Issue 78

A. Bacco et alii, Fracture and Structural Integrity, 78 (2026) 1-18; DOI: 10.3221/IGF-ESIS.78.01

are activated at the melting point, and for this reason the only heat that needs to be added is

body flux Q which is applied as a

volumetric source to the activated elements Eqn. (11),

T

T













s

s

sensible Q vol 

C dT m C dT  

(8)

seam

seam

T

T

0

0

latent seam latent Q m q 

(9)

real sensible Q Q Q   

* real seam Q Q L 

with

(10)

Q

body flux

latent

Q

body flux



Q

(11)

component

n

component

where: -

, seam seam L vol and seam m are the length, the volume and the mass of the seam, respectively; - s T is the solidus temperature; - component n is the number of components of the seam. To reproduce the progressive deposition of filler material, the weld bead is divided into discrete components. Each component receives heat input Eqn. (12) for a time interval corresponding to the torch travel speed Eqn. (13),

Q

body flux Q v

component





q 

(12)

vol

t

vol

L

component weld

seam component

L

component



t

(13)

weld

v

where component L is the length of components of the seam. Temperature-dependent thermal properties and phase-change effects are included, allowing accurate prediction of FZ and heat-affected zone geometry without requiring calibration of complex heat source models. This approach significantly reduces setup time while maintaining reliability in thermal field estimation. Mechanical analysis The mechanical analysis employs the nodal temperature history obtained from the thermal simulation as input to compute the stress–strain response of the welded joint. An elastoplastic material model was adopted, based on the von Mises yield criterion and isotropic hardening, accounting for temperature-dependent mechanical properties. This constitutive model, widely used for simulating steel [23,24], is expressed by the incremental form of the stress–strain law Eqn. (14), where the total stiffness matrix combines elastic and plastic contributions (15), incorporating thermal strains through the thermal stiffness term.

ep d D d C dT             th

(14)

    ep e p D D D      

(15)

where: -

ep D     is the total stiffness matrix; e D     is the elastic stiffness matrix;

-

8