PSI - Issue 38

Hendrik Bissing et al. / Procedia Structural Integrity 38 (2022) 372–381 Hendrik Bissing, Markus Knobloch, Marion Rauch / Structural Integrity Procedia 00 (2021) 000 – 000

374

3

Strain-Life Approach (SLA)

Crack Propagation Method (CPM)

Material

Material

Cyclic σ - ε -Behaviour

Failure (Crack Initiation)

Linear Elastic Fracture Mechanics (LEFM)

σ

σ

σ

Elastic modulus

Input data

Input data

ε

ε -Wöhler curves

Small plastic processes in the vicinity of the crack tip

ε

cyclic

ε

ε

N

σ

P = f( σ a , σ m , ε a , ...)

Masing

P r

Mode of Stress

Damage accumulation N N i

Crack Propagation

ε

Mode I

σ , ε

Memory

Crack propagation law (Paris, Forman, Walker, NASGRO)

L Geometry, Load

Calculation of Exposure Different Methods for Calculation of Δ K da/dN Δ K Δ K 0 m a L ˆ

Mode II

da / dn = f ( Δ K, R, … )

σ , ε

σ 0

L

Component Yielding Curve

Damage Calculation

Δ K c

Mode III

Crack

e.g. Miner Law

Masing

FEM or experiments ε =F(L)

σ 0 = c•L

 = i i N 1

1

ε

Application case / Crack shape

Elastic SCF c and approach ε =F(L)

Memory

Fatigue Life until Technical Crack

Load Time Function

L L- ε -Path

Load Time Function

SN p Curve

from Technical Crack until Critical Crack Length

L(t)

a1 L ˆ

L(t)

a L ˆ

SN Curve for Service Life

ε

a1 L ˆ

a1 L ˆ

a1 L ˆ

a1 L ˆ

Local. σ - ε -Path

σ

a1 L ˆ

a1 L ˆ

a1 L ˆ

N 1

N

ε

N 1

P i

N i

N p

+

= Total fatigue life N f

Fig. 1. Concept of the Two Stage Model with both submodels SLA and CPM included, according to Seeger (1996)

2. Probabilistic investigations using the Two Stage Model This section presents two studies regarding the influence of single parameters on one hand and the capability of the TSM as suitable fatigue assessment concept on the other hand. The selected parameters either influence the crack initiation life N i or the crack propagation life N p , which are explicitly distinguished in the following subsection. The probability distributions of input parameters in this study were established using own experimental test results, data provided in literature, and estimated values from numerical investigations, Table 1 and Table 2. As part of the research project “FutureWind” (IGF -No. 20987 N), the material characterisation for the SLA is realised using the Incremental Step Test according to Bissing et al. (2021). This investigation employs the values and probability distributions of three material domains that appear on the specimens, the base material (BM), the heat affected-zone (HAZ) and the weld metal (WM). The specimen design and the extraction domains are illustrated in Fig. 2. The definitions of the probability distributions are either chosen according to definitions in standards, i.e. JCSS (2002), prEN 1993-1-1 (2019), or estimated with a continuous PDF that best fits the histograms of the experimental results. The test series include eight specimens for the BM, eight specimens for the HAZ and six specimens for the WM that set up the basis for the probabilistic assessment. Even if the number of specimens is rather low, the small scatter proves the values to be reliable. The obtained parameters are checked for plausibility with Seeger et al. (1980) and Wächter (2016). The probability distributions for the CPM are entirely taken from literature, Table 2.