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

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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

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