Abstract
The well-known so-called `HRR-solution' (Hutchinson, 1968 and Rice and Rosengren, 1968) considers the elasto-plastic stress field in a power-law strain hardening material near a sharp crack. It provides a closed form explicit expression for the stress singularity as a function of the power-law exponent `n' of the material, but the stress angular variation functions are not found in closed form. More recently, similar formulations have appeared in the literature for sharp V-notches under mode I and II loading conditions. In such cases not only is the angular variation of the stress fields obtained numerically, but so is the singularity exponent of the stress field. In the present paper, approximate but accurate closed form solutions are first reported for sharp V-notches with an included angle greater than π/6 radians. Such solutions, limited here to Mode I loading conditions, allow a very satisfactory estimate of the angular stress components in the neighbourhood of the notch tip, in the entire range of notch angles and for the most significant values of n (i.e. from 1 to 15). When the notch opening angle tends towards zero, and the notch approaches the crack case, the solution becomes much more complex and a precise evaluation of the parameters involved requires a best-fitting procedure which, however, can be carried out in an automatic way. This solution is also reported in the paper and its degree of accuracy is discussed in detail.
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References
Chen D.H. and Ushijima K. (2000) Elastic-plastic stress singularity near the tip of a V-notch. International Journal of Fracture 106, 117–134.
Hutchinson J.W. (1968) Singular behaviour at the end of a tensile crack in a hardening material. Journal of Mechanics and Physics of Solids 16, 13–31.
Kuang Z.B., Xu X.P. (1987) Stress and strain fields at the tip of a V-notch in a power-law hardening material. International Journal of Fracture 35, 39–53.
Lazzarin P., Zambardi R., Livieri, P. (2001) Plastic Notch Stress Intensity Factors for Large V-Shaped Notches under Mixed Load Conditions. International Journal of Fracture 107, 361–377.
Ponte Castañeda P. (1985) Asymptotic fields in steady crack growth with linear strain-hardening. Journal of the Mechanics and Physics of Solids 35, 227–268.
Rice J.R. (1968) A path independent integral and the approximate analysis of strain concentration by notches and cracks. Journal of Applied Mechanics 35, 379–386.
Rice J.R., Rosengren, G.F. (1968) Plane strain deformation near a crack tip in a power-law hardening material. Journal of Mechanics and Physics of Solids 16, 1–12.
Sharma S.M. and Aravas N. (1991) Determination of higher-order terms in asymptotic elastoplastic crack tip solutions. Journal of the Mechanics and Physics of Solids 39, 1043–1072.
Sharma S.M. and Aravas N. (1993) On the development of variable-separable asymptotic elastoplastic solutions for interfacial cracks. International Journal of Solids and Structures 30, 695–723.
Xia L., Wang T. (1993) Singular behavior near the tip of a sharp V-notch in a power-hardening material. International Journal of Fracture 59, 83–93.
Yuan H., Lin G. (1994) Analysis of elastoplastic sharp notches. International Journal of Fracture 67, 187–216.
Zhang N., Joseph P.F. (1998) A nonlinear finite element eingenanalysis of singular plane stress fields in bimaterial wedges including complex eingenvalues. International Journal of Fracture 90, 175–207.
Williams M.L. (1952) Stress singularities resulting from various boundary conditions in angular corners of plates in tension. Journal of Applied Mechanics 19, 526–528.
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Filippi, S., Ciavarella, M. & Lazzarin, P. An approximate, analytical approach to the `HRR'-solution for sharp V-notches. International Journal of Fracture 117, 269–286 (2002). https://doi.org/10.1023/A:1022057621185
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DOI: https://doi.org/10.1023/A:1022057621185