strain
x y
1
2
2
x2yx2y
x y
2
2
2
x2yx2y
12 2 23 2 31 2 2 s 2
r21 Ks12co22s13si2n2 (for plane stress crack )
r2 1 K s 1 2 122co 22s4 3si2n (for plane strain crack )
And the width of the plastic area is
2
r0
1
2
K1
s
Leabharlann Baidu
(for plane stress crack )
r0
122
2
Ks1
2
(for plane strain crack )
Obviously, the width of the plastic area in plane stress state is much larger
Plastic passivation
Stress relaxation at the tip of crackⅠ
Elementary fracture mechanics
8.5 stress intensity factors (应力强度因子)
stress intensity factors
Discussion: ① Ki (i=Ⅰ,Ⅱ,Ⅲ) are independent of co-ordinate. They are parameters to describe
Elementary fracture mechanics (断裂力学基础）
8.1 Introduction （概述）
1．Definition of fracture：It is the process including formation and propagation of the macro-cracks and the fracture of the loaded piece
In plane stress state
In mediate state
In plane strain state
big enough to enhance Kic; When the thickness of the sample is
big enough, the crack tip will be in a state of plane strain. When the crack line moves, its plastic area is relatively small enough to decrease Kic KⅠc (plane strain fracture tenacity, 平面应变断裂韧度);
the intensity of the stress field around the crack tips
② Ki (i=Ⅰ,Ⅱ,Ⅲ) are close-related with the form, the size and the direction of the
cracks;
③ Ki (i=Ⅰ,Ⅱ,Ⅲ) are correlated with the value of the loading and the loading form ④ Ki (i=Ⅰ,Ⅱ,Ⅲ) are interrelated with the properties of the loaded material The physical meaning of Ki (i=Ⅰ,Ⅱ,Ⅲ) : They are mechanical parameters
The often used testing samples are shown as following:
(Details will be learned in another course Mechanical Properties of Materials
and Measurement and in a post-graduate course Damage and Fracture of Materials)
crack）.
When the thickness of the sample is small enough, the crack tip will be in a state of plane stress. When the crack line moves, its plastic area is relatively
than that in plane strain state.
And the plastic yielding of the material may result in stress relaxation at the tip of the crack.
The shape and size of the plastic area at the tip of crack Ⅰ
micro-cracks nucleation→propagation→macro-cracks formingdamage mechanics(损伤力学）
macro-cracks growing→propagation→metals fracture fracture mechanics（断裂力学）
2．Classification：tenacious fracture and brittle fracture (plastic deformation is more than or less than 5% before fracture) ; over-load fracture (the loading force is more than its strength b) and fatigue fracture (the loading force is much less than its yielding strength s, but in many cycles; about 85% cases are fatigue fracture)