PSI - Issue 28

Giovanni Meneghetti et al. / Procedia Structural Integrity 28 (2020) 1062–1083 G. Meneghetti/ Structural Integrity Procedia 00 (2019) 000–000

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2. Peak Stress Method (PSM) The Peak Stress Method (PSM) is a rapid, numerical tool to rapidly estimate the NSIF-terms K 1 , K 2 and K 3 , taking advantage of the opening, in-plane shear and out-of-plane shear peak stresses, respectively, calculated from a linear elastic FE analysis with coarse mesh, as shown in the example of Fig. 2 for a tube-to-flange joint. The estimated NSIF values can be obtained from the following expressions (Meneghetti, 2013, 2012; Meneghetti and Lazzarin, 2007): 1 1-λ * 1 FE θθ,θ=0,peak K K σ d    ; 2 1-λ ** 2 FE rθ,θ=0,peak K K τ d    ; 3 1-λ *** 3 FE θz,θ=0,peak K K τ d    (4) In previous expressions, σ θθ,θ=0,peak , τ rθ,θ=0,peak and τ θz,θ=0,peak are peak stresses defined in a local cylindrical coordinate system centred at the node at the V-notch tip; z -direction is tangential to the notch tip line; the θ -direction originates from the notch bisector line and r is the radial direction. The subscript ‘ θ =0’ highlights the direction along which local stresses must be evaluated; as an example, σ θθ,θ=0,peak means that the opening stress acts in normal direction with respect to the notch bisector, as shown in Fig. 2. Parameter d in Eq. (4) represents the average size of the finite elements which the FE analyst gives as input to the free mesh generation algorithm of the employed numerical software. Finally, parameters K * FE , K ** FE and K *** FE are dependent on the (Meneghetti et al., 2018): (i) element type and formulation; (ii) FE mesh pattern and (iii) procedure employed by the numerical software to extrapolate stresses at nodes. The estimation of NSIF-terms by using the PSM according to Eq. (4) is advantageous, since: (i) coarse FE meshes can be employed; moreover, (ii) only the linear-elastic peak stresses calculated at the notch tip are necessary, instead of a complete set of stress-distance numerical results as required to apply Eq. (1). A state-of-the-art review of the PSM has recently been published in (Meneghetti and Campagnolo, 2020), which the reader is referred to for additional details about the method. and 3D FE types (Campagnolo et al., 2019b; Campagnolo and Meneghetti, 2018; Meneghetti, 2013, 2012; Meneghetti and Guzzella, 2014; Meneghetti and Lazzarin, 2007; Visentin, 2020). Table 2 summarises the values of PSM coefficients K * FE , K ** FE and K *** FE as calibrated by using 4-node plane, 8-node brick and 4-node or 10-node tetra elements of Ansys® element library. In order to apply the PSM by adopting tetra elements, the variation of the peak stress along the notch tip profile due to intrinsically irregular free mesh pattern (see (Meneghetti and Campagnolo, 2020)) has been reduced by defining an average peak stress according to Eq. (5). More in detail, the average peak stress at the generic node n=k is the moving average of peak stresses calculated on three adjacent vertex nodes, i.e. n= k-1, k and k+1, according to the following expression (Campagnolo and Meneghetti, 2018): Moreover, the calibration of PSM based on tetra elements (Campagnolo et al., 2019b; Campagnolo and Meneghetti, 2018) requires that peak stresses evaluated at the nodes of the notch tip profile, which lay on the free surface of the analysed structure, are neglected, since their value can be affected by distorted mesh patterns (see Fig. 2). Furthermore, only peak stresses calculated at vertex nodes of tetra elements must be used in Eq. (5) to compute the average peak stress; therefore, when adopting 10-node tetra elements, peak stresses referred to mid-side nodes located along the notch tip profile must be neglected (see Fig. 2). Accordingly, PSM-parameters K * FE , K ** FE and K *** FE have been calibrated using either 4-node (Campagnolo et al., 2019b) or 10-node (Campagnolo and Meneghetti, 2018) tetra elements and by substituting the average peak stresses according to Eq. (5), i.e. , 0,peak    , r , 0,peak    and z , 0,peak    withing Eq. (4), in place of peak stresses σ θθ,θ=0,peak , τ rθ,θ=0,peak and τ θz,θ=0,peak , respectively. 2.2. Range of PSM applicability The calibration of PSM parameters K * FE , K ** FE and K *** FE has been performed under the conditions discussed in ij,peak,n=k-1 ij,peak,n=k ij,peak,n=k+1 ij,peak,n=k n=node σ +σ +σ σ = 3 (5) 2.1. Calibrated FE types The calibration of parameters K * FE , K ** FE and K *** FE has been performed in previous literature by using several 2D