THE ASYMPTOTIC STRUCTURE OF TRANSIENT ELASTODYNAMIC FIELDS AT THE TIPOF A STATIONARY CRACK

The asymptotic structure of the transient elastodynamic near-tip field s around a stationary crack is investigated for all three fracture mod es. The transient fields are obtained as the sum of their quasi-static counterparts and corresponding transient correction terms, in terms o f variable-separable expansions. By allowing the coefficients of terms in the quasi-static expansion to deviate from their quasi-static rest rictions, the correction terms are shown to be the particular solution s of a set of first order (for mixed mode I and II) or second order (f or mode III) ordinary differential equations with constant coefficient s and non-homogeneous terms involving only sine and cosine functions o f the independent variable. It is found that the transient effects of dynamic loading on the near-tip fields are to alter the universal angu lar variations of the quasi-static field quantities for the fifth and higher order terms in their variable-separable expansions; thus the fi rst four terms in the expansions have the same angular variations unde r both quasi-static and dynamic loading conditions. This seems to sugg est that transient effects on the crack-tip fields are in general less severe for a stationary crack than for a propagating crack where only the first two terms in the expansions hold the same angular variation s under both steady-state and transient crack growth conditions. Furth ermore, the transient higher order terms for a stationary crack do not depend on the time-rate of the stress intensity factors; in fact, the y only relate to the even order time-derivatives of the instantaneous values of the coefficients of the terms in the quasi-static expansions . This is also in contrast with the case of transient crack propagatio n where the time rates of the dynamic stress intensity factors play im portant roles in the higher order transient terms. Explicit expression s for the transient near-tip stress and displacement fields are provid ed.