McDiarmid method v.91

The McDiarmid criterion is widely used. It is implemented (MSC.Fatigue, FE-Fatigue) or at least commented (Fe-Safe) in commercial fatigue software. McDiarmid established its form on a basis of broad comparison of test data [McD91], [McD94]. The older version v.72 had no practical use, but the final version of the McDiarmid criteria is more acceptable:

or written in the convention used here generally:

The tAB symbol stands for choice between tA and tB fatigue limits corresponding to load conditions leading to a creation of cracks in A and B system. These two types of cracks correspond to cracks parallel to the surface (A type) or inwards from the surface (B type). This is a significant complicacy (and weak point), because such distinction is not usually recorded. The relation tAB = t-1 is generally fulfilled for plane bending combined with torsion ([CS01]).

At first [McD91], the criterion was designed with critical plane defined by maximum shear stress range. McDiarmid announced another proposal later [McD94] where the critical plane is set by maximisation of criterion‘s left hand side, i.e. by maximum caused damage. Both versions are implemented in PragTic. The MD variant usually leads to slightly better results.

Wherever the criterion is used, its results are not very promising, if small data sets are compared (see [PDG97], [CS01], [Ppg05]), because pronounced scatter of data, caused probably by its in-born empiric nature, can be observed. The thorough McDiarmid's validating nevertheless lets the criterion to achieve its strong point as a universal criterion - the results in the FatLim Database show very acceptable data scatter in comparison to other criteria tested. The users should be warned, that the mean value of this large data set is shifted to the non-conservative side of prediction and that also the standard deviation is very high. Some safety coefficient including also the potential effect of higher standard deviation of results should be applied, if the criterion is to be used.

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
	[MPa]		maximum normal stress on the plane examined
	[MPa]	SIG_ULT	tensile strength
tA , tB	[MPa]	TORS-1A, TORS-1B	fatigue limit in fully reversed torsion with crack in A or B system (see above)

Methods & Options & Variables of Calculation – Edit

Decomposition

- Whole load path

Elasto-plasticity

- No – currently no option implemented

Solution option

- CP criterion <0~MD, 1~MSSR, 2~MMES>

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

- Number of scanned planes

- Optimize <1~yes, 0~no>

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

- 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
SIG_ULT	[MPa]	tensile strength
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 DELTA_C shear stress range

FDD5 MAX_N maximum normal stress

FDD6 ALFA angle between the normal lines to the critical plane and to the free surface

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