Issue 47

D. Benasciutti et alii, Frattura ed Integrità Strutturale, 47 (2019) 348-366; DOI: 10.3221/IGF-ESIS.47.26

covariance matrix of x ( t ) and s ( t )

C , C’

C ' p d TB

covariance matrix in the principal coordinate system

( Ω p,i

( t ))

damage of stress projection Ω p,i total damage for stress vector Ω ( t )

( t ) by TB method

d ( Ω ) E [–] G ( f )

expected value

one-sided PSD matrix of x ( t )

, k τ

k σ

inverse slope of tension and torsion S-N curve

amplitude of the square root of second invariant of stress deviator

J  a2,

J

a

J A,  , J A, τ

, k  , k τ

amplitude strengths and inverse slopes of the tension and torsion S-N curves in MWD amplitude strength and inverse slope of the reference S-N curve in MWD

, k ref

J A,ref N A

reference number of cycles correlation coefficient between x i correlation matrix of x ( t ) correlation matrix of s ( t ) deviatoric stress vector two-sided PSD matrix of x ( t ) two-sided PSD matrix of s ( t ) two-sided PSD of hydrostatic stress σ H ( t ) ( t ) and x j

( t )

r ij

R (  ) R' (  )

s ( t )

( f )

S H S ( f ) S' ( f )

S ' p T f

( f )

two-sided PSD matrix in the principal coordinate system

time to failure (seconds)

matrix of eigenvectors (rotation matrix)

U

( t ))

variance of stress x i

( t )

Var ( x i

variance of hydrostatic stress σ H ( t ) stress vector in physical space

V H x ( t )



time lag

bandwidth correction factor for the PSD of stress projection Ω p,i ( t )

η TB,i

ρ ref σ A σ H σ x

stress ratio

strength amplitudes at N A

, τ A

cycles

( t )

hydrostatic stress stress components

( t ), σ y

( t ), τ xy

( t )

σ ( t ) σ' ( t ) Ω p,1 Ω ( t )

stress tensor

deviatoric stress tensor

( t ), Ω p,2

( t ) , Ω p,3

( t ) stress projections

vector of stress projections Modified Wöhler Diagram

MWD

366