Two-Parameter Model of a Mode I Crack in an Elastoplastic Body under Plane-Strain conditions

The Dugdale crack model is generalized to the case of plane strain. The governing equations are set up to determine the stresses in the plastic zone. Numerical results from specific problems are analyzed and compared with those for plane stress state and other cases. A relationship between the crack model and K _I-T theory is established in the case of small-scale yielding at the crack tip __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 6, pp. 44–55, June 2005.     

Two-parameter failure criterion for elastoplastic bodies with mode I cracks

The generalized Dugdale crack model is used to formulate two-parameter failure criteria for the cases of quasibrittle state and developed plastic zones at a mode I crack tip. The failure criteria relate the fracture strength characteristics and the stress mode at the crack tip through the plastic constraint factor. The critical state of bodies with cracks under uni-and biaxial loading is analyzed in the cases of plane stress and plane strain using the Tresca and von Mises yield criteria. A small-scale yield criterion, which is an analytic relation between the critical stress intensity factor and T-stresses, is established __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 7, pp. 47–57, July 2007.     

A centrally cracked thin circular disk, Part I: 3D Elastic–plastic finite element analysis

A full field solution, based on small deformation, three-dimensional elastic–plastic finite element analysis of the centrally cracked thin disk under mode I loading has been performed. The solution for the stresses under small-scale yielding and lo!cally fully plastic state has been compared with the HRR plane stress solution. At the outside of the 3D zone, within a distance of rσ_o/J=18, HRR dominance is maintained in the presence of a significant amount of compressive stress along the crack flanks. Ahead of this region, the HRR field overestimate the stresses. These results demonstrate a completely reversed state of stress in the near crack front compared to that in the plane strain case. The combined effect of geometry and finite thickness of the specimen on elastic–plastic crack tip stress field has been explored. To the best of our knowledge, such an attempt in the published literature has not been made yet. For the qualitative assessment of the results some of the field parameters have been compared to the available experimental results of K, gives a fair estimate of the crack opening stress near the crack front at a distance of order 10⁻² in. On the basis of this analysis, the Linear Elastic Fracture Mechanics approach has been adopted in analyzing the fatigue crack extension experiments performed in the disk (Part II).     

Effect of rising elastic modulus in surface layer on stress intensity and gradient

The relaxation element method is applied to obtain the stress field around a crack under normal tension. A surface layer is assumed to surround the crack periphery taken to be in the shape of a narrow ellipse. The elastic modulus within this layer increases from zero to the bulk value of the medium outside. Calculations show that the stresses are finite at the crack tip; they reach a maximum in the layer and then decay to the well known solution of Griffith outside the layer. The influence of plastic deformation on the crack front stresses can also be simulated by the surface layer model. Stress concentration at the crack front is found to be lower when plastic deformation takes place. Sharp decay of stress next to the crack is accompanied by increase of local stress gradients. Severity of the local stress fluctuation depends on the width of the crack surface layer.     

Reverse shear on inclined planes at the tip of a sharp crack

Plane strain plastic yielding at a crack tip has been represented by edge dislocations with Burgers vectors parallel to symmetrical planes inclined at 70° and 45° to the plane of the crack. The plastic displacement and the stresses near the crack tip were calculated by a numerical method and the effect of a reduction in applied stress was determined. Removal of the whole or a part of the initial load produces reverse shear in regions of the slip band nearest the crack tip. The amount of reverse shear depends only on the reduction in the load and not on its initial value. The reverse shear is associated with the presence of negative dislocations and the stresses near the crack tip may become compressive even though the applied (remote) stress is still tensile. The degree and extent of compression depends on the reduction in applied stress and on its original value. It is argued that the residual compressive stresses produced under fluctuating loads may produce crack closure and crack arrest. The effect of residual plasticity in a slip band left behind a growing crack has been estimated. It is shown that after an overload the excess residual plasticity opposing crack opening rises to a maximum value when the crack tip has advanced some distance from the point where the overload was applied.     

Stress state in the plastic zone on the continuation of an elliptic mode I crack under bi-and tri-axial loading

The spatial stress state in a circular plastic zone near an elliptic crack under bi-and tri-axial asymmetric loading at infinity is studied. It is shown that the plastic constraint factor peaks at the points with maximum external tensile tangential stresses on the crack boundary. The use of a two-parameter failure criterion leads to the conclusion that the limit state can first be reached at the ends of the major axis of the elliptic crack depending on the relation between the external stresses __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 11, pp. 24–30, November 2007.     

Mechanism of Fatigue-Crack Growth under Compressive External Stresses

A specimen with a crack shaped like a thin long defect with parallel edges and a rounded tip of finite radius is considered. When the specimen is subjected to compressive cyclic loads, the stresses in zones adjacent to the crack tip vary according to a sign-variable cycle because of plastic strains occurring at the crack tip. This can cause fatigue-crack growth. Results of numerical simulations and experimental data support the possibility of fatigue-crack growth in the field of compressive external stresses. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 6, pp. 108–115, November–December, 2005.     

Analysis of dynamic growth of a tensile crack in an elastic-plastic material

The influence of inertia on the stress and deformation fields near the tip of a crack growing in an elastic-plastic material is studied. The material is characterized by the von Mises yield criterion and J₂ flow theory of plasticity. The crack grows steadily under plane strain conditions in the tensile opening mode. Features of the stress and deformation state at points near the moving crack tip are described for elastic-perfectly plastic response and for several crack propagation speeds. It is found that inertia has a significant effect on the elastic-plastic response of material particles near the crack tip, and that elastic unloading may occur behind the crack tip for higher speeds. The relationship between the applied crack driving force, represented by a remote stress intensity factor, and the crack tip speed is examined on the basis of a critical crack tip opening angle growth criterion. The calculated result is compared with dynamic fracture toughness versus crack speed data for a 4340 steel.     

Wedge indentation into elastic-plastic single crystals, 1: Asymptotic fields for nearly-flat wedge

Asymptotic stress and deformation fields under the contact point singularities of a nearly-flat wedge indenter and of a flat punch are derived for elastic ideally-plastic single crystals with three effective in-plane slip systems that admit a plane strain deformation state. Face-centered cubic (FCC), body-centered cubic (BCC), and hexagonal-close packed (HCP) crystals are considered. The asymptotic fields for the flat punch are analogous to those at the tip of a stationary crack, so a potential solution is that the deformation field consists entirely of angular constant stress plastic sectors separated by rays of plastic deformation across which stresses change discontinuously. The asymptotic fields for a nearly-flat wedge indenter are analogous to those of a quasistatically growing crack tip fields in that stress discontinuities can not exist across sector boundaries. Hence, the asymptotic fields under the contact point singularities of a nearly-flat wedge indenter are significantly different than those under a flat punch. A family of solutions is derived that consists entirely of elastically deforming angular sectors separated by rays of plastic deformation across which the stress state is continuous. Such a solution can be found for FCC and BCC crystals, but it is shown that the asymptotic fields for HCP crystals must include at least one angular constant stress plastic sector. The structure of such fields is important because they play a significant role in the establishment of the overall fields under a wedge indenter in a single crystal. Numerical simulations—discussed in detail in a companion paper—of the stress and deformation fields under the contact point singularity of a wedge indenter for a FCC crystal possess the salient features of the analytical solution.     

单纤维与裂纹交互微力学:完整粘接纤维

使用微拉曼光谱技术研究裂纹前喙Kevlar49芳纶纤维交互微力学行为.在建立Kevlar49芳纶纤维轴向变形与拉曼频移线性关系的基础上,通过逐点测量裂尖前喙完整粘接纤维上的应力分布,探讨了裂纹与完整粘接纤维的交互作用,建立了完整粘接纤维上的应力传递模型.Ⅰ型裂纹切口前方的高应力区造成粘接完好纤维上出现应力集中,应力强度因子K1影响着纤维应力集中长度.     

Formation of the plastic zone in an anisotropic body with a crack

The influence of the length of a mode I crack on the plastic zone in an anisotropic body under hard loading is studied. The case of a generalized plane stress state is examined. A boundary-value problem is solved numerically to study the behavior of the main plastic zone at the crack tip, the additional plastic zone on the lateral face of the body, and the merged plastic zone Translated from Prikladnaya Mekhanika, Vol. 44, No. 9, pp. 36–52, September 2008.     

Optimization formulation of the evolutionary problem of crack propagation under quasibrittle fracture

For the evolutionary problem describing crack propagation in a solid with allowance for the irreversible work of plastic deformation due to the crack propagation, a general optimization formulation is proposed and investigated. For the optimum crack, data on the H²-smoothnesses of the displacement field in the solid and, hence, on the finiteness of the stress at the crack tip, are obtained. The solvability of the optimization problem (i.e., the existence of an optimum crack) is proved for a curvilinear crack propagation path specified a priori. For the particular case of a straight path, a generalized criterion of crack growth is proposed. The question of the choice of a crack propagation path is discussed and a comparison with existing fracture criteria is made. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 5, pp. 107–118, September–October, 2006.     

Analysis to the stress construction at the vicinity of crack tip for mode I fracture in 3-D state using finite element method

The stresses and strains are calculated for CT specimen of power hardening material in 3-D deformation state using ADINA finite element program, and the stress distribution at the vicinity of crack tip for Mode I fracture is analysed according to the results of calculation. It is found that the expression of stress can be written as the form of separation of variables of r and θ, then the function of r can be expanded in Laurant series. It is still found that the three normal stresses have the same order of magnitude. The conclusions offer two suppositions to obtain the theoretical expression of stress at the vinicity of crack tip for Mode I fracture with good ground, and the procedure of solution will be greatly simplified. This Work is Supported by the National Science Found.     

Singular behavior at the tip of a crack in an elastic-plastic material with plastic orthotropy

The two-dimensional stress field at the tip of a crack in a plastically orthotropic material is analyzed by the total deformation theory of plasticity in conjunction with the J-integral. A model of a plastically orthotropic material is constructed by the use of the theory proposed by R. Hill (1950) and the uniaxial stress-strain relation suggested by W. Ramberg and W.R. Osgood (1943). It is found that the stresses in the vicinity of the crack tip have a singularity of the same order as that in the case of isotropic materials, but their amplitudes are greatly influenced by the plastic orthotropy. Numerical work is carried out for two typical metals, and the effect of the plastic orthotropy is examined for the stress field, the crack opening displacement, the strain energy density, and the shape of the elastic-plastic boundary.     

Mode I and mode II crack tip asymptotic fields with strain gradient effects

The strain gradient effect becomes significant when the size of fracture process zone around a crack tip is comparable to the intrinsic material lengthl, typically of the order of microns. Using the new strain gradient deformation theory given by Chen and Wang, the asymptotic fields near a crack tip in an elastic-plastic material with strain gradient effects are investigated. It is established that the dominant strain field is irrotational. For mode I plane stress crack tip asymptotic field, the stress asymptotic field and the couple stress asymptotic field can not exist simultaneously. In the stress dominated asymptotic field, the angular distributions of stresses are consistent with the classical plane stress HRR field; In the couple stress dominated asymptotic field, the angular distributions of couple stresses are consistent with that obtained by Huang et al. For mode II plane stress and plane strain crack tip asymptotic fields, only the stress-dominated asymptotic fields exist. The couple stress asymptotic field is less singular than the stress asymptotic fields. The stress asymptotic fields are the same as mode II plane stress and plane strain HRR fields, respectively. The increase in stresses is not observed in strain gradient plasticity for mode I and mode II, because the present theory is based only on the rotational gradient of deformation and the crack tip asymptotic fields are irrotational and dominated by the stretching gradient. The project supported by the National Natural Science Foundation of China (19704100), National Natural Science Foundation of Chinese Academy of Sciences (KJ951-1-20), CAS K.C. Wong Post-doctoral Research Award Fund and Post-doctoral Science Fund of China     

J-integral and crack driving force in elastic–plastic materials

This paper discusses the crack driving force in elastic–plastic materials, with particular emphasis on incremental plasticity. Using the configurational forces approach we identify a “plasticity influence term” that describes crack tip shielding or anti-shielding due to plastic deformation in the body. Standard constitutive models for finite strain as well as small strain incremental plasticity are used to obtain explicit expressions for the plasticity influence term in a two-dimensional setting. The total dissipation in the body is related to the near-tip and far-field J-integrals and the plasticity influence term. In the special case of deformation plasticity the plasticity influence term vanishes identically whereas for rigid plasticity and elastic-ideal plasticity the crack driving force vanishes. For steady state crack growth in incremental elastic–plastic materials, the plasticity influence term is equal to the negative of the plastic work per unit crack extension and the total dissipation in the body due to crack propagation and plastic deformation is determined by the far-field J-integral. For non-steady state crack growth, the plasticity influence term can be evaluated by post-processing after a conventional finite element stress analysis. Theory and computations are applied to a stationary crack in a C(T)-specimen to examine the effects of contained, uncontained and general yielding. A novel method is proposed for evaluating J-integrals under incremental plasticity conditions through the configurational body force. The incremental plasticity near-tip and far-field J-integrals are compared to conventional deformational plasticity and experimental J-integrals.     

Effects of surface diffusion and resolved shear stress intensity factor on environmentally assisted cracking

Hydrogen induced crack-tip plastic deformation has been known as the primary mechanism of hydrogen assisted cracking and stress corrosion cracking. It has been systematically shown that the same mechanism of environmentally assisted crack-tip dislocation emission causes hydrogen assisted cracking, stress corrosion cracking, and liquid metal embrittlement cracking.An embrittling chemical species has to reach a crack tip in order to accelerate crack growth. Very close to a sharp crack tip, surface diffusion is shown to be the dominant transport process of embrittling species for stage-II crack growth. The role of surface diffusion in stage II crack growth is analyzed. The constant cracking velocity is proportional to the surface diffusion coefficient of an embrittling species and inversely proportional to a length parameter, , which is related to the transport process upstream.Dislocation emission at a crack tip is driven by crack-tip resolved shear stress. Crack-tip resolved shear stress field is characterized by resolved shear stress intensity factor, K_RSS·K_RSS is defined, the procedure for its calculation outlined, and its applications to crack-tip dislocation emission and environmentally assisted cracking discussed.     

Anti-plane shear cracks in ideally plastic crystals

Cracks in ductile single crystals are analyzed here for geometries and orientations such that two-dimensional states of anti-plane shear constitute possible deformation fields. The crystals are modelled as ideally plastic and yield according to critical resolved shear stresses on their slip systems. Restrictions on the asymptotic forms of stress and deformation fields at crack tips are established for anti-plane loading of stationary and quasistatically growing cracks, and solutions are presented for several specific orientations in f.c.c. and b.c.c. crystals. The asymptotic solutions are complemented by complete elastic-plastic solutions for stationary and growing cracks under small scale yielding, based on previous work by Rice (1967, 1984) and Freund (1979). Remarkably, the plastic zone at a stationary crack tip collapses into discrete planes of displacement and stress discontinuity emanating from the tip; plastic flow consists of concentrated shear on the displacement discontinuities. For the growing crack these same planes, if not coincident with the crack plane, constitute collapsed plastic zones in which velocity and plastic strain discontinuities occur, but across which the stresses and anti-plane displacement are fully continuous. The planes of discontinuity are in several cases coincident with crystal slip planes but it is shown that this need not be the case, e.g., for orientations in which anti-plane yielding occurs by multi-slip, or for special orientations in which the crack tip and the discontinuity planes are perpendicular to the activated slip plane.     

Characterization of crack tip stresses in plane-strain fracture specimens having weld center crack

Fracture toughness of metals depends strongly on the state of stress near the crack tip. The existing standards (like R-6, SINTAP) are being modified to account for the influence of stress triaxiality in the flaw assessment procedures. These modifications are based on the ability of so-called ‘constraint parameters’ to describe near tip stresses. Crack tip stresses in homogeneous fracture specimens are successfully described in terms of two parameters like J–Q or J–T. For fracture specimens having a weld center crack, strength mismatch ratio between base and weld material and weld width are the additional variables, along with the magnitude of applied loading, type of loading, and geometry of specimen that affect the crack tip stresses. In this work, a novel three-parameter scheme was proposed to estimate the crack tip opening stress accounting for the above-mentioned variables. The first and second parameters represent the crack tip opening stress in a homogeneous fracture specimen under small-scale yielding and are well known. The third parameter accounts for the effect of constraint developed due to weld strength mismatch. It comprises of weld strength mismatch ratio (M, i.e. ratio of yield strength of weld material to that of base material), and a plastic interaction factor (I_p) that scales the size of the plastic zone with the width of the weld material. The plastic interaction factor represents the degree of influence of weld strength mismatch on crack tip constraint for a given mismatch ratio. The proposed scheme was validated with detailed FE analysis using the Modified Boundary Layer formulation.     

Analysis of dynamic mixed-mode isochromatics

The mixed-mode, elastodynamic state of stress in the neighborhood of a constant-velocity crack tip is used to generate numerically unsymmetric isochromatics. Unsymmetry associated with the third-order terms of a mixed-mode stress field, with and without the Mode II singular stress term, is also investigated. In extractingK _I from an unsymmetric isochromatic pattern, errors in the Mode I fracture parameters due to the assumed presence ofK _II in aK _I stress field were found to be significant when data are taken more than 4 mm from the crack tip. Paper was presented at V International Congress on Experimental Mechanics held in Montreal, Quebec, Canada on June 10–15, 1984.