A criterion for plane strain,fully plastic,quasi-steady crack growth

Plane strain fracture by hole growth in ordinary-sized parts of low-to-medium strength steels is essentially rigid-plastic, and may be approximated as non-hardening. Quasi-steady crack growth for such materials is predicted for crack-tip fields approximated by a pair of slip lines, such as unequally grooved specimens in tension and deep singly-face-cracked specimens under combined bending and tension. The crack growth increment a is given in terms of material parameters, far-field geometry, and loadings and their increments.For the rigid-plastic, non-hardening approximation, stress and strain increment fields for growing cracks are identical to those for stationary cracks. For fields with a pair of symmetric slip-lines, the flanks of the decohering zone turn out to be rigid, and the decohering zone does not affect the crack-tip opening angle (CTOA), which then depends only on the micromechanisms of hole nucleation, growth and linkage by flow localization or fine cracking. These mechanisms are in turn approximately controlled by the near-field plasticity parameters: the angle of the slip plane _s, and the normal stress and displacement increment across the slip plane _s and u_s. Note the three-parameter characterization of the near-tip fields, in contrast to the one- or two-parameter characterization in elastic or nonlinear elastic fracture mechanics.A sliding off and shear-cracking model for a growing crack, based on a hole growth equation, gives an approximate CTOA in terms of _s, _s, and material parameters. When hole nucleation strain is negligible, the estimated CTOA exhibits an inverse exponential dependence on _s and a higher order parabolic dependence on _s. For a given material, a series of fully plastic crack growth experiments is suggested to determine the approximate material parameters needed to characterize the dependence of CTOA on _s and _s, or from kinematics, of the shear strain behind the slip plane, _f, on _s.     

Fully plastic analyses for notched bars and plates using finite element limit analysis

In the present work, fully plastic analyses for notched bars and (plane strain) plates in tension are performed, via finite element (FE) limit analysis based on non-hardening plasticity, from which plastic limit loads and stress fields are determined. Relevant geometric parameters are systematically varied to cover all possible ranges of the notch depth and radius. For the limit loads, it is found that the FE solutions for the notched plate agree well with the existing solution. For the notched bar, however, the FE solutions are found to be significantly different from known solutions, and accordingly the new approximation is given. Regarding fully plastic stress fields, it is found that, for the notched plate, the maximum hydrostatic (mean normal) stress overall occurs in the center of the specimen, which strongly depends on the relative notch depth and the notch radius-to-depth ratio. On the other hand, for the notched bar, the maximum hydrostatic stress can occur in between the center of the specimen and the notch tip. The maximum hydrostatic stress for a given notch depth can occur not for the cracked case, but for the notched case with a certain radius. This is true for both bars and plates. For a given notch radius, on the other hand, the maximum hydrostatic stress increases monotonically with the decreasing notch radius.     

Elastic-plastic fracture mechanics assessment of test data for circumferential cracked pipes

This paper presents experimental validation of two reference stress based methods for circumferential cracked pipes. One is the R6 method where the reference stress is defined by the plastic limit load. The other is the enhanced reference stress method, recently proposed by the authors, where the reference stress is defined by the optimised reference load. Using 38 published pipe test data, the predicted maximum instability loads according to both methods are compared with the experimental ones for pipes with circumferential through-thickness cracks and with part circumferential surface cracks. It is found that the R6 method gives conservative estimates of the maximum loads for all cases. Ratios of the experimental maximum load to the predicted load range from 0.54 to 0.98. On the other hand, the proposed method gives overall closer maximum loads than R6, compared to the experimental data. However, for part through-thickness surface cracks, the estimated loads were slightly non-conservative for four cases, and possible reasons are fully discussed.     

Finite element plastic loads for circumferential cracked pipe bends under in-plane bending

This paper proposes plastic loads (limit load and twice-elastic-slope (TES) plastic load) for pipe bends with circumferential through-wall and part-through surface cracks under in-plane bending, based on three-dimensional FE limit analyses. The material is assumed to be elastic-perfectly plastic, and both the geometrically linear (small strain) and nonlinear (large geometry change) effects are considered. Regarding a crack location, both extrados and intrados cracks are considered. Based on the FE results, closed-form approximations of limit and TES plastic loads are proposed for practical applications, and compared with corresponding solutions for straight pipes.     

Development of stress-modified fracture strain for ductile failure of API X65 steel

The present paper proposes ductile failure criteria in terms of true fracture strain (the equivalent strain to fracture) as a function of the stress triaxiality (defined by the ratio of the hydrostatic stress to the equivalent stress) for the API X65 steel. To determine the stress-modified fracture strain, smooth and notched tensile bars with four different notch radii are tested, from which true fracture strains are determined as a function of the notch radius. Then detailed elastic–plastic, large strain finite element analyses are performed to estimate variations of stress triaxiality in the tensile bars, which leads to true fracture strains as a function of the stress triaxiality, by combining them with experimental results. Two different failure criteria are proposed, one based on local stress and strain information at the site where failure initiation is likely to take place, and the other based on averaged stress and strain information over the ligament where ductile fracture is expected. As a case study, ligament failures of API X65 pipes with a gouge are predicted and compared with experimental data.     

Limit loads and approximate J estimates for axial through-wall cracked pipe bends

This paper presents plastic limit loads and approximate J estimates for axial through-wall cracked pipe bends under internal pressure and in-plane bending. These loads and estimates are based on small strain finite element limit analyses using elastic-perfectly plastic materials. Geometric variables associated with the crack and pipe bend are systematically varied, and three possible crack locations (intrados, crown and extrados) are considered. Effects of the bend and crack geometries on plastic limit loads are quantified, and closed-form limit load solutions are given. Based on the proposed limit load solutions, a reference stress based the J estimation scheme for axial through-wall cracked pipe bends under internal pressure and in-plane bending is proposed.     

Net-section limit moments and approximate J estimates for circumferential cracks at the interface between elbows and pipes

This paper firstly presents net-section limit moments for circumferential through-wall and part-through surface cracks at the interface between elbows and attached straight pipes under in-plane bending. Closed-form solutions are proposed based on fitting results from small strain FE limit analyses using elastic–perfectly plastic materials. Net-section limit moments for circumferential cracks at the interface between elbows and attached straight pipes are found to be close to those for cracks in the centre of elbows, implying that the location of the circumferential crack within an elbow has a minimal effect on the net-section limit moment. Accordingly it is also found that the assumption that the crack locates in a straight pipe could significantly overestimate the net-section limit load (and thus maximum load-carrying capacity) of the cracked component. Based on the proposed net-section limit moment, a method to estimate elastic–plastic J based on the reference stress approach is proposed for circumferential cracks at the interface between elbows and attached straight pipes under in-plane bending.     

Plastic loads of pipe bends under combined pressure and out-of-plane bending

This paper provides plastic limit and TES (twice-elastic-slope) plastic load solutions for 90° pipe bends under combined pressure and out-of-plane bending, via three-dimensional non-linear FE analyses using elastic-perfectly plastic materials. Without internal pressure, a closed-form approximation is given. For combined pressure and out-of-plane bending, tabulated data are given, from which TES plastic loads can be interpolated. It is found that TES plastic loads for pipe bends under out-of-plane bending are lower than those under in-plane opening bending, but are higher than those under in-plane closing bending. It suggests that the in-plane closing bending mode is the most critical loading mode for 90° pipe bends, which is fully consistent to existing findings.     

Determination of tensile properties and residual stresses of Ni-Co thin films

This paper reports tensile properties and residual stresses of Ni-Co thin films. To measure elastic (and plastic) properties, direct tensile tests using dog-bone type specimens are performed first. Assuming that residual stresses vary linearly through the film thickness, bending and membrane residual stress components are measured using cantilever beam and T-structure beam specimens, respectively. Averaged values of Young’s modulus, yield strength and tensile strength are found to be about 163GPa, 1,700MPa and 2,000MPa, respectively. The membrane and bending residual stress components are found to be about 825MPa and 47MPa, respectively.     

Reference Stress Approximations for J and COD of Circumferential Through-Wall Cracked Pipes

Reference stress approximations for the J integral and crack tip opening displacement (COD) for circumferential through-wall cracked pipes under tension and under bending are reported. The proposed J estimation equation is fully compatible with the existing reference stress based J estimation, currently embedded in the R6 assessment procedure, but involves a slightly different definition of the reference stress, using an optimised reference load instead of the limit load. This modification enhances the accuracy of the J estimation for circumferentially cracked pipes. Confidence in the proposed equation is gained from the significantly reduced hardening dependence of the plastic influence functions in the GE/EPRI method. The proposed COD estimation equation includes two further modifications. One is the use of a power-law fit to the plastic portion of the stress strain data, instead of the use of the actual stress strain data. In this context, a robust estimation equation for the strain hardening index is given. The other modification is to the plasticity correction term in contained yielding. A lower bound COD estimation equation is also given, similar to the R6 option 1 Jestimation curve, which is suitable when only limited tensile properties are available. The resulting estimation equations are simple to use. Comparisons with experimental pipe test data show that the proposed COD estimation equations provide overall good agreement, which gives confidence in applying them to Leak-before-Break (LBB) analyses.