The zip file includes files that compose the interface which allows computing strain courses from stress courses using kinematic hardening model of material. The starting file is Stress2Strain.m.
To run the model you must define material properties (button Material), generate stress courses (button generate stress courses) and press button Run.
The programmed model is based on the Mróz idea [2] who introduced the plastic modulus fields. According to this idea for the one-dimensional case, the non-linear curve of cyclic strain (strain - stress) is replaced by a sequence of linear segments. Each linear segment has its own modulus of plasticity (C(0), C(1), C(2), . . ., C(m-1)). The points on the new linearized curve of cyclic strain where moduli of plasticity change, determine fields with constant moduli of plasticity (fields of moduli of plasticity). The surfaces f(1), f(2), . . ., f(m) with constant module of plasticity are reduced
to circles in the case of selection of a proper scale and application of the Huber-Mises-Hencky condition of plasticity (H-M-H). The Mróz-Garud model assumes that the material
is homogeneous, isotropic, and influence of the loading rate can be neglected. Moreover, the model does not include thermal phenomena and assumes constancy of the Young's and Poisson's module.
The algorithm applies the following rules:
The yield criterion: Huber-Mises-Hencky
The flow rule: Normal
The hardening rule: Mróz-Garud [2,3]
The program accepts only two stress components: normal stress (e.g. \sigma_{xx}(t)) and shear stress (e.g. \tau_{xy}(t)). The outputs are: strain components: \epsilon{xx}(t), \epsilon{xy}(t), \espilon_{yy}.
Material properties are based on Ramberg-Osgood relation:
Eps_a=Sig_a/E+(Sig/K')^{1/n'} three coefficients are required: K' (MPa), n' (-), E (MPa). The Ramberg-Osgood relation is replaced by sequence of linear segments
The stress courses are generated using sinusoidal shape
If you deal with non-proportional loading it is necessary to use option: 'Slow start' which forces the initial stress state to be Sig=0 and Tau=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.
[1] 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.
[2] Mróz Z. On the description of anisotropic work hardening.,
J. Appl. Phys. Solids, 15, 1967, pp.163-175
[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. |