Dynamic Fracture Of Brittle Materials Research Articles

Shack–Hartmann wavefront sensing: A new approach to time-resolved measurement of the stress intensity factor during dynamic fracture

The stress intensity factor describes the stress state around a crack tip in a solid material and is important for understanding crack initiation and propagation. Because stresses cannot be measured directly, the characterization of the stress intensity factor relies on the measurement of deformation around a crack tip. Such measurements are challenging for dynamic fracture of brittle materials where the deformation is small and the crack tip velocity can be high. Digital gradient sensing (DGS) is capable of full-field measurement of surface deformation with a sub-micrometer sensitivity and a sub-microsecond temporal resolution, but it has only been demonstrated on centimeter-scale specimens with a spatial resolution of ∼ 1 mm. This makes it challenging to measure deformations close to the crack tip. Here, we demonstrate the potential of Shack–Hartmann wavefront sensing (SHWFS), as an alternative to DGS, for measuring surface deformation during dynamic brittle fracture of millimeter-scale specimens. Using an opaque commercial glass ceramic as an example material, we demonstrate the capability of SHWFS to measure the surface slope evolution induced by a propagating crack with a micrometer spatial resolution and a sub-microsecond temporal resolution. The SHWFS apparatus has the additional advantage of being physically more compact than a typical DGS apparatus. We interpret our SHWFS measurements of the surface slope by comparing them with 2D analytical predictions and phase-field simulations as well as 3D linear-elastic FEM simulations, based on which we discuss the relevance of 3D effects around the crack tip. Then, we introduce our procedure for extracting the apparent stress intensity factor associated with the propagating crack tip using SHWFS measurements. We conclude by discussing potential future enhancements of this technique and how its compactness could enable the integration of SHWFS with other characterization techniques including x-ray phase-contrast imaging (XPCI) for multi-modal characterization of dynamic fracture.

Antiplane two-scale model for dynamic failure

A new dynamic damage law is proposed for the anti-plane loading case. The model is deduced from the energy criterion describing the dynamic propagation of microcracks by using the mathematical homogenization method based on asymptotic expansions. A study of the local macroscopic response predicted by the new model is conducted to highlight the influence of parameters like the size of the microstructure and the rate of loading on the evolution of damage. Results of macroscopic simulations of dynamic failure and the associated branching instabilities are presented and compared with those reported by experimental observations and theoretical studies on dynamic fracture in brittle materials.

The Use of a Railgun Facility for Dynamic Fracture of Brittle Materials

Linear electromagnetic acceleration has a wide range of applications. Among them are applications in the field of materials science, where relatively small, inexpensive systems can be of high value. For instance, it was shown recently at the French-German Institute of Saint Louis, France, that the symmetric Taylor test-a method to investigate the deformation behavior of specimens at high deformation rates-can be realized with higher precision than attainable with other acceleration methods using a railgun with velocity control. In this paper, we present another example for an application of a railgun in the field of materials science, namely, the study of impact phenomena and terminal ballistics. One of the major advantages of railgun technology is that the acceleration profile can be well defined at velocity ranges from very low speeds (<;10 m/s) up to more than 2000 m/s-for one and the same launcher. Moreover, the geometry of a railgun projectile can be round, rectangular or, as in the case discussed here, hexagonal. Finally, electromagnetic acceleration does not require the use of propellants, which in the case of impact experiments could lead to complications-at least for the experimental application presented. The quest is to study the ejecta field of fractured brittle materials at moderate impact velocities (<;500 m/s). It transpires that a railgun can be a valuable tool for such investigations. Using high-speed cameras and novel data processing methods ejecta distribution-velocity relations are explored. Our contribution describes the experimental setup used and will introduce some of the major results obtained so far.

Phase field approximation of dynamic brittle fracture

Numerical methods that are able to predict the failure of technical structures due to fracture are important in many engineering applications. One of these approaches, the so-called phase field method, represents cracks by means of an additional continuous field variable. This strategy avoids some of the main drawbacks of a sharp interface description of cracks. For example, it is not necessary to track or model crack faces explicitly, which allows a simple algorithmic treatment. The phase field model for brittle fracture presented in Kuhn and Muller (Eng Fract Mech 77(18):3625---3634, 2010) assumes quasi-static loading conditions. However dynamic effects have a great impact on the crack growth in many practical applications. Therefore this investigation presents an extension of the quasi-static phase field model for fracture from Kuhn and Muller (Eng Fract Mech 77(18):3625---3634, 2010) to the dynamic case. First of all Hamilton's principle is applied to derive a coupled set of Euler-Lagrange equations that govern the mechanical behaviour of the body as well as the crack growth. Subsequently the model is implemented in a finite element scheme which allows to solve several test problems numerically. The numerical examples illustrate the capabilities of the developed approach to dynamic fracture in brittle materials.

A strong discontinuity based adaptive refinement approach for the modeling of crack branching

AbstractIn the current work, the physical phenomena of dynamic fracture of brittle materials involving crack growth, acceleration and consequent branching is simulated. The numerical modeling is based on the approach where the failure in the form of cracks or shear bands is modeled by a jump in the displacement field, the so called ‘strong discontinuity’. The finite element method is employed with this strong discontinuity approach where each finite element is capable of developing a strong discontinuity locally embedded into it. The focus in this work is on branching phenomena which is modeled by an adaptive refinement method by solving a new sub‐boundary value problem represented by a finite element at the growing crack tip. The sub‐boundary value problem is subjected to a certain kinematic constraint on the boundary in the form of a linear deformation constraint. An accurate resolution of the state of material at the branching crack tip is achieved which results in realistic dynamic fracture simulations. A comparison of resulting numerical simulations is provided with the experiment of dynamic fracture from the literature. (© 2011 Wiley‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Damage and dissipation mechanisms in the dynamic fracture of brittle materials: Velocity driven transition from nominally brittle to quasi-brittle

We present the results of recent dynamic fracture experiments (Scheibert et al., Phys. Rev. Lett. 104 (2010) 045501) on polymethylmethacrylate, the archetype of nominally brittle materials, over a wide range of crack velocities. By combining velocity measurements and finite element calculations of the stress intensity factor, we determine the dynamic fracture energy as a function of crack speed. We show that the slope of this curve exhibits a discontinuity at a well-defined critical velocity, below the one associated to the onset of micro-branching instability. This transition is associated with the appear- ance of conics patterns on the fracture surfaces. In many amorphous materials, these are the signature of damage spreading through the nucleation, growth and coalescence of micro-cracks. We end with a discussion of the relationship between the energetic and fractographic measurements. All these results suggest that dynamic fracture at low ve- locities in amorphous materials is controlled by the brittle/quasi-brittle transition studied here.

Visualization of Impact Damage in Ceramics Using the Edge‐On Impact Technique

Projectile impact generates severe fragmentation in ceramics which propagates at high velocities and precedes the penetration of the projectile. The high‐speed photographic technique of the Edge‐On Impact (EOI) has been developed at the Ernst‐Mach‐Institute (EMI) in order to visualize dynamic fracture in brittle materials. In a typical EOI test the projectile hits one edge of a specimen and fracture propagation is observed during the first 20 us after impact by means of a Cranz‐Schardin highspeed camera. EOI tests allow a characterization of different ceramics by the macroscopic fracture patterns, single crack velocities, and crack front velocities (damage velocities). The phenomenology of damage propagation in several ceramics and a ceramic‐metal composite is discussed. The EOI technique is useful for the evaluation of damage models for brittle materials because it enables a direct comparison of model predictions to experimental data obtained during the impact process.

Dynamic fracture in a discrete model of a brittle elastic solid

Dynamic fracture of brittle materials is studied by means of a molecular dynamics simulation of a two-dimensional (2D) lattice of point particles. By a particular discretization of the continuum equations of elasticity, we derive the Born model in such a way that the model parameters are related to the material properties. Numerical simulations are performed, which show a branching instability, under Mode I loading, occurring at a critical crack tip speed. The analysis of the dynamical stress tensor field near the tip shows a qualitative similarity to Yoffe's stress field.

Special features of dynamic fracture of brittle materials in the mode of ultimate fracture velocities

Based on the model of spherical cavity expansion in brittle materials, which involves the concept of ultimate fracture velocities, we consider a stress-strain state in the elastic precursor zone and in the region of material broken by radial cracks. We have noted the mechanical effects of dynamic overload and fracture retardation, which arise within this model.

The Dynamics of Fast Fracture

A new instability-dominated picture of dynamic fracture in brittle materials has arisen as a result of intensive research over the past few years, and is based on new high-resolution measurements of crack dynamics, This may have impact on the design of new energy-absorbing materials.

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).

On the interaction and branching of fast running cracks—a numerical investigation

Phenomena of dynamic fracture in brittle materials resulting from the interaction of fast running cracks are investigated numerically. These studies concern the influence of mutual shielding on crack paths, the stress intensity factor and crack tip speed variations, the stability of a simultaneous propagation of several cracks, and the interaction of cracks of different size. Furthermore, dynamic crack branching is investigated from a macroscopic point of view. The respective initial boundary value problem of linear elastodynamics is formulated as a system of time-domain boundary integral equations in conjunction with experimentally motivated criteria for crack growth and branching. The numerical evaluation is based on a boundary element method and an appropriate discretization of the fracture and branching criteria. Results obtained from numerical simulations are discussed with regard to the experimental findings.

On the role of microcracks in the dynamic fracture of brittle materials

The dynamic fracture behavior of brittle materials is investigated. The morphology of the fracture surface is examined in detail in four polymers: polymethylmethacrylate, Solithane-113, Homalite-100 and poly-carbonate. The fracture surface markings are examined to determine the micromechanisms of fracture. This examination reveals clearly that the operative micromechanism that governs dynamic fracture in brittle materials is the nucleation, growth and coalescence of microcracks. Following a quantitative characterization of the microcracking patterns, a very simple nucleation and growth model is then put forward. Imposing nucleation and growth criteria based on the experimental observations, the simulation recreates the experimental observations, not only of the microscope surface features, but also of the macroscopic behavior such as the constancy of the crack speed.

Microbranching instability and the dynamic fracture of brittle materials.

We describe experiments on the dynamic fracture of the brittle plastic, PMMA. The results suggest a view of the fracture process that is based on the existence and subsequent evolution of an instability, which causes a single crack to become unstable to frustrated microscopic branching events. We demonstrate that a number of long-standing questions in the dynamic fracture of amorphous, brittle materials may be understood in this picture. Among these are the transition to crack branching, ``roughness'' and the origin of nontrivial fracture surface, oscillations in the velocity of a moving crack, the origin of the large increase in the energy dissipation of a crack with its velocity, and the large discrepancy between the theoretically predicted asymptotic velocity of a crack and its observed maximal value. Also presented are data describing both microbranch distribution and evidence of a new three-dimensional to two-dimensional transition as the ``correlation width'' of a microbranch diverges at high propagation velocities. \textcopyright{} 1996 The American Physical Society.

Phenomenological equations of a dynamic fracture

Making use of the results of the lumped mass spring model of a crack, we have derived phenomenological equations of a dynamic fracture of brittle materials which take account of the surface roughness. One of the equations closely resembles that for laser radiation. The physics associated with the equations and its implication on the theory of dynamic fracture are discussed. It is also shown how to explain the recent observation of the oscillation of the crack velocity.