Crack Growth In Brittle Materials Research Articles

Low-cycle fatigue crack growth in brittle materials: Adaptive phase-field modeling with variable-node elements

This work presents an adaptive phase field framework for the simulation of crack nucleation and propagation in brittle materials subject to low-cycle loading. We introduce a fatigue history strain parameter within the phase-field framework to capture the fatigue effect. The resulting coupled differential equations are solved using a staggered iteration scheme. In order to improve the computational efficiency of the phase-field model, an adaptive refinement scheme is introduced. This scheme utilizes an artificial threshold that takes into consideration of both phase-field variables and cumulative fatigue history field variables to determine the elements to be refined. The handling of the hanging nodes resulting from mesh refinement is accomplished through the application of the variable-node element technique, offering a flexible and efficient mesh integration technique. We validate our proposed numerical scheme through five representative numerical examples: single-edge cracked specimen, compact tension specimen, double-edge cracked panel, plate with a hole and plate with multi-cracks and hole. The results demonstrate that the adaptive mesh refinement scheme significantly reduces computational costs without compromising the accuracy of the numerical predictions.

Visco-energetic solutions for a model of crack growth in brittle materials

Visco-energetic solutions have been recently advanced as a new solution concept for rate-independent systems, alternative to energetic solutions/quasistatic evolutions and balanced viscosity solutions. In the spirit of this novel concept, we revisit the analysis of the variational model proposed by Francfort and Marigo for the quasi-static crack growth in brittle materials, in the case of antiplane shear. In this context, visco-energetic solutions can be constructed by perturbing the time incremental scheme for quasistatic evolutions by means of a viscous correction inspired by the term introduced by Almgren, Taylor, and Wang in the study of mean curvature flows. With our main result we prove the existence of a visco-energetic solution with a given initial crack. We also show that, if the cracks have a finite number of tips evolving smoothly on a given time interval, visco-energetic solutions comply with Griffith's criterion.

Dual Horizon Peridynamic Approach for Studying the Effect of Porous Media on the Dynamic Crack Growth in Brittle Materials

Dual Horizon Peridynamic Approach for Studying the Effect of Porous Media on the Dynamic Crack Growth in Brittle Materials

Development of higher-order displacement discontinuity method to simulate fatigue crack growth in brittle materials

The 2D displacement discontinuity method (2D. DDM) is an indirect boundary element technique in which the stresses and displacements are expressed through normal and shear displacement discontinuities. The governing equations of fatigue crack growth are mostly power equations that depend on the stress intensity factor range. Accurate calculation of displacement discontinuity has importance in fatigue analysis of DDM. Therefore, in this study, DDM is extended using cubic variations of displacement discontinuity for ordinary and crack tip elements. This method also uses an appropriate algorithm based on the linear elastic fracture mechanics (LEFM) principle to analyze crack growth under cyclic fatigue loading. This process is accomplished by assuming the homogeneity of brittle material and the small plastic zone of the crack tip compared to the crack dimension. The condition of applying constant and stationary variable amplitude loading was provided. The algorithm is designed based on an iterative process, and the new incremental elements gradually are added to the crack tip until the failure criteria are reached; The size of these elements at each step of growth depends on the crack growth rate in the previous step. Therefore, the fatigue modeling of the structures with multiple cracks and different growth rates is enabled. Virtual crack criteria were employed to improve the accuracy and speed of analysis, which involves crack tips with a slower growth rate. Moreover, the direction of crack propagation is evaluated using the maximum circumferential stress criterion. Examples of simple and multi-fractured structures under constant and variable amplitude load are considered. Comparison of results with literature data shows excellent agreement with high accuracy.

A phase field numerical manifold method for crack propagation in quasi-brittle materials

In the present work, a phase field numerical manifold method (PFNMM) is proposed for crack growth in brittle materials. The advantages of the phase field method (PFM) in modeling crack initiation and crack branching, and those of the numerical manifold method (NMM) in discretizing the computational model are integrated together in the proposed numerical model. The proposed numerical model is very suitable for simulating multiple crack propagation problems. The implementation details of the proposed numerical model are well presented. Several benchmark examples are adopted to validate the proposed numerical approach. The results indicate that the crack propagation topologies and force-displacement curves obtained by the proposed numerical model are in good agreement with others, e.g. Miehe et al. (2010) and Molnar and Gravouil (2017) [3]. The convergence of numerical solution from the proposed numerical model is also investigated. The PFNMM deserves a further investigation.

A new development cracked chevron notched direct tension method for determining the mode I fracture toughness of rocks

A new development has been proposed to measure the tensile fracture toughness (KIc) of rocks. An innovative configuration of chevron notch was applied acting as a cracked chevron notched direct tension (CCNDT) method to determine the mode I fracture toughness, which also could be suggested as a direct method to specify the tensile fracture toughness. In this method, the initial crack is generally created in the form of a chevron notch by a simple rotary saw, and afterward, the crack is subjected to the direct tensile load. Using the chevron notch in the desired specimen is mainly due to the advantages of the sub-critical crack growth in brittle materials. In the present study, a new expression is proposed to calculate the fracture toughness of CCNDT specimens. Various finite element analyses are performed using different chevron crack geometries to obtain the minimum dimensionless stress intensity factor of the CCNDT specimen. The analytical approach based on Bluhm's slice synthesis method is also implemented for evaluating the minimum dimensionless stress intensity factor of the CCNDT specimens. Furthermore, several experiments are carried out on Hornfels using CCNDT and ASTM standard fracture toughness; single-edge notched bend (SENB) tests to verify the proposed method. The geometrical parameters of the CCNDT specimens are also provided to meet the plane strain fracturing condition.

The friction surface destruction mechanism in a magnetic field

The paper considers the mechanism of forming and developing brittle (quasi-coarse) cracks in a sample of ferromagnetic material in a magnetized state. It is shown that the external magnetic field affecting friction surfaces has the most significant effect on the wear process if the cracks open perpendicular to the magnetization vector. The paper describes the criterion of spontaneous crack growth in brittle materials taking into account magnetostatic energy.

A framework to model the fatigue behavior of brittle materials based on a variational phase-field approach

A novel variational framework to model the fatigue behavior of brittle materials based on a phase-field approach to fracture is presented. The standard regularized free energy functional is modified introducing a fatigue degradation function that effectively reduces the fracture toughness as a proper history variable accumulates. This macroscopic approach allows to reproduce the main known features of fatigue crack growth in brittle materials. Numerical experiments show that the Wöhler curve, the crack growth rate curve and the Paris law are naturally recovered, while the approximate Palmgren–Miner criterion and the monotonic loading condition are obtained as special cases.

The edge-notched clamped beam bend specimen as a fracture toughness test geometry

Edge-notched clamped beam bend fracture specimens provide the required geometric stability for controlled crack growth in brittle materials, enabling the measurement of R-curves and cyclic crack growth. In this paper, finite element simulations were carried out on this test geometry to extract the normalized stress intensity factor KI solutions for different useful specimen dimensions, loading tip radius and loads. Based on these results, geometric factors have been proposed that can fit various beam aspect and crack depth ratios. Crack stability analysis is carried out in terms of the R locus for various beam aspect ratios for the clamped beam geometry and compared to other fracture toughness tests. Experimental verification of the same has been carried out at the macro-scale using poly-methyl methacrylate (PMMA) and WC-Co as model materials.

Shear crack growth in brittle materials modeled by constrained Cosserat elasticity

The propagation of in-plane shear cracks is investigated in brittle microstructured materials modeled by the constrained Cosserat elasticity. This theory introduces characteristic material lengths in order to describe the scale effects that emerge from the underlying microstructure and has proved to be very effective for modeling complex microstructured materials. An exact solution is obtained based on integral transforms and the Wiener-Hopf technique. Numerical results are presented illustrating the dependence of the stress intensity factor and the energy release rate upon the loading profile, the propagation velocity, and the characteristic material lengths of Cosserat elasticity. It is shown that depending on the Cosserat microstructural lengths the limiting crack propagation velocity can be significantly lower than the classical Rayleigh limit. Moreover, strengthening effects are observed when the characteristic material lengths become comparable to the geometrical lengths of the problem, a behavior that has been experimentally verified in fracture of ceramics.

A chevron-notched bowtie micro-beam bend test for fracture toughness measurement of brittle materials

A micro-mechanical fracture testing method has been developed that uses a bowtie-shaped micro-beam specimen with a chevron notch. This clamped-clamped specimen can produce stable crack growth in brittle materials. Cyclic loading causes progressive crack extension, thereby producing multiple fracture toughness results in one experiment. The symmetric geometry eliminates the mixed mode fracture that exists in single-ended cantilevers. A 3D finite element analysis model was used to relate the crack length to the beam compliance, and then to the fracture toughness. The results of tests using fused quartz and glass-ceramic materials match very well with published fracture toughness values.

Experimental Study of Crack Growth in Rock-Like Materials Containing Multiple Parallel Pre-existing Flaws Under Biaxial Compression

Cracks and joints are common in rock masses and play a crucial role in rock mass stability. This study prepared specimens with multiple parallel pre-existing flaws by embedding iron sheets in rock-like materials and used the samples to investigate the crack growth characteristics of these materials. Biaxial compression experiments were performed on sixty specimens, and the influences of the number of pre-existing flaws, their angles and the lateral stress on crack growth were investigated based on video recordings of the crack growth. The results demonstrate that structural failure will occur due to crack growth when the sample contains a small number of pre-existing flaws and that as the number of cracks increases, the specimens will fail due to local failures. In addition, the types of rock bridge failures are summarized, including wing cracks, secondary shear cracks between horizontally-separated pre-existing flaws and secondary shear cracks between vertically-separated pre-existing flaws. Wing cracks play a significant role in the failure of the specimens. The results increase the understanding of crack growth in brittle materials that contain multiple parallel pre-existing flaws under biaxial compression.

A two-parameter fracture mechanics model for fatigue crack growth in brittle materials

Nonstandard samples were used to conduct fatigue experiments on brittle material (PMMA) to study the effect of local state of stress at crack tip on fatigue crack propagation rate (FCPR). Results indicated that FCPR cannot be generally characterized by cyclic stress intensity factor range alone and that a second parameter representing the influence of K-dominance zone size and nonsingular stress field is needed. New phenomenological model based on the two-parameter fracture mechanics is proposed for FCPR prediction. Model allows accurate transferability of laboratory data to life prediction in service situations of defects in engineering components under fatigue conditions.

A damage model for crack prediction in brittle and quasi-brittle materials solved by the FFT method

In this paper, we present a damage model and its numerical solution by means of Fast Fourier Transforms (FFT). The FFT-based formulation initially proposed for linear and non-linear composite homogenization (Moulinec and Suquet in CR Acad Sci Paris Ser II 318:1417–1423 1994; Comput Methods Appl Mech Eng 157:69–94 1998) was adapted to evaluate damage growth in brittle materials. A non-local damage model based on the maximal principal stress criterion was proposed for brittle materials. This non-local model was then connected to the Griffith criterion with the aim of predicting crack growth. By using the proposed model, we carried out several numerical simulations on different specimens in order to assess the fracture process in brittle materials. From these studies, we can conclude that the present FFT-based analysis is capable of dealing with crack initiation and crack growth in brittle materials with high accuracy and efficiency.

A viscosity-driven crack evolution

We present a model of crack growth in brittle materials which couples dissipative effects on the crack tip and viscous effects. We consider the 2-dimensional antiplane case with pre-assigned crack path, and firstly prove an existence result for a rate-dependent evolution problem by means of time-discretization. The next goal is to describe the rate-independent evolution as limit of the rate-dependent ones when the dissipative and viscous effects vanish. The rate-independent evolution satisfies a Griffith's criterion for the crack growth, but, in general, it does not fulfil a global minimality condition; its fracture set may exhibit jump discontinuities with respect to time. Under suitable regularity assumptions, the quasi-static crack growth is described by solving a finite-dimensional problem.

Numerical simulation of multiple crack growth in brittle materials with adaptive remeshing

AbstractIn this paper, an automated adaptive remeshing procedure is presented for simulation of arbitrary shape crack growth in multiple cracked bodies. The Zienkiewicz–Zhu error estimator is employed in conjunction with the modified superconvergent patch recovery (SPR) technique to obtain more accurate estimation of error. A stability analysis is performed to determine active cracks from a set of competitive cracks. Various crack growth criteria together with the respective crack trajectory prediction are compared. Several numerical examples are illustrated to demonstrate the efficiency, robustness and accuracy of computational algorithm in the simulation of multiple crack growth. Copyright © 2010 John Wiley & Sons, Ltd.

Slow crack growth: Models and experiments

.The properties of slow crack growth in brittle materials are analyzed both theoretically and experimentally. We propose a model based on a thermally activated rupture process. Considering a 2D spring network submitted to an external load and to thermal noise, we show that a preexisting crack in the network may slowly grow because of stress fluctuations. An analytical solution is found for the evolution of the crack length as a function of time, the time to rupture and the statistics of the crack jumps. These theoretical predictions are verified by studying experimentally the subcritical growth of a single crack in thin sheets of paper. A good agreement between the theoretical predictions and the experimental results is found. In particular, our model suggests that the statistical stress fluctuations trigger rupture events at a nanometric scale corresponding to the diameter of cellulose microfibrils.

Multiple cohesive crack growth in brittle materials by the extended Voronoi cell finite element model

This paper is aimed at modeling the propagation of multiple cohesive cracks by the extended Voronoi cell finite element model or X-VCFEM. In addition to polynomial terms, the stress functions in X-VCFEM include branch functions in conjunction with level set methods and multi-resolution wavelet functions in the vicinity of crack tips. The wavelet basis functions are adaptively enriched to accurately capture crack-tip stress concentrations. Cracks are modeled by an extrinsic cohesive zone model in this paper. The incremental crack propagation direction and length are adaptively determined by a cohesive fracture energy based criterion. Numerical examples are solved and compared with existing solutions in the literature to validate the effectiveness of X-VCFEM. The effect of cohesive zone parameters on crack propagation is studied. Additionally, the effects of morphological distributions such as length, orientation and dispersion on crack propagation are studied.

Influence of Stress Parallel to Crack Plan on Subcritical Crack Propagation in Glass under Biaxial Stress

The aim of this study is to demonstrate the influence of the stress parallel to the crack plane on subcritical crack growth in brittle materials by using a numerical code MFPA2D. The mechanism of this influence is also discussed. The curves of subcritical crack extension vs. strain of brittle materials under uniaxial and biaxial stress were obtained through numerical tests with acoustic emission consideration. The results showed that the tensile stress parallel to the crack plane has the effect on crack arrest, while the compressive stress parallel to the crack plane plays important role in crack opening process. The numerical results were consistent with experimental observed result, which shows the reliability of the numerical method, and provides theoretic foundation for failure analysis and life estimation of brittle materials.

Quasistatic Crack Growth in Nonlinear Elasticity

In this paper, we prove a new existence result for a variational model of crack growth in brittle materials proposed in [19]. We consider the case of n-dimensional nonlinear elasticity, for an arbitrary n≧1, with a quasiconvex bulk energy and with prescribed boundary deformations and applied loads, both depending on time.