Fracture Of Brittle Solids Research Articles

Phase-Field Based Peridynamics Implementation to Model Blast-Induced Fracture in Brittle Solids

Phase-Field Based Peridynamics Implementation to Model Blast-Induced Fracture in Brittle Solids

Crack tip kinematics reveal the process zone structure in brittle hydrogel fracture

When brittle hydrogels fail, several mechanisms conspire to alter the state of stress near the tip of a crack, and it is challenging to identify which mechanism is dominant. In the fracture of brittle solids, a sufficient far-field stress results in the complete loss of structural strength as the material ‘unzips’ at the tip of a crack, where stresses are concentrated. Direct studies of the so-called small-scale yielding zone, where deformation is large, are sparing. Using hydrogels as a model brittle solid, we probe the small-scale yielding region with a combination of microscopy methods that resolve the kinematics of the deformation. A zone over which most of the energy is dissipated through the loss of cohesion is identified in the immediate surroundings of the crack tip. With direct measurements, we determine the scale and structure of the process zone, and identify how the specific loss mechanisms in this hydrogel material might generalize for brittle material failure.

Effect of small pre-strain on the resistance of molybdenum [100] single crystal to high strain rate deformation and fracture

The evolution of shock compressive pulses and dynamic tensile (spall) strength of pristine and pre-strained (0.6% and 5.4% compression) samples of pure [100]-oriented molybdenum single crystals were studied in a series of planar impact tests accompanied by continuous monitoring of the free surface velocity of the samples by an optic velocimeter. The impact loading of Mo samples of different thicknesses was produced by copper impactors accelerated in the smooth bore gun up to a velocity of about 350 m/s. Analyzing the recorded waveforms showed that pre-straining results in a substantial decrease of the molybdenum Hugoniot elastic limit while the dynamic tensile (spall) strength increases with pre-straining. The spall fracture of all tested (and spalled) samples was found to be brittle and characterized by a weak dependence of spall strength on the tensile strain rate. The obtained results are discussed in the terms of generally accepted theories of elastic precursor decay in ductile and spall fracture in brittle solids.

Fracture of brittle solids under impact: The decisive role of stress waves

Measurement of the impact strength of brittle solids is traditionally conducted by split Hopkinson pressure bar (SHPB), where one stress wave is generated and loads on the specimen (uniaxial-unidirectional, UD). What if this single stress wave is split into two (or more) smaller pulses that load on the same specimen? Based on the classical one dimensional elastic stress wave theory, nothing different would happen. However, our experiments revealed the opposite results. Electromagnetic split Hopkinson pressure bar (ESHPB), a newly developed technique that can launch two stress pulses simultaneously in opposite directions along the coaxial bars (uniaxial-bidirectional, BD), was adopted to test the compressive strength of a glass. Results indicated that the loading stress waves largely determined the measured compressive strength, with all other conditions identical. Significant discrepancy (as large as 69.1%) was observed between UD and BD strength. Possible reason for this discrepancy was proposed by high-speed photography.

Crack velocity- and strain rate- dependent dynamic compressive responses in brittle solids

Crack velocity and strain rate have an important influence on the dynamic fracture in brittle solids. However, the correspondence between crack velocity- and strain rate- dependent dynamic compressive responses is hardly established. In this study, a dynamic compression-based model triggered by microcrack growth of brittle solids is proposed. This dynamic model consists of the improved model of wing crack extension containing crack inclination effect, the correlation of crack velocity and strain rate, and the crack velocity-related dynamic fracture toughness. This correlation of crack velocity and strain rate is obtained by the time derivative of crack extension relating to axial strain. Crack extension relating to axial strain is obtained by use of correlation of damage relating to crack and strain. The whole variations of strain rate- (or crack velocity-) dependent stress-strain constitutive relationships from low strain rate (or crack velocity) to high strain rate (or crack velocity) are studied. The micro-mechanisms corresponding to the dynamic stress-strain curves also are explained. Moreover, a unified conclusion revealing the sensitivities of strain rate on peak axial strain ε1peak appearing at peak strength and initial tangent modulus Eini of stress-strain curves is proposed. Influences of crack velocity and strain rate on crack initiation stress and dynamic strength are analyzed in compression. Effects of the size, inclination and friction of microcracks on dynamic strength also are illustrated. The reasonability of these proposed theoretical results is verified via the published experimental results.

A phase-field modeling for brittle fracture and crack propagation based on the cell-based smoothed finite element method

This work develops a phase field model in the framework of cell-based smoothed finite element method (CS-FEM) aiming to solve problems of brittle fracture in solids. The phase-field method is employed to model complex discontinuous behaviors including crack initiation, crack coalescence, crack branching without using any ad hoc models. The CS-FEM which has been proven softer than the standard FEM is used to solve the equations that govern the continuum mechanics of solids. The current CS-FEM phase field method offers advantages of both S-FEM and phase field method in accurately predicting the evolution process of complex fracture patterns in solids. This CS-FEM phase-field technique is implemented in the commercial software ABAQUS using its user-element (UEL) and user-material (UMAT) modules. The coupled non-linear system of equations is solved by the built-in solver by decoupling the phase and displacement field parameters. Several examples have been presented to demonstrate the feasibility and effectiveness of the present method.

Friction of Shear-Fracture Zones.

A shear fracture of brittle solids under compression undergoes a substantial evolution from the initial microcracking to a fully formed powder-filled shear zone. Experiments covering the entire process are relatively easy to conduct, but they are very difficult to investigate in detail. Numerically, the large strain limit has remained a challenge. An efficient simulation model and a custom-made experimental device are employed to test to what extent a shear fracture alone is sufficient to drive material to spontaneous self-lubrication. A "weak shear zone" is an important concept in geology, and a large number of explanations, specific for tectonic conditions, have been proposed. We demonstrate here that weak shear zones are far more general, and that their emergence only demands that a microscopic, i.e., fragment-scale, stress relaxation mechanism develops during the fracture process.

Developing a Crystal Plasticity Model for Metallic Materials Based on the Discrete Element Method

Failure of metallic materials due to plastic and/or creep deformation occur by the emergence of necking, microvoids, and cracks at heterogeneities in the material microstructure. While many traditional deformation modeling approaches have difficulty capturing these emergent phenomena, the discrete element method (DEM) has proven effective for the simulation of materials whose properties and response vary over multiple spatial scales, e.g., bulk granular materials. The DEM framework inherently provides a mesoscale simulation approach that can be used to model macroscopic response of a microscopically diverse system. DEM naturally captures the heterogeneity and geometric frustration inherent to deformation processes. While DEM has recently been adapted successfully for modeling the fracture of brittle solids, to date it has not been used for simulating metal deformation. In this paper, we present our progress in reformulating DEM to model the key elastic and plastic deformation characteristics of FCC polycrystals to create an entirely new crystal plasticity modeling methodology well-suited for the incorporation of heterogeneities and simulation of emergent phenomena.

Polymer liquids fracture like solids.

While fracture in brittle solids has been studied for centuries until today, there are few studies on fracture in polymer liquids. Recent developments in experimental techniques, especially the combination of controlled filament stretching rheometry and high speed imaging, have opened new windows into the detailed study of fracture processes for polymer liquids. High speed imaging shows that polymer liquids fracture like solids with initiation and propagation of an edge fracture. However, remarkable features such as highly reproducible critical stress, independent appearance of multiple fractures, and trumpet crack profiles, reveal mechanisms which are significantly different from solids.

Multiple Cracks Propagate Simultaneously in Polymer Liquids in Tension

Understanding the mechanism of fracture is essential for material and process design. While the initiation of fracture in brittle solids is generally associated with the preexistence of material imperfections, the mechanism for initiation of fracture in viscoelastic fluids, e.g., polymer melts and solutions, remains an open question. We use high speed imaging to visualize crack propagation in entangled polymer liquid filaments under tension. The images reveal the simultaneous propagation of multiple cracks. The critical stress and strain for the onset of crack propagation are found to be highly reproducible functions of the stretch rate, while the position of initiation is completely random. The reproducibility of conditions for fracture points to a mechanism for crack initiation that depends on the dynamic state of the material alone, while the crack profiles reveal the mechanism of energy dissipation during crack propagation.

A new continuum approach to the coupling of shear yielding and crazing with fracture in glassy polymers

AbstractOver the past decades, several constitutive models accounting for finite viscoplasticity and failure in glassy polymers were developed. However, depending on thermal and loading rate conditions, the response might change from ductile to brittle. This brittle response is characterized by inelastically deformed zones, so‐called crazes, having the thickness of micrometers and spanning at some fractions of a millimeter, containing a dense array of fibrils interspersed with elongated voids, detailed discussion e.g. [1]. The shear yielding and crazing are not completely independent excluding each other. Present models introduce crazing either discrete by cohesive surfaces, e.g. [2], or continuous, see [3]. In this work, we outline an extension of a ductile plasticity model towards (i) the description of volumetric directional plasticity effect due to crazing and (ii) the modeling of the local failure due to fracture. The ultimate amount of volumetric plastic craze strain is bounded by a limiting value, where failure occurs. In a second step, the modeling of subsequent failure mechanisms is realized by introducing a fracture phase field, characterizing via an auxiliary variable the crack. Here, we adopt structures of a continuum phase field model of fracture in brittle solids [4], and modify it for a fracture driving term related to the volumetric plastic deformation of the crazes. We demonstrate the performance of proposed formulation by means of a representative boundary value problem. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Towards the treatment of boundary conditions for global crack path tracking in three-dimensional brittle fracture

The aim of the present paper is a systematic elaboration of a three dimensional finite element analysis tool for discontinuous fracture in brittle solids. Brittle or quasi-brittle fracture usually occurs when a material reaches the limit of its strength and no plastic deformation has been observed prior to failure. In the present approach, this kind of failure is characterized by three sets of governing equations: (i) the elastic bulk problem and (ii) the cohesive interface problem regarding the solid deformation field and (iii) the crack tracking problem concerning the crack kinematics. This manuscript describes a unique modular tool set for the coupled set of nonlinear equations. We focus in particular on the boundary conditions for the crack tracking problem of this analysis tool. We critically discuss important implementation details: (i) the choice of crack onset boundary conditions for the additional global field, (ii) the numerical integration, (iii) the modeling of geometrically exact crack tips for cohesive fracture, and (iv) the post-processing procedure for the discontinuity visualization. The potential of the method to simulate brittle fracture is demonstrated by qualitative and quantitative comparisons with experiments from the literature as well as by common benchmark problems.

Use of a nanoindentation fatigue test to characterize the ductile–brittle transition

When considering grinding of minerals, scaling effect induces competition between plastic deformation and fracture in brittle solids. The competition can be sketched by a critical size of the material, which characterizes the ductile–brittle transition. A first approach using Vickers indentation gives a good approximation of the critical size through an extrapolation from the macroscopic to the microscopic scales. Nanoindentation tests confirm this experimental value. According to the grain size compared to the indent size, it can reasonably be said that the mode of damage is deformation-induced intragranular microfracture. This technique also enables to perform cyclic indentations to examine calcite fatigue resistance. Repeated loadings with a nanoindenter on CaCO 3 polycrystalline samples produce cumulative mechanical damage. It is also shown that the transition between ductile and brittle behaviour depends on the number of indentation cycles. The ductile domain can be reduced when the material is exposed to a fatigue process.

Edge chipping of brittle materials: effect of side-wall inclination and loading angle

An earlier analysis of chipping fracture in brittle solids is here extended to include the case of blocks with inclined side faces and non-normal contact loading. The simple relation PF = β Kch 3/2 for the critical chipping load PF in terms of indent location h and material toughness Kc is preserved, with angular coordinates simply incorporated into the β coefficient. Chipping fracture tests using a Vickers indenter near the edges of glass blocks with non-orthogonal faces is used to validate the analysis. Implications of the results in relation to practical engineering, biomechanical and anthropological structures are indicated.

A universal relation for edge chipping from sharp contacts in brittle materials: A simple means of toughness evaluation

An analysis of chipping fracture in brittle solids is presented. Cracks are introduced into the edges of selected materials, including soda-lime glass and fine-grain ceramics, using a Vickers indenter in monotonic loading. The ensuing chip morphology is examined and shown to exhibit a certain geometrical similarity, independent of material properties. A simple universal relation is derived for the critical chipping load in terms of indent location and material toughness. It is suggested that the method could be used as a simple and quick means for evaluating toughness values for glasses and fine-grain brittle materials.

Unified Model for Fracture of Brittle Solids

A unified model for fracture of brittle solid based on crack opening displacement is presented. The model allows the prediction of elastic and fracture response of brittle materials containing spherical and cylindrical pores and polycrystalline solids containing anisotropic residual stresses. The analysis can also be used to predict spontaneous cracking and fracture of two phase systems possessing mismatch stresses.

Multi-crack analysis of hydraulically pumped cone fracture in brittle solids under cyclic spherical contact

The evolution of surface damage in bilayers due to cyclic spherical indentation in the presence of incompressible lubricant is studied using an all-transparent glass/polycarbonate system as a model for more practical applications such as dental crowns and rolling contact fatigue. In situ observations and post-mortem material sectioning reveal that inner cone cracks evolve sequentially from the contact edge inward by slow growth in a process controlled by stress shielding from preceding cracks. The embryonic cracks are then accelerated by the action of fluid pressure into the flexural tensile stress at the lower part of the coating, where crossover fracture leading to delamination between the coating and substrate may ensue.

Robust Algorithm for Brittle Fracture based on Energy Minimization

AbstractThe paper outlines a variational formulation of brittle fracture in solids and considers its numerical implementation by a distinct finite element method. The starting point is a variational setting of fracture mechanics that recasts a monotonic quasistatic fracture process into a sequence of incremental minimization problems. The proposed implementation introduces discretized crack patterns with material‐force‐driven incremental crack‐segment releases. These releases of crack segments constitute a sequence of positive definite subproblems with successively decreasing overall stiffness, providing an extremely robust algorithmic setting in the postcritical range. The formulation is embedded into accompanying r‐adaptive crack‐pattern reorientation procedures with material‐force‐based indicators, providing reorientations of elements at the crack‐tip. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Hydraulically pumped cone fracture in brittle solids

An analysis of inner cone cracks in brittle solids subject to cyclic indentation in liquid is presented. These inner cone cracks, so named because they form well within the maximum contact circle, are postulated to be driven by a hydraulic pumping mechanism. Unlike their more traditional outer cone crack counterparts, inner cones do not appear in monotonic loading or even cyclic loading in the absence of liquid. According to the hydraulic pumping postulate, an expanding contact engulfs surface fissures or flaws, closing the crack mouths and squeezing entrapped liquid toward the subsurface tips, thereby enhancing downward penetration. Finite element modeling is used to analyze the stress and displacement fields in the vicinity of the growing cracks and to compute stress-intensity factors, using soda-lime glass loaded by a spherical indenter in water as a case study. A stepwise incrementing procedure determines the inner cone crack evolution, i.e., crack depth c as a function of number of indentation cycles n, for this system. The predicted c( n) response reproduces essential features of experimentally observed behavior, relative to companion outer cone cracks: notably, a sluggish start in the initial regions, where Hertzian stresses govern, followed by rapid acceleration as hydraulic pumping activates, ultimately dominating in the steady-state far-field.

Thermomechanics of brittle fracture

On the basis of the thermodynamics of thermoelastic deformation we propose an energy condition of the Griffith type for brittle fracture of solids under single loading. An analysis is given of the proposed condition under the plane stressed (strained) state for the two known models of an isolated defect. In the first model, stresses on the external (distant) surface of a solid with a defect are prescribed the same as in a similar solid without a defect. In the second model, displacements are prescribed on the external surface of a solid with a defect, which correspond to the load applied to the solid, but before the defect or crack was formed. Stresses on the surface of the defect in both models are equal to zero. It is shown that the first model in the isothermal case of deformation leads to the Griffith condition. The second model meets the energy condition of the Griffith type from which, under additional assumptions concerning the shape of the defect, and from conditions of isotropy and convexity, we obtain a curve of fracture (macroscopic criterion of fracture) in an ellipse form in the space of principal stresses. The orientation of the crack was determined. Coefficients of the curve of fracture obviously depend upon elastic constants, temperature, linear coefficient of thermal expansion and crack dimensions.