Crack Speed Histories Research Articles

Dynamic mode II crack growth along an interface between an elastic solid and a plastic solid

Dynamic crack growth is analyzed numerically for a planar bimaterial block with an initial edge crack subject to mode II impact loading along the side of the block. The crack is constrained to grow along a weak interface directly ahead of the initial crack tip. A cohesive constitutive relation, that relates tractions and displacement jumps, is specified across the weak interface. The normal traction along the interface is taken to be a linear function of the normal displacement across the interface while the shear traction is taken to be a nonlinear function with the shear traction approaching zero for large displacement jumps, thus allowing mode II crack propagation. The material on the impact side of the interface is taken to be a linear elastic (actually hypoelastic) solid while the material on the other side of the interface is taken to be an isotropically hardening elastic-viscoplastic solid. Both plastically incompressible and plastically compressible solids are considered. Results are presented for the effects of plastic deformation on the evolution of near crack tip fields, on the crack speed history, and on the tractions that develop at the interface. The effects of various parameter variations are also explored. It is found that plasticity can result in tensile normal tractions developing on the interface in the crack tip vicinity and that the transition to an intersonic crack speed via a daughter crack mechanism can take place in the presence of small amounts of plastic straining.

Deformation rates effects in softwoods: Crack dynamics with lattice fracture modelling

Present study contributes towards understanding crack toughness against the intrinsic deformation rate sensitivity. A methodology for characterizing fracture dependence in softwoods through experimental and numerical analysis has been developed. Time-dependence was found to be the characterising parameter. Image analysis of fracture data acquired with high-speed camera showed that the crack speed histories are stochastic and erratic. In the higher rate range, crack dynamics is characterized as episodic and locally heterogeneous, with irregular jumps and arrests. Critical crack propagation speed at the highest rate tested of 200 mm/min was found to be between 0.7 m/s and 4 m/s (14.3 km/h). Fracture toughness decreased at both slow static and high loading rates, with the mean maximum at 1 mm/min, which is a static deformation rate specific to short-term standard tests. At 200 mm/min deformation rate, inertial effects suggested dynamic fracture response. Explanations of loading rates effects relate to the micro-processes in the fracture process zone (FPZ) and fracture mechanisms, which are simulated with discrete lattice fracture model (LFM). The model included viscous bi-linear stress relaxation into the softening relation and random stochastic finite element properties. Novel characterisation of softwoods is crucial for sensible numerical modeling in seismic structural situations.

Impact failure characteristics in sandwich structures. Part II: Effects of impact speed and interfacial strength

In this paper, we describe the second part of an experimental investigation concentrating on the study of the effects of impact speed and interfacial bond strength on the dynamic failure of model sandwich structures. Results show that even small variations in impact speed and bond strength substantially influence the initiation behavior of delamination (location and nucleation time) and lead to substantially different inter-layer crack speed histories. These changes in inter-layer failure history influence the timing, sequence and final extent of subsequent intra-layer damage within the sandwich structures.

Dynamic delamination fracture toughness in unidirectional polymeric composites

A modified end-notched flexure (ENF) specimen was used to determine Mode-II-dominated dynamic delamination fracture toughness of fiber composites at high crack propagation speeds. A strip of FM-73 adhesive film was placed at the tip of the interlaminar crack created during laminate lay-up. This adhesive film with its greater toughness delayed the onset of crack extension and produced crack propagation at high speeds. Dynamic delamination experiments were performed on these ENF specimens made of unidirectional S2/8553 glass/epoxy and AS4/3501-6 carbon/epoxy composites. Crack speed was measured by means of conductive aluminum lines created by the vapor deposition technique. A finite-element numerical simulation based on the measured crack speed history was performed and the dynamic energy release rate calculated. The results showed that the dynamic fracture toughness is basically equal to the static fracture toughness and is not significantly affected by crack speeds up to 1100 m/s.

An Analysis of Intersonic Crack Growth Under Shear Loading

Crack growth in a homogeneous elastic solid under impact shear loading conditions is analyzed numerically, with the crack constrained to grow along a weak plane directly ahead of the initial crack tip. The configuration analyzed is a plane-strain model of that used in the experiments of Rosakis et al. (1999). A cohesive surface constitutive relation is specified along the weak plane that relates the tractions and displacement jumps across it and that allows for the creation of new free surface. The resistance to crack initiation and the crack speed history are predicted without invoking any additional failure criterion. The effect of cohesive strength and impact pulse time on the response is explored. In a certain parameter regime, the calculations reproduce, at least qualitatively, the type of crack speed histories seen in the experiments. For other parameter values, an abrupt transition from crack growth at the Rayleigh wave speed to a value above 2 times the shear wave speed is seen. This transition involves microcrack nucleation ahead of the main crack. At intersonic crack speeds, shock-like gradients in the near-tip stress field are found as seen in the experiments.

The effect of bond strength and loading rate on the conditions governing the attainment of intersonic crack growth along interfaces

Dynamic crack growth along a bimaterial interface under impact shear loading is analyzed numerically. The material on each side of the bond line is characterized by an isotropic hyperelastic constitutive relation. A cohesive surface constitutive relation is also specified that relates the tractions and displacement jumps across the bond line and that allows for the creation of new free surface. The resistance to crack initiation and the crack speed history are predicted without invoking any additional failure criterion. Full finite strain transient analyses are carried out. A plane strain model of the configuration used in experiments of Rosakis and co-workers is analyzed. Calculations are carried out for parameters characterizing a steel-PMMA bimaterial. For a sufficiently low impact velocity, the crack speed increases smoothly to the PMMA Rayleigh wave speed, whereas above a sharply defined transition impact velocity, the crack speed reaches a value somewhat less than the PMMA dilational wave speed. This high speed crack growth is associated with multiple crack face contact, separated by discrete micro-crack like openings behind the main shear crack. The calculations reproduce, at least qualitatively, the type of crack speed histories and crack tip fields seen in the experiments. They are also consistent with optical observations of finite multi-site contact occurring at intersonic crack speeds.

Energy dissipation in dynamic fracture of brittle materials

Dynamic crack growth in a plane strain strip is analysed using a cohesive surface fracture framework where the continuum is characterized by two constitutive relations: a material constitutive law that relates stress and strain, and a relation between the tractions and displacement jumps across a specified set of cohesive surfaces. The material constitutive relation is that of an isotropic hyperelastic solid. The cohesive surface constitutive relation introduces a characteristic length into the formulation. The resistance to crack initiation and the crack speed history are predicted without invoking any additional failure criterion. Finite-strain transient analyses are carried out, with a focus on the relation between the increase in fracture energy with crack speed and the increase in surface area due to crack branching. The numerical results show that, even with a fixed work of separation per unit area, there is a substantial increase in fracture energy with increasing crack speed. This arises from an increase in fracture surface area due to crack branching. The computational results are in good agreement with experimental observations in Sharon et al (1996).

Numerical simulations of dynamic interfacial crack growth allowing for crack growth away from the bond line

Dynamic crack growth is analyzed numerically for a plane strain bimaterial block with an initial central crack subject to impact tensile loading. The material on each side of the bond line is characterized by an isotropic hyperelastic constitutive relation. Potential surfaces of decohesion are interspersed in the material on either side of the bond line and along the bond line. The cohesive surface constitutive relation allows for the creation of new tree surface and dimensional considerations introduce a characteristic length into the formulation. Full transient analyses are carried out. The resistance to crack initiation, the crack speed history and the crack path are predicted without invoking any ad hoc failure criterion. Three calculations are carried out for a PMMA/Al bimaterial. The imposed loading and the properties of the adjacent materials are kept fixed, while the bond line strength is taken to be 1/4, 1/2, and 3/4 of the strength of PMMA. The nominal crack speed decreases with increasing bond line strength. When the bond line strength is 1/4 that of PMMA, the crack remains on the bond line although there is an attempt at branching off the bond line. For the intermediate case, a bond line strength 1/2 that of PMMA, repeated branching of the main crack off the bond line into the PMMA occurs, together with micro-crack nucleation on the bond line. The crack branches off the bond line into the PMMA when its strength is 3/4 that of PMMA, with the main direction of growth being parallel to the bond line, but with the crack progressively drifting further into the PMMA.

Numerical simulations of dynamic crack growth along an interface

Dynamic crack growth is analyzed numerically for a plane strain bimaterial block with an initial central crack. The material on each side of the bond line is characterized by an isotropic hyperelastic constitutive relation. A cohesive surface constitutive relation is also specified that relates the tractions and displacement jumps across the bond line and that allows for the creation of new free surface. The resistance to crack initiation and the crack speed history are predicted without invoking any ad hoc failure criterion. Full finite strain transient analyses are carried out, with two types of loading considered; tensile loading on one side of the specimen and crack face loading. The crack speed history and the evolution of the crack tip stress state are investigated for parameters characterizing a PMMA/Al bimaterial. Additionally, the separate effects of elastic modulus mismatch and elastic wave speed mismatch on interface crack growth are explored for various PMMA-artificial material combinations. The mode mixity of the near tip fields is found to increase with increasing crack speed and in some cases large scale contact occurs in the vicinity of the crack tip. Crack speeds that exceed the smaller of the two Rayleigh wave speeds are also found.

Determination of crack-speed history and tip locations for cracks moving with nonuniform velocity

This paper describes the use of Rayleigh waves as observed with the reflected-light method of caustics to obtain information pertaining to crack speed and tip location. The basic idea is to use the Doppler-shift effect as applied to elastic-wave emission from a running crack to geometrically reconstruct crack-tip locations. In addition to the usual information pertaining to the stress-intensity factor at the time when the photograph was taken, the process yields a complete history of crack-propagation velocities even along curved-crack paths.