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52 Fatigue Assessment of Truss Joints Based on Local Approaches 283
a standard unnotched specimen. Differences in surface, residual stresses and
in size of structures and test specimens can be considered. Crack initiation is
defined as a crack length of c =0.5mm, which is a crack depth a ≈ 0.25 mm.
As a result the number of cycles for crack initiation is obtained (Seeger [1]).
For the calculation of the local stress–strain history information must be
given for:
– The cyclic stress–strain law, usually as Ramberg–Osgood law
ɛa = ɛa,e + ɛa,p = σa
E +
�
σa
K ′
� ′
1/n
. (52.1)
– The hysteretic behaviour, usually the Masing hypothesis, which means the
doubling of the cyclic stress–strain law in stresses and strains.
The computation of the local stress–strain history can either be done by
full elastic–plastic finite-element-calculations with true strains, or by linearelastic
calculations with subsequent approximation of the plastic behaviour,
e.g. by Neuber’s-rule [2]
σɛE =(KtS) 2 = σ 2 lin.elast.
(52.2)
The strain–life curve, usually tested with polished, unnotched specimens at a
given stress ratio R = −1, can be described in the form of Manson, Coffin,
Morrow [3–5]
ɛa = ɛa,e + ɛa,p = σ′ f
E (2N)b + ɛ ′ f (2N) c . (52.3)
The influence of mean stresses, i.e. the case R �= −1, can be considered by
damage parameters P , e.g. in the form of Smith et al. [6]
PSWT = � (σa + σm)ɛaE. (52.4)
The cyclic material characteristics can be taken from the uniform material
law (UML) [7].
52.2.3 Crack Growth with Linear Elastic Fracture Mechanics
The calculation of crack propagation with linear elastic fracture mechanics
starts at the crack depth a =0.25 mm from local strain approach. The crack
depth dependent stress–intensity-factors KI(a) can be computed with FEMsoftware,
e.g. FRANC2D/L [8]. A defined fracture criterion stops the calculation
resulting in the number of cycles for crack growth.
Crack propagation can be calculated with the Paris-law [9]
da/dN = C(∆K) m . (52.5)
Both material constants C and m can be found in literature.