Critical Fracture Toughness Research Articles

Measurement of the fracture toughness of polycrystalline bubbly ice from an Antarctic ice core

Abstract. The critical fracture toughness is a material parameter describing the resistance of a cracked body to further crack extension. It is an important parameter for simulating and predicting the breakup behavior of ice shelves from the calving of single icebergs to the disintegration of entire ice shelves over a wide range of length scales. The fracture toughness values are calculated with equations that are derived from an elastic stress analysis. Additionally, an X-ray computer tomography (CT scanner) was used to identify the density as a function of depth. The critical fracture toughness of 91 Antarctic bubbly ice samples with densities between 840 and 870 kg m−3 has been determined by applying a four-point bending technique on single-edge v-notched beam samples. The examined ice core was drilled 70 m north of Kohnen Station, Dronnning Maud Land (75°00' S, 00°04' E; 2882 m). Supplementary data are available at doi:10.1594/PANGAEA.835321.

Influence of softening curves on the residual fracture toughness of post-fire normal-strength concrete

The residual fracture toughness of post-fire normal-strength concrete subjected up to <TEX>$600^{\circ}C$</TEX> is considered by the wedge splitting test. The initial fracture toughness <TEX>$K_I^{ini}$</TEX> and the critical fracture toughness <TEX>$K_I^{un}$</TEX> could be calculated experimentally. Their difference is donated as the cohesive fracture toughness <TEX>$K_I^c$</TEX> which is caused by the distribution of cohesive stress on the fracture process zone. A comparative study on determining the residual fracture toughness associated with three bi-linear functions of the cohesive stress distribution, i.e. Peterson's softening curve, CEB-FIP Model 1990 softening curve and Xu's softening curve, using an analytical method is presented. It shows that different softening curves have no significant influence on the fracture toughness. Meanwhile, comparisons between the experimental and the analytical calculated critical fracture toughness values further prove the validation of the double-K fracture model to the post-fire concrete specimens.

Experimental and numerical study on the improvement of interlaminar mechanical properties of Al/CFRP laminates

Improvement of interlaminar mechanical properties in Al/CFRP laminates, fabricated by carbon fiber reinforced plastic (CFRP) prepregs combined with Al alloy sheets, was studied experimentally and numerically. Three toughening methods including acid etching and mechanical patterning for surface treatment of Al alloy sheet, as well as addition of nanofiller (i.e., vapor grown carbon fiber (VGCF)) to the interface of CFRP and Al sheet, were investigated. Experimental results of double cantilever beam tests show the improvement on the interlaminar mechanical properties of Mode-I fracture in terms of much higher critical load PC and fracture toughness GIC. The highest GIC was obtained in the specimens with the combination of acid etching on Al sheet and 10g/m2 VGCF addition, which was 41 and 6.5 times higher than those of the pristine samples without any treatment and the samples with only acid etching, respectively. Although further mechanical patterning had a positive effect for the case without VGCF addition, the minor effect was observed for the case of VGCF addition because of difficult dispersion of VGCF. Crack propagation and fracture surface were also observed to interpret the improvement mechanism. Moreover, by using the above experimental GIC, finite element analyses were carried out based on cohesive zone model to numerically simulate delamination propagation. The numerically predicted interlaminar tensile strength of Al/CFRP laminates also shows great improvement of interlaminar mechanical properties using the above toughening methods.

Quasi-static mode II fracture tests and simulations of Z-pinned woven composites

Experimental results from quasi-static mode II ENF (end notch flexure) fracture tests for Z-pinned woven composites are used to investigate the influence of Z-pin density and Z-pin diameter on Mode II fracture toughness. The experimental results show that the 2% Z-pin composite and the 3% Z-pin composite have larger fracture toughness than the 1% Z-pin composite and a composite without Z-pins. Crack propagation changes from unstable propagation to stable propagation (crack arrest) as the Z-pin density increases. The additional fracture toughness provided by Z-pins prevents the primary crack to further propagate, enabling secondary and tertiary cracks to consume additional energy. While the primary crack is held from propagating by the frictional forces provided by Z-pins, the matrix in the composite is driven into the plastic state and enables the composite to absorb more energy. For numerical simulations, a discrete cohesive zone model (DCZM) is used to perform simulations. The simulations in conjunction with experimental results provide critical fracture toughness values.

The Effects of Tensile Softening Curve Parameters on Fracture in Concrete Based on Initial Fracture Toughness Criterion

The effects of tensile softening curve parameters on the crack propagation P-CMOD and P-CTOD curves were analyzed using a calculation method which adopted the initial fracture toughness as the crack propagation criterion. The results showed that: the whole process of the P-CMOD and P-CTOD curves were affected by the tensile softening curve parameters, especially for the descending segment of the curves, but the peak load and critical crack mouth opening displacement were less affected.

Statistical Analysis of the Progressive Failure Behavior for Fiber-Reinforced Polymer Composites under Tensile Loading

An analytical approach with the help of numerical simulations based on the equivalent constraint model (ECM) was proposed to investigate the progressive failure behavior of symmetric fiber-reinforced composite laminates damaged by transverse ply cracking. A fracture criterion was developed to describe the initiation and propagation of the transverse ply cracking. This work was also concerned with a statistical distributions of the critical fracture toughness values with due consideration given to the scale size effect. The Monte Carlo simulation technique coupled with statistical analysis was applied to study the progressive cracking behaviors of composite structures, by considering the effects of lamina properties and lay-up configurations. The results deduced from the numerical procedure were in good agreement with the experimental results obtained for laminated composites formed by unidirectional fiber reinforced laminae with different orientations.

Toughness Calculation of Postfire Normal Concrete

Fracture tests of postfire normal concrete with ten temperatures up to 600°C are implemented. Residual fracture toughness using analytical method is determined. Two situations are divided at critical load when calculating the cohesive fracture toughness. The initial and critical fracture toughness could be calculated from the complete load-crack opening displacement curves. Finally, the validation of double-Kfracture model to the postfire concrete specimens is proved.

Crack Onset and Propagation in Composite Materials Using Finite Fracture Mechanics on Elastic Interfaces

A method for the prediction of crack onset and propagation along an interface in a fibre-reinforced composite system is devel- oped. The method is based on the Linear Elastic-(Perfectly) Brittle Interface Model (LEBIM) and a coupled stress and energy criterion of the Finite Fracture Mechanics (FFM). Models similar to LEBIM, also called weak or imperfect interface models, are frequently applied to describe the behaviour of adhesively bonded joints. In the present paper the interface is modelled by a con- tinuous distribution of linear elastic-brittle springs where the normal and tangential stresses across the undamaged interface are, respectively, proportional to the relative normal and tangential displacements. The interface failure criterion applied takes into account the variation of the fracture toughness with the fracture mode mixity. In the present work a 2D collocational boundary element method (BEM) code is used to analyse debond onset and propagation at a fibre embedded in a matrix subjected to remote uniaxial transverse tension. One of the advantages of the method proposed here by applying the FFM criterion to the LEBIM is that we are able to make independent the two governing parameters of the model (critical stress and fracture toughness of the interface), which are related by an equation in the original LEBIM formulation. It seems that the predictions provided by FFM with LEBIM are quite similar to those obtained by the well-known Cohesive Crack Model (CCM). The advantage of the present method with respect to the CCM is evident, since a troublesome nonlinear analysis due to the softening can be avoided.

The effect of neutron irradiation on the fracture toughness of graphite

As a part of our irradiated graphite recycle program a small quantity of PCEA grade graphite was irradiated in the High Flux Isotope Reactor (HFIR) at ORNL. The graphite will provide the “raw material” for future recycle experiments. The geometry of the irradiated graphite allowed us to study the effects of neutron irradiation on the critical stress intensity factor, KIc, of graphite. The specimens were irradiated in two groups of 6 at an irradiation temperature of 900°C in “rabbit” capsules to doses of 6.6 and 10.2dpa, respectively. Following a full suite of pre- and post-irradiation examination, which included dimensions, mass, electrical resistivity, elastic constants, and thermal expansion (to 800°C) the samples were notched and tested to determine their KIc using the newly approved ATSM test method for SENB fracture toughness of graphite. Here we report the irradiation induced changes in the dimensions, elastic constants, resistivity, and coefficient of thermal expansion of PCEA graphite. Moreover, irradiation induced changes in the critical stress intensity factor, KIc, or fracture toughness, are reported and discussed. Very little work on the effect of neutron irradiation on the fracture toughness of graphite has previously be performed or reported.

Unit-sphere multiaxial stochastic-strength model applied to a composite material

The Batdorf “unit-sphere” methodology has been extended to predict the multiaxial stochastic strength response of anisotropic (specifically transversely isotropic) brittle materials, including polymer matrix composites, by considering (1) nonrandom orientation of intrinsic flaws and (2) critical strength or fracture toughness changing with flaw orientation relative to the material microstructure. The equations developed to characterize these properties are general and can model tightly defined or more diffuse material anisotropy textures describing flaw populations. In this paper, results from finite element analysis of a fiber-reinforced matrix unit cell were used with the unit-sphere model to predict the biaxial strength response of a unidirectional polymer matrix composite previously reported from the World-Wide Failure Exercise. Findings regarding stress–state interactions, thermal residual stresses, and failure modes are also provided. The unit-sphere methodology is an attempt to provide an improved mechanistic basis to the problem of predicting strength response of an anisotropic and composite material under multiaxial loading as compared to polynomial interaction equation formulations. The methodology includes consideration of strength scatter to predict material probability of failure, shear sensitivity of flaws, and accounting for multiple failure modes regarding overall failure response.

Evaluation of Three-Point Bending Fracture Tests of Concrete Specimens with Polypropylene Fibres via Double-&lt;i&gt;K&lt;/i&gt; Model

The fracture-mechanical parameter values of concrete, a quasi-brittle composite material, are determined via evaluation of records of experiments on specimens with stress concentrators. One of the fracture models applicable to concrete is the double-K model. This model combines the concept of cohesive forces acting on the effective crack increment with a criterion based on the stress intensity factor. The outputs of the model are critical crack tip opening displacement and fracture toughness values, including the initiation stress intensity factor value corresponding to the beginning of stable crack propagation. Outputs of three-point bending fracture tests of fibre reinforced concrete obtained using double-K fracture model are presented in this paper. The main aim is the determination and comparison of the above-mentioned parameter values of two types of the composite both without and with polypropylene fibres. Both types of tested composite had the same basic matrix consisting of cement, sand and water. In one case, gravel was used for normal weight concrete, in the other case lightweight aggregates were used for lightweight concrete. Both types of the testing matrix were designed with a similar value of compressive strength. Concretes were reinforced by spread polypropylene fibres of three lengths. There were made eight sets of testing concrete specimens: without fibres, and with fibres of 19 mm, 38 mm and 54 mm length. Dosage of fibres was 9 kg/m3 in all six cases.

A Study of Rock Crack Fracture under Different Temperatures

A series of critical fracture toughness of two kinds of rock materials under different temperature which varied from-50°C to 240°C are measured by I-II-III mixed mode fracture experiments adopting atypical three point bending specimens. Relative stress intensity factors of crack initiation are calculated by finite element method. Combining with calculated values, the experiment results show that, the mixed mode fracture toughness of the rocks decreases with the increase of temperature. The experimental and calculated results can be used in the design of deep underground engineering or disaster prevention and mitigation engineering.

Fracture Behaviors of Post-Fire Concrete

nvestigations on the residual Mode-I fracture behaviors of concrete subjected to elevated temperatures were implemented in present research. Test specimens of the same dimensions, 230×200×200 mm, were exposed to ten temperatures varying from 20oC to 600oC. The wedge splitting method was employed to obtain the complete load-crack mouth opening displacement curves (P-CMOD) of the post-fire specimens, from which the initial fracture toughness Kini, the critical fracture toughness Kic and the fracture energy GF were calculated. The results demonstrated that Kini, Kic decreased monotonically with increasing heating temperatures Tm owing to the thermal damage induced by high temperatures; whereas GF sustained a hold-increase-decrease tendency with Tm for the energy dissipation of multi-cracks.

Determination of Residual Fracture Toughness of Post-Fire Concrete

Determination of double-K fracture parameter using both analytical and weight function method is carried out in present research. In calculating the cohesive fracture toughness, two situations are divided at critical load. Wedge-splitting tests with ten temperatures varying from 20oC to 600oC are implemented. The complete load-crack opening displacement curves are obtained from which the initial and critical fracture toughness could be calculated experimentally. The validation of double-K fracture model to the post-fire concrete specimens is proved. Meanwhile the weight function method agrees well with the analytical method.

Determining residual double-K fracture toughness of post-fire concrete using analytical and weight function method

Determination of double-K fracture parameter using both analytical and weight function method is carried out in present research. In calculating the cohesive fracture toughness, two situations are divided at critical load. Wedge-splitting tests with ten temperatures varying from 20 to 600 °C are implemented. The complete load-crack opening displacement curves are obtained from which the initial and critical fracture toughness could be calculated experimentally. The validation of double-K fracture model to the post-fire concrete specimens is proved. Meanwhile the weight function method agrees well with the analytical method. Finally, an index to indicate the brittleness of concrete specimen through the ratio of initial fracture toughness and unstable fracture toughness is proposed.

Fracture of ECAP-deformed iron and the role of extrinsic toughening mechanisms

The fracture behaviour of pure iron deformed by equal-channel angular pressing via route A was examined. The fracture toughness was determined for different specimen orientations and measured in terms of the critical plane strain fracture toughness, KIC, the critical J integral, JIC, and the crack opening displacement for crack initiation, CODi. The results demonstrate that the crack plane orientation has a pronounced effect on the fracture toughness. Different crack plane orientations lead to either crack deflection or delamination, resulting in increased fracture resistance in comparison to one remarkably weak specimen orientation. The relation between the microstructure typical for the applied deformation route and the enormous differences in the fracture toughness depending on the crack plane orientation will be analyzed in this paper.

Impact of Metallic Foam’s Microstructure to its Mechanical Property

Explored the influence of pore structure of foam metal material on mechanical behavior of fracture. Discuss fracture toughness of several different micro geometric structure of foam metal material with finite element method. The author's calculations showed, microstructure and loading mode has an important effect on the fracture toughness of the foam metal material. due to ignoring the effects of cell structure on the mechanical properties of materials, the classic fracture toughness criterion -crack tip opening displacement (COD) is incomplete, it would be more efficient to take opening displacement change rate of the crack-tip as the parameter to characteristic the metallic foam material fracture toughness.

Estimation and comparative study of JIC using different methods for 20MnMoNi55 steel

Fracture toughness is one of the key input variables to compute critical load of the structural components. The resistance against ductile fracture can be quantified either by the initiation value or by the entire resistance curve. Different standard methods like JSZW, JSME and ASTM: E1820 etc. are mainly used to estimate the critical crack initiation value from the resistance curve developed by the J-integral test. However, the results vary from method to method and are even inconsistent for the same method. Pehrson and Landes suggested a simple method for estimation of the critical fracture toughness by identifying the critical point corresponding to the maximum load on load–displacement curve. In the present study, different standard methods along with the one suggested by Pehrson and Landes are used to find out the critical fracture toughness using 1T–CT and ½T–CT specimens of the material 20MnMoNi55 steel for varying temperatures and crack size. The results are analyzed to compare the merits of the different methods of estimation of fracture toughness.

Dynamic fracture toughness of Al–7Si–Mg (A357) aluminum alloy

Impact behavior related to crack initiation and growth of cast A357 (Al–7Si–0.7Mg) alloy was experimentally investigated. Dynamic fracture toughness for various artificial aging conditions were evaluated by exploiting instrumented impact Charpy V-notch experiments; impact tests were preferred instead of the standard fracture toughness tests in order to have a fast assessment of the effect of artificial aging on the fracture toughness behavior. Characteristic points of impact load–deflection curves related with cracking were identified and post-correlated with different artificial aging conditions. Absorbed impact energies for stable and unstable crack growth were calculated for 28 different aging conditions; resulting cracking velocity at the unstable crack regime (rebound compliance) was also calculated and it was found that rebound compliance is inversely related to ductility. Cracking initiation load values were identified by exploiting the compliance changing rate method; both stress intensity factor and J-integral analysis were employed to calculate critical dynamic fracture toughness values. They were found to be slightly higher than corresponding quasi-static properties and they are both changing with varying aging conditions. Limitations and results of both notch-fracture toughness analyses were discussed by taking into account the material aging condition. Performed scanning electron microscopy on the fracture surfaces revealed the fracture mechanism that is correlated with respective microstructure.

Finite element analysis of the plane strain crack-tip mechanical fields in pseudoelastic shape memory alloys

The plane strain mechanical fields near a stationary crack tip in a pseudoelastic shape memory alloy (SMA) are analyzed via the finite element method. The small scale transformation assumption is employed for the calculations using displacement boundary conditions on a circular region that encloses the stress-induced phase transformation zone. The constitutive law used adopts the classical rate-independent small strain flow theory for the evolution equations of both the transformation and plastic strains. Results on the size and shape of the stress-induced transformation and plastic zone formed near the stationary crack are obtained and a fracture toughness criterion based on the J-integral is discussed in view of the observed path-dependence of J. Moreover, the obtained results are discussed in relation to results for stationary cracks in conventional elastic–plastic materials.