Size effect in fracture of unidirectional composite plates

Fracture of notched, unidirectionally reinforced composite plates with well-bonded ductile matrices is typically preceded by the formation of long, discrete plastic shear zones aligned in the fiber direction. Onset of fracture is associated with a critical tension stress in a certain small process zone ahead of the notch tip; the critical stress is often equal to the tensile strength of the unnotched composite plate. Length of the shear zones can be estimated by plastic limit-analysis, and the local tension stress ahead of the notch found by superposition of the stress caused by remotely applied loads with the stress induced by the shear tractions in the plastic zone, which is shown to be dominated by a logarithmic singularity. In as-fabricated boron-aluminum composites, this fracture mechanism was analyzed and confirmed by numerous experiments (G.J. Dvorak, J. Zarzour and Y. Benveniste, Engineering Fracture Mechanics 42, 501–517, 1992). Since the notch tip field is not described by a stress intensity factor, experimental notched strength data cannot be interpreted in terms of a single material property, such as toughness. An alternative scaling procedure is outlined for prediction of notched strength of wide plates on the basis of data obtained from small size specimens. This revised version was published online in July 2006 with corrections to the Cover Date.     

Effect of martensite transformation on fracture behavior of shape memory alloy NiTi in a notched specimen

In this paper, the finite element calculation of the stress–strain distribution in front of a notch tip were carried out for two materials. One is a shape memory alloy NiTi with the stress-induced martensite transformation, and another is a fully transformed martensite NiTi without the transformation. Based on the results obtained, and combining a model of the fracture process zone, effect of martensite transformation on the fracture behavior of the shape memory alloy NiTi in a notched specimen of plane stress state is comparably analyzed. The results show that the martensite transformation increases the load to produce plastic deformation in the transformed martensite at the notch tip and decreases the maximum normal stress and plastic strain near the notch tip, and tends to suspend the crack nucleation and propagation in the fully transformed martensite in front of the notch tip, and thus increases the fracture load and improves the toughness. A quantitative analysis based on the model of the fracture process zone shows that the martensite transformation in the SMA NiTi causes about 47% increase in the apparent fracture toughness.     

Investigation of blunting line and evaluation of fracture toughness under mixed mode I/III loading in commercially pure titanium

Abstract

The blunting line and fracture toughness in commercially pure titanium under mode I and mixed mode I/III loading was studied. A modified compact tension geometry was used for determining the blunting line as well as mixed mode I/III fracture toughness. The results showed that the constraint factor m in the blunting line equation under mode I loading was 1.84. Also, there was no effect of notch root radius on the slope of the blunting line. The blunting line slope under mixed mode I/III loading was found to be lower than that under mode I loading and agreed with empirical correlations. The fracture toughness under mode I loading was found to be higher for specimens with larger notch root radius. However, notch root independent fracture toughness could be obtained from blunt notch specimen tests using stretch zone width measurements. The fracture toughness was found to decrease with increasing mode III loading.     

Relationship between the stress intensity and stress concentration factors for sharp and rounded notches

The method of singular integral equations is used to find the solution of the plane problem of the theory of elasticity for a plane containing an infinite V-shaped rounded notch. This enables us to establish the relationship between the stress intensity factor at the tip of the sharp V-shaped notch, the stress concentration factor for the corresponding rounded notch, and the radius of curvature at the notch tip. It is shown that the indicated relationship is not unique. Indeed, for the same curvature at the notch tip, we get different dependences for different shapes of its vicinity. __________ Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 42, No. 6, pp. 17–26, November–December, 2006.     

Analysis of the stress field in front of a notch

We performed the analytic, numerical, and experimental analyses of stresses in front of a sharp notch with an aim to establish a proper fracture criterion for the prediction of the onset of crack propagation from the notch. We reconsidered the Williams approach to the analysis of the general structure of the stress field. The finite-element method was used to deduce a formula for the stress concentration factor for a given geometry of the specimen. The method of caustics was used to obtain new relations for the stress concentration factors in front of the notch. We also carried out experimental investigations by the method of caustics and used the experimental data to postulate a fracture criterion. Department of Mechanical Engineering, Kielce University of Technology, Kielce, Poland. Published in Fizyko-Khimichna Mekhanika Materialiv, Vol. 34, No. 5, pp. 101–107, September–October, 1998.     

EFFECTS OF CRACK LENGTH, NOTCH ROOT RADIUS AND GRAIN SIZE ON FRACTURE TOUGHNESS OF FINE CERAMICS

Generally, fracture toughness and fracture stress of ceramics depend on crack length, notch root radius and grain size. These three parameters are most important when assessing the integrity of structural ceramic members and developing high-performance ceramics. A new failure criterion called the process zone size failure criterion, has been proposed based on the existence of a crack-tip process zone. Using this criterion, it is shown that theoretical values are in good agreement with many test results quoted from many papers. It is concluded that this failure criterion is useful when evaluating crack length and notch root radius problems. The effect of grain size on both the fracture toughness and on the toughening mechanism is also considered.     

Effect of notch root radius on fracture toughness of polycrystalline cubic boron nitride

The fracture toughness of five grades of polycrystalline cubic boron nitride (PCBN) has been determined using Single Edge V-Notched Beam specimens. Both coarse and fine grade materials were considered, containing CBN grain sizes of between 1 μm and 22 μm. The influence of notch root radius on the measured fracture toughness was examined. The notch root radius was found to have a major effect for materials with smaller CBN grain sizes while only a small effect was noted for the material with large CBN grain sizes. A simple analytical model was developed to explain the effect of the notch root radius on the fracture toughness and was found to agree well with experiment for all the materials tested. It was shown that the effect of notch root radius is directly linked to the size of the CBN grain. It is proposed that this effect results from the interaction between the microstructure and the stress field around the notch tip.     

Fracture Toughness Test with a Sharp Notch Introduced by Focussed Ion Beam

The validity of fracture toughness data obtained from tests with V-notched bending bars is affected by the notch root radius and the presence of R-curve behavior. A macroscopic test specimen has been developed that contains a notch introduced by focused ion beam machining. This produces a notch root radius of less than 0.1 μm, so that notch effects can be ignored for most ceramics. Also, due to the very small notch depths the influence of a rising R-curve should be very close to that of natural cracks. First tests, carried out on a Ce-doped zirconia ceramic resulted in a toughness of K _Ic ≈ 5.9 MPa√m.     

Notch root contraction as a fracture measurement

The value of displacement measurements in fracture toughness testing is discussed; in particular the measurement of notch root contraction. The mechanisms of plastic deformation at the notch tip are described, leading to a discussion of theoretical relationship between notch root contraction and crack opening displacement. Experimental work is described in which notched bend specimens of a low alloy steel were loaded to fracture. Each specimen was simultaneously instrumented with notch contraction, COD, and “clip-in” gauges. The equality between notch root contraction and COD was confirmed and observations are made on the relative value of the different measurements. Further observations on the distribution of contraction around the notch tip were made.     

Mechanics and physics of quasibrittle fracture of polycrystalline metals under conditions of stress concentration Part 3. Toughness of metals and alloys

We consider new characteristics of toughness based on the fundamental ideas concerning the micromechanism of quasibrittle fracture of metals and taking into account the specific features of fracture under the conditions of stress concentration. Unlike the existing characteristics of toughness (e.g., impact toughness), these characteristics can be directly used in the numerical analysis of load-carrying structural elements. By analogy with the safety margin, we introduce the concept of the “safety margin of toughness” of a metal. We propose analytic relations for the evaluation of the safety factor of toughness of a metal in products containing structural stress concentrators and macrocracks. For these types of concentrators, we deduce the relationships between the ordinary safety factor and the safety factor of toughness. We analyze the values of toughness for low-, medium-, and high-strength steels and propose optimal combinations of the strength and toughness characteristics of metals. The relationships between the new characteristics of toughness and K_lc are also established. Institute of Physics of Metals, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Problemy Prochnosti, No. 1, pp. 72–92, January–February, 2000     

Relationship between fracture toughness and deformation ahead of the crack tip

An analytical relationship for the calculation of the intensity of elastoplastic strains at the front of a mode I crack is obtained on the basis of the suggested model. A strain criterion of fracture toughness has been developed which relates the stress intensity factor to the width of the stretch zone, the mechanical properties of the material, and its elastic constants. A comparison of experimental and numerical (obtained by using the proposed equations) data of the stretch zone width for 15Kh2NMFA steel in a wide temperature range demonstrates good agreement between the theory and the experiment. This proves the possibility of calculating fracture toughness via the stretch zone width and mechanical properties of the material. Translated from Problemy Prochnosti, No. 2, pp. 33–40, March–April, 1997.     

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.     

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.     

Interfacial fracture of piezoelectric multilayer actuators under mechanical and electrical loading

The elastic stress and strain fields in a plate of finite thickness containing an elliptical hole are systematically investigated using the 3D finite element method. It is found that the stress and strain concentrations are different in the plate of finite thickness even if the plate is in an elastic state. The relation between the stress and the strain concentration factors depends on Poisson’s ratio, the hole’s geometric configuration and the plate thickness. The stress concentration factor is equal to the strain concentration factor only at the notch root of the plate surface. The stress (or strain) concentration factor at the notch root of the plate surface decreases rapidly with increasing thickness and becomes lower than the stress and strain concentration factors corresponding to the plane stress state or at the notch root of the mid plane. It is too low to reflect the overall stress concentration as the thickness increases or as the b/a ratio decreases. The maximum stress concentration factor occurs on the mid plane only when the plate is thinner than the transition thickness of the stress concentration factor. When the plate is thicker than the transition thickness of the stress concentration factor, the distance between the location of the maximum stress concentration factor and plate surface tends to be constant with increasing thickness for the plate with a given  b/a ratio. The differences between the maximum value and the surface value of the stress and strain concentration factors increase rapidly and tend to their respective constant values with increasing plate thickness. The smaller the b/a ratio, the larger these differences. The difference of the stress concentration factor is larger than that of the strain concentration factor in the same plate.     

陶瓷材料断裂韧性与缺口半径 Ⅱ 断裂韧性估算方法

在陶瓷材料裂纹尖端存在一个断裂过程区，当断裂过程区内平均应力达到断裂强度时，裂纹扩展。本文由理论推导结合实验数据，得到了新断裂过程区的大小是平均晶粒直径的四倍。并由平均应力断裂模型，给出了陶瓷材料断裂韧性和缺口半径及平均晶粒直径之间的关系式，由此关系式可以用宽缺口试件测出的断裂韧性去估算陶瓷材料的本质断裂韧性。     

Fracture toughness and hydrogen embrittlement of pipes with notches

A technique for experimental determination of fracture toughness and hydrogen embrittlement of pipes made of API 5L X52 steel is described. The tests were performed using arc-shaped specimens with a notch cut out from pipes under the conditions of a three-point bend. The fracture toughness was determined in terms of the J-integral and the stress intensity factor at the notch tip. The value of K _ρ,c was established using the volumetric method based on the experimentally measured critical load and the results of the FEM calculation of the distribution of elastic-plastic stresses ahead of the notch tip, and J _ρ,c was determined using the method of separable functions. The effect of hydrogen embrittlement was studied using electrolytically prehydrogenated specimens.     

Notch fracture toughness of high-strength Al alloys

In this study, the notch fracture toughness (NFT) of high-strength Al alloys was examined by a non-standardized procedure. The NFT is defined as the critical notch stress-intensity factor (NSIF) K_ρ,c, which is determined by using several methods of analysis and computing. A set of specimens with different notch root radii made from overaged 7xxx alloy forging was selected. The influence of the notch radius on the fracture toughness of the material was considered. It was found that the notch radius strongly affects the fracture behavior of forged 7xxx alloy in overaged condition. The notch fracture toughness was higher than the fracture toughness of a cracked specimen and increased linearly with notch radius. The critical notch radius was related to the spacing of intermetallic (IM) particles which promote an intergranular or transgranular fracture mechanism according to their size. It appeared that ductile transgranular fracture generated by the formation of dimples around dispersoids and matrix precipitates was predominant which indicates that intense strains are limited to a much smaller zone than the coarse IM particles spacing. This double mechanism is also operate for crack propagation of ductile fatigue. The nature and morphology of IM particles exert significant effects on the rate of fatigue crack growth and fracture toughness properties.     

Prediction of intrinsic fracture toughness for brittle materials from the apparent toughness of notched-crack specimen

In this investigation, fracture process zone model is used to establish a new relationship to predict the intrinsic fracture toughness from the apparent fracture toughness of a notched-crack specimen. The parameters needed in the proposed model are very rare, such as, the fracture process zone size of materials, the notch radius. Specimens made up of two kinds of polycrystalline alumina and one soda-lime glass with notch radii as small as a few micrometer are used to verify the predictions of this model. Besides, the results also show that fracture toughness of ceramics decreases with the decreasing of notch root radius. Under condition of the radius of crack tip is not greater than the averaged grain size, the apparent toughness can be approximately regarded as the fracture toughness of the materials.     

Fracture mechanisms of poly(ethylene terephthalate) and blends with styrene-butadiene-styrene elastomers

Poly(ethylene terephthalate) (PET) was blended with 5 wt % of an elastomeric block copolymer. The hydrogenated styrene-butadiene-styrene (SEBS) elastomers were functionalized with 0–4.5 wt % maleic anhydride grafted on the midblock. Notched tensile tests in the temperature range − 40–55 °C differentiated among the blends in terms of their toughness. The least effective elastomer was the unfunctionalized SEBS; all the functionalized SEBS elastomers effectively increased the toughness of PET. Fractographic analysis indicated that PET and the blend with unfunctionalized SEBS fractured through a pre-existing craze. Although adhesion of the unfunctionalized SEBS to the matrix was poor, the elastomer strengthened the craze somewhat, as indicated by an increase in length of the pre-existing craze when final separation occurred. A functionalized SEBS caused the fracture mechanism to change from crazing to ductile yielding. Graft copolymer formed by reaction of PET hydroxyl end groups with the anhydride in situ was thought to act as an emulsifier to decrease particle size and improve adhesion. These factors promoted cavitation, which relieved the triaxiality at the notch root and permitted the matrix to shear yield. This revised version was published online in November 2006 with corrections to the Cover Date.     

Mechanics and physics of quasibrittle fracture of polycrystalline metals under conditions of stress concentration. Part 2. Theoretical basis

We propose a physical model of quasibrittle fracture of polycrystalline metals as applied to the most general case of the complex stressed state and nonuniform distributions of stress and strain fields. Within the framework of this model, on the basis of the analysis of elementary acts of the process of initiation and loss of stability of incipient cracks, we explain, for the first time, the basic regularities of the variation of the local stress of quasibrittle fracture σ_c, of a metal under the conditions of stress concentration. It is shown that the value of σ_c depends not only on the length of incipient cracks but also on their number in the local plastic zone at the notch tip and on the law of their distribution over orientations. On this basis, we explain the causes of the, influence of the acuity of the notch and testing temperature on σ_c. It is shown that the application of the proposed model in combination with the finite-element method makes it possible to predict (with sufficiently high accuracy) both the mean value and the spread of the fracture load of a specimen with stress concentrator of any acuity, including fatigue cracks. Institute of Physics of Metals, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Problemy Prochnosti, No. 3, pp. 5–16, May–June, 1999.