Ductile fracture initiation and propagation modeling using damage plasticity theory

Ductile fracture is often considered as the consequences of the accumulation of plastic damage. This paper is concerned with the application of a recently developed damage plasticity theory incorporates the pressure sensitivity and the Lode angle dependence into a nonlinear damage rule and the material deterioration. The ductile damaging process is calculated through the so-called “cylindrical decomposition” method. The constitutive equations are discussed and numerically implemented. An experimental and numerical investigation for three-point bending tests is reported for aluminum alloy 2024-T351. Crack initiation and propagation in compact tension specimens are also studied numerically. These simulation results show good agreement with experiments. The present model can successfully predict slant fracture as well as the formation of shear lips.     

Molecular Dynamics Simulation of Porous Layer-enhanced Dislocation Emission and Crack Propagation in Iron Crystal

The internal stress induced by a porous layer or passive layer can assist the applied stress to promote dislocation emission and crack propagation, e.g. when the pipeline steel is buried in the soil containing water, resulting in stress corrosion cracking (SCC). Molecular dynamics (MD) simulation is performed to study the process of dislocation emission and crack propagation in a slab of Fe crystal with and without a porous layer on the surface of the crack. The results show that when there is a porous layer on the surface of the crack, the tensile stress induced by the porous layer can superimpose on the external applied stress and then assist the applied stress to initiate crack tip dislocation emission under lowered stress intensity KI, or stress. To respond to the corrosion accelerated dislocation emission and motion, the crack begins to propagate under lowered stress intensity KI, resulting in SCC.     

Crack propagation in thick cylinders of 1/2 CrMoV steel during thermal shock

Cylinders of 1/2 CrMoV turbine casing steel of external diameter 92 mm and bore diameters of 53 and 19 mm were subjected to repeated thermal shock by internal quenching from 550° with water in order to determine growth characteristics for longitudinal and circumferential cracks. It was found that somewhere between 3000 and 10000 cycles cracks became dormant when about halfway through the wall thickness in as-cast material (ferrite +5% pearlite). This was due to a relatively high threshold for crack arrest (~12 MPa √m) together with the influence of multiple cracking. Coarse grained bainite, however, had a much lower threshold and behaved unstably, a single circumferential crack from a starter groove breaking through by ~ 1600 cycles. Tempering the bainite delayed complete penetration in the case of a single crack and caused crack arrest at ~3/4 of the wall thickness when multiple cracking occurred.

These results are interpreted in terms of the stress intensity profile developed at the peak temperature gradient and the effects of multiple cracking using previously published correction factors. In addition, cyclic crack growth history was examined using oxide dating, striation measurement and DC potential drop techniques. These measured growth histories were compared with those predicted by integrating a known crack growth law (from isothermal tests) along the stress intensity profile. Because crack depths were underestimated, the law requires modification, as ‘wet’ conditions prevail at the crack tip in the early stages.     

Crack initiation and crack propagation under thermal cyclic loading

Theoretical and experimental investigations of crack initiation and crack propagation under thermal cyclic loading are presented. For the experimental investigation a special thermal fatigue test rig has been constructed in which a small circular cylindrical specimen is heated up to a homogeneous temperature and cyclically cooled down under well defined thermal and mechanical boundary conditions by a jet of cold water. At the end of the cooling phase the specimen is reheated to the initial temperature and the following cycle begins. The experiments are performed with uncracked and mechanically precracked specimens of the German austenitic stainless steel X6CrNi 1811.

In the crack initiation part of the investigation the number of load cycles to initiate cracks under thermal cyclic load is compared to the number of load cycles to initiate cracks under uniaxial mechanical fatigue loading at the same strain range as in the cyclic thermal experiment. The development of initiated cracks under thermal cyclic load is compared with the development of cracks under uniaxial mechanical cyclic load.

In the crack propagation part of the investigation crack growth rates of semi-elliptical surface cracks under thermal cyclic loading are determined and compared to suitable mechanical fatigue tests made on compact-tension and four-point bending specimens with semi-elliptical surface cracks. The effect of environment, frequency, load shape and temperature on the crack growth rate is determined for the material in mechanical fatigue tests.

The theoretical investigations are based on the temperature distribution in the specimen, which is calculated using finite element programs and compared to experimental results. From the temperature distribution, elastic and elastic-plastic stress distributions are determined taking into account the temperature dependence of the material properties. The prediction of crack propagation relies on linear-elastic fracture mechanics. Stress intensity factors are calculated with the weight function method and crack propagation is determined using the Paris relation.

To demonstrate the quality of the crack growth analysis the experimental results are compared to the prediction of crack propagation under thermal cyclic load.     

Bifurcation and propagation of a mixed-mode crack in a ductile material

The bifurcation and the propagation of a 2-D mixed-mode crack in a ductile material under static and cyclic loading were investigated in this work. A general methodology to study the crack bifurcation and the crack propagation was established. First, for a mixed-mode crack under static loading, a procedure was developed in order to evaluate the fracture type, the beginning of the crack growth, the crack growth angle and the crack growth path. This procedure was established on the basis of a set of criteria developed in the recent studies carried out by the authors [Li J, Zhang XB, Recho N. J-M^p based criteria for bifurcation assessment of a crack in elastic-plastic materials under mixed mode I-II loading. Engng Fract Mech 2004;71:329-43; Recho N, Ma S, Zhang XB, Pirodi A, Dalle Donne C. Criteria for mixed-mode fracture prediction in ductile material. In: 15th European conference on fracture, Stockholm, Sweden, August 2004]. A new criterion, by combining experimentation and numerical calculation, was developed in this work in order to predict the beginning of the crack growth. Second, in the case of cyclic loading, the crack growth path and crack grow rate are studied. A series of mixed-mode experiments on aluminium and steel specimens were carried out to analyse the effect of the mixed mode on the crack growth angle and the crack growth rate. On the basis of these experimental results, a fatigue crack growth model was proposed. The effect of the mixed mode on the crack growth rate is considered in this model. The numerical results of this model are in good agreement with the experimental results.     

Fracture of austenitic steel subject to a wide range of stress triaxiality ratios and crack deformation modes

The stress triaxiality ratio (hydrostatic pressure divided by von Mises equivalent stress) strongly affects the fracture behaviour of materials. Various fracture criteria take this effect into consideration in their effort to predict failure. The dependency of the fracture locus on the stress triaxiality ratio has to be investigated in order to evaluate these criteria and improve the understanding of ductile fracture.This was done by comparing the experimental results of austenitic steel specimens with a strong variation in their stress triaxiality ratios. The specimens had cracks with varying depths and crack tip deformation modes; tension, in-plane shear, and out-of-plane shear. The crack growth in fracture mechanics specimens was compared with the failure of standard testing specimens for tension, upsetting and torsion. By associating the experimental results with finite element simulations it was possible to compare the critical plastic equivalent strain and stress triaxiality ratio values at fracture. In the investigated triaxiality regime an exponential dependency of the fracture locus on the stress triaxiality ratio was found.     

Experimental crack propagation and failure analysis of the first stage compressor blade subjected to vibration

This paper presents results of experimental vibration tests of the helicopter turbo-engine compressor blades. The blades used in investigation were retired from maintenance under technical inspection of engine. Investigations were conducted for selected undamaged blades, without existence of preliminary cracks or corrosion pits. The blades during experiment were entered into transverse vibration. The crack propagation process was conducted in resonance condition. During the fatigue test, the growth of crack was monitored. In the second part of work, a nonlinear finite element method was utilized to determine the stress state of the blade during vibration. In this analysis a first mode of transverse vibration were considered. High maximum principal stress zone was found at the region of blade where the crack occurred.     

Crack propagation analyses with CTOA and cohesive model: Comparison and experimental validation

Two numerical models, namely an R-curve approach based on the crack tip opening angle (CTOA) and a cohesive model, are compared regarding their ability to predict ductile crack extension in thin aluminium sheets, which can be simulated under the assumption of plane stress. The experimental database is presented, the measuring techniques for the various quantities (optically and with clip gauges) are shown and the identification and validation of the respective model parameters are explained. A general concept for their identification is then derived for the case of thin walled structures under Mode I conditions.In order to investigate the performance of the models under different constraint conditions and the transferability of their parameters, C(T) specimens are used for parameter identification and M(T) specimens for validation. It is shown that for both models a single set of parameters describes the mechanical behaviour of both types of specimens. Cross-checking the two models, the crack tip opening angle is determined from the cohesive model calculations and compared with the experimental values.     

Some basic aspects of electromagnetic radiation during crack propagation in metals

Measurements of the electromagnetic radiation (EMR) emitted during crack propagation and fracture and the effect of modes of fracture, physical properties and high temperature on the characteristics of emitted EMR from metals have been discussed. It has been observed that all the three modes of fracture give rise to EMR emission; however, the relative amplitude in tearing mode is very low. A linear variation of EMR peak voltage with bond energy has been observed while frequency varies parabolically with bond energy. Both these curves indicate that no EMR emission or negligible EMR emission is expected in metals having bond energy <270 kJ/mole. EMR characteristics decrease with increase in lattice parameter. Higher tensile strength metals emit stronger EMR signals. Experiments conducted at high temperatures validate the prediction of Molotskii that an increase in specimen temperature should decrease the EMR frequency. One additional but important observation has been that while the EMR peak amplitude decreases with increase in temperature in steel, it increases with increase in temperature in copper.     

On a thermo-mechanical effect and criterion of crack propagation

A thermo-mechanical effect from partial conversion of fracture work into heat energy during crack propagation is considered with a simple mathematical model. It is assumed that the heat production zone in the vicinity of the crack tip is very small. Thus, the crack propagation process can be viewed as propagation of the crack in elastic material with a point thermal heat source fixed at the tip of the crack. This thermal heat source generates its own temperature and stress fields around the crack tip. As shown in this paper it also generates a negative stress intensity factor that specifies fracture mode I and has to be accounted for in the energetic fracture criterion. The model developed may help to explain many experimental observations such as the increase in the specific surface energy that accompanies an increase in the crack speed and why fracture mode I has a special role in crack propagation phenomena.     

Essential work of fracture analysis of the tearing of a ductile polymer film

The fracture behaviour of a 0.5 mm thick ethylene-propylene block copolymer, previously evaluated using the essential work of fracture method, has been analyzed again in more detail, using different plots, allowing the determination of the crack initiation displacement and stress. In such plots is evidenced that the specific essential work of fracture, w_e, corresponds to the energy just up to crack initiation value that can be related with J₀. Also, it has been found a novel relationship between the plastic term, βw_p and the crack initiation stress, σ_i.     

Environmentally-controlled non-equilibrium crack propagation in ceramics

A general framework is developed for environmentally-controlled non-equilibrium crack propagation and applied to ceramic materials that exhibit microstructurally-controlled fracture resistance variations. Increasing fracture resistance with crack length, arising from frictional interlocking of predominantly intergranular fracture surfaces, is modelled by the influence of a localized line force behind the crack tip. An indentation fracture mechanics analysis incorporates the fracture resistance variation to describe the inert strength of ceramic materials as a function of dominant flaw size. Non-equilibrium fracture is modelled as the competition between thermally-activated bond-rupture and bond-healing processes, in which the activation barriers are modified by the net mechanical energy release rate acting on a crack. The resulting dependence of crack velocity on mechanical energy release rate is used to describe the strength of ceramic materials as a function of applied stressing rate in a reactive environment. The deconvoluted crack velocity behavior allows both the macroscopic reactive environment fracture resistance and the atomistic lattice traps for fracture to be determined. An implication is that fracture resistance variations are more important in determining observed fracture behavior in reactive environments than in inert environments.     

Investigation of crack tunneling in ductile materials

Crack tunneling has been commonly observed in crack growth experiments on specimens made of ductile materials such as steel and aluminum alloys. The objective of this study is to investigate the crack tunneling phenomenon and study the effects of crack tunneling on the distribution of several mechanics parameters controlling ductile fracture. Three-dimensional (3D) elastic-plastic finite element analyses of stable tearing experiments involving tunneling fracture are carried out. Two model problems based on stable tearing experiments are considered. The first model problem involves a plate specimen containing a stationary, single-edge crack with a straight or tunneled crack front, under remote mode I loading. In the numerical analyses, the crack tip opening displacement, the von Mises effective stress, the mean stress, the stress constraint and the effective plastic strain around straight and tunneled crack fronts are obtained and compared. It is found that crack tunneling produces significant changes in the stress and deformation fields around the crack front. The second model problem involves a specimen containing a stably growing single-edge crack with a straight or tunneled crack front, under remote mode I loading. Crack growth events with a straight or tunneled crack front are simulated using the finite element method, and the effect of crack tunneling on the prediction of the load-crack-extension response based on a CTOD fracture criterion is investigated.     

Crack propagation toward a desired path by controlling the force direction

Controlling the crack propagation along a desired path has important applications in fabrication. We propose a method for extending a crack along a desired trajectory by controlling the direction of an applied external point force. Examples of crack propagation along arc and sinusoidal paths are illustrated, and verified through numerical simulations based on the extended finite element method (XFEM).     

Crack propagation in notched specimens of porous silicon carbide under cyclic loading

Notched specimens of porous silicon carbide with porosity 37% were fatigued under four‐point bending at frequencies of 30 and 0.3 Hz. The fatigue life expressed in terms of time was rather insensitive to the test frequency, while that expressed in terms of cycles was much shorter for the case of 0.3 Hz than for 30 Hz. A time‐dependent mechanism of stress corrosion cracking was mainly responsible for crack propagation, and stress cycling enhanced the crack‐propagation mechanism. The crack length was estimated from the change in compliance of the specimen. The crack‐propagation curve was divided into stages I and II. In stage I, the crack‐propagation rate decreased even though the applied stress intensity factor became larger with crack extension, and then turned to increase in stage II. The transition from stage I to II took place at a crack extension of around 0.8 mm. This anomalous behaviour is caused by crack‐tip shielding due to microcracking and asperity contact. Fractographic observations showed that the fracture path was along the binder phase between silicon carbide particles, or more precisely along the interface between particles and binders.     

Fracture initiation of geometrically scaled, notched three-point-bend bars of a low-alloy ferritic steel

The purpose of the experimental work reported in this contribution was to provide data that may serve for the development of scaling rules for ductile fracture at blunt notches. Bending experiments were performed with three sizes of geometrically scaled notched bend specimens of the ferritic pressure vessel material 20MnMoNi55, material number 1.6310 (heat number 69906) using carefully scaled supports, using geometrically similar U-notched bend bars with rectangular cross-sections and scaled blunt notches covering a scale range of 14. Fracture initiation was reliably detected by means of the dc potential drop technique. Comparison of the normalised load versus load-point-displacement curves revealed a significant size effect for the conditions of fracture initiation, with large specimens fracturing at smaller normalised displacements than smaller ones. The energy up to the initiation point normalised to the ligament can be linearly correlated with specimen size, while the energy normalised to the active volume (ligament size multiplied by notch width) consists of two terms: a hyperbolic decay term analogous to the initiation of crack extension in fracture mechanics and a constant term corresponding to the classical size independent plasticity theory. For the smallest specimens investigated the first term amounts to about 28% of the total volume specific work, for the largest specimens there is almost no contribution of the first term.     

Dislocation nucleation and propagation during thin film deposition under compression

In this paper, we study the nucleation of dislocations and their subsequent propagation, during thin film deposition, using the three-dimensional (3D) molecular dynamics (MD) method. Aiming to reveal the generic mechanisms, the case of tungsten on a substrate of the same material is investigated. The substrate is under uniaxial compression along the [1 1 1] direction, with the thermodynamically favored surface being horizontal. The simulation results indicate that the nucleation starts with a surface step where an atom is squeezed to the layer above, generating a half-dislocation loop at the surface. It may then either propagate into the film or become the bottom of a sessile dislocation loop. In the first case, the dislocation loop, having a Burgers vector on a (1 0 1) glide plane, propagates along the direction on the surface, and extends to about two atomic layers along the [1 1 1] direction. In the second case, the missing layer propagates along the [1 0 0] direction on the surface, extending to about four atomic layers along the [1 1 1] direction. In this case, the sessile dislocation has a Burgers vector on the plane (0 1 1).     

Interfacial fracture characteristic and crack propagation of thermal barrier coatings under tensile conditions at elevated temperatures

Thermal barrier coatings (TBCs) have been extensively used in aircraft engines for improved durability and performance for more than fifteen years. In this paper, thermal barrier coating system with plasma sprayed zirconia bonded by a MCrAlY layer to SUS304 stainless steel substrate was performed under tensile tests at 1000°C. The crack nucleation, propagation behavior of the ceramic coatings in as received and oxidized conditions were observed by high-performance camera and discussed in detail. The relationship of the transverse crack numbers in the ceramic coating and tensile strain was recorded and used to describe crack propagation mechanism of thermal barrier coatings. It was found that the fracture/spallation locations of air plasma sprayed (APS) thermal barrier coating system mainly located within the ceramic coating close to the bond coat interface by scanning electron microscope (SEM) and energy dispersive X-Ray (EDX). The energy release rate and interface fracture toughness of APS TBCs system were evaluated by the aid of Suo–Hutchinson model. The calculations revealed that the energy release rate and fracture toughness ranged, respectively, from 22.15 J m⁻² to 37.8 J m⁻² and from 0.9 MPa m^1/2 to 1.5 MPa m^1/2. The results agree well with other experimental results.