Effects of Energy Dissipation and Energy Screening on Fatigue Crack Extension in Viscoelastic-plastic Solids

Abstract

In the studies of fracture in dissipative media various asymptotic forms expressing the near Lip stress and strain fields have been proposed. The most commonly accepted form is that due to Hutchinson [1], Rice and Rosengren [2], the so-called HRR field which becomes singular at the crack tip, i.e., when r → 0. The HRR fields applicable to elasto-plastic fracture problems involving a stationary crack is of this form $$\begin{gathered} {\sigma _{ij}} = {\sigma _0}{\left( {\frac{{EJ}}{{\alpha \sigma _0^2{I_n}r}}} \right)^{\frac{1}{{n + 1}}}}{{\tilde \sigma }_{ij}}\left( {n,\theta } \right) \hfill \\ {\varepsilon _{ij}} = \alpha {\varepsilon _0}{\left( {\frac{{EJ}}{{\alpha \sigma _0^2{I_n}r}}} \right)^{\frac{1}{{n + 1}}}}{{\tilde \varepsilon }_{ij}}\left( {n,\theta } \right) \hfill \\ \end{gathered} $$ (1) Here n, e o = σo/E. and α are constants appearing in the constitutive relation e/eo = σ/σo + α(σ/σo)n while In is a quantity dependent on the hardening exponent n and Labulated by Shih [3]. The nondimensional angular distribution functions σij (n,θ) and eij(n,(θ) were obtained numerically by the authors of the original HRR field concept. As can be seen, the Rice’s integral $$J = \int_\Gamma {\left[ {Wdy - {\sigma _{ij}}{n_j}\frac{{\partial ui}}{{\partial x}}ds} \right]} $$ (2) plays the role of the field amplitude, and thus the “one parameter” characterization of fracture is extended onto the elasto-plastic domain. The scope of validity of such an asymptotic approach, however, is substantially restricted by the requirements of various nature. Above all, in an elasto-plastic medium proportional loading is required. Thus a propagating crack or a crack under cycling loading may not be controlled by a field of the HRR type. Since the HRR singularity is merely the leading term in an asymptotic expansion, and elastic strains were assumed to be negligible, the analysis is only valid near the crack tip, well within the plastic zone. For very small r values, however, the HRR solution is invalid because it neglects finite geometry changes at the crack tip. The large geometry changes at the crack tip cause local nonproportional loading, thereby eliminating the possibility of a single parameter description of stresses and strains. On the other hand, as the plastic zone increases in size and becomes comparable with the size of the structure L (say, the length of the uncracked ligament), the K-dominated zone disappears altogether, while the J dominated zone persists. Thus, even though K factor becomes meaningless in this case, the J integral (or the CTOD concept equivalent to J) is still an appropriate fracture criterion. Finally, in the limit of large scale yield (lsy) there is no longer a region uniquely characterized by J. Single parameter fracture mechanics becomes invalid, as the eritical J values exhibit a size and geometry dependenee.