Issue 66

Ch. F. Markides et alii, Frattura ed Integrità Strutturale, 66 (2023) 233-260; DOI: 10.3221/IGF-ESIS.66.15

-0.25 -0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20 0.25

 

o 90 

B

A

b

B 

A 

Deformed configuration

 N  F 

 H  J 

b

b

O

Undeformed configuration cracked / int act

y - axis [m]

C 

D 

b

D

C

 

-0.25-0.20-0.15-0.10-0.05 0.00 0.05 0.10 0.15 0.20 0.25

(a)

x - axis [m]

Deformed crack

90  Initial crack / line 2  Deformed line 2 

0.075

 

H

F

0.050

F 

H 

Deformed configuration intact Deformed configuration cracked

0.025





0.000





O

-0.025 y - axis [m]

N 

J 

Undeformed configuration cracked / int act

-0.050

J

N

 

-0.075

-0.075 -0.050 -0.025 0.000 0.025 0.050 0.075

(b)

x - axis [m]

Figure 21: a) The deformed versus the undeformed configurations of the cracked and the intact square plates under uniaxial pressure normal ( β =90 ο ) to the crack/line 2 α . (b) Magnified view of the crack area. It is once again concluded that the span of the crack and the line 2 α of the intact plate after deformation are equal only when ν =0.5 which cannot be the case. For ν <0.5, u (x)  is always bigger than in u (x) so that the span of the deformed crack will always exceed that of the line 2 α . What is more, for any fixed value of ν <0.5, it is easily seen that by decreasing E, the difference between u (x)  and in u (x) increases, explaining why for decreasing E-values, an increasing normal con tact stress is required in the cracked plate, compared to the respective normal stress in the intact one. It is here emphasized that what is discussed regarding the fact that ( yy xy σ , τ   ) >( in in yy xy σ , τ ), is a consequence of the basic assumption of the present study that the linear terms of the displacements provided by the traditional solution of the ‘initial problem’ of LEFM were accepted “as they are”. However this an assumption that must be further explored and validated, because if yy xy σ , τ   were to be equal to in in yy xy σ , τ , then u , v   should tend to in in u , v of the intact plate. This is the subject of an ongoing research project implemented according to a combined experimental and analytic manner.

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