Scale effects on the in-situ tensile strength and fracture of ice Part I: Large grained freshwater ice at Spray Lakes Reservoir, Alberta

At lab-scale, issues such as inhomogeneity and polycrystallinity are especially important to the fracture of S1 freshwater ice. S1 freshwater ice is typically composed of large grains with predominantly vertical c-axes. Because of the very large grain sizes that one can encounter in S1 macrocrystalline ice sheets, it is essential that the effects of sample size on the fracture behavior be determined. In other words, are small scale (lab-scale) results applicable at larger scales (at the scale of ice-structure interactions, for instance)? To answer this question, a set of lab- to structural-scale (0.34>L>28.64m) fracture tests were conducted on S1 freshwater lake ice at Spray Lakes, Alberta, using the base-edge-notched reverse-tapered plate geometry and covering a size range of 1:81. A Ba?ant-type size effect analysis of the measured fracture strengths (which do reveal a significant dependence on scale) is unexpectedly clouded by the fact that the data collected violates the associated scatter requirements, even though the size range tested is large. Moreover, via Hillerborg's fictitious crack model, large fracture energies were back-calculated (of order 20 J/m2), but for miniscule process zone sizes; in addition, not all of the measured deformations for each test could be matched simultaneously. Apparently, these very warm S1 macrocrystalline lake ice experiments were dominated by nonlocal deformation and energy release rate mechanisms, in all likelihood brought about by grain boundary sliding. The reduced effectiveness of both the Ba?ant-type size effect analysis and Hillerborg's fictitious crack model is due mainly to the lack of crack growth stability achieved in the experiments. These unstable fractures truncated the fracture process. Given the irregular and large grain structure, the very warm ice temperatures, and the diffuse grain boundary surface energy, there is a marked dependence on specimen size to grain size ratio and distinctly non-unique pre-failure process zones occurred. Micromechanical simulations are required to resolve these coupled issues.     

Size effects in concrete fracture – Part II: Analysis of test results

This paper presents an analysis of the extensive experimental program aimed at assessing the influence of maximum aggregate size and specimen size on the fracture properties of concrete. Concrete specimens used were prepared with varying aggregate sizes of 4.75, 9.5, 19, 38, and 76mm. Approximately 250 specimens varying in dimension and maximum aggregate size were tested to accomplish the objectives of the study. Every specimen was subjected to the quasi-static cyclic loading at a rate of 0.125mm/min (0.005in./min) leading to a controlled crack growth. The test results were presented in the form of load-crack mouth opening displacement curves, compliance data, surface measured crack length and crack trajectories as well as calculated crack length, critical energy release rate, and fracture toughness (G ₁). There is a well pronounced general trend observed: G ₁ increases with crack length (R-curve behavior). For geometrically similar specimens, where the shape and all dimensionless parameters are the same, the R-curve for the larger specimens is noticeably higher than that for the smaller ones. For a fixed specimen size, G ₁ increases with an increase in the aggregate size (fracture surface roughness). For the same maximum aggregate size specimens, the apparent toughness increases with specimen size. It was clear that the rate of increase in G ₁, with respect to an increase of the dimensionless crack length (the crack length normalized by the specimen width), increases with both specimen size and maximum aggregate size increase. The crack trajectory deviates from the rectilinear path more in the specimens with larger aggregate sizes. Fracture surfaces in concrete with larger aggregate size exhibit higher roughness than that for smaller aggregate sizes. For completely similar specimens, the crack tortuosity is greater for the larger size specimens. The crack path is random, i.e., there are no two identical specimens that exhibit the same fracture path, however, there are distinct and well reproducible statistical features of crack trajectories in similar specimens. Bridging and other forms of crack face interactions that are the most probable causes of high toughness, were more pronounced in the specimens with larger maximum size aggregates.     

Evaluation of the ISO <Emphasis Type="Italic">J</Emphasis> initiation procedure using the EURO fracture toughness data set

The multiple specimen J _0.2/BL initiation fracture toughness test procedure from the ISO standard, ISO 12135:2002, is evaluated using the EURO fracture toughness data set. This standard is also compared with the ASTM standard, ASTM E 1820, multiple specimen J _Ic procedure. The EURO round robin data set was generated to evaluate the transition fracture toughness methods for steels. However, many of the tests resulted in ductile fracture behavior giving final J versus ductile crack extension points. This is the information that is measured in a multiple specimen J initiation fracture toughness test. The data set has more than 300 individual points of J versus crack extension with four different specimen sizes. It may be the largest data set of that type produced for one material. Therefore, its use to determine J initiation values can provide an important evaluation of the standard procedures. The results showed that a J _0.2/BL value could be determined from the ISO standard for three of the four specimen sizes, the smallest size did not meet the specimen size requirement on J. The construction line slopes in this method are very steep compared with the ASTM construction line slopes. This resulted in low J initiation values, about a factor of two lower than the one from the ASTM method. Of the various criteria imposed to determine a valid J _0.2/BL value, the one limiting the maximum J value was the most questionable. It had an effect of eliminating small specimen data that was identical to acceptable large specimen data.     

A post yield fracture mechanics analysis of three-point bend specimens and its implications to fracture toughness testing

A Post Yield Fracture Mechanics analysis of three point bend specimens of a low strength, high toughness alloy steel, was performed on two series of tests. In the first the specimen dimensions were fixed and the crack length varied. In the second geometrically similar sub-standard specimens were tested. The smallest specimen tested was one-eighth valid size. The results were analysed using three post yield theories; the J-integral, the Bilby, Cottrell and Swinden (BCS) model and the Witt equivalent energy method. In the short crack length series the results were adequately described by the J-integral, the BCS model or by standard linear elastic fracture mechanics within the observed experimental scatter. In the geometrically similar series the Witt equivalent energy method consistently predicted toughness values within the scatter band of the valid tests. The BCS and J-integral methods underestimated the toughness for the two smallest sizes tested. This phenomenon is explained in terms of the relaxation of the plane strain plastic constraints towards the unconstrained plane stress state. The results of other workers on bend specimens are reproduced and retreated.     

Evaluation of R-curve behavior of ceramic-metal functionally graded materials by stable crack growth

This paper deals with the fracture toughness and R-curve behavior of ceramic-metal functionally graded materials (FGMs). A possibility of stable crack growth in a three-point-bending specimen is examined based on the driving force and resistance for crack growth in FGMs, and the distribution of fracture toughness or R-curve behavior is evaluated on FGMs fabricated by powder metallurgy using partially stabilized zirconia (PSZ) and stainless steel (SUS 304). The materials have a functionally graded surface layer (FGM layer) with a thickness of 1 mm or 2 mm on a SUS 304 substrate. Three-point-bending tests are carried out on a rectangular specimen with a very short crack in the ceramics surface. On the three-point-bending test, a crack is initiated from a short pre-crack in unstable manner, and then it propagates in stable manner through the FGM layer with an increase in the applied load. From the relationship between applied load and crack length during the stable crack growth in the FGM layer, the fracture toughness is evaluated. The fracture toughness increases with an increase in a volume fraction of SUS 304 phase.     

Effect of compressive transverse normal stress on mode II fracture toughness in polymeric composites

Effect of transverse normal stress on mode II fracture toughness of unidirectional fiber reinforced composites was studied experimentally in conjunction with finite element analyses. Mode II fracture tests were conducted on the S2/8552 glass/epoxy composite using off-axis specimens with a through thickness crack. The finite element method was employed to perform stress analyses from which mode II fracture toughness was extracted. In the analysis, crack surface contact friction effect was considered. It was found that the transverse normal compressive stress has significant effect on mode II fracture toughness of the composite. Moreover, the fracture toughness measured using the off-axis specimen was found to be quite different from that evaluated using the conventional end notched flexural (ENF) specimen in three-point bending. It was found that mode II fracture toughness cannot be characterized by the crack tip singular shear stress alone; nonsingular stresses ahead of the crack tip appear to have substantial influence on the apparent mode II fracture toughness of the composite.     

Recrystallization-etch approach to study the plastic energy absorbtion at crack initiation and extension of pressure-vessel steel A533B-1

To evaluate the elastic-plastic fracture toughness parameter of nuclear pressure-vessel steel A533B-1, a newly developed technique (the recrystallization-etch technique) for plastic strain measurement was applied to different sizes of compact tension specimens with a crack length/specimen width of 0.6–0.5 that were tested to generate resistance curves for stable crack extensions. By means of the recrystallization-etch technique, the plastic energy dissipation or work done within an intense strain region at the crack tip during crack initiation and extension was measured experimentally. Furthermore, the thickness effects on this crack tip energy dissipation rate were examined in comparison with other fracture-parameter J integrals. Thickness effects on critical energy dissipation and energy dissipation rate during crack extension were obtained and the energy dissipation rate dW _p/da in the mid-section shows a constant value irrespective of specimen geometry and size, which can be used as a fracture parameter or crack resistance property.     

Fatigue and fracture of a Ni–P amorphous alloy thin film on the micrometer scale

Fracture and fatigue tests have been performed on micro‐sized specimens for microelectromechanical systems (MEMS) or micro system technology (MST) applications. Cantilever beam type specimens with dimensions of 10 × 12 × 50 μm³, approximately 1/1000th the size of ordinary‐sized specimens, were prepared from a Ni–P amorphous thin film by focused ion beam machining. Fatigue crack growth and fracture toughness tests were carried out in air at room temperature, using a mechanical testing machine developed for micro‐sized specimens. In fracture toughness tests, fatigue pre‐cracks were introduced ahead of the notches. Fatigue crack growth resistance curves were obtained from the measurement of striation spacing on the fatigue surface, with closure effects on the fatigue crack growth also being observed for micro‐sized specimens. Once fatigue crack growth occurs, the specimens fail within one thousand cycles. This indicates that the fatigue life of micro‐sized specimens is mainly dominated by a crack initiation process, also suggesting that even a micro‐sized surface flaw may be an initiation site for fatigue cracks which will shorten the fatigue life of micro‐sized specimens. As a result of fracture toughness tests, the values of plane strain fracture toughness, K_IC, were not obtained because the criteria of plane strain were not satisfied by this specimen size. As the plane strain requirements are determined by the stress intensity, K, and by the yield stress of the material, it is difficult for micro‐sized specimens to satisfy these requirements. Plane‐stress‐ and plane‐strain‐dominated regions were clearly observed on the fracture surfaces and their sizes were consistent with those estimated by fracture mechanics calculations. This indicates that fracture mechanics is still valid for such micro‐sized specimens. The results obtained in this investigation should be considered when designing actual MEMS/MST devices.     

Scale effects on the in-situ tensile strength and fracture of ice. Part II: First-year sea ice at Resolute, N.W.T.

A set of lab- to structural-scale 0.5 < L < 80 m) in-situ full thickness (1.8 m) fracture tests were conducted on first-year sea ice at Resolute, N.W.T. using self-similar (plan view) edge-cracked square plates. With a size range of 1:160, the data is used, via size effect analyses, to evaluate the influence of scale effects on the fracture behavior of sea ice over the range 10-1 m (laboratory) to 100 m and to predict the scale effect on tensile strength up to ≈1000 m. Details of this large-scale sea ice fracture test program are presented in this paper. The experimental results are presented as well as the fracture modeling of the data. The influence of scale on the ice strength and fracture toughness is dramatic. The applicability of various size effect laws are investigated and criteria for LEFM test sizes are presented. For the thick first-year sea ice tested, the size-independent fracture toughness is of order 250 kPa , not the 115 kPa that is commonly used. The number of grains spanned by the associated test piece is 200, much larger than the number 15 typically quoted for regular tension-compression testing. The size-independent fracture energy is 15 J/m2, while the requisite LEFM test size for the edge-cracked square plate geometry (for loading durations of less than 600 s and an average grain size of 1.5 cm), is 3 m square. Size effect analyses of sub-ranges of the data show that unless the specimen sizes tested are themselves sufficiently large, the true nature of the scale effect is not revealed, which was a concern raised by Leicester 25 years ago. In the case of the fracture tests reported in this paper, based on the lab-scale and field-scale strength data measured between 0.1 and 3 m and using Bažant's size effect law, it is possible to accurately predict the tensile strengths for all of the remaining tests, up to and including 80 m. This revised version was published online in July 2006 with corrections to the Cover Date.     

Crack growth resistance curve and size effect in the fracture of cement paste

A general theory is presented for the fracture of cementitious materials. It is shown that crack growth resistance curves can be constructed for cement pastes using fracture data available in the literature. The crack growth resistance curves are used to explain the specimen size and crack length dependence of fracture toughness in cement pastes.     

Effect of yield stress and specimen size on the position of fracture toughness peak (FTP) in Ji-a/W curves

Early work showed that there was a fracture toughness peak (FTP) as the fracture toughness changed with crack length/specimen width (a/W). It could be thought of as a “safe crack” for the cracks whose length is smaller than that where the FTP is located. In the present paper, it is indicated that the crack length of FTP isJ_i-a/Wcurves decreases with increasing yield stress of material and specimen size and decreasing test temperature. The reason for the fracture toughness being insensitive to the (a/W) for the ultra-high strength and brittle material is explained.     

A new method for evaluating fracture toughness of brittle materials

A new testing procedure is suggested for measuring the fracture toughness of brittle materials as superconductors and ceramics. The idea is to perform a compression test on a subcompact square specimen which contains a central hole. The presence of the hole induces a tensile stress at a certain small region attached to the hole. In this region an artificial notch is introduced such that the fracture path satisfies a pure tensile opening mode (mode I) to which the linear fracture mechanics rules apply. The stress distribution on the fracture plane guarantees a certain amount of stable crack extension. The relationship between the critical compressive load and the stress intensity factor is formulated via an available Green function along with a numerical solution (FEM with ANSYS code). The testing procedure is demonstrated with specimens made of two types of tungsten carbide which differ by their grain size only. Test results are examined via fracture toughness and strength values produced by other conventional methods and the agreement is very good. The geometry and loading direction enable the fracture toughness results to be relatively insensitive to the notch tip radius and the crack length, thereby relaxing the requirements for accurate measurements.The small size of the suggested specimen (12.70mm×12.70mm×5mm) and the avoidance of gripping interfaces provide the major cost-wise advantages.     

Experimental and numerical investigation of cracked chevron notched Brazilian disc specimen for fracture toughness testing of rock

The cracked chevron notched Brazilian disc (CCNBD) specimen has been suggested by the International Society for Rock Mechanics to quantify mode I fracture toughness (K_Ic) of rock, and it has also been applied to mode II fracture toughness (K_IIc) testing in some research on the basis of some assumptions about the crack growth process in the specimen. However, the K_Ic value measured using the CCNBD specimen is usually conservative, and the assumptions made in the mode II test are rarely assessed. In this study, both laboratory experiments and numerical modeling are performed to study the modes I and II CCNBD tests, and an acoustic emission technique is used to monitor the fracture processes of the specimens. A large fracture process zone and a length of subcritical crack growth are found to be key factors affecting the K_Ic measurement using the CCNBD specimen. For the mode II CCNBD test, the crack growth process is actually quite different from the assumptions often made for determining the fracture toughness. The experimental and numerical results call for more attention on the realistic crack growth processes in rock fracture toughness specimens.     

Effects of sizes of ferrite grains and carbide particles on toughness of notched and precracked specimens of low-alloy steels

Four point bending (4PB) tests of notched specimens and COD tests of precracked specimens were carried out on two steels; one steel was treated into two groups with the same ferrite grain size but different carbide sizes, the other steel with different ferrite grain sizes but similar carbide sizes. The results of the tests show that the toughness measured in notched specimens is mainly determined by the grain sizes, which define the local fracture stress _f; the size of carbide particle plays a minor role. However, on the contrary, in precracked specimens the toughness is sensitive to the carbide sizes, which affect the critical plastic strain _pc for initiating a crack nucleus; the effect of grain size is indistinct. By these inferences the behavioral discrepancy of large grain steel in improvement of crack fracture toughness while reducing the notch toughness is explained.     

On fracture toughness and its size dependence for steels showing thickness delamination

The effect of thickness delamination on fracture toughness has been studied. The test material used was a martensitic-austenitic pressure vessel steel. Tests were performed on compact tension and three point bend specimens of varying sizes. All specimens were machined from plate material of 100 mm thickness. It was found that the ASTM practice of test evaluation leads to a size dependence of fracture toughness although data for all specimens fulfill the ASTM size requirements. This size dependence has been explained theoretically and it was shown that an evaluation method based on a fixed absolute amount of apparent crack extension would lead to coinciding data for all specimen sizes.     

Experimentally determined key curves for fracture specimens

Crack extension during fracture toughness tests of ferritic structural steels cannot be determined from measurements of unloading compliance or electric potential change when the specimen is dynamically tested. Measurements of crack extension in fracture toughness tests are also very difficult when the test temperature is high or the test environment is aggressive. To circumvent this limitation, researchers for years have been developing key curve and normalization function methods to estimate crack extension in standard elastic-plastic fracture toughness test geometries. In the key curve method (Ernst et al., 1979; Joyce et al., 1980) a load-displacement curve is measured for a so-called `source' specimen that is sub size or has a blunt notch so that the crack will not initiate during elastic-plastic loading. The load and displacement are then converted to normalized stress-strain units to obtain a key curve that can be used to predict crack extension in geometrically similar `target' specimens of same material loaded at similar loading rates and tested under similar environmental conditions. More recently Landes and coworkers (Herrera and Landes, 1990; Landes et al., 1991) proposed the normalization data reduction technique – Annex A15 of ASTM 1820 specification – that presents an alternative to the standard E1820 unloading compliance procedure. Although the normalization method works well in many cases, it has serious drawbacks: the load, displacement and crack length at the end of the test must be measured; the prescribed functional form that is fitted to the initial and final data may not be accurate for all materials; and the iterative method of inferring crack length from the combination of the data and the normalization function is complex. The compliance ratio (CR) method developed in this paper determines key curves for predicting crack extension as follows. First, a statically loaded source specimen with the unloading compliance procedure specified in ASTM 1820. Second, the so-called CR load-displacement curve is calculated for the source specimen, which is the load-displacement record that would have been obtained if the crack had not extended. Third, non-dimensionalizing the CR load by the maximum load and the displacement by the elastic displacement at the maximum load, P ^* _i/P _max and v _i/v _{el max} from the source specimen yields the adjusted key curve. Analysis of extensive data shows that the key curve is independent of notch type, initial crack length and temperature. But it is dependent on specimen size and steel type. Assuming that the key curves of the source and target specimens are one and the same, the compliance of the target specimens are calculated with a reverse application of the compliance ratio method, and the crack length is obtained using the equations in ASTM E1820. The CR Method is found to be much simpler than the normalization method described in the Annex A15 of ASTM 1820. With the compliance ratio method, Joyce et al. (2001) successfully predicted crack extension in dynamically loaded specimens using a key curve of a statically loaded specimen.     

An experimental cum numerical technique to determine dynamic interlaminar fracture toughness

A method combining experimental and finite element analysis is developed to determine interlaminar dynamic fracture toughness. An interlaminar crack is propagated at very high speed in a double cantilever beam (DCB) specimen made of two steel strips which are bonded together by epoxy with a precrack of about 40 mm length. The face of the front cantilever is bonded to a large solid block and a special fixture is designed to apply impact load to the rear cantilever through a load bar. In the load bar, a compressive square shaped elastic stress pulse is generated by impacting it with a striker bar which is accelerated in an air gun. The rear cantilever is screwed to the load bar; when the incident compressive pulse reaches the specimen, a part of the energy is reflected into the load bar and the rest of it passes to the specimen. By monitoring the incident and the reflected pulses in the load bar through strain gauges, deflection of cantilever-end is determined. The crack velocity is determined by three strain gauges of 0.2 mm gauge length bonded to the side face of the rear cantilever. Further, the first strain gauge, bonded very close to the tip of the precrack, and the crack velocity determine the initiation time of crack propagation.

The experimental results are used as input data in a finite element (FE) code to calculate J-integral by the gradual release of nodal forces to model the propagation of the interlaminar crack. The initiation fracture toughness and propagation fracture toughness are evaluated for an interlaminar crack propagating with a velocity in the range of 850 to 1785 m/s. The initiation toughness and propagation toughness were found to vary between 90–200 J/m² and 2–13 J/m², respectively.     

Influence of microcracking on crack-tip toughness of alumina

Al₂O₃-samples with different grain sizes were produced and the crack-tip toughness K_I0, also called intrinsic fracture toughness, was determined using two different measurement techniques. It appeared that K_I0 depends strongly on specimen grain size with the mechanistic link provided by the increase of microcrack density with grain size. Results obtained using measurements of crack opening displacements (COD) lie considerably lower than values based on a method using bending tests of pre-notched bend bars. It is suggested that the latter method relies on the use of a notch with a microcrack, which in fact is different than the behavior of a long crack alone.     

Einfluß der Probengröße auf die bruchmechanischen Eigenschaften von Sinterstahl

Influence of Specimen Size on the Fracture Mechanical Behaviour of Sintered Steel Fracture mechanics testing was carried out with small and big specimens using high-temperature sintered Fe-2%Cu-2.5%Ni-alloys in the densities of ρ = 7.1 and 7.4 g/cm³. These steels are often used in the manufacturing of PM-parts. Due to the different dismensions the crack propagation is for the bigger sizes faster than for the smaller sizes. Also the conditional fracture toughness of the big specimens is superiour to the toughness of the small specimens. But under consideration of a plain strain state for the big specimens and of a plain stress state for the small specimens valid fracture toughness values being independent from the specimen size can be calculated applying linear-elastic fracture mechanics. These results were obtained for both densities investigated. The increase of the density delivers principally better fracture mechanical data. Hereby the relation of strength data with the microstructure is also discussed.     

用变裂缝单一尺寸试样确定大理岩的断裂韧度

采用具有不同长度裂缝单一尺寸的中心圆孔平台圆盘试件,测定了大理岩的断裂韧度。基于Bazant的尺度律理论,根据有限元分析的结果拟合得到了无量纲能量释放率g(α0)的函数表达式,当无量纲裂缝长度α0=a0/R在0.28~0.51的范围时,与试件形状有关的函数g′(α0)/g(α0)的变化范围为1.0～5.8,能够满足Bazant尺度律公式中对脆性数β范围的需求。由试验结果得到了与试件尺寸无关的断裂韧度的真实值KImc和断裂过程区长度cf。用该方法确定岩石的断裂韧度,能够避免使用较大尺寸的试件,以及为得到足够大的β值范围而使用两种或两种以上试件的准备和试验带来的困难。