Crack Growth In Materials Research Articles

The effects of residual stress on elastic-plastic fracture propagation and stability

Residual stresses in materials affect their resistance to the initiation of fracture and to subsequent crack growth. Using full-field strain measurements and finite element analysis we demonstrate that the effect of residual stress on a material's crack growth resistance curve can be understood using elastic-plastic fracture mechanics. It is shown that Lei's modified J-integral formulation (Jmod) is a good predictor of the load vs crack extension behaviour of an elastic-plastic material containing residual stresses.

Characterization of Loading Rate Effects on the Interactions between Crack Growth and Inclusions in Cementitious Material

The microcapsule-enabled cementitious material is an appealing building material and it has been attracting increasing research interest. By considering microcapsules as dissimilar inclusions in the material, this paper employs the discrete element method (DEM) to study the effects of loading rate on fracturing behavior of cementitious material specimens containing the inclusion and crack. The numerical model was first developed and validated based on experimental results. It is then used to systematically study the initiation, propagation and coalescence of cracks in inclusion-enabled cementitious material. The study reveals that the crack propagation speed, first crack initiation stress, coalescence stress, compressive strength and ultimate strain increase with the loading rate. The initiation position, propagation direction, cracking length and type of the initiated cracks are influenced by the loading rates. Two new crack coalescence patterns are observed. It is easier to cause the coalescence between the circular void and a propagating crack at a slow loading rate than at a fast loading rate.

A novel characterization of fatigue crack growth behavior in metallic materials: The physical relationship between the uncracked section size and the remaining fatigue life

A physically based universal functional is shown to uniquely correlate the fatigue crack growth data of metals in high-cycle fatigue, generated at various stress ratios, extremely well. The functional is proposed based on the hypothesis that at any stage during fatigue, the remaining fraction of fatigue cycles required for final fracture is proportional to the fractional uncracked section size that remains to be severed by the fatigue crack. The basis for such a hypothesis is that the microscopic mechanism of fracture, such as striation formation in fatigue, is largely independent of the details (e.g. mean stress or stress ratio) of high-cycle fatigue loading. Experimentally, the functional is found to be a simple power law relating the fractional remaining uncracked section (net-section) size to the fractional (normalization by total fatigue life) remaining fatigue life. It is also shown that the surrogate form of the functional provides excellent descriptions of the raw crack-length-versus-cycles data generated in high-cycle fatigue experiments. The functional seems to provide a new physical basis, which is different from fracture mechanics, to characterize the effect of stress ratio on fatigue crack growth in 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.

Numerical simulation of crack growth in piezoelectric structures by BEM

In this paper, a dual boundary element computer program is developed for numerical simulation of a crack propagating in piezoelectric plates under a combined quasi-static electric and mechanical loading. To determine the crack growth path, two fracture criteria are taken into account: the maximum of hoop stress intensity factor (HSIF) and hoop mechanical strain energy release rate (HMERR). By using the displacement extrapolation method, these fracture parameters of any small kinked crack branch are obtained and validated by comparing with the available analytical results. The critical fracture loads for some test specimens are numerically analyzed based on the maximum HMERR fracture criterion. Different electrical boundary conditions on the crack faces are considered and checked with the experimental data. Finally, one crack or a pair of cracks propagating in infinite or finite piezoelectric plates is numerically simulated. The influences of the loading conditions, the anisotropic fracture toughness and the interaction between the cracks on the crack growth paths are also studied. The comparisons with the exiting finite element results show the accuracy and efficiency of the present BEM program for numerical simulation of crack growth in piezoelectric materials.

A new numerical methodology for simulation of unstable crack growth in time independent brittle materials

This paper focuses on a new algorithm for the quasi-static simulation of unstable crack propagation in time-independent brittle material. The proposed approach is based on a combination of the standard Newton’s algorithm with a fictive path loading algorithm. First, a time step refinement process, associated to the Newton’s algorithm, enables us to efficiently detect the beginning of unstable crack extension. Then, a fictive path loading algorithm is performed to assess an estimation of the post instability solution. Finally, this estimated solution is used as initial guess in the standard Newton’s algorithm for the same time increment. The final converged solution satisfies both the mechanical equilibrium and the mechanical behaviour integration. This paper highlights several advantages of the proposed algorithm such as robustness, easy implementation on an existing Newton’s type solver, genericity for different unstable nonlinear physical problems. An application of this new method is presented for a smeared crack model, based on a local continuous damage formulation, devoted to the simulation of brittle nuclear fuel rupture. The efficiency of the proposed algorithm is demonstrated through a set of 2d and 3d simulation results.

A simplified evaluation of the mechanical energy release rate of kinked cracks in piezoelectric materials using the boundary element method

Based on the concept of the hoop field intensity factors of an initial crack prior to any kink, an apparent hoop mechanical (strain) energy release rate (MERR) is defined to approximate the MERR of a piezoelectric crack with an infinitesimal kink at any arbitrary angle. The validity and the efficiency of the simplified approximation are examined by numerical examples using the boundary element method (BEM). The generalized crack-opening-displacements or displacement jumps are computed by the traction boundary integral equations (BIEs). By using the displacement extrapolation method, the crack-tip field intensity factors of any arbitrarily kinked crack in linear piezoelectric materials are obtained and the BEM results are validated by comparing them with the available reference analytical results. Then, the differences between the conventional field intensity factors and MERR of an infinitesimally kinked crack and the hoop field intensity factors and hoop MERR of the main crack prior to any kink are numerically analyzed. Finally, the crack propagation in an infinite linear piezoelectric material is numerically simulated. The paths of the crack growth are predicted by adopting four different fracture criteria, namely, the maximum hoop stress intensity factor (SIF) and MERR fracture criteria for the main crack-tip before the next propagation, and the maximum KI and MERR fracture criteria for the kinked tip of the main crack with an infinitesimal branch at an arbitrary kinking angle evaluated by using a trial crack extension technique. The comparisons among these results show that the present simplified approximation can efficiently provide a sufficient accuracy for numerical simulation of crack growth in linear piezoelectric materials.

Some fractographic contributions to understanding fatigue crack growth

Some fractographic and metallographic contributions to understanding fatigue crack growth in metallic materials are reviewed, with an emphasis on environmentally assisted fatigue. The formation of ductile and brittle striations at intermediate-to-high ΔK, where each stress cycle produces a striation, is reasonably well understood at the microscopic level, but the details of the dislocation activity involved are still controversial. The evidence suggests that, in fairly benign environments, egress of dislocations around crack tips predominates, whereas environmentally assisted fatigue crack growth of many materials in liquid-metal, hydrogen, and aqueous environments involves an adsorption-induced dislocation-emission (AIDE) process at crack tips. There is also fractographic evidence that nanovoids often form just ahead of crack tips at intermediate-to-high ΔK in all environments. The effects of variables such as solution composition, electrode potential, and cycle frequency can be qualitatively explained largely in terms of surface-reaction kinetics and adsorbed-hydrogen coverage in many cases, but a quantitative understanding is lacking. Fatigue crack growth at low ΔK, even in inert environments, is not well understood, and only speculative explanations can be offered.

Identification Damage Model for Thermomechanical Degradation of Ductile Heterogeneous Materials

The failure of ductile materials subject to high thermal and mechanical loading rates is notably affected by material inertia. The mechanisms of fatigue-crack propagation are examined with particular emphasis on the similarities and differences between cyclic crack growth in ductile materials, such as metals, and corresponding behavior in brittle materials, such as intermetallic and ceramics. Numerical simulations of crack propagation in a cylindrical specimen demonstrate that the proposed method provides an effective means to simulate ductile fracture in large scale cylindrical structures with engineering accuracy. The influence of damage on the intensity of the destruction of materials is studied as well.

Kinetics of fatigue crack growth and crack closure effect in long term operating steel manufactured at the turn of the 19th and 20th centuries

In this paper the fatigue crack growth behaviour in structural components from the old 19th century structures (e.g. bridges) has been investigated. The delivered material for investigation was extracted from a beam made of puddled iron, commonly used in the 19th century. The obtained results from several ancient railway metallic bridges (located in Lower Silesia, Poland) have shown the presence of microstructural degradation processes in puddled iron. The kinetic fatigue fracture diagrams (KFFD) have been obtained for post-operated steel. The problem of crack closure has been involved in fatigue crack growth process during the experiments and its understanding is fundamental for the analysis of stress ratio effects on KFFD. An experimental and numerical approach has been considered for the evaluation of the crack closure/opening forces based on the hysteresis loop deformation. The implemented algorithm in the numerical environment gives promising results in the description of the kinetics of fatigue crack growth of the old metallic materials with consideration of crack closure effects. The problem of fatigue crack growth rate description from the energy point of view has been presented and discussed. The Universal Graph method (based on Dimensional Analysis approach) was used for phenomenological formulation of the kinetic equation.

The formation and growth of echelon cracks in brittle materials

Cracks subjected to mode III shear loading fragment into numerous daughter cracks. The formation of such patterns—called echelon cracks—is explored in this work through a phase-field model of fracture. It is shown that the phase field method predicts that a crack subjected to mixed-mode I $$+$$ III grows along the extension of the parent crack plane, contrary to experimental observations. In order to replicate the experimentally observed fragmentation of crack fronts, defects are introduced in the vicinity of the crack front to trigger fragmentation of the front; examples of successful formation and growth of these echelon cracks is demonstrated in this paper. It is also shown that the intrinsic scale parameter in the phase field model must be very small in comparison to the scale of formation of the echelon cracks.

A universal functional for the physical description of fatigue crack growth in high-cycle and low-cycle fatigue conditions and in various specimen geometries

A simple universal functional is shown here to correlate fatigue crack growth data of a wide variety of materials (metals, polymers), test conditions (high-cycle and low-cycle fatigue), and specimen configurations (tension and bending). The proposed functional is a power law that relates the normalized remaining ligament size to the normalized remaining fatigue life in a cyclically loaded specimen. The functional evolved from the idea that at any stage during fatigue, the remaining fraction of cycles required to fracture the specimen, completely, depends on the remaining fraction of section to be broken by the fatigue crack before that final fracture. More importantly, the surrogate form of the functional is shown to provide excellent descriptions of the raw crack-length-versus-cycles data in fatigue crack growth. The functional provides a new physical basis to characterize fatigue crack growth in materials and is promising for extensions in to more complicated fatigue loading conditions.

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.

Finite Element Simulation of Complex Thermomechanical Fatigue Evolution

Fatigue failures occur due to the application of fluctuating stresses that are much lower than the stress required to cause failure during a single application of stress. The process is dangerous because a single application of the load would not produce any ill effects, and a conventional stress analysis might lead to assumption of safety that does not exist. The fatigue process is thought to begin at an internal or surface flaw here the stresses are concentrated, and consists initially of shear flow along slip planes. The mechanisms of fatigue-crack propagation are examined with particular emphasis on the similarities and differences between cyclic crack growth in ductile materials, such as metals, and corresponding behavior in brittle materials, such as intermetallic and ceramics. Fatigue, as understood by materials technologists, is a process in which damage accumulates due to the repetitive application of leads that may be well below the yield point.

Mass-Transport Process in Subcritical Crack Growth in Carrara Marble

Information of subcritical crack growth in rock is essential to ensure the long-term integrity of a rock mass surrounding various structures and various architectures made of rock materials. In this study, using Carrara marble as a rock sample, subcritical crack growth was investigated experimentally. Especially, the load relaxation method of the double-torsion test was used for all measurement under controlled temperature and relative humidity. It was shown that the crack velocity in air increased with increasing temperature. The crack velocity increased with increasing the stress intensity factor. However, we found a region where the increase of the crack velocity with stress intensity factor was not significant. It is also found that the crack velocity in this region increased with temperature. This is similar to Region II of subcritical crack growth observed in glass in air. The Region II in glass is controlled by the mass-transport to the crack tip. In the case of rock, the transport of water to crack tip is important. In general, Region II is not observed for subcritical crack growth in rock materials, because rocks contain water. Since the porosity of Carrara marble is very low, the contained amount of water is also very small. Therefore, it is considered that Region II is observed in Carrara marble. Since the crack velocity increased in the environment with higher temperature, it is concluded that the condition with low temperature in air is desirable for the long-term integrity of a carbonate rock mass. Additionally, it is concluded that mass-transport is an important process for subcritical crack growth in rock with low porosity.

Existence and Convergence Questions in Computational Modelling of Crack Growth in Brittle and Quasi-Brittle Materials

Computational modelling of the crack growth in brittle and quasi-brittle materials used in mechanical, civil, etc. engineering applies the cohesive zone model with various traction separation laws; determination of micro-mechanical parameters comes then from static tests, microscopic observation and numerical calibration. Although most authors refer to ill-possedness and need of artificial regularization in inverse problems (identification of material parameters), some difficulties originate even in nonlinear formulations of direct and sensitivity problems. This paper demonstrates the possibility of proper analysis of the existence of a weak solution and of the convergence of a corresponding numerical algorithm for such model problem, avoiding non-physical assumptions.

شبیهسازی رفتار ناحیه آسیب نوک ترک مواد اورتوتروپیک با استفاده از مدل ویسکوالاستیک

In Fracture phenomenon of orthotropic materials, generally in crack tip vicinity, an area called damaged zone appears that in quasi-brittle materials, is known as fracture process zone. This area contains a multitude of micro cracks which due to various reasons, failure analysis and fracture process of these materials has been difficult. Determination of Mechanical properties in this region can help to predict the value or even the direction of crack growth in orthotropic materials. So far, several models have been proposed to determine the mechanical properties of this region, but due to the immense complexity of this region, the results have not been expressed the behavior of this region properly. Moreover, the existence methods have not been verified with new experimental and numerical data, yet. the present paper, it was attempted to present a new numerical model based on viscoelastic theory (the linear springs and damping) and, according to Perony series, the mechanical properties of the damaged zone simulated. In new approach, that is based on experimenal and FEM results, the mechanical behavior of damaged zone can accurately simulated.

3D Continuum Damage Approach for Simulation of Crack Initiation and Growth in Ceramic Materials

This paper focuses on the numerical simulation of crack initiation and growth in ceramic materials. This work is devoted to nuclear fuel modelling under irradiation and more precisely to fuel pellet fragmentation assessment at macroscopic and microscopic scales. Simulation tools are developed in the framework of a cooperative program between the CEA, EDF and AREVA devoted to a unified fuel performance software environment called PLEIADES. A smeared crack model is proposed to have a continuous description of crack nucleation and growth at macroscopic scale. This unified description is based on crack extension process from the microscopic scale up to the macroscopic scale. In order to deal with unstable crack extension a specific algorithm is proposed to solve the quasi static nonlinear mechanical problem. A 3D application is presented to illustrate performances and robustness of the smeared crack approach to simulate crack extension in nuclear fuel ceramics. In this application with an internal pressure loading a new methodology is proposed in order to avoid convergence problem due to the indetermination of the quasi static formulation of a softening material equilibrium under Neumann boundary condition.

A homogenized multigrid XFEM to predict the crack growth behavior of ductile material in the presence of microstructural defects

In this work, stable crack growth behavior of SA508 carbon steel has been evaluated through experimental and numerical investigations. The effect of various types of flaws has been observed on the load carrying capacity of the structures. A homogenized multigrid XFEM approach has been proposed to simulate the stable crack growth in ductile material using finite strain plasticity. The geometric nonlinearity has been modeled by updated Lagrangian approach whereas the material nonlinearity has been modeled by von-Mises yield criterion using isotropic strain hardening. The accuracy and effectiveness of the proposed approach has been verified by solving several stable crack growth problems.