Residual strength of unidirectional fibre-metal laminates based on JC toughness of C(T) and SE(B) specimens: comparison with M(T) test results

Fibre‐metal laminates (FMLs) are structural composites designed with the aim of producing very low fatigue crack‐propagation rate, damage‐tolerant and high‐strength materials, if compared to aeronautical Al alloys. Their application in aeronautical structures demands a deep knowledge of a wide set of mechanical properties and technological values, including both fracture toughness and residual strength. The residual strength of FMLs have been traditionally determined by using wide centre‐cracked tension panels M(T). The use of this geometry requires large quantities of material and heavy laboratory facilities. In this work, fracture toughness ( J_C) of some unidirectional FMLs laminates was measured using a recently proposed methodology for critical fracture toughness evaluation on compact tension C(T) and single‐edge bend SE(B) specimens. Additionally, residual strength values of wider M(T) specimens with different widths (W from 150 to 200 mm) and several crack to width ratios (2a/W) were experimentally obtained. Some experimental residual strength values of M(T) specimens (W from 150 to 400 mm and different 2a/W ratios) of Arall were also obtained from the bibliography. Based on J_C results from C(T) and SE(B) specimens, and either using or not using crack‐tip plasticity corrections, the residual strengths of the M(T) specimens were predicted and compared to the experimental ones. The results showed good agreement, especially when crack‐tip plasticity corrections were applied.     

Crack resistance curves of GLARE laminates by elastic compliance

The objective of this work was to study the applicability of the elastic compliance technique for crack resistance curves evaluation of commercial GLARE laminates using small SE(B) and C(T) specimens. The experimental evaluation of R-curves of 25.0 mm wide SE(B) specimens of unidirectional GLARE 1 3/2 0.3 and 50.0 mm wide C(T) specimens of bidirectional GLARE 3 5/4 0.3 was performed. Fracture toughness was measured through a recently proposed experimental methodology based on standardized specimens and elastic-plastic methodologies (J-integral and CTOD δ₅), whereas crack growth was measured optically and estimated by elastic compliance. According to the results the elastic compliance technique seemed to be applicable to GLARE laminates, accurately predicting stable crack growth during the tests.     

Synthesis and mechanical properties of high-purity Cr2AlC ceramic

High-purity and dense Cr₂AlC has been successfully fabricated by hot-pressing, using Cr, Al and graphite as raw materials. Delamination, kink bands, monolamellar kink, transgranular crack and transgranular fracture of bulk Cr₂AlC are found during the room-temperature test. The density, Vickers hardness, flexural strength, Young's modulus, compressive strength and fracture toughness of the Cr₂AlC are 5.17 g/cm³, 4.9 GPa, 469 ± 27 MPa, 282 GPa, 949 ± 22 MPa and 6.22 ± 0.26 MPa m^1/2, respectively. The strength of Cr₂AlC could be greatly improved by second phase of Cr₇C₃. And the slipping of basal planes and slip system cold be hindered by Cr₇C₃, thus resulting in a lower toughness.     

Fracture mechanics of plastic-fiber composites

The concept of fracture mechanics is introduced to characterize the toughness of fiber-reinforced composites which should be distinguished from tensile strength. A material may have a high tensile strength but a low toughness meaning that it has a low resistance to crack extension. Depending on the analytical model used, the same experimental data may report different fracture toughness values. In general, the combination of crack propagation in directions parallel and perpendicular to the fibers makes the composite problem very difficult to analyze.Composites with well-aligned fibers are more susceptible to crack propagation parallel than perpendicular to the fibers and can be analyzed with a reasonable degree of accuracy by using the existing K_c or S_c-theory in fracture mechanics. The K_c-theory is used primarily in laboratory testing where the load is aligned normal to the crack plane whereas the S_c-theory is not subjected to such a restriction. The K_c or S_c values for several composites are reported and applied to solve various example problems illustrating the advantage of fiber reinforcement.     

Fracture behaviour of chemical vapour deposited and hot isostatically pressed zinc sulphide ceramics

Fracture behaviour of zinc sulphide ceramics prepared by chemical vapour deposition (CVD) followed by hot isostatic pressing (CVD + HIP) was investigated in terms of flexural strength (σ_f), plane-strain fracture toughness (K_Ic), even conditional fracture toughness (K_IQ), R-curve behaviour (variation of total fracture energy release rate, J_c with crack extension, δ/δ_c) and fracture mode. The corresponding Knoop Hardness number (KHN) and its correlations to flexural strength (σ_f) are also evaluated and reported. The present study showed that the zinc sulphide (ZnS) ceramics processed by CVD exhibited higher fracture resistance compared to ZnS processed by CVD + HIP condition. This observation is principally attributed to higher grain size associated with post-CVD HIPing process. In both conditions, the ZnS materials exhibited conditional fracture toughness (K_IQ) that decreased moderately with increased crack length due to the change in fracture mode form grossly tensile to predominant shear. A constantly rising R-curve behaviour was indicated in both the materials with significant increase in total fracture energy release rate (J_c with the normalised displacement (δ/δ_c), a parameter representing crack extension.     

Effect of crack depth on the shift of the ductile-brittle transition curve of steels

Nuclear reactor pressure vessel (RPV) steels degrade due to neutron irradiation during normal operation. As a result, the ductile-brittle transition curve of the steel shifts to higher temperature which decreases operation margins in both the temperature and pressure. The loss of these margins however can be offset somewhat by appealing to arguments based on constraint of potential/postulated shallow cracks. In this paper, it is demonstrated that the fracture toughness values for shallow flaws are higher than those determined from standard deep cracked test specimens based on constraint consideration. The J-A₂ three-term solution is used to characterize the crack-tip stress field where J represents the level of loading and A₂ quantifies the level of constraint. Based on the RKR cleavage model, procedures to quantify the temperature shift between specimens with different constraint levels are developed. The experimental data by Sherry et al. [Sherry AH, Lidbury DPG, Beardsmore DW. Validation of constraint based structural integrity assessment methods. Final report, Report No. AEAT/RJCB/RD01329400/R003, AEA Technology, UK, 2001] for the A533B RPV steel are used to demonstrate the procedure and it is shown that the ductile-brittle transition curve shifts to lower temperature from high constraint to low constraint specimens.     

The energy dissipation rate approach to tearing instability

Stable and unstable tearing in metals is currently analysed by J integral theory, or by the G_R curve approach. This paper explains an alternative analysis route based on energy dissipation rate, D. It is shown that the implication of increasing toughness with crack growth in G_R and J_R curves is misleading. Even in small scale yielding (SSY), it is possible to have stable tearing under increasing G or J whilst at the same time D is constant (or even reducing) with crack growth. New terms: C for crack driving force, D^* for geometry normalised D, D_ssy for D in SSY, and crack stability index are explained. A D based fracture analysis diagram is introduced. Comparisons are made between energy dissipation rate, J integral, and G_R curve instability prediction methods. It is shown that, in most instances, these different approaches are compatible; but that the use of J_R curves derived in fully yielded test pieces to predict failure in SSY has the potential to lead to an unconservative instability prediction. The practical advantage of the energy dissipation rate approach is that it can be applied to all product thicknesses at any extent of crack growth. The major advantage compared to the G_R approach is that toughness measurements can be made on much smaller specimens.     

High rate toughness of ductile polymers

Impact toughness of two highly ductile polymers: acrylonitrile-butadiene-styrene (ABS) terpolymer and polypropylene block copolymer (PPBC) - was evaluated using the essential work of fracture (EWF) - and a J-R resistance single specimen curve - S_pb techniques. The EWF has proved to be capable of determining toughness from the total fracture energy of several samples differing in initial ligament length and the linear regression of the data. On the other hand, the S_pb method, which is based on the load separation principle, is able of constructing J-R curves by inferring instantaneous crack growth length from the sole comparison between one sharp and one blunt-notched load-displacement traces. Results show that both methodologies can be used under impact conditions when evaluating ABS polymers. However, ABS impact fracture toughness value yielded by the EWF method, w_Ie, was larger than the J_0.2 value obtained from the S_pb method. This difference was imputed to the more progressive development of the necking zone in front of the crack tip under plane strain conditions. On the contrary, for very ductile fracture behavior like that demonstrated by PPBC in which J-controlled conditions were not achieved and hence J-R curves could not be built the EWF appeared as a valuable alternative to characterize impact toughness.     

Calculation of mixed-mode stress intensity factors for a crack normal to a bimaterial interface using contour integrals

A pair of contour integrals J_kε are proposed in this paper. The integrals are shown to be path-independent in a modified sense and so they can be accurately evaluated without using any particular singular finite elements. Also, the relationship between J_kε and the generalized stress intensity factors (SIFs) is analytically derived and expressed as functions of the bimaterial mechanical constants. Once the J_kε-integrals are accurately computed, the generalized SIFs and, consequently, the asymptotic mixed-mode stress field can then be properly determined. Numerical results in this study show that the contribution from mode II stress component appears to be more dominant when the uncracked material is relatively stiffer, and vice versa.     

Preparation and properties of nano-SiC strengthening Al2O3 composite ceramics

The processing and mechanical behaviors of Al₂O₃-xwt.%SiC (x = 1, 2, 5, ASx) nano-composites prepared by the in situ synthesis of SiC from polycarbosilane (PCS) were investigated. The composites were densified by hot pressing. The microstructure and mechanical properties of the sintered composites were analyzed. The results showed that a fully dense structure was obtained when a few nano-SiC were doped and that the fracture toughness and strength were highly improved compared with those of monolithic Al₂O₃. The fracture toughness reached 5.1 MPa m^1/2 in AS2 composite. The maximum flexural strength was 516 MPa obtained in AS1 composite.     

Fracture behavior of as-cast pearlitic nodular iron

The fatigue crack propagation and fracture toughness behavior of an ASTM A536, as-cast, pearlitic nodular iron with a bull's-eye structure was studied. The material had an ultimate strength of 76 ksi, a yield strength of 59 ksi, and an elongation of 1.6%. Fracture toughness tests were conducted on compact tension specimens with thicknesses of 0.30, 0.50, 0.70, and 1.00 inches. The conditional fracture toughness, K_Q, was found to be insensitive to the specimen thickness in the above range and to have a value of approximately 30 ksi-in^1/2. The dependence of the fatigue crack growth rate, da/dN, on the stress intensity factor, δK, was determined for stress ratios of 0.1, 0.3, 0.5, and 0.7. At the same °K level, the da/dN rates were higher for the higher stress ratios. The parameters, C and n, of the Paris equation, da/dN=C(δK)ⁿ were determined for each stress ratio. Near-threshold tests were also conduced for the stress ratio of 0.1. The threshold stress intensity factor, δK_TH, was found to be in the range of 6.3 to 7.7 ksi-in^1/2. A statistical model was used to calculate the agreement of the results of two duplicate fatigue crack growth tests.     

Size effect on the fracture toughness of metallic foil

The size effects on fracture behavior of Cu foil are investigated by a new optical technique, the digital speckle correlation method (DSCM). Displacement and strain fields around a crack tip are analyzed for different thicknesses of Cu foil. Then, the J integral and fracture toughness J _C are evaluated directly from the strain fields around the crack tip. The fracture toughness J _C is obtained as a function of foil thickness. The results indicate that J _C indeed depends on foil thickness within a certain range of thickness (the thickness varies from 20 micron to 1 millimeter in this work).     

Magnetic relaxation and critical current in Bi2Sr2CaCu2O8+x single crystals

The anisotropy of critical current densityJ _c in Bi₂Ba₂CaCu₂O_8+x single crystals has been investigated as a function both of the temperature and of the applied magnetic field. An anisotropic behavior ofJ _c has been found. The decay of the remanent magnetization has been studied for fields applied both parallel and perpendicular to thec axis. A logarithmic behavior was found. A pinning energyU ₀ of about 0.01 eV, independent of the direction of the applied field, was obtained.     

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 behavior and mechanism of 2D C/SiC-BCx composite at room temperature

2D C/SiC composite was modified with partial BC_x matrix by low pressure chemical vapor infiltration technique (LPCVI), which was named as 2D C/SiC-BC_x composite. The flexural fracture behavior, mechanism, and strength distribution of 2D C/SiC-BC_x composite are investigated. The results indicate that the flexural strength, fracture toughness, and fracture work are 442.1 MPa, 22.84 MPa m^1/2, and 19.2 kJ m⁻², respectively. The flexural strength of C/SiC-BC_x composite decrease about 20% than that of C/SiC composite. However, the fracture toughness and fracture work increase about 19% and 18.5%, respectively. The properties varieties between C/SiC-BC_x composite and C/SiC composite can be attributed to the weak-bonding interface between BC_x/SiC matrices according to the results of detailed microstructure analysis. The strength distribution of 2D C/SiC-BC_x composite follows as Normal distribution or Weibull distribution with σ_u = 0, and m = 8.1393. The mean value of flexural strength for 2D C/SiC-BC_x composite is 443 MPa obtained by theory calculation, which is consistent with experiment result (442.1 MPa) very well.     

An asymptotic approach to size effect on fracture toughness and fracture energy of composites

Size effect on fracture toughness and fracture energy of composites is investigated by a simple asymptotic approach. This asymptotic analysis based on the elastic/plastic fracture transition of a large plate with a small edge crack is extended to study fracture of composite. A reference crack length, a^*, is used in the model, which indicates an ideal elastic/plastic fracture transition defined by the yield strength and plane strain fracture toughness criteria. Experimental results of cementitious materials available in literature are analyzed and compared. It is shown that the common K_R-curves can also be obtained by the current asymptotic model. Furthermore, a local fracture energy distribution concept is also discussed and compared with the present asymptotic approach.     

Weight function approach for determining crack extension resistance based on the cohesive stress distribution in concrete

The use of universal form of weight functions for determining the K_R-curves associated with the cohesive stress distribution for complete fracture process of three-point bending notched concrete beam is reported in the paper. Closed form expressions for the cohesion toughness with linear and bilinear distribution of cohesive stress in the fictitious fracture zone during monotonic loading of structures are obtained. Comparison with existing analytical method shows that the weight function method yields results without any appreciable error with improved computational efficiency. The stability analysis and the size-effect study using K_R-curves of crack propagation are also described.     

Luminescence properties of Eu ions doped in Y2−xGdxO3 thin films grown by pulsed laser deposition method

Luminescence properties of Y_2−xGd_xO₃:Eu³⁺ (x = 0 to 2.0) thin films are investigated by site-selective laser excitation spectroscopy. The films were grown by pulsed laser deposition method on SiO₂ (100) substrates. Cubic phase Y₂O₃ and Gd₂O₃ and monoclinic phase Gd₂O₃ are identified in the excitation spectrum of the ⁷F₀ → ⁵D₀ transition of Eu³⁺. The emission spectra of the ⁵D₀ → ⁷F_J (J = 1 and 2) transition from individual Eu³⁺ centers were obtained by tuning the laser to resonance with each excitation line. The excitation line at around 580.60 nm corresponds to the line from Eu³⁺ with C₂ site symmetry of cubic phase. New lines at 578.65 and 582.02 nm for the C_S sites of Gd₂O₃ with monoclinic phase are observed by the incorporation of Gd in Y₂O₃ lattice. Energy transfer occurs between Eu³⁺ ions at the C_S sites and from Eu³⁺ ions at the C_S sites to those at the C₂ site in Y_2−xGd_xO₃.     

Domain-independent values of the J-integral for cracks in three-dimensional residual stress bearing bodies

This paper describes an approach for computing domain-independent values of the J-integral in the finite element context for three-dimensional bodies containing residual stress. In the analysis of cracked bodies containing residual stress, the usual domain integral formulation results in domain-dependent values of J, and this paper discusses modifications that yield domain independence. Two correction terms are defined. The first of these relates to the spatial gradients of non-mechanical strains in the crack-driving direction, and the second accounts for plastic dissipation included in the material state, but unrelated to fracture. The paper further presents results for two examples recently discussed in the literature. Application of the corrections in these two cases demonstrates the ability of the approach to obtain path-independent domain integral results in residual stress bearing bodies.