Effect of cracked weld joint and yield strength dissimilarity on crack tip stress triaxiality

This paper is concerned with an elasto-plastic analysis of a weld joint containing a central crack in the weld material (WM) whose yield strength may differ from that of the base material (BM). Stress triaxiality along the path of expected crack extension is found to be influenced not only by the applied tensile load level and crack length relative to the specimen width but also by the degree of BM/WM mismatch in the yield strength.Three different cases are analyzed by application of a two-dimensional finite element analysis. They are referred to as under-match, even-match and over-match which correspond, respectively, to the WM yield strength being less than, equal to and greater than that of the BM. In general, the stress triaxiality along the crack front tends to increase for an under-matched weld and decrease for an over-matched weld using the even-matched case as a reference. As the crack length is reduced for a given specimen width, the stress triaxiality decreases accordingly and the BM/WM material dissimilarity becomes more obvious. Displayed graphically are also the crack front plastic zone size that increases with the applied tensile load level and suffers a discontinuity across the weld line.     

The near crack tip fields of stress and damage for concrete

The crack tip fields of stress, strain and damage for concrete under both antiplane shear and plane strain conditions are investigated based on the damage model proposed by Mazars and Lemaitre [2]. The structures of near tip fields obtained are similar to those for an elastic-perfectly-plastic material. It has been found that damage boundaries can not be determined by the near-tip analysis due to the discontinuities of stresses on the damage boundaries induced by the damage model used in the present paper.The Project is Supported by National Natural Science Fundation of China.     

Hydrostatic stress and crack opening displacement in three-point bend specimens with shallow cracks

A theoretical analysis is given for the slip-line field in a three-point bend specimen containing a sharp short crack. It is shown that the hydrostatic stresses are larger for deeper cracks. These results support the observation that the crack opening displacement at the initiation of a ductile tear is bigger for shallow cracks than deep ones. An analytical relationship for the ratio of plastic crack tip opening to crack mouth opening displacement is also established which is in agreement with experimental replica measurements. Application of the analysis to practical crack opening displacement measurements for shallow cracks is discussed.     

Equivalence of the notch stress intensity factor,tip opening displacement and energy release rate for a sharp V-notch

For an infinite elastic plane with a sharp V-notch under the action of symmetrically loading at infinity, the length of crack initiation ahead of the V-notch’s tip is estimated according to a modified Griffith approach. Applying a new conservation integral to the perfectly plastic strip (Dugdale model) ahead of the V-notch’s tip, the relationship between notch stress intensity factor (NSIF) and notch tip opening displacement (NTOD) is presented. Also, the relationship between NSIF and perfectly plastic strip size (PPSS) is found. Since there are three fracture parameters (NSIF, NTOD, and PPSS) with changeable notch opening angle in two basic relationships, it is necessary to select one critical parameter with changeable notch opening angle or two independent critical parameters, respectively. With the help of a characteristic length, it is found by this new conservation integral that the NSIF, NTOD and energy release rate are equivalent in the case of small-scale yielding. Especially, the characteristic length possesses clear physical meaning and, for example, depends on both the critical NSIF and SIF or both the NTOD and CTOD, respectively, in which SIF and CTOD are from the tip of a crack degenerated from the sharp V-notch. The dependence of NSIF on NTOD and PPSS is presented according to the equivalence, and the critical NSIF depending on the critical NTOD with a notch opening angle is also predicted.     

Correlation of modified crack tip opening distance with heat input to the heat affected zone of high-strength low-alloy steels

Investigated is the dependency of the crack tip opening displacement (CTOD) on the local microstructure of the heat affected zone in high-strength low-alloy (HSLA) microalloyed steel. Since the initiation of the crack tip location could not be controlled in fatigue, any possible correlation between heat iput in welding and fracture toughness could be smeared. Modified CTOD data are defined; they show that the fracture resistance of the weld joint decreased as the heat input increased.     

Fatigue crack opening stress based on the strip-yield model

The modified strip-yield model based on the Dugdale model and two-dimensional approximate weight function method were utilized to evaluate the effect of in-plane constraint, transverse stress, on the fatigue crack closure. The plastic zone sizes and the crack opening stresses considering transverse stress were calculated for four specimens: single edge-notched tension (SENT) specimen, single edge-notched bend (SENB) specimen, center-cracked tension (CCT) specimen, double edge-notched tension (DENT) specimen under uniaxial loading. And the crack opening behavior of the center-cracked specimen under biaxial loading was also evaluated. Normalized crack opening stresses σ_op/σ_max for four specimens were successfully described by the normalized plastic zone parameter Δω^′_rev/ω^′ considering transverse stress, where Δω^′_rev and ω^′ are the size of the reversed plastic zone at the moment of first crack tip closure and the size of the forward plastic zone for maximum stress, respectively. The normalized plastic zone parameter with transverse stress also was satisfactorily correlated with the behavior of crack closure for CCT specimen under biaxial loading.     

The elastostatic plane strain mode I crack tip stress and displacement fields in a generalized linear neo-Hookean elastomer

A general asymptotic plane strain crack tip stress field is constructed for linear versions of neo-Hookean materials, which spans a wide variety of special cases including incompressible Mooney elastomers, the compressible Blatz–Ko elastomer, several cases of the Ogden constitutive law and a new result for a compressible linear neo-Hookean material. The nominal stress field has dominant terms that have a square root singularity with respect to the distance of material points from the crack tip in the undeformed reference configuration. At second order, there is a uniform tension parallel to the crack. The associated displacement field in plane strain at leading order has dependence proportional to the square root of the same coordinate. The relationship between the amplitude of the crack tip singularity (a stress intensity factor) and the plane strain energy release rate is outlined for the general linear material, with simplified relationships presented for notable special cases.     

Nano-ductile crack propagation in glasses under stress corrosion: spatiotemporal evolution of damage in the vicinity of the crack tip

Recent experiments have evidenced the existence of a ductile fracture mode at the nanometer scale in Aluminosilicate glass. The present study is designed to check whether such a ductile mode is inherent to the amorphous nature of glass. Therefore, the slow crack advance is observed in real time via an Atomic Force Microscope in a minimal glass, amorphous Silica, under stress corrosion. In this case, the Crack propagation proceeds by the nucleation, growth and coalescence of damage cavities as in the Aluminosilicate glass, but the cavity size is significantly larger. We focus here on the kinematics of crack propagation by looking at the spatio-temporal evolution of both the tip of the main crack and the cavity ahead. It is shown that the velocity of the main crack tip is significantly lower than the one of the cavity edge toward the main crack tip, like in metallic alloys. Moreover, the velocities of the different fronts (main crack, frontward and backward cavity tips) at these nanometric scales is one order of magnitude smaller than the crack tip velocity at the continuum scale. This has important consequences for the modelling of stress corrosion, especially at ultra-slow crack propagation.     

Meso-mechanical investigation of the three-dimensional displacement fields around a crack tip

Experimental Techniques -     

Analysis on the cohesive stress at half infinite crack tip

The nonlinear fracture behavior of quasi-brittle materials is closely related with the cohesive force distribution of fracture process zone at crack tip. Based on fracture character of quasi-brittle materials, a mechanical analysis model of half infinite crack with cohesive stress is presented. A pair of integral equations is established according to the superposition principle of crack opening displacement in solids, and the fictitious adhesive stress is unknown function . The properties of integral equations are analyzed, and the series function expression of cohesive stress is certified. By means of the data of actual crack opening displacement, two approaches to gain the cohesive stress distribution are proposed through resolving algebra equation. They are the integral transformation method for continuous displacement of actual crack opening, and the least square method for the discrete data of crack opening displacement. The calculation examples of two approaches and associated discussions are give     

On the determination of elastodynamic crack tip stress fields

A linear elastic body in plane strain which contains a stationary crack and which is initially at rest and stress free is considered. It is shown that if the elastodynamic displacement field and stress intensity factor are known, as functions of crack length, for any symmetrical distribution of time-varying forces which acts on the body, subsequent to t=0, then the stress intensity factor due to any other symmetrical load system whatsoever which acts on the same body may be directly determined. The other load system may be of arbitrary spatial distribution and time variation. Further, that part of the elastodynamic displacement field due to the other load system, which arises from the presence of the crack, may also be directly determined. The results are obtained by extension of Rice's mode of derivation of the corresponding Bueckner-Rice elastostatic results to Laplace-transformed elastodynamic variables. Likewise, the existence of a universal elastodynamic “weight function” for any given cracked body is demonstrated. As an application, Freund's recent result for the stress intensity factor due to suddenly applied concentrated forces on the crack surfaces is derived directly by our method, from de Hoop's earlier solution for suddenly applied uniform pressures.     

Relationships between the J-integral and the crack opening displacement for stationary and extending cracks

Relationships between the J-integral and the crack opening displacement δ_t are obtained by exploiting the dominance of the Hutchinson-Rice-Rosengren singularity in the crack-tip region. The coefficient d_n that relates J to δ_t, is dependent on the material deformation properties and is independent of crack configuration under small-scale yielding conditions. For low hardening materials, d_n appears to be configuration dependent in the fully yielded state. Similarly, the slope of the J-resistance curve is relatable to an operationally defined crack opening angle if J-controlled crack growth conditions are met. These relationships are corroborated by finite element results for the complete regime of elastic-plastic deformation and experimental data for A533B steels, HY-80 steels and several other ductile metals.     

Investigation on critical triaxiality along unified yield loci at crack tip under mixed mode (I + II) fracture

Metallic components used in industries and day to day appliances often contain micro-cracks. In general, cracks occur in various orientations to the loading axis. The present paper discusses the criticality of stress triaxiality, a well-known ductile fracture parameter, on the yield loci at the crack tip. In the process, an old model of stress triaxiality has been generalized using unified strength theory to incorporate various convex and nonconvex failure criteria, including single shear, twin shear, etc. The new triaxiality model also reveals about the effect of intermediate principal stress at the crack tip for materials with and without strength difference. The crack initiation angles at the crack tip, obtained through the proposed model have been found to be in unison with those obtained through other fracture criteria.     

Accumulative damage near crack tip for welded bridge members: fatigue life determination

The behavior of crack growth for the fatigue damage accumulation near tip where damage is most severe is analyzed. Fatigue life is assessed for the welded members of bridges under traffic loading. Two parts are considered. They consist of the development of a fatigue damage accumulation model for welded bridge members and a method for calculating the stress intensity factor that is needed for evaluating the fatigue life of welded bridge members with cracks. Based on the concept of continuum damage accumulation and fatigue and fatigue crack growth relations, results are obtained to describe the relationship between the cracking count rate and the effective stress intensity factor. Crack growth and fatigue life are found for two types of welded members assisted by using fatigue experimental results. The stress intensity factors are modified by correcting for the geometric shape of the welded members in order to reflect the influence of the weldment and geometry. This is accomplished via the stress intensity factor. The calculated and measured fatigue lives were generally in good agreement for the initial cracking conditions of two types of welded members widely used in steel bridges.     

A note on the stress singularity at a non-uniformly moving crack tip

The stress-singularity at a crack tip moving arbitrarily in an elastic plate under plane strain conditions is investigated. By formulating the wave-equations in a polar coordinate system attached to the crack-tip, it is found by an asymptotic analysis that the angle-dependence of the singularity is only dependent on the instantaneous cracktip velocity. This result is used to derive a relation between the dynamic stress-intensity factor and the energyrelease rate.     

A model for piecewise linear stress near the concrete crack tip and the solution

A model for the piecewise linear stress near the tip of a crack in concrete is proposed. Based on this model and FCM, the analytical solutions of the stress and displacement fields for mode I crack in concrete are obtained. The functional relationship between the dimensions of fracture process zone and the initial crack length is established.     

Special approach for the determination of fracture mechanical parameters at an interface crack tip

An interface crack of finite length is considered between two semi-infinite planes with an artificial contact zone at one of the two crack tips. A transcendental equation and certain simple asymptotic formulas are established for the real contact zone (in the Comninou-Dundurs sense) in terms of the stress intensity factors (SIFs) of the considered model. In these terms analytical expressions are also provided for the energy release rate and for the SIF of the classical interface crack model with an oscillating singularity at the crack tip. The appropriate length of the artifical contact zone is shown to be attainable on the basis of the analysis of the stresses at the crack tip. The use of the proposed model is suggested for integrity assessment of inhomogeneous structural elements of composites containing interface cracks. Received 26 March 1997; accepted for publication 12 September 1997     

Computer simulation of creep damage at crack tip in short fibre composites

Creep damage at crack tip in short fibre composites has been simulated by using the finite element method (FEM). The well-known Schapery non-linear viscoelastic constitutive relationship was used to characterize time-dependent behaviour of the material. A modified recurrence equation was adopted to accelerate the iteration. Kachanov-Rabotnov's damage evolution law was employed. The growth of the damage zone with time around the crack tip was calculated and the results were shown with the so-called “digit photo”, which was produced by the printer. The project supported by the National Natural Science Foundation of China and the LNM of Institute of Mechanics, CAS     

On the asymptotics of the stress and strain fields near a crack tip

The problem is solved under the plane strain conditions for a crack of general form, which in general is neither a mode I nor a mode II crack. We assume that the strains are small and the material is nonlinearly elastic. The mathematical statement of the problem is reduced to the eigenvalue problem for a system of ordinary nonlinear differential equations. Its solution is obtained numerically. We show that, for an incompressible material with power-law relations between the stress and strain deviators, the solution (the well-known HRR-asymptotics [1, 2]) exists only for mode I and II cracks. In the general case, we can only speak of approximate solutions. A similar conclusion can be made for different-modulus materials. We analyze the results of the preceding papers [1–7], where specific cases of the problem were considered.