Effect of the loading rate on mode I interlaminar fracture toughness of laminated composites

The objective of the present study is to determine the influence of the loading rate on the critical energy release rate G_Ic of fibre-reinforced epoxy laminates. In order to perform pure mode I loading at higher opening velocities, a new test device is developed. The approach is based on a symmetrical opening displacement applied to a DCB specimen. In the data reduction, the influence of the kinetic energy has to be taken into account. The results obtained on the unidirectional carbon-epoxy laminate T300/914 at crack opening rates up to 1.6 m/s show a slight effect of the loading rate on G_Ic.     

Effect of loading rate on fracture toughness of bonded joints

Feasibility studies in using adhesive bonding to replace conventional fastening methods have been proved successful. At this stage it is essential to furnish the designer with the data required for such type of fabrication. One of the main factors affecting the bonded joint strength is the loading rate. Therefore, the objective of this study is to investigate the role of loading rate on fracture toughness of bonded joints. Cleavage strength tests were carried out at different loading rates using epoxy resin as an adhesive material and two adherend materials, namely aluminium and brass. Tests were carried out to cover seven different loading rates. The results indicate a significant role of the strain rate on the fracture strength.     

Change of fracture mode in Charpy toughness transition temperature range

Abstract

A transition layer of width 5 - 10 μm was found on the boundary between ductile and brittle fracture for Charpy V notch specimens in the transition temperature range of a structural steel having a microstructure of polygonal ferrite -pearlite. The fracture mode in the transition layer was shearing with occasional submicrometre dimples. From tensile tests on notched specimens, the cleavage fracture stress and flow stress by ductile decohesion were determined. Based on the experimental data and the assumption that the volume of metal involved in the plastic deformation during fracture was related to the volume of the dimples, it was deduced that the transition layer width represents the size of the plastic zone immediately before cleavage initiation. The crack opening displacement and the crack tip radius for the change of fracture mode were calculated.     

Effect of loading rate on dynamic fracture initiation toughness of brittle materials

Numerical simulation is carried out to investigate the effect of loading rate on dynamic fracture initiation toughness including the crack-tip constraint. Finite element analyses are performed for a single edge cracked plate whose crack surface is subjected to uniform pressure with various loading rate. The first three terms in the Williams’ asymptotic series solution is utilized to characterize the crack-tip stress field under dynamic loads. The coefficient of the third term in Williams’ solution, A ₃, was utilized as a crack tip constraint parameter. Numerical results demonstrate that (a) the dynamic crack tip opening stress field is well represented by the three term solution at various loading rate, (b) the loading rate can be reflected by the constraint, and (c) the constraint A ₃ decreases with increasing loading rate. To predict the dynamic fracture initiation toughness, a failure criterion based on the attainment of a critical opening stress at a critical distance ahead of the crack tip is assumed. Using this failure criterion with the constraint parameter, A ₃, fracture initiation toughness is determined and in agreement with available experimental data for Homalite-100 material at various loading rate.     

Size and loading mode effects in fracture toughness testing of polymers

Experimental work is described which examines the applicability of plane-strain fracture toughness testing techniques to several polymers. The fracture behaviour of five polymers was studied using pre-notched test specimens and was characterized by the linear elastic fracture parameter,K _c. Two test geometries and loading modes were used; SEN tension and three-point bending have been investigated by varying both thickness and width. It has been established that the ASTM criterion for plane-strain conditions ofB>2.5 (K _c1/σ _y)² is sufficient for SEN bending but not for tension where an extrapolation method is needed. For width effects the BCS model was shown to describe the observations and this with a limiting nominal stress analysis gave quite close agreement with the ASTM criterionW>5 (K _c1/σ _y)². This value was shown to be a good estimate of the practical minimum width. There is some evidence that PP, which gives substantial crazing and whitening, can give satisfactory values at sizes about half these limiting values.     

Influence of mixed mode I/III loading on fracture toughness of mild steel at various strain rates

Abstract

The effect of loading angle &phis; on the fracture toughness of mild steel at various strain rates has been studied. The fracture toughness was found to decrease with increasing loading angle (or increasing mode III component) at strain rates 10^-5 to 10⁰ s^-1 where ductile fracture was observed. Under impact conditions (strain rate 10² s^-1), fracture was by cleavage and the fracture toughness was found to increase with increasing loading angle. The results showed that the mixed mode fracture behaviour of mild steel changed from Class C in the strain rate range 10^-5 to 10⁰ s^-1 to a combination of Class A and B under impact conditions. In the strain rate range 10^-5 to 10^-2 s^-1, the fracture toughness behaviour with increasing strain rate was found to be similar for the three loading angles studied, namely &phis;= 0, &phis;= 30 and &phis;= 45°. At the strain rates 10^-2 to 10² s^-1, fracture toughness at &phis;= 0° decreased sharply, while for loading angles &phis;= 30° and &phis;= 45°, the fracture toughness increased with strain rate. The increase in mixed mode fracture toughness with strain rate in this strain rate regime has been attributed to the inertial effects which are known to reduce the T stress ahead of the crack.     

Influence of loading rate on concrete cone failure

Three different effects control the influence of the loading rate on structural response: creep of bulk material, rate dependency of growing microcracks and structural inertia. The first effect is important only at extremely slow loading rates whereas the second and third effects dominate at higher loading rates. In the present paper, a rate sensitive model, which is based on the energy activation theory of bond rupture, and its implementation into the microplane model for concrete are discussed. It is first demonstrated that the model realistically predicts the influence of the loading rate on the uniaxial compressive behaviour of concrete. The rate sensitive microplane model is then applied in a 3D finite element analysis of the pull-out of headed stud anchors from a concrete block. In the study, the influence of the loading rate on the pull-out capacity and on the size effect is investigated. To investigate the importance of the rate of the growing microcracks and the influence of structural inertia, static and dynamic analyses were carried out. The results show that with an increase of the loading rate the pull-out resistance increases. For moderate loading rates, the rate of the microcrack growth controls the structural response and the results of static and dynamic analysis are similar. For very higher loading rates, however, the structural inertia dominates. The influence of structural inertia increases with the increase of the embedment depth. It is shown that for moderately high-loading rates the size effect becomes stronger when the loading rate increases. However, for very high-loading rate the size effect on the nominal pull-out strength vanishes and the nominal resistance increases with an increase of the embedment depth. This is due to the effect of structural inertia.     

Investigation of loading rate and plate thickness effects on dynamic fracture toughness of PMMA

To investigate the effects of loading rate and plate thickness on the fracture toughness of PMMA (polymethyl methacrylate) under impact loading, two methods, A method and B method, are applied as follows. In the A method, a dynamic finite element method and a strain gage method are applied to measure the dynamic fracture toughness in the fracture test using an air gun. In the B method, a single axis strain gage method is applied to measure the critical dynamic stress intensity factor, namely dynamic fracture toughness, in the fracture test using a weight dropping type apparatus. The dimensions of the PMMA specimen are L = 140 mm length and W = 30 mm width. Three values of the plate thickness B, 15.0 mm, 10.0 mm and 5.0 mm, are selected to investigate the plate thickness effect in the fracture test. Both results by the A and B methods precisely indicated the minimum value and the loading rate effect on the dynamic fracture toughness.     

Influence of shear parameters on mixed–mode fracture of concrete

The influence of the mode II fracture parameters on the mixed mode fracture experimental tests of quasibrittle materials is studied. The study is based on experimental results and numerical analyses. For the numerical study, a procedure for mixed mode fracture of quasibrittle materials is presented. The numerical procedure is based on the cohesive crack approach, and extends it to mixed mode fracture. Four experimental sets of mixed mode fracture were modelled, one from Arrea and Ingraffea and another from a nonproportional loading by the authors, both with bending concrete beams. Two other sets of experimental fracture were modelled, based on double-edge notched testing; in these tests an important mode II is beforehand expected. The numerical results agree quite well with experimental records. The influence of the main parameters for mode II fracture on the mixed mode fracture is studied for the four experimental set of tests and compared with these results. In all them, large changes in the mode II fracture energy hardly modify the numerical results. The tangential and normal stresses along the crack path during the loading proccess are obtained, also with different values of the mode II fracture energy. For the studied experimental tests it is concluded that the crack is initiated under mixed mode but propagated under predominant mode I. This allows a development of mixed mode fracture models, mainly based on standard properties of the material measured by standard methods, avoiding the problems associated with the measurement of mode II fracture parameters, such as mode II fracture energy and cohesion.     

A short-beam shear fracture approach to measure the mode II fracture toughness of materials with preferred interfaces

A short-beam shear fracture approach is developed to characterize the mode II fracture toughness, (K _IIC) of materials with preferred interfaces such as wood, fiber composite materials and bonded materials. This approach is easy to implement using the Iosipescu shear fixture and is free of friction between the cracked faces thereby offering a more reasonable value of K _IIC than previous methods. Another feature of our new approach is the measurement of accurate crack initiation load due to a clear load drop. Additionally, calibration charts for bonded polymers and composite materials are generated. Finite element analysis along with cohesive elements is used to validate experimental load-displacement curves which are obtained by testing bonded polymers. This new approach is compared with the four-point bending fracture experiment, and the measured fracture toughnessess of the same bonded materials of two kinds of approaches are shown to be close (15–25% difference).     

Influence of autofrettage on fracture toughness

A specimen, called the ring specimen, was developed to determine the fracture toughnessK _tc, under conditions of autofrettage. Tests were carried out on standard arc shaped specimens and ring specimens without autofrettage to obtainK _tc values of a gun barrel steel chosen for study and seen to yield similar results. Tests were also performed on autofrettaged (100 percent overstrain) ring specimens at various crack lengths producing results with a dramatic decrease inK _tc of 60 per cent. From this, it may be inferred that the critical length of a crack in an autofrettaged gun barrel made of this material will be less than anticipated. Although cold work or autofrettage enhances fatigue life by decreasing crack propagation rate, it is seen to decreaseK _tc creating, from this point of view, more dangerous conditions. For a design which must guarantee long life, the accompanying decrease in critical crack size may indeed prove a liability. Of course, this is a result for one particular material with a specific heat treatment and therefore not general; other materials must be tested, as well.

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Résumé On a étudié une éprouvette, dénommée éprouvette en anneau, en vue de déterminer la ténacité à la ruptureK _tc sous des conditions d'auto-frettage. Des essais ont été effectués sur des éprouvettes standards en forme d'arc et sur des éprouvettes en anneau sans auto-frettage en vue d'obtenir les valeurs deK _tc dans le cas d'un acier pour âme de canon choisi pour l'étude. Ces essais ont conduit à des résultats similaires. Des essais ont également été effectués sur des échantillons en anneau auto-frettés à 100% de sur-dilatation correspondant à diverses longueurs de fissure. Les résultats ont montré une diminution deK _tc de l'ordre de 60%. On peut déduire de cette observation que la longueur critique relative à une fissure dans une âme d'un canon auto-fretté réalisé dans ce matériau sera plus faible que prévu. Bien que l'écrouissage où l'auto-frettage améliore l'endurance en fatigue par des croissances de la vitesse de propagation d'une fissure, on constate qu'elle diminue leK _tc, occasionnant de ce point de vue des conditions plus dangereuses. Dans le cas d'une construction qui doit garantir un service de longue durée, la décroissance de la dimension critique d'une fissure peut être pénalisante. Bien entendu, ceci n'est qu'un résultat pour un matériau particulier avec un traitement thermique spécifique, qui dès lors ne peut être généralisé. D'autres matériaux doivent être également testés.

     

Model for fracture toughness alteration due to cyclic loading

A new model that is capable of predicting and explaining the effect of cyclic loading on the apparent fracture toughness of materials was developed. The model combines macroscopic fracture criteria with the assumption that transient flow properties of material in the cyclic plastic zone can be simulated by those of macroscopic low cycle fatigue specimens, tested in reversed strain control. Little or no changes in the cleavage fracture toughness due to cyclic loading is predicted or observed for materials that cycle strain harden (e.g., rail steel) and in the fracture toughness of other materials that cycle strain harden (e.g., the commercial 2000 series Al-Cu alloys) and fracture by rupture. However, an increase in the fracture toughness is predicted and observed for materials that cycle strain soften (e.g., 1Cr-Mo-V and 18 Ni 300 maraging steels), irrespective of fracture mode (cleavage or rupture). The changes in the fracture toughness are predicted and observed to increase with both the number of cycles of applied load and the reversed plastic strain range (or stress intensity range for precracked specimens).

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Résumé On a développé un modèle à même de prédire et d'expliquer l'effet de mise en charge cyclique sur la ténacité apparente des matériaux. Ce modèle combine les critères de rupture macroscopique avec l'hypothèse que les propriétés d'écoulement transitoire d'un matériau dans une zone où se produit une déformation plastique cyclique peut être simulée par les propriétés d'éprouvettes de fatique olygocyclique macroscopique essayées en déformation alternée. On ne prédit ni n'observe que peu ou pas de changement de la ténacité à la rupture, par clivage dû à une sollicitation cyclique dans le cas de matériaux qui font état d'un écrouissage cyclique, par exemple les aciers à rail. Il en est de même en ce qui regarde la ténacité à la rupture pour les autres matériaux qui durcissent par écrouissage cyclique, par exemple la série commerciale 2000 des alliages AlCu et qui se rompent de manière ductile. Toutefois, on prédit et on observe un relèvement de la ténacité à la rupture dans le cas de matériaux qui s'adoucissent sous l'effet de déformations cycliques, par exemple les aciers 1 CrMoV et les aciers maraging 18Ni300, quel que soit le mode de rupture, c'est-à-dire par clivage ou par rupture ductile. On peut prédire et l'on observe effectivement un accroissement de la ténacité à la rupture avec le nombre de cycles de la charge appliquée et avec l'étendue de la déformation plastique alternée (ou l'étendue de l'intensité de contrainte dans le cas des échantillons préfissurés).

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(The authors wish to dedicate this paper in memory of the late Professor Alan S. Tetelman.)     

Influence of prior-austenite grain size and fracture mode on the fracture toughness of 12% Cr steel

The prior-austenite grain size of a 12% Cr steel has been varied by altering the austenitising temperature. The effect of these variations on the K _Ic fracture toughness has been studied for the as-quenched condition and after subsequently tempering at temperatures up to 550°C. The fact that different fracture modes occurred within this range of heat-treatment has allowed the effect of grain size variations on fracture toughness to be compared for specific fracture morphologies.

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Résumé En modifiant la température d'austénitisation d'un acier à 12% Cr, on a fait varier son grain austénitique primaire et l'on a étudié l'effet de ces variations sur la ténacité à la rupture K _Ic dans l'état brut de trempe et après des revenus allant jusqu'à 550°C. Pour ces divers traitements thermiques, on a constaté des modes de rupture différents, ce qui a permis d'évaluer les effets de variations de la taille du grain sur la ténacité à la rupture, pour des morphologies de rupture bien spécifiques.

     

Mixed mode fracture toughness of GFRP composites

Glass fibre reinforced polymer (GFRP) composites are used in a wide range of applications as a structural material. They have high specific mechanical properties but are prone to delamination as a result of manufacturing defects and impact/shock loading. The ability of the structure to continue to carry load after damage and the subsequent propensity of the damage to propagate are important considerations for the design of damage tolerant composite structures. In order to accurately predict the stability of damage under load, relevant mechanical properties of the material must be accurately determined. In particular, mixed mode fracture toughness data is required in order to study the damage criticality in such structures. This paper describes an experimental study to determine Mixed Mode fracture toughness for thick glass/vinylester specimens. The test methodology used for the experiments and its difficulties will be discussed. Mixed mode fracture toughness results are presented, as are Mode I and Mode II fracture toughness results obtained via Double Cantilever Beam (DCB) and End Notch Flexure (ENF) tests, respectively.