Strain Crack Growth Research Articles

A reassessment of the multiaxial ductility C* creep crack growth equation based on the strain energy integral of the HRR singular field terms

A revaluation of the upper bound plane strain multiaxial C* crack growth rates is undertaken for a range of materials. The analysis assumes that the multiaxial ductility factor can be approximated by taking the integrated dimensionless deviatoric and hydrostatic strain energy density of the HRR singular fields. Using the equivalency approximation between the plastic and elastic strain energy, a damage mechanics approach is used to determine the crack tip triaxial constraint. The new multiaxial factor was found to be independent of the power law behaviour, and for plane stress HRR fields gave a multiaxial factor of close to one. The new factor enables estimates of the upper bound crack rates under plane strain in the Nikbin Smith Webster equation to be undertaken. Creep crack growth data from nine materials were used to assess the new approximation for upper bound crack growth rates. The results suggest the current upper bound plane strain crack growth rates could be decreased from the current thirty times to three times the plane stress results for a range of materials.

Fracture of Irradiated Austenitic Stainless Steel with Special Reference to Irradiation Assisted Stress Corrosion Cracking

This paper deals with fracture of neutron irradiated austenitic Ti-stabilized stainless steel 08Ch18N10T. The steel had been tested in air and in water environment (320°C) using several tests representing different stress strain conditions for crack initiation and growth; Slow Strain Rate and Crack Growth Rate tests were performed in the water. Without irradiation the steel did not suffer from stress corrosion cracking in the water, but on irradiated specimens appeared areas of intergranular fracture mixed with transgranular cleavage-like facets and secondary cracks typical for IASCC phenomenon. The differences between fracture of irradiated and non-irradiated specimens in air and in water are documented and discussed.

A Comparison of the Prediction of Fatigue Damage and Crack Growth in Adhesively Bonded Joints Using Fracture Mechanics and Damage Mechanics Progressive Damage Methods

Lifetime prediction of adhesively bonded joints under constant amplitude fatigue has been carried out using two finite element-based, progressive damage modelling methods. The first method used a fracture mechanics (FM)-based crack growth law in which the relationship between strain energy release rate and crack growth rate under fatigue was determined from experiments using compound double cantilever beam specimens. It was found that the FM approach predicted the fatigue life well at higher fatigue loads but under-predicted the fatigue life at lower fatigue loads. This was attributed to the increasing importance of crack initiation at lower fatigue loads. This problem was solved in the second predictive method, which was based on a continuum damage mechanics approach. A power law relationship to plastic strain was used to define the damage rate. The damage law was able to simulate damage evolution prior to crack growth and excellent predictions of fatigue life were found at all fatigue loads.

Modelling Crack Growth in the Life Assessment of Elevated Temperature Components

Modelling of Creep Crack Growth (CCG) using analytical and numerical methods is relevant to life assessment procedures of components operating at elevated temperatures. This paper compares an analytical crack prediction and a numerical based virtual CCG technique used in fracture mechanics components with sample experimental results. Two approaches are presented. First the well developed strain exhaustion model called the NSW and the modified NSW-MOD models which predict plane stress/strain bound crack initiation and growth rates for engineering alloys and the second a damage-based approach used to numerically predict the crack propagation rate in Finite Element models of fracture mechanics specimens. The results from both methods are correlated against an independently determined C* parameter. As an example the NSW and the extended NSW-MOD strain exhaustion models are applied to compare to the experimental data and FE predictions for two steels at Carbon-Manganese steel tested at 360 oC and a weld 316H stainless steel at 550 oC. For values of C* within the limits of the present creep crack growth data presented the plane strain crack growth rate predicted from the numerical analysis is found to be less conservative than the plane strain NSW model but more conservative than plane strain NSW-MOD model.

3D-FEM Simulation for EAC Crack Growth Evaluation and its Implication to Specimen Size Effects on Crack Growth Behavior

The primary objective of this study is to develop a quantitative model to predict the effects of materials, environment and mechanics such as loading configuration on environmentally-assisted cracking (EAC) of stainless steels in high-temperature water. It has basically been accepted that crack propagation in oxygenated high temperature water is controlled by a slip-dissolution and/or deformation-oxidation mechanism. According to this mechanism, the crack-tip strain rate is an extremely important mechanical parameter for determining the crack growth rates. Based upon a formulation obtained by combining Faraday’s equation with an elastic plastic analysis of the strain singularity at a growing crack-tip in work hardening materials, a theoretical formulation of crack-tip strain rate has been derived for plane strain and plane stress conditions. The FEM analysis for 3D crack growth can be compared to the theoretical 2D analysis. In this paper, we first make a CCP (Center Crack Plane) model, and performed a 3-dimensional Finite Element Analysis (3D-FEA) to evaluate the crack-tip stain rate paying attention to the element mesh size and to the loading history. After optimization these parameters, the calculated crack-tip strain distribution, including its logarithmic singularity, was founded to agree well with the theoretical distribution. The significance of the crack-tip strain rate upon the crack-tip strain distribution and crack growth rate was demonstrated. The specimen size effects on crack growth rates were discussed from this point of crack-tip strain distribution. Finally, we focused on the importance of crack-tip strain rate as a unique mechanical parameter that controls the crack growth rate.

Intergranular Stress Corrosion Cracking of Platinum Treated Type 304 Stainless Steels in High Temperature Water

Electrochemical polarization analyses, slow strain rate tensile (SSRT) tests and crack growth tests were conducted to investigate the intergranular stress corrosion cracking (IGSCC) characteristics of platinum treated Type 304 stainless steels in 288°C pure water. All specimens were thermally sensitized and pre-oxidized before the tests, and some of them were additionally treated with platinum via hydrothermal deposition. Test environments were specifically designed in a circulation loop to create water chemistry conditions of hydrogen to oxygen molar ratios (MH/O)of 0, 0.5, and 2.7 in the coolant. Test results showed that the corrosion current densities of the specimens treated with platinum were higher than those of the pre-oxidized ones under oxygenated conditions, but the corrosion potentials of the treated specimens could be either lower or higher than those of the untreated ones. In addition, IGSCC was not observed on all specimens (treated or untreated) when the MH/O in the test coolant was 0.5 or 2.7. However, the platinum treated specimens actually showed severer IGSCC after the SSRT tests conducted under the coolant condition of MH/O=0. Crack growth test results indicate a similar but worse trend to that in the SSRT tests. It was therefore suggested that one must exercise extra caution to use corrosion potential as a sole indicator in evaluating the influence of noble metal treatment on the IGSCC susceptibility of Type 304 stainless steels, especially when the MH/O in the coolant is relatively low or the dissolved oxygen concentration remains comparatively high.

Creep crack growth prediction using a damage based approach

This paper presents a numerical study of creep crack growth (CCG) in a fracture mechanics specimen. The material properties used are representative of a carbon–manganese steel at 360 °C and the constitutive behaviour of the steel is described by a power law creep model. A damage-based approach is used to predict the crack propagation rate in a compact tension specimen and the data are correlated against an independently determined C ∗ parameter. Elastic–creep and elastic–plastic–creep analyses are performed using two different crack growth criteria to predict crack extension under plane stress and plane strain conditions. The plane strain crack growth rate predicted from the numerical analysis is found to be less conservative than the plane strain upper bound of an existing ductility exhaustion model, for values of C ∗ within the limits of the present CCG testing standards. At low values of C ∗ the predicted plane stress and plane strain crack growth rates differ by a factor between 5 and 30 depending on the creep ductility of the material. However, at higher loads and C ∗ values, the plane strain crack growth rates, predicted using an elastic–plastic–creep material response, approach those for plane stress. These results are consistent with experimental data for the material and suggest that purely elastic–creep modelling is unrealistic for the carbon–manganese steel as plastic strains are significant at relevant loading levels.

Thermodynamic equivalence of steady-state shocks and smooth waves in general media; Applications to elastic-plastic shocks and dynamic fracture

By comparing the First Law of thermodynamics in its shock wave form to its smooth wave form, and applying standard continuum mechanical conservation laws and geometrical compatibility, we prove for arbitrary media that a shock wave which propagates without rotating under steady-state conditions is thermodynamically identical to a suitably-chosen steadily propagating smooth wave (and that this is not so in general for nonsteady shocks). This legitimizes the derivation of restrictions on steady-state shock waves by the analysis of suitably-chosen steady smooth waves in purely mechanical material models. Doing so for a broad class of rate-independent elastic-plastic materials rigorously corroborates several recentlypublished shock restrictions whose derivations involved some (now validated) heuristic arguments, and substantially generalizes the material class for which these restrictions apply. Thus, e.g. within smalldisplacement-gradient theory, stress jumps are ruled out across steadily propagating shock waves in quasistatic deformations of any nonsoftening material satisfying plastic normality and positive-definiteness of the elastic modulus tensor (removing the previous limitation of this result to materials that satisfy the global maximum plastic work inequality and whose current yield locus always incorporates all prior yield loci). We also confirm that steady-state shock waves in dynamic anti-plane strain or plane strain deformations cannot exist except at elastic wave speeds for nonhardening materials in the same broad constitutive class unless the yield surface contains a linear segment. Application of these results to steady-state dynamic subsonic plane strain crack growth in elastic-ideally plastic Prandtl-Reuss-Mises material proves that this problem's solution must be shock-free. This implies that certain solutions containing strong discontinuity surfaces, obtained in a recently-published numerical finite element study of this dynamic crack growth problem, are not physically realizable. The conclusion is that either a more robust numerical procedure is necessary which incorporates the thermodynamics-mandated shock restrictions derived here, or that steadystate subsonic dynamic plane-strain elastic-plastic crack growth is not possible in this material model (and potentially not in nature for materials exhibiting plastic normality, purely nonlinear yield surfaces and no hardening).

Study of stable crack growth resistance based on local displacement at the crack tip: Study of evaluation of stable crack growth resistance of mismatched welded joints (3rd Report)

Summary The previously reported numerical results of stable crack growth simulations (three-dimensional FEM analysis) using equivalent plastic strain show good agreement with the experimental results despite heterogeneous specimens being tested. The results show that the equivalent plastic strain is a characteristic value not susceptible to the effect of strength mismatch in the ductile fracture process. To determine the equivalent plastic strain, however, it is necessary to perform three-dimensional FEM calculations, whereas the local displacement is satisfactorily obtainable by experimental measurements regardless of numerical simulations. The local displacement is affected by the measurement distance from the initial crack tip. The value of the local displacement at the shifted location of the crack tip does not change with an increase in stable crack growth. The authors also specify a similar relationship between the equivalent plastic strain and stable crack growth in a previous publication. The local displacement measured at the mid-thickness is not susceptible to the effect of strength mismatch, but such measurements are never easy to perform. When, for practical purposes, the local displacement is measured on the specimen surface, the effect of strength mismatch on the ratio of the local displacement at the specimen surface to its value at the mid-thickness should be determined. The strain estimated by the local displacement can be used as a substitute for the equivalent plastic strain. Moreover, it expresses the stable crack growth resistance of mismatched joints in terms of the local displacement measured on the specimen surface.

Strip model plasticity analysis of mixed mode crack opening displacement in aluminum alloy LY12

Under mixed mode loading, the crack tip blunts and undergoes displacements in two directions, the normal and shear component corresponding to Mode I and Mode II loading, respectively. These local displacements are determined by the duplicated film method and used to analyze the behavior of mixed mode fracture in aluminum alloy LY12. The mixed mode resultant crack opening displacement (COD) at fracture initiation tends to increase more rapidly with increase of the Mode II shear component. The fracture initiation value of COD for pure Mode II loading is six (6) times greater than that for Mode 1 loading. The same applies to the maximum effective plastic strain crack growth near the crack front. Observed are two typical morphologies, the equal-axes dimples and the parabolic dimples with evidence of slippage as dominated, respectively, by Mode I and Mode II loading.

Crack Initiation in Fiber‐Reinforced Brittle Laminates

In fiber‐reinforced brittle laminates, crack growth under monotonic tension generally consists of crack tunneling along the weaker ply (usually the 90° ply) followed by plane strain crack growth through the adjacent, more resistant plies (the 0° plies). In this paper, the details of this transition in crack mode are examined. The tunneling crack configuration is generalized to allow the crack to penetrate the 0° ply during tunneling. The effects of crack bridging in the 0° plies on the energetics of tunneling are computed numerically for general cases and combined with analytical results for certain limits. The nature of the transition from tunneling to plane strain cracking is found to depend on the ratio of the toughnesses of the 90° and 0° plies. Implications for laminate design are discussed.

Elastic-plastic crack growth on plane strain bimaterial interface

Finite element computation are carried out to simulate plane strain crack growth on a bimaterial interface under the assumption of small scale yielding. The modified Gurson constitutive equation and the element vanish technique introduced by Tvergaard et al. are used to model the final formation of an open crack. It is found from the calculation that the critical fracture toughness for crack growth is much lower in bimaterials than that in homogeneous material. The critical fracture toughness is strongly dependent on material properties of the bimaterial pair and the mixed mode of remote loads. The interface crack grows in the more compliant (lower hardening) material or in the weaker (lower yield strength) material. In Mode-I loading, the crack grows zigzag along the interface.

Analysis of the spontaneous interfacial decohesion of a thin surface film

Results of a numerical and experimental study of thin film delamination are reported. Spontaneous delamination is induced by a cut in a thin film attached to a substrate. The delamination is driven by the residual stress caused by thermal strain mismatch between the film and substrate. From the measured shape of the delamination, interfacial fracture criteria are examined. Parametric studies of fracture criteria are carried out numerically using a boundary integral equation (BIE) formulation. The analysis includes a new numerical scheme, based on the M-integral, for evaluating the stress intensity factor at the ends of the cut. Experiments are conducted with a polyimide film on a glass substrate. The level of residual stress is controlled by thermal strain mismatch between the film and substrate, varying the test temperature in the range of 20–255°C. Both numerical and experimental studies cover delamination of large extent. The experiment shows that the polyimide—glass interface is much tougher in the anti-plane shearing mode (mode 3). The measured interface toughness is 4.1–4.5 J/m 2 for plane strain crack growth caused by tensile residual stress of the film. On the other hand, the measured mode 3 fracture toughness of the interface is 14.9–16.5 J/m 2.

Crack growth in oriented SiC-whisker-reinforced 2124 aluminum composites

Fatigue crack growth behavior has been examined in an oriented 5 vol.% SiC-whisker-reinforced 2124 aluminum composite. Both macro- and microcrack growth were found to depend on the whisker orientation and applied stress intensity. Macrocrack extension, either parallel or perpendicular to the primary whisker orientation, was self-similar, independent of the maximum stress intensity, while crack growth at other orientations depended on the orientation and maximum stress intensity. At a fixed angle between the principal whisker direction and the mode I crack plane, decreasing K max led to an increasing tendency for crack deflection and propagation along the principal reinforcement direction. A model to account for the dependence of the plane strain crack growth direction on the stress intensity level and whisker alignment is presented. Microcrack extension, at orientations other than parallel to the primary whisker direction, involved the avoidance of whisker-rich regions at low K max and wedging, whisker bridging and fracture-pull-out at higher K max. Little interaction with SiC whiskers was noted when the crack propagation was parallel to the primary whisker orientation.

Stress Corrosion Cracking of Inconel Alloys and Weldments in High-Temperature Water — the Effect of Sulfuric Acid Addition

Abstract The stress corrosion cracking (SCC) susceptibilities of Alloys 600 and 690, AISI 316 NG stainless steel (SS), ASTM A508 carbon steel, and a number of compatible weld metals have been evaluated at 288 C in pure water and in pure water containing sulfuric acid additions. The sulfuric acid was added to simulate the effects of a resin release from the demineralizer system of a boiling water reactor (BWR). A combination of creviced and noncreviced slow strain rate, constant load, and crack growth rate tests were used in the evaluation. The results indicated that all of the alloys tested in the uncreviced condition were immune to cracking in the pure water environment. The presence of crevices in the pure water environment produced a susceptibility to SCC in Alloy 600, in Inconel I-82 and I-182 weld metals, and ASTM A508 steel, but not in Alloy 690. Cracking was enhanced by the addition of 1 ppm H2SO4 in slow strain rate tests (SSRTs) and constant load tests, but crack growth rates were not enhanced. All of the alloys tested in the resin intrusion environment were susceptible to cracking, except for the high chromium weld metals R-135 and Inconel I-72.

The effect of reverse bending on the instability of (a) plane strain crack growth in a beam and (b) through-wall circumferential crack growth in a pipe

A theoretical analysis for a ductile material shows that (a) plane strain growth of a deep crack in a beam and (b) growth of a long through-wall circumferential crack in a pipe are more likely to be unstable when the bending is such as to close the crack where it intersects with the free surface than if the bending is such as to open the crack.

The stability of growth of a through-wall circumferential crack in a pipe subject to combined bending and tensile loadings

The stability of growth of a through-wall circumferential crack in a pipe is analysed for the case where the material has a high crack growth resistance, the analysis being based on the tearing modulus procedure. Rotations and lateral displacements are applied at the ends of the pipe, and this allows the combined effects of bending and tensile loadings on the stability of crack growth to be assessed. The general conclusion is that tensile loadings can have an adverse effect on crack stability, in accord with the conclusion reached in the author's earlier studies of plane strain crack growth in a beam. The stability results are compared with those obtained by Tada, Paris and Gamble, who allowed the tensile loadings to affect the position of the neutral axis, but did not consider instability in terms of the deformations produced by these loadings.

Plane strain crack growth in a ductile solid subject to bending deformation

Plane strain crack growth in a ductile solid subject to bending deformation is modelled from the basis that crack growth is associated with the maintenance of a constant crack tip opening angle. A theoretical analysis focuses on the stability or otherwise of crack growth under fixed displacement conditions, particular consideration being given to the possibilities that (a) instability might occur after some stable crack growth, and (b) arrest might occur after some unstable growth. The conclusions have relevance to practical problems such as the stability of through-wall circumferential cracks in pipes.

Predicting stress corrosion crack growth rates at high stress levels II: The general yield situation

In an earlier paper by the present author a methodology for predicting the growth rate of a stress corrosion crack at high stress levels was developed. It was assumed that the cracktip-opening angle (CTOA) depends on the growth rate d c/d t. A functional relation between these two parameters was obtained by coupling theoretical results for plane strain (inert environment) crack growth under small-scale yielding conditions with the experimentally determined power law relation between the crack tip stress intensity K and d c/d t for environmentally assisted crack growth under linear elastic fracture mechanics (LEFM) conditions. On the assumption that this functional relation is valid outside the LEFM regime, then by determining the CTOA at high stresses, it is in principle possible to predict the stress corrosion crack growth rate at high stresses. A specific model was analysed: that of an edge crack in a solid subjected to a sustained tensile stress such that yielding was extensive although contained; with this model, J increases as the crack propagates. It was concluded that high stress crack growth predictions based on the usual LEFM procedures will be non-conservative in cases where d J/d c is positive. In this paper the earlier work is extended by examining a case where there is general yield and where J remains constant during crack propagation. In this case, crack predictions based on LEFM procedures are conservative.

Some comments on the geometry dependence of theJ versusc relation for plane strain crack growth

Rice, Drugan, and Sham have recently presented a discussion on the elastic-plastic stress and deformation fields at the tip of a crack growing in an ideally plastic solid under plane strain small-scale yielding conditions. Coupling their asymptotic analysis results with a crack tip opening angle criterion which requires that a constant angle 0 (measured at a characteristic distancer m behind the tip) be maintained, leads to a differential equation describing crack growth: $$\frac{{dJ}}{{dc}} = \frac{{\sigma _0 \theta }}{\alpha } - \frac{{\beta \sigma _0^2 }}{{\alpha E}}\ln \lgroup {\frac{{eR}}{{r_m }}} \rgroup,$$ wherec = crack length, σo = yield strength,E = Young's modulus, andJ denotes the far-field value of theJ integral: (1 − ν2)K2/E for small-scale yielding conditions, where ν = Poisson's ratio. The asymptotic analysis thatβ = 5.08 (for ν = 0.3), but does not give the values of the parameters α andR. However, comparisons with finite element results suggest that α has approximately the same value for stationary and growing cracks, whileR scales approximately with the plastic zone size. For large-scale yielding, Rice, Drugan, and Sham argue that a similar growth equation is expected to apply with possible variations in α and β at least in cases which maintain triaxial constraint at the crack tip. They speculate thatR increases linearly withJ at first, but then saturates in the general yield state at some fraction of the dimension of the uncracked ligament. The present paper analyses the highly idealized Dugdale-Bilby-Cottrell-Swinden model of a growing crack tip, and the results provide support for the speculations regarding the magnitude ofR in the large-scale plasticity and general yield states.