Showing papers in "International Journal of Fracture in 2007"

Local strain energy to assess the static failure of U-notches in plates under mixed mode loading

Abstract: The averaged value of the strain energy density over a well-defined volume is used to predict the static strength of U-notched specimens under mixed-mode conditions due to combined bending and shear loads. The volume is centered in relation to the maximum principal stress present on the notch edge, by rigidly rotating the crescent-shaped volume already used in the literature to analyse U- and V-shaped notches subject to mode I loading. The volume size depends on the ultimate tensile strength σu and the fracture toughness KIC of the material. In parallel, an experimental programme was performed. All specimens are made of polymethyl-metacrylate (PMMA), a material which exhibits quasi-brittle behaviour at -60°C. Good agreement is found between experimental data for the critical loads to failure and theoretical predictions based on the constancy of the mean strain energy density over the control volume.

Fracture assessment of U-notches under mixed mode loading: two procedures based on the ‘equivalent local mode I’ concept

Abstract: Two fracture criteria are proposed and applied to blunt-notched components made of brittle materials loaded under mixed mode; the former is based on the averaged strain energy density over a given control volume, the latter on the cohesive crack zone model. In both instances use of the equivalent local mode I hypothesis is made. Only two material properties are needed: the ultimate tensile strength and the fracture toughness. Numerical predictions of rupture loads from the two criteria are compared with experimental measurements from more than 160 static tests with notched beams. The samples are made of PMMA and tested at − 60°C to assure a bulk behaviour almost linear elastic up to rupture. Notch root radii range from 0.2 to 4.0 mm and load mixicity varies from pure mode I to a prevailing mode II. The good agreement between theory and experimental results adds further confidence to the proposed fracture criteria.

On the dynamics of necking and fragmentation – I. Real-time and post-mortem observations in Al 6061-O

Abstract: In this series of papers, we investigate the mechanics and physics of necking and fragmentation in ductile materials. The behavior of ductile metals at strain rates of about 10,000 per second is considered. The expanding ring experiment is used as the vehicle for examining the material behavior in this range of strain rates. In the present paper, the details of the experiment and the experimental observations on Al 6061-O are reported. Specifically, the design of the expanding ring experiment is evaluated through an analysis of the electromagnetic and mechanical aspects of the problem. Then, through an innovative use of high-speed, high-spatial resolution imaging we determine the sequence of deformation and failure in the expanding ring. In particular, the high speed photographs reveal that multiple necks nucleate along the circumference of the ring near a critical strain level; this is followed by a sequence of fractures, and eventually the fragments are unloaded and move as a rigid body. The strain at the onset of localized deformation, the time of fracture initiation, and the sequence of fragmentation are~all quantified in these experiments. These experimental results facilitate detailed comparison to analytical and numerical models of the fragmentation process. Following this, quantitative interpretation of the experimental observations is pursued. First, the uniform expansion of the ring is considered; the observed radial expansion is shown to agree well with an analytical solution of the problem based on a strain-rate-independent plasticity model. The evolution of the strain in the specimen and the onset of necking are evaluated quantitatively and shown to exhibit no dependence on the applied strain rate for this material; the strain at final fracture, averaged over the entire ring, is shown to be an inadequate measure of the ductility of the material. The fragmentation process is modeled with finite element analysis, incorporating the concept of the Mott release waves; this simulation provides a detailed numerical characterization of the experimental observations. Finally, the statistics of the necking and fragmentation are evaluated; these are interpreted both with the predictions of the linear perturbation analysis and a Weibull/Mott model of necking and fragmentation. In the sequel, we will explore the effect of material ductility, strain rate dependence, the effect of geometry and constraint, and finally the effect of a compliant cladding or coating on the development of necking and fragmentation.

Towards a new model of crack tip stress fields

Abstract: This work introduces a novel mathematical model of the stresses around the tip of a fatigue crack, which considers the effects of plasticity through an analysis of their shielding effects on the applied elastic field. The ability of the model to characterize plasticity-induced effects of cyclic loading on the elastic stress fields is assessed and demonstrated using full-field photoelasticity. The focus is on determining the form of the shielding stress components (induced by compatibility requirements at the elastic–plastic interface along the crack flank and via the crack tip plastic zone) and how they influence the crack tip elastic stress fields during a load cycle. The model is successfully applied to the analysis of a fatigue crack growing in a polycarbonate CT specimen.

Development of stress-modified fracture strain for ductile failure of API X65 steel

Abstract: The present paper proposes ductile failure criteria in terms of true fracture strain (the equivalent strain to fracture) as a function of the stress triaxiality (defined by the ratio of the hydrostatic stress to the equivalent stress) for the API X65 steel. To determine the stress-modified fracture strain, smooth and notched tensile bars with four different notch radii are tested, from which true fracture strains are determined as a function of the notch radius. Then detailed elastic–plastic, large strain finite element analyses are performed to estimate variations of stress triaxiality in the tensile bars, which leads to true fracture strains as a function of the stress triaxiality, by combining them with experimental results. Two different failure criteria are proposed, one based on local stress and strain information at the site where failure initiation is likely to take place, and the other based on averaged stress and strain information over the ligament where ductile fracture is expected. As a case study, ligament failures of API X65 pipes with a gouge are predicted and compared with experimental data.

Simulation of dynamic crack growth using the generalized interpolation material point (GIMP) method

Abstract: Dynamic crack growth is simulated by implementing a cohesive zone model in the generalized interpolation material point (GIMP) method. Multiple velocity fields are used in GIMP to enable handling of discrete discontinuity on either side of the interface. Multilevel refinement is adopted in the region around the crack-tip to resolve higher strain gradients. Numerical simulations of crack growth in a homogeneous elastic solid under mode-II plane strain conditions are conducted with the crack propagating along a weak interface. A parametric study is conducted with respect to varying impact speeds ranging from 5 m/s to 60 m/s and cohesive strengths from 4 to 35 MPa. Numerical results are compared qualitatively with the dynamic fracture experiments of Rosakis et al. [(1999) Science 284:1337–1340]. The simulations are capable of handling crack growth with crack-tip velocities in both sub-Rayleigh and intersonic regimes. Crack initiation and propagation are the natural outcome of the simulations incorporating the cohesive zone model. For various impact speeds, the sustained crack-tip velocity falls either in the sub-Rayleigh regime or in the region between $$\sqrt 2 c_{S}$$ (c S is the shear wave speed) and c D (c D is the dilatational wave speed) of the bulk material. The Burridge–Andrews mechanism for transition of the crack-tip velocity from sub-Rayleigh to intersonic speed of the bulk material is observed for impact speeds ranging from 9.5 to 60 m/s (for normal and shear cohesive strengths of 24 MPa). Within the intersonic regime, sustained crack-tip velocities between 1.66 c S (or 0.82 c D ) and 1.94 c S (or 0.95 c D ) were obtained. For the cases simulated in this work, within the stable intersonic regime, the lowest intersonic crack-tip velocity obtained was 1.66 c S (or 0.82 c D ).

J-integral evaluation for U- and V-blunt notches under Mode I loading and materials obeying a power hardening law

Abstract: The paper deals with calculations of the J-integral for a plate weakened by U- and V-blunt notches under mode I loading in the case of a linear and nonlinear elastic material. The main aim of the study is to suggest simple equations suitable for rapid calculations of the J-integral. The semicircular arc of the notch, which is traction free, is assumed as integration path and the J-integral is given as a function of the strain energy over the notch edge. For a numerical investigation of the strain energy density distribution on the notch edge the equation W(θ)=Wmax cosδ(θ) has been assumed, where δ has been determined from finite element analyses. In particular, the following values of the notch acuity a/ρ and the opening angle 2α have been analyzed: 4 ≤ a/ρ ≤ 400 and 0 ≤ 2α ≤ 3π /4. Considering plates weakened by lateral and central notches under symmetric mode I loading, the approximate relationships for the strain energy density, which require the presence of a non zero notch radius for their application, and the J-integral are discussed firstly considering a linear elastic material and then a material obeying a power hardening law during the loading phase. The predicted results of the J-integral are consistent with those directly obtained from finite element analyses.

Modeling of hydrogen-assisted ductile crack propagation in metals and alloys

Abstract: This paper presents a finite element study of the hydrogen effect on ductile crack propagation in metals and alloys by linking effects at the microstructural level (i.e., void growth and coalescence) to effects at the macro-level (i.e., bulk material deformation around a macroscopic crack). The purpose is to devise a mechanics methodology to simulate the conditions under which hydrogen enhanced plasticity induces fracture that macroscopically appears to be brittle. The hydrogen effect on enhanced dislocation mobility is described by a phenomenological constitutive relation in which the local flow stress is taken as a decreasing function of the hydrogen concentration which is determined in equilibrium with local stress and plastic strain. Crack propagation is modeled by cohesive elements whose traction separation law is determined through void cell calculations that address the hydrogen effect on void growth and coalescence. Numerical results for the A533B pressure vessel steel indicate that hydrogen, by accelerating void growth and coalescence, promotes crack propagation by linking simultaneously a finite number of voids with the crack tip. This “multiple-void” fracture mechanism knocks down the initiation fracture toughness of the material and diminishes the tearing resistance to crack propagation.

Theory of dynamic crack branching in brittle materials

Abstract: The problem of dynamic symmetric branching of a tensile crack propagating in a brittle material is studied within Linear Elastic Fracture Mechanics theory. The Griffith energy criterion and the principle of local symmetry provide necessary conditions for the onset of dynamic branching instability and for the subsequent paths of the branches. The theory predicts a critical velocity for branching and a well defined shape described by a branching angle and a curvature of the side branches. The model rests on a scenario of crack branching based on reasonable assumptions and on exact dynamic results for the anti-plane branching problem. Our results reproduce within a simplified 2D continuum mechanics approach the main experimental features of the branching instability of fast cracks in brittle materials.

Fracture toughness of two-dimensional cellular material with periodic microstructure

Abstract: The brittle fracture behavior of periodic 2D cellular material weakened by a system of non-interacting cracks is investigated. The material is represented as a lattice consisting of rigidly connected Euler beams which can fail when the skin stress approaches some limiting value. The conventional Mode I and Mode II fracture toughness is calculated first and its dependence upon the relative density is examined. To this end the problem of a sufficiently long finite length crack in an infinite lattice produced by several broken beams is considered. It is solved analytically by means of the discrete Fourier transform reducing the initial problem for unbounded domain to the analysis of a finite repetitive module in the transform space. Four different layouts are considered: kagome, triangular, square and hexagon honeycombs. The results are obtained for different crack types dictated by the microstructure symmetry of the specific material. The obtained results allowed to define the directional fracture toughness characterizing the strength of a material with many cracks for the given tensile loading direction. This quantity is presented in the form of polar diagrams. For all considered layouts the diagrams are found to be close to circles thus emphasizing quasi-isotropic fracture behavior. The deviation from isotropy in the case of a square honeycomb is essentially less than for the corresponding published axial stiffness polar diagram.

Stress Intensity Factors for an Interface Kinked Crack in a Bi-Material Plate Loaded Normal to the Interface

Abstract: Stress intensity factors for a kinked crack originating at interface of two bonded dissimilar materials subjected to normal tension are found by the finite element method.

Role of plasticity on interface crack initiation from a free edge and propagation in a nano-component

Abstract: In order to elucidate the role of plasticity on interface crack initiation from a free edge and crack propagation in a nano-component, delamination exper- iments were conducted by a proposed nano-cantilever bend method using a specimen consisting of ductile Cu and brittle Si and by a modified four-point bend method. The stress fields along the Cu/Si interface at the critical loads of crack initiation and crack prop- agation were analyzed by the finite element method. The results reveal that intensified elastic stresses in the vicinity of the interface edge and the crack tip are very different, although the Cu/Si interface is identical in both experiments. The plasticity of Cu was then esti- mated on the basis of the nano-cantilever deflection measured by in situ transmission electron microscopy. The plasticity affects the stress fields; the normal stress near the interface edge is intensified while that near the crack tip is much reduced. Both the elasto-plastic stresses are close to each other in the region of about 10 nm. This suggests that the local interface fracture, namely, the crack initiation at the interface edge and

Influence of interfacial delamination on channel cracking of elastic thin films

Abstract: Channeling cracks in brittle thin films have been observed to be a key reliability issue for advanced interconnects and other integrated structures. Most theoretical studies to date have assumed no delamination at the interface, while experiments have observed channel cracks both with and without interfacial delamination. This paper analyzes the effect of interfacial delamination on the fracture condition of brittle thin films on elastic substrates. It is found that, depending on the elastic mismatch and interface toughness, a channel crack may grow with no delamination, with a stable delamination, or with unstable delamination. For a film on a relatively compliant substrate, a critical interface toughness is predicted, which separates stable and unstable delamination. For a film on a relatively stiff substrate, however, a channel crack grows with no delamination when the interface toughness is greater than a critical value, while stable delamination along with the channel crack is possible only in a small range of interface toughness for a specific elastic mismatch. An effective energy release rate for the steady-state growth of a channel crack is defined to account for the influence of interfacial delamination on both the fracture driving force and the resistance, which can be significantly higher than the energy release rate assuming no delamination.

Crack shielding and amplification due to multiple microcracks interacting with a macrocrack

Abstract: We investigate the effect of crack shielding and amplification of various arrangements of microcracks on the stress intensity factors of a macrocrack, including large numbers of arbitrarily aligned microcracks. The extended finite element method is used for these studies. In some cases the numerical XFEM simulation provides results that are more accurate than currently available analytical approximations because the assumptions are less restrictive than those made in obtaining analytical approximations. Stress intensity factors for the tip of a macrocrack under the influence of nearby microcracks are calculated under far field mode 1 boundary conditions. For a microcrack aligned with the macrocrack the numerical results agree quite well with the analytically exact stress intensity factors. The influence of the distance to the macrocrack tip and the rotation angle is investigated for unaligned microcracks, and it is shown in several examples with many randomly distributed microcracks that the influence of those microcracks which are not in close proximity to the macrocrack tip is on the order of 5%.

A computational framework of configurational-force-driven brittle fracture based on incremental energy minimization

Abstract: A variational formulation of quasi-static brittle fracture in elastic solids at small strains is proposed and an associated finite element implementation is presented. On the theoretical side, a consistent thermodynamic framework for brittle crack propagation is outlined. It is shown that both the elastic equilibrium response as well as the local crack evolution follow in a natural format by exploitation of a global Clausius–Planck inequality. Here, the canonical direction of the crack propagation associated with the classical Griffith criterion is the direction of the material configurational force which maximizes the local dissipation at the crack tip. On the numerical side, we first consider a standard finite element discretization in the two-dimensional space which yields a discrete formulation of the global dissipation in terms of configurational nodal forces. Next, consistent with the node-based setting, the discretization of the evolving crack discontinuity for two-dimensional problems is performed by the doubling of critical nodes and interface segments of the mesh. A crucial step for the success of this procedure is its embedding into a r-adaptive crack-segment re-orientation algorithm governed by configurational-force-based directional indicators. Here, successive crack propagation is performed by a staggered loading-release algorithm of energy minimization at frozen crack state followed by nodal releases at frozen deformation. We compare results obtained by the proposed formulation with other crack propagation criteria. The computational method proposed is extremely robust and shows an excellent performance for representative numerical simulations.

Distributed dislocation approach for cracks in couple-stress elasticity: shear modes

Abstract: The distributed dislocation technique proved to be in the past an effective approach in studying crack problems within classical elasticity. The present work aims at extending this technique in studying crack problems within couple-stress elasticity, i.e. within a theory accounting for effects of microstructure. As a first step, the technique is introduced to study finite-length cracks under remotely applied shear loadings (mode II and mode III cases). The mode II and mode III cracks are modeled by a continuous distribution of glide and screw dislocations, respectively, that create both standard stresses and couple stresses in the body. In particular, it is shown that the mode II case is governed by a singular integral equation with a more complicated kernel than that in classical elasticity. The numerical solution of this equation shows that a cracked material governed by couple-stress elasticity behaves in a more rigid way (having increased stiffness) as compared to a material governed by classical elasticity. Also, the stress level at the crack-tip region is appreciably higher than the one predicted by classical elasticity. Finally, in the mode III case the corresponding governing integral equation is hypersingular with a cubic singularity. A new mechanical quadrature is introduced here for the numerical solution of this equation. The results in the mode III case for the crack-face displacement and the near-tip stress show significant departure from the predictions of classical fracture mechanics.

Evaluation of fracture parameters in continuously nonhomogeneous piezoelectric solids

Abstract: A contour integral method is developed for computation of stress intensity and electric intensity factors for cracks in continuously nonhomogeneous piezoelectric body under a transient dynamic load. It is shown that the asymptotic fields in the crack-tip vicinity in a continuously nonhomogeneos medium is the same as in a homogeneous one. A meshless method based on the local Petrov-Galerkin approach is applied for computation of physical fields occurring in the contour integral expressions of intensity factors. A unit step function is used as the test functions in the local weak-form. This leads to local integral equations (LBIEs) involving only contour-integrals on the surfaces of subdomains. The moving least-squares (MLS) method is adopted for approximating the physical quantities in the LBIEs. The accuracy of the present method for computing the stress intensity factors (SIF) and electrical displacement intensity factors (EDIF) are discussed by comparison with available analytical or numerical solutions.

Experimental and numerical analysis of in-plane and out-of-plane crack tip constraint characterization by secondary fracture parameters

Abstract: In this study, several two-parameter- concepts are analyzed experimentally and numerically with respect to their capability of characterizing in-plane and out-of-plane crack tip constraint effects. Different approaches utilizing the second term Tstress of the linear-elastic crack tip stress field, a higher term A2 of the power-law hardening crack tip stress field, a hydrostatic correction term Q for a reference stress field or the local triaxiality parameter h are compared. Experimental results for a pressure vessel steel 22NiMoCr3-7 are investigated by means of the different approaches regarding their capability of constraint characterization for enhanced transferability. Theoretical aspects are investigated in a modified boundary layer analysis and in three-dimensional nonlinear elastic-plastic finite element analyses of the specimens. It is found that, with respect to their capability of quantifying combined in-plane and out-of-plane constraint effects, the investigated concepts differ significantly.

Discrete 3D model as complimentary numerical testing for anisotropic damage

Abstract: It is proposed to use a discrete particle model as a complimentary “numerical testing machine” to identify the hydrostatic elasticity-damage coupling and the corresponding sensitivity to hydrostatic stresses parameter. Experimental tri-axial tensile testing is difficult to perform on concrete material, and numerical testing proves then its efficiency. The discrete model used for this purpose is based on a Voronoi assembly that naturally takes into account heterogeneity. Tri-tension tests on a cube specimen, based on a damage growth control, are presented. A successful identification of the hydrostatic sensitivity function of a phenomenological anisotropic damage model is obtained.

Mixed mode failure criteria for brittle elastic V-notched structures

Abstract: Three mixed mode failure initiation criteria at reentrant corners in brittle elastic materials are examined. Prediction of failure load and crack initiation angle are compared to experimental observations carried out on PMMA (polymer) and MACOR (glass ceramic) V-notched specimens. Since the mode mixity ratio influences greatly both the failure load and crack initiation angle, a detailed experimental procedure has been followed, focusing on obtaining a wide range of mode mixity ratios. It is demonstrated that by assuming a sharp V-notch tip some failure criteria predict reasonably well both the crack initiation angle and failure load.

Determination of the effective mode-I toughness of a sinusoidal interface between two elastic solids

Abstract: A finite element model of crack propagation along a sinusoidal interface with amplitude A and wavelength λ between identical elastic materials is presented. Interface decohesion is modeled with the Xu and Needleman (J Mech Phys Solid 42(9):1397, 1994) cohesive traction–separation law. Ancillary calculations using linear elastic fracture mechanics theory were used to explain some aspects of stable and unstable crack growth that could not be directly attained from the cohesive model. For small aspect ratios of the sinusoidal interface (A/λ ≤ 0.25), we have used the analytical Cotterell–Rice (Intl J Fract 16:155–169, 1980) approximation leading to a closed-form expression of the effective toughness, K Ic , given by $$K_{Ic}\sqrt{(1- u^{2})/E\phi_n}=2/\left(1+\left[1+4\pi^{2}(A/\lambda)^{2}\right]^{-1/2}\right),$$ where $$\phi_n$$ is the work of separation, E is Young’s modulus, and ν is Poisson’s ratio. For A/λ > 0.25, both the cohesive zone model and numerical J-integral estimates of crack tip stress intensity factors suggest the following linear relationship: $$K_{Ic} \sqrt{(1- u^{2})/E\phi_n}=0.81+1.89(A/\lambda).$$ Parametric studies show that the length of the cohesive zone does not significantly influence K Ic , although it strongly influences the behavior of the crack between the initiation of stable crack growth and the onset of unstable fracture.

Application of incubation time approach to simulate dynamic crack propagation

Abstract: The incubation time criterion for dynamic fracture is applied to simulate dynamic crack propagation. Being incorporated into ANSYS finite element package, this criterion is used to simulate the classical dynamic fracture experiments of Ravi-Chandar and Knauss on dynamic crack propagation in Homalite-100. In these experiments a plate with a cut simulating the crack was loaded by an intense pressure pulse applied on the faces of the cut. The load consisted of two consequent trapezoidal pulses. This, in the experimental conditions used by Ravi-Chandar and Knauss, resulted in a crack initiation, propagation, arrest and reinitiation. Dependence of the crack length on time was measured in those experiments. The results for crack propagation obtained by FEM modelling are in agreement with experimental measurements of crack length histories. This result shows the applicability of the incubation time approach to describe the initiation, propagation and arrest of dynamically loaded cracks.

Alternative test method for interlaminar fracture toughness of composites

Abstract: Two methods of determining the mode I interlaminar fracture toughness for fiber-reinforced polymer matrix (FRPM) composites using a double cantilever beam (DCB) test are compared. The standard method of determining GIC is based in linear-elastic fracture mechanics theory and requires a visual measurement of the crack length, presenting data acquisition and analysis difficulties. The proposed method makes use of elastic–plastic fracture mechanics theory and an analytical closed form solution to the J-integral to relate the fracture toughness JIC, load, and angular displacement at the load application points. This method has the advantage of replacing visually acquired data with data easily obtained using inexpensive transducers as well as being applicable to a broader class of materials.

Elasticity Theories with Higher-order Gradients of Inertia and Stiffness for the Modelling of Wave Dispersion in Laminates

Abstract: Dispersive wave propagation is simulated with a continuum elasticity theory that incorporates gradients of strain and inertia. The additional parameters are the Representative Volume Element (RVE) sizes in statics and dynamics, respectively. For the special case of a periodic laminate, expressions for these two RVE sizes can be provided based on the properties of the two components. The fourth-order governing equations are rewritten in two sets of coupled second-order equations, whereby the two sets of unknowns are the macroscopic displacements and the microscopic displacements. The resulting formulation is thus a true multi-scale continuum. In a numerical wave propagation example it is shown that the higher-order continuum model provides an excellent approximation of an explicit model of the heterogeneous laminate.

Mixed-mode crack growth in ductile thin-sheet materials under combined in-plane and out-of-plane loading

Abstract: Cracks in thin structures often are subjected to combined in-plane and out-of-plane loading conditions leading to complex mixed mode conditions in the crack tip region. When applied to ductile materials, large out-of-plane displacements make both experimentation and modeling difficult. In this work, the mixed-mode behavior of thin, ductile materials containing cracks undergoing combined in-plane tension (mode I) and out-of-plane shear (mode III) deformation is investigated experimentally. Mixed-mode fracture experiments are performed and full, three-dimensional (3D) surface deformations of thin-sheet specimens from aluminum alloy and steel are acquired using 3D digital image correlation. General characteristics of the fracture process are described and quantitative results are presented, including (a) the fracture surface, (b) crack path, (c) load-displacement response, (d) 3D full-field surface displacement and strain fields prior to crack growth, (e) radial and angular distributions of the crack-tip strain fields prior to crack growth and (f) singularity analysis of the crack-tip strains prior to crack growth. Results indicate that the introduction of a mode III component to the loading process (a) alters the crack tip fields relative to those measured during nominally mode I loading and (b) significantly increases the initial and stable critical crack-opening-displacement. The data on strain fields in both AL6061-T6 aluminum and GM6208 steel consistently show that for a given strain component, the normalized angular and radial strains at all load levels can be reasonably represented by a single functional form over the range of loading considered, confirming that the strain fields in highly ductile, thin-sheet material undergoing combined in-plane tension and out-of-plane shear loading can be expressed in terms of separable angular and radial functions. For both materials, the displacement and strain fields are (a) similar for both mixed-mode loading angles Φ = 30° and Φ = 60° and (b) different from the fields measured for Mode I loading angle Φ = 0°. Relative to the radial distribution, results indicate that the in-plane strain components do not uniformly exhibit the singularity trends implicit in the HRR theory.

Edge chipping of brittle materials: effect of side-wall inclination and loading angle

Abstract: An earlier analysis of chipping fracture in brittle solids is here extended to include the case of blocks with inclined side faces and non-normal contact loading. The simple relation PF = β Kch 3/2 for the critical chipping load PF in terms of indent location h and material toughness Kc is preserved, with angular coordinates simply incorporated into the β coefficient. Chipping fracture tests using a Vickers indenter near the edges of glass blocks with non-orthogonal faces is used to validate the analysis. Implications of the results in relation to practical engineering, biomechanical and anthropological structures are indicated.

Further developments in J evaluation procedure for growing cracks based on LLD and CMOD data

Abstract: Laboratory testing of fracture specimens to measure resistance curves (J − Δa) have focused primarily on the unloading compliance method using a single specimen. Current estimation procedures (which form the basis of ASTM E1820 standard) employ load line displacement (LLD) records to measure fracture toughness resistance data incorporating a crack growth correction for J. An alternative method which potentially simplifies the test procedure involves the use of crack mouth opening displacement (CMOD) to determine both crack growth and J. However, while the J-correction for crack growth effects adopted by ASTM standard holds true for resistance curves measured using load line displacement (LLD) data, it becomes unsuitable for J-resistance measurements based upon the specimen response defined in terms of load-crack mouth opening displacement (CMOD). Consequently, direct application of the evaluation procedure for J derived from LLD records in laboratory measurements of resistance curves using CMOD data becomes questionable. This study provides further developments of the evaluation procedure for J in cracked bodies that experience ductile crack growth based upon the eta-method and CMOD data. The introduction of a constant relationship between the plastic components of LLD (Δp) and CMOD (Vp) drives the development of a convenient crack growth correction for J with increased loading when using laboratory measurements of P-CMOD data. The methodology broadens the applicability of current standards adopting the unloading compliance technique in laboratory measurements of fracture toughness resistance data (J resistance curves). The developed J evaluation formulation for growing cracks based on CMOD data provides a viable and simpler test technique to measure crack growth resistance data for ductile materials.

Mixed mode fracture separation in viscoelastic orthotropic media: numerical and analytical approach by the Mθv -integral

Abstract: An analytical and numerical procedure based on an independent integral path and finite element analysis for mixed-mode fracture in viscoelastic orthotropic media is developed. The separated method employs virtual mechanics fields induced by the classical singular analytical forms. The viscoelastic generalization uses a thermodynamic approach by defining an energy release rate only taking into account a perfect uncoupling between free and viscous energies. The implementation of the Mθ-integral in finite element software and its integration into the viscoelastic incremental formulation are presented. As results, the analytical and numerical solutions are compared by the way of the energy release rate in pure mode I, pure mode II and mixed modes. In shows that, the developed model lead to accurate and efficient separated fracture mode in viscoelastic materials.

Interaction of interface delamination and plasticity in tensile steel members reinforced by CFRP plates

Abstract: This paper presents experimental and numerical results related to double shear lap tests performed on steel specimens reinforced using CFRP plates. These tests have been simulated taking into account the elastic–plastic behavior of the steel and the delamination between steel and CFRP by means of a cohesive approach. The results obtained are discussed in terms of: (i) maximum load bearing capacity, (ii) minimum bond length in order to exploit the maximum load bearing capacity, (iii) brittle to ductile transition of the interface failure (iv) combination of interface delamination and plastic deformation of the steel. Design formulas for the definition of the minimum bond length and the load bearing capacity of the joint are validated.

Development of a simple mixed-mode fracture test and the resulting fracture energy envelope for an adhesive bond

Abstract: Characterizing the fracture energy of bonded adhesive joints over a range of mode mixities often requires special fixtures or a variety of test configurations. By pairing a tapered and a constant thickness adherend, a hybrid double cantilever beam (DCB) specimen is proposed. This asymmetric tapered DCB configuration can be used to determine the fracture energy as a function of mode mixity. As the debond propagates, the relative stiffness of the adherends varies in a systematic manner, resulting in a range of mode mixities from 0° to approximately 20°. Strain energy release rates were obtained using corrected beam theory and a finite element fracture analysis. Single-leg bending tests were used to determine the fracture energy at mode mixity up to 56°. Constant thickness and tapered DCB tests were used to determine the mode I fracture energy. The resulting fracture envelope was constructed in order to show the dependence of the fracture energy on mode mixity for a two part acrylic adhesive.