Dynamic failure of solids

Shock compression of solids

The theory of linear elastic dynamic fracture mechanics for Heaviside loading of an isolated crack is employed to formulate the response to constant strain-rate loading of a single crack. Numerical integration of the Heaviside solution is shown to lead to fracture initiation stresses that are dependent upon the imposed strain rate. These fracture initiation stresses are also shown to be relatively independent of the crack size and crack shape. The results are used to explain the strain-rate dependent fracture stress observed in some rocks as being a structural response, rather than a basic material property.

Strain-rate dependent fracture initiation

The micromechanical damage mechanics formulated by Ashby and Sammis, 1990, “The Damage Mechanics of Brittle Solids in Compression,” Pure Appl. Geophys., 133(3), pp. 489–521, and generalized by Deshpande and Evans 2008, “Inelastic Deformation and Energy Dissipation in Ceramics: A Mechanism-Based Constitutive Model,” J. Mech. Phys. Solids, 56(10), pp. 3077–3100. has been extended to allow for a more generalized stress state and to incorporate an experimentally motivated new crack growth (damage evolution) law that is valid over a wide range of loading rates. This law is sensitive to both the crack tip stress field and its time derivative. Incorporating this feature produces additional strain-rate sensitivity in the constitutive response. The model is also experimentally verified by predicting the failure strength of Dionysus-Pentelicon marble over strain rates ranging from ~10^(−6) to 10^3s^(−1). Model parameters determined from quasi-static experiments were used to predict the failure strength at higher loading rates. Agreement with experimental results was excellent.

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A Micromechanics Based Constitutive Model for Brittle Failure at High Strain Rates

Explosive or percussive breakage of rock relies on impulsive rock fracture and both the fracture stress and fracture energy under such conditions are observed to be significantly greater than measured quasi-statically. The implication of rate dependence has been verified in recent tensile fracture studies and in the present report this data has been compiled, significant trends noted, and comparisons made with earlier impulsive fracture criteria.

Criteria for impulsive rock fracture

A plate impact method was used to produce internal penny‐shaped cracks in polycarbonate and to study the response of these cracks to short tensile pulse loads. The observed crack instability behavior could not be explained by classical static fracture mechanics. A short‐pulse fracture mechanics was developed from static fracture mechanics concepts. The instability criterion was obtained from considerations of the early time stress intensity histories experienced by cracks struck by short‐pulse loads. This criterion, which requires that the dynamic stress intensity exceed the dynamic fracture toughness for a certain minimum time, gave results in accord with the experimental data. Short‐pulse fracture mechanics defines the conditions for which simple static expressions can be used to determine dynamic fracture toughness. The dynamic fracture toughness of polycarbonate at a stress intensification rate of 107 MN m−3/2 sec−1 was measured to be 2.2±0.2 MN m−3/2, about 60% of the quasistatic value. This result supports the view that material toughness does not increase sharply at high loading rates, but rather decreases monotonically with increasing stress intensification rate until a constant minimum value is reached.

J. F. Kalthoff

Papers

Instability of cracks under impulse loads