Constant Energy Release Rate Research Articles

A finite crack growth energy release rate for interlaminar fracture analysis of composite material at different temperatures

The interlaminar fracture toughness of unidirectional fiber reinforced polymer composite material is temperature and crack growth history dependence. The non-constant interlaminar fracture toughness challenges the wide application of the linear elastic fracture mechanics-based approach for analyzing the interlaminar crack growth in composite material and structures. In addition, a quantitative relationship between the ductility of the matrix and interlaminar fracture toughness of the fiber reinforced composite is still highly desirable. In this paper, both pure resin and composite double cantilever beam (DCB) are tested at different temperatures. A finite crack growth energy release rate is used to analyze the interlaminar crack growth behavior of composite material at different temperatures. The plasticity of the composite DCB is modeled by Hill’s anisotropic plasticity, with the properties determined from multiscale analyses. It is found that a single constant finite growth energy release rate can well predict the interlaminar mode I crack growth of composite material at different temperatures. The roles of the ductility of matrix, thickness of the DCB, and crack growth history on the interlaminar mode I fracture toughness of composite material are quantitatively determined by using the present method.

A finite crack growth energy release rate for elastic-plastic fracture

The concept of energy release rate proposed by Griffith originally used for elastic brittle material was extended for ductile material by Irwin and Orowan using the sum of the surface energy and the work of plastic dissipation as fracture resistance. This fracture resistance, however, depends on the load type and specimen geometry, which hinders its wide application. In contrast, in this paper, a finite crack growth energy release rate is proposed by assuming a finite crack growth, which is conveniently applicable to finite element analysis. The effect of the plastic dissipation on the crack growth is considered in the driving force. Elastic-plastic finite element analysis is used to apply the present energy release rate. Compared to the experiment results, it is shown that for a fixed finite crack growth, a constant critical energy release rate can well predict the stable crack growths and residual strengths of sheets with single and various collinear cracks subjected to different types of loads. The present finite crack growth energy release rate is conceptually simple, has a solid physical foundation, and would be appealing for ductile crack growth analysis.

Toughness of network materials: Structural parameters controlling damage accumulation

Many materials have a network of fibers as their main structural component and are referred to as network materials. Their strength and toughness are important in both engineering and biology. In this work we consider stochastic model fiber networks without pre-existing cracks and study their rupture mechanism. These materials soften as the crosslinks or fibers fail and exhibit either brittle failure immediately after the peak stress, or a more gradual, ductile rupture in the post peak regime. We observe that ductile failure takes place at constant energy release rate defined in the absence of pre-existing cracks as the strain derivative of the specific energy released. The network parameters controlling the energy release rate are identified and discussed in relation to the Lake-Thomas theory which applies to crack growth situations. We also observe a ductile to brittle failure transition as the network becomes more affine and relate the embrittlement to the reduction of mechanical heterogeneity of the network. Further, we confirm previous reports that the network strength scales linearly with the bond strength and with the crosslink density. The present results extend the Lake-Thomas theory to networks without pre-existing cracks which fail by the gradual accumulation of distributed damage and contribute to the development of a physical picture of failure in stochastic network materials.

Crack initiation and slow growth in soda-lime glass from a self-healed crack

Soda-lime glass (SLG) is a widely used structural material with many advantages in terms of thermal, physical and mechanical properties besides esthetics, sustainability and environmental impact. As a highly brittle, low-toughness and high-stiffness material, understanding its failure behavior in general and fracture mechanics in particular is critical for structural applications. The propensity for hairline crack formation at stress concentration sites during service is particularly a critical issue. Hairline cracks in SLG can occasionally heal when the structure is unloaded, become optically invisible and go undetected, causing unexpected and catastrophic failure upon reloading. In this work, crack initiation and quasi-static crack growth from a self-healed crack in SLG plate is recreated and investigated under laboratory conditions. A wedge-splitting test (WST) geometry is adopted to carry out the study. A pre-cut notch is loaded using a wedge to generate a hairline crack and let to heal without any external stimulus. An opto-mechanical study of crack (re)initiation and growth is carried out while mapping the crack-tip stress gradients in the whole field using the transmission-mode Digital Gradient Sensing (DGS) method. An abrupt re-initiation and extension of the self-healed crack, subsequent initiation of the natural crack-tip followed by a slow crack growth are all captured by the far-field load–displacement response as well as the local crack-tip fields. The stress intensity factor (SIF) history for the entire event is extracted subsequently. The results indicate approx. 50% lower value of critical SIF at re-initiation of the self-healed crack relative to the natural/virgin crack. The crack growth resistance behavior shows a nominally constant energy release rate of 6.5 ± 0.5 J/m2 during slow crack growth. A companion finite element (FE) model that mimics optical measurements is also included. The simulations suggest that the contact stiffness of the self-healed crack is about 60% of the virgin material.

Effective Toughness of Heterogeneous Materials with Rate-Dependent Fracture Energy.

We investigate the dynamic fracture of heterogeneous materials experimentally by measuring displacement fields as a rupture propagates through a periodic array of obstacles of controlled fracture energy. Our measurements demonstrate the applicability of the classical equation of motion of cracks at a discontinuity of fracture energy: the crack speed jumps at the entrance and exit of an obstacle, as predicted by the crack-tip energy balance within the brittle fracture framework. The speed jump amplitude is governed by the fracture energy contrast and by the combination of the rate dependency of the fracture energy and the inertia of the medium, which allows the crack to cross a fracture energy discontinuity at a constant energy release rate. This discontinuous dynamics and the rate dependence cause higher effective toughness, which governs the coarse-grained behavior of these cracks.

Fatigue crack growth properties of carbon-polyamide 6 thermoplastic composites using a multi-ΔG control method

The present paper presents a new multi-ΔG control approach to perform mode I fatigue crack growth tests using several constant cyclic energy release rate ranges (ΔG) on only one specimen. It was successfully applied on carbon/polyamide 6 unidirectional composite specimens. After validation checks on the approach, results show that the crack propagation behaviour exhibits three different crack propagation regimes that can be accurately described using the Hartman-Shijves equation. This work has shown that the multi-ΔG control method can provide reliable crack growth propagation results and a complete ΔG versus cycles description.

Effects of span-depth ratios on the energy release rate for three-point bending beams

The effects of span-depth ratios on the energy release rate for three-point bending beams were examined. Expressions for the energy release rate for three-point bending specimens with various span-depth ratios were developed using linear interpolation method. The double-G fracture parameters were calculated through tests of three-point bending beams with the same span (800 mm) but various depths (100 mm, 150 mm, 200 mm, 250 mm and 300 mm) and the findings in literature. Results indicate that (1) with increasing the span-depth ratio, an almost constant initial fracture energy release rate was obtained, and slight decrease tendency of the unstable energy release rate was observed; (2) The empirical relationship between the initial fracture energy and total fracture energy suggested in size effect model was conformed using the unstable fracture energy release rate which was the same as the initial fracture energy; (3) Equivalence between double-G and double-K fracture model was verified; (4) Moreover, the analytical results of unstable fracture energy release rate exhibited a good consistency with the experimental ones, which were insensitive to the softening function.

Simple mechanics model and Hertzian ring crack initiation strength characteristics of silicon nitride ceramic ball subjected to thermal shock

This study investigated the ring crack initiation strength characteristics of silicon nitride ceramic balls subjected to thermal shock. Sphere indentation tests were conducted on ceramic balls following water quenching and furnace cooling operations performed in air and vacuum. The ring crack radius was significantly smaller because of the very thin silicon oxide (SiO2) layer formed owing to heat treatment in air at high temperatures. In addition, the ring crack initiation load and Weibull shape parameter of water-quenched ceramic balls decreased with increasing temperature difference and remained relatively unaffected by the high-temperature oxidation. This phenomenon was mainly due to microscopic damage, which occurs near the surface of ceramic balls, caused by transient thermal stress developed during water quenching. A simple mechanics model based on the constant energy release rate criterion has been proposed for comparing experimental results obtained in this study against theoretical predictions, and results of the said comparison adequately verify strength characteristics of the aforementioned ceramic balls subjected to thermal shock.

Intralaminar fatigue crack growth properties of conventional and interlayer toughened CFRP laminate under mode I loading

Intralaminar and interlaminar fatigue crack growth behaviours under mode I loading were investigated with conventional and interlayer toughened unidirectional CFRP laminates. For intralaminar crack growth tests, initial defects were introduced using “intralaminar film insertion method”, in which a release film is inserted inside a single lamina prepreg. A fatigue test under a constant maximum energy release rate, Gmax, was carried out using DCB specimens. It was found that the intralaminar fatigue crack growth property of the interlayer toughened CFRP laminates was the same as that of the conventional CFRP laminates. For the interlayer toughened CFRP laminates, the Gmax with a given crack growth rate, da/dN, was much lower for intralaminar crack growth than for interlaminar crack growth. The da/dN-Gmax curve at zero crack extension, Δa=0, which was estimated by extrapolating the da/dN-Δa relationship, was not affected by bridging fibres, and most conservative for the interlayer toughened CFRP laminates.

Fatigue crack propagation in polyvinylchloride and polyethersulfone polymer foams

Crack growth in cross-linked polyvinylchloride and thermoplastic polyethersulfone foams under mode [Formula: see text] fatigue cycling has been experimentally examined. Polyvinylchloride foams of densities ranging from 45 to 100 kg/m3 and polyethersulfone foams of densities ranging from 60 to 130 kg/m3 were considered. All cyclic tests employed the sandwich double cantilever beam test specimen. The test results revealed that crack growth rate (da/dN) compared at a constant cyclic energy release rate (ΔG) decreased with increasing density of the foam. The crack propagation rates in low-density polyethersulfone foams were much less than in polyvinylchloride foams of similar density. The crack growth rate in the high-density polyethersulfone foam was highly dependent on the loading R-ratio. The crack front in the low-density polyethersulfone foam displayed marked deviations from a straight shape, where the edge regions propagated faster than the center of the specimen. All polyvinylchloride foams and high-density polyethersulfone foam displayed straight crack fronts.

Micromechanical Interpretation of the Dissipation Associated With Mode I Propagation of Microcracks in Brittle Materials

This paper deals with the dissipation associated with quasistatic microcracking of brittle materials exhibiting softening behavior. For this purpose an elastodamaging cohesive zone model is used, in which cohesive tractions decrease (during crack propagation) with increasing displacement discontinuities. Constant cohesive tractions are included in the model as a limiting special case. Considering a representative volume element containing a dilute distribution of many parallel microcracks, we quantify energy dissipation associated with mode I microcrack propagation. This is done in the framework of thermodynamics, without restricting assumptions on the size of the cohesive zones. Model predictions are compared with exact solutions, which are accessible for constant cohesive tractions. The proposed model reliably predicts both onset of crack propagation and the dissipation during microcracking. It is shown that the energy release rate is virtually equal to the area under the softening curve, if the microscopic tensile strength is at least twice as large as the macroscopic tensile strength. This result justifies approaches relying on the concept of constant energy release rate, such as those frequently used in the engineering practice.

Anisotropic X-ray emission in active galactic nucleus accretion discs

Abstract Straightforward models of X-ray reflection in the inner region of accretion discs predict that the primary X-ray flux and the flux reflected off the surface of the disc should vary together, albeit with a short light traveltime delay. Most of the observations, however, show that the X-ray flux can vary while the reflected features remain constant. Here we propose a simple explanation for this. In all likelihood, the emission of a moderately optically thick magnetic flare atop an accretion disc is anisotropic. A constant energy release rate in a flare will appear to produce a variable X-ray flux as the flare rotates with the accretion disc anchoring the magnetic tube. The reflector, on the other hand, receives a constant X-ray flux from the flare. Since the reflected emission is azimuthally symmetric, the observer will see a roughly constant reflected flux (neglecting relativistic effects). The model does not produce quasi-periodic oscillations if magnetic flux tubes are sheared out faster than they complete one orbit.

An optimized predictor–corrector scheme for fast 3D crack growth simulations

An optimized predictor–corrector scheme for the accelerated simulation of 3D fatigue crack growth is presented. Based on experimental evidence, it is assumed that the crack front shape ensures a constant energy release rate. Starting from a crack front satisfying this requirement a predictor step is performed. Usually, the new crack front does not fulfill the requirement of a constant energy release rate. Therefore, several corrector steps are needed. Within the new predictor–corrector scheme the history of crack growth is taken into account to reduce the number of corrector steps. The efficiency of the new scheme is shown on two numerical examples providing a speed up of a factor above three.

Models for compaction band propagation

Abstract A compaction band is modelled as a thin, ellipsoidal heterogeneity with an imposed inelastic compactive strain and different elastic moduli from the surrounding matrix. Previously published results are used to determine the stress state in the band. For a wide variation of properties, stress conditions, and inelastic strain, the stress state in the band for aspect ratios observed in the field, 10 −3 –10 −4 , is indistinguishable from the result in the zero aspect ratio limit. In this limit, the compressive stress immediately adjacent to the band tip is roughly 10–100 times the far-field stress for parameters representative of field conditions. This value is relatively insensitive to the elastic mismatch between the band and the surrounding material, and is primarily controlled by the ratio of the far-field stress to twice the shear modulus times the inelastic compactive strain. This ratio is inferred to be about 0.02–0.05 from published field results, but may be several times larger for laboratory specimens. The ratio of tip to far-field stress increases with decrease of band shear modulus and becomes unbounded if both the shear modulus and aspect ratio go to zero. A combined anti-crack–dislocation model, in which a compactive relative displacement 2 h is specified in the centre of the band and uniform traction elsewhere, predicts that for growth at constant energy release rate h is proportional to L where L is the half-length of the band. For an energy release rate of 40 kJ m −2 , inferred in an earlier study from field observations and comparable with compaction energies inferred from laboratory tests on circumferentially notched compression samples, the constant of proportionality is consistent with that inferred from laboratory observations and earlier field data.

A bending specimen for constant energy release rate under controlled displacement conditions

A bending specimen that gives a constant energy release rate (independent on the crack length) under controlled displacement conditions is developed. It is assumed that engineering beam theory is applicable, i.e. that among other things, small deformations and linear elastic isotropic material can be assumed. A specific geometry is analyzed numerically by use of the finite element method and experimentally by manufacturing a specimen with the actual geometry in PMMA (polymethylmetacrylate) and then determining the specimen stiffness for different crack lengths. It is found that the geometry considered gives a constant energy release rate under controlled displacement conditions.

Dynamic fracture toughness versus crack tip speed relationship at lower than room temperature for high strength 4340VAR structural steel

A transient finite element analysis is carried out to provide insight into the low temperature dynamic material toughness versus crack tip relationship for high strength structural steels under intense stress pulse loading. The problem analyzed here is plane strain fracture of an edge cracked specimen under plane wave loading conditions. The finite element formulation employed accounts for the effects of finite geometry changes, material inertia, and heat conduction. The material is characterized as an isotropically hardening and thermally softening elastic-viscoplastic von-Mises solid. To model crack initiation and crack advance various crack-tip equations of motion based on elastodynamic modelling of crack growth are used.In particular, relatively simple forms for the crack tip equation of motion corresponding to crack growth at either constant energy release rate, or a constant stress intensity factor, or a constant crack tip speed, along with more complicated forms involving a sharp upturn in fracture resistance at a limiting crack tip speed are employed. The results of these models emphasize the existence of a sharp upturn in dynamic fracture toughness in high strength structural steels at a material characteristic limiting crack tip speed at test temperatures as low as −80°C and with crack tip loading rates of the order of K̇ I ≈ 10 8 MPa m \\ s .

Computational Simulation of Interlaminar Crack Extension in Angle-Ply Laminates due to Transverse Loading

We try to computationally predict the two-dimensional interlaminar crack extension behavior in angle-ply laminates with different fiber-orientations subjected to transverse loading. Unlike previous investigations, a prediction method free from any assumption on the shape of interlaminar cracks is aimed in this study. We focus our attention onto the local energy release rate along the interlaminar crack front. Under the concept of constant critical energy release rate, the interlaminar crack extension in three-layered angle-ply laminates with various fiber orientations is computationally simulated. Simulation results appear basically in good agreement with experimental results, and the variation of the shape of interlaminar cracks can be automatically predicted without any prior knowledge of their appearance.

Mesoscopic Fracture Mechanism of Mode II Delamination Fatigue Crack Propagation in Interlayer-Toughened CFRP.

Delamination crack growth behavior under mode II cyclic loading was investigated with interlayer-toughened CFRP laminate, T800H/3900-2. Fatigue tests under a constant maximum energy release rate showed that the growth rate was independent of the crack length. Then, load-shedding tests were carried out under various stress ratios. The fatigue crack growth resistance of the interlayer-toughened CFRP was higher than that of conventional CF/epoxy. The crack growth rate under various stress ratios was well correlated to the stress intensity range near the threshold region. Thus, the mechanism of fatigue fracture under mode II loading is completely different from that under mode I loading. Fractographic observation showed that the fatigue fracture occurred on the principal shear stress plane. Large hackle patterns which are typical for static mode II tests were not observed under fatigue loading. A mesoscopic fracture model was proposed to explain the microscopic observation and the stress ratio dependence.

Mesoscopic Fracture Mechanism of Mode II Delamination Fatigue Crack Propagation in Interlayer-Toughened CFRP.

Delamination crack growth behavior under mode II cyclic loading was investigated with interlayer toughened CFRP laminate, T800H/3900-2. Fatigue tests under a constant maximum energy release rate showed that the growth rate was independent of the crack length. Then, load-shedding tests were carried out under various stress ratios. The fatigue crack growth resistance of the interlayer toughened CFRP was higher that of conventional CF/epoxy. The crack growth rate under various stress ratios was well correlated to the stress intensity range near the threshold region. Thus, the mechanism of fatigue fracture under mode II loading is completely different from that under mode I loading. Fractographic observation showed that the fatigue fracture occurred on the principal shear stress plane. Large hackle patterns which are typical for static mode II tests were not observed under fatigue loading. A mesoscopic fracture model was proposed to explain the microscopic observation and the stress ratio dependence.

A Numerical Approach to the Interlaminar Crack Formation Process in Cross-Ply Laminates due to Transverse Loading.

Interlaminar crack extension in continuous fiber-reinforced laminates due to accidental transverse loading is one of the most serious problems in actual service applications of this kind of composite. Here we attempt to numerically obtain the relation between the in-plane two-dimensional extent of interlaminar cracks and the transverse load applied to the laminate by quasi-static indentation. Our attention is focused on the local energy release rate along the interlaminar crack front. The two-dimensional multi-layered finite-element method is developed, which employs two-dimensional bending elements of each lamina stacked to represent the laminate. This FEM enables us to easily estimate the energy release rate at any point on the interlaminar crack front. Under the condition of a constant critical energy release rate, we carry out the computational simulation of interlaminar crack extension for the case of a three-layered cross-ply laminate. Simulated extension behavior of interlaminar cracks under increasing indentation load appears to be in good agreement with the experimental observations.