PSI - Issue 43

Arnab Bhattacharyya et al. / Procedia Structural Integrity 43 (2023) 35–40 Author name / Structural Integrity Procedia 00 (2022) 000 – 000

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hyperbolic relation with critical fracture strain ( C

f  ) as per Kruciz et al. [2009] and Byun et al [2000], and C S t , true fracture strain ( f  ) and stress triaxiality parameter during uniform tensile f  can be

determined from the knowledge of I deformation ( t T ), using the relation: . / C T I S f f t t  = 

(2) The critical value of the mean contact pressure corresponding to imaginary fracture of the material is determined from critical fracture strain, termed here as critical mean contact pressure, and is expressed by the equation: ( ) ( ) 2 / 3 n C I C m S f p t K  = + (3) where, K and n are the strength coefficient and strain hardening exponent of a material and can be derived from either tensile or BI test. The IEF is determined numerically by integrating the equation 0 f h m p dh  up to the critical mean contact pressure: where 2 4 / m p P d  = , P , h and d are the instantaneous values of applied load, indentation depth and indentation diameter. The indentation depth ( h f ) corresponds to the point of imaginary fracture.

1000 1200 1400 1600

AISI 316LN AISI 304LN 0.14% C steel

SA333 IF steel

200 400 600 800

Indentation load, N

0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0

Total indentation depth, mm

Figure 4. Typical plots of indentation load vs. total indentation depth for the investigated steels: (a) AISI 316LN stainless steel, (b) AISI 304LN stainless steel, (c) 0.14% C steel, (d) SA333 Gr.6 steel, and (e) IF steel. Using the generalized Griffith theory under plane strain condition and the definition of fracture toughness for a crack in an infinite plate, the relationship between fracture energy, W f = ( W 0 + IEF ), and fracture toughness, K JC , can be expressed as 1 1 2 2 0 2 2 2 2 ( ) 1 1 JC f EW E W IEF K   +   = =     −  −      or 1 2 2 2 ( ) 1 JC E IEF K   =    −   (4) where, W 0 is the cleavage fracture energy of the material and can be neglected for ductile materials (Byun et al., 2000), E is the modulus of elasticity and  is Poisson’s ratio. The values of I S t , C f  , K, n and C m p of the five investigated steels are given in Table 3. The values of stress triaxiality and C m p of the selected steels are found to be in appropriate order when compared with stress triaxiality at fracture and mean contact pressure at fracture of RPV steels determined by Byun et al (2000). Table 3 Ball indentation parameters for estimating fracture toughness of the investigated steels Material I S t c f  K MPa n MPa IF steel 3.30 0.173 515 0.376 1058 316LN SS 2.36 0.281 1285 0.374 2475 304LN SS 2.47 0.274 1360 0.37 2640 0.14%C steel 2.58 0.125 850 0.25 1625 SA333 steel 2.78 0.177 945 0.34 1720 4. Discussion The estimated fracture toughness of AISI 304LN stainless steel and SA333 Gr.6 steel using the suggested approach of analysing BIT results coupled with tensile data are in good agreement with those obtained by conventional J integral fracture toughness test results (ASTM E 1820). Conventional fracture toughness tests could not be performed on other three materials (AISI 316LN stainless, 0.14% C and interstitial free steels) due to material restriction. The estimated fracture toughness of 0.14% C steel was validated by comparing its value with the fracture toughness values of low carbon steels as reported by Timofeev et al. (1998) in the range between 150 and 200 MPa.m 1/2 . Therefore the estimated fracture toughness of 250 MPa.m 1/2 for steel having carbon percentage of