Orthotropic material fatigue analysis

The number of reversals to failure, N, is related to the stress amplitudes, σxx, σyy, and σxy, by the following equation NOTE:

F(σxx, σyy, σxy, X(σm,xx, N), Y(σm,yy, N), S(σm,xy, N)) = 1				where:F is the failure index.X, Y, and S are the 1-direction, 2-direction, and in-plane fatigue strengths respectively. They are functions of mean stresses and the number of reversals to failure.σm,xx, σm,yy, and σm,xy are the 1-direction, 2-direction, and in-plane mean stresses respectively.

The failure index equation changes depending on the selected orthotropic fatigue life criterion.

• For Hill fatigue life criterion:F = (σxx/X)2 – σxx**σyy/X2 + (σyy/Y)2 + (σxy/S)2

• For Tsai-Wu fatigue life criterion:F = (σxx/X)2 + F12σxx**σyy + (σyy/Y)2 + (σxy/S)2F12 is the specified Tsai-Wu interaction coefficient. It is a material property. If you do not specify this value, F12 is set to zero.

• For maximum stress fatigue life criterion:F = (σxx/X), (σyy/Y), (σxy/S)For this life criterion, three separate values are computed for the 1-direction, 2-direction, and in-plane respectively.

The fatigue strengths, X, Y, and S, are given by:

X(σm,xx, N) = mcx**X0NbxY(σm,yy, N) = mcy**Y0NbyS(σm,xy, N) = S0Nbs				where:mcx and mcy are the 1-direction and 2-direction mean stress correction coefficients respectively.X0, Y0, and S0 are the 1-direction, 2-direction, and in-plane fatigue strength coefficients respectively.bx, by, and bs are the 1-direction, 2-direction, and in-plane fatigue strength exponents respectively.

The fatigue strength coefficients and exponents are the specified orthotropic material properties. If you specify user-defined S-N curves, the durability solver obtains the coefficients and exponents by curve fitting the S-N curves.

The value of the mean stress correction coefficients depends on the mean stress correction method you specify.

	No mean stress correction	Goodman mean stress correction	Gerber mean stress correction	Morrow mean stress correction
1-direction tensile mean stress, σm,xx>0	mcx = 1	mcx = (XT_static – σm,xx)/XT_static	mcx = (XT_static – σm,xx)2/X2T_static	mcx = X0 – σm,xx
1-direction compressive mean stress, σm,xx<0	mcx = (XC_static + σm,xx)/XC_static	mcx = (XC_static + σm,xx)2/X2C_static	mcx = X0 + σm,xx
2-direction tensile mean stress, σm,yy>0	mcy = 1	mcy = (YT_static – σm,yy)/YT_static	mcy = (YT_static – σm,yy)2/Y2T_static	mcy = Y0 – σm,yy
2-direction compressive mean stress, σm,yy<0	mcy = (YC_static + σm,yy)/YC_static	mcy = (YC_static + σm,yy)2/Y2C_static	mcy = Y0 + σm,yy

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Orthotropic material fatigue analysis, Simcenter 3D 2021.1 Series

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Philippidis, T.P. and Vassilopoulos, A.P., “Fatigue Strength of Composites Under Variable In-Plane Stress”, Chapter 18 of Fatigue in Composites, Bryan Harris, Editor, CRC Press, 2003.

Shokrieh, M. and Lessard, L., “Multiaxial Fatigue Behavior of Unidirectional Plies Based on Uniaxial Fatigue Experiments: I. Modeling”, International Journal of Fatigue, Volume 19, No. 3, 1997, pp. 201–207.

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