Linear Elastic Fracture Mechanics Predictions Research Articles

On the use of the plastic component of the CTOD for fatigue analysis in austenitic stainless steel

In this work a new methodology for characterising the fatigue crack propagation of metallic alloys is proposed. The methodology is based on the plastic component of the Crack Tip Opening Displacement (CTODp) as a driving force. This CTODp parameter is evaluated from full-field displacement maps obtained by Digital Image Correlation (DIC). The method is applied on austenitic stainless steel but appears to be very suitable to a wide range of metal alloys. The methodology appears to improve some of the issues related to Linear Elastic Fracture Mechanics predictions for fatigue crack growth.

A computational investigation of length-scale effects in the fracture behaviour of a graphene sheet using the atomistic J-integral

The overarching objective of this paper is to investigate the validity of application of continuum-based linear elastic fracture mechanics (LEFM) methodology, which is often employed by researchers to model fracture processes at the “discrete” atomic scale. The potential sources of error in the application of LEFM at the nanoscale are: (a) Length-scale effects, (b) non-local effects due to long range inter-atomic forces, and (c) entropic effects due to random thermal motion of atoms. The material selected for this study is monolayer graphene, primarily because extensive data, both experimental and analytical, already exist for this material in the literature for model validation. Further, an atomistic J-integral is implemented as a nano-scale fracture metric to investigate flaw-tolerance at the nanoscale reported by many researchers, and to develop a methodology to predict the initiation fracture toughness of the material. For this purpose, a bond-order based potential (ReaxFF) available in LAMMPS molecular dynamics (MD) software is utilized to accurately pinpoint bond separation. Predictions obtained using the atomistic J are compared with LEFM predictions for the case of a single (zig-zag) graphene sheet with a center-crack under tensile loading at room temperature, and show significant deviation from LEFM for crack lengths below a certain threshold.

Mapping Microscale Strain Fields Around a Crack Tip in Molybdenum Via Geometric Phase Analysis and Digital Image Correlation

Uniaxial tension tests were conducted on single-edge-notched tensile specimens of pure molybdenum with a mesh grid pattern in front of the notch. A series of images of crack initialization and propagation with a distorted mesh grid pattern were obtained by means of in situ scanning electron microscopy. Strain fields around the crack tip were mapped successively using geometric phase analysis and digital image correlation techniques, and then compared with the predictions obtained through linear elastic fracture mechanics (LEFM). The comparison shows that the measured strain distribution ahead of the crack tip is consistent with the LEFM predictions of up to 25 $$\upmu $$ m from the crack tip.

Numerical investigation of dynamic brittle fracture via gradient damage models

Gradient damage models can be acknowledged as a unified framework of dynamic brittle fracture. As a phase-field approach to fracture, they are gaining popularity over the last few years in the computational mechanics community. This paper concentrates on a better understanding of these models. We will highlight their properties during the initiation and propagation phases of defect evolution. The variational ingredients of the dynamic gradient damage model are recalled. Temporal discretization based on the Newmark- $$\beta $$ scheme is performed. Several energy release rates in gradient damage models are introduced to bridge the link from damage to fracture. An antiplane tearing numerical experiment is considered. It is found that the phase-field crack tip is governed by the asymptotic Griffith’s law. In the absence of unstable crack propagation, the dynamic gradient damage model converges to the quasi-static one. The defect evolution is in quantitative accordance with the linear elastic fracture mechanics predictions. These numerical experiments provide a justification of the dynamic gradient damage model along with its current implementation, when it is used as a phase-field model for complex real-world dynamic fracture problems.

The fracture behavior of birch and spruce in the radial-tangential crack propagation direction at the scale of the growth ring

Abstract Crack-tip displacement fields have been computed based on digital image correlation for spruce (Picea abies [L.] Karst.) and birch (Betula pendula Roth.) wood, which were submitted to pure mode I loading in the RT-direction under both green and air-dried conditions. Moreover, crack propagation was modeled based on both linear elastic fracture mechanics (LEFM) and nonlinear fracture mechanics, relying on the fictitious crack model (FCM). The measured and modeled load versus the crack-mouth opening displacement (CMOD) curves and displacement fields were compared. In the case of spruce, the load-CMOD curves simulated by the FCM coincide well with the measured ones. On the contrary, measured near crack-tip displacement fields in both green and air-dried spruce are better comparable with the LEFM predictions than with the FCM predictions. In the case of green birch, the simulated FCM curve follows the measured curve quite well, but in air-dried birch the simulated FCM curve has a better fit than the LEFM-curve only before maximum load. In birch, the FCM predicts the displacement fields better than the LEFM. In both species, moisture content has a big effect on the softening behavior. In both spruce and birch, the FCM overestimates the displacements ahead of crack tip, whereas the LEFM model underestimates the displacements.

Cohesive zone modeling of interfacial stresses in plated beams

The elastic analysis of interfacial stresses in plated beams has been the subject of several investigations. These studies provided both first-order and higher-order solutions for the distributions of interfacial shear and normal stresses close to the plate end in the elastic range. The notable attention devoted to this topic was driven by the need to develop predictive models for plate end debonding mechanisms, as the early models of this type adopted debonding criteria based on interfacial stresses. Currently, approaches based on fracture mechanics are becoming increasingly established. Cohesive zone modeling bridges the gap between the stress- and energy-based approaches. While several cohesive zone analyses of bonded joints subjected to mode-II loading are available, limited studies have been conducted on cohesive zone modeling of interfacial stresses in plated beams. Moreover, the few available studies present complex formulations for which no closed-form solutions can be found. This paper presents an analytical cohesive zone model for the determination of interfacial stresses in plated beams. A first-order analysis is conducted, leading to closed-form solutions for the interfacial shear stresses. The mode-II cohesive law is taken as bilinear, as this simple shape is able to capture the essential properties of the interface. A closed-form expression for the debonding load is proposed, and the comparison between cohesive zone modeling and linear-elastic fracture mechanics predictions is discussed. Analytical predictions are also compared with results of a numerical finite element model where the interface is described with zero-thickness contact elements, using the node-to-segment strategy and incorporating decohesion and contact within a unified framework.

Fault-induced perturbed stress fields and associated tensile and compressive deformation at fault tips in the ice shell of Europa: implications for fault mechanics

Secondary fractures at the tips of strike-slip faults are common in the ice shell of Europa. Large magnitude perturbed stress fields must therefore be considered to be a viable driving mechanism for the development of part of the fracture sequence. Fault motions produce extensional and compressional quadrants around the fault tips. Theoretically, these quadrants can be associated with tensile and compressive deformational features (i.e. cracks and anti-cracks), respectively. Accordingly, we describe examples of both types of deformation at fault tips on Europa in the form of extensional tailcracks and compressional anti-cracks. The characteristics of these features with respect to the plane of the fault create a fingerprint for the mechanics of fault slip accumulation when compared with linear elastic fracture mechanics (LEFM) models of perturbed stress fields around fault tips. Tailcrack kink angles and curving geometry can be used to determine whether opening accompanies sliding motion. Kink angles in the 50–70° range are common along strike-slip faults that resemble ridges, and indicate that little to no opening accompanied sliding. In contrast, tailcrack kink angles are closer to 30° for strike-slip faults that resemble bands, with tailcrack curvatures opposite to ridge-like fault examples, indicating that these faults undergo significant dilation and infill during fault slip episodes. Anti-cracks, which may result from compression and volume reduction of porous near-surface ice, have geometries that further constrain fault motion history, corroborating the results of tailcrack analysis. The angular separation between anti-cracks and tailcracks are similar to LEFM predictions, indicating the absence of cohesive end-zones near the tips of Europan faults, hence suggesting homogeneous frictional properties along the fault length. Tailcrack analysis can be applied to the interpretation of cycloidal ridges: chains of arcuate cracks on Europa that are separated by sharp kinks called cusps. Cusp angles are reminiscent of tailcrack kink angles along ridge-like strike-slip faults. Cycloid growth in a temporally variable tidal stress field ultimately resolves shear stresses onto the near-tip region of a growing cycloid segment. Thus, resultant slip and associated tailcrack development may be the driving force behind the initiation of the succeeding arcuate segment, hence facilitating the ongoing propagation of the cycloid chain.

The effects of geometry and material properties on the fracture of single lap-shear joints

A review of the mechanics of lap-shear joints is followed by a detailed analysis of the problem using a cohesive-zone approach. The cohesive-zone model allows not only the influence of geometry to be considered, but also allows the cohesive properties of the interface and plastic deformation of the adherends to be included in the analysis. The first part of the paper examines the strength of elastic joints, with an emphasis on the effects of geometry, the cohesive strength of the adhesive, and mode-mixedness. The cohesive-zone models show a transition to the predictions of linear-elastic fracture mechanics under conditions where these are expected to apply. The second part of the paper examines the effect of plasticity in the adherends, and looks at the transition between the elastic and plastic regimes. The final part of the paper makes comparisons between the predictions of the numerical calculations and experimental observations for a model system consisting of a commercial adhesive used to bond an aluminum alloy. Using cohesive-zone parameters previously determined for this particular combination of materials, the numerical predictions show excellent agreement with the experimental observations.

In-situ SEM measurements of crack tip displacements in composite laminates to determine local G in mode I and II

The strain energy release rate, G, in cracked composite test coupons and laminates is usually calculated from global parameters such as applied loads and displacements. The global G does not necessarily reflect the conditions at the crack tip, e.g. when fibres are bridging the crack. This paper presents a method for the experimental determination of the local strain energy release rate based on the crack opening displacement (COD) and crack shear displacement (CSD) profiles at the crack tip, for the case of mode I and mode II loading of composite laminates. It is shown analytically that the singular region, in terms of displacements, is three times larger behind the crack tip, than the singular region in terms of stresses and strains ahead of it, making the technique well suited for the experimental determination of the local G. The local G is determined as follows: load is applied to short Double Cantilever Beam (DCB) and End Loaded Split (ELS) specimens using shims and a special loading fixture, respectively. The loaded specimens are placed inside a scanning electron microscope (SEM) where a series of micrographs, of the region behind the crack tip, are taken. From the micrographs COD and CSD profiles are generated, from which it can be determined if a square root singularity exists. If a square root singularity exists, the local energy release rate can be calculated from the COD and CSD profiles using orthotropic linear elastic fracture mechanics (LEFM). The technique was applied to unidirectional AS4/3501-6 delamination beam specimens. It was found that there is a square root singularity near the crack tip, and that the magnitudes of the measured COD and CSD profiles agree well with analytical LEFM predictions. For the tested DCB specimen, with a laminate thickness of 3.4 mm, it was seen that the singular region, in terms of the displacements, extends to approximately 500 μm behind the crack tip.

COD measurements at various positions along a crack

Load versus crack-opening displacement (COD) was measured at various positions along the border of a fatigue crack as it grew from a small surface crack on the edge of an aluminum specimen into a through-the-thickness crack. Displacements were measured with a laser-based interferometric system with a gage length of 70 μm and a resolution of 0.01 μm. These load-COD curves can be used to determine opening loads and thereby investigate the effect of closure on the growth of cracks. In general, the opening loads decrease as the crack grows. The compliances after the crack is fully open can also be measured, and show generally good agreement with the predictions of linear-elastic fracture mechanics.

Effects of fibre bridging on GIC of a unidirectional glass/epoxy composite

Mode I fracture properties, in particular the critical strain energy release rate G IC, of a unidirectional glass/epoxy composite for crack growth parallel to the fibres, were studied in two ways using double cantilever beam specimen geometry. In the first case, a crack was propagated by repeated loading-unloading cycles. The specimens deviated from linear elastic beam and linear elastic fracture mechanics predictions with respect to their compliance and load at crack propagation, and G IC showed a continuous increase with crack growth, owing to the progressive build-up of a fibre-bridged zone behind the crack tip. In the second case, the crack was propagated in a similar manner but the bridging fibres were removed periodically using a stress corrosion treatment in a solution of 2 n HCl. This treatment effectively restored the linear elastic beam behaviour and reduced G IC to an unbridged value which is independent of crack length.

Fatigue crack growth from sharp notches

Notch-like stress raisers occur widely in engineering components. They are preferred sites for crack initiation when the components are subjected to cyclic loadings. Thus the growth of cracks initiated from notches is very relevant to design against fatigue failures. Schematic models proposed to explain the departure of notch crack growth from linear elastic fracture mechanics predictions are briefly reviewed. Different methods of measuring crack closure are compared. It is found that the commonly employed notch-mouth clip-gauge method is not sensitive enough to detect the closure of short cracks in regions of notch plasticity. Various mechanics parameters have been claimed to be able to bring the notch crack and long crack growth rate data to a single base. In the present work on double-edge notched AISI 316 stainless steel specimens, it is found that none of them is able to correlate satisfactory all the experimental data.

The comparison between three different elements within a center crack plate considering elastic-plastic action

Stress near a crack tip in plasticity was analyzed using three different finite element modelings; a constant strain triangle, eight-noded quadrilaterial, and a crack tip singularity element all considering viscoplasticity. The specimen under consideration was a center cracked plate made from IN-100, a nickel-base superalloy containing a half-crack length equal to 0.1367 in. (3.472 mm). An elastic solution was formulated in conjunction with two different loadings to generate plasticity. Fine mesh and coarse mesh solutions for the higher order elements were generated and compared considering equal number of degrees of freedom in two specific regions referred to as the near field and the far field regions. The authors determined that the elements whose elastic solutions conformed best to linear elastic fracture mechanics predictions were the constant strain triangle and the eight-noded quadrilateral in a fine mesh. The crack tip element did not perform as well as expected. For the plastic analysis, the constant strain triangle exhibited the largest plastic region. The eight-noded isoparametric element came within 15% of the stress levels generated from the constant strain triangle. The stress singularity that is characteristic of the crack tip element forced that element to behave unnaturally stiff immediately adjacent to the crack tip. Because it is not as stiff as either the crack tip element or the eight-noded element, the constant strain triangle offered the most promising solutions as verified through experimentation. It was therefore determined that the constant strain triangle offered the best solution to elastic-plastic finite element problems for the center cracked plate.