Critical Fracture Stress Research Articles

Cytoskeletal polymer networks: The molecular structure of cross-linkers determines macroscopic properties

In living cells the mechanical properties of the actin cytoskeleton are defined by the local activation of different actin cross-linking proteins. These proteins consist of actin-binding domains that are separated and geometrically organized by different numbers of rod domains. The detailed molecular structure of the cross-linking molecules determines the structural and mechanical properties of actin networks in vivo. In this study, we systematically investigate the impact of the length of the spacing unit between two actin-binding domains on in vitro actin networks. Such synthetic cross-linkers reveal that the shorter the constructs are, the greater the elastic modulus changes in the linear response regime. Because the same binding domains are used in all constructs, only the differences in the number of rod domains determine their mechanical effectiveness. Structural rearrangements of the networks show that bundling propensity is highest for the shortest construct. The nonlinear mechanical response is affected by the molecular structure of the cross-linker molecules, and the observed critical strains and fracture stress increase proportional to the length of the spacing unit.

Hertzian fracture at unloading

Hertzian fracture through indentation of flat float glass specimens by steel balls has been examined experimentally. Initiation of cone cracks has been observed and failure loads together with contact and fracture radii determined at monotonically increasing load but also during unloading phases. Contact of dissimilar elastic solids under decreasing load may cause crack inception triggered by finite interface friction and accordingly the coefficient of friction was determined by two different methods. In order to make relevant predictions of experimental findings, a robust computational procedure has been developed to determine global and local field values in particular at unloading at finite friction. It was found that at continued loading it is possible to specify in advance how the contact domain divides into invariant regions of stick and slip. The maximum tensile stress was found to occur at the free surface just outside the contact contour, the relative distance depending on the different elastic compliance properties and the coefficient of friction. In contrast, at unloading invariance properties are lost and stick/slip regions proved to be severely history dependant and in particular with an opposed frictional shear stress at the contact boundary region. This causes an increase of the maximum tensile stress at the contour under progressive unloading. Predictions of loads to cause crack initiation during full cycles were made based on a critical stress fracture criterion and proved to be favourable as compared to the experimental results.

Evaluation of six fracture models in high velocity perforation

A systematic evaluation of six ductile fracture models is performed to identify the most suitable fracture criterion for high velocity perforation problems. Included in the paper are the Wilkins, the Johnson–Cook, the maximum shear stress, the modified Cockcroft–Latham, the constant fracture strain, and the Bao–Wierzbicki fracture models. These six fracture models are implemented into ABAQUS/Explicit by means of a user material subroutine (VUMAT), and applied to model the failure processes of a steel and an aluminum target plate impacted by a projectile. The numerical simulations are examined by comparing with the experimental results published in the open literature. The Wilkins fracture model predicts spallation of the impacted zone of the target plate beneath the projectile. This unrealistic result is due to its power law form of the pressure term. The maximum shear stress fracture criterion fails to capture the shear plugging failure pattern in a wide range of the impact velocity. Material fracture properties cannot be fully characterized with the constant fracture strain and the modified Cockcroft–Latham fracture models. Various tensile tests on round bars do not give a consistent critical damage. The calculated residual velocities of the projectile are sensitive to the magnitude of the fracture parameters. The Johnson–Cook and the Bao–Wierzbicki fracture models formulated in the space of the stress triaxiality and the equivalent plastic strain to fracture are capable of predicting the realistic fracture patterns and at the same time the correct residual velocities. Finally, the limitations of the Johnson–Cook fracture model are discussed.

Mechanical behaviour of iron oxide scale: Experimental and numerical study

The paper addresses the identification of constitutive parameters of thick, brittle layers on metal substrates. Application is to the iron oxide behaviour during hot rolling processes of steel, where oxide scale breaking and embedding is one of the major causes of surface defects. Contact management of a FEM software has been adapted in order to address the transitions corresponding to transverse oxide fracture, along with two other mechanisms, namely delamination and interfacial stick/slip. It is applied to the hot strip rolling process to show pre-bite cracking and its consequences (“micro-extrusion” of the metal). To approximate the stress state prevailing at roll bite entry, the Four-Point Hot Bending Test (4PHBT) has been selected for the measurement of oxide properties. Oxidation is made in situ in the test rig under conditions similar to a hot strip mill (HSM) environment. Comparison of load-deflection curves for oxidized and non-oxidized samples allows the mechanical properties of the oxide to be determined. Above a critical temperature T c – around 700 °C, but depending on strain rate – the oxide is ductile (with a very narrow plastic strain range, ɛ p < 10 −2) and elastic-viscoplastic (EVP) constitutive parameters are identified numerically. Below T c, brittleness is manifested by an array of transverse, through-thickness cracks. Acoustic emission (AE) has been used to help detect the onset of fracture, while numerical simulation gives the critical fracture stress at the corresponding point of the load-deflection curve. Results for four low carbon steel grades are compared.

Interrelation between nonlinear elastic surface pulses and dynamic fracture

Initiation of impulsive fracture near the source of a nonlinear surface acoustic wave (SAW) pulse, launched by laser-based transient pressure shocks, is investigated. A numerical method is developed that solves the problem of nonlinear SAW generation, the propagation of SAW pulses in nonlinear media, and the initiation and growth of cracks by such pulses. The characteristic features of SAW profiles in linear media, nonlinear media with quadratic nonlinearity, and nonlinear media with crack induction provide a tool to determine the critical stress of dynamic fracture. Former discrepancies between theoretical and experimental pulse shapes were eliminated by taking into account the effects of fracture. Good agreement was obtained with experiments in isotropic fused quartz. By calculating the stress field of the nonlinear SAW pulse modified by the interaction with a crack and by applying the condition of vanishing shear stress at the crack tip, the angle of crack penetration into the solid was estimated. At a depth of 7.1μm, for example, this angle was approximately 50° to the surface normal, in reasonable agreement with previous measurements in isotropic fused quartz.

Nanotechnological applications of nonlinear surface acoustic waves: Mechanism of brittle fracture

Strongly nonlinear surface acoustic waves (SAWs) with shock fronts were used to study impulsive fracture in anisotropic silicon crystals and isotropic fused quartz. With this method, spatially localized dynamic fracture was studied without an artificial pre-cracking. SAWs allow the investigation of mode I tensile stress and mode II shear stress fracture. For silicon, the difference between the measured critical fracture stress of 1–2 GPa and the theoretical tensile strength of 22 GPa is discussed in terms of Griffith's approach. However, due to the biaxial stress field applied with SAWs and the low ideal shear stress of 6.8 GPa, the nucleation process may not be uniaxial and purely tensile in silicon. In fused quartz, nucleation occurred via tensile crack opening at the surface and propagation into the bulk proceeded at an angle of 55°–60° to the surface normal in the direction of SAW propagation. This behavior could be described theoretically by calculating the energy release rate as a function of direction and assuming that stable tip propagation is obtained under pure mode I conditions.

Critical Level of Intergranular Fracture to Affect the Toughness of Embrittled 2.25Cr-1Mo Steels

In general, the low-temperature brittle fracture mode of unembrittled ferritic steel is transgranular cleavage. During temper embrittlement, impurity elements, such as sulfur (S), phosphorus (P), antimony (Sb), arsenic (As), and tin (Sn), segregate to prior austenite grain boundaries, which results in a decrease in the grain boundary cohesive strength. As a result, the brittle transgranular cleavage fracture mode changes to intergranular decohesion in association with the decrease in the critical fracture (stress (σ F) as well as the fracture toughness (K). However, the appearance of intergranular facets on the fracture surface does not cause a decrease in the K and σ F values. In this work, quenched and fully tempered 2.25Cr-1Mo steel (in an unembrittled condition that exhibits almost 100% brittle transgranular cleavage fracture) has been embrittled for 24, 96, and 210 h at 520 °C to produce different proportions of intergranular fracture. These unembrittled and embrittled steel specimens were tested to measure K (at −120 and −196 °C) and σ F (at −196 °C). The experimental results and detailed fractographic observations show that the K and σ F values decrease with an increase in the area fraction of intergranular fracture, provided that the area fraction of the intergranular facet on the brittle fracture surface exceeded a certain critical level, approximately 20–22%.

Tensile and fatigue strength of free-standing CVD diamond

Chemical vapour deposited (CVD) diamond is finding increased application and it is important to study its strength and fatigue properties. The present paper describes research on a batch of di-electric (optical) grade CVD material. The procedure in the experiments was to use some samples from a batch to obtain an average failure load. Other samples were then stress cycled to a chosen fraction of this average load. If they survived 10 7 cycles, they were considered to be immune to fatigue at that load, and their strengths were measured using a three-point bend test. Some samples survived at least 95% of their critical fracture stress for 10 7 cycles without fatiguing. In other experiments, a 4-point (double torsion) rig was used to stress samples with macro-flaws in different environments. The observation that fatigue does not reduce the strength of CVD diamond in normal environments adds to its attractiveness for various applications.

Specimen size effects on ductile–brittle transition temperature in Charpy impact testing

One key issue for small specimen test techniques is to clarify specimen size effects on test results. In consideration of size effects on determining the ductile-to-brittle transition temperature (DBTT) in Charpy impact testing, a method to evaluate the plastic constraint loss for differently sized Charpy V-notch (CVN) specimens is proposed and applied to a ferritic–martensitic steel, 2WFK, developed by JNC. In the method, a constraint factor, α, that is an index of the plastic constraint is defined as α=σ ∗/σ y ∗ . Here, σ ∗ is the critical cleavage fracture stress which is a material constant and σ y ∗ is the uniaxial yield stress at the DBTT at the strain rate generated in the Charpy impact test. The procedures for evaluating each of σ ∗ and σ y ∗ are described and a result of σ ∗ and σ y ∗ , thus the value of α, is presented for different types of miniaturized and full-sized CVN specimens of 2WFK.

Fragmentation of Kidney Stone by Shock Wave-Experimental Approach

To understand fundamentals of kidney stone™s fragmentation by shock wave impingement, experimental approach was carried out. Air gun system was used to transfer a well-controlled stress wave into a thin disk specimen. The specimen was fabricated with plaster and its dimensions are 10 mm in diameter and 1.2 mm in thickness. The obtained results are summarized as follows: As the stress pulse duration is decreased from 12 microseconds to 5 microseconds, the critical stress for fracture increased tremendously. The critical fracture stress for a specimen with a small hole in the specimen center is about one fifth of that for the plain specimen. The fracture takes place along the diameter perpendicular to the stress wave incident direction. Numerical stress analysis suggests that the principal stress criterion can explain the fracture mode.

An Energy Gradient Fracture Criterion Based on Virtual Crack Vector Model with Application to T-Stress Problem

A virtual crack vector model is proposed in this paper to simulate the branched crack propagation and simplify its calculation of energy release rate. An energy gradient fracture criterion is constructed based on this model. It can take account of the effects of biaxial loads or T-stress on brittle mixed mode fracture and agrees well with the test data of biaxial tensile fracture and the specially conducted experiment of the influences of ox on the mixed mode fracture of plexiglas. Considering its advantage of predicting initial propagation angle and critical fracture stress independently without the determination of the core region radius, it can be used as a practical fracture criterion for brittle mixed mode fracture under biaxial tension.

Constraint Correction of Fracture Toughness CTOD for Fracture Performance Evaluation of Structural Components

Abstract A correction of CTOD for constraint loss in large-scale yielding conditions is made on the basis of the Weibull stress fracture criterion that eliminates an excessive conservatism in the conventional fracture assessment and material fracture toughness requirement. A CTOD ratio β = δ3P / δWP (&amp;lt;1) is proposed, where δWP is the CTOD of a wide plate component and δ3P is an equivalent CTOD of the fracture toughness specimen at which the toughness specimen gives a compatible Weibull stress with the wide plate. The CTOD ratio β is decreased to a large extent after full yielding of the wide plate component, which is more significant for a high yield ratio YR and a deep surface crack in the wide plate. The Weibull modulus m exerts a marginal influence on β. A case study is presented on the application of the CTOD ratio β to the fracture performance assessment of full-scale column-to-beam connections subjected to cyclic and dynamic loading.

Mode II interlaminar fracture of carbon/epoxy multidirectional laminates

This paper reports an experimental study on the mode II interlaminar fracture of carbon/epoxy multidirectional laminates. A 3D finite element analysis was first performed to define appropriate stacking sequences for end-notched flexure (ENF) specimens with starter delaminations on θ/− θ and 0°/ θ interfaces. The analysis concerned the shape of widthwise distributions of the mode II strain energy release rate, G II, the level of mode-mixity, the effect of residual stresses on G II and the applicability of data reduction schemes. The experimental G IIc values increased with the ply angle θ for both θ/− θ and 0°/ θ specimens. These trends were found to be in agreement with an average interlaminar stress fracture criterion. However, this criterion proved to be of limited practical usefulness, as its predictions were dependent on a characteristic length. Therefore, G IIc measurements on multidirectional specimens remain essential for the application of accurate fracture mechanics based design criteria.

Mode II interlaminar fracture of glass/epoxy multidirectional laminates

An experimental study was conducted on the mode II interlaminar fracture of woven fabric glass/epoxy multidirectional laminates. A preliminary Finite Element analysis was used to choose stacking sequences for End-Notched Flexure specimens with starter delaminations on θ/−θ and 0°/θ interfaces. The experimental GIIc values generally increased with the ply angle θ for both θ/−θ and 0°/θ specimens. These results were in agreement with the predictions of an average interlaminar stress fracture criterion. In contrast with previous studies on unidirectional laminates, GIIc values from a mode II precrack were significantly higher than those from the film, thus revealing a pronounced R-curve effect.

On the statistical analysis of local fracture stresses in notched bars

Test results for critical local fracture stresses are analysed statistically for both “as-received” and “degraded” pressure-vessel weld metal. The values were determined from the fracture loads of blunt-notch four-point-bend specimens fractured over a range of low test temperatures, making use of results from a finite-element stress analysis of the stress–strain distributions ahead of the notch root. The “degraded” material tested in this work has been austenitized at a high temperature, followed by both prestraining and temper embrittlement. This has led to a situation in which the fracture stress for the “degraded” material is reduced significantly below that for the “as-received” material. The fracture mechanisms are different in that the “degraded” material shows evidence of intergranular fracture as well as cleavage fracture (in coarse grain size) whereas the “as-received” material shows only cleavage fracture (in fine grain size). The critical stress ( σ F) distributions plotted on normal probability paper show that the experimental cumulative distribution function (CDF) is linear for each condition with different mean values: 1560 MPa for “as-received” material and 1400 MPa for “degraded” material. The values of standard deviation are small and almost identical (33– 35 MPa ). The decrease of the local fracture stress after degradation is related to the local fracture micro-mechanisms. Statistical analysis of the results for the two conditions supports the hypothesis that the values of σ F are essentially single valued, within random experimental errors. A similar analysis of the data treating both conditions as a single population reveals some interesting points relating to statistical modelling and lower-bound estimation for mechanical properties. Comparisons are made with Weibull analysis of the data. A further conclusion is that it is extremely important to base any statistical model on inferences drawn from micro-mechanical modelling of processes, and that examination of “normal” CDFs can often provide good indications of when it is necessary to subject data to further statistical and physical analysis.

Failure criterion with given survivability for ceramic notched elements under combined tension/torsion

In the present study, a generally applied failure criterion is developed for the elements of brittle materials under combined tension/torsion based on the normal stress fracture criterion. First, the applicability of the failure criterion mentioned above is objectively checked by test results of the fracture stress of Al 2O 3 ceramic under combined tension/torsion given in the available literature. Furthermore, the failure criterion is modified to take account on the greater effect of the shear stress component on the fracture of Al 2O 3 ceramic under combined tension/torsion, and rechecked by test results of the fracture stress of Al 2O 3 smooth tubes and round rods under combined tension/torsion. Tests also were carried out to determine the fracture stress of Al 2O 3 notched tubes under combined tension/torsion, which are used to test the general applicability of the failure criterion. Finally, the failure criteria with given survivability for Al 2O 3 smooth- and notched elements under combined tension/torsion are predicted from the probability distribution parameters of the tensile fracture strength and the shear fracture strength of ceramics and checked by test results.

Shear viscosity, extensional viscosity, and die swell of polypropylene in capillary flow with pressure dependency

AbstractThe shear and extensional viscosities of a polypropylene resin were studied using a capillary rheometer and capillary dies of 1‐mm diameter and length of 10, 20, and 30 mm. Melt temperatures at 190, 205, and 220°C and shear rates between 100 and 5000 s−1 were used. At the highest shear rate a visible melt fracture was observed. An equation relating the pressure drop and die length was derived with consideration of pressure effects on melt viscosities and the end effect. After the correction for pressure effects the true wall shear stress and end effect at zero pressure were calculated. The end effect showed a critical stress of melt fracture around 105 Pa, and increased rapidly when shear stress increased above the critical stress. From shear stress the shear viscosity was calculated, and a power law behavior was observed. Extensional viscosity was calculated from the end effect and showed a decreasing trend when strain rate increased. After time–temperature superposition shift shear viscosity data correlated well, but an upward trend was observed in extensional viscosity when melt fracture occurred. Die swell ratio at different temperatures can be plotted as a function of wall shear stress and was higher for shorter dies. © 2002 Wiley Perioodicals, Inc. J Appl Polym Sci 84: 1269–1276, 2002; DOI 10.1002/app.10466

Fracture Mechanical Evaluation of GaAs Wafers

ABSTRACTStrength and fracture toughness of (100) oriented GaAs wafers are analyzed by fracture and indentation testing. Using finite element method (FEM) critical fracture stresses are calculated from the fracture loads of wafers tested under biaxial bending, whereas atomic force (AFM), scanning electron microscopy (SEM) and acoustic C-scan microscopy of deformation and cracking patterns around micro- and nano-indentations provided information on yielding, crack initiation and crack growth resistance. Through fracture mechanical evaluation of these results critical defect sizes are derived, which are tolerable without strength degradation. It is shown, that a fracture strength of at least 800MPa can be achieved by careful fabrication even of 6' wafers. This figure is much higher then the prescribed minimum strength level estimated to avoid premature failures during wafer handling and processing routes.

Evaluation of Prestraining and Dynamic Loading Effects on the Fracture Toughness of Structural Steels by the Local Approach

On the occasion of recent great earthquakes, great concern is focused on the prevention of unstable fracture of steel structures against the seismic loading. This paper employs the local approach for the evaluation of prestraining and dynamic loading effects, experienced during an earthquake, on the fracture toughness of structural steels. The prestraining and dynamic loading lead to a similar result: increasing the yield stress and tensile strength and decreasing the fracture toughness. It is shown, however, that the combined effects of prestraining and dynamic loading is not equivalent to the sum of each individual effect. The analysis using the local approach demonstrates that the critical Weibull stress at brittle fracture initiation is independent of prestraining and dynamic loading. Based on the Weibull stress fracture criterion, the prestraining and dynamic loading effects on the fracture toughness can be predicted from static toughness results of the virgin material. As an engineering application, a simplified method is proposed for the estimation of fracture toughness under the seismic condition. This method uses a reference temperature concept: the dynamic fracture toughness at the service temperature T with prestrain is displaced by the static toughness of the virgin material at a lower temperature T−ΔTPD, where ΔTPD is a temperature shift of the fracture toughness caused by prestraining and dynamic loading. The temperature shift ΔTPD is provided as a function of the flow stress elevation in the seismic condition.

Tensile fracture strength of boron/aluminum laminates with holes and slits

This paper improves the stress fracture criteria proposed by Whitney–Nuismer known as the point stress criterion (PSC) and the average stress criterion (ASC), to predict the strength of composite laminates containing holes and slits. A simple relation is used for the characteristic length to improve the accuracy while evaluating the notched strength of laminates. The applicability of the proposed approach is examined by considering the notched strength data on carbon/epoxy and boron/aluminum laminates. The analytical results obtained in the present study correlate well with the test results of different notched configurations. This study confirms that the present modification in the stress fracture criteria can be used for notched strength evaluation of composite laminates.