Previsione della durata a fatica su provino SAE utilizzando un approccio combinato di fatica oligociclica e meccanica della frattura

Page  11 
Frost has reported [6] that May [9] proposed a model of growth that is expressed in the 
following relationship: 
 
 f F e
z w w
b
= �
- + -Ρ
Σ|
Τ|
Υ
ς
|
Ω|
χ η2
e  t
 
 
where: 
 
• w is the valley width 
• f is the fraction of valleys with width w and depth between z and z dz+  
• t is the number of cycles 
• F a slowly varying function of z, w, and t  
• b is the slip vector 
• e is the plastic strain range. 
 
The slip vector b and the plastic strain range ε were assumed constant for a given 
test. He then assumed that at some large value of z (say Z)a valley was deep enough to be 
considered a crack. Thus Z be was regarded as a time constant T, controlling the rate at 
which valleys attained the depth Z. From this point the subsequent growth rate was 
considered to be rapid so that t could be regarded as the life of he specimen. May assumed 
that a valley of depth ten times its width was a true crack (a macro crack), that is Z w= 10 , 
which for w = −10 6 mm , b = × −5 10 6 mm , and ε = −10 3 gave a value for T of 2 106×  
cycles; from this he concluded that this model could predict lives of the right order. 
The real usefulness of this approach in a practical problem falls down for the 
troubles to find so particular material properties, such as the value of b, which requires a 
very sharp metallographic analysis. 
However it is clear now that the real initiation of a crack is something that happens 
at a grain level; after the first stage of slipping there is an intermediate process in which the 
crack grows for a length of some grains, in the same direction of the slipping, i.e. as the 
maximum shear stress. It remains so until the micro crack is of a sufficient size that the 
amount of opening and closing is enough to affect a sufficient volume of material along its 
edge for which the influence of the crack is not at a grain level anymore, but as in a 
continuum. The growth process is now associated with the magnitude of the tensile strain 
range in the volume of material just ahead of the crack edge. The direction of growing is 
now that which allow the maximum crack opening during the fatigue cycle. Ideally, this is 
approximately perpendicular to the nominal maximum cyclic tensile stress and is independent 
of any crystalline slip plane, although in the early stage the crack may follow a 
crystallographic plane close to the ideal direction. 
 
 
L'ipotesi di materiale isotropo che viene generalmente fatta parlando di 
metalli, non può sussistere se essi vengono riguardati a livello microscopico. Infatti 
ogni grano ha sue proprietà, orientazione, dimensioni, forma, e difetti interni, come