Defect tolerance assessment of ARIANE 5 structures on the basis of damage mechanics material modelling

Damage mechanics based material models have been applied to establish fracture control procedures for the failure prediction of ARIANE 5 main structural components as the booster cases including welds, the main stage, and the upper stage cryogenic tank. The main goals of the damage mechanics based investigations were the accurate failure prediction, the clarification of dependency of fracture toughness on geometry, the calibration of analytical methods and the interpretation and optimisation of small scale fracture tests for material characterization and quality assurance.The results of these investigations allowed a failure prediction accuracy with analytical tools which is close to 3D numerical simulations. This could be demonstrated both with ductile (Gurson) and brittle (RKR) damage mechanics models.     

Measurement techniques for determination of ductile crack initiation on Charpy specimens

In the engineering practice it is of importance to know the effect of loading rate on the material behaviour including the fracture mechanics properties. Depending on the material behaviour under a given loading condition, different fracture mechanics parameters should be determined. The critical values of these parameters are usually related to the onset of crack initiation which can be determined easier in the case of brittle fracture. But in the case of ductile fracture additional measurement techniques are required. This paper presents some possibilities to characterise the fracture resistance against ductile fracture using instrumented impact testing. The magnetic emission technique will be introduced as a potential measurement method for determining the onset of ductile crack propagation in magnetizable metals.     

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.     

Microstructural effects on ductile fracture in heterogeneous materials. Part II: Applications to cast aluminum microstructures

This is the second of a two part paper aimed at investigating the effects of microstructural morphology, material properties and loading on rate-dependent ductile fracture of heterogeneous materials. The locally enhanced Voronoi cell finite element method (LE-VCFEM) is used for micromechanical analyses of deformation and failure in complex microstructural volume elements. The first part of this paper sequence evaluates the sensitivity of strain to failure of computer simulated microstructures to loading rate, microstructural morphology and material properties. In this second part, LE-VCFEM simulations of actual microstructures of a cast aluminum alloy micrograph are used to validate a strain to failure model developed in the first part. A method for identification of critical regions within a heterogeneous microstructure is also developed and validated using in-situ observations of a two-point bending test. The influence of applied strain rates on ductile fracture of micrograph-based complex microstructures is also investigated.     

Computational analysis of thin coating layer failure using a cohesive model and gradient plasticity

Thermal barrier coatings (TBC) are widely used to prevent transient high temperature attack and allow components high durability. Due to strong inhomogeneous material properties the TBC failure often initiates near the interface between the brittle oxide layer and the ductile substrate. A reliable prediction of the TBC failure requires detailed information about the crack tip field and the consequent fracture criteria. In the present paper both cohesive model and gradient plasticity are used to simulate the failure process and to study interdependence of the interface stress distribution with the specific fracture energies. Computations confirm that combination of the two models is able to simulate different failure mechanisms in the TBC system. The computational model has the potential to give a realistic prediction of the crack propagation process.     

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.     

Fracture surfaces and the associated failure mechanisms in ductile iron with different matrices and load bearing

Ductile iron (DI) is a family of cast alloys that covers a wide range of mechanical properties, depending on its matrix microstructure. For instance, ferritic matrices used in parts, such as automotive suspension components, demand high impact properties and ductility among some of their main requirements. On the other hand, pearlitic and martensitic matrices are used when hardness, strength and wear resistance are of particular concern. When it comes to very high strength parts, ausferritic matrices, typically austempered ductile iron (ADI), are widely used.DI has been employed to replace cast and forged steels in a large number of applications and its production has shown a sustained rate of growth over the last decades.Knowing about failure modes and fracture mechanisms associated to materials with the properties mentioned above is crucial, since they can be of great value for designers of mechanical components.This paper deals with the analysis of fracture surfaces of ductile cast iron generated under different conditions of load application, temperature and environments.The studies include the examination of fracture surfaces obtained by means of tensile tests, impact tests and by samples used to determine fracture toughness properties, where the zones of fatigue pre-crack and monotonic load condition were evaluated. A special case of ductile iron fracture is also examined.The study of the different surfaces permitted to establish patterns that contributed to unveil the fracture mechanisms of ductile iron with different matrices, nodule count, etc.     

Mechanistic fracture criteria for the failure of human cortical bone

A mechanistic understanding of fracture in human bone is critical to predicting fracture risk associated with age and disease. Despite extensive work, a mechanistic framework for describing how the microstructure affects the failure of bone is lacking. Although micromechanical models incorporating local failure criteria have been developed for metallic and ceramic materials, few such models exist for biological materials. In fact, there is no proof to support the widely held belief that fracture in bone is locally strain-controlled, as for example has been shown for ductile fracture in metallic materials. In the present study, we provide such evidence through a novel series of experiments involving a double-notch-bend geometry, designed to shed light on the nature of the critical failure events in bone. We examine how the propagating crack interacts with the bone microstructure to provide some mechanistic understanding of fracture and to define how properties vary with orientation. It was found that fracture in human cortical bone is consistent with strain-controlled failure, and the influence of microstructure can be described in terms of several toughening mechanisms. We provide estimates of the relative importance of these mechanisms, such as uncracked-ligament bridging.     

The Brittle Versus the Ductile Nature of Fracture Modes I and II

Failure surface orientations are determined for states of uniaxail tensile stress and shiar stree appropriate to fracture Modes I and II. The method uses a newly developed failure criterion along with the associated flow rule. The failure angles show a sharp demarcation between ductile and brittle material types. Only the brittle materials class show consistency and likely represents a shear localization effect rether than explicit fracture.     

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.     

Micromechanics modelling of ductile fracture in tensile specimens using computational cells

This study extends the computational cell framework to model ductile fracture behaviour in tensile specimens. In the computational cell model, ductile damage occurs through void growth and coalescence (by cell extinction) within a thin layer of material located well inside the fracture process zone for the ductile process. Laboratory testing of a high strength structural steel provides the experimental stress–strain data for round bar and circumferentially notched tensile specimens to calibrate the cell model parameters for the material. Numerical simulations employing the micromechanics model reproduce the essential features of the ductile behaviour for the tensile specimens, including the development of intense necking and void growth in the centre of the specimen cross section. The resulting methodology enables the detailed study of ductile failure in small‐scale tensile specimens.     

A probabilistic model for cleavage fracture with a length scale - Parameter estimation and predictions of growing crack experiments

A probabilistic model for the cumulative probability of failure by cleavage fracture was applied to experimental results where cleavage fracture was preceded by ductile crack growth. The model, introduced by Kroon and Faleskog [Kroon M, Faleskog J. A probabilistic model for cleavage fracture with a length scale - influence of material parameters and constraint. Int J Fract 2002;118:99-118], includes a non-local stress with an associated material related length scale, and it also includes a strain measure to account for the number of nucleated cleavage initiation sites. The experiments were performed on single edge cracked bend test specimens with three different crack lengths at the temperature 85 °C, which is in the upper transition region for the steel in question. The ductile rupture process is modelled using the cell model for nonlinear fracture mechanics. The original cleavage fracture model had to be modified in order to account for the substantial number of cleavage initiators being consumed by the ductile process. With this modification, the model was able to accurately capture the experimental failure probability distribution.     

Effect of thermal treatments on the fracture behaviour of notched polyethylene terephthalate ribbons

The application of different thermal treatment procedures to thin polyethylene terephthalate (PET) sheets yields to microstructures of different molecular weight/ degree of crystallinity combination. As a consequence, variations in the mechanical properties, especially the fracture properties and the particular fracture mechanisms occur. This is demonstrated in this paper by measurements of elastic modulus, maximum stress, failure initiation energy, and total work to fracture of notched PET-ribbons. Failure mechanisms analysed by the use of optical and scanning electron microscopy vary between highly ductile via semi-brittle after crazing, to absolute brittle at very low stresses. The results are summarized in terms of a three-dimensional failure energy map divided into regions of particular failure behaviour for particular molecular weight/ degree of crystallinity combination. In addition, the typical values of material strength, defined as the product of resistance to damage initiation (maximum stress) and crack propagation (total work to failure) are given for each region. The optimum fracture resistance was achieved for PET material with moderately low molecular weight and moderately high degree of crystallinity.