Numerical modelling of damage behaviour of laser-hybrid welds

The effect of laser-hybrid welds on deformation and failure behaviour of fracture mechanics specimens is investigated in order to provide quantitative prediction of damage tolerance and residual strength. The simulation of crack initiation and crack extension in hybrid welds is performed by applying GTN damage model. The identification of damage parameters requires combined numerical and experimental analyses. The tendency to crack path deviation during crack growth depends strongly on the constraint development at the interface between base and weld metal. In order to quantify the influence of local stress state on the crack path deviation, the initial crack location is varied. Finally, the results from fracture mechanics tests are compared to real component, beam-column-connection, with respect to fracture resistance.     

Homogenized mechanical behavior of composite micro-structures including micro-cracking and contact evolution

The aim of this paper is to study the effects of micro-cracking on the homogenized constitutive properties of elastic composite materials. To this end a novel micro-mechanical approach based on homogenization techniques and fracture mechanics concepts, is proposed and an original J-integral formulation is established for composite micro-structures. Accurate non-linear macroscopic constitutive laws are developed for a uniaxial and a shear macro-strain path by taking into account changes in micro-structural configuration owing to crack growth and crack face contact. Numerical results, carried out by coupling a finite element formulation and an interface model, are applied to a porous composite with edge cracks and a debonded short fiber-reinforced composite. The composite micro-structure is controlled by the macroscopic strain and the micro-to-macro transition, settled in a variational formulation, is obtained for three types of boundary conditions, i.e. linear displacements, uniform tractions and periodic fluctuations and anti-periodic tractions. The accuracy of the determined macroscopic constitutive properties to represent the failure characteristics of locally periodic defected composites is also investigated in terms of energy release rate predictions, by comparisons between a direct analysis and homogenization approaches. Results highlight the dependence of the macroscopic constitutive law for a micro-structure with evolving defects on both the macro-strain path and the type of boundary conditions and the capability of the proposed model to provide a failure model for a composite material undergoing micro-cracking and contact.     

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.     

Shear fracture tests of concrete

Symmetrically notched beam specimens of concrete and mortar, loaded near the notches by concentrated forces that produce a concentrated shear force zone, are tested to failure. The cracks do not propagate from the notches in the direction normal to the maximum principal stress but in a direction in which shear stresses dominate. Thus, the failure is due essentially to shear fracture (Mode II). The crack propagation direction seems to be governed by maximum energy release rate. Tests of geometrically similar specimens yield maximum loads which agree with the recently established size effect law for blunt fracture, previously verified for tensile fracture (Mode I). This further implies that the energy required for crack growth increases with the crack extension from the notch. The R-curve that describes this increase is determined from the size effect. The size effect also yields the shear fracture energy, which is found to be about 25-times larger than that for Mode I and to agree with the value predicted by the crack band model. The fracture specimen is simple to use but not perfect for shear fracture because the deformation has a symmetric component with a non zero normal stress across the crack plane. Nevertheless, these disturbing effects appear to be unimportant. The results are of interest for certain types of structures subjected to blast, impact, earthquake, and concentrated loads.     

On the use of embedded discontinuity elements with crack path continuity for mode-I and mixed-mode fracture

In this paper, strong discontinuities embedded in finite elements are used to model discrete cracking in quasi-brittle materials. Special attention is paid to (i) the constitutive models used to describe the localized behaviour of the discontinuities, (ii) the enforcement of the continuity of the crack path and (iii) mixed-mode crack propagation. Different constitutive relations are adopted to describe the localized behaviour of the discontinuities, namely two damage laws and one plasticity law. A numerical algorithm is introduced to enforce the continuity of the crack path. In the examples studied, an objective dissipation of energy with respect to the mesh is found. Examples of mode-I and mixed-mode crack propagation are presented, namely a double notch tensile test and a single-edge notched beam subjected to shear. In the former case different crack patterns are obtained depending on the notch offset; in the latter case special emphasis is given to the effect of shear on the global structural response. In particular, both the peak load and the softening response of the structure are related to the amount of shear tractions allowed to develop between crack faces. The results obtained are compared to experimental results. As a general conclusion, it is found that crack path continuity allows for the development of crack patterns similar to those found in experiments, even when reasonably coarse meshes are used.     

Finite element simulations of crack propagation in functionally graded materials under flexural loading

Cracks in stepped and continuously graded material specimens under flexural loading were investigated via finite element analysis. Calculation of mechanical energy release rates and propagation angles with crack-opening displacement correlation and the local symmetry (K_II = 0) criterion, respectively, provided results most efficiently and accurately, as compared with compliance and J-integral approaches and other deflection criteria. A routine was developed for automatic crack extension and remeshing, enabling simulation of incremental crack propagation. Effects of gradient profile and crack geometry on crack-tip stresses and crack propagation path are examined, and implications of these for optimal design of graded components against failure by fast fracture are discussed.     

The model of the residual life time estimation of tribojoint elements by formation criteria of the typical contact fatigue damages

A two-dimensional theoretical model is proposed for investigation of the fracture processes and assessing residual contact durability of solids subjected to cyclic contact. The model is based on the step-by-step calculation of fatigue crack propagation paths in the contact region which includes the criteria of local fracture of materials under complex stress–strain state, characteristics of fatigue crack growth resistance of materials and also presupposes the possible change of fracture mechanisms (transversal shear – normal opening fracture mechanisms). Within the frames of the model the peculiarities of formation of such typical contact fatigue damages like pits, spalls, squat (“dark spot”) and cracking (“checks”) in rolling bodies and edge cracks growth in the elements of fretting couples under conditions of sliding/sticking between them are investigated. Examples of assessing the life time by damages formation (pitting and spalling) in the contact region are presented.     

A STUDY ON FATIGUE CRACK GROWTH UNDER OUT-OF-PHASE COMBINED LOADINGS

Abstract— Fatigue tests were performed on thin-walled tubular specimens of S45C steel under tension-compression, pure torsion, in-phase and out-of-phase axial-torsional loadings. The relationship between cracking behaviour and stress components on the crack plane was investigated. Measurement of microcrack density showed that microcracking was governed predominantly by the shear stress amplitude acting on the crack plane for all loading conditions. The failure crack was formed by coalescence of many cracks initiated near the maximum shear planes. The cracks grew turning their orientation to the direction perpendicular to the maximum normal stress. The transition of crack orientation occurred at relatively longer crack lengths at a higher stress ratio. The crack growth behaviour for all loading modes can be correlated using an equivalent strain intensity parameter based on shear and normal strains on the crack plane.     

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.     

Numerical simulation of reinforced concrete beams with different shear reinforcements under dynamic impact loads

The behavior of concrete/reinforced concrete structures is strongly influenced by the loading rate. Reinforced concrete structural members subjected to impact loads behave quite differently as compared to the same subjected to quasi-static loading. This difference is attributed to the strain-rate influence on strength, stiffness, and ductility as well as to the activation of inertia forces. These influences are clearly demonstrated in experiments. Moreover, for concrete structures, which exhibit damage and fracture phenomena, the failure mode and cracking pattern depend significantly on loading rate. In general, there is a tendency that with the increase of loading rate the failure mode changes from mode-I to mixed mode. Furthermore, theoretical and experimental investigations indicate that after the crack reaches critical speed of propagation there is crack branching. The present paper focuses on 3D finite-element study of reinforced concrete beams with different amount of shear reinforcement under impact. The experiments reported in literature are numerically simulated using the rate sensitive microplane model as constitutive law for concrete, while the strain-rate influence is captured by the activation energy theory. Inertia forces are implicitly accounted for through dynamic finite element analysis. However, the impact was modeled not by explicit modeling of two bodies but by incrementing the load point displacement till the maximum value and at the rate reported from the test. The results of the numerical study show that the numerical analysis using the procedure followed in this work can very well simulate the impact behavior of reinforced concrete beams. The static and dynamic reactions, crack patterns and failure modes as predicted in analysis are in close agreement with their experimentally observed counterparts. It was concluded that under impact loads, of the order as simulated in this work (blunt impact with velocity of around 1 m/s), the shear reinforcement does not get activated and therefore the dynamic reactions, unlike static reactions, are almost independent of the amount of shear reinforcement in the beams. However, the presence of shear reinforcement significantly affects the crack pattern and the cracks are well distributed in the presence of shear reinforcement, thus avoiding the formation of shear plugs.     

Observations of crack path changes caused by periodic underloads in AA7050-T7451

In order to predict variable amplitude crack growth it is necessary to understand the different mechanisms present in variable amplitude and constant amplitude fatigue crack growth. AFM and SEM observations have been made of the fatigue crack fracture surface in AA7050-T7451 alloy, produced by some simple load sequences consisting of periodic underloads (R = −1) in between groups of high stress ratio (R = 0.5) loading cycles. These observations have revealed complex fracture surface features that include ridges, depressions and fissures. These features are a result of the slip band formation associated with underloads, which reduces the tendency for a new slip band to occur at the crack tip in the same direction as nearby slip bands. These slip bands change the path of the crack and result in the production of a ridge on the fracture surface. This effect suggests a model of striation formation that also explains the formation of ridges and other associated features, based on the influence of two or more active slip systems combined with the planar slip behaviour of this material.     

Numerical characterisation of the fibre-matrix interface crack growth in composites under transverse compression

Inter-fibre failure under compression transverse to the fibres is studied at micromechanical level. Interfacial fracture mechanics concepts, associated to both the open model and the contact model, are applied. A numerical study is performed using the boundary element method aimed at explaining the origin and evolution of the damage at micromechanical level, considered as fibre-matrix interface cracks. Assuming that the damage starts as small debonds originated by shear stresses at the position where their maximum values are reached, it has been found that the crack shows different morphologies at both tips: an open one and a closed one with a large contact zone. Then the interface crack grows unstably in mixed mode only on the open tip side until this growth changes to stable, once the crack closes at this tip, with the generation of a contact zone.     

Modellierungskonzept für die Versagensbewertung von Laserschweißverbindungen

Failure assessment of laser weldments based on numerical modelling Classical fracture mechanics based assessments are no more sufficient to provide realistic predictions of the deformation and failure behaviour of welded structures. This situation can be improved by numerical modelling based on damage mechanics. A new concept will be provided, which is based on a cohesive model for crack growth simulation. The determination of the relevant material parameters is also considered where testing is combined with numerical simulation. For a laser weld joint, the gradient of the material properties has to be properly characterized. With miniature sized specimens, the material properties can be discretized by homogeneous layers. A new method, based on the digital image technique, has been introduced to determine the stress‐strain curves also in the large strain region due to necking. Test results on small bend bars containing a thin laser weld and a crack like defect in the centre show different crack path developments resulting from a competitive fracture situation. Mainly shear fracture mode occurs, in some cases also a pure normal fracture mode or a combination of both were observed. The concept presented is able to consider the crack development, if all occuring fracture modes are included in the analysis. However, a complete simulation of an extensive crack extension through a heterogeneous structure has not yet been verified.     

J-M based criteria for bifurcation assessment of a crack in elastic-plastic materials under mixed mode I-II loading

In this work, a set of J-M^p based criteria is proposed to assess the bifurcation angle of an elastic-plastic crack in plane strain under mixed mode loading. We first establish a criterion in order to study the competition between the tensile fracture (T-type fracture) and the shear fracture (S-type fracture) in the frame of RKR conception [J. Mech. Phys. Solids 21 (1973) 395]. Based on the generalized HRR [ASTM STP 560 (1974) 187] solution and on the knowledge of the mixity parameter M^p, the RKR based criterion is transformed into a J-M^p based criterion. When the crack grows in tensile manner, the maximum circumferential stress criterion is adopted to determine the crack bifurcation angle. When the crack grows in shear manner, the traditional theory of plasticity, according to which the plastic flow develops essentially along one of the slip bands immediately ahead of the crack tip, is used to determine the crack growth direction. All these proposed criteria are given as function of the mixity parameter M^p and the hardening exponent n of the material. Finally, we carry out some numerical computations by applying the proposed criteria and then compare the obtained results with experimental data gathered in literature. It is shown that these criteria are physically reasonable and highly accurate. Another advantage is that the parameters used are easy to identify numerically and experimentally, therefore, these criteria are simple to apply in engineering structures.     

A theoretical note on mode-I crack branching and kinking

An energy-based fracture mode has been derived for the mode-I crack branching and kinking. The classic J_i-integral has been further explored by a new partial integral path and the analytical solution of the energy release rate for crack branching and kinking from a mode-I crack tip has been established. The crack branching/kinking angle has also been analytically derived. It shows that the Griffith’s theorem and conservation law can be applied to both mode-I crack extension and mode-I crack branching and kinking. The branching mechanism for quasi-static mode-I crack has been theoretically investigated. The branching toughness and the K-based criterion for crack branching have been defined. The crack branching phenomena predicted by the present model are in well agreement with the experimental observations reported in the literatures.     

Mixed mode I/II fracture of 2024-T3 friction stir welds

For the first time, a series of mixed mode I/II fracture experiments have been performed on both base material and three families of friction stir welds (FSWs) in 6.4 mm thick, 2024-T351 aluminum plate; the FSW joints are designated hot, medium and cold due to the level of nominal weld energy input per unit weld length (specific weld energy) during the joining process.Results from the fracture tests indicate that the measured critical crack opening displacement (COD) at a fixed distance behind the crack tip properly correlates both load-crack extension response and microstructural fracture surface features for both the base metal and all FSWs, providing measure of a quantitative fracture toughness. The COD values also indicate that transition from mode I to mode II dominant crack growth occurs at lower loading angles for FSW joints having higher specific weld energy input, with a truly mixed mode I/II COD measured during crack growth in the medium FSW joint. Using results from recent detailed FSW metallographic studies, specific features in the fracture process are correlated to the FSW microstructure. Finally, the observed ductile crack growth path in all three welds tends to exit the under-matched FSW weld region as the far-field applied shear loading is increased, with the medium FSW being the only case where the flaw remained within the FSW region for all combinations of shear and tensile loading.     

The effect of microstructural inhomogeneity on the growth paths of surface-cracks in copper processed by equal channel angular pressing

The growth behavior of cracks is monitored on specimens of ultrafine grained copper produced by equal channel angular pressing. Temporary retardation of crack growth under low stress amplitudes occurs when the crack length reaches about 0.1 mm, but there is no similar retardation at high stress amplitudes. Dependent on stress amplitude, different crack growth path morphologies develop. Analysis of the fracture surfaces is conducted by scanning electron microscopy, showing planer, granular and striated surfaces. The physical background of growth path and fracture surface formation is discussed by considering crack growth mechanism and microstructural inhomogeneity.     

MODELLING THE CONDITIONS FOR FATIGUE FAILURE IN METAL MATRIX COMPOSITES

Abstract— An investigation on the fatigue crack growth (FCG) and fatigue failure in metal matrix composites (MMCs) has been conducted using a model based on micromechanical elasto-plastic fracture mechanics (EPFM) principles. To evaluate the model, comparisons between experimental and predicted fatigue life have been made for two silicon carbide strengthened (SCS)-6/Ti-based MMCs. Conditions for crack arrest and crack instability have also been considered in order to define the fatigue damage limits. Crack arrest occurs from the added effects of fibre bridging and the constraint provided by the fibre on matrix microplasticity, while crack instability is achieved when the fibre constraint effect is minimum and the fatigue resistance of the material is reduced due to the accumulation of fatigue damage. Comparisons of the predicted fatigue damage limits with experimental results show good agreement which underlines the usefulness of a microstructural fracture mechanics model.     

A discussion on major factors affecting crack path of concrete-to-concrete interfacial surfaces

This paper elaborates major factors affecting the crack path of concrete-to-concrete interfacial surfaces produced with placing joint. Eleven types of specimens were employed for the evaluation of tension softening diagram followed by surface observation of the ligament after fracture test. The surface analysis revealed that the layer of Ca(OH)₂ plays a primary role on the crack path. The authors discuss the relationship between fracture mechanics parameters and the ratio of fractured part which excludes detached part in the ligament. The mechanism for determining crack path near concrete-to-concrete interface is proposed using ‘scattered hole model’.