PSI - Issue 77

P. Santos et al. / Procedia Structural Integrity 77 (2026) 339–347 P. Santos et al. / Structural Integrity Procedia 00 (2025) 000 – 000 5 loads per unit thickness p applied at a depth x. The superposition principle and the reciprocity theorem as formulated by Rice (1972) for Hookean bodies allow the stress intensity factor K  and the crack opening field, ω = ω (x, a) to be determined for any compressive stress distribution  (x) acting symmetrically on both faces of the crack (Fig. 3a): ω = ω (x,a)= E 2 ∫ G(t,x) x a K σ (t)dt [2] where E, the elastic modulus of the steel and the plane stress condition has been assumed. The Green function of Chell (1976) becomes: G(a,x)= √ W k ( W a ) h , 2 (a,x) [3] where h, 2 (a, x) is the derivative of the given function h(a, x), with respect of its second variable: h(a,x)=1 −( 1 − W x ) 2 π 2 arcos ( x a WW − − a x ) [4] and the factor k(a/W) results from the stress intensity factor, K ∞ , of SENT specimen subjected to uniform stresses along the crack,  (x) =  ∞ , or equivalently, loaded in tension with the remote stress  ∞ far away from the crack. K ∞ = ∫ σ 0 a ∞ G(a, t)dt = σ ∞ √ W k ( W a ) [h(a, t)] 0a = σ ∞ √ W k ( W a ) [5] The substitution in Eq.5 of K ∞ given in Tada et all, (2000), leads to the following function k(a/W): k ( W a ) = K ∞ σ ∞ √W = √ 2tan π 2W a 0 . 752+2 . 02 Wa +0 . 37(1−sen πW a ) 3 cos 2 π Wa [6] 343

Fig. 3. Stress intensity factors of the SENT specimen for: a) an arbitrary compressive symmetric load on the cohesive crack faces; b) the applied load and cohesive stresses.

The condition of zero stress intensity factor (K ∞ – K Y ) that occur because of the combined action of the remote stresses  ∞ and the stresses Y developed in the cohesive zone determines the total depth A that the cohesive crack acquires when the SENT specimen is tensile loaded (Fig. 3).