Description |
The function [T, EPS, SIG]=strain2stress creates an interface that allows computing stress courses from strain courses (from strain gages) using the incremental kinematic model of material hardening which was formulated by Mróz-Garud [1,2].
Where: T is time vector, SIG =[Sig_xx Sig_yy Tau_xy], Sig_xx, Sig_yy normal stress courses, Tau_xy is shear stress course, EPS is array of strain courses of the following order: [Eps_xx Eps_yy Eps_zz Eps_xy] (x - the direction of Sig_xx, etc.).
This model is based on the Mróz idea [1] who introduced the plastic modulus fields.
The algorithm applies the following rules:
The yield criterion: Huber-Mises-Hencky
The flow rule: Normal
The hardening rule: Mróz-Garud [1,2]
The program accepts only three strain components (e.g. from STRAIN GAGES:
Eps_xx(t), Eps_yy(t) and Eps_xy(t)). The outputs are:
stress components: Sig_xx(t), Sig_yy(t), Tau_xy(t) and additinaly the missing strain component Eps_zz(t). So, the output EPS=[Eps_xx Eps_yy Eps_zz Eps_xy].
Warning: assumption: Sig_zz(t)=0 (the plane stress state)!
Cyclic material properties are based on the Ramberg-Osgood relation:
Eps_a = Sig_a/E+(Sig/K')^{1/n'},
where three coefficients are required: K' (MPa), n' (-), E (MPa)
The Ramberg-Osgood relation is replaced by sequence of linear segment.
Also, the Poisson ratio \ni is needed.
The stran courses are generated using sinusoidal shape or imported from text file. The file must contain four rows [T Eps_xx Eps_yy Eps_xy], the first row is a time vector. The increments of strains cannot be too large, e.g. \Delta\epsilon_{ij}<2e-4. If you deal with non-proportional loading it is necessary to use option: 'Slow start' which forces the initial strain state to be EPS = 0
If you used this program or any of the included functions for scientific purpose please respect my effort and cite the paper [3] in which the algorithm was applied. The paper [4] includes details about the Mroz-Garud model, but it is in Polish.
[1] Mróz Z. On the description of anisotropic work hardening., J. Appl. Phys. Solids, 15, 1967, pp.163-175.
[2] Garud Y.S. Prediction of stress-strain response under general multiaxial loading, Mechanical Testing for Deformation Model Development, ASTM STP 765, 1982, pp. 223-238.
[3] Karolczuk A. Non-local area approach to fatigue life evaluation under combined reversed bending and torsion, International Journal of Fatigue, 30, 2008, pp. 1985-1996. http://dx.doi.org/10.1016/j.ijfatigue.2008.01.007
[4] Karolczuk A., Łagoda T., Ogonowski P.: Verification of low cycle fatigue energy-based criteria for metals, Politechnika Opolska, Studia i monografie, z. 186, Opole 2006, ps. 109 (in Polish).
Author: Aleksander Karolczuk, 8 July 2010, a.karolczuk@po.opole.pl
Opole University of Technology, Poland |