Local Fracture Criterion Research Articles

Local fracture criterion for quasi-cleavage hydrogen-assisted cracking of tempered martensitic steels

Electrochemical permeation cell built on a Instron tensile testing machine allows fracturing notched specimens under hydrogen flux while monitoring simultaneously the flow stress and the permeation anodic current. Analysis of the fracture surfaces reveals that cracking initiates at the hydrogen-entry surfaces as quasi-cleavage regions followed by ductile propagation. Quasi-cleavage zones were fully developed at the maximum engineering stress and often initiate around inclusions for unnotched specimens. The observation of multiple cracks at the hydrogen-entry surfaces and correlations between quasi-cleavage features and martensitic boundaries suggest that cracking is related to decohesion of cropping out and inner boundaries. The local mechanical states and diffusible hydrogen concentration and flux at quasi-cleavage failure were calculated by finite element method (FEM). The results predict local failure criteria in terms of decrease of local maximum principal stress and equivalent plastic strain with local diffusible hydrogen concentration, revealing that the inclusion of hydrogen-mechanical-structural interactions at the charging surfaces is necessary to complete fracture analysis.

Fracture of Protective Structures from Heavy Reinforcing Cement During Interaction with High-velocity Impactor

In this work, the fracture of a reinforced concrete barrier made of heavy reinforced ce- ment is numerically simulated during normal interaction with a high-velocity titanium projectile. The projectile has the initial velocity 750 m/s. The problem of impact interaction is numerically solved by the finite element method in a three-dimensional formulation within a phenomenological framework of solid mechanics. Numerical modeling is carried out using an original EFES 2.0 software, which al- lows a straightforward parallelization of the numerical algorithm. Fracture of concrete is described by the Johnson-Holmquist model that includes the strain rate dependence of the compressive and tensile strengths of concrete. The computational algorithm takes into account the formation of discontinuities in the material and the fragmentation of bodies with the formation of new contact and free surfaces. The behavior of the projectile material is described by an elastoplastic medium. The limiting value of the plastic strain intensity is taken as a local fracture criterion for the projectile material. A detailed numerical analysis was performed to study the stress and strain dynamics of the reinforced concrete target and the effect of shock-wave processes on its fracture. The influence of reinforcement on the resistance of a heavy cement target to the penetration of a projectile has been investigated

On the Formulation of Local Brittle Fracture Criterion for Predicting Crack Resistance of High-Strength Steel

On the Formulation of Local Brittle Fracture Criterion for Predicting Crack Resistance of High-Strength Steel

On the definition of the local brittle fracture criterion to predict the crack resistance of high-strength steel

The use of local brittle fracture criteria for predicting the crack resistance of low-alloy steels is a generally accepted approach. The paper analyzes the possibility of its use for experimental melts of highstrength low-alloy steel sheets with yield strength of about 1000 MPa, the structural state of which was previously studied. Cylindrical specimens with an annular notch of three types differing in the stress-strain state in the net cross-section were tested. It is found that the use of the simplest formulation of such a criterion in the form of an energy condition for the propagation of microcracks through structural barriers (large-angle grain boundaries) gives acceptable results for notched specimens made of metal with different grain sizes, and allows linking these results with the crack resistance of the studied materials.

Competing mechanisms in fracture of amorphous films resting on ductile substrates

The architecture consisting of a thin film resting on a substrate is a common feature in a wide variety of applications. Understanding of the failure mechanisms is essential for design of reliable film/substrate systems. Recent experiments showed that shear banding induced fracture and brittle cracking of films are two major fracture modes in the structure composed of an amorphous metallic glass film bonded to a metal substrate. In this study, we carry out numerical analyses of fracture in amorphous films resting on ductile substrates, with the aim to unveil the mechanisms governing the competition between the two fracture modes observed in the experiments. In the calculations, the brittle cracking of amorphous films is modeled using the cohesive zone framework and the shear banding induced fracture in films is characterized by a simple local fracture criterion. The results show that brittle cracking of amorphous films occurs in the case of thin films, while the shear banding induced fracture dominates in the case of thick films. For the films with intermediate thickness, the mixed fracture modes are observed. Such a film thickness effect predicted by numerical simulations is consistent with the experimental observations. We further reveal that the film thickness effect is related to substrate constraint. In addition, it is identified that the cohesive strength and toughness of amorphous films also play an important role in controlling the fracture modes of the film/substrate systems.

The features of fracture processes of the ceramic composite

The phenomenon of material fracture spans many different length scales. The paper is devoted to the numerical investigation of the features of fracture processes in alumina-zirconia composite ceramics at the mesoscale subjected to uniaxial compression. A structural model of the composite mesovolume based on the experimental SEM image is adopted. The mechanical behavior of the composite is described by a constitutive model of the damageable elastic-brittle medium. Two local fracture criteria are used that are based on the limit values of damage and tensile pressure. The energy dissipation process in the ceramic composite mesovolume during damage accumulation is analyzed. It is shown that the damage accumulation results in nonlinear dissipation of potential energy and the following kinetic energy increase. The last is accompanied by the appearance and growth of cracks in matrix and inclusions at the final stages of deformation.

Corrosion effect, constraint and path orientation estimated in cracked gas turbine blade

The severe damage of gas turbine is due to the failure of the blade, in which the occurrence of a serious pitting occurred on the blade surfaces was evidence of fatigue marks in the fracture surface. This paper deals with the effect of semi-elliptical crack propagation on the crack path using a basic approach in predicting crack paths, namely, incremental methods. The crack position was chosen at the node coordinate where we have the maximum principal stresses. In this node, we have created a semi-elliptical crack and we have compared the results with the Stress Intensity Factors and T-stress values. The local fracture criterion of the maximum average tangential stress in the vicinity of fracture process zone including two terms of the Williams series solution for the mixed mode I/II loading has been used for predicting the angle of surface crack growth. The volumetric method (VM) for the compression-sensitive materials is described by a linear combination of the effective stress and the effective stress intensity factor. The results of our finite element computations based on a two-parameter fracture mechanics formulation showed that the T-stress has significant effects on the crack path.

Numerical simulation of dynamic fracture toughness tests: using RKR criterion

This paper examines the numerical simulation on dynamic fracture toughness values derived from SHPB testing programs with three-point bending specimens using RKR criterion. Three-dimensional and two-dimensional finite element analyses are performed by using software ABAQUS and 3D fracture mechanics code ZENCRACK. The finite element model includes the bullet, incident bar, specimen and supports. Three-point bending specimens with different ratios values of initial crack lengths to width are utilized for the simulations under the identical initial conditions. The fracture initiation time is explored with the RKR local stress fracture criterion. The dynamic fracture toughness value of the material is determined by the combination of response curve of the dynamic stress intensity factor and fracture initiation time. The experimental data are taken as a benchmark to verify the results of three-dimensional and two-dimensional finite element computations. It is found that the computational results from 3D finite element are more accurate.

A nonlocal fracture criterion and its effect on the mesh dependency of GraFEA

Recently, Khodabakhshi et al. (Meccanica 51(12):3129–3147, 2016. https://doi.org/10.1007/s11012-016-0560-6 ) presented a new method (by the name GraFEA) capable of studying fracture based on edge breakage within a classical FEA scheme which combines the best features of FEA and bond-breakage methods in a single framework. In this study, an attempt is made to investigate the mesh dependency of GraFEA by a set of numerical examples, and it is shown that using a local fracture criterion for edge failure will yield mesh-dependent results, as is already well known. A physically motivated nonlocal fracture criterion is implemented along with the edge breakage model, and its efficacy in eliminating the mesh sensitivity is investigated. The nonlocal criterion introduces a length scale into the problem. It is shown that by increasing the magnitude of the length scale parameter from zero, the damage pattern moves from localized fracture to diffuse damage pattern, yet with complete material separation (fracture) across a certain plane. It is shown by numerical results that, as expected, the introduction of the nonlocal fracture criterion eliminates the issue of mesh sensitivity, and thus predictions of the approximate crack paths and damage zone can be done within the classical FEA framework without the need for special formulations.

A 3D automatic mesh refinement X-FEM approach for fatigue crack propagation

A new approach combining the eXtended Finite Element Method (X-FEM) and automatic Adaptive Mesh Refinement (AMR) is presented taking advantage of both methods. The X-FEM, developed over the past two decades by a large community, have proven its efficiency to handle evolving discontinuities in a variety of fracture analysis. Since this method enables to describe the crack and its propagation independently of the mesh of the structure, a simple hierarchical mesh refinement procedure can be applied. Automatic adaptive remeshing is a valuable method in 3D elastic-plastic crack propagation analysis since it permits a locally fine mesh and then an accurate description of physical quantities in a limited area around the crack front. This is particularly important when local fracture criteria are concerned. Moreover local refinement saves computational effort, which is relevant for engineer-sized problems, particularly when the propagation path is not a priori known. In the present work, it is shown that both methods combine with minimal effort: the kinematic continuity relations and the field transfer process, needed for history-dependent material, must include in a proper way the enrichment of the model. If this requirement is not fulfilled, numerical error may be introduced. Implementation of this combined X-FEM/AMR approach is presented in detail. In particular, an innovative field transfer strategy is proposed. Numerical applications in 2 and 3 dimensions of crack propagation in elastic-plastic media demonstrate accuracy, robustness and efficiency of the technique.

Fracture Process Zone at the Tip of a Mode I Crack in a Nonlinear Elastic Orthotropic Material

A body with a fracture process zone at the crack front is considered. The constitutive equations relating the components of the stress vectors at points on the opposite boundaries of the fracture process zone and the components of the vector of relative displacements of these points are derived. A local fracture criterion is formulated. A boundary-value problem for a plate made of a nonlinear elastic orthotropic material with a mode I crack is stated in terms of the components of the displacement vector. By solving the problem numerically, it is revealed how the fracture process zone develops under loading. Features of the deformation field at the end of the fracture process zone are established. The critical load on the plate that causes the crack to grow is determined.

Stress Analysis for Perforated Cylinders with Combined Use of the Boundary Element Method and Nonlocal Fracture Criteria

When using local fracture criteria, it is usually assumed that a fracture begins when the maximum equivalent stress reaches the limit value at least at one point of the body. However, under conditions of an inhomogeneous stress state, it is suitable to use nonlocal failure criteria which take into account the nonuniformity of the stress distribution and yield limit load estimates that are closer to the experimental data. An algorithm of the joint use of the boundary element method (in the version of the fictitious stress method) and gradient fracture criterion for calculations of the strength of plane construction elements is composed. The computations are carried out using a program written in FORTRAN. Results on the limit loading obtained numerically and analytically based on the local criterion of maximum stress and nonlocal fracture criteria (gradient criterion and Nuismer criterion) are compared both among themselves and with the experimental data on the failure of ebonite specimens. A brittle fracture of ebonite cylinders with a hole under diametric compression is studied experimentally. It is shown that nonlocal criteria lead to limit loading values which are closer to the experimental ones than the local criterion. The estimates obtained by the local maximum stress criterion are significantly less than the experimental ones. The estimates found for limit loads by the Nuismer criterion are greater than similar ones determined by the local criterion; nevertheless, they are less than the experimental ones, while the limit load values according to the gradient criterion are closest to the experimental values. Using the nonlocal fracture criteria in designing constructions with stress concentrators will allow us to increase the design values of the limit loads.

An Approach to Assessment of the Lifetime Characteristics of Steels under Creep Conditions Using Fracture Mechanics Criteria

The current status of activities associated with the assessment of conditions and prospects for prolonging the service life of equipment operating for a long time at thermal power stations (TPS) is described. The history of the creation and development of an industry system for diagnosing and prolonging the lifetime of heat-generating and mechanical equipment is briefly outlined. The core of the system was the results of investigations into long-term strength and creep of heat-resistant steels, and a regulatory base governing effective application of the system was formed and continuously improved within the system framework. It is noted that more and more extensive investigations resulted in the attempts to extend the criterial strength base using the cracking resistance criteria, including local creep fracture criteria. The advantages and disadvantages of the most-used local control method, i.e., the replica method, are analyzed. It is proposed to use the fracture mechanics criteria and, in particular, the threshold stress intensity factor (SIF) below which creep cracking does not occur in analyzing the process of steel creep fracture. It is demonstrated that the threshold SIF for a specific material depends functionally not only on the temperature but also on the loading time. Considering this fact, it is proposed to account for the accumulation of local (at the crack tip) and total damageability of the metal in the concept of threshold SIF. A similar approach can also be used for describing the subcritical crack growth. Therefore, it is proposed to construct crack growth diagrams using isochronous curves for the specified test times. It is demonstrated that dimensions of allowable flaws that do not lead to crack propagation can be predicted for given operating conditions. The cases were analyzed that occurred while obtaining results of examination of a structural member operating under creep conditions for prediction of the size of allowable (nonpropagating) crack-like flaws. This analysis has revealed that the application of the threshold SIF criterion and isochronous creep crack growth rate diagrams can be useful for setting forth the substantiated frequency of examinations for high-temperature equipment and establishing the time by which the equipment service life can be prolonged.

Cracking elements: A self-propagating Strong Discontinuity embedded Approach for quasi-brittle fracture

In this paper, we present a self-propagating Strong Discontinuity embedded Approach (SDA) for quasi-brittle fracture. The method is based on the Statically Optimal Symmetric formulation (SOS) of the SDA using the 8-node quadrilateral element which avoids local stress locking. A non-continuous crack path is assumed such that the crack is modelled by a set of disconnected cracking segments. Hence, no complex crack tracking procedure and no explicit (or implicit) representation of the crack surface are needed. A local fracture criteria is proposed for determining the orientation of the crack. Several numerical tests with irregular discretizations are performed, demonstrating the effectiveness and robustness of the presented method.

A phase‐field approach to fracture coupled with mass transport for the simulation of environmentally‐assisted damage

AbstractWith the introduction of a mass transport mechanism the entire problem is subjected to a time frame that dictates the time‐dependent action of soluted species on mechanical properties. A numerical framework within the phase‐field approach is presented with an embrittlement‐based coupling mechanism. The underlying functionals are expressed in terms of the displacement, mass concentration and crack phase‐field. Within the phase‐field approach the modelling of sharp crack discontinuities is replaced by a diffusive crack model facilitating crack initiation and complex crack topologies without the requirement of a predefined crack path. The isotropic hardening of the elasto‐plastic deformation model and the local fracture criterion are affected by the species concentration. This allows for embrittlement and leads to an accelerated crack propagation. An extended mass transport equation for hydrogen embrittlement, accounting for mechanical stresses and deformations, is implemented. For stabilisation purposes a staggered scheme is applied to solve the system of partial differential equations by a multi‐field finite‐element method. A thermodynamically consistent coupling relation that accommodates the required mechanisms is presented. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

A Phase Field Approach to Fracture with Mass Transport Extension for the Simulation of Environmentally-Assisted Cracking

The fracture mechanics assessment of materials exposed to harmful environments requires the understanding of the interaction between the soluted species and the affected mechanical behaviour. With the introduction of a mass transport mechanism the entire problem is subjected to a time frame that dictates the time-dependent action of soluted species on mechanical properties. A numerical framework within the phase field approach is presented with an embrittlement-based coupling mechanism showing the influence on crack patterns and fracture toughness. Within the phase field approach the modeling of sharp crack discontinuities is replaced by a diffusive crack model facilitating crack initiation and complex crack topologies such as curvilinear crack patterns, without the requirement of a predefined crack path. The isotropic hardening of the elasto-plastic deformation model and the local fracture criterion are affected by the species concentration. This allows for embrittlement and leads to accelerated crack propagation. An extended mass transport equation for hydrogen embrittlement, accounting for mechanical stresses and deformations, is implemented. For stabilisation purposes a staggered scheme is applied to solve the system of partial differential equations. The simulation of showcases demonstrates crack initiation and crack propagation aiming for the determination of stress-intensity factors and crack-resistance curves.

Analysis of crack interacting with the composite microstructure of dentin

Abstract Dentin possesses strong fracture resistance, which is attributed to various toughening mechanisms associated with its unique hierarchical structure. In this study, the effects of microstructural features on crack growth in dentin are analyzed. A plasticity model incorporating a local fracture criterion is used to model the mechanical behavior of intertubular dentin (ITD), and a brittle cracking model is used for the peritubular dentin (PTD). Computational simulations of fracture behavior of microstructured dentin are performed, showing that crack growth in microstructured dentin is accompanied by microcracking of PTD ahead of the primary crack, and that fracture of dentin is caused by the merging of the primary crack and microcracks nucleating in PTD. It is identified that the decrease in tubule radius and PTD thickness can lead to the development of a significant degree of microcracking in PTD, thereby enhancing toughness. We further reveal that the toughness of microstructured dentin is dependent on tubule density. The transition in fracture mechanism from multiple void interactions to crack-void interaction occurs as the tubule density decreases, which promotes toughness of dentin. In addition, the effect of the arrangement of dentin tubules is also discussed. The findings of this study provide a mechanistic insight into the region dependent fracture behavior of dentin.

Two basic approaches in a search of the crack propagation angle

AbstractTwo basic approaches in predicting crack paths have been analysed, namely, incremental method and integral (global) method. Incremental methods are associated with the local criterion of fracture mechanics and pointed out on the estimation of an angle between directions of the initial crack propagation and succeeding crack increment. The local fracture criterion of the maximum average tangential stress in the vicinity of fracture process zone including two terms of the Williams series solution for the mixed mode I/II loading has been used for predicting the angle of surface crack growth under conditions of rolling–sliding. The integral method is associated with a variation principle of fracture mechanics. This principle postulates the minimum of the certain functional. This functional contains the weight function depending on the stress and strain state in the uncracked solid and search functions which are described the crack propagation angle on the surface. To validate the variation principle in the search of crack trajectory, this trajectory has been estimated for plates under different loading conditions.

Strength calculations of perforated cylinders with combined use of the boundary element method and non-local fracture criteria

When using local fracture criteria, it is usually assumed that fracture begins when the maximum equivalent stress reaches the limit value at least at one point in the body. But under conditions of an inhomogeneous stressed state, it is advisable to use nonlocal failure criteria, which take into account the uneven distribution of stresses and give estimates of ultimate loads that are closer to the experimental data. A numerical algorithm for the strength of plane construction elements is constructed using the gradient fracture criterion and the boundary element method (the fictitious stress method). Numerical calculation was carried out with the help of a program written in Fortran. Calculation results obtained using the criterion of maximum stress, gradient fracture criterion; point stress criteria are compared both among themselves and with the experimental data. Results of brittle fracture experiments on hard rubber cylinders with a hole are presented. It is shown that the values of limit loads provided by nonlocal criteria are closer to the experimental values than given by local criterion. The estimates obtained with the help of the local criterion for maximum stresses are substantially lower than the experimental ones. The Nuismer criterion gives higher estimates of ultimate loads compared to the local criterion, but these estimates are still less than the experimental values, while the values of the ultimate load by the gradient criterion are the closest to the experimental results. The use of nonlocal failure criteria in the design of structures with stress concentrators will increase the estimates of ultimate loads.

A stress-based fracture criteria validated on mixed microstructures of ferrite and bainite over a range of stress triaxialities

Hot stamping is a sequential process for formation and heat-treatment of sheet metal components with superior mechanical properties. By applying different cooling rates, the microstructural composition and thus the material properties of steel can be designed. By controlling the cooling rate in different sections of a blank, the material properties can be tailored depending on the desired toughness. Under continuous cooling, various volume fractions of ferrite and bainite are formed depending on the rate of cooling. This paper focuses on the ductile fracture behavior of a thin sheet metal made of low-alloyed boron steel with varying amounts of ferrite and bainite. An experimental setup was applied in order to produce microstructures with different volume fractions of ferrite and bainite. In total, five different test specimen geometries, representing different stress triaxialities, were heat treated and tensile tested. Through full-field measurements, flow curves extending beyond necking and the equivalent plastic strain to fracture were determined. Experimental results were further investigated using a mean-field homogenization scheme combined with local fracture criteria. The mean-field homogenization scheme comprises the influence of microstructure composition and stress triaxiality with usable accuracy, connoting auspicious possibilities for constitutive modeling of hot-stamped components.