Effect of loading condition,specimen geometry,size-effect and softening function on double-<Emphasis Type="BoldItalic">K</Emphasis> fracture parameters of concrete

This paper presents numerical investigation of the influence of the specimen geometry, loading condition, size-effect and softening function of concrete on double-K fracture parameters. The input data needed for computation of the double-K fracture parameters are obtained from the well-known version of Fictitious Crack Model (FCM). FCM is developed for three standard specimens: three-point bend test, compact tension specimen and four-point bend test of size range 100–600 mm at relative size of initial crack length 0.3. The analysis of numerical results shows some interesting behaviour of double-K fracture parameters.     

A fracture mechanics approach to ceramo-metal bond evaluation

The incidence of mechanical failure of cast metal/porcelain dental restorations has promoted a study to develop reliable methods of characterizing and improving bond strengths when produced under standard dental laboratory conditions. Single-edge notch beam specimens were prepared by firing porcelain from a single blended frit to either side of a central metal coupon and subjecting these to four-point bending at 20 ± 2° C and 0.5 mm min^–1 crosshead speed. Specimens of three representative dental alloys and an experimental alloy were prepared in two specimen sizes and three notch widths. The fracture toughness (K _Ic) values were independent of notch width and specimen size over the range of these variables examined and good discrimination was obtained. The fracture toughness of all bonds was improved by a commercial hot isostatic pressure cycle. SEM examination of the fractured surfaces suggested that this improvement was due to the reduction in microporosity at the interface.     

Mode II Brittle Fracture Assessment Using ASFPB Specimen

The four-point bend specimen subjected to anti-symmetric loading (ASFPB) is frequently used for determining pure mode II fracture resistance of rock materials. It is shown in this paper that, when the applied loads are close to the crack plane, the ASFPB specimen does not provide pure mode II condition, since the effect of mode I also appears in crack tip deformation. A set of fracture test were also conducted on a type of marble using ASFPB configuration. The test results showed that fracture resistance is strongly dependent on the loading distance from the crack plane. The effective fracture toughness increases when the distance between the loading points and the crack plane decreases. It is shown that the enhanced fracture resistance of marble samples could be mainly because of very large negative T-stresses that exist for the mentioned loading situations.     

Thickness effect on the mode III fracture resistance and fracture path of rock using ENDB specimens

Study of the thickness effect in predicting the crack growth behavior and load bearing capacity of rock‐type structures is an important issue for obtaining a relation between the experimental fracture toughness of laboratory subsized samples and the real rock structures with large thickness. The fracture of rock masses or underground rock structures at deep strata may be dominantly governed by the tensile or tear crack growth mechanism. Therefore, in this research, a number of mode I and mode III fracture toughness experiments are conducted on edge notch disc bend (ENDB) specimen made of a kind of marble rock to investigate the effect of specimen thickness on the corresponding K_Ic and K_IIIc values. It is observed that the fracture toughness of both modes I and III are increased by increasing the height of the ENDB specimen. Also, the ratio of K_IIIc/K_Ic obtained from each thickness of the ENDB specimens is compared with those predicted by some fracture criteria, and it was shown that the minimum plastic radius (MPR) criterion is the main suitable criterion for investigating the fracture toughness ratio K_IIIc/K_Ic . Also, the effect of ENDB height on fracture trajectory of tested samples is assessed. It is shown that the crack grows curvilinearly in thicker ENDB samples and cannot extend along the crack front in small specimens.     

Mode II fracture mechanics properties of wood measured by the asymmetric four-point bending test using a single-edge-notched specimen

Using a single-edge-notched specimen of spruce, an asymmetric four-point bending test was conducted to obtain the mode II fracture toughness G_IIc and critical stress intensity factor K_IIc, and the test method was numerically and experimentally analyzed. A three-point bend end-notched flexure test was also conducted and the results were compared with those of the asymmetric four-point bending tests. The crack length had a small influence on the load/loading-line displacement relationship in the asymmetric four-point bending test, so it was difficult to determine the value of G_IIc, which requires the measurement of loading-line displacement. In contrast, the value of K_IIc obtained by two tests was similar when the initial crack length ranged from 0.7 to 0.85 times the depth of the specimen. These results show that the asymmetric four-point bending test is a promising means of determining K_IIc.     

Application of the method of caustics to the centre-cracked diametral compression test specimen

Normalized Mode I stress intensity factors,N ₁(a/R), for symmetrical radial cracks in diametral compression test specimens were experimentally evaluated using disc specimens of polymethyl methacrylate and the method of caustics. The method of caustics was first employed with precracked three-point bend specimens to assess the optical constant for the test material. This material property and the diameters of the caustics as a function of the applied load at different relative crack lengths (a/R) yielded the non-dimensional stress intensity factors using equations presented by Theocaris. These experimental values agreed closely with the theoretical solutions reported in the literature. Disc specimens of a polycrystalline alumina were also tested in diametral compression at temperatures up to 1000° C and the measured fracture toughness values were compared to those measured with chevron-notched bend specimens. It is shown that the centre-cracked diametral compression specimens give very reproducible fracture toughness measurements, and the specimen and the test technique can be usefully employed to assess the fracture toughness of structural ceramics at both ambient and elevated temperatures.     

Effect of skin fracture on failure of a bilayer polymer structure

A thin skin of low tensile failure strain, if bonded to the tensile surface of an un-notched impact bend specimen of much tougher material, can change the global failure mode from ductile to brittle. A novel model of this well-known effect is developed and applied to results from impact tests on a tough core of polyamide-polyethylene blend, with a single skin of brittle EVOH. At a fixed crosshead speed, notched specimens of the blend become brittle at a relatively low temperature T _bt. Un-notched bilayer specimens continue to show skin fracture up to a considerably higher temperature T _fs; above this temperature they do not fail at all but below T _bt they too fail in a brittle manner. Within the temperature range from T _fs down to T _bt there is a transition from crack arrest, either at the skin/core interface or further into the core where a crack would not normally propagate, to brittle fracture. This brittle fracture temperature is predicted by modelling the process as a three-phase impact event. In the first phase, the striker bends the bilayer quasi-statically. The second phase begins with instantaneous fracture of the skin at its failure strain. The skin ends retract at finite speed, and a craze grows in the adjacent core material to accommodate the local strain singularity. The last phase is a striker-driven impact event similar to that in a notched bend specimen of the core material, except that the crack-tip craze already bears the adiabatic temperature distribution generated while it was driven open by skin retraction. The criterion for craze decohesion, and hence for a crack jump, is the same adiabatic decohesion criterion which accounts for the speed-dependence of impact fracture in notched monolayer specimens. Applied computationally, this model predicts whether a bilayer structure fails in a brittle way or whether cracks initiated in the skin are arrested, either temporarily or permanently, at the skin/core interface.     

Compliance crack length relations for the four-point bend specimen

Compliance crack length relations for the four-point bend specimen geometry have not been reported in the literature in spite of this geometry being one of the popularly used specimens for fatigue crack growth studies. An effort has been made in the present work to fill this gap. Accordingly, the finite element technique was employed to simulate loading and calculate displacements at various locations in a four-point bend specimen. The load-displacement data thus obtained were processed to yield compliance crack length relations. These relations were employed to calculate the crack length during fatigue testing of four-point bend specimens in which the crack length was also measured by optical means. A good correlation was observed between the predicted crack length and that measured optically.     

Mechanical and metallurgical aspects of fracture behaviour of an Al-alloy

Fracture toughness testing was carried out on an Al-⁴C% Cu alloy in the form of a fully heat treated 21/2-in thick plate. Three types of test, the three point slow bend, instrumented Charpy impact, and double cantilever beam tests, enabled values of plane strain fracture toughness (K _1c ) to be studied over a range of temperature, testing speed and specimen size. Dependence of K _1c upon temperature (?200°C to +160°C) was found to be relatively small except at very low temperatures. The alloy was found not to be appreciably strain rate sensitive over the range of testing speeds (0.002 in/min to 2000 in/min) used. Higher toughness values, obtained from plane strain fractures of the smaller size specimens, were compared with low results from large specimens. The results became variable when curved fracture surfaces developed in the smallest DCB specimens. There was an apparent increase in toughness towards the centre of the plate and the effects of specimen size were most marked in the lower yield strength metal of this layer. The results indicate a genuine increase in toughness K _1c with decreasing temperature, but also show that large specimens are required to approach the lowest and constant K _1c value in circumstances where the yield strength decreases. The DCB test is also shown to be still valid for the measurement of K _1c for this non-brittle alloy, where yield strength may be only about 40,000 lbf/in². Electron fractography showed a ductile intergranular fracture mode. The results are consistent with theories of solute precipitation in Al-alloys.     

On fracture testing of piezoelectric ceramics

Fracture tests carried out on unpoled and poled PZT-5H four-point bend specimens are presented in this paper. The crack faces were parallel to the poling direction. Both mechanical loads and electric fields were applied to the poled specimens. The experimental results were analyzed by means of the finite element method and a conservative M-integral including the crack face boundary conditions. Fracture tests on four-point bend PIC-151 specimens with the crack faces perpendicular to the poling directions were also analyzed here; the experimental results were taken from the literature. A mixed mode fracture criterion is proposed for piezoelectric ceramics. This criterion is based upon the energy release rate and two phase angles. This criterion was implemented with experimental results from the literature and from this investigation. Excellent agrement was found between the fracture curve and the experimental results of the specimens with the crack faces perpendicular to the poling direction. With some scatter, reasonable agreement was observed between the fracture curve and the experimental results of the specimens with crack faces parallel to the poling direction.     

The fracture mechanics of some graphite fibre-reinforced epoxy laminates part 2: (± 45) ns laminates

The fracture behaviour of (± 45)_ns laminates of T300/934 graphite fibre-reinforced epoxy was studied using compact tension specimens of several widths and thicknesses, centre-notched tension, and three-point bend specimens. The process of damage initiation and propagation was studied and is discussed in detail. The critical stress intensity factor was evaluated and its variation with specimen size and type is shown. On the basis of these investigations, a suitable specimen for the evaluation of meaningful fracture toughness is suggested.     

Fracture toughness measurement with fatigue-precracked single edge-notched beam specimens of WC-Co hard metal

The plain-strain fracture toughness of WC-8%Co hard metal, K _IC, was measured using single edge-notched beam (SENB) specimens with fatigue precrack. The fatigue precrack was introduced with compressive fatigue cycling in four-point bending at room temperature. Since stable fatigue-crack propagation was obtained from the notch tip, it was easy to control the fatigue-precrack length. A reasonable K _IC value of 13.3 MPa m^1/2 was obtained with the fatigue-precracked SENB specimens in four-point bending. The compressive fatigue-precracking technique in four-point bending was simple and convenient, and is therefore applicable to precracking in a variety of brittle materials prior to fracture-toughness measurements.     

The use of interlayers in modeling interface crack propagation

Delaminations are a common mode of failure at interfaces between two material layers which have dissimilar elastic constants. There is a well-known oscillatory nature to the singularity in the stress fields at the crack tips in these bimaterial delaminations, which creates a lack of convergence in the modewise energy release rates. This makes constructing fracture criteria somewhat difficult. An approach used to overcome this is to artificially insert a thin, homogeneous, isotropic layer (the interlayer) at the interface. The crack is positioned in the middle of this homogeneous interlayer, thus modifying the original ‘bare’ interface crack problem into a companion ‘interlayer’ crack problem. Individual modes I and II energy release rates are convergent and calculable for the companion problem and can be used in the construction of a fracture criterion or locus. However, the choices of interlayer elastic and geometric properties are not obvious. Moreover, a sound, consistent, and comprehensive methodology does not exist for utilizing interlayers in the construction and application of mixed-mode fracture criteria in interface fracture mechanics. These issues are addressed here. The role of interlayer elastic modulus and thickness is examined in the context of a standard interface fracture test specimen. With the help of a previously published analytical relation that relates the bare interface crack stress intensity factor to the corresponding interlayer crack stress intensity factor, a suitable thickness and elastic modulus are identified for the interlayer in a bimaterial four-point bend test specimen geometry. Interlayer properties are chosen to make the interlayer fracture problem equivalent to the bare interface fracture problem. A suitable mixed-mode phase angle and a form for the fracture criterion for interlayer-based interface fracture are defined. A scheme is outlined for the use of interlayers for predicting interface fracture in bimaterial systems such as laminated composites. Finally, a simple procedure is presented for converting existing bare interface crack fracture loci/criteria into corresponding interlayer crack fracture loci.     

Effects of weld strength mismatch on <Emphasis Type="Italic">J</Emphasis> and CTOD estimation procedure for SE(B) specimens

This work examines the effect of weld strength mismatch on fracture toughness measurements defined by J and CTOD fracture parameters using single edge notch bend (SE(B)) specimens. A central objective of the present study is to enlarge on previous developments of J and CTOD estimation procedures for welded bend specimens based upon plastic eta factors (η) and plastic rotational factors (r _p ). Very detailed non-linear finite element analyses for plane-strain models of standard SE(B) fracture specimens with a notch located at the center of square groove welds and in the heat affected zone provide the evolution of load with increased crack mouth opening displacement required for the estimation procedure. One key result emerging from the analyses is that levels of weld strength mismatch within the range ±20% mismatch do not affect significantly J and CTOD estimation expressions applicable to homogeneous materials, particularly for deeply cracked fracture specimens with relatively large weld grooves. The present study provides additional understanding on the effect of weld strength mismatch on J and CTOD toughness measurements while, at the same time, adding a fairly extensive body of results to determine parameters J and CTOD for different materials using bend specimens with varying geometries and mismatch levels.     

Fracture toughness and fatigue crack growth behaviour of an Al2O3-SiC composite

The fracture toughness and fatigue crack growth characteristics of an Al₂O₃-SiC whisker composite were investigated. Quasi static fracture experiments were conducted on double edge-notched tension specimens and on four-point bend specimens containing a through-thickness Mode I crack which was introduced under uniaxial cyclic compression. The toughness results obtained using this procedure are more reproducible than those derived from the indentation technique and the notched bend bar method. The fracture toughness of the composite is about 60% higher than that of the unreinforced matrix material. Crack growth characteristics at room temperature were also investigated in notched plates of Al₂O₃-SiC subjected to fully compressive far-field cyclic loads. In the presence of a stress concentrator, this composite is found to be highly susceptible to fatigue crack growth under cyclic compressive loads.     

An insight into mode II fracture toughness testing using SCB specimen

The effect of friction forces between the test specimen and its bottom supports on the mode II fracture toughness values obtained using the semicircular bend (SCB) specimen is investigated. First, a number of experiments were conducted on SCB specimen in order to determine the mode II fracture toughness of polymethyl methacrylate (PMMA) according to the conventional approaches available in the literature. Three different types of supports that have been frequently employed by researchers in recent years were used to evaluate the effect of support type on the fracture loads. It was found that the friction forces between the supports and the SCB specimen have a significant effect on the value of mode II fracture toughness measured using the SCB samples. Then, the specimen was simulated using finite element method for more detailed investigation on the near crack tip stress field evolution when friction forces increase between the supports and the SCB specimen. The finite element results confirmed that the type of support affects not only the stress intensity factors K_I and K_II but also the T‐stress. The experimental and numerical results showed that the use of the crack tip parameters available in literature for frictionless contact between the supports and the SCB specimen can result in significant errors when the mode II experiments are performed by using the fixed or roller‐in‐grove types of supports.     

Effect of fracture path on the toughness of weld metal

The crack propagation direction may affect weld metal fracture behavior. This fracture behavior has been investigated using two sets of single edge notched bend (SENB) specimens; one with a crack propagating in the welding direction (B×2B) and the other with a crack propagating from the top in the root direction (B×B) of a welded joint. Two different weld metals were used, one with low and one with high toughness values. For Weld Metal A, two specimen types have been used (B×B and B×2B) both with deep cracks. The weld metal A (with high toughness values) has reasonably uniform properties between weld root and cap. The resulting J-R curves show little effect of the specimen type, are ductile to the extent that the toughness exceeds the maximum J_max, value allowed by validity limits and testing is in the large –scale yielding regime. In the case of weld metal B (with low toughness values) with two specimen types (B×B and B×2B) the B×B specimen has shallow cracks while the B×2B specimen has deep cracks. Both resulting J-R curves show unstable behavior despite the fact that the types of specimen and their constraints are different. The analysis has shown that crack propagation direction is most influential for a weldment with low toughness in the small scale yielding regime, whereas its influence diminishes due to ductile tearing during stable crack growth and large scale yielding. The results have shown that these effects are different in both the crack initiation phase and during stable crack growth, indicating a dependence on weld metal toughness and the microstructure of the weld metal. It can be concluded that, if resistance curves during stable crack growth do not show differences in both notch orientations, the fracture toughness values of the whole weld metal can be treated as uniform.     

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.     

Fracture toughness of acrylic bone cements

Clinical experience has shown that fracture of PMMA-based bone cements is a significant factor in the failure of orthopaedic joint replacements. Earlier studies of the fracture toughness properties of bone cement have been limited to relatively large test specimens — ASTM standard test methods require the use of specimens with dimensions considerably larger that those associated with bone cement in clinical use. In this study, a miniature short-rod specimen was used to measure the fracture toughness (K _IC) or two bone cements (Simplex-P and Zimmer LVC). The dimension of our mini specimens approaches the cross-section of bone cements as usedin vivo. The short-rod elastic-plastic fracture toughness test method introduced by Barker was utilized to ascertain the effect of specimen preparation and ageing in distilled water on fracture toughness. Our study indicated that slow hand-mixed specimens possess comparable fracture toughness to centrifuged specimens. After ageing in water, however, centrifuged and slow hand-mixed specimens are more fracture resistant than specimens prepared by mixing the cement quickly. An optimum void content for the bone cements studied was suggested by the experimental results; for Simplex-P bone cement it appeared to be less than 1.6% whereas it was between 1.6 and 3.6% for Zimmer LVC cement. Simplex-P bone cement also showed superior fracture toughness compared to Zimmer LVC cement after storage in water for 60 days at 37° C.