Constraint effects on ductile fracture processes near a notch tip under mixed-mode loading

In this work, the effect of constraint on ductile fracture process of microvoid growth and coalescence near a notch tip in a ductile material under mode I and mixed mode loading (involving modes I and II) is investigated. To this end, two sets of finite element simulations are carried out under two-dimensional plane strain conditions. In the first set, a modified boundary layer formulation is employed in which the mixed mode elastic K–T field is prescribed as remote boundary conditions. Several analyses are carried out corresponding to different values of T-stress and remote elastic mode-mixity. Next, ductile four point bend specimens subjected to mode I and mixed mode loading are considered. In both sets of simulations, the interaction between a notch tip and a pre-nucleated hole ahead of it is modelled. The background material is represented by the Gurson constitutive model and micro-void nucleation at uniformly distributed small scale particles is also taken into account. The accumulation of matrix plastic strain and porosity in the ligament between the notch tip and the hole as well as the growth of the hole are studied. Finally, the effect of crack tip constraint on the relationship between the fracture toughness and mode mixity is examined.     

Numerical simulations of fracture initiation in ductile solids under mode I, dynamic loading

In this paper, an overview of some recent computational studies by the authors on ductile crack initiation under mode I, dynamic loading is presented. In these studies, a large deformation finite element procedure is employed along with the viscoplastic version of the Gurson constitutive model that accounts for the micro-mechanical processes of void nucleation, growth and coalescence. A three-point bend fracture specimen subjected to impact, and a single edge notched specimen loaded by a tensile stress pulse are analysed. Several loading rates are simulated by varying the impact speed or the rise time and magnitude of the stress pulse. A simple model involving a semi-circular notch with a pre-nucleated circular hole situated ahead of it is considered. The growth of the hole and its interaction with the notch tip, which leads to plastic strain and porosity localization in the ligament connecting them, is simulated. The role of strain-rate dependence on ductile crack initiation at high loading rates, and the specimen geometry effect on the variation of dynamic fracture toughness with loading rate are investigated.     

A numerical investigation of ductile fracture initiation in a high-strength low-alloy steel

In this work, static and drop-weight impact experiments, which have been conducted using three-point bend fracture specimens of a high-strength low-alloy steel, are analysed by performing finite-element simulations. The Gurson constitutive model that accounts for the ductile failure mechanisms of microvoid nucleation, growth and coalescence is employed within the framework of a finite deformation plasticity theory. Two populations of second-phase particles are considered, including large inclusions which initiate voids at an early stage and small particles which require large strains to nucleate voids. The most important objective of the work is to assess quantitatively the effects of material inertia, strain rate sensitivity and local adiabatic temperature rise (due to conversion of plastic work into heat) on dynamic ductile crack initiation. This is accomplished by comparing the evolution histories of void volume fraction near the notch tip in the static analysis with the dynamic analyses. The results indicate that increased strain hardening caused by strain rate sensitivity, which becomes important under dynamic loading, plays a benign role in considerably slowing down the void growth rate near the notch tip. This is partially opposed by thermal softening caused by adiabatic heating near the notch tip.     

A finite element analysis of dynamic fracture initiation by ductile failure mechanisms in a 4340 steel

In some recent dropweight impact experiments [5] with pre-notched bend specimens of 4340 steel, it was observed that considerable crack tunneling occurred in the interior of the specimen prior to gross fracture initiation on the free surfaces. The final failure of the side ligaments happened because of shear lip formation. The tunneled region is characterized by a flat, fibrous fracture surface. In this paper, the experiments of [5] (corresponding to 5 m/s impact speed) are analyzed using a plane strain, dynamic finite element procedure. The Gurson constitutive model that accounts for the ductile failure mechanisms of micro-void nucleation, growth and coalescence is employed. The time at which incipient failure was observed near the notch tip in this computation, and the value of the dynamic J-integral, _J d, at this time, compare reasonably well with experiments. This investigation shows that J-controlled stress and deformation fields are established near the notch tip whenever J _d , increases with time. Also, it is found that the evolution of micro-mechanical quantities near the notch root can be correlated with the time variation of J _d .The strain rate and the adiabatic temperature rise experienced at the notch root are examined. Finally, spatial variations of stresses and deformations are analyzed in detail.     

A comparative study of dynamic, ductile fracture initiation in two specimen configurations

In this work a single edge notched plate (SEN(T)) subjected to a tensile stress pulse is analysed, using a 2D plane strain dynamic finite element procedure. The interaction of the notch with a pre-nucleated hole ahead of it is examined. The background material is modelled by the Gurson constitutive law and ductile failure by microvoid coalescence in the ligament connecting the notch and the hole is simulated. Both rate independent and rate dependent material behaviour is considered. The notch tip region is subjected to a range of loading rates J by varying the peak value and the rise time of the applied stress pulse. The results obtained from these simulations are compared with a three point bend (TPB) specimen subjected to impact loading analysed in an earlier work [3]. The variation of J at fracture initiation, J _c, with average loading rate J is obtained from the finite element simulations. It is found that the functional relationship between J _c and J is fairly independent of the specimen geometry and is only dependent on material behaviour.     

Numerical analysis of ductile failure of undermatched interleaf in tension

Ductile failure of an interleaf tension specimen consisting of a metal interleaf bonded between two elastic substrates, with a crack located in the centre of the metal, is studied by means of detailed finite element (FE) analyses. The rate-independent version of the Gurson model is used. This accounts for ductile failure mechanisms of micro-void nucleation, growth and coalescence within the framework of a finite deformation plasticity theory. Also, the rapid evolution of void density due to coalescence, which leads to ultimate failure, is considered. The effect of the interleaf thickness on failure (crack initiation and limited amount of crack growth) is investigated. The results show that the interleaf thickness affects crack initiation only slightly. For all specimens considered, crack initiation takes place at the crack tip. However, after crack initiation, the interleaf thickness affects stress and strain distributions significantly. Reducing the interleaf thickness significantly increases the load-carrying capacity. Moreover, reducing the interleaf thickness increases the maximum hydrostatic stress in the interleaf, which is no longer developed at the crack tip but at a distance far away from the crack tip. The resulting fracture toughness thus decreases as the interleaf thickness decreases. The shielding of the crack tip due to constrained plasticity is observed at higher load levels for interleaf specimens. This revised version was published online in August 2006 with corrections to the Cover Date.     

A critical shear displacement criterion for ductile–brittle transition under mixed mode I and II loading

Abstract

Micromechanisms producing ductile and brittle damage operate in parallel at a crack tip. The dominant mode of failure depends upon which of the two (ductile or brittle) damage parameters first reaches its critical value. This has been shown by a study of ductile–brittle transition behaviour in HY100 steel under mixed mode I and II loading. The transition from ductile to brittle behaviour in HY100 steel was found to be affected by mixed mode I and II ratio (ratio of imposed tensile and shear loading) in a manner such that with increasing shear the transition temperature decreased. In the present paper, a criterion is proposed based on the shear strain ahead of a notch tip, to predict the fracture behaviour at any given temperature and mixed mode ratio.     

Effect of pre-strain on fracture toughness of ductile structural steels under static and dynamic loading

The ductile fracture process consists of void nucleation, growth and coalescence. The whole ductile process can be divided into two successive steps: (I) the initial state to void nucleation, followed by (II) void growth up to void coalescence. Based on this suggestion, resistance to ductile fracture could be divided into the resistance to stage I and stage II, and accordingly the whole fracture toughness could be regarded to be due to contributions from stages I and II. The fracture toughness contributed from the two steps is, respectively, denoted as void nucleation-contributed fracture toughness and void growth-contributed fracture toughness. The effect of plastic pre-strain on the fracture toughness of ductile structural steels under static and dynamic loading (4.9 m/s) within the ductile fracture range was evaluated by summing contributions due to void nucleation-contributed and void growth-contributed fracture toughness. The effect of strain rate on fracture toughness was also investigated by the same means. The results show that both plastic pre-strain and high-speed loading decrease the void nucleation-contributed fracture toughness while their effects on the void growth-contributed fracture toughness depend on the variations in strength and ductility. Moreover, fracture toughness of structural steels generally decreases with increasing strain rate.     

Dynamic ductile crack growth and transition to cleavage – a cell model approach

The fracture behavior of ferritic steel in the transition regime is controlled by the competition between ductile tearing and cleavage. Many test specimens that failed by catastrophic cleavage showed significant amounts of ductile tearing prior to cleavage fracture. The transition from ductile tearing to cleavage has been attributed to the increase in constraint and sampling volume associated with ductile crack growth. This work examines the role of dynamic ductile crack growth on the fracture mode transition by way of a cell model of the material. The cell model incorporates the effects of stress triaxiality and strain rate on material failure characteristics of hole growth and coalescence. Loading rate and microstructure effects on the stress fields that evolve with rapid (ductile) crack growth are systematically studied. The stress fields are employed to compute the Weibull stress which provides probability estimates for the susceptibility to cleavage fracture. A center-cracked panel subjected to remote tension is the model problem under study. The computational model uses an elastic-viscoplastic constitutive relation which incorporates enhanced strain rate hardening at high strain rates. Adiabatic heating due to plastic dissipation and the resulting thermal softening are also accounted for. Under dynamically high loading rate, our model shows the crack speed achieves its peak value soon after crack initiation and quickly falls off to slower speeds with further crack growth. Remarkably, the Weibull stress follows a similar pattern which suggests that the transition to the cleavage fracture is most likely to occur, if at all, at the peak speed of ductile crack growth. Key words: Dynamic fracture, ductile tearing, crack growth, transition regime, cleavage fracture, cell model, finite element.     

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.     

Effect of lattice orientation on crack tip constraint in ductile single crystals

In this work, the effect of lattice orientation on the fields prevailing near a notch tip is investigated pertaining to various constraint levels in FCC single crystals. A modified boundary layer formulation is employed and numerical solutions under mode I, plane strain conditions are generated by assuming an elastic–perfectly plastic FCC single crystal. The analysis is carried out corresponding to different lattice orientations with respect to the notch line. It is found that the near‐tip deformation field, especially the development of kink or slip shear bands is sensitive to the constraint level. The stress distribution and the size and shape of the plastic zone near the notch tip are also strongly influenced by the level of T ‐stress. The present results clearly establish that ductile single crystal fracture geometries would progressively lose crack tip constraint as the T ‐stress becomes more negative irrespective of lattice orientation. Also, the near‐tip field for a range of constraint levels can be characterized by two‐parameters such as K–T or J–Q as in isotropic plastic solids.     

Thickness effect on crack tip deformation at fracture

The crack tip deformation at the onset of surface crack growth for four single edge cracked specimens having four different thicknesses were studied. The specimens were made of the ductile and tough HY-80 steel. The thickness contraction in the crack tip region and the tensile strain in the direction of load were measured. The crack tip necking-in acts like a notch. The depths, the root radii, and the angle changes of the necking-in notches were measured. The results indicated that the near tip strain can be used as a fracture criterion of ductile and tough materials. It was also found that the fracture strengths of the cracked specimens can be correlated with the tensile ductilities measured with Clausing specimens.     

A three-dimensional numerical investigation of fracture initiation by ductile failure mechanisms in a 4340 steel

Fracture initiation in ductile metal plates occurs due to substantial tunneling of the crack in the interior of the specimen followed by final failure of side ligaments by shear lip formation. The tunneled region is characterized by a flat, fibrous fracture surface. This phenomenon is clearly exhibited in a recent experimental investigation [8] performed on pre-notched plates of a ductile heat treatment of 4340 carbon steel. Experimental evidence obtained in [8] suggests that tunneling begins at an average value of J which is significantly lower than the J value at which gross initiation is observed on the free surface. In the present work, fracture initiation in the 4340 steel specimens used in [8] is analyzed by performing a 3-dimensional numerical simulation. A damage accumulation model that accounts for the ductile failure mechanisms of void nucleation, growth, and void coalescence is employed. Results indicate that incipient Cmaterial failure at the center-plane of the 3-dimensional specimen is predicted quite accurately by this computation. Also, good agreement between results obtained at the center-plane of the 3-dimensional specimen and a plane strain analysis, suggests that a local definition of J can be used to characterize fracture initiation in the center-plane of the specimen. Finally, radial and thickness variations of the stress and porosity fields are examined with view of understanding the subsequent propagation of the failure zone.     

Mode II delamination failure mechanisms of polymer matrix composites

The failure process of mode II delamination fracture is studied on the basis of the microscopic matrix failure modes (microcracks and hackles) as well as fracture mechanics principles. The crack tip matrix stresses leading to delamination is analysed by examining an adhesive bond with a crack analogous to a delamination crack in the resin layer of a composite. Such crack tip stresses induce matrix microcracks involving two major events: (a) single microcrack initiation and (b) development of multiple microcracks with regular spacing. The microcrack initiation shear stress τ* is found by the use of fracture mechanics to be related to certain resin properties (shear modulus G and mode I fracture toughness GIC) and microcrack length of the order of the resin layer thickness t (related to resin content). The more or less regular microcrack spacing S deduced from shear lag considerations can be related to resin properties GIC, G, τy (resin yield strength) and t. The multiple microcracks reduce the effective resin modulus and strongly affect the subsequent microcrack coalescence process. As a result of the detailed analysis of the failure process, mode II laminate fracture toughness GIIC can be quantitatively expressed as a function of resin GIC and (τ2y/G). The failure process modelled is used to interpret the mode II delamination behaviour of several carbon/epoxy systems studied here and that reported in the literature. This study reveals the critical importance of resin fracture (GIC related) and deformation (yielding) mechanisms in controlling mode II delamination resistance of laminated composites. This revised version was published online in November 2006 with corrections to the Cover Date.     

Fracture Criteria for Automobile Crashworthiness Simulation of Wrought Aluminium Alloy Components

In automobile crashworthiness simulation, the prediction of plastic deformation and fracture of each significant, single component is critical to correctly represent the transient energy absorption through the car structure. There is currently a need, in the commercial FEM community, for validated material fracture models which adequately represent this phenomenon. The aim of this paper is to compare and to validate existing numerical approaches to predict failure with test data. All studies presented in this paper were carried out on aluminium wrought alloys: AlMgSi1.F31 and AlMgSiCu‐T6. A viscoplastic material law, whose parameters are derived from uniaxial tensile and compression tests at various strain rates, is developed and presented herein. Fundamental ductile fracture mechanisms such as void nucleation, void growth, and void coalescence as well as shear band fracture are present in the tested samples and taken into consideration in the development of the fracture model. Two approaches to the prediction of fracture initiation are compared. The first is based on failure curves expressed by instantaneous macroscopic stresses and strains (i. e. maximum equivalent plastic strain vs. stress triaxiality). The second approach is based on the modified Gurson model and uses state variables at the mesoscopic scale (i. e. critical void volume fraction). Notched tensile specimens with varying notch radii and axisymmetric shear specimens were used to produce ductile fractures and shear band fractures at different stress states. The critical macroscopic and mesoscopic damage values at the fracture initiation locations were evaluated using FEM simulations of the different specimens. The derived fracture criteria (macroscopic and mesoscopic) were applied to crashworthiness experiments with real components. The quality of the prediction on component level is discussed for both types of criteria.     

Locally enhanced Voronoi cell finite element model (LE‐VCFEM) for simulating evolving fracture in ductile microstructures containing inclusions

Ductile heterogeneous materials such as cast aluminum alloys undergo catastrophic failure that initiates with particle fragmentation, which evolves with void growth and coalescence in localized bands of intense plastic deformation and strain softening. The Voronoi cell finite element model (VCFEM), based on the assumed stress hybrid formulation, is unable to account for plastic strain‐induced softening. To overcome this shortcoming of material softening due to plastic strain localization, this study introduces a locally enhanced VCFEM (LE‐VCFEM) for modeling the very complex phenomenon of ductile failure in heterogeneous metals and alloys. In LE‐VCFEM, finite deformation displacement elements are adaptively added to regions of localization in the otherwise assumed stress‐based hybrid Voronoi cell finite element to locally enhance modeling capabilities for ductile fracture. Adaptive h‐refinement is used for the displacement elements to improve accuracy. Damage initiation by particle cracking is triggered by a Weibull model. The nonlocal Gurson–Tvergaard–Needleman model of porous plasticity is implemented in LE‐VCFEM to model matrix cracking. An iterative strain update algorithm is used for the displacement elements. The LE‐VCFEM code is validated by comparing with results of conventional FE codes and experiments with real materials. The effect of various microstructural morphological characteristics is also investigated. Copyright © 2008 John Wiley & Sons, Ltd.     

Ductile fracture by multiple void growth and interaction ahead of a notch tip in polycrystalline plastic solids

The objectives of this paper are to study the effects of plastic anisotropy and evolution in crystallographic texture with deformation on the ductile fracture behaviour of polycrystalline solids. To this end, numerical simulations of multiple void growth and interaction ahead of a notch tip are performed under mode I, plane strain, small scale yielding conditions using two approaches. The first approach is based on the Hill yield theory, while the second employs crystal plasticity constitutive equations and a Taylor-type homogenization in order to represent the ductile polycrystalline solid. The initial textures pertaining to continuous cast Al–Mg AA5754 sheets in recrystallized and cold rolled conditions are considered. The former is nearly-isotropic, while the latter displays pronounced anisotropy. The results indicate distinct changes in texture in the ligaments bridging the voids ahead of the notch tip with increase in load level which gives rise to retardation in porosity evolution and increase in tearing resistance for both materials.     

The transition from ductile to slow crack growth failure in a copolymer of polyethylene

The failures of ethylene-hexene copolymer single-edge notch tensile specimens were observed under a constant tensile load. The notch opening was measured against time over a range of stress. Three failure modes were observed: ductile, brittle and transitional. The microscopic changes at the notch tip were correlated with each of the modes of failure. Early in the test the ultimate mode of failure can be predicted from the microstructural changes in the notch. In the transition region, the lifetime increases as the stress increases because the blunting of the notch offsets the effect of the applied stress-stress field. The ductile failure is controlled by the macroscopic creep behaviour and the brittle failure occurs by slow crack growth that starts at a craze.     

A finite element analysis of fracture initiation in ductile/brittle periodically layered composites

A near-tip plane strain finite element analysis of a crack terminating at and normal to the interface in a laminate consisting of alternate brittle and ductile layers is conducted under mode-I loading. The studies are carried out for a system representing steel/alumina composite laminate. The Gurson constitutive model, which accounts for the ductile failure mechanisms of microvoid nucleation, growth and coalescence, is employed within the framework of small deformation plasticity theory. Evolution of plastic zone and damage in the ductile layer is monitored with increasing load. High plastic strain localization and microvoid damage accumulation are found to occur along the brittle/ductile interface at the crack-tip. Fracture initiation in the ductile phase is predicted and the conditions for crack renucleation in the brittle layer ahead of the crack are established for the system under consideration. Ductile fracture initiation has been found to occur before plasticity spreads in multiple ductile layers. Effects of material mismatch and yield strength on the plastic zone evolution are briefly discussed. This revised version was published online in August 2006 with corrections to the Cover Date.