Mixed Mode Fracture of Cracks and Wedge Shaped Notches in Expanded PVC Foam

Fracture initiated from a sharp crack or wedge shaped notch in a homogeneous material, subjected to different loading is considered. Singularities in the stress fields at edges and vertices are discussed. A point-stress criterion is used to predict fracture for sharp cracks as well as 90° wedge notches in expanded PVC foam. The point-stress criterion is formulated in a manner allowing failure predictions in general 3D stress situations. The influence of nonsingular T-stress at cracks is discussed and substantiated by experimental results.     

Abschätzung von Bruchzähigkeitskennwerten aus der Bruch‐ oder Kerbschlagarbeit

Estimation of Fracture Toughness from the Charpy Fracture Energy By means of a simplistic mechanical model a mathematical relation between the total fracture energy of an edge‐cracked beam under bending and the fracture toughness was derived. Inserting the parameters of the standard Charpy specimens and accounting for the finite root radius and the shallowness of the notch, an equation to calculate fracture toughness from the Charpy fracture energy was obtained. Unlike the commonly used empirical correlation formulas, the presented equation is applicable to any elastic‐plastic material. From its theoretical basis and the underlying assumptions it is expected to be conservative in any case. Although the derivation only holds for the upper‐shelf regime, it also is applicable to the brittle‐to‐ductile transition regime as a lower bound. In this range, the degree of conservatism can be reduced by accounting for the well‐known shift of the transition temperature. Comparison with experimental data confirm these features of the presented formula.     

The impact behavior of aluminum alloy 6061: Effects of notch severity

In this paper the influence of notch acuity and test temperature on the impact behavior of aluminum alloy 6061 is presented and discussed. Notch angles of 45°, 60°, 75° and 90° were chosen for a standard charpy impact test specimen containing two such notches positioned at right angles to the applied load. For a given angle of the notch the dynamic fracture toughness increased with an increase in test temperature. At a given test temperature, the impact toughness of a ductile microstructure decreased with an increase in notch severity. For the least severe notch dynamic fracture surfaces revealed the occurrence of localized mixed-mode deformation at the elevated temperature. An increase in notch severity resulted in essentially Mode-I dominated fracture at all test temperatures. The results are discussed in light of alloy microstructure, fracture mechanisms and deformation field ahead of the advancing crack tip.     

Three dimensional finite element investigations into the effects of thickness and notch radius on the fracture toughness of polycarbonate

Fracture toughness of polycarbonate (PC), a commercially important glassy amorphous polymer, is known to be sensitively dependent on a number of factors including molecular weight, ageing time, loading rate and specimen geometry. In this work, we analyze the effect of notch radius and specimen thickness on the near tip fields and the consequence of these on the mode I fracture initiation. To this end, we have performed extensive three dimensional Finite Element simulations within the framework of large deformation elasto-plasticity based on a realistic constitutive model that has been carefully calibrated for PC. Using a simple set of criteria for fracture initiation by void nucleation or ductile tearing, we are able to reproduce experimentally observed brittle to ductile transitions that occur in PC with decrease in thickness and increase in notch radius.     

BT20钛合金激光焊接接头的断裂韧性研究

对BT20钛合金及其激光焊接接头的断裂韧性进行了研究.同时分析了合金及激光焊接接头的硬度分布及显微组织.断裂实验表明,除了一个焊接接头紧凑拉伸(CT)试样是脆性启裂外,其它CT试样均在裂纹延性启裂并缓慢扩展后,发生脆性失稳断裂.母材的断裂韧性明显高于焊接接头,轧制方向对母材断裂韧性的影响不明显.焊接热影响区的断裂韧性介于母材和焊缝金属之间.本研究采用的焊后热处理没有改善焊接接头的断裂韧性,还有进一步恶化的趋势.添加活性剂对焊缝金属的断裂韧性没有明显作用,但对延性裂纹扩展长度有所改善.     

Fracture toughness of bulk adhesives in mode I and mode III and curing effect

Failure load predictions of adhesively bonded lap joints are either done based on a stress/strain limit criterion or using concepts of fracture mechanics. For the former case, the stress-strain curves of the adhesive must be determined accurately and for the latter case the toughness of the adhesive is needed. The present study gives for two adhesives, one brittle and one ductile, the strength and fracture properties in the bulk form. Stress-strain curves are given in tension and shear. The toughness was measured in mode I using a three point bending specimen and in mode III with a circular specimen with a notch under torsion. Mixed-mode criteria are discussed and it is shown that the experimental results are in good agreement with the strain energy theory. Finally, the effect of shrinkage stresses on the fracture toughness was studied and it is shown that they have a substantial effect on the fracture toughness.     

The effects of thermal pre-treatment and molecular weight on the impact behaviour of polycarbonate

Notched impact fracture experiments have been conducted on specimens of polycarbonate in three different conditions, (a) as received, (b) annealed at 125° C, and (c) electron beam irradiated to reduce the molecular weight. By consideration of the behaviour of a wide range of notch geometries four different failure modes were identified which were present in different proportions for each material. (1) Razor notched specimens failed in a completely brittle manner, well described by linear elastic fracture mechanics. (2) Small notch tip radii specimens failed in an apparently brittle manner through the formation of a single craze. (3) Some intermediate notch tip radii specimens failed in a predominantly brittle manner with small shear lips indicative of plane stress yielding. A fracture mechanics approach was used here, the measured toughness correlating with the extent of plane stress yielding. (4) Fully ductile failure was observed for large notch tip radii for all materials. It has been established that the embrittlement of polycarbonate caused by annealing is due to an increase in the yield stress, whereas that caused by reducing the molecular weight is due to a reduction of the crazing stress. In both cases, more specimens of intermediate notch tip radius are caused to fail in the low energy brittle mode designated (2) above. By varying the yield stress and crazing stress independently we have thus been able to distinguish clearly how both influence the brittle-ductile transition.     

Tenacite de WC-Co 15 %

Fracture mechanics have been applied to the brittle material, WC-Co 15 wt. % by a bend test of notched specimens in order to determine, by several methods, the fracture energy γ and the fracture toughness. The experimental results indicate that the K_IC value so determined represents a lower limiting value of fracture toughness, which is 19 ± 2 MP√m. The critical notch radius is about 70 μm.     

On the relation between the mode I fracture toughness of a composite laminate and that of a 0° ply: Analytical model and experimental validation

This paper proposes a simple model to predict the fracture toughness of multidirectional carbon–epoxy composite laminates using the fracture toughness of the 0° ply. The model is based on a combination of Linear-Elastic Fracture Mechanics and lamination theory, and uses as material properties the ply elastic properties and the fracture toughness of the 0° ply measured in compact tension test specimens. A good correlation is obtained by comparing the model predictions and experimental data obtained in center-cracked specimens manufactured using different lay-ups and materials.     

A criterion for brittle fracture in U-notched components under mixed mode loading

A failure criterion is proposed for brittle fracture in U-notched components under mixed-mode static loading. The criterion, called UMTS, is developed based on the maximum tangential stress criterion and also a criterion proposed in the past for mode I failure of rounded V-shaped notches [Gomez FJ, Elices M. A fracture criterion for blunted V-notched samples. Int J Fracture 2004;127:239-64]. Using the UMTS criterion, a set of fracture curves are derived in terms of the notch stress intensity factors. These curves can be used to predict the mixed mode fracture toughness and the crack initiation angle at the notch tip. An expression is also obtained from this criterion for predicting fracture toughness of U-notched components in pure mode II loading. It is shown that there is a good agreement between the results of UMTS criterion and the experimental data obtained by other authors from three-point bend specimens.     

Influence of notch radius and microstructure on the fracture behavior of Al–Zn–Mg–Cu alloys of different purity

The influence of notch radius on the fracture behavior of two high-strength Al–Zn–Mg–Cu alloys with different Fe content in the T73 condition was investigated. The fracture toughness tests were performed on non-fatigue-precracked notched bending specimens with different notch radii ranged from 0.15 mm to 1.0 mm. The obtained data were interpreted using the concept of Notch Fracture Mechanics combined with finite-element method (FEM) calculations. It was found that both alloys are very sensitive to the notch radius. The fracture toughness increases with increasing notch radius. For a given notch radii, the increase in fracture toughness is more significant for the more pure alloy. The fracture behavior of investigated alloys with respect to microstructural features and their relation with the fracture micromechanisms were analyzed.     

Effects of ferrite grain size, notch acuity and notch length on brittle fracture stress of notched specimens of low carbon steel

The effects of ferrite grain size, notch acuity and notch length on brittle fracture stress and fracture toughness of notched specimens were experimentally studied at −196°C for a low-carbon steel.

For the case of smaller notch root radius, fracture stress and fracture toughness are not so much conspicuously affected by ferrite grain size. The effect of ferrite grain size will increase with increase of notch root radius. Fracture stress and fracture toughness will decrease with increase of d^−1/2 (d = grain size diameter) a smaller range of d^−1/2, and increase nearly linearly with increase of d^−1/2 in larger range of d^−1/2, and, thus have minimum at some value of d^−1/2.     

An asymptotic matching approach to shallow-notched structural elements

Fracture in brittle material specimens with V-notches is satisfactorily described assuming as governing parameter the generalized (or notch) stress intensity factor, whose anomalous physical dimensions depend on the notch opening angle. Its critical value, i.e. the generalized toughness, can then be linked to the material strength and toughness according to a number of fracture criteria available in the literature. However, all these criteria provide an infinite failure load as the notch depth tends to zero, this undesirable property being shared with Linear Elastic Fracture Mechanics when applied to vanishing cracks. Aim of the present paper is to overcome this shortcoming. The analysis of the notched specimens is carried out by means of a multiscale approach according to which the problem is solved separately in the region far away from the notch (the outer field) and in the region close to the notch (the inner field). Hence, the asymptotic matching technique can be exploited to achieve the overall solution. Although the procedure is general, i.e. it may be applied to any notch shape, numerical computations refer to sharp V-notches with a re-entrant corner equal to 120°. Comparison with experimental data obtained by testing polystyrene specimens turns out to be more than satisfactory.     

Investigation of mixed mode brittle fracture in rounded-tip V-notched components

A criterion is proposed for brittle fracture analysis in rounded-tip V-notched components. This criterion, called RV-MTS, is developed based on the maximum tangential stress (MTS) criterion proposed earlier for investigating mixed mode brittle fracture in sharp cracks. Using the RV-MTS criterion, a set of fracture curves is presented based on the notch stress intensity factors (NSIFs) for predicting mixed mode and also pure mode II fracture toughness of rounded-tip V-notches. The criterion is also able to predict fracture initiation angles under mixed mode loading. The validity of the criterion is evaluated by several fracture tests performed on the rounded-tip V-notched Brazilian disc (RV-BD) specimens made of PMMA. A good agreement is shown to exist between the theoretical predictions and the experimental results for various notch opening angles and different notch radii.     

桥梁高性能钢HPS485W断裂韧性试验研究

为了研究桥梁高性能钢的断裂韧性,对中国舞阳钢厂生产的高性能钢HPS 485W进行了一系列的断裂韧性试验研究。通过夏比V形缺口冲击试验得到HPS 485W在不同温度下的冲击韧性,并应用Boltzmann函数求解韧脆转变温度曲线,试验结果表明:与传统桥梁用钢相比,HPS 485W冲击韧性更高且韧-脆转变温度更低。由HPS 485W延性断裂韧度(J_IC)试验,测得板厚18mm和28mm的HPS 485W试样的J积分值,试验结果表明HPS 485W具有优良的断裂韧性。对8mm和14mm的HPS 485W进行裂纹尖端张开位移(CTOD)试验,试验结果表明HPS 485W有良好的塑性和韧性。基于HPS 485W拉伸试验获得的应力-应变曲线结果,运用失效评定曲线方法对CTOD试验值进行评定,HPS 485W的母材断裂韧性(CTOD)落在评定曲线的合格范围内。该文的研究为高性能钢桥的安全评定和防断裂设计提供了试验依据。     

A criterion for low-stress brittle fracture of notched specimens based on combined micro- and macro fracture mechanics—1

Based on the combined micro- and macro fracture mechanics, the two requisites necessary for the crack propagation, that is, the energy unstable requisite and the critical local stress requisite, are derived for the low-stress brittle fracture of notched specimens. Thus the fracture criterion was obtained. The criterion is compared with the experimental data, such as on the relationships between the fracture stress or the fracture toughness and the grain size diameter, the crack length, the notch tip radius or the yield stress. The good agreement is obtained.     

Brittle fracture in rounded-tip V-shaped notches

Two failure criteria are proposed in this paper for brittle fracture in rounded-tip V-shaped notches under pure mode I loading. One of these criteria is developed based on the mean stress criterion and the other based on the point stress criterion which both are well known failure criteria for investigating brittle fracture in elements containing a sharp crack or a sharp V-notch. To verify the validity of the proposed criteria, first the experimental data reported by other authors from three-point bend (TPB) and four-point bend (FPB) tests on PMMA at −60 °C and Alumina–7% Zirconia ceramic are used. Additionally, some new fracture tests are also carried out on the rounded-tip V-notched semi-circular bend (RV-SCB) specimens made of PMMA for various notch opening angles and different notch tip radii. A very good agreement is shown to exist between the results of the mean stress criterion and the experimental data.     

STRUCTURAL COLLAPSE, THE FAILURE ASSESSMENT DIAGRAM AND "OFF-THE-SHELF" OPERATION

Abstract— The criteria for determining whether ferritic material exhibits fully ductile behaviour are generally based on the fracture toughness vs temperature relationship determined from standard laboratory test pieces (e.g. Charpy V Impact tests or fracture toughness specimens). This relationship defines a ductile-brittle transition region. When fully ductile, microvoid coalescence behaviour is experienced, and fracture toughness is described as being on the “upper shelf”. At “off the shelf” temperatures brittle, cleavage fracture is experienced. On the lower shelf the material is entirely brittle, exhibiting 100% crystallinity on the fracture face. As the temperature increases, initiation of tearing by microvoid coalescence occurs and some stable tearing can occur prior to the cleavage event. Material toughness increases with temperature until the upper shelf condition is achieved. The characteristics of fracture toughness tests in terms of the toughness level exhibited and the extent of ductile tearing experienced have been used as a guide to whether the structural application (e.g. a pressure vessel) will behave in a brittle or a ductile manner. This paper reports on a feasibility study where various worked examples have been performed to examine the concept of using a “cut off” on the failure assessment diagram, determined from the conditions required to cause plastic collapse of a pressure vessel, as a criterion for defining effective “ductile” operation. Fracture assessment procedures (R6 revisions 2 and 3 and PD6493 levels 2 and 3) have been utilised to determine the influence on pressure vessel performance of the behaviour of fracture toughness test specimens. The procedure of plotting a structural collapse “cut off” on a failure assessment diagram enables the assessment of whether a particular flaw geometry would result in gross deformation of the structure at failure. The use of this procedure provides an unambiguous demarcation between “fracture dominated” and “collapse controlled” conditions. This procedure facilitates judgements on the level of toughness necessary to ensure ductile operation and whether a “tearing plus toughness” requirement is necessary. It is recommended that consideration be given to including structural collapse into fracture assessment procedures carried out using R6 revision 3 or PD 6493:1991 procedures in order to determine the conditions when enhanced toughness no longer influences structural performance (i.e. when effective “upper shelf” conditions are attained).     

A Finite Fracture Mechanics approach to the asymptotic behaviour of U‐notched structures

A Finite Fracture Mechanics (FFM) criterion is formalized to predict the critical failure loads of brittle U‐notched specimens, subjected to mode I loading. The criterion, recently applied to V‐notched structures, requires the contemporaneous fulfilment of stress requirements and energy conditions for fracture to propagate: the stress field ahead of the notch tip and the stress intensity factor related to a crack stemming from the root are involved. Both the apparent fracture toughness and the critical crack advancement result to be structural parameters. For sufficiently slender notches, the root radius becomes the only relevant geometric dimension. The consistency of the approach is proved by the comparison with experimental data available in the Literature.     

A two-parameter approach to assessing notch fracture behaviour in clay/epoxy nanocomposites

Fracture toughness and other mechanical properties of epoxy are known to be affected by the addition of nanoclays. Fracture toughness has been shown by many researchers to depend on the nanocomposite structure with well-dispersed and distributed nanoparticles resulting in improvements in this property by up to 50%. Notch fracture toughness depends on the acuity of the notch as well as on the structure of the nanocomposite. In the present work, a two-parameter fracture criterion based on a critical notch stress intensity factor, K_ρ,c, and effective T-stress, T_ef, was used to study the effect of notch severity and nanoclay addition on the fracture toughness of the epoxy matrix. The results show that the average value of K_ρ,c for neat epoxy increased with increasing notch radius while the absolute value of T_ef decreased with notch radius. The addition of nanoclay to pristine epoxy reduced the average value of K_ρ,c and increased the absolute value of T_ef. The critical notch radius was found to be around 1.0 mm and the notch sensitivity was higher for neat epoxy. SEM analysis of the fractured surfaces revealed that the lower K_ρ,c for nanocomposites in both mode I and mixed mode fractures was due to early crack initiation at clay clusters or voids at the notch root.