Microstructural effects on ductile fracture in heterogeneous materials. Part I: Sensitivity analysis with LE-VCFEM

Ductile failure of heterogeneous materials, such as cast aluminum alloys and discretely reinforced aluminums or DRA’s, initiates with cracking, fragmentation or interface separation of inclusions, that is followed by propagation in the matrix by a ductile mechanism of void nucleation and growth. Damage localizes in bands of intense plastic deformation between inclusions and coalesces into a macroscopic crack leading to overall failure. Ductile fracture is very sensitive to the local variations of the microstructure morphology. This is the first of a two part paper on the effect of microstructural morphology and properties on the ductile fracture in heterogeneous ductile materials. In this paper the locally enhanced Voronoi cell finite element method (LE-VCFEM) for rate-dependent porous elastic–viscoplastic materials is used to investigate the sensitivity of strain to failure to loading rates, microstructural morphology and material properties. A model is also proposed for strain to failure, incorporating the effects of important morphological parameters.     

Deterministic and stochastic analyses of fracture processes in a brittle microstructure system

Variations in constituent properties, phase morphology, and phase distribution cause deformation and failure at the microstructural level to be inherently stochastic. This paper focuses on the stochasticity of fracture processes that arises as a result of measurement uncertainties in the properties of the constituents in the heterogeneous microstructures of an Al₂O₃/TiB₂ ceramic composite system. Basic postulate here is that for a microstructure local material properties vary around their macroscopically measured value with the macroscopically measured value being the mean of the variation. A micromechanical cohesive finite element framework with explicit resolution of arbitrary fracture patterns and arbitrary microstructural morphologies is used in the analyses carried out in this paper. The randomness in the constituent properties at any given point in the microstructure is specified relative to the local mean values of the corresponding properties. A deterministic analysis and a stochastic analysis are carried out simultaneously. The combination of determinism and stochasticity is achieved by integrating a perturbation analysis of the influence of stochastic property variations around their mean values and a deterministic analysis for the microstructure with the mean values of the constituent properties. Calculations are carried out for actual and idealized microstructures of the Al₂O₃/TiB₂ material system. Calculations focus on analyzing the fracture response variation with varying levels of variation of material properties for a particular microstructural morphology as well as on analyzing the variations in fracture response with variations in microstructural morphology. It is observed that microstructural morphology is intricately linked to the variations in fracture response when material properties have stochastic origin. A microstructure less prone to fracture shows higher variations in fracture response when compared to the one which offers least resistance to the crack propagation. In addition, for a particular microstructural morphology, the levels of variations in the crack surface area generated and the variations in the energy release rate are of the same order as the levels of variations in constituent properties. The observations support the conclusion that a material designer needs to make conservative estimates for a material’s performance if its microstructural construction imparts uncertainty to local material properties.     

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.     

The Theory of Critical Distances to estimate the static strength of notched samples of Al6082 loaded in combined tension and torsion. Part I: Material cracking behaviour

The present paper is the first of a two-part series reporting an experimental and theoretical study of the fracture of circumferentially notched samples of a commercial aluminium alloy, i.e. Al6082, subjected to tension, torsion and mixed tension/torsion loading. The overall aim of the work was to investigate the use of a particular method of failure prediction, known as the Theory of Critical Distances. This first part reports the experimental data - load-deflection curves and observed material failure modes - and discusses the consequences of these findings for the development of the theory, which is covered in the second part. It was observed that relatively blunt notches loaded in tension failed by a conventional ductile fracture mode similar to plain (unnotched) specimens. However, in tensile specimens containing sharp notches, failure occurred via the initiation, stable propagation and, finally, unstable propagation, of circumferential ring cracks. Under torsional loading, and independent of the notch root radius, static failures of the tested samples always occurred by the formation and stable propagation of ring cracks. Under mixed-mode loading there was a gradual transition between the ductile and brittle modes and between stable and unstable cracking. For all types of loading, it was observed that crack initiation always coincided with peak loading conditions, and that cracks invariably grew on the plane perpendicular to the specimen’s longitudinal axis.     

Development of the Local Approach to Fracture over the Past 25 years: Theory and Applications

This review paper is devoted to the local approach to fracture (LAF) for the prediction of the fracture toughness of structural steels. The LAF has been considerably developed over the past two decades, not only to provide a better understanding of the fracture behaviour of materials, in particular the failure micromechanisms, but also to deal with loading conditions which cannot easily be handled with the conventional linear elastic fracture mechanics and elastic–plastic fracture mechanics global approaches. The bases of this relatively newly developed methodology are first presented. Both ductile rupture and brittle cleavage fracture micromechanisms are considered. The ductile-to-brittle transition observed in ferritic steels is also briefly reviewed. Two types of LAF methods are presented: (i) those assuming that the material behaviour is not affected by damage (e.g. cleavage fracture), (ii) those using a coupling effect between damage and constitutive equations (e.g. ductile fracture). The micromechanisms of brittle and ductile fracture investigated in elementary volume elements are briefly presented. The emphasis is laid on cleavage fracture in ferritic steels. The role of second phase particles (carbides or inclusions) and grain boundaries is more thoroughly discussed. The distinction between nucleation and growth controlled fracture is made. Recent developments in the theory of cleavage fracture incorporating both the effect of stress state and that of plastic strain are presented. These theoretical results are applied to the crack tip situation to predict the fracture toughness. It is shown that the ductile-to-brittle transition curve can reasonably be well predicted using the LAF approach. Additional applications of the LAF approach methods are also shown, including: (i) the effect of loading rate and prestressing; (ii) the influence of residual stresses in welds; (iii) the mismatch effects in welds; (iv) the warm-prestressing effect. An attempt is also made to delineate research areas where large improvements should be made for a better understanding of the failure behaviour of structural materials.     

Mechanical properties and microstructure of friction stir welded tailor-made blanks

This paper studies the microstructural features and mechanical properties of friction stir welds with dissimilar alloys and different thicknesses. The welds are produced in five different thickness/material combinations from 2024-T3 and 7075-T6 sheets with different thicknesses. A parametric study is conducted to optimize the welding parameters such that the different configurations can be compared. The paper is divided into two chapters: microstructural features and mechanical properties. In the first chapter, a study of the chemical composition and microstructure of the welds shows that a narrow chemical mixing zone is present in the dissimilar-alloy welds and that the stirring zone embodies the union rings and exhibits heterogeneous texture for most configurations. Study of the hardness, tensile properties and fracture surfaces in the second chapter shows that an asymmetric softened region, which is harder at the advancing side and extends more into the retreating side, is formed in the stirring zone and that the mechanical properties decrease as the thickness ratio increases. The fracture was partially ductile and partially brittle for all configurations.     

On continuum models of ductile fracture

Several fracture criteria are reviewed with respect to ductile fracture. It is suggested that both critical crack-tip displacement, 2V _c ^*, and critical fracture strain,∃ ^*, criteria may describe the fracture of a ductile second phase rod in a ductile matrix. As a first approximation, this is experimentally verified by observations of ductile stainless steel fibres fracturing in an age-hardened aluminium matrix. For 0.05, 0.10 and 0.20 volume fraction composites, the average fracture strains are calculated to be 1.15 as compared to a measured average of 0.93 while the average critical crack-tip displacement is calculated to be 0.50 mm as compared to an “observed” average of 0.40 mm. The statistical variation in the fracture strain was not sufficiently small to allow any choice between these proposed criteria. In fact, both the experimental and theoretical evidence point to the equivalency of these criteria as given by 2V _c ^*=π/^*∃^* where /^* is the microstructural unit in front of the crack over which the strain is greater than or equal to∃ ^*.     

Modelling of nucleation and void growth in dynamic pressure loading, application to spall test on tantalum

Dynamic ductile fracture is a three stages process controlled by nucleation, growth and finally coalescence of voids. In the present work, a theoretical model, dedicated to nucleation and growth of voids during dynamic pressure loading, is developed. Initially, the material is free of voids but has potential sites for nucleation. A void nucleates from an existing site when the cavitation pressure p _c is reached. A Weibull probability law is used to describe the distribution of the cavitation pressure among potential nucleation sites. During the initial growth, the effect of material properties is essentially appearing through the magnitude of p _c. In the later stages, the matrix softening due to the increase of porosity has to be taken into account. In a first step, the response of a sphere made of dense matrix but containing a unique potential site, is investigated. When the applied loading is a pressure ramp, a closed form solution is derived for the evolution of the void that has nucleated from the existing site. The solution appears to be valid up to a porosity of 0.5. In a second part, the dynamic ductile fracture of a high-purity grade tantalum is simulated using the proposed model. Spall stresses for this tantalum are calculated and are in close agreement with experimental levels measured by Roy (2003, Ph.D. Thesis, Ecole Nationale Supérieure de Mécanique et d’Aéronautique, Université de Poitiers, France). Finally, a parametric study is performed to capture the influence of different parameters (mass density of the material, mean spacing between neighboring sites, distribution of nucleation sites...) on the evolution of damage.     

High-strength medium Mn quenching and partitioning steel with low yield ratio

ABSTRACT

A new microstructural design is proposed to develop a strong and ductile quenching and partitioning (Q&P) steel with low yield ratio. This steel has a heterogeneous dual phase microstructure which is developed by varying austenite thermal stability through Mn segregation. The heterogeneous microstructure contains large austenite grains which contribute to the low yield strength. The ultra-high tensile strength and good ductility are ascribed to the enhanced strain hardening behaviour resulted from the continuous transformation-induced plasticity (TRIP) effect. The present microstructural design enables a conventional medium Mn steel with high tensile strength, good ductility and low yield ratio, which promises easy forming and potential applications in automotive industries.

This paper is part of a Thematic Issue on Medium Manganese Steels.     

Numerical Simulation of Elastic Behaviour and Failure Processes in Heterogeneous Material

A general numerical approach is developed to model the elastic behaviours and failure processes of heterogeneous materials. The heterogeneous material body is assumed composed of a large number of convex polygon lattices with different phases. These phases are locally isotropic and elastic-brittle with the different lattices displaying variable material parameters and a Weibull-type statistical distribution. When the effective strain exceeds a local fracture criterion, the full lattice exhibits failure uniformly, and this is modelled by assuming a very small Young modulus value. An auto-select loading method is employed to model the failure process. The proposed hybrid approach is applied to plane stress problems with fracture patterns and effective load-displacement curves presented to illustrate the full failure process.     

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.     

An analysis of dynamic,ductile crack growth in a double edge cracked specimen

Dynamic crack growth is analysed numerically for a plane strain double edge cracked specimen subject to symmetric impulsive tensile loading at the two ends. The material behavior is described in terms of an elastic-viscoplastic constitutive model that accounts for ductile fracture by the nucleation and subsequent growth of voids to coalescence. Two populations of second phase particles are represented, including large inclusions or inclusion colonies with low strength, which result in large voids near the crack tip at an early stage, and small second phase particles, which require large strains before cavities nucleate. The crack growth velocities determined here are entirely based on the ductile failure predictions of the material model, and thus the present study is free from ad hoc assumptions regarding appropriate dynamic crack growth criteria. Adiabatic heating due to plastic dissipation and the resulting thermal softening are accounted for in the analyses. Different prescribed impact velocities, inclusion spacings and values of the inclusion nucleation stress are considered. Predictions for the dynamic crack growth behavior and for the time variation of crack tip characterizing parameters are obtained for each case analyzed.     

Analysis of mechanical properties and its associated fracture surfaces in dual‐phase austempered ductile iron

This work aims at evaluating the fracture surfaces of tensile samples taken from a new kind of ductile iron referred to as ‘dual‐phase Austempered Ductile Iron (ADI)’, a material composed of ausferrite (regular ADI microstructure) and free (or allotriomorphic) ferrite. The tensile fracture surface characteristics and tensile properties of eight dual‐phase ADI microstructures, containing different relative quantities of ferrite and ausferrite, were studied in an alloyed ductile cast iron. Additionally, samples with fully ferritic and fully ausferritic (ADI) matrices were produced to be used as reference. Ferritic–pearlitic ductile irons (DI) were evaluated as well. For dual‐phase ADI microstructures, when the amount of ausferrite increases, tensile strength, yield stress and hardness do so too. Interesting combinations of strength and elongation until failure were found. The mechanisms of fracture that characterise DI under static uniaxial loading at room temperature are nucleation, growth and coalescence of microvoids. The fracture surface of fully ferritic DI exhibited an irregular topography with dimples and large deformation of the nodular cavities, characteristic of ductile fracture. Microstructures with small percentages of ausferrite (less than 20%) yielded better mechanical properties in relation to fully ferritic matrices. These microstructures presented regions of quasi‐cleavage fracture around last‐to‐freeze zones, related to the presence of ausferrite in those areas. As the amount of ausferrite increased, a decrease in nodular cavities deformation and a flatter fracture surface topography were noticed, which were ascribed to a higher amount of quasi‐cleavage zones. By means of a special thermal cycle, microstructures with pearlitic matrices containing a continuous and well‐defined net of allotriomorphic ferrite, located at the grain boundaries of recrystallised austenite, were obtained. The results of the mechanical tests leading to these microstructures revealed a significant enhancement of mechanical properties with respect to completely pearlitic matrices. The topographies of the fracture surfaces revealed a flat aspect and slightly or undeformed nodular cavities, as a result of high amount of pearlite. Still isolated dimple patterns associated to ferritic regions were observed.     

Effect of strength mis-match and dynamic loading on ductile fracture initiation

It has been well known that ductile fracture of steels is accelerated by triaxial stresses. The characteristics of ductile crack initiation in steels are evaluated quantitatively using a two-parameter criterion based on equivalent plastic strain and stress triaxiality.The present study focuses on the effects of geometrical discontinuity, strength mis-match, which can elevate plastic constraint due to heterogeneous plastic straining, and loading rate on the critical condition for ductile fracture initiation using a two-parameter criterion. Fracture initiation testing has been conducted under static and dynamic loading using circumferentially notched round-bar specimens. In order to evaluate the stress/strain state in the specimens, especially under dynamic loading, a thermal elastic-plastic dynamic finite element (FE) analysis considering the temperature rise due to plastic deformation has been carried out.The tensile tests on specimens with an undermatching interlayer showed that the relationship between the critical equivalent plastic strain to initiate ductile fracture and stress triaxiality was equivalent to that obtained on homogeneous specimens under static loading. Moreover, the two-parameter criterion for ductile fracture initiation is shown to be independent of the loading rate. It was demonstrated that the critical global strain to initiate ductile fracture in specimens with strength mis-match under various loading rate can be estimated based on the local criterion, that is two-parameter criterion obtained on homogeneous specimens under static tension, by mean of FE-analysis taken into account accurately both strength mis-match and dynamic loading effects on stress/strain behaviors.     

Numerical simulations of hole growth and ductile fracture initiation under mixed-mode loading

Numerical simulations of ductile fracture initiation caused by the interaction between a notch tip and a nearby hole under mixed-mode loading involving modes I and II are performed. Attention is restricted to plane strain, small-scale yielding conditions. The Gurson constitutive model that accounts for the ductile failure mechanisms of micro-void nucleation, growth and coalescence is employed within the framework of a finite deformation plasticity theory. The failure of the ligament connecting the notch tip and the hole by either microvoid coalescence or by intense plastic strain localization is modelled. The effect of mode-mixity on the notch tip deformation, hole growth and the critical value of J at fracture initiation is examined. The dominant failure mechanism which is operative near the notch tip for various extents of mixity of modes I and II is identified.     

Key factors of stretch-flangeability of sheet materials

Stretch-flangeability evaluated using hole-expansion testing represents the ability of sheet materials to resist edge fracture during complex shape forming. Despite a property imperative for automotive part applications of advanced high-strength steels, factors governing stretch-flangeability are not yet well understood. In this study, the mechanical properties of a selected group of materials with different microstructures were investigated using tensile, fracture toughness, and hole-expansion tests to find the factor governing the stretch-flangeability that is universally applicable to a variety of metallic materials. It was found that the fracture toughness of materials, measured using the fracture initiation energy, is a universal factor governing stretch-flangeability. We verified that fracture toughness is the key factor governing stretch-flangeability, showing that the hole-expansion ratio could be well predicted using finite element analysis associated with a simple ductile damage model, without explicitly taking into account the microstructural complexity of each specimen. This validates the use of the fracture toughness as a key factor of stretch-flangeability.     

A method for modelling microstructural material discontinuities in a finite element analysis

A new method is proposed for studying the effects of various microstructural material discontinuities, within a body, in a finite element analysis. The material discontinuities are accounted for by introducing a transformation strain in those regions. This formulation leads to two matrix equations; the first corresponds to the finite element analysis of the body without material discontinuities, and the second accounts for the microstructure. An important feature of the new method is that the first equation is solved only once, then the second equation can be solved repetitively for different microstructures. Thus, it is possible to study the effect of different microstructures within the body without reanalysing the entire body. It is expected that this method will be particularly useful in materials research to study the mechanisms that occur in materials at the microstructural level. The transformation strain formulation is reviewed, and the matrix equations for the new method are derived. Several numerical examples are presented to illustrate the versatility of the new method.     

Towards Prediction of Failure in Ti‐6AI‐4V Aerospace Materials by Surface Observations

Abstract: This paper deals with the development of a methodology for the prediction of material failure in metallic aerospace alloys by evaluating changes in surface characteristics directly prior to unstable fatigue crack propagation. The study is based on in situ nondestructive characterisation of the depression zone ahead of the crack tip of fatigue‐pre‐cracked titanium alloy specimens subjected to static loading. A relationship between the surface characteristics of the deformation zone ahead of the crack and the stress intensity factor of the material was obtained. This relationship was common to a variety of microstructural conditions such as mill‐annealed and β‐annealed microstructures. Based on the analysis, prediction of the impending fracture in cracked samples of the material was enabled. The outcome of this study can be used for optimising the service life of structural components.     

A numerical investigation of porous titanium as orthopedic implant material

Porous titanium is being developed as an alternative orthopedic implant material to alleviate the inherent problems of bulk metallic implants by reducing the stiffness to be comparable to bone stiffness and allowing complete bone ingrowth. However, a porous microstructure is susceptible to local permanent plastic strain and residual stress under cyclic loading which reduces damage tolerance and therefore limits their application as orthopedic implants. The mechanical properties of porous titanium are governed by the microstructural configurations such as pore morphology, porosity, and bone ingrowth. To understand the influence of these features on performance, the macroscopic and microscopic responses of porous Ti are studied using three-dimensional finite element models. The models are generated based on simulated microstructures of experimental materials at porosities of 15%, 32% and 50%. The results show the effect of porosity and bone ingrowth on Young’s modulus, yield stress, and microscopic stress and strain distribution. Importantly, simulations predict that the bone ingrowth reduces the stress and strain localization under cyclic loading so significantly that it counteracts the concentration condition caused by the increased porosity of the structure.     

Microstructure,tensile properties and fracture behaviour of aluminium alloy 7150

A study has been made to understand the microstructure, tensile properties and fracture characteristics of aluminium alloy 7150. Detailed optical and transmission electron microscopical observations were used to analyse the intrinsic microstructural features of the alloy in the T77 condition. The alloy was deformed to failure over a range of strain rates in environments of 3.5% sodium chloride solution and laboratory air. The environment was found to have little influence on strength of the alloy. The strength only marginally increased with an increase in strain rate. However, for all strain rates, the ductility of the alloy degraded in the aggressive environment. The ratio of strain to failure in sodium chloride solution to that in laboratory air indicates that the alloy is only mildly susceptible to stress corrosion cracking. The fracture behaviour was different in the two environments. However, in a given environment the fracture behaviour was essentially the same. In the aggressive environment fracture was predominantly intergranular while fracture revealed a ductile transgranular failure in laboratory air. An attempt is made to discuss the kinetics of the fracture process in terms of competing mechanistic effects involving intrinsic microstructural features, matrix deformation characteristics, environment and strain rate.