Exploring the fracture toughness KIE and KIC of a medium-Strength steel plate using the surface-flaw test

The fracture toughness of a 30 CrMnSiA steel plate of three thicknesses (10,8 and 5 mm) and three widths (110,80 and 56 mm) has been investigated by using surface-flaw method under room temperature. It is not easy to compute the value of K_IE by the maximum applied load. But the values of K_IE and K_IC could be obtained easily, if the computation of the conditional applied load P₁₀ and P₅ based on the relative effective extension Δa/a₀ = 10% and 5% were adopted, together with the conditions of P_max/P₁₀ 1.2 and P_max/P₅ 1.3. The K_R — Δ_a curve, i.e. the resistance-curve described by the parameter K, has been plotted. The values of K_IC and K_IE are then the resistances corresponding to the real extensions of flaws of Δ/a₀ = 2 and 7%, respectively. These values so obtained are in good agreement with the computed values of K_IC and K_IE by using the conditional applied loads. The values of K_IC and K_IE so obtained are also in agreement with the value of K_IC converted from the J-integral and the effective value of K_IE computed by the maximum applied load, respectively.

An approximate relation between K_IC and K_IE has been found to be: K_IC = (0.85˜0.95)K_IE.

The requirements for the dimensions of specimens are: Thickness of plate: B 1.0(K_IC/σ_0.2)² or 1.25(K_ICσ_0.2)²]; Width of plate: 8 W/B 10, 4 W/2c 5; Effective length: l 2W.     

Review of the fracture mechanics approach to creep crack growth in structural alloys

The application of the fracture mechanics approach to time-dependent high temperature crack growth has been reviewed. Available data on several structural alloys indicate that depending on the environmental sensitivity and creep ductility of the material, creep crack growth can be characterized by either linear elastic parameter, K, non-linear elastic-plastic parameter, J^*-integral, or reference stress, σ_ref. In particular for materials that are significantly sensitive to environment, K can adequately characterize the growth rate, and for materials that are significantly creep ductile, σ_ref can be used to predict creep life of a cracked body. Finally, for materials that are relatively ductile and wherein crack growth occurs predominantly by a deformation process, J^* integral appears to be the characterizing parameter for the growth rate. Data for several materials indicate that under steady state crack growth conditions, there may be a unique growth rate-J^* relation independent of temperature and material. This would have a profound impact in terms of the utility of fracture mechanics approach to predict creep crack growth rate and needs to be examined further. Conditions under which K, J^* or σ_ref is applicable are discussed in detail.     

The scatter in KIC-results

Scatter in K_IC-results can often be quite extensive, and to make reliable interpretations of the results it is of great importance to understand the nature of it. Cleavage fracture in steels is of a statistical nature and therefore the scatter in K_IC-results will behave similarly.

Two different approaches, one based on a microstructural statistical model and an other based on the Weibull distribution are applied to evaluate the theoretical scatter in K_IC-results. With both methods it is shown that the theoretical value of the relative scatter described through the Weibull slope factor is constant and equal to four.

The reason for the discrepancy between the theoretical value and the experimentally determined values of the slope factor is shown to be caused by inadequate number of experimental K_IC-measurements. The existence of a lower limiting K_min value is verified and a simple procedure for conservative estimation of the K_Ic-mean and lower bound values is presented.     

On the effect of sampling volume on the microscopic cleavage fracture stress

Reported observations of an experimental variation in the microscopic fracture stress for transgranular cleavage (σ^*_f) with specimen geometry and size are quantitatively examined in terms of a weakest-link statistical model for brittle fracture, wherein failure coincides with the critical propagation of a particle microcrack into the matrix. By analysing the onset of fracture in the ‘sharp-crack’ (K_Ic) specimen, the ‘rounded-notch’ (Charpy) specimen, and the uniaxial tensile specimen, it is shown that values of σ^*_f are reduced progressively in the ‘sharp-crack’, notched and unnotched geometries and with increasing specimen size, consistent with an increase in statistical sampling volume. Quantitative predictions for the magnitude of this variation are given for a low strength steel.     

Ti-content and annealing temperature dependence of transformation behavior of TiXNi(92-XCu8 shape memory alloys

Ti-content and annealing temperature dependence of the transformation behavior of Ti_XNi_(92-X)Cu_8.0 (at,%) (X = 49.0–5l.0) alloys was investigated by varying the annealing temperature from 573 to 1273 K. It was found that the peak temperature of B2–B19 transformation (O^*) increases with increasing annealing temperature from 673 to 873 K for all of the alloys. With annealing at temperatures above 873 K, the influence of annealing on O^* depends on Ti-content. In the range of 50.4–51.0 at.% Ti, O^* shows little dependence on annealing temperature. In the range of 49.3–50.2 at.% Ti, O^* firstly decreases and then keeps constant with increasing annealing temperature. For the alloy of 49.0 at.% Ti, O^* continuously decreases with increasing annealing temperature from 873 to 1273 K. On the basis of the above data, a partial phase diagram of Ti-Ni-8.0Cu (at.%) was proposed. The transformation hysteresis also showed unique Ti-content and annealing temperature dependence.     

Studies on fracture toughness and fractographic features in Fe---Mn base alloys

Fractographic examinations of fracture surfaces of single edge crack plate tension fracture toughness test specimens of some new Fe---Mn base maraging alloys have been conducted. The interrelations between the fractographic features, fracture toughness and other mechanical properties of these alloys have been studied. It is observed that the width of the stretched zone between fatigue and rapid fracture is related to K/σ_ys of the material where K is either K_IC, K_Q or the stress intensity for onset of microscopic slow crack growth. The stretched zone width is approximately equal to the average dimple size. Also it is of the order of the process zone size (calculated by modified Krafft's model) and the critical crack opening displacement in plane strain condition. Hahn and Rosenfield's model to estimate K_Ic was found to show much higher values in those cases where the fracture mode was predominantly cleavage, quasicleavage or intergranular.     

Probabilistic description of fatigue crack growth in polycrystalline solids

A stochastic model describing the crack evolution and scatter associated with the crack propagation process has been built on the basis of the discontinuous Markovian process. The evolution and scatter are identified in terms of constant probability curves whose equation is derived as In P_r(i) = B(e^KI₀ − e^Ki), i ≥ I₀, where i is the number of cycles, B and K are crack-length-dependent variables, P_r(i) is the probabiliity of the crack being at position r along the fracture surface after i cycles elapse and I₀ is the minimum number of cycles required for the crack to advance from one position on the fracture surface to the next. The validity of the model is established by comparing the crack growth curves generated for Al 2024-T3 at a specific loading condition with those experimentally obtained.     

Effect of crack-front width on fracture toughness of Douglas-fir

The variation of K_Ic with crack-front width is investigated for Douglas-fir wood using beam and compact tension specimens. A study of within-board variation for the RT, TR, TL and RL systems of propagation showed a trend of decreasing K_Ic as the crack-front width increased from 0.5 to 5.5 in. The observed size effects are consistent with a weakest link failure mechanism. The longitudinal (TL and RL) systems of propagation in glued-laminated Douglas-fir are investigated using beam and compact tension specimens with crack-front widths of 3–12.25 in. The weakest link model is verified and results obtained for the large specimens are consistent with observations of K_Ic on specimens with crack-front widths as small as 0.2 in. A cumulative distribution function is presented for K_Ic for longitudinal propagation in Douglas-fir wood at 12% moisture content.     

A study of the effects of mechanical and environmental variables on fatigue crack closure

Using the potential drop technique, fatigue crack closure has been monitored in pin loaded SEN specimens of -titanium, a titanium alloy and EN24 steel. The specimens were tested in tension-tension under conditions closely approximating to plane strain, and closure was only detected in vacua of better than 133 mN m⁻² (10⁻³ torr). No significant closure was detected in air. The extent of the crack area closed at minimum load varied with air pressure, applied stress, R ratio (R = L_min/L_max), crack length, material, and loading mode. Additional experiments made with a dip gauge showed that the COD/applied load response of the crack was non-linear in vacuum above minimum load in the fatigue cycle confirming that crack closure was occcurring. It is shown that for a given material, loading mode and air pressure, the effect of loading and crack length variables on crack area closed at minimum load can be characterised in terms of the parameter (K²_min-ΔK², this being proportional to the calculated COD at minimum load. The extent of closure in vacuum is influenced extensively by this parameter.     

Stage II fatigue crack growth

The linear part of the fatigue crack growth diagram is found to be divided into Stages IIa and IIb by the point O whose coordinates K^* and A are dependent on the physical and structural characteristics of the material. In Stage IIa K_eff remains constant as the microcrack advances in increments corresponding to the dislocation cell structure size, λ, pausing for (dN−1) cycles to accumulate the elastic energy required for the crack opening. During Stage IIb K_op remains constant and the microcrack opens during each cycle and advances irrespective of the substructure but in accordance with an increasing value of K_eff. The effects of temperature and vacuum on K^* are considered; the A values correspond to those of λ and are independent of the above effects.     

Fracture toughness of turbine-generator rotor forgings

A comprehensive program is being conducted relative to applying fracture mechanics technology to large turbine-generator rotors. One facet of this program involves the determination of plane-strain fracture toughness (K_Ic) over a range of temperatures for various types of rotor steels. Data have been obtained for ten large production forgings, representing three alloys, using various types of compact K_IC and spin burst test specimens. These results demonstrate that valid K_IC data can be obtained in these types of intermediate-strength, high-toughness steels in the temperature range of practical interest. Data indicate that the plane-strain fracture toughness of these steels increases rapidly with increasing temperature and is rather high (K_tc/σ_YS > 1 in^1/2), in the application range. As a result, the critical defect sizes for catastrophic failure upon a single cycle of loading are relatively large. The plane-strain fracture toughness measurements, as well as the application of these data, are presented and discussed.     

Anomalous elastic response of amorphous alloys suggesting collective motions of many atoms

The dynamic Young’s modulus, E, of amorphous (a-) Zr₆₀Cu₃₀Al₁₀ (numbers indicate at.%) alloy was measured as a function of frequency, f, with a strain amplitude, _t, of 10⁻⁶, E(10⁻⁶,f), and also as a function of _t for f near 10² Hz, E(_t,10² Hz), by means of the vibrating reed methods. The elasticity study under the passing of electric current (PEC) was carried out too. E(10⁻⁶,f) is lower than E₀ for f between 10 and 10⁴ Hz showing local minima near 5×10, 5×10² and 5×10³ Hz, which are indicative of the resonant collective motion of many atoms, where E₀ is the static Young’s modulus. E(_t,10² Hz) increases showing saturation with increasing _t. Qualitatively, the outlines of E(10⁻⁶,f) and E(_t,10² Hz) observed for a-Zr₆₀Cu₃₀Al₁₀ are similar to those reported for various a-alloys. Quantitatively, a change in E(_t,10² Hz) for a-Zr₆₀Cu₃₀Al₁₀ is smallest among that reported for various a-alloys, presumably reflecting that the crystallization volume, (ΔV/V)_x, is smallest for a-Zr₆₀Cu₃₀Al₁₀. The effective charge number, Z^*, estimated from the change in E(10⁻⁶,10² Hz) due to PEC is 3.0×10⁵, which is comparable with Z^* reported for various a-alloys. We surmise that the number of atoms in the collective motions excited near 10² Hz is similar among various a-alloys. The E(10⁻⁶,f) data suggest that the spatial sizes of the density fluctuations may show a distribution.     

Application of instrumented impact testing for studying dynamic fracture behaviour of rotor steels

The viability of the instrumented Charpy impact testing for studying dynamic fracture behaviour of rotor steels is investigated. This encompasses determination of dynamic fracture toughness (K_Id) and dynamic J-integral (J_Id), establishing correlation between oscilloscope profiles and fracture morphology of the ruptured samples and identifying fracture mechanisms involved. The predicted oscilloscope profiles for common fracture modes, their experimental counterparts, and the inferences drawn from these concerning operating fracture mechanisms are in good accord with the fractographic observations made on broken samples. Thus, the respective oscillographs vividly manifest the observed variations in the fracture processes. Fracture mechanics analysis of load-time and energy-time records of pre-cracked Charpy samples gave dynamic fracture toughness (K_Id) values of 43, 74 and 124MN/m3/2, and dynamic J-integral (J_Id) values of 0.008, 0.03 and 0.06 MJ/m² at −180°, 26° and 96°C respectively. It is possible that the deduced J_Id values correspond to a small but finite amount of crack extension instead of Zero Crack extension, in line with the emerging trends of J_Id estimation. Apart from increasing with temperature, both parameters recorded a true transition around 35°C which is attributed to the combined influence of a change in the fracture mode and relaxation of crack tip constraint. Another significant outcome of this investigation concerns about the existence of a minimum crack depth ratio for valid J_Id determination which, based on a detailed fractographic study, is interpreted in terms of the collective influence of crack tip plasticity and notch constraint.     

Relaxation of residual stress with fatigue loading

Investigations have been carried out to study the relaxation of the surface residual stress in 0.23% C steel due to the application of fatigue loading. The residual stress was induced in the specimen by pre-straining and was measured by X-ray back reflection method using Cr-K radiation. The surface residual stress induced, depends on the plastic strain and appears to bear a relation of the type σ_R = σ_o(e_p)^0.78. The decay of the residual stress appears to depend on log N, given by the relation σ_R1 = σ_RO−K log N, where N is the number of fatigue cycles. The constant K depends on the initial value of the residual stress.     

The micropolar thermoelastic problem of uniform heat-flow interrupted by an insulated penny-shaped crack

The classical problem of uniform heat-flow disturbed by an insulated penny-shaped crack is solved in the context of micropolar elasticity. The mode II stress intensity factor, K_II is found to depend on two new non-dimensional parameters N and τ − N is a measure of the coupling of the displacement field with the microstructure or the medium (0 N √2) and τ is the ratio of a material characteristic length to the crack radius. K_II remains higher than its classical value when N > 0, τ > 0 and attains the classical value as N and τ vanish. A closed-form expression to K_II is obtained in the physically important limiting case of τ → 0 with N fixed. In this limit the relative increment in K_II, over its classical value, is found to be (1 − v')N² where v' is the micropolar Poisson's ratio.     

On the calculation of closure-free fatigue crack propagation data in monolithic metal alloys

A computational method is described for the determination of ΔK_b, corresponding to a fatigue crack growth rate of b/cyc, where b is the Burgers vector for a monolithic metal alloy. ΔK_b is found to be numerically equal to E√b for the case of closure-free crack growth behavior. Given that the closure-free FCP rate of many monolithic metals varies with ΔK³, the growth rate of metal alloys at ΔK ΔK_b is given by da/dN = (ΔK/E)³(1/√b. Excellent agreement is found between experimental and computed FCP data for the case of monolithic metal alloys. The limits of these relations for metal-matrix composites and ceramics are discussed.     

Zn3-xMnxTeO6的晶体结构与吸收光谱和磁性研究

本工作主要研究Mn ²⁺离子掺杂的类刚玉系氧化物Zn₃TeO₆(0<x≤2.0)的晶体结构与光学性质和磁性的变化。Zn_3-xMn_xTeO₆粉末样品通过固相反应合成。Mn掺杂量的相图表明, x<1.0时保持单斜(C2/c)结构, 1.0≤x≤1.6为单斜(C2/c)和三方六面体混合相(R-3), x≥1.8时完全转变为R-3相, 且x=2.0时形成ZnMn₂TeO₆, Te-O和Mn/Zn-O键长增大, 八面体发生更大畸变。X射线粉末衍射结构精修也表明R-3相中Zn/MnO₆为畸变八面体。随着Mn ²⁺掺杂含量的增加, Zn_3-xMn_xTeO₆系列化合物不仅结构发生变化, 其颜色也由浅变深。紫外吸收光谱中随着掺杂浓度的增加, 400~550 nm处的吸收增强, 样品的光学带隙也由3.25 eV (x=0.1)逐渐减小到2.08 eV (x=2.0), 分析表明, 可见区吸收的增强是源于MnO₆八面体中Zn/MnO₆八面体中Mn ²⁺离子的d-d跃迁, 导致样品由浅黄色逐渐变为暗黄色。 磁性测试表明, 固溶体的反铁磁转变温度随着Mn ²⁺掺杂量的提高而逐渐增加, 且掺入的Mn ²⁺离子以高自旋态 存在。     

Growth mechanism of stress corrosion cracking in high strength steel

Stress corrosion crack growth rates are measured at sveral stress intensity levels for low-tempered 4340 steel in 0.1N H₂SO₄ solution. The characteristics of the growth rates are divided into three regions of stress intensity factors: Region I near K_1SCC; Region III near unstable fracture toughness, K_1SC; and Region II, which lies between the two. K_1SCC is the value of K at which no crack growth can be detected after 240 hr.

In order to explain these experimental results, the crack initiation analysis reported in a previous paper is extended to the growth rates. A detached crack initiates and grows at the tip of an already existing crack. When the detached crack reaches the tip of the main crack, the process repeats as a new existing crack.

A relationship between crack growth rate, v, and stress intensity factor, K, is obtained as a function of b/a and a = b + d, where b is the distance from the tip of the main crack to the detached crack, and d is the ydrogen atom saturated domain.

The experimental data are in good agreement with the theoretical values in Region II when a = 0.02 mm, b/a = 0.8, c₁/c₀ = 2.8 for 200°C tempered specimens and a = 0.015 mm, b/a = 0.7, c₁/c₀ = 3.0, ρ_b = 0.055 mm for 400°C tempered specimens, where ρ_b is a fictitious notch radius. The plateau part in Region II for 400°C tempered specimens is also successfully explained by the present theory. For Region III, the value of b/a will be almost equal to 1 because v → ∞ for b/a → 1. On the other hand, for Region I, b/a will be zero, since the value of v becomes negligibly small and no crack growth is observable.     

Fatigue crack growth characteristics of rotor steels

Room temperature fatigue crack growth rate data were generated for Ni-Mo-V (ASTM A469, Cl-4), Cr-Mo-V (ASTM A470, Cl-8) and Ni-Cr-Mo-V (ASTM A471, Cl-4 and a 156,000 psi yield strength grade) rotor forging steels. Testing was conducted with WOL type compact toughness specimens and the results presented in terms of fracture mechanics parameters. Data show that the Ni-Cr-Mo-V steels exhibit slower fatigue crack growth rates at a given stress intensity range (ΔK) than do the Ni-Mo-V steels. In addition, the Cr-Mo-V steel was found to exhibit slower growth rates than the other alloys at ΔK levels below 40 ksi √in but somewhat foster rates at ΔK levels in excess of 45 ksi √in. The fatigue crack growth rate properties of the alloys studied conform to the generalized fracture mechanics crack growth rate law where da/dN = C₀ΔK^R. It was noted that the fatigue crack growth rate parameters n and C₀ tend to decrease and increase, respectively, with increasing material toughness, K_ic.     

Creep crack growth behaviour in air and sodium for an unstabilized austenitic stainless steel and assessment of evaluation concepts

The austenitic stainless steels used for permanent structures in the heat transfer systems of liquid metal fast breeder reactors (LMFBR's) are subjected to flowing sodium at elevated temperatures. During this exposure to sodium environment the structural materials can undergo compositional and microstructural changes which could alter the mechanical behaviour as compared to air. An investigation of creep crack growth in air and flowing liquid sodium was performed on the austenitic stainless steel X6 CrNi 18 11 (similar to AISI 304 ss) under constant load at 823 K using compact tension specimens. The sodium conditions are characterized by an upstream position in a non-isothermal loop with a temperature gradient of 170 K. The experimental data are evaluated correlating the crack growth rate with the net section stress σ_net, the stress intensity factor K_Q, and the energy rate integral C^*, respectively.