Crack Tip Constraint for Anisotropic Sheet Metal Plate Subjected to Mode-I Fracture

Document Type: Research Paper

Authors

Department of Industrial and Production Engineering, National Institute of Technology, Jalandhar, India

Abstract

On the ground of manufacturing, sheet metal parts play a key role as they cover about half of the production processes. Sheet metals are commonly obtained from rolling and forming processes which causes misalignment of micro structure resulting obvious anisotropic characteristics and micro cracks. Presence of micro cracks poses serious attention, when stresses at the tip reach to the critical value. Present research deals with a thin anisotropic plate, containing an edge crack subjected to mode-I condition. To predict the nature of crack propagation, anisotropic triaxiality is formulated with special reference to Lankford’s coefficient and degree of anisotropy. The distribution of magnitude of anisotropic triaxiality is shown with respect to polar angle at crack tip supplemented by plastic zone shapes. Numerical evaluation has been carried out by considering five different cases of plane stress condition using Hill-von Mises yield criteria. Critical values so obtained apropos respective cases, as traced on the yield locus had been used to predict the location of crack propagation in sheet metal. It is revealed that the angle through which the crack propagate do not remain invariable for all combinations of Lankford’s coefficient and degree of anisotropy but it shifts for two of the five cases taken into consideration.

Keywords

Lou Y., Yoon J. W., Huh H., 2014, Modeling of shear ductile fracture considering a changeable cut-off value for stress triaxiality, International Journal of Plasticity 54: 56-80.
[2] Ognedal A.S., Clausen A. H., Dahlen A., Hopperstad O. S., 2014, Behavior of PVC and HDPE under highly triaxial stress states: An experimental and numerical study, Mechanics of Materials 72: 94-108.
[3] Lou Y., 2013, Evaluation of ductile fracture criteria in a general three-dimensional stress state considering the stress triaxiality and the, Acta Mechanica Solida Sinica 26(6): 642-658.
[4] Paul S. K., 2013, Effect of martensite volume fraction on stress triaxiality and deformation behavior of dual phase steel, Materials & Design 50: 782-789.
[5] Jackiewicz J., 2011, Use of a modified Gurson model approach for the simulation of ductile fracture by growth and coalescence of microvoids under low, medium and high stress triaxiality loadings, Engineering Fracture Mechanics 78(3): 487-502.
[6] Peirs J., Verleysen P., Degrieck J., 2011, Experimental study of the influence of strain rate on fracture of Ti6Al4V, Procedia Engineering 10: 2336-2341.
[7] Ha S., Ã K. K., 2010, Void growth and coalescence in f . c . c . single crystals, International Journal of Mechanical Sciences 52(7):863-873.
[8] Trattnig G., Antretter T., Pippan R., 2008, Fracture of austenitic steel subject to a wide range of stress triaxiality ratios and crack deformation modes, Engineering Fracture Mechanics 75: 223-235.
[9] Bru M., Chyra O., Albrecht D., 2008, A ductile damage criterion at various stress triaxialities, International Journal of Plasticity 24:1731-1755.
[10] Zhang W., Deng X., 2007, Mixed-mode I/II fields around a crack with a cohesive zone ahead of the crack tip, Mechanics Research Communications 34: 172-180.
[11] Zhu H., Zhu L., Lv X., 2007, Investigation of fracture mechanism of 6063 aluminum alloy under different stress states , International Journal of Fracture 146:159-172.
[12] Bao Y., 2005, Dependence of ductile crack formation in tensile tests on stress triaxiality, stress and strain ratios, Engineering Fracture Mechanics 72(4):505-522.
[13] Bao Y., Wierzbicki T., 2005, On the cut-off value of negative triaxiality for fracture, Engineering Fracture Mechanics 72 :1049-1069.
[14] Bao Y., Wierzbicki T., 2004, On fracture locus in the equivalent strain and stress triaxiality space, International Journal of Mechanical Sciences 46: 81-98.
[15] Kim Y., Schwalbe K., 2004, Numerical analyses of strength mis-match effect on local stresses for ideally plastic materials, Engineering Fracture Mechanics 71:1177-1199.
[16] Hopperstad O. S., Børvik T., Langseth M., Labibes K., Albertini C., 2003, On the influence of stress triaxiality and strain rate on the behaviour of a structural steel, European Journal of Mechanics- A/Solids 22: 1-13.
[17] Shama A., Zarghamee M., Ojdrovic R., Schafer B., 2003, Seismic damage evaluation of a steel building using stress triaxiality, Engineering Structures 25: 271-279.
[18] Ores B., Co M., Str A., 2001, The effect of stress triaxiality on tensile behavior of cavitating specimens, Journal of Materials Science 6: 5155-5159.
[19] City K., 2000, Fracture and yield behavior of adhesively bonded joints under triaxial stress conditions, Journal of Materials Science 5: 2481-2491.
[20] Zhu Y., Dodd B., Caddell R. M., Hosford W. F., 1987, Convexity restrictions on non-quadratic anisotropic yield criteria, International Journal of Mechanical Sciences 29(10): 733-741.
[21] Hance B.M., 2005, Influence of Discontinuous Yielding on Normal Anisotropy (<I>R</I>-Value) Measurements, Journal of Materials Engineering and Performance 14: 616-622.
[22] Bhadauria S. S., Hora M. S., Pathak K. K., 2009, Effect of stress triaxiality on yielding of anisotropic, Journal of Solid Mechanics 1(3): 226-232.