## Size Effect Griffith Theory

13 In his quest for an explanation of the size effect, Griffith came across Inglis's paper, and his "strike of genius" was to assume that strength is reduced due to the presence of internal flaws. Griffith postulated that the theoretical strength can only be reached at the point of highest stress concentration, and accordingly the far-field applied stress will be much smaller.

14 Hence, assuming an elliptical imperfection, and from equation 11.2

a is the stress at the tip of the ellipse which is caused by a (lower) far field stress a^f'. Asssuming p « a0 and since 2yO' ^ 1, for an ideal plate under tension with only one single elliptical flaw the strength may be obtained from

theor

_2a^J — ao hence, equating with Eq. 11.12, we obtain

From this very important equation, we observe that

1. The left hand side is based on a linear elastic solution of a macroscopic problem solved by Inglis.

2. The right hand side is based on the theoretical strength derived from the sinusoidal stress-strain assumption of the interatomic forces, and finds its roots in micro-physics.

Finally, this equation would give (at fracture)

As an example, let us consider a flaw with a size of 2a = 5,000ao

40 a

100,000

Thus if we set a flaw size of 2a = 5,000a0 in 7 « this is enough to lower the theoretical fracture strength from —= to a critical value of magnitude 100—10, or a factor of 100. As an example

200aca

act act a act cr a cr

Therefore at failure cr _theor

E00 10

which can be attained. For instance for steel 2 E00

30,000 2,000

act a act a cr max

0 0