Equations for Chapter 7,8 & 9

s_ij = K_I / [(2pr)^1/2] [f(Q)]

K_I = Y s (pa)^1/2 [Y = 1.12 for a single (or double) edge notch crack]

[Y = 1 for small center through crack]

[Y = 0.7 for a surface semi-circular crack]

K_IC = Y s_f (pa_c)^1/2; s_y = s₀ + k_y D^-1/2 and s_c = s_0c + k_c D^-1/2

r_y » [1/(2p)] (K_I/s_y)²

B = 2 r_y ; s_j = Y_j K_bj / (r_j) ^½ = M_j / (r_j) ^½ (mirror, mist …)

d = G_I / l s_y = K_I² / E¢ l s_y

K_I² = E¢ G = 2 E¢ g ; K_IC = d (E/H)^1/2 [P / a ^3/2] (indentation)

J = - 1/B (dU/da)

J = G = K² / E¢ = l s_y d J = (2A) / (B b)

E¢ = E (plane stress); E¢ = E/ (1-n²) [plane strain]

t and a ³ 2.5 (K_I/s_y)²

K_eff = s (pa)^1/2 / [ 1 – ½ (s/s_y²)]^1/2

s_c = [(2E¢ g_s)]^1/2 / (pa)^1/2 [Griffith Eq.]

s_max/s_appl = k_t » 2 (a/r)^1/2

s_max/s_appl = (1 + 2 a/b)

ln [1 /P(V₀)] = (s/s₀)^m

F_i(V₀) = 1 – P_i(V₀) = i / (N + 1)

P_i(V₀) = (N + 1 – i) / (N + 1)

V = n V₀

ln P(V) = - (V/V₀) (s/s₀)^m

s₁/s₂ = (V₂/V₁)^1/m