PSI - Issue 83

Niccolò Vilotta et al. / Procedia Structural Integrity 83 (2026) 246–255 σ y = 0.0039 HB 2 + 1.62 HB 2 +3.3 HB

248

(2)

σ UTS = 0.0012 HB

(3) Two different methods were used to determine the true stress-true strain curves: the method by Lopez & Fatemi and the method by Kamaya [13,14]. The first method requires the local values of yield strength σ y and ultimate tensile strength σ UTS , together with the yield strain ε y and the true strain at ultimate tensile strength ε UTS , the latter obtained from the experimental response of the non welded base material. To reconstruct the local elastic-plastic response, a Ramberg–Osgood-type constitutive relation was adopted [14]: ε = ε e + ε p = σ E + ( σ K ) 1/n (4) where is the true strain, σ is the true stress, E is Young’s modulus, K is the strength coefficient, and n is the strain hardening exponent. Since the Ramberg–Osgood curve passes through the points ( ε y , σ y ) and ( ε UTS , σ UTS ), the constitutive hardening equation is applied at these points; by taking their ratio, the strain-hardening exponent is obtained: The strength coefficient is derived from the plastic hardening equation: K = σ y ε y n (6) The true strain at ultimate tensile strength ε UTS , was obtained from experimental tensile tests performed on the non-welded DMLS base material and used as calibration reference. The plastic strain at yielding ε py , was determined from the same experimental tensile test on base-material. Once calibrated on the base material, the same procedure was applied locally using hardness-derived strength values to obtain zone-specific true stress-true strain curves. The Kamaya approach estimates a Ramberg–Osgood-type curve using σ y and σ UTS as primary inputs for integrity assessments [14]. In practice, the method defines the true curve by requiring it to pass through two points: the yielding and the ultimate tensile condition. The curve must therefore pass through the yield point at 0.2% offset. At the yield point: K = σ y ε py n ⁄ where ε py = 0. 2% (7) Setting m=1/n and normalising for the yield stress, a Ramberg–Osgood equation is obtained in the following form: E ε σ y = σ σ y + α ( σ σ y ) m (8) Where: α = E ε py σ y (9) m = 3.93 [ ln ( σ UTS σ y )] - 0.754 ( ε py = 0.002 ) (10) Here, ε py indicates the plastic strain at yielding, calibrated from the experimental base-material response as described above. Determining the true curves from hardness using empirical correlations between strength and specific steels, makes it possible to characterise and evaluate the material’s response in terms of stresses and strains. Static tensile tests were carried out on DMLS-manufactured AISI 316L dog-bone specimens in both non-welded and welded conditions, using a ZwickRoell universal testing machine equipped with a 600 kN load cell, in accordance with ASTM E8/E8M-25, Standard Test Methods for Tension Testing of Metallic Materials. The experimental arrangement is shown in Figure 2(a), while Figure 2(b) reports a detail of a welded DMLS specimen after fracture. The tensile campaign was used both to characterize the global mechanical response of the investigated configurations and to provide the calibration data required for the local constitutive reconstruction [21]. Static tensile tests were carried out on DMLS-manufactured AISI 316L dog-bone specimens in both non-welded and welded conditions, using a ZwickRoell universal testing machine equipped with a 600 kN load cell, in accordance with ASTM E8/E8M-25, Standard Test Methods for Tension Testing of Metallic Materials. The experimental arrangement is shown in Figure 2(a), while Figure 2(b) reports a detail of a welded specimen after fracture. n = ln ( σ UTS σ y ⁄ ) ln ( ε UTS ε y ⁄ ) (5)