Stress and Strain Analysis of Notched Bodies Subject to Non-Proportional Loadings
In this paper, an analytical simplified method for
calculating elasto-plastic stresses strains of notched bodies subject to
non-proportional loading paths is discussed. The method was based
on the Neuber notch correction, which relates the incremental elastic
and elastic-plastic strain energy densities at the notch root and the
material constitutive relationship. The validity of the method was
presented by comparing computed results of the proposed model
against finite element numerical data of notched shaft. The
comparison showed that the model estimated notch-root elasto-plastic
stresses strains with good accuracy using linear-elastic stresses. The
prosed model provides more efficient and simple analysis method
preferable to expensive experimental component tests and more
complex and time consuming incremental non-linear FE analysis.
The model is particularly suitable to perform fatigue life and fatigue
damage estimates of notched components subjected to nonproportional
loading paths.
[1] Neuber, H., Theory of Stress Concentration for Shear Strained Prismatic
Bodies with Arbitrary Stress–Strain Law, Journal of Appl. Mechanics,
Vol. 28, pp. 544-550, 1961.
[2] Molski, K., Glinka, G., A Method of Elastic-Plastic Stress and Strain
Calculation at a Notch Root, Materials Science and Engineering, Vol.
50, pp. 93- 100, 1981.
[3] Ince, A. and Glinka, G., A Generalized Damage Parameter for
Multiaxial Fatigue Life Prediction under Proportional and Non-
Proportional Loadings, International Journal of Fatigue, Vol.62, pp. 34-
41, 2014.
[4] Hoffmann, M., Seeger, T., A Generalized Method for Estimating
Multiaxial Elastic–Plastic Notch Stresses and Strains, Part I: Theory,
Journal of Engineering Materials and Technology, Vol. 107, pp. 250-
254, 1985.
[5] Moftakhar, A., Buczynski, A. and Glinka, G., “Calculation of Elasto-
Plastic Strains and Stresses in Notches under Multiaxial Loading”,
International Journal of Fracture, Vol.70, pp. 357-373, 1995.
[6] Singh, M.N.K., Notch Tip Stress-Strain Analysis in Bodies Subjected to
Non-Proportional Cyclic Loads, Ph.D. Dissertation, Dept. Mech. Eng.,
University of Waterloo, Ontario, Canada, 1998.
[7] Buczynski, A., and Glinka, G., Elastic-plastic Stress-Strain Analysis of
Notches under Non-Proportional Loading Paths, in Proceedings of the
International Conference on Progress in Mechanical Behaviour of
Materials (ICM8), Victoria, May 16-21, 1999, eds. F. Ellyin and J.W.
Provan, 3, pp. 1124-1130, 1999.
[8] Koettgen, V.B., Barkey, M.E., Socie, D.F., Pseudo Stress and Pseudo
Strain Based Approaches to Multiaxial Notch Analysis, Fatigue of
Engineering Materials and Structures 34, pp.854–867, 2001.
[9] Ince, A. and Glinka, G., A Numerical Method for Elasto-Plastic Notch-
Root Stress-Strain Analysis, Journal of Strain Analysis for Engineering
Design, Vol. 48, No. 4, pp. 229-224, 2013.
[10] Ince, A., Glinka, G. and Buczynski, A., A Computational Modeling
Technique of Elasto-Plastic Stress-Strain Response for Notched
Components, International Journal of Fatigue, Vol.62, pp. 42-52, 2014.
[11] Garud, Y.S., A New Approach to the Evaluation of Fatigue under
Multiaxial Loadings, Journal of Engineering Materials and Technology,
103, pp. 118- 125, 1981.
[12] Prandtl, W., Spannungsverteilung in Plastischen Kerpern, Proceedings
of the First International Congress on Applied Mechancis, pp. 43, 1924.
[13] Reuss, E., Beruecksichtigung der elastischen Formaenderungen in der
Zeit- schrift fur Angewandte Mathematik und Mechanik, Vol. 10, pp.
266-274, 1930.
[14] Ince, A. and Glinka, G., “Innovative Computational Modeling of
Multiaxial Fatigue Analysis for Notched Components”, International
Journal of Fatigue, 2015, doi:10.1016/j.ijfatigue.2015.03.019
[15] Ince, A., “A novel technique for multiaxial fatigue modelling of ground
vehicle notched components”, International Journal of Vehicle Design,
Vol. 67, No.3, pp. 294-313, 2015, doi: 10.1504/IJVD.2015.069486.
[1] Neuber, H., Theory of Stress Concentration for Shear Strained Prismatic
Bodies with Arbitrary Stress–Strain Law, Journal of Appl. Mechanics,
Vol. 28, pp. 544-550, 1961.
[2] Molski, K., Glinka, G., A Method of Elastic-Plastic Stress and Strain
Calculation at a Notch Root, Materials Science and Engineering, Vol.
50, pp. 93- 100, 1981.
[3] Ince, A. and Glinka, G., A Generalized Damage Parameter for
Multiaxial Fatigue Life Prediction under Proportional and Non-
Proportional Loadings, International Journal of Fatigue, Vol.62, pp. 34-
41, 2014.
[4] Hoffmann, M., Seeger, T., A Generalized Method for Estimating
Multiaxial Elastic–Plastic Notch Stresses and Strains, Part I: Theory,
Journal of Engineering Materials and Technology, Vol. 107, pp. 250-
254, 1985.
[5] Moftakhar, A., Buczynski, A. and Glinka, G., “Calculation of Elasto-
Plastic Strains and Stresses in Notches under Multiaxial Loading”,
International Journal of Fracture, Vol.70, pp. 357-373, 1995.
[6] Singh, M.N.K., Notch Tip Stress-Strain Analysis in Bodies Subjected to
Non-Proportional Cyclic Loads, Ph.D. Dissertation, Dept. Mech. Eng.,
University of Waterloo, Ontario, Canada, 1998.
[7] Buczynski, A., and Glinka, G., Elastic-plastic Stress-Strain Analysis of
Notches under Non-Proportional Loading Paths, in Proceedings of the
International Conference on Progress in Mechanical Behaviour of
Materials (ICM8), Victoria, May 16-21, 1999, eds. F. Ellyin and J.W.
Provan, 3, pp. 1124-1130, 1999.
[8] Koettgen, V.B., Barkey, M.E., Socie, D.F., Pseudo Stress and Pseudo
Strain Based Approaches to Multiaxial Notch Analysis, Fatigue of
Engineering Materials and Structures 34, pp.854–867, 2001.
[9] Ince, A. and Glinka, G., A Numerical Method for Elasto-Plastic Notch-
Root Stress-Strain Analysis, Journal of Strain Analysis for Engineering
Design, Vol. 48, No. 4, pp. 229-224, 2013.
[10] Ince, A., Glinka, G. and Buczynski, A., A Computational Modeling
Technique of Elasto-Plastic Stress-Strain Response for Notched
Components, International Journal of Fatigue, Vol.62, pp. 42-52, 2014.
[11] Garud, Y.S., A New Approach to the Evaluation of Fatigue under
Multiaxial Loadings, Journal of Engineering Materials and Technology,
103, pp. 118- 125, 1981.
[12] Prandtl, W., Spannungsverteilung in Plastischen Kerpern, Proceedings
of the First International Congress on Applied Mechancis, pp. 43, 1924.
[13] Reuss, E., Beruecksichtigung der elastischen Formaenderungen in der
Zeit- schrift fur Angewandte Mathematik und Mechanik, Vol. 10, pp.
266-274, 1930.
[14] Ince, A. and Glinka, G., “Innovative Computational Modeling of
Multiaxial Fatigue Analysis for Notched Components”, International
Journal of Fatigue, 2015, doi:10.1016/j.ijfatigue.2015.03.019
[15] Ince, A., “A novel technique for multiaxial fatigue modelling of ground
vehicle notched components”, International Journal of Vehicle Design,
Vol. 67, No.3, pp. 294-313, 2015, doi: 10.1504/IJVD.2015.069486.
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:69924", author = "A. Ince", title = "Stress and Strain Analysis of Notched Bodies Subject to Non-Proportional Loadings", abstract = "In this paper, an analytical simplified method for
calculating elasto-plastic stresses strains of notched bodies subject to
non-proportional loading paths is discussed. The method was based
on the Neuber notch correction, which relates the incremental elastic
and elastic-plastic strain energy densities at the notch root and the
material constitutive relationship. The validity of the method was
presented by comparing computed results of the proposed model
against finite element numerical data of notched shaft. The
comparison showed that the model estimated notch-root elasto-plastic
stresses strains with good accuracy using linear-elastic stresses. The
prosed model provides more efficient and simple analysis method
preferable to expensive experimental component tests and more
complex and time consuming incremental non-linear FE analysis.
The model is particularly suitable to perform fatigue life and fatigue
damage estimates of notched components subjected to nonproportional
loading paths.", keywords = "Elasto-plastic, stress-strain, notch analysis,
nonprortional loadings, cyclic plasticity, fatigue.", volume = "9", number = "6", pages = "935-5", }
