Straight Crack Path Research Articles

Role of topology in dictating the fracture toughness of mechanical metamaterials

The systemic comparison between sheet-based triply minimal surfaces (TPMS), strut-based ordered lattice topologies and plate-based lattice topologies offer insights into designs for damage tolerant and tough structures. In this work, we explore the topology-fracture toughness relationship of several classes of periodic cellular materials via a series of finite element simulations in mode I, mode II and combined loading. Results showed that sheet lattices are the toughest at higher densities, and their performance tends to degrade faster at lower relative densities ∝ρ3 due to plate buckling as opposed to ρ2 for their strut counterparts in mode I. In a low-density regime, TPMS sheet-based topologies lattices present a better alternative than plate-based topologies for their near-linear scaling with density for fracture toughness. Crack propagation paths for 3D cellular structures depend on fracture geometry. In center-crack fracture geometries, 3D lattices exhibit a straight crack path that is topology independent in mode I. On the other hand, crack propagation paths are topology dependent for edge-crack fracture geometries due to the T-stresses’ contribution: T13 and T11 arising from topology discreteness. Our results shed new light on the structure-property relationship that will facilitate the design of tougher and better crack-resistant 3D cellular structures.

Micro-mechanisms of failure in nano-structured maraging steels characterised through in situ mechanical tests

High-pressure-torsion (HPT) processing introduces a large density of dislocations that form sub-grain boundaries within the refined nano-scale structure, leading to changes in precipitate morphology compared to hot-rolled maraging steels. The impact of such nanostructuring on the deformation and fracture micro-mechanisms is being reported for the first time using in situ characterization techniques along with transmission electron microscopy and atom probe tomography analysis, in this study. Digital image correlation has been used to quantify the full field strain maps in regions of severe strain localization as well as to determine the fracture toughness through critical crack tip opening displacements. It is seen that the phenomenon of planar slip leads to strain softening under uniaxial deformation and to crack branching under a triaxial stress state in hot rolled maraging steels. On the other hand, nano-structuring after HPT processing creates a large number of high angle grain boundaries as dislocation barriers, leading to strain hardening under uniaxial tension and nearly straight crack path with catastrophic fracture under triaxial stress state. Upon overaging, the hot-rolled sample shows signature of transformation induced plasticity under uniaxial tension, which is absent in the HPT processed overaged samples, owing to the finer reverted austenite grains containing higher Ni concentration in the latter. In the overaged fracture test samples of both the hot-rolled and HPT conditions, crack tips show a signature of strain induced transformation of the reverted austenite to martensite, due to the accompanying severe strain gradients. This leads to a higher fracture toughness even while achieving high strengths in the overaged conditions of the nanocrystalline HPT overaged samples. The results presented here will aid in design of suitable heat treatment or microstructure engineering of interface dominated nano-scale maraging steels with improved damage tolerance.

Calibration of cohesive parameters for a castable refractory using 4D tomographic data and realistic crack path from in-situ wedge splitting test

Crack propagation in an alumina castable refractory with mullite-zirconia aggregates was investigated in-situ using a wedge splitting test performed inside a laboratory tomograph. Four-dimensional (i.e., 3D space and time) data from digital volume correlation were used to investigate the influence of a realistic crack path on the simulation of the fracture process. A cohesive law was chosen, since toughening mechanisms were present, and calibrated via finite element model updating. When a straight crack path was assumed instead of the experimental crack path, a 10% higher fracture energy and a 35% higher cohesive strength were calibrated. Although the force alone could be used in the minimized cost function, the kinematic information gives valuable insight into the trustworthiness of the geometrical hypotheses assumed in the finite element model. Such framework can be applied to study nonlinear fracture processes for different materials with complex toughening mechanisms such as crack deflection or branching.

Interaction of rod decussation and crack growth in enamel

Enamel possesses ingenious hierarchical structure that gives rise to superior fracture resistance. Despite considerable efforts devoted to characterization of fracture behavior of enamel, the role of rod decussation in fracture of enamel is largely unknown. In this study, the features of rod decussation in the inner enamel are experimentally identified, and analyses of crack growth in enamel are carried out using a micromechanical model of enamel, in which the structural features of the outer enamel and rod decussation of the inner enamel are incorporated. We carry out calculations within a framework based on the extended finite element method, and the crack growth and crack path selection are natural outcomes of imposed loading. We show that crack deflection in enamel is controlled by rod decussation. For crack growth in the parazone, the crack path is oriented along the axis of enamel rods, leading to gross crack deflection. The microstructure of inner enamel with intermediate inclination angle enables multiple crack deflections, giving rise to enhanced toughness. For crack growth in the diazone, the transition in orientation of crack deflection occurs as inclination angle increases. The relatively straight crack path emerges in the case of the microstructure of enamel with intermediate inclination angle, leading to weak fracture resistance. It is further found that compared with the diazone, the gross crack deflection in the parazone provides greater contribution to fracture resistance of enamel. The findings of this study provide a good mechanistic understanding of the role of rod decussation in enamel.

Towards a New Concept of Crack Path: A Tribute to James R. Rice

This paper tries to advance towards a new concept of crack path covering different length scales (multi-scale approach) and distinct points of view (multi-perspective approach). With regard to the fracture/crack path profile in a vertical plane of analysis (i.e., perpendicular to the crack front), it can be studied by means of fracto-materialographic analysis to obtain the physical crack path that can be evaluated at different length scales: (i) microstructurally-induced crack paths, (ii) crack paths micro-roughness, (iii) crack-path micro-deflections, (iv) locally multi-axial crack paths, (v) kinked crack paths; (vi) deflected crack paths, (vii) bifurcated crack paths. In all these phenomena, material microstructure plays a relevant role producing the local deviations of the otherwise straight crack path (macroscopic crack path), thereby increasing the real (physical) crack path length and increasing the material resistance to fatigue and fracture. In the matter of the crack shape in a horizontal plane, the crack aspect ratio evolution (with the existence or not of a preferential propagation path) is the object of analysis, thereby representing another aspect of crack paths. Examples of the different approaches are provided in the framework of previous research by the author in the field of fatigue, fracture, stress corrosion cracking and hydrogen embrittlement. In addition, the reverse approach to the concept of crack paths (crack paths versus paths near cracks) provides the idea of paths in cracks, or paths near cracks, in the framework of the mathematical formulation of a path independent integral near a crack tip (a path near a crack, and an integral whose value is independent of the particular path), so that this paper is a heartfelt tribute to James R. Rice and his J-Integral.

Mechanistic fatigue in Ni-based superalloy single crystals: A study of crack paths and growth rates

The mechanistic basis of microstructurally short crack paths and growth rates is investigated in Ni-based superalloy single crystals using Crystal Plasticity (CP) and eXtended Finite Element (XFEM) analyses of experimental edge-cracked samples over a range of crystal orientations. Crack paths are determined to be those along crystallographic slip systems within which the slip is highest. Crack growth rates are determined by the crack tip critical stored energy density. Experimental observations of tortuous crack paths and their dependence on crystal orientation are reasonably well captured by the mechanistic model. Key features of alternating and straight crack paths are reproduced. The experimentally measured crack growth rates as a function of crystal orientation are also captured by the mechanistic model and controlled by the crack tip critical stored energy density which was found to be 385 Jm−2 in the Ni-based superalloy single crystals analysed. A new methodology for determination of critical stored energy density and mechanistic quantification of short crack growth rates is presented.

Structure-Property Relationships of Polyamide 12 Grades Exposed to Rapid Crack Extension.

Thermoplastic materials have established a reputation for long-term reliability in low-pressure gas and water distribution pipe systems. However, occasional Slow Crack Growth (SCG) and Rapid Crack Propagation (RCP) failures still occur. SCG may initiate only a small leak, but it has the potential to trigger RCP, which is much rarer but more catastrophic and destructive. RCP can create a long, straight or meandering axial crack path at speeds of up to hundreds of meters per second. It is driven by internal (residual) and external (pressure) loads and resisted by molecular and morphological characteristics of the polymer. The safe installation and operation of a pipe throughout its service lifetime therefore requires knowledge of its resistance to RCP, particularly when using new materials. In this context, the RCP resistance of five different polyamide (PA) 12 grades was investigated using the ISO 13477 Small-Scale Steady State (S4) test. Since these grades differed not only in molecular weight but also in their use of additives (impact modifiers and pigments), structure-property relationships could be deduced from S4 test results. A new method is proposed for correlating these results more efficiently to evaluate each grade using the crack arrest lengths from individual S4 test specimens.

Experimental and Numerical Investigation of the Effect of Bedding Layer Orientation on Fracture Toughness of Shale Rocks

Fracture toughness is a critical parameter responsible for fracture initiation and propagation. Fracture toughness in shale gas reservoir, however, is highly variable because of its anisotropy and spatial variation of clay content. In this paper, a series of laboratory and numerical experiments are carried out to estimate shale fracture toughness at different bedding plane orientations with respect to loading direction (angle of bedding layer with respect to Cracked Chevron notched Brazilian disc (CCNBD) test samples) and in different brine solutions. The CCNBD test was conducted on 12 cylindrical samples for fracture toughness. Shale samples were prepared at four different angles (0°, 30°, 45° and 90°) relative to the bedding plane. The prepared specimens were saturated in potassium chloride (KCL) solutions of different concentrations. The laboratory results of toughness have shown to be highly variable with respect to both bedding plane and brine concentration and that the sample at the angle of 90° in 4% KCL concentration exhibited the highest fracture toughness. Numerical simulations based on extended finite element method (XFEM) were also carried out to simulate fracture evolution and propagation in CCNBD samples with different bedding planes. The results have shown that the bedding layers caused the fracture path to deflect. The deviation from straight crack path is caused by mixed mode fracture initiation and propagation instead of tension mode. The mixed mode fracture propagation behavior was verified by analyzing fracture propagation path using both laboratory experiments and numerical simulation.

Crack growth behaviour in biaxial stress fields: Calculation of K-factors for cruciform specimens

The aim of this study is to propose a simplified method for calculating the Mode I stress intensity factor K for cruciform specimens under planar biaxial loading. It is assumed that two cracks have to grow with a similar crack growth rate. The straight crack paths of the two single cracks with the length a should also be similar. The calculations are carried out on an aluminum and a steel specimen, respectively. For different load cases and materials, the stresses resulting from the forces are first considered. It was found that the elastic constants E and ν have only a small influence of less than 3%. In addition, the coupling between the forces of the load axes, which should be minimized by slotted arms, is considered. Moreover, K-factors are calculated by finite elements (FE) for different crack lengths. These K-values together with the transmission factor allow to find a K-factor formula for cruciform specimens, which is based on the prescribed forces. Finally, the results of the FE-calculation of the exact straight crack paths were compared to experimentally determined crack paths. Furthermore, a comparison of the fatigue crack growth rates versus K-factor range for different loading is shown.

A numerical study of crack shielding/anti-shielding in layered architectures

Previous research has indicated the potential effectiveness of adopting micro-scale layered architectures to improve the fatigue damage resistance of coatings. However, the optimisation of these coatings is difficult due to the existence of many different factors affecting fatigue performance in such micro-scale layered architectures. In particular, the interaction of successive shielding and anti-shielding processes on crack growth resistance is therefore addressed in this paper by numerical simulation analysis. The crack tip fields in a series of layered architectures were simulated based on varying assumed constitutive materials properties to reveal the interaction of shielding/anti-shielding characteristics in complex architectures in a simple exemplar system. The evolution of crack driving force (CDF) with crack length was calculated and linked to fatigue crack life under relatively simple conditions, including straight crack path and Paris law assumptions, to investigate the effect of the ordering of shielding/anti-shielding characteristics on the crack tip field and hence on fatigue crack life. Layered architectures with different numbers, ordering and placing of layers, were assessed and parametric studies of 4 layered architectures were carried out. This allows analysis of the effect of these individual factors on shielding and their interactive effect with anti-shielding in multi-layered architectures. Understanding the combined effect on crack growth performance and overall fatigue life controlled by crack propagation provides insight into the generic design of micro-scale layered architectures.

Phase field fracture in elasto-plastic solids: Variational formulation for multi-surface plasticity and effects of plastic yield surfaces and hardening

The phase field modelling has been extended from brittle fracture to ductile fracture by incorporating plasticity. However, the effects of plastic yield functions and hardening on the fracture behaviour have not been examined systematically to date. The phase field fracture coupled with multi-surface plasticity is formulated in the variational framework for the unified yield criterion, which is able to facilitate the study on different yield surfaces. First, the homogeneous solutions of fracture in elasto-plastic solids are derived analytically for 1D and 2D cases. The results show that a greater hardening modulus would lead to an ascending branch of the stress versus strain curve; and the yield function may significantly affect the stress state and phase field damage. Second, the finite element (FE) technique is implemented for modelling the phase field fracture in elasto-plastic solids, in which the stress update and consistent tangent modular matrix are derived for the unified yield criterion. Finally, three numerical examples are presented to explore the effects of the yield function and material hardening. It is found that the yield function and material hardening could significantly affect the crack propagation and the final fracture pattern. In particular, the Tresca yield function tends to create a straight crack path orthogonal to the first principal stress, while the other yield functions show no sizeable difference in their crack paths.

Cruciform specimens for the determination of crack growth behaviour in biaxial stress fields: calculation of K-factors

The aim of this study is to propose a simplified calculation of the Mode I stress intensity factor K for the cruciform specimen design proposed by Brown and Miller. To calculate K, both cracks have to grow with a similar crack growth rate and the crack paths of the two single cracks with the length a should also be similar. The calculations are carried out on an aluminum specimen and a steel specimen. For all load cases and materials, the stresses resulting from the forces are first considered. It was found that the elastic constants E and ν have only a small influence of less than 3 %. In addition, the coupling between the forces of the load axes, which should be minimized by the slotted arms, is considered. Furthermore K-factors are calculated by FE for different crack lengths. These K-values together with the transmission factor allow to find a K-factor formula for cruciform specimens, which is based on the prescribed forces. Finally, the results of the FE calculation of the exact straight crack paths were compared to experimentally determined crack paths.

Influence of Steel Fibers on Fracture Energy and Shear Behavior of SCC

The fracture behavior and the dilatant crack opening in the shear response of self-consolidating concrete (SCC) with discrete steel fiber reinforcement were investigated. The volume fraction of hooked-end steel fibers in concrete was 0.75%. The fracture behavior of steel fiber reinforced SCC (SFRSCC) was investigated using notched beams tested in flexure. In SFRSCC, there was a significant increase in fracture energy at a small crack opening. The significant postcracking resistance to crack opening provided by fibers in an SCC matrix resulted in a twofold increase in energy up to 0.1 mm crack opening. In SFRSCC, there was a tenfold increase in energy up to 1.0 mm crack opening, which was associated with multiple cracking in the matrix. In the second stage of the experimental evaluation, the shear behavior of SCC with and without steel fibers was investigated using a shear beam arrangement. The dilatant behavior of the shear crack was established from in situ full-field displacement measurements from across the primary shear crack, obtained using digital image correlation (DIC). There was a continuous slip between the faces of the shear crack, which produced a continuous increase in the crack opening. Shear crack in SCC beams curves in a direction governed by the applied stress field. Failure in SCC is very brittle and occurs at small crack openings which are less than 0.1 mm. The sudden loss of internal stress transfer across the primary shear crack produces failure in SCC beams. In SFRSCC, the primary shear crack formed at a load that was nearly double the load at the formation of the shear crack in SCC. The dilatant behavior in SFRSCC was identical to the dilatant behavior obtained from SCC without fibers. In SFRSCC, there was an increase in load-carrying capacity with a continued opening of the shear crack, and load transfer across the primary shear crack was sustained for a larger crack opening. Due to increased contact stress on the crack faces induced by high cohesive crack closing stress produced by fibers, the shear crack at the neutral axis continued to propagate along the initial angle, resulting in a straight crack path without curvature. There was a stress transfer across primary shear crack openings up to 1 mm due to the crack closing stress provided by the fibers. A secondary shear crack in SFRSCC beams led to failure. The improvement in the fracture response of SCC with the addition of fibers results in an increase in shear capacity through better crack control.

Compressive test and numerical simulation of center‐notched composite laminates with different crack configurations

Experimental and computational studies of the composite laminates with thin center notches under axial compressive loading are carried out. A series of compressive testing of the composites with different crack lengths and angles between the loading vector and 0° fiber direction were conducted. The damage mechanisms as well as load–displacement curves are obtained from the test to analyze the effects of crack dimensions on stress distribution and ultimate load. It was shown that the compressive strength of composites drastically reduces when the crack angle goes from 0° to 90°. By studying the fracture surfaces of the tested specimens, all initial cracks within the laminates are found to extend without a straight crack path until fibers fracture simultaneously. Cases that involve crack propagation are modeled for different crack dimensions with a 3D progressive damage finite element analysis using the Abaqus. Numerical simulations qualitatively reproduce the general observations made in the laboratory experiments. POLYM. COMPOS., 38:2631–2641, 2017. © 2015 Society of Plastics Engineers

Fatigue crack propagation behaviour in wire+arc additive manufactured Ti‐6Al‐4V: Effects of microstructure and residual stress

Fatigue crack propagation tests of Ti‐6Al‐4V fabricated by the Wire+Arc Additive Manufacturing (WAAM) process are analysed. Crack growth rate and trajectory are examined before and after the crack tip crossing an interface between the WAAM and wrought alloys. The study has focused on the microstructure and residual stress effect. First, the differences in crack growth rate and path between WAAM and wrought alloys are attributed to their different microstructure; the equiaxed wrought alloy has straight crack path, whereas the WAAM lamellar structure causes tortuous crack path resulting in lower crack growth rate. Second, based on measured residual stress profile in the as-built WAAM piece, retained residual stress in the much smaller compact tension specimens and its effect on crack growth rate are calculated by the finite element method. Numerical simulation shows considerable residual stress in the test specimen and the stress magnitude depends on the initial crack location and propagation direction in relation to the WAAM-wrought interface. Residual stress is released immediately if the initial crack is in the wrought substrate; hence it has little effect. In contrast, when crack grows from WAAM to wrought, residual stress is retained resulting in higher stress intensity factor; hence greater crack growth rate.

An adaptive algorithm for cohesive zone model and arbitrary crack propagation

This paper presents an approach to the numerical simulation of crack propagation with cohesive models for the case of structures subjected to mixed mode loadings. The evolution of the crack path is followed by using an adaptive method: with the help of a macroscopic branching criterion based on the calculation of an energetic integral, the evolving crack path is remeshed as the crack evolves in the simulation. Special attention is paid to the unknown fields transfer approach that is crucial for the success of the computational treatment. This approach has been implemented in the finite element code Z-Set (jointly developed by Onera and Ecole des Mines) and is tested on two examples, one featuring a straight crack path and the other involving a complex crack propagation under critical monotonous loading monotonous.

Conditions for Mode I crack deviation in orthotropic plane subjected to biaxial loading

A problem of a Mode I crack deviation is considered. It is assumed that a crack is located initially on a symmetry axis of an orthotropic plane and subjected to biaxial loading. A crack is modeled as a thin elliptical hole. The maximal tensile stresses are taken as a crack growth criterion. To stress the role of elastic anisotropy for a crack rotation, the strength properties of the material are assumed to be isotropic. Conditions for a crack deviation and stability of a straight crack path are obtained. The obtained results generalize previous results of the authors, where an analogical problem was considered for the case of uniaxial tension. Presented results are compared with the results following from the traditional model of the crack, considering a crack as an ideal cut.

An adaptive algorithm for cohesive zone model and arbitrary crack propagation

This paper presents an approach to the numerical simulation of crack propagation with cohesive models for the case of structures subjected to mixed mode loadings. The evolution of the crack path is followed by using an adaptive method: with the help of a macroscopic branching criterion based on the calculation of an energetic integral, the evolving crack path is remeshed as the crack evolves in the simulation. Special attention is paid to the unknown fields transfer approach that is crucial for the success of the computational treatment. This approach has been implemented in the finite element code Z-Set (jointly developed by Onera and Ecole des Mines) and is tested on two examples, one featuring a straight crack path and the other involving a complex crack propagation under critical monotonous loading.

Micromorphic approach to single crystal plasticity and damage

Eringen’s micromorphic approach for materials with microstructure is applied to the plasticity and damage of single crystals. A plastic microdeformation variable and its rotational part are introduced in a standard crystal plasticity model in order to predict size effects in the overall stress response of crystalline solids. In the case of an ideal laminate microstructure including a purely elastic layer and a plastic layer undergoing single slip, the model, called microcurl, is shown to produce a kinematic hardening component that depends on the size of the layers. In a second part of the paper, a microdamage variable is introduced that accounts for cleavage or plasticity induced pseudo-cleavage phenomena in single crystals. The formulation accounts for straight crack paths but also allows for crack branching and bifurcation.

Dependence of a crack growth path on the elastic moduli of an anisotropic solid

One of the ways to increase the resistance of a structure to catastrophic fracture is to force a main line crack to deviate from its path. For this reason the influence of the elastic moduli of an anisotropic material on crack rotation are studied. In particular a linear elastic problem for a straight Mode I crack, located on a symmetry axis of an orthotropic plane is considered. The strength properties of the material are assumed to be isotropic. Several crack models are considered for studying the direction of a crack growth path. It is shown that a crack modeled as a thin, elongated, elliptical hole leads to more plausible results concerning crack rotation conditions than an ideal cut model. The maximal tensile stresses are taken as a crack growth criterion. It is shown that for a class of orthotropic materials a crack deviates from the straight path just after it starts to grow, even in the conditions of uniaxial normal tension. The problem of the stability of a straight crack path under Mode I loadings is also considered. This problem is reduced to the problem of the fracture direction determination for thin, elongated, elliptical cavities slightly inclined to the initial direction. The conditions of instability are obtained within the framework of the proposed approach. It is shown that for a class of orthotropic materials a straight crack path is unstable in the conditions of uniaxial normal tension. This class of materials is larger than the one for which a crack deviates from the straight crack path just after its start.