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

1/7M.Chrzanowski: Strength of Materials 3

SM3-02: Theoretical strength

THEORETICAL STRENGTH OF SOLIDS

Lennart-Jones model

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

2/7M.Chrzanowski: Strength of Materials 3

SM3-02: Theoretical strength

na

a sCF m

rr s

CF

s

mo

rno

a

sC

sC

ra FF

Fr FaFa Fr

Reactive force (repulsion) Active force (attraction)

m > n (m10, n 5)

For s=so

so

Fr FaFa Fr

nmo

mnom

o

no

r

a

ss

ss

CC

1

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

3/7M.Chrzanowski: Strength of Materials 3

SM3-02: Theoretical strength

m

mo

n

no

no

am

mo

mo

rn

no

no

amr

na

ra ss

ss

sC

ss

sC

ss

sC

sC

sCFFF

s > so no

amo

r

sC

sC

Fr FaFa FrF F

so

F

0=s-so

F

s0

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

4/7M.Chrzanowski: Strength of Materials 3

SM3-02: Theoretical strength

m

o

o

n

o

ono

am

on

ono

am

mo

n

no

no

a

ss

ss

sC

ss

ss

sC

ss

ss

sCF

F

0

F=FR

=R

mnno

amn

no

a

m

o

n

ono

a

sC

sC

sssCF

111

11

11

11

1

0R

ddF

011 11 mR

nRn

o

a mnddF

sC

R

nmmn

R 111 =R

=s-so

os

nmm

nmn

no

aR n

mnm

sCF

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

5/7M.Chrzanowski: Strength of Materials 3

SM3-02: Theoretical strength

%1515,01215

10 51510

1

R

nmm

nmn

no

aR n

mnm

sCF

m=10, n =5

11

nm

R nm

no

ano

ano

aR s

CsC

sCF 25,022

510

510 21510

10510

5

=(101000)x(dośw FR)

Reasons of model to experiment discrepancy:

1. Very simplistic model

2. Defects of real crystal arrangement neglected (see Theory of Dislocations)

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

6/7M.Chrzanowski: Strength of Materials 3

SM3-02: Theoretical strength

Further idealisation

=R

F

0

F=FR AF

R

2sinR

R2sin1

%2525,04/1 R

Edd

0

0

2cos2

RE

EER 3,02/

ER 001,0Experimental value:

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

7/7M.Chrzanowski: Strength of Materials 3

SM3-02: Theoretical strength

25,0

021 d

=0,25

0

R

=0,50

xdxdR sin21

212sin

21

0

25,0

0

x2

00

x

2/25,0

x

22

dxddxd

4cos

4

2/

0

RR x

Energy consumed

Energy density per unit volume to cause failure

Further considerations in Fracture Mechanics