PSI - Issue 66

G. Cricrì et al. / Procedia Structural Integrity 66 (2024) 282–286 Author name / Structural Integrity Procedia 00 (2025) 000–000

284

3

This result allows estimating the post-critical load displacement curve in parametric form. From eq. (1), two limit values of the failure load may be obtained. The first one, denoted as 0 P is the failure load pertaining to very short joints and is calculated making the limit as . The second limit value, to which we will refer as P  is for very long joints and is achieved evaluating the limit of eq. (1) as L  : � �� � � ; � ���2Γ � ℎ � ����� (3) Since � is proportional to the maximum shear stress value c  and to the joint length L , it may be argued that short joints should be designed according to the nominal stress criterion. On the other hand, � is independent from c  or L , and is dependent on the fracture energy  ; hence, it seems that very long joints should be designed according to the Griffith criterion.

Tab. A – Adherends and adhesive properties Property Adherends Young moduli - E 1 , E 2 [ GPa ] Adherends Poisson ratios -  1 ,  2 [ - ] Adhesive fracture energy -  [ N/mm ] Adhesive critical normal stress -  c [ MPa ] Adhesive critical shear stress -  c [ MPa ]

206.0

0.27

3.7

60

30 ÷ 60

a)

b)

Fig.2 – Lap joint finite element model: a) elements mesh, b) deformed shape.

3. Validation To analyse the application field of the theoretical results, a validation study has been carried by the finite element method. A series of 2D joint models were built in the simulation environment Ansys by means of a macro written in APDL, fig. 2. The models considered the geometrically non-linear effects due to adherends bending. Four node plane strain elements SOLID185 were used for the adherends. For the adhesive layer, four nodes cohesive elements INTER200 were instead adopted. Linear elastic behaviour was assumed for the adherends, while the exponential model of Xu and Needleman (1994) was used for the mechanical behaviour of the adhesive layer. The values of the adherends and adhesive constitutive parameters are listed in tab. A. The optimal element size has been identified by a trial-and-error method: it has resulted that stress and strain in the adherends and adhesive layer were accurately estimated with a mesh of elements having mean size equal to one eighth of the minor thickness 1 h For the validation activity 32 FE models were analysed. More in detail, two different values, 30 and 60 MPa, of