Statistical description of the effect of Zr addition on the behavior of microcracks in Cu–6Ni–2Mn–2Sn–2Al Alloy

As possible substitutes for high-strength Cu–Be alloys, Cu–6Ni–2Mn–2Sn–2Al alloys have been developed. To clarify the physical background of the effect of trace Zr on the fatigue strength of such alloys, the initiation and propagation behavior of a major crack that led to the fracture of the tested specimens was monitored. When the stress amplitude was less than σ _a = 350 MPa, the fatigue life of the alloys with Zr was about 2–2.5 times larger than that of the alloy without Zr. When σ _a > 350 MPa, the effect of Zr addition on the fatigue life dramatically decreases as the stress amplitude increases. The increased fatigue life due to Zr addition resulted from an enhancement of the crack initiation life and microcrack growth life. The enhanced crack initiation life was mainly attributed to the strengthening of grain boundaries due to the precipitation of SnZr compounds. A statistical analysis of the behavior of multiple cracks was made to quantitatively evaluate the scatter in fatigue behavior. The statistical analysis supported the conclusions obtained from the behavior of a major crack.     

Fatigue properties of a modified 7075 aluminum alloy containing scandium

Fatigue properties such as the fatigue strength, fatigue notch sensitivity, and fatigue crack propagation rate, of a modified Al-7075 + Sc aluminum alloy were investigated in this study. The effects of solution treatment on the fatigue performance of this alloy were also investigated. The ultimate tensile strength of the as-extruded sample was 705.5 MPa. The ultimate tensile strength decreased by 12% after solution treatment. The fatigue limit σ_e of the as-extruded sample decreased from 201.2 to 154.4 MPa after solution treatment. The fatigue notch sensitivity for the as-extruded and solution-treated (ST) samples was 0.97 and 0.64, respectively. The crack growth rate in the as-extruded sample with fine precipitates was clearly lower than that of the ST sample that had coarse precipitates at R = 0.1 when ΔK < 15 MPa?m \sqrt m . However, the growth rates of both the samples were approximately the same when ΔK > 15 MPa?m \sqrt m . The higher yield strength of the as-extruded sample led to a lower crack growth rate when compared to the ST sample.     

Surface modifications to improve Ti–porcelain bonding

Investigations of surface modifications on cast titanium surfaces and titanium-ceramic adhesion were performed. Cast pure titanium was subjected to surface modification by preoxidation and introduction of an intermediate layer of SnO _x by sol–gel process. Surfaces only sandblasted with alumina were used as controls. Specimen surfaces were characterized by XRD and SEM/EDS. The adhesion between the titanium and porcelain was evaluated by three-point flexure bond test. Failure of the titanium–porcelain with preoxidation treatment predominantly occurred at the titanium-oxide interface. Preoxidation treatment did not affect the fracture mode of the titanium–ceramic system and did not increase the bonding strength of Ti–porcelain. However, a thin and coherent SnO _x film with small spherical pores obtained at 300 °C served as an effective oxygen diffusion barrier and improved titanium–ceramic adhesion. The SnO _x film changed the fracture mode of the titanium–ceramic system and improved the mechanical and chemical bonding between porcelain and titanium, resulting in the increased bonding strength of titanium–porcelain.     

Effect of material plasticity on fatigue crack propagation under complex stress state

The maximum energy release rate criterion, i.e., G _max criterion, is commonly used for crack propagation analysis. However, this fracture criterion is based on the elastic macroscopic strength of materials. In the present investigation, a modification has been made to G _max criterion to implement the consideration of the plastic strain energy. This criterion is extended to study the fatigue crack growth characteristics of mixed mode cracks in steel pipes. To predict crack propagation due to fatigue loads, a new elasto-plastic energy model is presented. This new model includes the effects of material properties like strain hardening exponent n, yield strength σ_y and fracture toughness and stress intensity factor ranges. The results obtained are compared with those obtained using the commonly employed crack growth law and the experimental data.     

Synthesis and properties of dental zirconia–leucite composites

The dental zirconia–leucite composites were synthesized by high temperature solid-state method using potash feldspar, potassium carbonate and zirconia as raw materials. The mechanical properties and the coefficient of thermal expansion (CTE) of the prepared zirconia–leucite composites were tested. The results show that the bending strength, the fracture toughness and the metal–ceramic bonding strength of the prepared samples are about 110 MPa, 3·5 MPa/m^1/2 and 45 MPa, respectively. The CTE was about 13·73×10^–6 °C^–1 and close to that of Ni–Cr dental alloy (14·0×10^–6 °C^–1). The results indicate that the introduction of zirconia is beneficial to the improvement in the mechanical properties and CTE adjustment of porcelain material. The clinical application of the zirconia–leucite composites with good metal–ceramic bonding strength in the dental restoration could be envisioned.     

R-curve effect on strength and reliability of toughened ceramic materials

An improved theoretical analysis is presented for the strength and mechanical reliability of ceramic materials with an R-curve characteristic. There is good agreement between the predicted flexural strength distribution of an Al₂O₃/ZrO₂ ceramic and experimental datA. Unlike the conventional two-parameter Weibull approach, this new analysis is able to predict the non-linearity observed in the lnln 1/(1–P _f) versus In _f strength distribution curve. Compared to the untoughened Griffith material, the R-curve material has higher strength and better strength reliability.     

Effects of moisture-assisted slow crack growth on ceramic strength

An investigation was made of strength degradation caused by moisture-assisted slow crack growth of surface flaws in two dense polycrystalline ceramics. Specimen sizes were varied. The observed strength degradation of each ceramic was predictable usingK _IC as a material property in fracture-mechanics relations, suggesting that the only material variable involved was critical flaw size. The strength of one of the ceramics in water decreased significantly with increased specimen size, but its Weibull modulus was essentially unaffected by specimen size and slow crack growth.     

Fatigue crack growth in 15KH2MFA steel subjected to aging in high-temperature hydrogen

We study the influence of high-temperature aging in gaseous hydrogen on the cyclic crack-growth resistance of 15Kh2MFA steel by taking into account the effect of fatigue crack closure. We show that aging in hydrogen promotes the intense pulverization and homogenization of the structural components. Changes in the structure of steel and a decrease in the effective fatigue threshold ΔK _{th eff} on holding in hydrogen are caused primarily by the action of hydrogen and the load is an additional factor accelerating this process. We discovered that the effect of internal hydrogen on the effective fatigue threshold is ambiguous depending on the level of stresses in the process of holding in hydrogen. Thus, ΔK _{th eff} increases on holding at σ=120 MPa as compared with the degassed metal but decreases on holding at σ=240 MPa. Karpenko Physicomechanical Institute, Ukrainian Academy of Sciences, L'viv. Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 33, No. 4, pp. 121–126, July–August, 1997.     

Unified model of nucleation and growth of fatigue cracks. Part 1. Use of force parameters of fracture mechanics of materials in the stage of crack nucleation

According to the phenomenological model of nucleation of a fatigue macrocrack, the process is considered as a two-parameter process. The process is described by the local stress or strain range and a certain linear parameter of the material. We propose the corresponding parameters, namely, the local stress range Δσ _y ^* and the characteristic sized ^* of the prefracture zone. The formation of this zone is caused by the anomaly of the yield strength of the material in subsurface layers, the microstructure, the loading amplitude, the cyclic strain hardening, and the environment. The quantityd ^* is a constant of the material, which is independent of the geometry of notch and specimen. the boundary of the prefracture zone is considered as a macrobarrier that determines the growth of microstructurally short and physically small cracks. The moment when a physically small crack oversteps the boundary of the prefracture zone is defined by the quantitative criterion (a ₀=d ^*) of the initial sizea ₀ of a macrocrack in the material. The proposed dependences of (Δσ _y ^* ,N _i ),N _i ) and (d ^*,N _i ) can be regarded as a basis for the determination of characteristics of resistance of the material to the nucleation of a fatigue macrocrack. Karpenko Physicomechanical Institute, Ukrainian Academy of Sciences, L'viv. Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 34, No. 1, pp. 7–21, January–February, 1998.     

Influence of threshold parameters on cleavage fracture predictions using the Weibull stress model

This study explores applications of three-parameter Weibull stress models to predict cleavage fracture behavior in ferritic structural steels tested in the transition region. The work emphasizes the role of the threshold parameters (_th and _{w – min}) in cleavage fracture predictions of a surface crack specimen loaded predominantly in tension for an A515-70 pressure vessel steel. A recently proposed procedure based upon a toughness scaling methodology using a modified Weibull stress (^* _w) extends the calibration scheme for the Weibull modulus, m, to include the threshold parameters. The methodology is applied to calibrate the Weibull stress parameter for the tested material and then to predict the toughness distribution for the surface crack specimen. While the functional relationship between ^* _w and m suggests a strong effect of the threshold stress, _th, on the calibrated m-parameter, the results show a remarkably weak dependence of fracture predictions on _th as does the dependence of fracture predictions on _w–min for this specimen.     

Experimental estimation of the probability distribution of fatigue crack growth lives

This paper deals with a method to estimate numerically the reliability of fatigue sensitive structures with respect to fatigue crack growth. A method is proposed to experimentally determine the probability distribution functions of material parameters of the Paris law, da/dN = C(ΔK/K₀)^m, using stress intensity factor controlled tests. The auto-correlation function of the resistance to fatigue crack growth, 1/C, is also estimated from the experimental data. The results of a high tensile strength steel show that the distribution of the parameter, m, is approximately normal and that of 1/C is a 3-parameter Weibull. The merit of the proposed method is that only a small number of tests are required to determine these functions. The probability distribution of the fatigue crack length after a given number of load cycles or the number of load cycles for a crack to reach a given length can be estimated by simulations of non-Gaussian random processes having these functions.     

Evaluation of fracture parameters of concrete from bending test using inverse analysis approach

In this study, an inverse analysis approach is developed to obtain the fracture parameters of concrete, including stress–crack opening relationship, cracking and tensile strength as well as fracture energy, from the results of a three-point bending test. Using this approach, the effects of coarse aggregate size (5–10, 10–16, 16–20 and 20–25 mm) and matrix strength (compressive strength of 40 and 80 MPa, respectively) on the fracture parameters are evaluated. For normal strength concrete, coarse aggregate size and cement matrix strength significantly influence the shape of σ–w curve. For a given total aggregate content, small aggregate size leads to a high tensile strength and a sharp post-peak stress drop. The smaller the coarse aggregate, the steeper is the post-peak σ–w curve. By contrast, in high strength concrete, a similar σ–w relationship is obtained for various aggregate sizes. The post-peak stress drop for high strength concrete is more abrupt than that for normal strength concrete. Also, the smaller the coarse aggregate size, the higher is the flexural strength. For both normal and high strength concrete, fracture energy and characteristic length are found to increase with increase of coarse aggregate size.     

An investigation of the effect of high-temperature cyclic straining and creep loading on tensile mechanical properties of GH4145/SQ alloy

The effect of the reverse cyclic straining and the creep loading on the resultant tensile mechanical properties, such as the strength parameter (σ_0.2 and σ_b), the ductile parameter (δ and ϕ_f) and the composite parameter of the strength and ductility, the static toughness (U_t), for the precipitation-strengthened nickel-based superalloy GH4145/SQ used for high-temperature turbine and valve studs/bolts in power plant was investigated systematically at a temperature of 538°C. The experimental results show that in the case of the reverse cyclic straining both σ_0.2 and σ_b increases at early stages of cyclic straining and, after reaching their saturated values, σ_0.2 remains relatively constant until about 90% of fatigue life, while σ_b exhibits continuous reduction up to a level equal to the maximum applied stress amplitude. With the increasing number of straining cycles, both δ and ϕ_f as well as U_t decrease significantly until final fracture. In the case of creep loading the strength parameters (σ_0.2 and σ_b) tend to increase, as a whole, while the ductile parameters (δ and ϕ_f) and the static toughness (U_t) exhibit continuous decrease characterization as the amount of the creep deformation increases. The variation of the aforementioned various tensile mechanical properties during cyclic straining and creep loading of the alloy was further discussed by means of the observations of the deformation microstructures as well as the examinations of the fracture features of the specimens.     

Überlebensrate und Sicherheit von keramischen Kugelköpfen für Hüftendoprothesen

Survival Rate and Reliability of Ceramic Femoral Heads for Total Hip Arthroplasty Femoral heads and sockets made of alumina ceramics are successfully used in total hip replacement. The in vivo fracture rate of Biolox heads is lower than 0.02%. An extremely high load (e. g. accident) can initiate subcritical crack growth causing fracturing. 107 retrieved Biolox heads were investigated. When measuring their fracture load no fatigue was detected. This result can be explained by the relation between crack velocity and stress intensity (v-K-diagram). The stress intensity of ceramic heads when loaded with standard conditions (e. g. walking, max. load 3 kN) is in the order of 0.6 MPa m^1/2. Stress intensities like that are below alumina's fatigue limit K_Io which is in the order on 1 MPa m^1/2. Biolox alumina heads are examples for engineering ceramics that are reliable despite tensile stress over very long periods of time.     

FATIGUE CRACK GROWTH BEHAVIOUR AND FRACTURE RESISTANCE IN CERAMICS

Fatigue crack growth and the fracture resistance curve (R-curve) were investigated in a polycrystalline alumina (AD90) and a silicon carbide whisker-reinforced alumina composite (Al₂O₃-SiC_w) at room temperature in air using a combined loading technique for stabilizing crack growth, and a surface film technique for monitoring crack length. Fatigue crack growth was evaluated successfully with those experimental techniques. Load shedding tests were performed until the crack became dormant, in order to determine the threshold stress intensity factor K_th. Subsequently, the specimens were used for quasi-static crack growth tests under a monotonic loading condition. The R-curves were determined in this experiment; however, fracture resistance did not increase markedly with crack growth. Detailed observations of the crack growth behaviour revealed that the flat R-curve was attributed to the shielding effect of the fatigue crack tip wake. Thus, the fatigue precrack introduced by the load shedding test was not regarded as an ideal crack for determining the R-curve. Fractographic observations were performed to investigate the mechanistic difference between fatigue and quasi-static crack growth. It was found that the cyclic loading produced fretting damage in the wake region and it reduced the shielding effect of the fatigue cracks. Based on the experimental results, the relationship between the fatigue crack growth and the R-curve is discussed as is the significance of K_th as a material parameter.     

Estimation procedure for the Weibull parameters used in the local approach

The local approach was recently proposed by Beremin and Mudry for evaluating the statistical behaviour of toughness results of materials. This approach introduces a stress parameter _w , termed the Weibull stress, as a measure of the fracture resistance of materials instead of the conventional toughness parameters such as K _c, _c and J _cl (critical stress intensity factor, CTOD and J-integral, respectively). The Weibull stress _w obeys the Weibull distribution with the two parameters m and _u (the shape and the scale parameter, respectively). The first parameter m is normally estimated to be 22 irrespective of the kind of material. In this paper a procedure for the determination of the Weibull parameters m and _u is developed. This procedure consists of the determination of the plastic zone ahead of the crack tip, from which cleavage fracture originates, and of the maximum likelihood estimation of the parameters m and _u based on the stress distribution in the plastic zone. Calculations using this procedure confirm that the distribution of the Weibull stress _w is a material property independent of specimen thickness, and in particular that the shape parameter m depends on the material, e.g. m12 for a German reactor pressure vessel steel (20 Mn Mo Ni 5 5). Using these parameters for the distribution of the Weibull stress the size effect in fracture toughness values is predicted and an improved agreement between theory and experiments is obtained compared to the Weakest Link model.     

Correlation between Weibull moduli for tensile and bending strength of brittle ceramics: a numerical simulation analysis based on a three-parameter Weibull distribution

A numerical simulation was designed and performed to produce uniaxial tensile strength and three-point bending strength data. It was assumed that the specimen could be divided into many small units of volume for which the tensile strength followed a three-parameter Weibull distribution, characterized by the parameters m, ₀ and _u. Statistical analysis of the strength data showed that the variation of the bending strength could be characterized by the explicit form of the three-parameter Weibull function as deduced from only the tensile test data. A strong correlation was found to exist between the Weibull modulus, m _E,B, estimated for the bending strength and that for tensile strength, m _E,T. The difference between m _E,B and m _E,T is dependent on m but independent of the ratio of ₀ to _u.     

Preparation,microstructure and mechanical properties of dense polycrystalline hydroxy apatite

Hydroxy apatite ceramic blocks of varying density have been prepared from a commercial powder. The elastic properties, fracture toughness, strength and sub-critical crack growth of these materials have been investigated. Young's modulus for the nearly fully dense material is 112 GPa while the compressive strength is about 800 MPa. For the same material the strength and fracture toughness under dry conditions are 115 MPa and 1.0 MPa m^1/2, respectively. Substantial slow crack growth was found under these conditions. Under wet conditions the values for strength and fracture toughness drop to about 75% of their “dry” values. In this case very serious slow crack growth is present.     

The effect of temperature on fatigue damage of FRP composites

The present study intends to investigate the effect of temperature on cumulative fatigue damage (D) of laminated fibre-reinforced polymer (FRP) composites. The effect of temperature on fatigue damage is formulated based on Ramkrishnan–Jayaraman and Varvani-Farahani–Shirazi residual stiffness fatigue damage models. The models are further developed to assess the fatigue damage of FRP composites at various temperatures (T). This task is fulfilled by formulating the temperature dependency of Young’s modulus (E) and ultimate tensile strength (σ_ult) as the inputs of the models. Temperature-dependant parameters of Young’s modulus and ultimate tensile strength are found to be in good agreement with the experimentally obtained data when used for unidirectional, cross-ply and quasi-isotropic FRP laminates. The proposed fatigue damage model is evaluated using six sets of fatigue damage data. The proposed temperature-dependent model was also found promising to predict the fatigue damage of unidirectional (UD) and orthogonal woven FRP composites at different temperatures.     

Elevated-temperature crack growth in polycrystalline alumina under static and cyclic loads

An experimental investigation has been conducted to study the crack growth characteristics of a 90% pure aluminium oxide in 1050 °C air under static and cyclic loads. It is shown that the application of both sustained and fluctuating tensile loads to the ceramic, tested in a precracked four-point bend specimen configuration, results in appreciable subcritical crack growth. The crack velocities under cyclic loading conditions are up to two orders of magnitude slower than those measured in static loading under the same maximum stress intensity factor. Cyclic crack growth rates are markedly affected by the loading frequency, with a decrease in test frequency causing an increase in the rate of crack advance. Detailed optical and electron microscopy observations have been made in an attempt to study the mechanisms of stable crack growth and the mechanistic differences between static fatigue fracture. Under both static and cyclic loads, the predominant mode of fracture is intergranular separation. The presence of a glass phase along the grain boundaries appears to have a strong effect on the mechanisms of crack growth. Apparent differences in the crack velocities between static and cyclic fatigue in alumina arise from crack-wake contact effects as well as from the rate-sensitivity of deformation of the glass phase. Our results also indicate that the cyclic fatigue crack growth rates cannot be predicted solely on the basis of sustained load fracture data. White stable crack growth occurs in the 90% pure alumina over a range of stress intensity factor spanning 1.5 to 5 MPa m^1/2, such subcritical fracture is essentially suppressed in a 99.9% pure alumina, ostensibly due to the paucity of a critical amount of glass phase. Both static and cyclic fracture characteristics of the 90% pure alumina are qualitatively similar to those found in an Al₂O₃-SiC composite wherein situ formation of glass phases, due to the oxidation of SiC in high-temperature air, is known to be an important factor in the fracture process.