Issue 78

G. Palomba et alii, Fracture and Structural Integrity, 78 (2026) 233-247; DOI: 10.3221/IGF-ESIS.78.14

Two complementary models were applied to derive mechanical properties from hardness measurements: the Lopez & Fatemi [9] and Kamaya [10] correlations. The Lopez model relates the yield strength ( σ ᵧ ) and ultimate tensile strength ( σ UTS ) to Brinell hardness (HB) as reported in Eqns. (1) and (2):

2

y 

0.0039 HB 1.62 HB 

σ

(1)

2

UTS 

0.0012 HB 3.3 HB 

σ

(2)

Vickers hardness values obtained experimentally were converted to Brinell values, in order to apply Eqn. (1) and (2), as follows [22] : HB 0.9801 HV  (3) These empirical equations, obtained from extensive experimental data sets on steels, provide reliable first-order estimates of tensile properties, reported in Table 1. 0.9941

Derived Yield Strength σ y (MPa)

Derived Ultimate Strength σ UTS (MPa)

Converted Hardness (HB)

Experimental Yield Strength σ y (MPa)

Experimental Ultimate Strength σ UTS (MPa)

Metallurgical Region Base Material (BM) Heat-Affected Zone (HAZ)

Hardness (HV)

170

162

364

355(2.41%.)*

565

551 (2.43%*)

180 200

171 190

391 392

/ /

600 670

/ /

Weld Metal (WM)

*The values in brackets refers to the percentage error.

Table 1: Estimates of tensile properties from empirical equations.

The experimental tensile tests show an average engineering yield strength of 355 MPa. Comparing this to the hardness derived estimation of 364 MPa, the error is only +2.41%. With regards to the ultimate tensile strength, the experimental results indicate an average value of 551 MPa, which compared to the hardness-derived estimation of 565 MPa, produce an error equal to +2.43%. An error margin of under 2.5% for both critical threshold limits provides an appropriate quantitative justification for the baseline validity of this approach. The obtained values for σ ᵧ σ UTS were used to obtain true stress-strain curves through common Ramberg-Osgood equations based on σ ut , σ y , ε ut , ε y , considering Lopez-Fatemi method and the Kamaya model. The applied procedure is described and summarized in Tab. 2. True stress-strain curve calculation Method 1: Lopez and Fatemi [9] Method 2: Kamaya [10] Common Ramberg-Osgood equation based on σ ut , σ y , ut , y : 1 n Ramberg-Osgood equation according to the method developed by Kamaya based only on σ ut and σ y : m

E H           where:     ; y ut y     

y y     E              y

where:

log / log / ut

n   y



0.754



ut      

y



E





n

H

 

py



3.93  



m

ln   

;

  



y

y

242