Local Fracture Criterion Research Articles

Parametric evaluation of progressive damage in polymer concretes: Size effect and statistics

Fracture and effective stress–strain graphs in two-dimensional random composites subjected to a uni-axial in-plane uniform strain are characterized. The inclusions are arranged randomly in the matrix. Both inclusions and matrix are isotropic and elastic-brittle. We conduct this analysis numerically using a very fine two-dimensional triangular spring network and simulate the crack initiation and propagation by sequentially removing of the bonds, which exceed a local fracture criterion. In particular, the focus of this paper is on effects of scale (size of inclusion) and geometric randomness in such composites. We consider several “windows of observation” (scales) and study crack patterns, types of constitutive responses, and statistics of the corresponding scale-dependent effective elastic stiffness and strength of such composites. Parametric study is conducted to cover a wide range of material combinations defined by the stiffness ratio and the strain-to-failure ratio and a damage plane in terms of these two parameters to illustrate the results is employed.

BRITTLE FRACTURE OF STRUCTURAL MEMBERS CONSIST OF DIFFERENT STEEL MATERIALS

In beam-to-column welded connection of steel structure, brittle fracture may occur from two or more fracture initiation points, e.g. scallop, end-tab, weld metal and HAZ. As a basic study on the local fracture criteria, the fracture of a steel member that is composed of more than one element, such as a welded joint, is investigated. Fractural experiments on steel elements with notches are carried out, by using two materials that have different fracture toughness. The effects of the notches on the brittle failure and the fractural features of the composition of two different steel materials are comprehended in this paper.

Three-dimensional effects on the dynamic fracture determination of Al 7075-T651 using TPB specimens

Here we present a numerical analysis of three-dimensional effects on the dynamic three-point-bending fracture tests on Al 7075-T651 alloy specimens performed in a modified Split Hopkinson Pressure Bar. Using the Finite Element Method implemented in a commercial code the whole experimental device has been modeled. Different thicknesses and initial crack-to-width ratio specimens are simulated at different impact velocities to study the possible effect on the Crack Mouth Opening Displacement and, using a local stress fracture criterion, in the critical Stress Intensity Factor. The numerical results are compared with experimental results found by the authors.

Roughness of a mode I in-plane crack front propagating along a heterogeneous cohesive interface

The roughness of the crack front of an interfacial crack propagating along a weak plane in a heterogeneous disordered medium has been repeatedly studied both experimentally and numerically. For an interfacial toughness varying randomly on the interface, the front is self-affine. Quite often, however, the calculated roughness exponent differs from the experimental estimate. Several theoretical models have been employed up to now in the numerical simulations (elastic line depinning, random fuse and spring or beam models). In this paper we present finite element simulations (FEA) of the macroscopic mode-I static propagation of a crack front along a planar interface of an elastic or elastic-plastic coating adhered to a rigid substrate. The interfacial elements separate obeying a cohesive law, their toughness spatially fluctuating at random. The cohesive elements here employed allow for taking into account local I + II + III mixed-opening mode, i.e., allow for mode mixity at the local level. Our results indicate that for a given macroscopic toughness the crack front roughness is strongly sensitive to both the local cohesive law and the local fracture criterion.

Analysis of Hydrogen Diffusion in Notched High-Strength Steel Wires

Fick's laws were used to model the hydrogen diffusion in notched high-strength steel wires loaded in tension under elastic-plastic conditions. The plastic deformation at the notch tip has an effect on the peak distribution of the hydrostatic stress ( h σ ). So, in stress-assisted diffusion analysis, elastic-plastic material behavior should be considered. Coupled diffusion elastic-plastic finite element analysis was implemented in the finite element program ABAQUS using the user element subroutine (UEL) and the coupled temperature-displacement solver routine to solve the variational form of the diffusion equation in order to obtain the hydrogen concentration distribution ahead of the notch tip in high-strength steel wires under plane strain conditions. The analysis results are compared with those obtained from elastic analysis, which shows that, if a critical hydrogen concentration is regarded as a local fracture criterion, the elastic-plastic analysis results can be used to evaluate the hydrogen embrittlement of high-strength steel wires.

Ductile failure analysis of API X65 pipes with notch-type defects using a local fracture criterion

A local failure criterion for API X65 steel is applied to predict ductile failure of full-scale API X65 pipes with simulated corrosion and gouge defects under internal pressure. The local failure criterion is the stress-modified fracture strain as a function of the stress triaxiality (defined by the ratio of the hydrostatic stress to the effective stress). Based on detailed finite element (FE) analyses with the proposed local failure criterion, burst pressures of defective pipes are estimated and compared with experimental data. For pipes with simulated corrosion defects, FE analysis with the proposed local fracture criterion indicates that predicted failure takes place after the defective pipes attain maximum loads for all cases, possibly due to the fact that the material has sufficient ductility. For pipes with simulated gouge defects, on the other hand, it is found that predicted failure takes place before global instability, and the predicted burst pressures are in good agreement with experimental data, providing confidence in the present approach.

A critical stress–critical area statistical model of the [formula omitted] curve for MA957 in the cleavage transition

We model the temperature ( T) dependent fracture toughness K J c ( T ) of MA957 based on a statistically modified critical stress–critical stressed area ( σ ∗– A ∗) local fracture criteria. The K J c ( T ) of MA957 is strongly dependent on the specimen orientation. Analysis of cleavage initiation in the longitudinal–radial (L–R) orientation, with the highest K J c ( T ) , yielded the highest σ ∗ ≈ 3600 MPa. In contrast, the σ ∗ for the circumferential–longitudinal (C–L) orientation, with the lowest K J c ( T ) , yielded the lowest σ ∗ ≈ 2850 MPa, while for the circumferential–radial (C–R) orientation with intermediate K J c ( T ) , σ ∗ ≈ 3000 MPa. The A ∗ ranged from ≈ 30 to 400 μm 2. The cleavage initiation sites are μm-scale Al 2O 3 particles aligned in the textured low toughness extrusion direction.

Novel Estimation of Critical Frontal Process Zone of Ceramics by a Single-Edge V-Notched-Beam Technique

A novel estimation for the critical size of the frontal process zone of ceramics is proposed using a single-edge V-notched beam (SEVNB) technique. A three-point flexure test is carried out on aluminum titanate ceramics containing a sharp V-shaped notch with different depth. An exact solution of the critical local stress is analyzed at a critical distance from the notch tip. The critical frontal process zone size is determined as the distance between the notch tip and the point where the critical local stress equals the flexural strength of specimens without notches, based on the local fracture criterion and the Griffith-Irwin criterion. The critical size of the frontal process zone, the fracture toughness and the flexural strength were also estimated for several materials, such as, alumina, porous alumina, and alumina-based nanocomposites. The relationship between these mechanical properties indicated that there was an almost linear relationship between the fracture toughness and the resultant of strength and square root of the critical frontal process zone size, and that both of them must be increased to improve the fracture toughness of ceramics.

An alternative formulation of the Ritchie–Knott–Rice local fracture criterion

In the paper an alternative formulation of the RKR local fracture criterion is proposed. It is based on the features of the stress distribution in front of a blunted crack in an elastic–plastic material. The stress distribution is computed using the finite strain option in the finite element method. It is postulated that the opening stress in front of the crack should be greater than the critical one, σ c, over the distance l ⩾ l c, where l c is considered as a material parameter. The hypothesis is applied to estimate the influence of the in-plane constraint on fracture toughness. New formulas to compute the critical value of the J-integral are derived both for the small scale yielding and large plastic deformations in front of the crack. The results obtained are compared with the Sumpter and Forbes experimental results and with the O’Dowd analytical formula concerning the J c = J c( J IC, Q) relation.

Dynamic instabilities and failures in impact tension, compression and shear

Several aspects of Dynamic Fracture Mechanics and Dynamic Failure Mechanics are discussed in this paper. In the first part the local fracture criteria are briefly discussed, but the main part is focused on the failure criteria to be applied in fast or impact loading. A phenomenon of delayed fracture is discussed when a stationary crack is loaded by an impulse in tension or shear. Some local failure criteria are evoked and applied to cases of dynamic failures in tension, compression and shear. Conditions for stability in different modes of dynamic loading leading to failures are defined. The Critical Impact Velocities (CIV) in tension and shear, as the last stage of dynamic failure, are discussed as well. Another case of dynamic failure is the phenomenon of spalling. A local failure criterion based on delayed accumulation of defects and generalized to a wide range of temperatures is introduced.

Local fracture criterion to describe failure assessment diagrams for a body with a crack/notch

The cohesive zone model and the criterion of average stress in the cohesive zone ahead of the crack/notch tip are used to describe failure assessment diagrams for cracked and notched bodies. The type of loading as well as the elastic stress concentration factor can significantly change the character of the failure assessment diagram.

A numerical approach for the simulation of ductile fracture with embedded discontinuities

AbstractIn the present study, a computational approach for the numerical simulation of ductile fracture within the framework of the finite element method is proposed. In the developed macroscopic formulation, the inelastic behavior in the bulk of the material is described by the finite elasto‐plastic material model proposed in [4]. The failure process is modeled by introducing discontinuities when a special local fracture criterion is satisfied. The discontinuities are incorporated via special triangular finite elements with embedded interfaces following the line of [2]. Finally, the numerical procedure is evaluated for a twodimensional representative test problem. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Fracture in human cortical bone: local fracture criteria and toughening mechanisms

Micromechanical models for fracture initiation that incorporate local failure criteria have been widely developed for metallic and ceramic materials; however, few such micromechanical models have been developed for the fracture of bone. In fact, although the fracture event in “hard” mineralized tissues such as bone is commonly believed to be locally strain-controlled, only recently has there been experimental evidence (using double-notched four-point bend testing) to support this widely held belief. In the present study, we seek to shed further light on the nature of the local cracking events that precede catastrophic fracture in human cortical bone, and to define their relationship to the microstructure. Specifically, numerical computations are reported that demonstrate that the stress and strain states ahead of such a notch are qualitatively similar irrespective of the deformation mechanism (pressure-insensitive plasticity vs. pressure-sensitive microcracking). Furthermore, we use the double-notched test to examine crack–microstructure interactions from a perspective of determining the salient toughening mechanisms in bone and to characterize how these may affect the anisotropy in fracture properties. Based on preliminary micromechanical models of these processes, the relative contributions of various toughening mechanisms are established. In particular, crack deflection and uncracked-ligament bridging are identified as the major mechanisms of toughening in cortical bone.

セラミックスの破壊じん性とき裂前方損傷域寸法

Our previous technique for estimating critical sizes of the frontal process zone (FPZ) in ceramics was improved using exact solutions of stress distributions around crack and elliptical hole tips in an infinite plate for calculating local fracture stresses. The local fracture stress was calculated at the characteristic distance from the notch tip on the basis of a local fracture criterion. A three-point flexure test for alumina was carried out using V-notched specimens, and a formula for the relation between the strength and the notch depth including the short notch depth region was successfully established. The critical FPZ size of alumina was estimated from the fracture toughness and strength of the material. The critical FPZ sizes for alumina-based nanocomposites were also estimated. A concept of material design for toughened ceramics was discussed on the basis of these data. It was proved that there was a linear relationship between the fracture toughness and the product of strength and square-root of the FPZ size for these materials. This relation suggests that both the strength and the critical FPZ size must be increased to enhance the fracture toughness of ceramics.

Local fracture criterion to describe failure assessment diagrams for a body with a crack/notch

Local fracture criterion to describe failure assessment diagrams for a body with a crack/notch

A local approach to brittle fracture analysis and its physical interpretation

The paper presents a review of studies dedicated to the development of a local approach to brittle fracture in metals and alloys. To work out a statistical criterion of local fracture in a metal in the vicinity of a stress concentrator is shown to be the key task of the local approach. The author substantiates a possibility of describing the process of brittle (quasibrittle) fracture in metals ahead of the notch on the basis of “primary principles,” i.e., on the basis of the analysis of the processes of formation and catastrophic growth of crack nuclei. The physical effects have been established, which must be allowed for in the development of the local fracture criterion. The author considers the main factors that govern the size of the “process zone.” This parameter has been found to depend on the value of the relative gradient of the local plastic strain intensity. The appropriateness of using the Weibull distribution to describe quasibrittle fracture of metals is analyzed. It is demonstrated that the Weibull parameters are not material's constants as postulated in the conventional variant of the local approach. Their values depend on the local plastic strain and the metal stress state in the vicinity of the stress concentrator.

Mezzo-scopic Analysis of Fracture Toughness in Steels

The cleavage fracture toughness of steels was mezzo-scopically analyzed on the basis of the statistical local fracture criterion approach. The statistical stress criterion at the crack tip region suggests that the cleavage fracture toughness in steels can be described as a function of the yield stress, the cleavage fracture stress, and other mechanical properties of the materials. Formulation of the cleavage fracture toughness was first examined through an investigation on correlation between the cleavage toughness and the cleavage fracture stress obtained in notched round bar specimens in accordance with the theoretical prediction. Then, the scatter of the toughness, specimen thickness effect on the toughness, deterioration of the toughness due to cold working and irradiation, and improvement of the toughness caused by the Ni addition, were analyzed through the formulation of the toughness.

Pitting of the rolling bodies contact surface

A calculational model for investigation of the fracture processes and durability of the surface contact zones of rolling bodies has been proposed within the framework of the fatigue fracture mechanics concepts. Unidirection rolling in conditions of dry friction and boundary lubrication has been investigated. The model basis is the algorithm step-by-step construction of the crack growth paths developed with application of singular integral equations of two-dimensional problem of the elasticity theory for bodies with curvilinear cracks and local fracture criteria for a complex stress-strain state. The paths calculation algorithm also takes into account redistribution of stresses, caused both by crack growth and mutual motion of contacting bodies. In the case of rolling with lubrication, that can fill the crack, its action is modeled by stresses, additionally distributed on the crack faces. Propagation paths of edge cracks have been constructed. The dependence of path form on friction coefficient between contacting bodies, the length and orientation of the initial crack, and in the presence of lubrication, on the intensity of its pressure on the crack faces, has been investigated. In calculations the generalized mode I fracture criterion ( σ θ -criterion) has been used. An attempt has been made to explain the mechanism of development of such crack-like defect as pitting and ‘squat’, often met during rolling contact fatigue. As an example, the residual durability of the ShH-15 bearing steel presurface layer under boundary lubrication has been estimated.

Paths of Edge Cracks in Rolling Bodies under the Conditions of Boundary Lubrication

We propose an analytical model for investigation of the processes of fracture of a near-surface layer of bodies in the case of their unidirectional rolling under conditions of limit lubrication. The step-by-step calculation of trajectories of propagation of fatigue cracks using the criteria of local fracture in a complicated stressed state and with regard for the specific features of loading in a contact cycle is a key element of the model. We investigate trajectories of propagation of an edge crack depending on the angle of its initial inclination to the boundary of the body, the friction coefficient between the contacting bodies, and the pressure of lubricant on the crack lips. The theoretical results confirm the experimental data and the known hypothesis of Way, according to which a lubricant plays the decisive role in the appearance of a pit.

Indirect Estimation of Critical Frontal Process-Zone Size Using a Single-Edge V-Notched-Beam Technique.

The size of the frontal process-zone at the crack tip of ceramics is an important factor to assess the toughening mechanisms operative in the material. An indirect technique is proposed here to estimate the critical size of the frontal process zone in ceramics using a single-edge V-notched beam (SEVNB) method. A three-point flexure test was carried out on alumina specimens containing a sharp V-shaped notch whose depth was varied. Then, a critical local stress was calculated at a critical distance from the notch tip. The frontal process-zone size at the beginning of crack propagation, namely, the critical frontal process-zone size, was determined as the distance between the notch tip and the point where the critical local stress has the same value as the flexural strength of the specimen. This concept is based on a local fracture criterion. The calculated critical frontal process-zone size of alumina ceramics was 11.4μm based on the linear elasticity, and 22.8μm based on the Dugdale model.