The value of the J-integral at the onset of crack extension from a weld defect: Weld material is softer than parent material

The paper addresses the problem of crack extension in a weld in an engineering structure for the case where the weld crack is parallel to the plane of the weld, a situation for which the J-integral is path independent with regard to any contour surrounding a crack tip. Assuming that crack extension is associated with the attainment of a critical crack tip opening displacement _w, a theoretical analysis based on the strip yield representation of plastic deformation shows, for the case where the weld material is softer than the parent material, how the relation between the value of J at the onset of crack extension and _w depends on the flow properties of the weld and parent materials, the crack size and the weld thickness.     

Effects of rate,temperature and absorption of organic solvents on the fracture of plain and glass-filled polystyrene

The rate/temperature dependent fracture behaviour of plain and glass-filled polystyrene has been investigated over the crack speed (a) range of 10^–6 to 10^–2 m sec^–1 and in the temperature (T) range of 296 to 363 K. TheK _c (a, T) relationships obtained, whereK _c is the stress intensity factor at fracture, are shown to follow those given by the Williams/Marshall relaxation crack growth model and the toughness-biased rate theory. Crack propagation in both materials is shown to be controlled by a-relaxation molecular process associated with crazing. Crack instabilities observed in plain polystyrene are analysed successfully in terms of isothermal-adiabatic transitions at the crack tip. Fracture initiation experiments are also conducted in which the effects of organic liquids on the fracture resistances of both plain/glass-filled polystyrene have been determined. Good correlations betweenK _i ² (K _i being the crack initiation stress intensity factor) and _s, solvent solubility parameter, of various liquid environments have been obtained, which give a minimumK _i ² value at _{s p}, where _p is the solubility parameter of the polymer. For a given temperature, liquid environment and crack speed, the glass-filled polystyrene is shown to possess greater resistances to crack propagation than plain polystyrene.     

Strength Assessment for Butt Joints of Steel 50 by the Fracture Toughness Criteria

We propose an experimental-theoretical engineering procedure for assessing the strength of butt-welded joints using the force (K_Ic) and strain (_c) criteria of the brittle and quasibrittle fracture mechanics, respectively. For this purpose, beam specimens with square and bevel welds and an initial edge crack or notch in the weld metal are tested under three-point bending. The parameter K_Imax controlling fracture of a bent beam with an inclined (Mode I + Mode II) crack is assessed taking into account the values of the stress intensity factors K_I and K_II, and the crack inclination angle ^*. We also studied the plastic zone at the crack tip and the crack propagation kinetics depending on the weld geometry and the V-notch tip radius for butt-welded joints. The data obtained allow one to rate such joints by their strength according to the fracture toughness criteria K_Ic and _c.     

A transferability model for brittle fracture including constraint and ductile tearing effects: a probabilistic approach

This study describes a computational framework to quantify the influence of constraint loss and ductile tearing on the cleavage fracture process, as reflected by the pronounced effects on macroscopic toughness (J _c , _c). Our approach adopts the Weibull stress _w as a suitable near-tip parameter to describe the coupling of remote loading with a micromechanics model incorporating the statistics of microcracks (weakest link philosophy). Unstable crack propagation (cleavage) occurs at a critical value of _w which may be attained prior to, or following, some amount of stable, ductile crack extension. A central feature of our framework focuses on the realistic numerical modeling of ductile crack growth using the computational cell methodology to define the evolution of near-tip stress fields during crack extension. Under increased remote loading (J), development of the Weibull stress reflects the potentially strong variations of near-tip stress fields due to the interacting effects of constraint loss and ductile crack extension. Computational results are discussed for well-contained plasticity, where the near-tip fields for a stationary and a growing crack are generated with a modified boundary layer (MBL) formulation (in the form of different levels of applied T-stress). These analyses demonstrate clearly the dependence of _w on crack-tip stress triaxiality and crack growth. The paper concludes with an application of the micromechanics model to predict the measured geometry and ductile tearing effects on the cleavage fracture toughness J _c of an HSLA steel. Here, we employ the concept of the Dodds-Anderson scaling model, but replace their original local criterion based on the equivalence of near-tip stressed volumes by attainment of a critical value of the Weibull stress. For this application, the proposed approach successfully predicts the combined effects of loss of constraint and crack growth on measured J _c -values.     

Evaluation of crack-growth rate under conditions of simultaneous action of static loading and corrosive media

We construct a numerical model of subcritical growth of cracks in metals subjected to the simultaneous action of loading and corrosive hydrogen-containing media. The model is based on the hypothesis that hydrogen plays the predominant role, that under the conditions of stress corrosion, the process of crack growth passes through two stages, and on the deformation criterion of fracture. The crack-growth rate was determined as a function of the crack tip opening displacement , its critical value _c, standard electrode potential of the metalE ₀, and pH value of the medium. The reliability of the model under consideration is corroborated by experimental results.Karpenko Physicomechanical Institute, Ukrainian Academy of Sciences, L'viv. Translated from Fiziko-Khimicheskaya Mekhanika Materialov, Vol. 31, No. 2, pp. 68–74, March – April, 1995.     

Chemical Control of Underdoped and Overdoped States in Y(Ba2 ? ySry)Cu3O6 + δ

The chemical control of underdoped and overdoped states in the Y(Ba_{2 – y} Sr _y )Cu₃O_{6 +} (0.1 and 0.9) compounds has been observed by high-resolution O K-edge X-ray-absorption near-edge-structure spectra. The chemical substitution of Sr for Ba in the fully-oxygenated Y(Ba_2–y Sr _y )Cu₃O_{6 +} (0.9) compounds gives rise to high hole concentrations within both the CuO₂ planes and the out-of-plane sites, leading to the overdoped state and the decrease in the superconducting transition temperature from 92 K for y=0 to 84 K for y=0.8. In contrast, an increase in the Sr content in the oxygen-deficient Y(Ba_{2 – y} Sr _y )Cu₃O_{6 +} (0.1) compounds did not indicate superconductivity. The oxygen-deficient compounds exhibit the underdoped state due to the low hole concentration.     

Combined processing of YBa2Cu3O7-δ superconducting wire by mechanical work and melt growth technique

The combination of mechanical work by powder-in-tube processing and melt growth of YBa₂Cu₃O_7- was investigated. During the heat treatment of Ag-sheathed YBa₂Cu₃O_7- wire above the melting point of Ag, the sheath was melted and removed from the superconducting wire, but a small portion of Ag infiltrated into the core. Mechanical working before the heat treatment is beneficial for improvingJ _c. Heat treatments above 1015°C resulted in higherJ _c values for drawn wires than the samples without mechanical working. A proper combination of mechanical working and melt growth appears very promising for making high-J _c wire with good strength.     

The flexural strength and microhardness of YBa2Cu3O6+δ

The flexural strengths of rectangular YBa₂Cu₃O₆₊ bars, prepared from mixed oxides and carbonates or spray-dried precursors, have been measured at room temperature and at 77 K. Strengths ranged from 17.8 to 57.6 M Pa at room temperature, depending on processing history, and were 20% greater when measured at 77 K. Corrosion of YBa₂Cu₃O₆₊ in humid air at 38° C created two layers of corrosion products, but did not weaken the uncorroded core when failure loads were corrected for the decreased sample dimensions. The Knoop hardness of polycrystalline YBa₂Cu₃O₆₊ ranged from 436 to 447 KHN while the hardness of individual grains of YBa₂Cu₃O₆₊ was 498 KHN. Variations in flexural strength with microstructure were observed and are discussed.     

Study of the relationship between J-integral and COD parameters under mixed mode I + II loading in aluminum alloy Ly 12

In this paper, the relationship between the J-integral and COD under mixed mode I+II loading was proposed and investigated. The J-integral was calculated by the Finite Element Method, and COD was defined by Rice`s model and measured by a duplicating method in an aluminum alloy Ly12. The critical values of the J-integral and COD for a stable mixed crack initiation were also determined by a resistance curve. It shows that: (1) the mixed J-integral, J _M, and the mixed COD satisfy the relations of J _M=dn₀CTOD+ds₀CTSD and J _M=d_yieldCOD, where dn, ds and d are coefficients; CTOD and CTSD are the mode I and mode II components of COD, respectively; ₀ and ₀ are the tensile and shear stresses at the crack tip strip, respectively, and (2) the initiation values of the J-integral and COD of mixed stable crack growth increase with an increasing mode II component, the J _IIC value is 2 times greater than that of J _IC, and the COD_i for a pure mode II crack is 6 times greater than that of COD_i for a pure mode I crack.     

Fracture mechanics of blunt cracks in a ductile steel

The propagation of blunt notches in stainless steel has been studied experimentally and analysed using generalized fracture mechanics (GFM), which takes account of inelastic and non-linear deformation. According to this theory, the critical apparent energy release rate, which is equivalent toJ _c, is given byJ _c=k ₁ (₀)cW _0c for an edge crack of lengthc in a thin sheet (plane stress), wherek ₁ (₀) is a dimensionless function of strain, ₀, andW _0c is the input energy density remote from the crack at the time of crack propagation. The validity of this equation was demonstrated for blunt cracks and the functionk ₁ (₀) evaluated. The value ofJ _c was measured for blunt cracks of different lengths and tip diameters, and also for different crack extensions.J _c was found to be independent of crack length for the smallest tip radius, but became systematically length-dependent as the radius increased. However, the dependence ofJ _c on crack length, tip radius and crack extension can be expressed by a single empirical function, as is suggested by GFM. The propagation of cracks from blunt notches in ductile materials can, therefore, be handled by fracture mechanics methods.     

Synthesis of high-T c superconducting Bi-Pb Sr-Ca-Cu-O ceramics prepared by an ultrastructure processing via the oxalate route

The oxalate precursor yielded by a sol-gel processing can be pyrolysed and oxidized at 840 ° C for 40h into the desired high-T _c superconductor in the lead-doped Bi-Sr-Ca-Cu-O system withT _c(onset) = 140 K andT _c(zero) = 104K. The mechanisms of the sol-gel reaction were monitored by analysis of Fourier transformation infrared (FTIR) spectroscopy. Moreover, identification of the various phases existing on the specimens after firing at selected temperatures, was made by analysis by FTIR spectroscopy and X-ray diffractometry. Based on the experiment results, the mechanisms of forming Bi₂Sr₂CaCu₂O₈₊ (phase 2212) might be identified as the reaction of Bi₂Sr₂CuO⁶⁺, Ca₂CuO₃ and CuO at 800 ° C. Furthermore, Bi₂Sr₂Ca₂Cu₃O₁₀₊ (phase 2223) might be synthesized by the reaction of phase 2212, Ca₂CuO₃ and CuO at 840 ° C. Ca₂PbO₄ found in lead-doped materials may catalyse the formation reaction of Ca₂CuO₃ at 650 ° C and play a role of a flux to fuse Bi₂Sr₂CaCu₂O₈₊, CuO and residual Ca₂CuO₃ and then improve the further synthesis of Bi₂Sr₂Ca₂Cu₃O₁₀₊ at 840 C.     

Deformation parameters of separation failure in tension and compression

The results are presented of experimental examination of the displacement of the edges of a separation crack in brittle (silicated glass) and quasi-brittle (polymethyl methacrylate) materials deformed in uniaxial static loading in tension, compression, and bending (eccentric tension). The results of analysis of these data are used to introduce the new interpretation of various basic concepts, such as the end region of the crack d, opening displacement ₁ and the crack tip opening ₁. It is attempted to obtain values of the strain parameters d, _{1 1}, invariant to the method of determination. These values correspond to the start of crack propagation in the examined materials. It is shown that the quantities _Ii in brittle failure and _Ii in quasi-brittle failure are relatively independent of the type of tested specimen.Translated from Problemy Prochnosti, No. 10, pp. 25–31, October, 1991.     

Fracture initiation and crack propagation of acrylonitrile-butadiene-styrene (ABS) in organic solvents

The effects of organic liquid environments on the fracture behaviour of acrylonitrile-butadiene-styrene (ABS) have been investigated. Fracture initiation experiments showed thatK _i ² , (K _i being the stress intensity factor at crack/craze initiation), could be meaningfully correlated with the solvent solubility parameter ( _s) of the different liquid environments and had a minimum value at _s= _p, where _p was the solubility parameter of ABS. For the range of organic liquids used, hydrogen bonding did not have any significant effects on the correlations. It was demonstrated that theK _i ² – _s correlations could also be usefully extended to other materials such as plain and glass-filled polystyrenes. At a common crack speed (å), the fracture toughness (R) values in crazing liquids (i.e. alcohols) were greater than those in cracking solvents (i.e. acetone, benzene, toluene, etc.) which usually caused a dissolution effect on the plastic. From crack propagation experiments, and using fracture mechanics analyses, definiteR(å) andK _c(å) relationships for ABS immersed in toluene, carbon tetrachloride and methanol were determined. These experimental results showed that crack propagation was relaxation controlled and agreed well with a recent theoretical analysis due to Williams and Marshall for environmental crack and craze growth in polymers. Finally, SEM pictures were presented to show the remarkable differences in the fracture morphologies of ABS in both crazing and cracking liquid environments.     

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.     

Non-linear creep behaviour of PET

The non-linear creep behaviour has been studied on PET films at room temperature. A particular value of the stress, _c, was used to characterize the change between the linear to the non-linear domain. The variations of the elastic modulus, the relaxed modulus and _c revealed great sensitivity to the morphology of the crystallization. A molecular model of non elastic deformation, assuming (i) hierarchical correlated molecular motion, and (ii) nucleation and expansion of sheared-microdomains, was used to analyse the role of stress on anelasticity. To take into account the two-phase structure of semicrystalline films, a phenomenological series/parallel model was applied to express the mechanical coupling between amorphous and crystalline phases. Quantitative agreement was found between theoretical predictions and experimental data for low and high stresses. However, there was a discrepancy in the rate of recovery because the model predicts a strain recovery slower than the experimental behaviour. Consequently, it is proposed to develop further the molecular model mentioned above by specifying the energy profile of a sheared-microdomain and its stress dependence. Then, the difference between creep and recovery strain rate could be explained.Nomenclature A Anelastic equilibrium compliance - A Parameter proportional to the relaxation strength - b Shear vector - Correlation parameter - _i Particular value in the distribution - _e Average value in the material ( = 0.27) - Correlation parameter characterizing the ability of chain orientation - d _a Amorphous density - d _c Crystalline density - Parameter of the mechanical mixing law - E Tensile modulus - E _c Crystalline Young's modulus - g _i Statistical weight in the distribution - G ₀ Shear modulus at 0 K - J _max Creep compliance at the end of the creep time - J _max(0) Value ofJ _max for low stresses - J _u Unrelaxed compliance - J _i( _i;A _i) Calculated compliance for a couple ( _i;A _i) - J _exp Experimental creep compliance - J _a Compliance of the amorphous part - J _c Compliance of the crystalline part - J _sc Compliance of the semi-crystalline material - k Boltzmann's constant - Parameter of the mechanical coupling law - R Radius of a shear micro domain - ₀ Stress necessary to cross the energy barrier only by mechanical activation - T _c Crystallization temperature - t _c Creep time - _mol Time for a translational motion of a structural unit over a distance comparable to its size - Particular value of _mol in the time distribution - Characteristic time for the secondary relaxation - ₀ Time proportional to the Debye time - t ₀ Scaling time parameter determined by the experimental value of _mol - U Activation energy for an elementary molecular motion - X _c Crystallinity ratio - V _a Volume fraction of the amorphous part - V _c Volume fraction of the crystalline part     

Polymer/metal interfacial crack growth characterized by C*

This paper establishes a simple testing scheme to simultaneously measure the linear elastic strain energy release rate G, the non-linear J-integral, and the rate-dependent C ^*-integral for a growing crack at a polymer/metal interface. The test is applicable to fracture of adhesive bonds. A criterion governing C ^*-controlled fracturing is derived, analogous to the Hutchinson-Paris -criterion for J-controlled growth. The interfacial toughness of an adhesive commonly used for bonding metal plates is characterized at room temperature, and is shown to fracture in a C ^*-controlled manner. A relationship between C ^* and the crack growth rate is observed. The nature of this relationship warrants further exploration.     

Dependence of the Gap Ratio on the Fermi Level Shift in a Van Hove Superconductor

The dependence of the zero temperature gap to the critical temperature for s- and d-wave superconductors on the Fermi level shift () from the Van Hove singularity is studied within the BCS theory. Exact numerical calculations for the s and d gap ratios are carried out and approximate analytic expressions for the ratio are given. We find that the maximum gap ratio occurs at = 0 and it decreases slowly with increasing , and that this behavior is symmetric with respect to .     

Piezoelectric and mechanical properties of ceria-doped lead zirconate titanate ceramics

Phases, microstructures and properties of lead-zirconate-titanate (PZT) ceramics with the compositions Pb(Zr_0.535– Ce Ti_0.465) O₃ where =0.0, 0.001, 0.01, 0.02 and 0.05 were studied. Rhombohedral and tetragonal phases were present at =0.0. The amount of the rhombohedral phase increased with increasing , and only the tetragonal phase was present for >0.001. Thec/a ratio of the tetragonal phase also increases with increasing . Particles of CeO₂ were found to be present in compositions with >0.01, indicating that the solubility of CeO₂ is less than 1a/o on the metals basis. The piezoelectric and electromechanical constants achieved maximum values for =0.001. The hardness increased monotonically with increasing . The modulus of rupture and the fracture toughness, however, went through a minimum and both stayed lower than their values for =0.     

Heat transfer in plane film formation

A mathematical model is obtained for the process of cooling with formation of a planar film. The solution obtained is verified experimentally.Notation mean axial velocity gradient - v_x current axial velocity - v_o initial polymer velocity - v₁ sampling velocity - K draw ratio - deformation rate tensor - x, y, z spatial coordinates - X, Y dimensionless coordinates - L() differential operator - T temperature - T_o initial temperature - T_c temperature of surrounding medium - dimensionless temperature - dimensionless temperature averaged over film thickness - thermal-diffusivity coefficient - 2_o initial film thickness - thermal conductivity - heat-transfer coefficient - f(X) distance function - Bi Biot criterion, Bi_o, Biot criterion calculated for initial film thickness - Gz* modified Graetz criterion - V dimensionless velocity - ₁, ₂, ₃ heat-transfer coefficients produced by radiation, free convection, and forced convection - v_c, _c mean velocity and film half-thickness in formation zone - T₁ calculated temperature value - T₂ experimental temperature value - l formation zone length Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 37, No. 5, pp. 854–858, November, 1979.