Showing papers in "International Journal of Fracture in 2014"

Crack propagation with adaptive grid refinement in 2D peridynamics

Abstract: The most common technique for the numerical implementation of peridynamic theory is based on a mesh-free approach, in which the whole body is discretized with a uniform grid and a constant horizon. As a consequence of that computational resources may not be used efficiently. The present work proposes adaptive refinement algorithms for 2D peridynamic grids. That is an essential component to generate a concurrent multiscale model within a unified approach. Adaptive grid refinement is here applied to the study of dynamic crack propagation in two dimensional brittle materials. Refinement is activated by using a new trigger concept based on the damage state of the material, coupled with the more traditional energy based trigger, already proposed in the literature. We present as well a method, to generate the nodes in the refined zone, which is suitable for an efficient numerical implementation. Moreover, strategies for the mitigation of spurious reflections and distortions of elastic waves due to the use of a non-uniform grid are presented. Finally several examples of crack propagation in planar problems are presented, they illustrate the potentialities of the proposed algorithms and the good agreement of the numerical results with experimental data.

Quasi-static and dynamic fracture behaviour of rock materials: phenomena and mechanisms

Abstract: An experimental investigation is conducted to study the quasi-static and dynamic fracture behaviour of sedimentary, igneous and metamorphic rocks The notched semi-circular bending method has been employed to determine fracture parameters over a wide range of loading rates using both a servo-hydraulic machine and a split Hopkinson pressure bar The time to fracture, crack speed and velocity of the flying fragment are measured by strain gauges, crack propagation gauge and high-speed photography on the macroscopic level Dynamic crack initiation toughness is determined from the dynamic stress intensity factor at the time to fracture, and dynamic crack growth toughness is derived by the dynamic fracture energy at a specific crack speed Systematic fractographic studies on fracture surface are carried out to examine the micromechanisms of fracture This study reveals clearly that: (1) the crack initiation and growth toughness increase with increasing loading rate and crack speed; (2) the kinetic energy of the flying fragments increases with increasing striking speed; (3) the dynamic fracture energy increases rapidly with the increase of crack speed, and a semi-empirical rate-dependent model is proposed; and (4) the characteristics of fracture surface imply that the failure mechanisms depend on loading rate and rock microstructure

The Sandia Fracture Challenge: blind round robin predictions of ductile tearing

Abstract: Existing and emerging methods in computational mechanics are rarely validated against problems with an unknown outcome. For this reason, Sandia National Laboratories, in partnership with US National Science Foundation and Naval Surface Warfare Center Carderock Division, launched a computational challenge in mid-summer, 2012. Researchers and engineers were invited to predict crack initiation and propagation in a simple but novel geometry fabricated from a common off-the-shelf commercial engineering alloy. The goal of this international Sandia Fracture Challenge was to benchmark the capabilities for the prediction of deformation and damage evolution associated with ductile tearing in structural metals, including physics models, computational methods, and numerical implementations currently available in the computational fracture community. Thirteen teams participated, reporting blind predictions for the outcome of the Challenge. The simulations and experiments were performed independently and kept confidential. The methods for fracture prediction taken by the thirteen teams ranged from very simple engineering calculations to complicated multiscale simulations. The wide variation in modeling results showed a striking lack of consistency across research groups in addressing problems of ductile fracture. While some methods were more successful than others, it is clear that the problem of ductile fracture prediction continues to be challenging. Specific areas of deficiency have been identified through this effort. Also, the effort has underscored the need for additional blind prediction-based assessments.

The MLS-based numerical manifold method with applications to crack analysis

Abstract: In order to solve problems, from a continuum point of view and in a unified way, involving continuum and discontinuum deformation, and small deformation and large movement, the numerical manifold method (NMM) introduces two covers, namely the mathematical cover (MC) and the physical cover (PC). This study generates the MC with the influence domains of nodes in the moving least squares (MLS) interpolation instead of commonly-used finite element meshes, significantly simplifying the generation of PCs and the simulation of crack growth. Advantageous over the conventional meshfree method, the MLS-based NMM can naturally treat complex geometry without recourse to those complicated but contrived criteria or operations. Moreover, the treatment of large movement caused by cracking is much easier with the MLS-based NMM than with the FE-based NMM.

Atomistic and continuum modelling of temperature-dependent fracture of graphene

Abstract: This paper presents a comprehensive molecular dynamics study on the effects of nanocracks (a row of vacancies) on the fracture strength of graphene sheets at various temperatures. Comparison of the strength given by molecular dynamics simulations with Griffith’s criterion and quantized fracture mechanics theory demonstrates that quantized fracture mechanics is more accurate compared to Griffith’s criterion. A numerical model based on kinetic analysis and quantized fracture mechanics theory is proposed. The model is computationally very efficient and it quite accurately predicts the fracture strength of graphene with defects at various temperatures. Critical stress intensity factors in mode I fracture reduce as temperature increases. Molecular dynamics simulations are used to calculate the critical values of $$J$$ integral ( $$J_\mathrm{IC}$$ ) of armchair graphene at various crack lengths. Results show that $$J_\mathrm{IC}$$ depends on the crack length. This length dependency of $$J_\mathrm{IC}$$ can be used to explain the deviation of the strength from Griffith’s criterion. The paper provides an in-depth understanding of fracture of graphene, and the findings are important in the design of graphene based nanomechanical systems and composite materials

Cohesive crack, size effect, crack band and work-of-fracture models compared to comprehensive concrete fracture tests

Abstract: The simplest form of a sufficiently realistic description of the fracture of concrete as well as some other quasibrittle materials is a bilinear softening stress-separation law (or an analogous bilinear law for a crack band). This law is characterized by four independent material parameters: the tensile strength, $$f'_t$$ , the stress $$\sigma _k$$ at the change of slope, and two independent fracture energies—the initial one, $$G_f$$ and the total one, $$G_F$$ . Recently it was shown that all of these four parameters can be unambiguously identified neither from the standard size effects tests, nor from the tests of complete load-deflection curve of specimens of one size. A combination of both types of test is required, and is here shown to be sufficient to identify all the four parameters. This is made possible by the recent data from a comprehensive test program including tests of both types made with one and the same concrete. These data include Types 1 and 2 size effects of a rather broad size range (1:12.5), with notch depths varying from 0 to 30 % of cross section depth. Thanks to using identically cured specimens cast from one batch of one concrete, these tests have minimum scatter. While the size effect and notch length effect were examined in a separate study, this paper deals with inverse finite element analysis of these comprehensive test data. Using the crack band approach, it is demonstrated: (1) that the bilinear cohesive crack model can provide an excellent fit of these comprehensive data through their entire range, (2) that the $$G_f$$ value obtained agrees with that obtained by fitting the size effect law to the data for any relative notch depth deeper than 15 % of the cross section (as required by RILEM 1990 Recommendation), (3) that the $$G_F$$ value agrees with that obtained by the work-of-fracture method (based on RILEM 1985 Recommendation), and (4) that the data through their entire range cannot be fitted with linear or exponential softening laws.

A geometrically nonlinear phase field theory of brittle fracture

Abstract: Phase field theory is developed for solids undergoing potentially large deformation and fracture. The elastic potential depends on a finite measure of elastic strain. Surface energy associated with fracture can be anisotropic, enabling description of preferred cleavage planes in single crystals, or isotropic, applicable to amorphous solids such as glass. Incremental solution of the Euler–Lagrange equations corresponds to local minimization of an energy functional for the solid, enabling prediction of equilibrium crack morphologies. Predictions are in close agreement with analytical solutions for pure mode I or pure mode II loading, including the driving force for a crack to extend from a pre-existing plane onto a misoriented cleavage plane. In an isotropic matrix, the tendency for a crack to penetrate or deflect around an inclusion is shown to depend moderately on the ratio of elastic stiffness in matrix and inclusion and strongly on their ratio of surface energy. Cracks are attracted to (shielded by) inclusions softer (stiffer) than the surrounding matrix. The theory and results apparently report the first fully three-dimensional implementation of phase field theory of fracture accounting for simultaneous geometric nonlinearity, nonlinear elasticity, and surface energy anisotropy.

A mesh-independent finite element formulation for modeling crack growth in saturated porous media based on an enriched-FEM technique

Abstract: In this paper, the crack growth simulation is presented in saturated porous media using the extended finite element method. The mass balance equation of fluid phase and the momentum balance of bulk and fluid phases are employed to obtain the fully coupled set of equations in the framework of $$u{-}p$$ formulation. The fluid flow within the fracture is modeled using the Darcy law, in which the fracture permeability is assumed according to the well-known cubic law. The spatial discritization is performed using the extended finite element method, the time domain discritization is performed based on the generalized Newmark scheme, and the non-linear system of equations is solved using the Newton–Raphson iterative procedure. In the context of the X-FEM, the discontinuity in the displacement field is modeled by enhancing the standard piecewise polynomial basis with the Heaviside and crack-tip asymptotic functions, and the discontinuity in the fluid flow normal to the fracture is modeled by enhancing the pressure approximation field with the modified level-set function, which is commonly used for weak discontinuities. Two alternative computational algorithms are employed to compute the interfacial forces due to fluid pressure exerted on the fracture faces based on a ‘partitioned solution algorithm’ and a ‘time-dependent constant pressure algorithm’ that are mostly applicable to impermeable media, and the results are compared with the coupling X-FEM model. Finally, several benchmark problems are solved numerically to illustrate the performance of the X-FEM method for hydraulic fracture propagation in saturated porous media.

Choosing a proper loading rate for bonded-particle model of intact rock

Abstract: Bonded-particle model (BPM) is widely used to model geomaterials, in which calibration against the results from uniaxial/triaxial compressive tests, Brazilian tensile tests and shear tests have been commonly conducted. However, since different loading rates were used, it is difficult to assess the numerical results of these studies if the effects of the loading rate are ignored. This paper discusses the loading mechanisms associated with different loading rates in the BPM and examines the numerical outputs under these different rates. The results indicate that the time step is an important factor controlling the loading rate of the BPM and should be considered in addition to the velocity of the loading platen. The strain rate, which is usually employed to describe the loading rate in a physical test, cannot be used for the direct comparison of different numerical tests in $$\hbox {PFC}^{\mathrm{2D}}$$ due to the time step. A proposed “step strain rate”, which considers the time step, is found to be more appropriate for comparing the loading velocity on specimens of varying sizes. Six different loading rates (0.005, 0.01, 0.02, 0.08, 0.2 and 0.6 m/s) are employed in uniaxial compressive tests and Brazilian tests during this study. After comprehensive examinations, a maximum step strain rate of $$1.1 \times 10^{-8}\, \hbox {step}^{-1}$$ is considered to be appropriate for quasi-static uniaxial compressive tests and Brazilian tests using the BPM.

A new view on J -integrals in elastic–plastic materials

Abstract: It is well known that the application of the conventional $$J$$ -integral is connected with severe restrictions when it is applied for elastic–plastic materials. The first restriction is that the $$J$$ -integral can be used only, if the conditions of proportional loading are fulfilled, e.g. no unloading processes should occur in the material. The second restriction is that, even if this condition is fulfilled, the $$J$$ -integral does not describe the crack driving force, but only the intensity of the crack tip field. Using the configurational force concept, Simha et al. (J Mech Phys Solids 56:2876–2895, 2008), have derived a $$J$$ -integral, $$J^{\mathrm{ep}} $$ , which overcomes these restrictions: $$J^{\mathrm{ep}} $$ is able to quantify the crack driving force in elastic–plastic materials in accordance with incremental theory of plasticity and it can be applied also in cases of non-proportionality, e.g. for a growing crack. The current paper deals with the characteristic properties of this new $$J$$ -integral, $$J^{\mathrm{ep}}$$ , and works out the main differences to the conventional $$J$$ -integral. In order to do this, numerical studies are performed to calculate the distribution of the configurational forces in a cyclically loaded tensile specimen and in fracture mechanics specimens. For the latter case contained, uncontained, and general yielding conditions are considered. The path dependence of $$J^{\mathrm{ep}} $$ is determined for both a stationary and a growing crack. Much effort is spent in the investigation of the path dependence of $$J^{\mathrm{ep}} $$ very close to the crack tip. Several numerical parameters are varied in order to separate numerical and physical effects and to deduce the magnitudes of the crack driving force for stationary and growing cracks. Interpretation of the numerical results leads to a new, completed picture of the $$J$$ -integral in elastic–plastic materials where $$J^{\mathrm{ep}} $$ and the conventional $$J$$ -integral complement each other. This new view allows us also to shed new light on a long-term problem, which has been called the “paradox of elastic–plastic fracture mechanics”.

Characterization of crack tip stress fields in test specimens using mode mixity parameters

Abstract: The aim of this study is to represent the combined effect of mode mixity, specimen geometry and relative crack length on the $$T$$ -stress, elastic–plastic stress fields, integration constant $$I_{n}$$ , angle of initial crack extension, and the plastic stress intensity factor. The analytical and numerical results are obtained for the complete range of mixed modes of loading between mode I and mode II. For comparison purposes, the reference fields for plane mixed-mode problems governing the asymptotic behavior of the stresses and strains at the crack tip are developed in a power law elastic–plastic material. For the common experimental fracture mechanics specimen geometries considered, the numerical constant of the plastic stress field $$I_{n}$$ and the $$T$$ -stress distributions are obtained as a function of the dimensionless crack length and mode mixity. A method is also suggested for calculating the plastic stress intensity factor for any mixed-mode I/II loading based on the $$T$$ -stress and power law solutions. It is further demonstrated that in both plane stress and the plane strain, the plastic stress intensity factor can be used to characterize the crack tip stress fields for a variety of specimen geometries and different mixed-mode loading. The applicability of the plastic stress intensity factor to analysis of the in-plane and out-of-plane constraint effect is also discussed.

Simulation of fatigue crack growth with a cyclic cohesive zone model

Abstract: Fatigue crack growth is simulated for an elastic solid with a cyclic cohesive zone model (CZM). Material degradation and thus separation follows from the current damage state, which represents the amount of maximum transferable traction across the cohesive zone. The traction–separation relation proposed in the cyclic CZM includes non-linear paths for both un- and reloading. This allows a smooth transition from reversible to damaged state. The exponential traction–separation envelope is controlled by two shape parameters. Moreover, a lower bound for damage evolution is introduced by a local damage dependent endurance limit, which enters the damage evolution equation. The cyclic CZM is applied to mode I fatigue crack growth under $$K_{\mathrm{I}}$$ -controlled external loading conditions. The influences of the model parameters with respect to static failure load $$K_{\mathrm{0}}$$ , threshold load $$\varDelta K_{\mathrm{th}}$$ and Paris parameters $$m, C$$ are investigated. The study reveals that the proposed endurance limit formulation is well suited to control the ratio $$\varDelta K_{\mathrm{th}}/K_{\mathrm{0}}$$ independent of $$m$$ and $$C$$ . An identification procedure is suggested to identify the cohesive parameters with the help of Wohler diagrams and fatigue crack growth rate curves.

Crack stability in edge-notched clamped beam specimens: modeling and experiments

Abstract: Stability of a fracture toughness testing geometry is important to determine the crack trajectory and R-curve behavior of the specimen. Few configurations provide for inherent geometric stability, especially when the specimen being tested is brittle. We propose a new geometrical construction called the single edge notched clamped bend specimen (SENCB), a modified form of three point bending, yielding stable cracking under load control. It is shown to be particularly suitable for small-scale structures which cannot be made free-standing, (e.g., thin films, coatings). The SENCB is elastically clamped at the two ends to its parent material. A notch is inserted at the bottom center and loaded in bending, to fracture. Numerical simulations are carried out through extended finite element method to derive the geometrical factor f(a/W) and for different beam dimensions. Experimental corroborations of the FEM results are carried out on both micro-scale and macro-scale brittle specimens. A plot of vs a/W, is shown to rise initially and fall off, beyond a critical a/W ratio. The difference between conventional SENB and SENCB is highlighted in terms of and FEM simulated stress contours across the beam cross-section. The `s of bulk NiAl and Si determined experimentally are shown to match closely with literature values. Crack stability and R-curve effect is demonstrated in a PtNiAl bond coat sample and compared with predicted crack trajectories from the simulations. The stability of SENCB is shown for a critical range of a/W ratios, proving that it can be used to get controlled crack growth even in brittle samples under load control.

Experiments and modeling of edge fracture for an AHSS sheet

Abstract: With the emergence of advanced high strength steels (AHSSs) and other light–weight materials, edge fracture has been one of the important issues evading reliable prediction using CAE tools To study edge fracture behavior of AHSS, a comprehensive hole expansion test (HET) program has been carried out on a DP780 sheet Specimen with three different edge conditions (milled edge, water jet cut edge and punched edge) are manufactured and tested Results reveal that the hole expansion ratio (HER) of the present DP780 sheet is around 38 % for milled specimen and water jet cut specimen, and about 14 % for punched specimen A novel method of a central hole specimen tension is also introduced for edge fracture study, showing a similar trend as found in HET The paper briefly presents a procedure and the results for a full calibration of the DP780 sheet for plasticity and fracture, where a hybrid testing/simulation method is used to obtain parameters for Hill 48 plasticity model and modified Mohr–Coulomb fracture model The finite element simulation gives an accurate prediction of HER, as well as the load displacement response and specimen deflection distribution in the hole expansion tests on uncracked material The correlation between simulation and tests on central hole specimen also turns out to be very good The paper also presents a very interesting insight of the initiation and propagation of cracks from the hole edge during a hole expansion test by numerical simulation in comparison with testing observation The number of final cracks are accurately predicted Other new aspects of the present paper include an improved 3D DIC measurement technique and a simplified analytical solution, from which a rapid estimation of displacement and hoop strain field can be made (see “Appendix 2”)

Unstructured polygonal meshes with adaptive refinement for the numerical simulation of dynamic cohesive fracture

Abstract: This paper presents a scheme for adaptive mesh refinement on unstructured polygonal meshes to better capture crack patterns in dynamic cohesive fracture simulations. A randomly seeded polygonal mesh leads to an isotropic discretization of the problem domain, which does not bias crack patterns, but restricts the number of paths that a crack may travel at each node. An adaptive refinement scheme is proposed and investigated through a detailed set of geometric studies. The refinement scheme is selectively chosen to optimize the number of paths that a crack may travel, while still maintaining a conforming domain discretization. The details of the refinement scheme are outlined, along with the criterion used to determine the region of refinement and the method of interpolating nodal attributes. Extrinsic cohesive elements are inserted when and where necessary, and follow the constitutive response of the Park–Paulino–Roesler cohesive model. The influence of bulk and cohesive material heterogeneity is investigated through the use of a statistical distribution of material properties. The adaptive mesh modifications are handled through a compact topological data structure. Numerical examples highlight the features of adaptive refinement in capturing physical fracture patterns while addressing computational cost. Thus, the present approach is a step towards obtaining accurate dynamic fracture patterns and fields with polygonal elements.

A finite difference-augmented peridynamics method for reducing wave dispersion

Abstract: A method is presented for the modeling of brittle elastic fracture which combines peridynamics and a finite difference method to mitigate the wave dispersion properties of peridynamics. Essentially, a finite difference method is used in the bulk for wave propagation modeling, while peridynamics is automatically inserted in high strain areas to model crack initiation and growth. The dispersion properties of finite difference methods and discretized peridynamics are reviewed and the interface reflection properties between the two regions are investigated. Results show that the augmented method can improve the modeling of wave propagation and boundary conditions. In addition, the numerical stress intensity factor computed at a crack tip shows reduced oscillations in the augmented method, likely due to the improved dispersion properties of the bulk. Dynamic fracture simulations show a difference in crack paths between the methods.

Further examination of the criterion for crack initiation under mixed-mode I+III loading

Abstract: Mixed-mode fracture presents spectacular, scale-independent, pattern formation in nature and engineering applications. The criteria for crack initiation and growth under such mixed mode loading, however, are not well established. This work is aimed at exploring the failure criteria and the pattern formation under combined modes I and III. Specific designs of specimens based on boundary element simulations are considered with the aim of examining crack path selection at nucleation, threshold behavior of crack front fragmentation and, spacing of fragmentation. Experimental investigations with these specially designed geometries show that there does not exist a threshold ratio of $$K_{III}^{\infty }/K_{I}^{\infty }$$ below which a crack will propagate smoothly without fragmenting into facets. The crack front is shown to fragment immediately as soon as it is perturbed by a small amplitude mode III loading. The experimental results show further that spacing of the fragmentation is set not by any intrinsic length scale of the material, but by the characteristic dimension of the driving crack and the global loading.

Temperature, moisture and mode-mixity effects on copper leadframe/EMC interfacial fracture toughness

Abstract: A systematic investigation and characterization of the interfacial fracture toughness of the bi-material copper leadframe/epoxy molding compound is presented. Experiments and finite element simulations were used to investigate delamination and interfacial fracture toughness of the bi-material. Two dimensional simulations using virtual crack closure technique, virtual crack extension and J-integral proved to be computationally cheap and accurate to investigate and characterize the interfacial fracture toughness of bi-material structures. The effects of temperature, moisture diffusion and mode-mixity on the interfacial fracture toughness of the bi-material were considered. Testing temperature and moisture exposure significantly reduce the interfacial fracture toughness, and should be avoided if possible.

Investigation of fatigue crack growth characteristics of NR/BR blend based tyre tread compounds

Abstract: Tyre tread directly comes in contact with various road surfaces and is prone to damage due to cuts from sharp objects during service. As tyres undergo millions of fatigue cycles, these cuts propagate continuously and lead to catastrophic failure. Therefore fatigue crack growth (FCG) characteristics should be an essential criterion for tread compound selection. The present study investigates FCG behavior of blends comprising of Natural Rubber (NR) and Polybutadiene Rubber (BR) over a wide range of tearing energy. Pure shear specimens with a notch on both edges were tested in a Tear Analyser. Rapid increase in FCG rate after a certain strain level was observed. This transition point appeared in a strain range of 20–35 %, depending on the blend composition. The higher BR containing compounds exhibited better FCG characteristics below the transition point but reversal of ranking was seen above this point. The influence of temperature, R ratio, waveforms and cure system on FCG characteristics was also investigated in NR and 60–40 NR/BR blend compounds. Higher FCG rate was achieved under pulse loading compared to the sine waveform. The relaxation time between pulse cycles played an important role. With an increase in relaxation time, FCG rate decreases significantly. The higher sensitivity towards R ratio was observed in NR compound. The 60–40 NR/BR blend showed higher FCG rate with increase in temperature compared to the NR compound. The NR compound with high Sulfur/Accelerator (S/Ac) ratio showed better FCG characteristics whereas for 60–40 NR/BR blend with low S/Ac ratio achieved superior FCG characteristics.

Steady-state propagation of a mode II crack in couple stress elasticity

Abstract: The present work deals with the problem of a semi-infinite crack steadily propagating in an elastic body subject to plane-strain shear loading. It is assumed that the mechanical response of the body is governed by the theory of couple-stress elasticity including also micro-rotational inertial effects. This theory introduces characteristic material lengths in order to describe the pertinent scale effects that emerge from the underlying microstructure and has proved to be very effective for modeling complex microstructured materials. It is assumed that the crack propagates at a constant sub-Rayleigh speed. An exact full field solution is then obtained based on integral transforms and the Wiener–Hopf technique. Numerical results are presented illustrating the dependence of the stress intensity factor and the energy release rate upon the propagation velocity and the characteristic material lengths in couple-stress elasticity. The present analysis confirms and extends previous results within the context of couple-stress elasticity concerning stationary cracks by including inertial and micro-inertial effects.

Obtaining S–N curves from crack growth curves: an alternative to self-similarity

Abstract: A crack growth model that allows us to obtain the S–N curves from the crack growth rate curves is presented in an attempt to harmonize the stress based and fracture mechanics approaches in lifetime prediction of long cracks propagation. First, using the Buckingham theorem, the crack growth rate curve $$\frac{da}{dN}-\varDelta K$$ is defined over all its range as a cumulative distribution function based on a normalized dimensionless stress intensity factor range $$\varDelta K^+$$ . Then, a relevant theorem is derived that provides an alternative to self-similarity allowing significant reduction of experimental planning. In this way, different $$a-N$$ crack growth curves for different stress ranges $$\varDelta \sigma $$ and initial crack lengths $$a_0$$ can be obtained from a particular crack growth curve under some conditions. The S–N field is obtained from the crack growth curves, showing the close relation between the fracture mechanics and stress approaches. Finally, the model is applied to a particular set of experimental data to obtain the crack growth rate curve and the S–N curves of a certain material for a subsequent fatigue lifetime assessment

A modeling approach for the complete ductile–brittle transition region: cohesive zone in combination with a non-local Gurson-model

Abstract: The present study deals with the simulation of crack propagation in the ductile–brittle transition region on the macro-scale. In contrast to most studies in the literature, not only the ductile softening by void growth and coalescence is incorporated but also the particular material degradation by cleavage. A non-local Gurson-type model is employed together with a cohesive zone to simulate both failure mechanisms simultaneously. This consistent formulation of a boundary value problem allows arbitrary high mesh resolutions. The results show that the model captures qualitative effects of corresponding experiments such as the cleavage initiation in front of a stretch zone, the formation of secondary cracks and possible crack arrest. The influence of the temperature on the predicted toughness is reproduced in the whole ductile–brittle transition region without introducing temperature-dependent fit parameters. A comparison with experimental data shows that the shift of the ductile–brittle transition temperature associated with a lower crack-tip constraint can be predicted quantitatively.

Tensile characteristics and fracture energy of fiber reinforced and non-reinforced ultra high performance concrete (UHPC)

Abstract: In the framework of this study, various mixtures of fiber reinforced and non-reinforced ultra high performance concrete (UHPFRC and UHPC) were produced and tested with focus on the determination of the fracture energy and its comparison to standard mechanical material parameters. For some mixtures a compressive strength of more than 300 MPa was reached still retaining good fresh characteristics of the UHPC. These mixtures were examined for properties of fresh and hardened concrete, focusing on tensile strength properties and fracture energy. The fracture energy was determined to describe the work capacity, i.e. the potential energy intake until the failure of the material. Thereby, a significant increase of the work capacity could be achieved by the addition of steel fibers. Furthermore, the impact of a vacuum treatment of the freshly mixed concrete in regard to fresh and hardened concrete characteristics as well as the influence of aftertreatment (heat treatment and water storage) on compressive and tensile properties of the UHPC was investigated.

Stretchability of indium tin oxide (ITO) serpentine thin films supported by Kapton substrates

Abstract: Indium tin oxide (ITO) has been widely used as the electrode material in touch-screen displays and solar cells attributing to its combined high electrical conductivity and optical transparency. Moving forward from wafer based electronics to flexible/stretchable electronics, brittle electronic materials like ITO are significantly hindering the deformability of the integrated systems. To minimize strains in inorganic materials when subjected to stretch, thin metallic and ceramic films can be patterned into serpentine shapes. Although metallic serpentines have received extensive studies, experimental investigations on ceramic serpentines have not been reported. We perform uniaxial tension tests on Kapton-supported ITO serpentine thin films with in situ electrical resistance measurements. It is found that the narrower serpentine ribbons are more stretchable than their wider counterparts. We propose a generic empirical equation to predict the stretchability using three dimensionless geometric parameters. Conclusions reached for Kapton-supported ITO serpentine films are generally applicable to gold, silicon, and other stiff serpentine films bonded to stiff polymer substrates such as Kapton and polyethylene terephthalate.

Assessment of split-beam-type tests for mode III delamination toughness determination

Abstract: Four split-beam-type tests are proposed for determining the mode III delamination toughness of laminated composite materials. Each test is first assessed via three dimensional finite element analysis. Experimental evaluations are then conducted, for which two different unidirectional carbon/epoxy materials are considered. For either material, it is shown that the same mode III toughness is obtained by the four different tests, provided that specimens with the same delamination length are tested. However, when a single test configuration is utilized to investigate the effect of delamination length, the apparent mode III toughness is observed to decrease with increasing delamination length. In order to understand the mechanisms behind this, transverse section cuts were taken at the delamination front of tested specimens. Photomicroscopic examinations of these cross sections revealed matrix cracks at the delamination front that were oriented at an inclination of \(45^{\circ }\) to the plane of the delamination. Based on previous observations of mode III crack initiation in homogeneous materials, it is hypothesized that these matrix cracks initiate prior to or concurrent with delamination advance, and therefore are responsible for the observed geometry-dependence of the mode III delamination toughness in laminated polymeric composites.

Sandia Fracture Challenge: blind prediction and full calibration to enhance fracture predictability

Abstract: The Impact and Crashworthiness Lab at Massachusetts Institute of Technology participated in the Sandia Fracture Challenge and predicted the crack initiation and propagation path during a tensile test of a compact tension specimen with three holes (B, C, and D), using a very limited number of material properties, including uniaxial tensile tests of a dog-bone specimen. The maximum shear stress and modified Mohr–Coulomb fracture models were used. The predicted crack path of A–C–E coincided with two out of thirteen experiments performed by Sandia National Laboratories, and the maximum load, as well as the load level at the first and second crack initiation, was accurately captured. However, the crack-tip opening displacements (CODs) corresponding to the initiation of the two cracks were overestimated by 12 and 24 %, respectively. After the challenge ended, we received the leftover material from Sandia and did full plasticity and fracture calibration by conducting extra fracture tests, including tensile tests, on a specimen with two symmetric round notches, a specimen with a central hole, and a butterfly specimen with double curvature. In addition, pure shear tests were carried out on a butterfly specimen. Newly identified fracture parameters again predicted the A–C–E crack path, but the force–COD response could be reproduced almost perfectly. Detailed calibration procedures and validation are discussed. Furthermore, in order to investigate the influence of the machining quality on the results, a pre-damage value was introduced to the first layer of finite elements around the starter notch, A, and the three holes, B, C, and D. This accelerated shear localization between holes A and D (and between D and C as well) and changed the crack path to A–D–C–E. Parametric study on the pre-damage value showed that there exist two competing crack paths, and the corresponding force–COD curve is influenced by the pre-damage value. The effect of mesh size and boundary conditions are also discussed.

Unified parameter of in-plane and out-of-plane constraint effects and its correlation with brittle fracture toughness of steel

Abstract: In this work, the equivalent plastic strain $$\varepsilon _{p}$$ distributions ahead of crack tips for the experimental specimens with combined in-plane and out-of-plane constraints under brittle fracture condition in the literature were calculated by three-dimensional finite element. The constraint parameter $$A_{p}$$ based on the areas surrounded by $$\varepsilon _{p}$$ isolines ahead of crack tips has been comparatively analyzed with several constraint parameters ( $$T$$ -stress, $$A_{2}$$ , $$Q$$ and stress triaxiality $$h$$ ) based on the crack-tip stress fields, and the capability of parameter $$A_{p}$$ for characterizing in-plane and out-of-plane crack-tip constraint effects for brittle fracture has been identified. The results show that the parameter $$A_{p}$$ has a good correlation with brittle fracture toughness $$K_{Jc}$$ and $$J_{c}$$ of various specimens with different constraint levels, and it is a unified measure parameter of in-plane and out-of-plane constraint for brittle fracture. The unified correlation lines and formulae of the normalized brittle fracture toughness $$K_{Jc}/K_{ref}$$ and $$J_{Ic}/J_{ref}$$ with $$\sqrt{A_p}$$ have been obtained for the steel, and they may be used to determine constraint-dependent or structurally relevant fracture toughness of specimens or cracked components with any constraint levels. The application methodology of the constraint parameter $$A_{p}$$ for structural integrity assessments needs to be further investigated by numerical calculations and experiments.

Comparison of several BEM-based approaches in evaluating crack-tip field intensity factors in piezoelectric materials

Abstract: From the viewpoint of fracture mechanics, of importance is the near-tip field which can be characterized as field intensity factors. In this paper, the crack-tip field intensity factors of the stress and electric displacement in two dimensional piezoelectric solids are evaluated by using four approaches including the displacement extrapolation, the stress method, the J-integral and the modified crack closure integral method (MCCI) based on a boundary element method (BEM). The strongly singular displacement boundary integral equations (BIEs) are applied on the external boundary of the cracked solid, while the hypersingular traction BIEs are used on the crack faces. Three numerical examples are presented to show the path independence and the high accuracy of the J-integral in piezoelectric materials and to analyze the pros and cons of these approaches in evaluating the field intensity factors.

Improved decohesion modeling with the material point method for simulating crack evolution

Abstract: A combined elastoplasticity and decohesion model is used with the material point method for the crack problem as described in the Sandia National Laboratories challenge. To predict the cracking path in a complex configuration with the least computational cost, the decohesion modeling is improved by making the failure mode adjustable and by replacing the critical normal and tangential decohesion strengths with the tensile and shear peak strengths, without performing discontinuous bifurcation analysis in each loading step after the onset of failure is identified. It is found that there is a transition between different failure modes along the cracking path, which depends on the stress distribution around the path due to the nonlocal nature of failure evolution. Based on the parametric study and available experimental data, the proposed model-based simulation procedure could be calibrated to predict the essential feature of the observed cracking response.

A new basis for the application of the J-integral for cyclically loaded cracks in elastic–plastic materials

Abstract: Fatigue crack propagation is by far the most important failure mechanism. Often cracks under low-cycle fatigue conditions and, especially, short fatigue cracks cannot be treated with the conventional stress intensity range $$\Delta K$$ -concept, since linear elastic fracture mechanics is not valid. For such cases, Dowling and Begley (ASTM STP 590:82–103, 1976) proposed to use the experimental cyclic $$J$$ -integral $$\Delta J^{\exp }$$ for the assessment of the fatigue crack growth rate. However, severe doubts exist concerning the application of $$\Delta J^{\exp }$$ . The reason is that, like the conventional $$J$$ -integral, $$\Delta J^{\exp }$$ presumes deformation theory of plasticity and, therefore, problems appear due to the strongly non-proportional loading conditions during cyclic loading. The theory of configurational forces enables the derivation of the $$J$$ -integral independent of the constitutive relations of the material. The $$J$$ -integral for incremental theory of plasticity, $$J^{\mathrm{ep}}$$ , has the physical meaning of a true driving force term and is potentially applicable for the description of cyclically loaded cracks, however, it is path dependent. The current paper aims to investigate the application of $$J^{\mathrm{ep}}$$ for the assessment of the crack driving force in cyclically loaded elastic–plastic materials. The properties of $$J^{\mathrm{ep}}$$ are worked out for a stationary crack in a compact tension specimen under cyclic Mode I loading and large-scale yielding conditions. Different load ratios, between pure tension- and tension–compression loading, are considered. The results provide a new basis for the application of the $$J$$ -integral concept for cyclic loading conditions in cases where linear elastic fracture mechanics is not applicable. It is shown that the application of the experimental cyclic $$J$$ -integral $$\Delta J^{\exp }$$ is physically appropriate, if certain conditions are observed.