Modeling of hydrogen-assisted ductile crack propagation in metals and alloys

This paper presents a finite element study of the hydrogen effect on ductile crack propagation in metals and alloys by linking effects at the microstructural level (i.e., void growth and coalescence) to effects at the macro-level (i.e., bulk material deformation around a macroscopic crack). The purpose is to devise a mechanics methodology to simulate the conditions under which hydrogen enhanced plasticity induces fracture that macroscopically appears to be brittle. The hydrogen effect on enhanced dislocation mobility is described by a phenomenological constitutive relation in which the local flow stress is taken as a decreasing function of the hydrogen concentration which is determined in equilibrium with local stress and plastic strain. Crack propagation is modeled by cohesive elements whose traction separation law is determined through void cell calculations that address the hydrogen effect on void growth and coalescence. Numerical results for the A533B pressure vessel steel indicate that hydrogen, by accelerating void growth and coalescence, promotes crack propagation by linking simultaneously a finite number of voids with the crack tip. This “multiple-void” fracture mechanism knocks down the initiation fracture toughness of the material and diminishes the tearing resistance to crack propagation.     

NUCLEATION,BLUNTING OR PROPAGATION OF A NANOCRACK IN DISLOCATION-FREE ZONES OF THIN CRYSTALS

Nucleation, blunting and propagation of nanocracks in dislocation-free zones (DFZs) ahead of crack tips in ductile and brittle metals have been investigated by tensioning in situ with a TEM, and analysed using microfracture mechanics. The results show that in either ductile or brittle metals, many dislocations could be emitted from a loaded crack tip and a DFZ formed after equilibrium. The stress in the DFZ may be up to the cohesive strength of the material, and then a nanocrack is initiated in the DFZ or directly from the crack tip. In ductile metals, the nanocrack is blunted into a void or notch during constant displacement. In brittle metals, the nanocrack propagated as a cleavage microcrack rather than being blunted.     

A numerical analysis of failure characteristics of ductile layers in laminated composites

In this study, the failure of the ductile layers from collinear, multiple and delaminating cracks that occur in laminated composite systems was studied using a constitutive relationship that accounts for strength degradation resulting from the nucleation and growth of voids. The results indicate that, in laminated composites, void nucleation and growth ahead of the cracks occur at a much faster rate because of evolution of much higher stress values in the interface region. Except for short crack extensions, collinear and multiple cracks develop crack resistance curves similar to that seen for a crack in the ductile layer material as a homogenous isotropic cases. For delaminating crack cases, the fracture behaviour is strongly influenced by the delamination length. The resistance of the ductile layers to crack extension can be significantly reduced by short delamination lengths; however, for large delamination lengths the resistance to crack extension becomes greater than that seen for the ductile material. The results also show that, if the crack tip is at the interface, similar maximum stress values develop in the ductile layers as in the fracture test of the same ductile material, suggesting that ductile–brittle fracture transition behaviour of the ductile layers is dependent upon the extent of the cracks in the brittle layers and fracture characteristics of the brittle layers.     

A unified model of fatigue kinetics based on crack driving force and material resistance

Fatigue in Al-alloys is largely a process of crack growth from pre-existing defects occurring by several different mechanisms, each of which dominates a particular rate-driven segment of fatigue kinetics. These include fatigue void formation through interfacial cracking of secondary particulates, crack extension by brittle micro-fracture (BMF) in near-threshold fatigue, slip driven crack growth in the Paris regime and quasi-static crack extension by the well-known micro-void coalescence (MVC) and the less known fatigue void coalescence (FVC). BMF is mean stress and sequence-sensitive.Mechanism selection for fatigue crack extension in each load cycle occurs on the principle of least resistance to crack driving force represented by ΔK and K_max. Crack extension will switch to a different failure mechanism given reduced resistance to that mechanism by comparison to the current one. Increasing driving force will thus force a switch from BMF to shear and then onto MVC or FVC in that order, over each rising load half-cycle. Higher growth rates will therefore always be associated with a mix of all these mechanisms.     

Investigation on fracture mechanisms of metals under various stress states

Fracture mechanisms for widely used metal materials are investigated under various loading conditions. Several specimens and different loading methods are deliberately designed to produce various stress states. The stress triaxiality is used to rate the level of tension and compression under various stress states. The stress triaxiality increases with adding a notch in the specimen under tension loading and decreases by changing the loading from tension to compression. Scanning electron microscopes are used to observe the microscopic features on the fracture surfaces. The fracture surfaces observed in the tests indicate that with the decreasing stress triaxiality the fracture mechanism for a given metal material includes intergranular cleavage, nucleation, growth, void coalescence, and local shear band expansion. With the fracture mechanisms changing from intergranular cleavage to nucleation, growth, and coalescence of voids, and expansion of a local shear band, four possible fracture modes can be observed, which are quasi-cleavage brittle fracture, normal fracture with void, shear fracture with void, and shear fracture without void. Quasi-cleavage brittle fracture and normal fracture with void are both normal stress-dominated fracture modes; however, their mechanisms are different. Shear fracture with and without void are both shear stress-dominated fracture, and shear fracture with void is also influenced by the normal stress. To a certain metal material, under high stress triaxiality, quasi-cleavage brittle fracture and normal fracture with void tend to occur, and under low stress triaxiality, shear fracture with and without void tend to occur. In addition, the critical positions and fracture criteria adapted to each fracture mode will also be different.     

Cavity growth in ductile particles bridging a brittle matrix crack

The addition of a dispersed ductile phase in a brittle ceramic can result in an increased fracture toughness, mainly due to plastic dissipation during crack bridging. The large elastic-plastic deformations of a ductile particle intercepted by a brittle matrix crack are here analysed numerically with main focus on the effect of the growth of a single void in the particle centre, as has been observed experimentally. Particle-matrix debonding is incorporated in the numerical model, represented in terms of a cohesive zone formulation, and so is the effect of initial residual stresses induced by the thermal contraction mismatch during cooling from the processing temperature. The bridging behaviour is studied for different combinations of material parameters, and the void growth behaviour is related to previous results for cavitation instabilities in elastic-plastic solids.     

Crack extension and arrest in contact stress fields

Sudden crack extension and arrest is observed when indenters are pressed into the surface of brittle materials. The energetics of this system are examined. Crack extension is defined by a condition of decreased free energy (after A. A. Griffith) and crack arrest is defined by a condition of increased free energy with a further increase in crack size. The analysis shows that the critical stress required for crack extension depends on the dimension of the stress field and other factors, viz., crack size and material properties, usually associated with Griffith's fracture equation. The dependence on the dimension of the stress field explains Auerbach's empirical law which shows that the apparent strength of a brittle material increases with the decreasing size of the contact stress field. Experimental observations for hot-pressed Si₃N₄ and SiC are presented to examine this size effect and its predicted relation to material properties.     

A new approach to the evaluation of danger of short fatigue cracks

We demonstrate the possibility of using new physically substantiated characteristics of toughness of metals and the embrittling action of stress concentrators proposed by the authors somewhat earlier in the analysis of brittle fracture initiated by short cracks. We describe a procedure for the experimental determination of a parameter characterizing the embrittling action of these defects and obtain an approximate expression for its evaluation in the presence of a short crack. For typical structural steels, we establish the dependence of the toughness margin of steel with a short crack on the level of strength of this material. We also formulate the requirements on the level of toughness of steels guaranteeing that defects of this type are not dangerous. Institute of Physics of Metals, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Problemy Prochnosti, No. 3, pp. 106–114, May–June, 2000.     

A model of brittle fracture propagation part I—continuum aspects

The micromechanism of crack propagation in steel is described and analyzed in continuum terms and related to the macroscopic fracture behavior. It is proposed that propagation of cleavage microcracks through favorably oriented grains ahead of the main crack tip is the principal weakening mode in brittle fracture. This easy cleavage process proceeds in the Griffith manner and follows a continuous, multiply connected, nearly planar path with a very irregular front which spreads both forward and laterally and leaves behind disconnected links which span the prospective fracture surface. A discrete crack zone which extends over many grains thus exists at the tip of a running brittle crack. Final separation of the links is preceeded by plastic straining within the crack zone and occurs gradually with the increasing crack opening displacement. It is suggested that in low stress fracture, straining of the links is the only deformation mode. However, it is recognized that under certain conditions plastic enclaves may adjoin the crack zone. This deformation mode is associated with high stress fracture, energy transition and eventually with crack arrest.

Energy dissipation resulting from the two deformation mechanisms is related to crack velocity, applied load and temperature and the crack velocity in a given material is expressed as a function of the external conditions. Fracture initiation and crack arrest are then discussed in terms of the conditions which are necessary to maintain the propagation process. Finally, the dimensions of a small scale crack tip zone for a steady state, plane strain crack are evaluated as functions of material properties and the elastic stress intensity factor.

The microstructural aspects of brittle fracture will be discussed in a separate Part 2 [1].     

Why do cracks branch? A peridynamic investigation of dynamic brittle fracture

In this paper we review the peridynamic model for brittle fracture and use it to investigate crack branching in brittle homogeneous and isotropic materials. The peridynamic simulations offer a possible explanation for the generation of dynamic instabilities in dynamic brittle crack growth and crack branching. We focus on two systems, glass and homalite, often used in crack branching experiments. After a brief review of theoretical and computational models on crack branching, we discuss the peridynamic model for dynamic fracture in linear elastic–brittle materials. Three loading types are used to investigate the role of stress waves interactions on crack propagation and branching. We analyze the influence of sample geometry on branching. Simulation results are compared with experimental ones in terms of crack patterns, propagation speed at branching and branching angles. The peridynamic results indicate that as stress intensity around the crack tip increases, stress waves pile-up against the material directly in front of the crack tip that moves against the advancing crack; this process “deflects” the strain energy away from the symmetry line and into the crack surfaces creating damage away from the crack line. This damage “migration”, seen as roughness on the crack surface in experiments, modifies, in turn, the strain energy landscape around the crack tip and leads to preferential crack growth directions that branch from the original crack line. We argue that nonlocality of damage growth is one key feature in modeling of the crack branching phenomenon in brittle fracture. The results show that, at least to first order, no ingredients beyond linear elasticity and a capable damage model are necessary to explain/predict crack branching in brittle homogeneous and isotropic materials.     

On Stressed State of Transversely Isotropic Medium with an Arbitrarily Oriented Spheroidal Void or Penny-Shaped Crack under Internal Pressure

The paper addresses the problem of stress distribution in an elastic transversely isotropic material containing an arbitrarily oriented spheroidal void or a penny-shaped crack under internal pressure. A solution to the problem is set up using the equivalent-inclusion method, triple Fourier transform in space variables, and the Fourier image of Green's function for infinitely anisotropic space. Some double integrals over a finite domain for the void as well as loop integrals for the crack are computed by Gaussian quadrature formulas. The results obtained in particular cases are compared with the data reported elsewhere. The effects of the void geometry, material's elastic properties, orientation of a void or a crack on the stress distribution on the void surface or on the stress intensity factor at the crack front are studied. The most critical void orientation has been found. __________ Translated from Problemy Prochnosti, No. 5, pp. 58 – 70, September – October, 2005.     

Constructing critical stress diagrams for anisotropic brittle materials

The problem of critical equilibrium in a plate with a crack in biaxial tension/compression was analyzed for the case in which the plate material is brittle and anisotropic with respect to its breaking stress. The obtained solutions were used to construct critical state diagrams for brittle solids of this kind. Strength diagrams for orthotropic materials were constructed.     

Significance of K-dominance zone size and nonsingular stress field in brittle fracture

Stress intensity factor has been used to characterize the fracture toughness of a brittle material. This practice is apparently based on the assumption that the singular stress alone at the crack tip is responsible for fracture and that the nonsingular part of the near tip stress has no effect on fracture. In this study, mode I fracture experiments were conducted on a brittle material (PMMA) with four different specimen configurations. The result indicated that fracture toughness cannot be described by stress intensity alone and that a second parameter representing the influence of the nonsingular stress is needed. A two-parameter fracture model was proposed and validated with the experimental result. This two-parameter model was shown to be able to account for various effects created by specimen configurations, crack sizes, and loading conditions, on the fracture behavior of brittle materials.     

Effect of stress triaxiality levels in crack tip regions on the characteristics of void growth and fracture criteria

The behaviour of void growth in the crack tip regions of four specimen geometries with different stress triaxiality levels have been investigated by the FEM method and experimental observations in plane strain and plane stress cases respectively. It was found that the shape change of growing voids, the configurations of a blunting crack tip and the sizes of decreasing ligament between the void and the crack tip are strongly dependent upon the stress triaxiality levels. Under the condition of plane stress, the stress triaxiality on the ligaments of cracks are nearly the same for different specimen geometries, also the void growth, crack tip blunting asnd decreasing of ligament size are identical for various specimens with increasing load levels, which lead to the conclusion that the J_i-value is independent of specimen geometries. However, in the plain strain case, different void growth, crack tip blunting and decreasing in ligament size for various stress triaxiality levels directly caused the J_i-value to be dependent on the specimen geometries. It was found that when the void is linked to the blunting crack tip by the extrapolation to the zero ligament from FEM calculations, the J_i values, measured experimentally, are underestimated slightly.     

Fracture of a brittle plate upon collision with a plastic striker

The article presents the numerical solution of the problem of interaction of an elastoplastic striker with a brittle target at medium speeds (up to 1000 m/sec) of impact. It uses the model of destruction of brittle material by detachment according to which fracture occurs by the formation of a crack in a plane normal to the direction of action of the maximal tensile stress after it has attained its limit value. It is shown that upon nucleation and propagation of a crack the distortions thereby caused bring about a substantial change of the state of stress of the material and affect the further development of fracture.Translated from Probiemy Prochnosti, No. 8, pp. 41–45, August, 1992.     

THE RELATION BETWEEN STRESS INTENSITY FACTOR AND ENERGY RELEASE RATE IN THE PRESENCE OF R-CURVE BEHAVIOUR

Abstract— Failure of ceramic materials occurs when the stress intensity factor of the most serious crack in a component reaches a critical value K_I,_C, the fracture toughness of the material. In case of ideal brittle materials the fracture toughness is independent of the crack extension and, consequently, identical with the stress intensity factor K_I,_Onecessary for the onset of stable crack growth. It is a well-known fact that failure of several ceramics is influenced by an increasing crack-growth resistance curve. The effect of increasing crack resistance has consequences on many properties of ceramic materials. In this report the authors discuss some aspects of R -curve behaviour as represented by stress intensity factors or energies.     

A modeling approach for the complete ductile–brittle transition region: cohesive zone in combination with a non-local Gurson-model

The present study deals with the simulation of crack propagation in the ductile–brittle transition region on the macro-scale. In contrast to most studies in the literature, not only the ductile softening by void growth and coalescence is incorporated but also the particular material degradation by cleavage. A non-local Gurson-type model is employed together with a cohesive zone to simulate both failure mechanisms simultaneously. This consistent formulation of a boundary value problem allows arbitrary high mesh resolutions. The results show that the model captures qualitative effects of corresponding experiments such as the cleavage initiation in front of a stretch zone, the formation of secondary cracks and possible crack arrest. The influence of the temperature on the predicted toughness is reproduced in the whole ductile–brittle transition region without introducing temperature-dependent fit parameters. A comparison with experimental data shows that the shift of the ductile–brittle transition temperature associated with a lower crack-tip constraint can be predicted quantitatively.     

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 rates on the fracturing behavior of cementitious specimens containing the inclusion and the crack. The numerical model was first developed and validated based on experimental results. It is then used to systematically study the initiation, the propagation and the coalescence of cracks in inclusion-enabled cementitious materials. The study reveals that the crack propagation speed, the first crack initiation stress, the coalescence stress, the compressive strength and the ultimate strain increase with the loading rate. The initiation position, the propagation direction, the cracking length and the 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.     

The stress-driven diffusion of point defects to a slowly moving crack

The stress-driven diffusion of point defects to a slowly moving brittle crack is studied under the condition of pure drift. In the pure-drift approximation it is assumed that the point defect flow in the vicinity of a crack tip is dominated by the elastic interaction between the stress field of the crack and a point defect and that concentration gradient effects can be neglected. The first-order drift-diffusion equation for a slowly moving crack at uniform velocity is solved. This yields the flow lines of the point defects and the impurity segregation rate directly in terms of the crack growth rate. The flow line patterns reveal important insights with respect to the point defect migration kinetics near a steadily advancing crack.