Carpinteri & Spagnoli method v.MD

The form of damage parameter designed by Carpinteri & Spagnoli ([CS01], [Spa01]) looks like this:

with material parameters derived from two simple uniaxial tests:

NOTIFICATION: Papuga in [Ppg05] tested behavior of this damage parameter. He found that the inclusion of the mean stress effect is too strong. The implementation in PragTic thus uses the following form of the method:

with the mean stress effect alike to Smith, Watson & Topper (SWT) The original form using the quadrate of maximum normal stress gives poor results for higher values of mean stress, thus it is not implemented at all.

There are two distinct versions of Carpinteri & Spagnoli method implemented in PragTic. Both use the same SWT modification. The original method by Carpinteri & Spagnoli using the CPD concept is described elsewhere.

The same damage parameter was tested in [Ppg05] within the MD concept, where the critical plane is set by maximization of the damage parameter. When the analysis of the aS and bS is performed in the same manner as by Papuga PC criterion, it results into the same coefficients as stated above for the original method. The problem with such a solution is, that it has similar problems as the original Papuga PC criterion [Ppg05] before revision to PCr [PR07].

The maximization of the damage parameter under reversed axial loading shows according to the computed second partial derivations that the resulting plane is the MD for cases of materials with only. Higher values (i.e. common ductile steels) lead to the plane with minimum damage. Reversed torsion loading gives the correct MD plane. This problem leads to a very mild shift to the conservative side of prediction (average value of fatigue index error was only 1.3% for gathered 70 experiments with fully alternate loads in [Ppg05]). A similar aspect is further mentioned in Papuga PC method; see [Ppg05] for a more detailed explanation if interested.

Before a revision similar to Papuga PCr method will be prepared a use for is recommended only. Note also that the damage parameter is very close to Ninic method.

Nomenclature:

Mark	Unit	PragTic variable	Meaning
	[MPa]		shear stress amplitude on an examined plane
	[MPa]	TENS-1, BEND-1	fatigue limit in fully reversed axial loading
	[-]		ratio of fatigue limits ()
	[MPa]		amplitude of normal stress on the plane examined
			mean (average value of maximum and minimum values) normal stress on the plane examined
	[MPa]	TORS-1	fatigue limit in fully reversed torsion

Methods & Options & Variables of Calculation – Edit

Decomposition

- Whole load path

Elasto-plasticity

- No – currently no option implemented

Solution option

- Searched planes <0~BS algorithm, 1~globe analogy, 2~random>

- Number of scanned planes

- Only every x-th data-point taken from load history

- Optimize <1~yes, 0~no>

- Evaluate envelope curve only <1~yes, 0~no>

Solution variable

- Minimum damage – this option is not active for this high-cycle fatigue method

Material parameters

E	[MPa]	tensile modulus
NU	[-]	Poisson’s ratio
TENS-1	[MPa]	fatigue limit in fully reversed push-pull (or plane bending)
TORS-1	[MPa]	fatigue limit in fully reversed torsion

Result detail variables

Damage fatigue index is computed, not the damage as a reciprocal value to number of cycles or repetitions

FDD1 NCX x-coordinate of the normal line vector of the critical plane

FDD2 NCY y-coordinate of the normal line vector of the critical plane

FDD3 NCZ z-coordinate of the normal line vector of the critical plane

FDD4 ALFA angle between the normal lines to the critical plane and to the free surface

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