SM3-03: Failure of structures Failure of Structures Fatigue & Fracture Mechanics M.Chrzanowski: Strength of Materials 3 Project “The development of the didactic potential of.
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Slide 1
SM3-03: Failure of structures
Failure of Structures
Fatigue & Fracture Mechanics
M.Chrzanowski: Strength of Materials 3
Project “The development of the didactic potential of Cracow University of Technology in the range of modern construction” is co-financed by the European Union
within the confines of the European Social Fund and realized under surveillance of Ministry of Science and Higher Education
1/4
Slide 2
SM3-03: Failure of structures
Brittle failure
=P/A
RH= Rm
Rpl
RH
Plastic
(ductile)
failure
S – safety belt
ekspl
Linear elastic
material
Nonlinear,
elasto-plastic
material
=Δl/lo
ekspl =Rm - S < RH
M.Chrzanowski: Strength of Materials 3
1. Far enough from failure
2. Within elastic domain
Project “The development of the didactic potential of Cracow University of Technology in the range of modern construction” is co-financed by the European Union
within the confines of the European Social Fund and realized under surveillance of Ministry of Science and Higher Education
2/4
Slide 3
SM3-03: Failure of structures
1. Far enough from failure
Experiment: evaluation of Rm
2. Within elastic domain
Experiment: evaluation of RH
3. Determine ekspl
ij
Equilibrium equations
(statics)
Kinetics of
deformation
x j
2 ij
Caonstitutive equation
(Hooke’s law)
Solve Boundary Value Problem (BVP)
ui
x j
Pi 0
q i ij vj
Statics boundary condition
u j
xi
uk uk
xi x j
ij 2 G ij kk ij
Aσ=3K A
ui ui
S
ui x j ui x j
S
Kinematical boundary conditions
E ij 1 ij kk ij
Dσ=2G D
Tσ=3K A+2G D
M.Chrzanowski: Strength of Materials 3
Project “The development of the didactic potential of Cracow University of Technology in the range of modern construction” is co-financed by the European Union
within the confines of the European Social Fund and realized under surveillance of Ministry of Science and Higher Education
3/4
Slide 4
SM3-03: Failure of structures
Fulfilment of below condition :
ekspl =Rm/s < RH
Happens to be insufficient in at least two cases :
When external loading does not remain constant in time: q=q(t) , P=P(t)
σ
FATIGUE of a material
t
Fatigue Mechanics
When irregularities in geometry of a specimen
(structure) like notches or defects yield stress
concentrations
CRACKING of a material
Fracture Mechanics
M.Chrzanowski: Strength of Materials 3
Project “The development of the didactic potential of Cracow University of Technology in the range of modern construction” is co-financed by the European Union
within the confines of the European Social Fund and realized under surveillance of Ministry of Science and Higher Education
4/4
SM3-03: Failure of structures
Failure of Structures
Fatigue & Fracture Mechanics
M.Chrzanowski: Strength of Materials 3
Project “The development of the didactic potential of Cracow University of Technology in the range of modern construction” is co-financed by the European Union
within the confines of the European Social Fund and realized under surveillance of Ministry of Science and Higher Education
1/4
Slide 2
SM3-03: Failure of structures
Brittle failure
=P/A
RH= Rm
Rpl
RH
Plastic
(ductile)
failure
S – safety belt
ekspl
Linear elastic
material
Nonlinear,
elasto-plastic
material
=Δl/lo
ekspl =Rm - S < RH
M.Chrzanowski: Strength of Materials 3
1. Far enough from failure
2. Within elastic domain
Project “The development of the didactic potential of Cracow University of Technology in the range of modern construction” is co-financed by the European Union
within the confines of the European Social Fund and realized under surveillance of Ministry of Science and Higher Education
2/4
Slide 3
SM3-03: Failure of structures
1. Far enough from failure
Experiment: evaluation of Rm
2. Within elastic domain
Experiment: evaluation of RH
3. Determine ekspl
ij
Equilibrium equations
(statics)
Kinetics of
deformation
x j
2 ij
Caonstitutive equation
(Hooke’s law)
Solve Boundary Value Problem (BVP)
ui
x j
Pi 0
q i ij vj
Statics boundary condition
u j
xi
uk uk
xi x j
ij 2 G ij kk ij
Aσ=3K A
ui ui
S
ui x j ui x j
S
Kinematical boundary conditions
E ij 1 ij kk ij
Dσ=2G D
Tσ=3K A+2G D
M.Chrzanowski: Strength of Materials 3
Project “The development of the didactic potential of Cracow University of Technology in the range of modern construction” is co-financed by the European Union
within the confines of the European Social Fund and realized under surveillance of Ministry of Science and Higher Education
3/4
Slide 4
SM3-03: Failure of structures
Fulfilment of below condition :
ekspl =Rm/s < RH
Happens to be insufficient in at least two cases :
When external loading does not remain constant in time: q=q(t) , P=P(t)
σ
FATIGUE of a material
t
Fatigue Mechanics
When irregularities in geometry of a specimen
(structure) like notches or defects yield stress
concentrations
CRACKING of a material
Fracture Mechanics
M.Chrzanowski: Strength of Materials 3
Project “The development of the didactic potential of Cracow University of Technology in the range of modern construction” is co-financed by the European Union
within the confines of the European Social Fund and realized under surveillance of Ministry of Science and Higher Education
4/4