JCSS Model Code Fatigue inspection and reliability Ton

JCSS Model Code Fatigue, inspection and reliability Ton Vrouwenvelder TNO / TU-Delft The Netherlands

JCSS Probabilistic Model Code • Part 1 Basis of Design • Part 2 Modeling of loads • Part 3 Modeling of structural properties • http: //www. jcss. ethz. ch/ • select “publications” • select “jcss model code”

Part 3 Resistance models 3. 0 3. 1 3. 2 3. 3 3. 4 3. 5 General Concrete Reinforcement Prestr steel Steel Timber 3. 6 3. 7 3. 8 3. 9 3. 10 3. 11 Aluminium Soil Masonry Model uncert. Dimensions Imperfections

• fatigue crack growth based on Paris-Erdogan relation: crack size a stress range C and m material parameters

Limit state function for crack through failure: Elaboration for constant amplitude, m=3 & Y=1 :

Crack growth model da/dn = C (DK ) m K = U Y M S ( a) / Q a = crack size C = material parameter m = material parameter K = stress intensity factor S = stress, including SCF U = crack closure factor Y = crack geometry factor M = weld geometry factor Q = elliptic shape factor Paris, 1962

Crack growth model (C 1, m 1) and (C 2, m 2)

crack growth model

Crack growth model – 2 dimensional A semi-elliptical crack in a steel plate at/near the weld toe

Limit state formulations Fixed critical crack size ( plate thickness) Fatigue-fracture g (X, t) = min { R - (Kr 2 + Lr 2) } Kr = Ks (a) / Kmat Lr = S (a) / Sy

Fatigue fracture Dijkstra (1991)

Statistical properties

Statistical properties

Statistical properties • Random variable - average value - standard deviation - distribution type • Vectors/fields/processes 1. 0 - correlation in time - correlation in space x, t

relevant types of correlation • member to member (system reliability) • before and after inspection (updating)

Correlation in space C material property ai initial crack size d wall thickness S stress level Correlation in time cycle rate S stress level

Correlation from hotspot to hotspot • Paris Law parameter: V(C) = 0. 50 (global scatter) V(C) = 0. 20 (internal scatter) ρ = 1 – (0. 202 / 0. 502) = 0. 85 • initial crack size: same order of magnitude • wall thicknes: ρ = 0. 7 (JCSS Model Code, ch 2. 11) • stress (systematic part) ρ = 0. 6 (estimate)

Reliability index (one year period)

Reliability index (one year period) given crack found at tins = 10 yr Correlation is related to C and before and after inspection

spotlight on C

model • Ferry Borges Castanheta model • V(C) = 0. 2 d. C = 40 mm • V(C) = 0. 3 d. C = 5 mm • V(C) = 0. 4 d. C = 1 mm

proposal for correlations

Fatigue assessment of a welded detail 25 m 25 m 30 m 25 m 30 m 25 m 5 m 5 m Detail location Cover plate detail

Loading data sr = 40 MPa Narrow band Gaussian process; Rayleigh amplitudes = 106 cycles per year

• Calculation procedure PF(t) Fixed critical crack size: 1. P( a(t)>d ) Fatigue fracture approach: g = R – ( Kr 2 + Lr 2) 1. PF(t) = P(g(a(t), max S( )) < 0 ) 2. Add the annual probabilities 3. Outcrossing approach 4. Conditional failure rate approach

general case (g 1(X), g 2(X) and g 3(X)) Sorensen 1. 0 E+00 0 2 4 Pf 8 x 1. 0 E-01 1. 0 E-02 6 g 1, 2(X), 10**4 simulations g 3(X), 10**4 simulations x simple case 1. 0 E-03 1. 0 E-04 log(N) Sudret Result of Righiniotis X X

Conclusion: This talk is over, The work is not.