Crack tip and associated domain integrals from momentum and energy balance

Cracks in brittle materials have terminal velocities far below theoretical predictions. To address this problem we have investigated the propagation of cracks in a brittle plastic (polymethylmethacrylate). Velocity measurements with resolution an order of magnitude better than past experiments reveal the existence of a critical velocity at which the velocity begins to oscillate, the mean acceleration drops sharply, and a pattern is formed on the fracture surface. Thus the dynamics of cracks may be governed by a dynamical instability.

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Instability in dynamic fracture

https://www.cavs.msstate.edu/publications/docs/1999/01/837Void-crack.pdf

A void–crack nucleation model for ductile metals

At high crack velocities in metallic materials nearly all plastic strain accumulates at very high strain-rates, typically in the range 10 3 s −1 to 10 5 s −1 . At these rates, dislocation motion is limited by dynamic lattice effects and the plastic strain-rate increases approximately linearly with stress. The problem for a crack growing at high velocity is posed for steady-state, small scale yielding in elastic/rate-dependent plastic solids. A general expression is derived for the near-tip stress intensity factor in terms of the remote intensity factor, or equivalently for the near-tip energy release-rate in terms of the overall release-rate. An approximate calculation of the plastic strain-rates provides this relation in analytical form. Imposition of the condition that the near-tip energy release-rate be maintained at a critical value provides a propagation equation for the growing crack. A single, nondimensional combination of material constants emerges as the controlling parameter. Implications for dynamic crack propagation are discussed.

High strain-rate crack growth in rate-dependent plastic solids

I n order to investigate rapid Mode I crack propagation in steel under large scale yielding conditions a finite element program was developed in which the material is treated as elastic-viscoplastic, based on a theory by P. P erzyna . In this model, rate effects in the plastic deformation process are accounted for. The parameters of the constitutive model were determined from ordinary tensile tests on small specimens by varying the loading rate. It was found that the strain rate can satisfactorily be related to the increase of the inelastic stress-strain relation raised to some power n . The FEM-program was applied to a number of crack propagation experiments on highly loaded SEN specimens of a high strength steel. For comparison some experiments were also analysed assuming linear elastic and simulated elastic-plastic material behaviour with no rate sensitivity. It was found that combined plastic and viscous effects are of great importance for an adequate description of rapid crack growth when large scale yielding is at hand. The energy flow to the crack tip region in the viscoplastic case, which is used as a fracture parameter, seems to converge to finite and non-trivial values for sufficiently small values of the element size along the crack tip. This may be due to the asymptotic dominance of the elastic field at the crack-tip for the particular rate-dependent model used. Geometry effects, which are present in a linear elastic analysis, are shown to be negligible in the present elastic-viscoplastic analysis with respect to different specimen heights.

A viscoplastic analysis of rapid crack propagation experiments in steel

Crack arrest experiments are performed on edge-notched specimens of a high strength steel. The crack velocity and the displacements at the boundaries are continuously measured during the experiments. This information is then used in a subsequent FEM analysis to evaluate the dynamic stress intensity factor before and after crack arrest. Dynamic effects are seen to influence the process a considerable time after the arrest. A discussion of the validity of the arrest condition in a linear theory is made based upon experimental results. The inverse problem is also considered, i.e. to predict the crack growth event, the arrest length and the corresponding stress intensity factors when the crack propagation toughness is known for the material. The predicted values are shown to exhibit good agreement with the experimental results.

A FEM analysis of crack arrest experiments

A number of crack propagation experiments are performed on sheets of a high strength steel. Momentaneous forces, crack lengths and velocities are measured. With this as input the dynamic stress-intensity factor is calculated with aid of a FEM program especially modified for the purpose. Observations regarding the dependence of crack propagation toughness on crack tip velocity and acceleration are made. A simple statistical analysis of the results is performed.

Björn Brickstad

Papers

A viscoplastic analysis of rapid crack propagation experiments in steel

A FEM analysis of crack arrest experiments

Numerical evaluation by FEM of crack propagation experiments