Fracture Mechanics Assumptions Research Articles

Simulations of complex crack paths using a robust and cost-efficient continuous–discontinuous approach

Prediction of complex crack propagation is necessary to guarantee performance in service of critical parts of transport vehicles despite the presence of a crack. In cases where linear fracture mechanics assumptions are not valid, e.g. for ductile rupture, this prediction may require continuous–discontinuous strategies to insert a strong discontinuity (i.e. a crack) into a continuous model based on a scalar variable related to material degradation. These strategies still face difficult challenges regarding robustness and cost-efficiency, in particular for 3D problems. To overcome these challenges, it is useful to consider the different ingredients that constitute a continuous–discontinuous strategy and try to optimize each of them. With this perspective, this work addresses the simulation of crack initiation and propagation in ductile metals and proposes new contributions to some rarely addressed points: (i) a simple geometrical approach to initiate realistic crack shapes in 3D meshes, (ii) a new 3D insertion criterion to minimize the number of transfer operations, (iii) a pragmatic remeshing procedure to refine only Active Process Zones, and (iv) an equilibrium recovery method meant to improve the convergence rate after the insertion of a discontinuity.The effectiveness of these new ingredients is demonstrated in 2D axisymmetric, 2D plane strain, and 3D cases in the case of test specimens used to characterize ductile failure in metals. This includes axisymmetric specimens exhibiting cup-cone fracture, plane strain specimens with slant fracture, and pre-cracked CT-like specimens with crack blunting and large crack propagation.

On tailoring fracture resistance of brittle structures: A level set interface-enriched topology optimization approach

We propose a fully immersed topology optimization procedure to design structures with tailored fracture resistance under linear elastic fracture mechanics assumptions for brittle materials. We use a level set function discretized by radial basis functions to represent the topology and the Interface-enriched Generalized Finite Element Method (IGFEM) to obtain an accurate structural response. The technique assumes that cracks can nucleate at right angles from the boundary, at the location of enriched nodes that are added to enhance the finite element approximation. Instead of performing multiple finite element analyses to evaluate the energy release rates (ERRs) of all potential cracks—a procedure that would be computationally intractable—we approximate them by means of topological derivatives after a single enriched finite element analysis of the uncracked domain. ERRs are then aggregated to construct the objective function, and the corresponding sensitivity formulation is derived analytically by means of an adjoint formulation. Several numerical examples demonstrate the technique’s ability to tailor fracture resistance, including the well-known benchmark L-shaped bracket and a multiple-loading optimization problem for obtaining a structure with fracture resistance anisotropy.

Tension Failure Simulation of Notched Composite Laminate Using Floating Node Method Combined with In-Situ Effect Theory

In order to model the progressive failure of laminates under tensile load, the finite element model adopting the floating node method combined with In-Situ effect strength theory is developed in this paper. The floating node method is based on the original finite elements to assign more additional degree of freedoms on the edges or nodes. In this way, it can realize crack propagation explicitly and prevent the singularity caused by the integration of body elements at the damage points. The calculation method of In-Situ strength theory based on the assumption of fracture mechanics is introduced and deduced, which improves the accuracy of the failure strength prediction. Two kinds of notched composite laminates’ tensile experiments were carried out. Experiment results show that different ply sequences ([453/903/-453/03]s and [45/0/-45/90]3s) have different failure strength and failure progress. In this paper, the reliability of the model is verified by comparing the experimental results with the simulation results. The comparison results demonstrate that this model can realize the explicit crack propagation and predict the failure strength precisely. In addition, this model can represent some failure modes such as fiber breakage, matrix damage, and delamination, which were observed from experimental phenomenon. The traditional failure criteria compared to the improved criteria's accuracy is significantly improved. It demonstrated that the analysis in considering the In-Situ effect is very necessary.

Crack growth behavior in dissimilar welded Ti based alloys under biaxial fatigue loading

This study aims at describing fatigue crack growth in dissimilar welding of Ti based alloys under macroscopic multiaxial loading. The proposed methodology involves the experimental analysis of fatigue crack behavior under equibiaxial tension and macroscopic combination of mode I and II for Ti17, Ti6242 and laser welded specimen of both base metals. Based on these experiments, crack path, fatigue crack growth rate and crack interaction with microstructure have been addressed. The 3D finite element analysis of cracks shapes has enabled to derive stress intensity factor (SIF) investigated for opening, in-plane and out-of-plane shear modes based on linear elastic fracture mechanics assumptions. Finally, an equivalent SIF has been proposed to take into account the local mode mixity induced by both macroscopic shear and 3D crack shape. As a conclusion, the dissimilar welding of Ti based alloys increase the fatigue crack growth rate (FCGR) for any macroscopic loading - with or without shear. Moreover, the microstructure of Ti6242 alloy, is well known to inhibit FCGR by multiples local bifurcation of crack path induced by the coarse microstructure of this alloy. This point was confirmed during equibiaxial tension but anomalous and very high FCGR was observed for macroscopic mode I + II loading. For the welded material, the fatigue crack to microstructure interactions have shown that the FCGR was clearly limited by coarse α needles inducing local bifurcation and conversely that in both fusion zone and heat-affected zone, local refinement of α needles could not slow down the crack propagation.

Characterization of Fracture Toughness Properties of Aluminium Alloy for Pipelines

Continuous critical loading of pressure equipments can affect the structural stability of these plants. The structural stability and mechanical resistance under pressure loads can also be affected by defects. Fracture mechanics assumptions were applied to aluminium alloys to study their effect on its mechanical behaviours. A 3-point bending standard test was employed and the critical Stress Intensity Factor, K (SIF) in mode I was determined in order to provide a quantitative/qualitative evaluation of the performance. Additional experiments were carried out to validate the numerical results gained from the Finite Element Method (FEM) and the Extended Finite Element Method (X-FEM). The crack propagation process is discussed in this study focussing on the effect of crack tip radius.

Estimation of fatigue crack growth under complex loading using an accumulative approach

A model procedure to obtain estimates for thermo-mechanical fatigue crack growth rates based on isothermal test results is presented. This ‘O.C.F.-model’ consists of a linear accumulation of temperature independent fatigue crack growth and two temperature dependent crack growth parts. Temperature dependent crack growth is constituted from creep crack and oxidation damage. For the oxidative damage part, the formation of a γ′-free zone at the crack tip and sub-sequent softening is considered to be determining. The possibility to assess creep crack growth in alloys with very limited creep ductility using linear-elastic fracture mechanics assumptions is investigated and compared to visco-plastic approaches. The isothermal data presented in this paper allows for an estimation of crack growth under both isothermal and anisothermal conditions with and without dwell times. Furthermore it allows assessing the fractions of crack growth caused by the different sources.

Specimen geometry and specimen size dependence of the $${\mathcal {R}}$$ R -curve and the size effect law from a cohesive model point of view

An analytic model has been developed for a Compact Tension specimen subjected to a controlled displacement and corresponding load within a cohesive model framework. The model is able to capture the material response while the Fracture Process Zone is being developed, obtaining the evolution of multiple variables such as the crack opening and the cohesive stresses, for an arbitrary Cohesive Law shape. The crack growth prediction based on the $${\mathcal {R}}$$ -curve and the nominal strength prediction based on Bažant’s Size Effect Law have been implemented using the output variables available from the proposed analytic model. The minimum specimen size has been found in order to properly apply $${\mathcal {R}}$$ -curve based methods. The study has concluded that only the cohesive model is able to properly capture the changes of the Specimen Geometry and Specimen Size, as unlike in other theories, no Linear Elastic Fracture Mechanics assumptions are made.

Adaptive Finite Element Modeling of Fatigue Crack Propagation

An adaptive finite element interactive program has been developed for fatigue crack propagation simulation under constant amplitude loading condition. The purpose of this model is on the determination of 2D crack paths and surfaces as well as on the evaluation of components Lifetimes as a part of the damage tolerant assessment. As part of a linear elastic fracture mechanics analysis, the determination of the stress intensity factor distribution is a crucial point. The fatigue crack direction and the corresponding stress-intensity factors are estimated at each small crack increment by employing the J-integral technique. The propagation is modeled by successive linear extensions, which are determined by the stress intensity factors under linear elastic fracture mechanics assumption. The stress intensity factors range history has to be recorded along the small crack increments. Upon completion of the stress intensity factors range history recording, fatigue crack propagation life of the examined specimen is predicted. Verification of the predicted fatigue life is validated with relevant experimental data and numerical results obtained by other researchers. The comparisons show that this model is capable of demonstrating the fatigue life prediction results as well as the fatigue crack path satisfactorily.

Stress intensity factor calibration for a longitudinal crack in a fuselage barrel and the bulging effect influence

Aircraft structures require minimum weight configurations with high strength in order to support all operational stresses with high reliability. Framework construction is the base of these airframes where cross sectional shapes are connected into a rigid assembly. The vertical and horizontal cross-members are arranged to withstand all structural loads and the skin to support the pressure gradient. This type of fuselage has been in use for about 80 years; it is very strong and relatively lightweight when used with materials of high specific strength. Due to the difficulty of producing defect free structures and to avoid damage during the life of a structure, damage tolerance is an important requirement. Damage tolerance is a design philosophy predominantly applied in the primary structural parts of civil airframes in order to tolerate a defect that can be detected and repaired during the next maintenance check. In this article, the stress intensity factor (SIF) for a longitudinal crack under the pressurization load was studied. For this purpose, a barrel composed of two frames with the longitudinal stiffeners and with the geometry usually found in civil airframes was chosen. A central crack, between the two frames, was simulated in a geometrically nonlinear finite element model composed by solid elements. The stress intensity factor for different crack lengths, until the crack tips reach the frame, was calculated using linear elastic fracture mechanics assumptions and the modified virtual crack closure technique. In addition, stress intensity factors along the skin thickness were determined. The variation of the SIF values along the thickness due to the bulging effect is modeled, and comparisons were made with the behavior of an equivalent reinforced flat panel.

Influence of the notch sharpening technique on the fracture toughness of bulk ethylene–propylene block copolymers

The effect of the notch sharpening procedure on the fracture toughness computed under linear-elastic and elastic-plastic conditions (at low and high loading rates, respectively) of a bulk ethylene–propylene block copolymer has been investigated. The specimens utilized for fracture characterization were sharpened using a steel razor blade and the femtosecond laser ablation technique. The crack growth initiation parameter, J IC, determined with the help of the elastic-plastic fracture approach, and the fracture toughness, K IC, obtained with specimens verifying linear-elastic fracture mechanics assumptions, of the steel razor blade sharpened samples were higher than that of the femtolaser sharpened specimens. The plastic deformation occurring ahead of the crack tip during the sharpening method seems to be the reason for the dissimilarity of the fracture values. Moreover, the strain hardening suffered by the material close to the notch tip reduces the stable crack growth resistance evaluated under elastic-plastic conditions.

A discrete cohesive model for fractal cracks

The fractal crack model described here incorporates the essential features of the fractal view of fracture, the basic concepts of the LEFM model, the concepts contained within the Barenblatt–Dugdale cohesive crack model and the quantized (discrete or finite) fracture mechanics assumptions proposed by Pugno and Ruoff [Pugno N, Ruoff RS. Quantized fracture mechanics. Philos Mag 2004;84(27):2829–45] and extended by Wnuk and Yavari [Wnuk MP, Yavari A. Discrete fractal fracture mechanics. Engng Fract Mech 2008;75(5):1127–42]. The well-known entities such as the stress intensity factor and the Barenblatt cohesion modulus, which is a measure of material toughness, have been re-defined to accommodate the fractal view of fracture. For very small cracks or as the degree of fractality increases, the characteristic length constant, related to the size of the cohesive zone is shown to substantially increase compared to the conventional solutions obtained from the cohesive crack model. In order to understand fracture occurring in real materials, whether brittle or ductile, it seems necessary to account for the enhancement of fracture energy, and therefore of material toughness, due to fractal and discrete nature of crack growth. These two features of any real material appear to be inherent defense mechanisms provided by Nature.

Fracture Probability Integral Applied to Reactor Vessel Life Estimate1

The conventional method of fracture probability calculations such as that adopted by the NRC-sponsored PRAISE CODE and the FAVOR CODE developed in this laboratory are both based on Monte Carlo simulation. Heavy computations are required. A new method of fracture probability calculation is developed by direct probability integration. The preliminary version of the development was published in an earlier paper. More detailed development of the method is presented here. The present approach offers simple and expedient method to obtain numerical values of fracture probability. This method can be applied to problems as general as the method of Monte Carlo simulation. This approach also provides a clear physical picture on the meaning of the probability of fracture. Parametric studies are made in this paper to show the variation of the numerical values of the probabilities of fracture as a result of the change of the standard deviation of either fracture toughness or the radiation-induced temperature shift. Also, it is shown numerically that a limiting probability can be obtained if the standard deviation of the fracture toughness approaches zero that implies a deterministic fracture toughness. It confirms the theoretical proof shown in Eq. (11). The limiting probability is the simplistic probability of crack count used by this author where both toughness and temperature shift are assumed to be deterministic values. The general probability of fracture developed here is simply a generalization of the crack count, except the crack count is selected with the appropriate fracture toughness in the toughness distribution. The toughness for the problem considered here is then multiplied by the appropriate temperature shift in the distribution function of the temperature shift. Although the present development is based on linear fracture mechanics assumption and applied to the radiated reactor vessel steel, there is no difficulty in viewing the present development as a general formulation that is capable of handling as many random variables as required by the fracture model. The multiplicity of the integration corresponds to the number of random variables. The probability integral is applied in this paper to calculate the probability of fracture for the high flux isotope reactor (HFIR) vessel that has been weakened due to the radiation embrittlement. The random variables used here are the crack length, the fracture toughness, and the radiation-induced temperature shift that is needed in the parametric representation of the radiated vessel steel.

LEFM Applications to Concrete Gravity Dams

The evaluation of the safety factor of old dams under higher flood levels in the last few years has been investigated under the assumptions of fracture mechanics. The extensive need for research in this field was recognized by the U.S. Army Corps of Engineers that now requires a fracture mechanics investigation prior to the rehabilitation of cracked massive concrete structures. In large structures, such as dams, because of the smaller size of the fracture process zone with respect to the structure size, limited errors should occur under the assumptions of linear elastic fracture mechanics (LEFM). In this paper, theoretical considerations and approximate expressions for the evaluation of stress intensity factors and crack propagation in concrete dams are presented. Furthermore, a parametric study of gravity dams under the assumptions of LEFM is performed. Finally, a scale law for the evaluation of the maximum water level carried by cracked dams is proposed.

A finite element model for delamination propagation in composites

In this paper the theory and application of a modelling technique for three-dimensional planar delamination growth in laminated composites has been presented. The method is based on linear elastic fracture mechanics assumptions for delamination cracks and uses a strain energy release rate criterion. For a given component, strain energy release rate is considered to be a non-linear function of the location of the delamination front. Hence, satisfaction of the growth criterion reduces to the solution of a non-linear system of equations. A generalized secant method, by the Broyden's update method, is used to solve the system of non-linear equations. Several examples of the application of the technique are presented.

Developing Normalized Crack Growth Curves for Tracking Damage in Aircraft

This paper directs attention to the interrelationship between crack growth rate equations and the Normalized Crack Growth (NCG) curve concept used in the F-4 fighter damage tracking program. Crack growth rate equations, based on linear elastic fracture mechanics assumptions, provide the capability for predicting the influences of geometrical changes or of stress scaling. For the crack growth rate equations that describe the flight-by-flight generated data presented herein, generalized integral (or inverted) formulas are suggested that provide the rationale for developing NCG curves. Subject to the limitations described within the body of the paper, the NCG curve invariance assumption for tracking damage at different locations in an aircraft appears reasonable.