Stress intensity factors for crack tip shielding or anti-shielding by impurity atoms

The average value of the crack tip stress intensity factor produced by a row of impurity atoms is calculated in this paper. The row of impurity atoms lies parallel to the crack front and is situated at an arbitrary position about a crack. The impurity atom produced mode I shielding/antishielding stress intensity factor L _iI for a row of impurity atoms very close to the crack tip is given by the expression: 295-1 where 2a is the crack length, a ^* is either the atomic radius of the host atoms (for substitutional impurities) or the radius of the vacant interstitial site (for interstitial impurities), 295-2 and 295-3 where G is the shear modulus, c is the fraction of impurity atoms in the impurity atom row and is the misfit parameter of the impurity atoms, r ₂ is the distance from the crack tip, and 295-4 is the angle the radius r ₂ makes with the crack plane.

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Résumé On calcule dans ce travail la valeur moyenne du facteur d'intensité de contraintes occasionné par une rangée d'atomes étrangers, située parallèlement à un front the fissure, et en une position arbitraire par rapport à la fissure.L'atome intersticiel ou de substitution génère une facteur d'intensité de contrainte de mode I, qui interfère sur une rangée d'atomes étrangers très proche de l'extrémité de la fissure, selon une expression ou interviennent la longueur de la fissure, le rayon atomique des atomes donnant lieu à une substitution ou à une insertion d'atomes étrangers, le module de cisaillement, la fraction d'atomes étrangers présents sur une rangée, le paramètre de désaxement des atomes étrangers, la distance de la rangée par rapport à l'extrémité de la fissure, et l'angle qui caractérise cette distance par rapport au plan de la fissure.

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This research has been performed under the auspices of the U.S. Department of Energy.     

Crack tip shielding by asperity contact as determined by acoustic measurements

Asperity contact along the fracture surface of a crack is one of the mechanisms of crack closure. This contact shields the crack tip, in part, from the externally applied driving force. We have now succeeded in using information from acoustic transmission and diffraction experiments, obtained under plane strain conditions, to determine the size and density of the contacting asperities in the closure region. We have also succeeded in estimating values for the static stress across a partially closed crack as well as the stress intensity factor,K_I (local), which shields the crack tip below the stress intensity factor K_Iclosure at which the first contact during unloading occurs. It is suggested that when crack closure has an important influence on crack propagation, the shielding stress intensity factor provides information that can be used to estimate the fatigue crack propagation rate.     

Crack tip shielding in elastic particulate composites undergoing damage

A simple rate-independent phenomenological constitutive model is used to model fracture behavior in elastic particulate composites undergoing damage. The constitutive model consists of two damage functions that govern the degradation of the bulk and the shear moduli. The elastic modulus is assumed to reach a saturation level under uniaxial conditions. Using the path independence of the J-integral and the concept of cracktip shielding, the remote or the applied stress intensity K_∞ is related to the cracktip stress intensity factor K_t. The results from the model are used to predict the cracktip conditions in particulate composites undergoing damage. The model compares well with experimental results in predicting the crack opening profile as well as the displacement field in the vicinity of a cracktip.     

Crack tip damage in rubber compounds

The application of the crack layer theory to fatigue crack propagation (FCP) in rubber compounds is discussed. A crack tip damage evolution coefficientμ is employed to assess the extent of damage as a fraction of the damage associated with critical crack propagation. The results can be expressed in the form $$\frac{{da}}{{dN}} = \frac{{\beta {\rm T}^2 }}{{\mu T_c - T}} ,$$ where da/dN is the rate of FCP,T is the tearing energy (energy release rate) whose critical value isT _c, andβ is a phenomenological constant. Experimental data for two rubber compounds, previously obtained by other workers, have been analyzed using the crack layer approach. Although damage, sometimes, cannot be easily detected in the case of rubber samples,μ increases during stable crack propagation. The value of the damage coefficientμ evolves differently for each compound approaching unity at catastrophic failure.     

Crack tip finite elements are unnecessary

It is shown that a singularity occurs in isoparametric finite elements if the mid-side nodes are moved sufficiently from their normal position. By choosing the mid-side node positions on standard isoparametric elements so that the singularity occurs exactly at the corner of an element it is possible to obtain quite accurate solutions to the problem of determining the stress intensity at the tip of a crack. The solutions compare favourably with those obtained using some types of special crack tip elements, but are not as accurate as those given by a crack tip element based on the hybrid principle. However, the hybrid elements are more difficult to use.     

Crack tip fields in ductile crystals

Results on the asymptotic analysis of crack tip fields in elastic-plastic single crystals are presented and some preliminary results of finite element solutions for cracked solids of this type are summarized. In the cases studied, involving plane strain tensile and anti-plane shear cracks in ideally plastic f c c and b c c crystals, analyzed within conventional small displacement gradient assumptions, the asymptotic analyses reveal striking discontinuous fields at the crack tip.For the stationary crack the stress state is found to be locally uniform in each of a family of angular sectors at the crack tip, but to jump discontinuously at sector boundaries, which are also the surfaces of shear discontinuities in the displacement field. For the quasi-statically growing crack the stress state is fully continuous from one near-tip angular sector to the next, but now some of the sectors involve elastic unloading from, and reloading to, a yielded state, and shear discontinuities of the velocity field develop at sector boundaries. In an anti-plane case studied, inclusion of inertial terms for (dynamically) growing cracks restores a discontinuous stress field at the tip which moves through the material as an elastic-plastic shock wave. For high symmetry crack orientations relative to the crystal, the discontinuity surfaces are sometimes coincident with the active crystal slip planes, but as often lie perpendicular to the family of active slip planes so that the discontinuities correspond to a kinking mode of shear.The finite element studies so far attempted, simulating the ideally plastic material model in a small displacement gradient type program, appear to be consistent with the asymptotic analyses. Small scale yielding solutions confirm the expected discontinuities, within limits of mesh resolution, of displacement for a stationary crack and of velocity for quasi-static growth. Further, the discontinuities apparently extend well into the near-tip plastic zone. A finite element formulation suitable for arbitrary deformation has been used to solve for the plane strain tension of a Taylor-hardening crystal panel containing, a center crack with an initially rounded tip. This shows effects due to lattice rotation, which distinguishes the regular versus kinking shear modes of crack tip relaxation. and holds promise for exploring the mechanics of crack opening at the tip.     

Crack tip stresses under creep conditions

Linear elastic fracture mechanics predicts a characteristic distribution of tensile stress ahead of a crack tip in a body subjected to a remote tensile stress normal to the crack faces. The relaxation of this stress distribution, arising from steady state creep behaviour, is here examined. An approximate method, due to Hoff, is used to predict the relaxed stress distribution. The approximate method is reasonable for cases where the elastic strains may be ignored in comparison with the steady state creep strains. The results show that the relaxed steady state stress distribution depends on the steady state creep characteristics of the material.     

焊接接头中的裂端应力三轴性

采用弹塑性有限元方法研究了平面应变条件下裂位于焊缝中心不同强度匹配和裂纹深度焊接接头的裂端应力三轴性。结果发现,与均匀材料相比,同等载荷水平下,高匹配接头裂端应力三轴性降低,低匹配接头裂端应力三轴性升高;随裂纹变浅,应力三轴性降低,强度匹配的影响也更为显著。从焊缝和母材塑性变形与应变硬化交互作用方面进行了解释。     

Crack tip closure and environmental crack propagation

Crack propagation rate, da/dN, and crack tip closure stress, σ_cc, in part-through crack fatigue specimens of aluminum alloys are drastically affected by gaseous environments. The present studies indicate that the crack closure reflects the influence of the environment on the plastic deformation at the crack tip, and, therefore, on the crack propagation rates. Postulating that da/dN is mainly determined by $\text{ΔK}{}_{\mathrm{eff}}\text{∝ (σ}{}_{\max }\text{?σ}{}_{\mathrm{cc}}\text{)}$ (instead of $\text{ΔK ∝ (σ}{}_{\max }\text{?σ}{}_{\min }\text{)}$, as is done traditionally) leads to the relationship $\text{da/dN = A(ΔK}{}_{\mathrm{eff}}\text{)}{}^{\mathrm{n}}$ in which $\text{A}$ and $\text{n}$ are virtually independent of the gaseous environment. The exponents are $\text{n ≈ 3.3}$ for Al 7075 T651 and $\text{n ≈ 3.1}$ for Al 2024 T351, respectively.     

Effect of impurity atoms in ferromagnets on magnetic relaxation

Results are presented from an experimental study of magnetic relaxation in iron specimens containing various amounts of carbon.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 47, No. 6, pp. 991–995, December, 1984.     

Generalized diffusion equation for impurity atoms in semiconductor crystals

A diffusion equation is obtained for impurity atoms migrating by means of the formation of equilibrium complexes with intrinsic point defects, the distribution of which is nonequilibrium and nonuniform.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 57, No. 5, pp. 805–810, November, 1989.     

Experimental evidence of crack tip shielding mechanisms in quasi-brittle materials

To gain insight into the shielding processes in quasi-brittle materials, in situ crack propagation and crack profile measurements were performed inside the scanning electron microscope (SEM). Crack tip shielding phenomena were studied in monolithic alumina and in SiC fibre-reinforced alumina matrix composites as a function of fibre coatings. The crack in the fibre-reinforced composite samples is bridged by a row of fibres which contains a fibre area fraction of 10%. The applied stress intensity factor necessary to extend the crack in the composite materials increased 25% for the gold coated fibre-reinforced alumina matrix composites and 13% for the polymer-coated fibre-reinforced composites, compared to the monolithic samples. Crack extension in the monolithic samples and in the fibre-reinforced composites occurred after the crack opening displacements close to the crack tip approached the critical crack tip profile corresponding to the intrinsic toughness of alumina. A hypothesis on the effect of closure stresses on crack profile shape and net toughness has been developed. Furthermore, crack profiles revealed that grain bridging in the vicinity of the fibres was operative in the fibre-reinforced composites at stress intensity factors far exceeding the critical stress intensity factor of the monolithic matrix material. The additional grain bridging in the vicinity of the fibres has never been reported and can only be revealed through crack profile measurements. This revised version was published online in November 2006 with corrections to the Cover Date.     

Crack tip parameters and elastic-plastic fracture of metals

By using optical displacement-measuring techniques we obtain the crack tip fields in terms of crack tip strain, crack opening angle (COA) and crack tip opening angle (CTOA). Thin plates with different crack configurations made of six elastic-plastic materials with strain hardening exponent ranging from 3 to are studied. We find that the COA resistance curve assumes certain characteristics common to all the materials. The experimental results indicate that the critical value of COA may be used as a fracture toughness parameter for these materials.

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Résumé En utilisant une technique de mesure optique des déplacements, on obtient les champs régnant à l'estrémité d'une entaille, qui s'experiment par la déformation d'extrémité d'entaille, l'angle d'ouverture de la crique (COA et l'angle d'ouverture de la pointe de la crique (CTOA). On étudie des feuillards présentant différentes configurations de fissures et réalisés en six matériaux élasto-plastiques dont les modules d'écrouissage s'échelonnent de 3 à l'infini.On trouve que la courbe de résistance COA suppose certaines caractéristiques communes à tous les matériaux. Les résultats expérimentaux indiquent que la valeur critique du COA peut être utilisée comme paramètre de ténacité à la rupture pour les matériaux étudiés.

     

Nonlinear motion of crack tip atoms during cleavage processes

Nonlinear features of cleavage processes under mode I loading are explored from an atomic scale. Crack tip atom string models coupling with the continuum mechanics analysis are devised. As the stress intensity factor increases, dynamic analysis shows that the atom motion at a crack tip changes from quasi-periodic to chaotic and back to quasi-periodic. The chaotic atom motion characterizes a cleavage precursor in which the inter-atomic bond disintegrates under certain adhesion.     

Crack tip opening displacement in micro-cracked concrete by an embedded optical fiber sensor

Crack tip opening displacement (CTOD) is an important parameter that is often employed in characterization of fracture in engineering materials. Due to inherent difficulties in direct determination of CTOD, the crack mouth opening displacement (CMOD) has been measured during fracture tests of concrete beams and then related to CTOD. Analytical schemes are used for the determination of CTOD from the measured crack mouth opening displacements, which leads to the determination of other fracture parameters of importance. The research presented here describes development of an experimental technique for direct determination of CTOD based on embedded fiber optic sensors. The transduction mechanism is based on the correlation between the applied strain and the light intensity variation of speckle patterns generated at the output end of the multimode optical fiber due to mode redistribution.The measured displacements, CTOD, and CMOD, are compared and the validity of analytical schemes in estimation of CTOD is evaluated.