Study on the behavior of elastic-plastic fracture under mixed I+II mode loading in aluminum alloy Ly12-J-integral analysis

The elastic-plastic fracture behavior of aluminum alloy Ly12 under mixed I+II mode loading was studied by finite element method and fracture test. A mixed mode elastic-plastic fracture criterion of J-integral was proposed by using the J-resistance curve, and the maximum fracture effective plastic strain _p max of different mixed ratios at crack tip were also calculated. The results show that(1) the initiation J-integral values of different mixed ratios have the equation

Prediction of fracture toughness for heat-resistant steels considering specimen dimensions. Report 2. Ductile fracture

A model of ductile failure of a body with a crack has been developed which enables predicting fracture toughness on the upper shelf of the fracture toughness temperature dependence taking into account the influence of the stress state. The model is based on the physical-mechanical model of ductile failure which is controlled by the critical value εf reached by plastic strain at the crack tip ε _i ^ρ . In this case it is assumed that both the ε _i ^ρ value, which precedes the crack growth onset by the mechanism of pore coalescence, and the critical strain εf are functions of specific stress state parameters, namely: the critical strain is a function of the stress state triaxiality σ _m /σ _n (σ _m is the hydrostatic stress, σ _i is the stress intensity), and ε _i ^ρ is a function of the parameter χ introduced, which is an explicit function of all three principal local stresses in the process zone at the crack tip and which defines the degree to which the stress state approaches the plane strain conditions for a body of specified thickness. The model developed has two modifications one of which enables predicting fracture toughness of large-size bodies from the results of testing only small cylindrical specimens without cracks (smooth and with a circular recess) and the other from the results of testing small cylindrical specimens and small specimens with a crack. Translated from Problemy Prochnosti, No. 2, pp. 5–19, March–April, 1997.     

Notch tip stress distribution in strain hardening materials

Using the results of elastic-plastic stress analyses for notched bars, it is shown that a modified form of slip-line field solution can satisfactorily explain the variation of longitudinal stress ahead of notch tips in strain hardening materials.

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Résumé En utilisant les résultats d'analyses de contrainte élastoplastique dans le cas de barres entaillées, on montre qu'il est possible d'utiliser une forme simplifiée de solution du champ des lignes de glissement pour expliquer de façon satisfaisante la variation des contraintes longitudinales en avant d'extrémités d'entaille dans des matériaux susceptibles d'un écrouissage.

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Nomenclature _yy longitudinal tensile stress in the notch tip plastic zone - _xx transverse stress in the x-direction - _zz transverse stress in the z-direction - k yield stress in shear - ₀ yield stress in tension - ₀ ^* strain hardened yield stress (flow stress) - _{0/* c} flow stress at notch tip - _total total strain _pl plastic strain _l principal strain - _{1 c} maximum principal strain at notch tip - _1pl plastic strain in they-direction - _{1 cp1} E_{1 pl} at notch tip - _eff effective plastic strain - _{c eff eff} at notch tip - ₀ yield strainC Stress decay constant in the notch tip region - /e_pl linear strain hardening rate - n strain hardening exponent in power hardening law - 2 flank angle of notch - distance from notch tip - p notch tip radius - k _I applied stress intensity for Mode I loading - E Young's modulus - V _c crack tip opening displacement     

Study on cleavage fracture criteria of the quasi-brittle and micro-inhomogeneous materials

On the bases of recent achievements on the micro-mechanism of cleavage this paper analyses the inherent deficiencies of the stress intensity factor K _I which is used to evaluate the fracture toughness of quasi-brittle and micro-inhomogeneous materials. The K _I parameter can uniquely determine the field intensity ahead of a crack tip in the condition of elastic and small scale yielding (SSY). However, the K _I cannot uniquely determine the critical condition triggering the cleavage fracture in a quasi-brittle and inhomogeneous steel where the cleavage fracture process is not a direct extension of the precrack but is initiated at a variable distance from the precrack tip. The variable distances of cleavage initiations invoke varied critical values of K _I. On the bases of authors' experiments, this paper analyses the physical meaning of the local fracture stress _f, its stability and the feasibility to be used as an engineering parameter for assessing the fracture toughness.     

Some multiple comparisons using sample quasi ranges on censored data

We considerk(k)≥2 independent populations (treatments or systems) and an solutely continuous member of location-scale family of distributions, index by the location parameter μ _i (-∞ < μ _i < ∞) and scale parameter θ _i (θ _i > 0), is used to model the observations from the ith population,i=1,...k. The problem of simultaneous selection of two subsets, one containing population associated with the smallest ϕ-value and other containing population with the largest ϕ-value with probability at least a pre-specified value is considered when the data are censored. We also construct 100P ^*% simultaneous upper and two-sided confidence intervals for where θ_[1] ≤ ... ≤ θ_[k] denotes the ordered values of ϕs. The proposed procedures, based on sample quasi ranges, are useful when the experimenter has smaller samples or censored samples or there is suspicion of outliers in the samples. The results are applied to exponential populations model and, for thes casi: (i) the constants have been computed to apply the proposed multiple comparisons; (ii) two members of the proposed class have been compared with the existing procedure. A numerical example is also given.     

Investigation of failure criteria for a sharp notch

In this study, a method of evaluating the static strength of a V-shaped notch based on the singular stress field at the notch tip is studied. The singular stress fields is defined by two parameters, and , which correspond to the intensities of symmetric stress field and the skew-symmetric field, respectively. Four kinds of fracture criteria are considered; two of them are based on the tensile strength σ _B and the other two are based on the fracture toughness K _IC . The usefulness of the criteria is investigated through the experimental results carried out on plane specimens of acrylic resin having a sharp notch for various notch configurations such as the opening angle, the inclined angle and the notch depth. It is shown that the criteria using stress intensity factor and the energy release rate not sensitive to the length of the virtual crack .     

A simplified method for determining double-K fracture parameters for three-point bending tests

A simplified method for determining the double-K fracture parameters K _Ic ⁱⁿⁱ and K _Ic ^un for three-point bending tests is proposed. Two empirical formulae are used to describe the crack mouth opening displacement CMOD and the stress intensity factor K _I ^c caused by the cohesive force (x) on the fictitious crack zone for three-point bending beams. It has been found that the two empirical formulae are accurate for a large practical region of a/D. Experiments carried out by many researchers showed that the new formula of CMOD for three-point bending beams can be directly used to predict the initial crack length for precracked beams, the notch depth and the critical effective crack length, as well as the crack length in the post-critical situation with a satisfactory accuracy. Further verification is demonstrated to determine the double-K parameters K _Ic ⁱⁿⁱ and K _Ic ^un. They are very close to those determined by the method proposed in our previous work. Using the simplified procedure, the experiments can be performed even without a closed-loop testing facility and the calculation can be carried out on a pocket calculator.     

Transition to chaotization and loss of self-averaging in two-dimensional two-phase media at the flow threshold

Giant fluctuations of the electric field recently identified experimentally in two-dimensional two-phase media at the percolation threshold are discussed. An example of a hierarchical realization of these media is used to show that for Re σ _i=0 (where σ₁ and σ₂ are the phase conductivities) and Im σ ₂/Im σ₁>0, the hierarchy construction procedure yields the Dykhne expression , whereas for Im σ ₂/Im σ₁<0, the procedure becomes randomized and the medium loses its property of self-averaging. Pis’ma Zh. Tekh. Fiz. 23, 89–95 (July 12, 1997)     

Requirements to Crack Resistance of Materials of Oil and Gas Equipment Operating in Hydrogen-Sulfide Media

We investigate the crack resistance of low-alloy pipe steels, their welds, and nickel and titanium alloys in air and in a hydrogen-sulfide solution NACE. We determine the stress intensity factors in the course of testing in air K _c and in hydrogen sulfide K _Issc as well as the coefficients of medium influence B _Issc = K _Issc /K _c. We establish minimum admissible values K _Issc ^min and B _Issc ^min that ensure high serviceability of structural materials of oil and gas industry. We obtain that K _Issc ^min 33MPa· for low-alloy steels and welds, K _Issc ^min 70MPa· for nickel alloys, and K _Issc ^min 50MPa· for titanium alloys. The criterion B _Issc ^min 0.6 is the same for various materials. We recommend to include the criteria of crack resistance K _Issc ^min and B _Issc ^min in the corresponding standards, specifications, etc.     

High-temperature fracture and diffusional deformation mechanisms in Si-Al-O-N ceramics

A comparison has been made of hot-pressed Si-Al-O-N ceramics, with different impurity sintering aids (MgO and Mn₃O₄), in relation to microstructure, high-temperature creep and fracture. The Mn-containing ceramic exhibits a mechanism for creep of grainboundary sliding accompanied by cavitation at triple junctions, nucleated within an impurity silicate residue. The measured non-integral stress exponent (n∼1.5) and activation energyQ in the creep equation = const. σ ⁿ exp (-Q/kT) are typical of commercial silicon nitrides. A similar cavity-interlinkage is the principal mechanism for sub-critical crack growth, characterized by a low value for the stress-intensity exponent (n) in the relationV (crack velocity)=const.K ₁ ⁿ determined on double-torsion test specimens. Triple-junction silicate, and hence cavitation, is absent in the Mg-containing ceramic, which exhibits a Coble diffusional creep mechanism (stress exponentn=1). Sub-critical crack growth occurs only over a narrow range of stress intensity, near toK _lC withn∼13 in theV-K ₁ ⁿ relation. A grain-boundary de-segregation caused mainly by extraction of impurities into an oxide film results in further improvement in creep and resistance to sub-critical crack growth.     

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.     

Experimental Observations and Computational Modeling of Fracturing in an Anisotropic Brittle Crystal (Sapphire)

The commonly used fracture criteria-maximum K_I, zero K_II, maximum hoop-stress, and maximum energy-release rate-predict similar fracture paths in isotropic materials, but not in anisotropic materials. In the general anisotropic case, the fracture path depends on the material-symmetry properties, the nature of the applied loads, and the overall geometry of the specimen. In addition, anisotropy in the material's resistance to fracturing plays a key role in defining crack initiation and its propagation path. Experiments are performed on notched specimens made from sapphire, a microscopically homogeneous and brittle single-crystal solid. The force required for fracture initiation is measured. The experimental measurements/observations are compared with the numerical results of the FEM simulations. A stress-based fracture parameter, is shown to be a good measure of the fracture criterion, where σ and E, respectively, are the tensile stress and Young's modulus in the direction normal to the cleavage plane, with surface energy γ , and R is a characteristic length, e.g., the notch radius. This parameter takes into account the effects of the surface energy of the corresponding cleavage plane, as well as the strength of the atomic bonds in the direction normal to the cleavage plane. More than two-thirds of the notched specimens fractured at the point and along a cleavage plane where A is maximum. The measurements of the applied force made it possible to quantitatively obtain a critical value for parameter A. Finally, experiments show that for the notched sapphire specimens the weakest family of cleavage planes, , are the fracture planes, although a few specimens fractured along non-cleavage planes. This revised version was published online in July 2006 with corrections to the Cover Date.     

Three-dimensional elastic stress fields ahead of blunt V-notches in finite thickness plates

Based on detailed three-dimensional (3D) finite element analyses, elastic fields in front of blunt V-notches in finite thickness plates subjected to uniaxial far-end tensile stress have been investigated. By comparison with the corresponding planar V-notch fields and 3D through-thickness sharp crack fields, various aspects of the 3D fields of the blunt V-notches in finite thickness plates are revealed: (1) The plate thickness and notch angle have obvious effects on the stress concentration factor (SCF) K _t, which is higher in finite thickness plates than in the plane stress and plane strain cases. When the notch angle is smaller than 90°, the SCF is insensitive to the notch angle, but has close relation with the dimensionless plate thickness. With the notch angle increasing further, the SCF decreases and the effect of dimensionless plate thickness on it becomes weaker. (2) For any notch angle considered, the variation of the opening stress _yy normalized by its value _yy0 at the notch-root with the distance x from the root normalized by the root-radius , is insensitive to the plate thickness and coincides well with the two-dimensional (2D) planar solution. (3) The 3D distribution of the out-of-plane constraint factor T _z=_zz/(_yy+_xx) is controlled by the plate thickness (B), the notch-radius () as well as the notch angle (), but for deeper V-notches with 90°, the distribution of T _z coincides well with that of a U-notch as well as a sharp 3D through-thickness crack and an explicit empirical expression of T _z is presented. (4) The distribution of the in-plane stress ratio T _x=_yy/_xx in front of the 3D V-notch is nearly independent of the plate thickness and coincides well with the corresponding 2D solutions when the opening angle is smaller than 120°. (5) The gradient of the out-of-plane strain _zz is significant near the free surface in finite thickness plates. On the free surface, the _zz can be 3.5 times the value on the mid-plane, and the through-thickness gradient of the _zz increases with decreasing notch angle. It is of interest to note that most of the field quantities ahead of V-notches are insensitive to the notch angles when the notch angle is smaller than 90°.     

Cleavag Fracture Criterion of Low Alloy Steal and Weld Metal in Notched Specimens

The cleavage fracture criterion of low alloy steel and weld metal in notched specimens is investigated in detail based on a great number of experimental data. It has been found that the most cleavage fractures initiate at a distance shorter (left side) than that of the peak stress location below a notch root, and the cleavage fracture in notched specimens must satisfy a dual criterion, i.e., a critical plastic strain (ε_p ≥ ε_pc) for initiating a crack nucleus, and a critical tensile stress (σ_yy ≥ σ_f) for its propagation. According to the dual criterion model, the great number of experimental data of 4PB (four-point bending) tests for the low alloy steel and weld metal and their statistical distribution are explained. The effects of temperature , the local fracture stress σ_f and the critical plastic strain ε_pc on the locations of cleavage initiation sites and the controlling steps of cleavage fracture process are discussed. This revised version was published online in August 2006 with corrections to the Cover Date.     

Investigation of shear stress distribution in notch problem under sliding mode case

The shear stress distribution for the notch problem of plane elasticity in the sliding mode case is investigated in this paper. Particular features of the shear stress distribution beneath the crown point of notch are analyzed by means of the Muskhelishvili method [1]. It is found that the maximum shear stress _{xy, max} is always reached at some point below the surface of the notch. The smaller the radius of the notch, the larger is the maximum shear stress _{xy, max}. A relation between _{xy, max} and stress intensity factor K _II of the corresponding crack problem is found to be Several specific examples are given to prove the validity of the obtained relation.% MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaiaadUeadaWgaaWcbaGaaeysaiaabMeaaeqaaOGaeyypa0ZaaSaa% aeaacaaIZaWaaOaaaeaacaaIZaGaeqiWdahaleqaaaGcbaGaaGOmaa% aadaWfqaqaaiGacYgacaGGPbGaaiyBaaWcbaGaeqyWdiNaeyOKH4Qa% aGimaaqabaGcdaGcaaqaaiabeg8aYjabeo8aZbWcbeaakmaaBaaale% aacaWG4bGaamyEaiaacYcaciGGTbGaaiyyaiaacIhadaahaaadbeqa% amXvP5wqonvsaeHbuLwBLnhiov2DGi1BTfMBG0evGueE0jxyGi0BSr% gaiuaacqWFUaGlaaaaleqaaaaa!6261!\[K_{{\text{II}}} = \frac{{3\sqrt {3\pi } }}{2}\mathop {\lim }\limits_{\rho \to 0} \sqrt {\rho \sigma } _{xy,\max ^. } \]This research project is supported by the National Science Foundation of China.     

Fracture behavior of stitched warp-knit fabric composites

Pilot studies are conducted to characterize the macroscopic fracture resistance behavior using linear elastic fracture mechanics and attempt to quantify the fracture parameters in which may govern the fracture and failure patterns of stitched warp-knit fabric composites. Methods based on the J-integral method and Betti's reciprocal theorem in extracting the fracture parameters, critical stress intensity factors, T-stress, and the second term of _y(r,0) near the crack tip prior to fracture initiation are formulated. Two fracture criteria, [_c,r _c] and [_c,r _c] are attempted to characterize the failure initiation for the fiber-dominated failure mode and self-similar crack extension in a given thickness of the laminate. Based on linear elastic fracture mechanics principle, these criteria are transformed into crack-driving forces [K _Q,T] and [K _Q,g ₃₂]. The two-parameter fracture criteria, [K _Q,T] and [K _Q,g ₃₂] provide a good correlation for the CCT and SENT specimens, but not for the high constraint CT specimens. With the limited experimental data, the results tend to show that the large tensile T-stress and large magnitude of negative g ₃₂ may inhibit the crack extension in the same crack plane and promote crack kinking.     

Dynamic toughness: Fracture mechanics interpretation of the drop-weight (NDT) test

The possibility of estimatingK _Id at the NDT from the crack geometry and load conditions used in the drop-weight (NDT) test has been re-examined. Theory and experiment support the usefulness of the relationK _Id / _yd = 0.075 m at the NDT temperature.

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Résumé On ré-examine les possibilités d'estimer la valeur deK _Id à la température NDT déterminée par l'essai drop-weight en se basant sur la géométrie de la rupture et sur les conditions de la mise en charge.L'approche théorique et les résultats expérimentaux souiignent la pertinence de la relation.K _Id /_yd = 0.0075 m ₁ ² à la température NDT, dans le cas des aciers de qualité navale.

     

Vacancy concentration in strain ageing of substitutional f c c alloys

The relation between vacancy concentration, C _v and tensile plastic strain, ɛ, has been constantly expressed as C _v ∞ ɛ ^m . To take into account the grain-size effect, we have recently proposed that C∞ ɛβ_v ∞ϱ_m, where ϱ_m is the mobile dislocation density. With the conventional expression that ϱ_m d ⁻ⁿ , where d is the average grain size, the strain and grain-size dependence of vacancy concentration appears to be C _v ∞ ɛ^βγ d ^-nγ. This equation has proved effective in rationalizing the onset strain, ɛ_c, and stress amplitude, Δσ, of flow instability associated with the Portevin-LeChatelier effect of substitutional f c c alloys, where ɛ_c and Δσ are described by

Oxide scale stresses in polycrystalline Ni200

An X-ray diffraction (sin² ψ) method has been successfully used to measure the oxidation stresses at room temperature in annealed and electropolished samples of polycrystalline Ni200 coupons oxidized in the temperature range 760 to 982° C for 4 h. The stresses on the free surface of the oxide (σ ₁₁ andσ ²²) were compressive and the average stress through the thickness normal to the oxide layer was found to be tensile. Surface stresses on the oxides formed at temperatures up to 927° C were found to be isotropic and both surface stresses and the average normal stress increased with increasing temperature of oxidation. At 982° C, the surface stresses were lower and this was attributed to the deformation and fracture of oxide layer resulting in stress relaxation.