Project “The development of the didactic potential of Cracow University of Technology in the range...
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![Page 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.](https://reader036.fdocuments.net/reader036/viewer/2022082620/5a4d1aeb7f8b9ab05997ac59/html5/thumbnails/1.jpg)
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
![Page 2: Project “The development of the didactic potential of Cracow University of Technology in the range of modern construction” is co-financed by the European.](https://reader036.fdocuments.net/reader036/viewer/2022082620/5a4d1aeb7f8b9ab05997ac59/html5/thumbnails/2.jpg)
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
![Page 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.](https://reader036.fdocuments.net/reader036/viewer/2022082620/5a4d1aeb7f8b9ab05997ac59/html5/thumbnails/3.jpg)
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
![Page 4: Project “The development of the didactic potential of Cracow University of Technology in the range of modern construction” is co-financed by the European.](https://reader036.fdocuments.net/reader036/viewer/2022082620/5a4d1aeb7f8b9ab05997ac59/html5/thumbnails/4.jpg)
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
![Page 5: Project “The development of the didactic potential of Cracow University of Technology in the range of modern construction” is co-financed by the European.](https://reader036.fdocuments.net/reader036/viewer/2022082620/5a4d1aeb7f8b9ab05997ac59/html5/thumbnails/5.jpg)
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)
![Page 6: Project “The development of the didactic potential of Cracow University of Technology in the range of modern construction” is co-financed by the European.](https://reader036.fdocuments.net/reader036/viewer/2022082620/5a4d1aeb7f8b9ab05997ac59/html5/thumbnails/6.jpg)
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:
![Page 7: Project “The development of the didactic potential of Cracow University of Technology in the range of modern construction” is co-financed by the European.](https://reader036.fdocuments.net/reader036/viewer/2022082620/5a4d1aeb7f8b9ab05997ac59/html5/thumbnails/7.jpg)
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