Elastic-plastic Crack Front Research Articles

Two-parameter J-A estimation for weld centerline cracks of welded SE(T) specimen under tensile loading

This work examines the J–A two-parameter characterization of elastic–plastic crack front fields for weld centerline cracks under tensile loading. Extensive finite element analyses (FEA) have been conducted to obtain solutions of the A-term for modified boundary layer (MBL) model and welded SE(T) fracture specimen. Solutions of the constraint parameter A were obtained for the material following the Ramberg-Osgood power law with variation of strain hardening exponent between 5 and 20. The crack geometries analyzed include shallow to deep cracks and remote tension loading levels cover from small-scale to large-scale yielding conditions for welded SE(T) specimen. The effects of material mismatch and weldment geometries on crack tip constraint were considered in the FEA based on an idealized tri-material weldment. A constraint parameter AMis, only caused by material mismatch, is defined and its parametric equation was obtained from MBL model. The total constraint in the tri-material weld structure for welded SE(T) specimen can be predicted by adding together AMis and A of homogeneous SE(T) specimen. Overall, Good agreements were achieved for welded SE(T) specimen with different crack sizes and weldment geometries from small-scale to large-scale yielding conditions. This methodology would be useful for performing constraint-based elastic-plastic fracture analyses of other welded test specimens.

Two-parameter characterization of elastic–plastic crack front fields: Surface cracked plates under uniaxial and biaxial bending

In this paper the J–Q two-parameter characterization of elastic–plastic crack front fields is examined for surface cracked plates under static uniaxial and biaxial bending. Extensive three-dimensional elastic–plastic finite element analyses are performed for semi-elliptical surface cracks in a finite thickness plate, under remote uniaxial and biaxial bending conditions, covering from small-scale to large-scale yielding. Surface cracks with aspect ratios a/c=0.2, 1.0 and relative depths a/t=0.2, 0.6, corresponding to four specimen configurations, are investigated. The full stress field solutions are obtained in topological planes perpendicular to the crack fronts. The question of J–Q characterization is addressed by comparing these elastic–plastic crack-front stress fields with J–Q family of stress fields. It is found that the J–Q characterization provides good estimate for the constraint loss for crack front stress fields. It is also shown that for medium load levels, reasonable agreements are achieved between the T-stress based Q-factors and the Q-factors obtained from the finite element analyses. Complete distributions of the J-integral and Q-factors for the wide range of geometry and loading conditions are obtained. Size requirements in terms of crack depth (for shallow cracks) or ligament size (for deep cracks) that are necessary to ensure J–Q characterization of crack front fields in surface cracked plates are also discussed.

J– Q characterized stress fields of surface-cracked metallic liners – II. Composite overwrapped pressure vessels

Two-parameter J– Q elastic–plastic crack front fields are developed for surface-cracked metallic liners of composite overwrapped pressure vessels (COPV). Uniaxial tensile data from 6061-T6 aluminum coupon specimens for the metallic liner and anisotropic elastic material properties for the filament wound carbon fiber epoxy are used in three-dimensional finite element models. Modified boundary layer (MBL) finite element solutions are used to evaluate near tip dominance and parameterization limits. Semicircular surface cracks of varying depths inserted in the inner liner surface are investigated. J and Q crack front distributions, and the corresponding parameterization limits, and near tip triaxiality trends are obtained and the effects of elastic–plastic material discontinuity of the heterogeneous joint and the biaxiality of stresses are evaluated. J– Q predicted fields maintain accuracy for higher far-field loads and lower near tip deformations compared to the liner only models for angles near the free surface. However, for the critical crack growth region, Q does not maintain a radially independent measure of constraint for loads seen in a typical COPV; therefore, these fracture predictors may not be applicable. In the COPV, large-scale yielding marks a transition where triaxiality is higher as a function of constraint compared to the linear relationship common to homogeneous structures. Results from this study will facilitate the implementation of proof test logic and accurate fracture prediction of COPV liners with emphasis on geometric limits and fracture specimen applicability.

Two-parameter characterization of elastic–plastic crack front fields: Surface cracked plates under tensile loading

In this paper the J–Q two-parameter characterization of elastic–plastic crack front fields is examined for surface cracked plates under uniaxial and biaxial tensile loadings. Extensive three-dimensional elastic–plastic finite element analyses were performed for semi-elliptical surface cracks in a finite thickness plate, under remote uniaxial and biaxial tension loading conditions. Surface cracks with aspect ratios a/c=0.2, 1.0 and relative depths a/t=0.2, 0.6 were investigated. The loading levels cover from small-scale to large-scale yielding. In topological planes perpendicular to the crack fronts, the crack stress fields were obtained. In order to facilitate the determination of Q-factors, modified boundary layer analyses were also conducted. The J–Q two-parameter approach was then used in characterizing the elastic–plastic crack front stress fields along these 3D crack fronts. Complete distributions of the J-integral and Q-factors for a wide range of loading conditions were obtained. It is found that the J–Q characterization provides good estimate for the constraint loss for crack front stress fields. It is also shown that for medium load levels, reasonable agreements are achieved between the T-stress based Q-factors and the Q-factors obtained from finite element analysis. These results are suitable for elastic–plastic fracture mechanics analysis of surface cracked plates.

On the quantification of the constraint effect along a three-dimensional crack front

Abstract In this paper we examined the characterization of constraint effects for surface cracked plates under uniaxial and biaxial tension loadings. First, three-dimensional (3D) modified boundary layer analyses were conducted using the finite element method to study the constraint effect at a typical 3D crack front. The analyses were carried out using small geometry change formulation and deformation plasticity material model. Elastic-plastic crack front stress fields at a constant J and various T-stress levels were obtained. Three-dimensional elastic-plastic analyses were performed for semi-circular surface cracks in a finite thickness plate, under remote uniaxial and biaxial tension loading conditions. In topological planes perpendicular to the crack fronts, the crack stress fields were obtained. Then, J-Q and J-T two-parameter approaches are used in characterizing the elastic-plastic crack-tip stress fields along the 3D crack front. It is found that the J-Q characterization provides good estimate for the constraint effect for crack-tip stress fields. Reasonable agreements are achieved between the T-stress based Q-factors and the Q-factors obtained from finite element analysis.

C-Specimen Fracture Toughness Testing: Effect of Side Grooves and η Factor

Elastic-plastic crack front fields in arc-shaped tension specimens (C-specimens) were analyzed by a three-dimensional finite element method. The effect of side grooves on the ductile fracture behavior was investigated by studying the J-integral distribution, plane-strain constraint parameter, and development of plastic zones and comparing to experimental data. The applicability of the η factor (derived for use with compact tension specimens) for the calculation of J-integral values for the C-specimen was also investigated. The results show that side grooves promote and establish near plane strain conditions at the crack front in sub-size specimens. It was also found that a two-dimensional plane-strain analysis in conjunction with the standard American Society for Testing and Materials (ASTM) tests was sufficient to determine the fracture toughness values from side-grooved C-specimen. The results indicate the η factor for compact tension specimen as specified in the ASTM standards appears to produce reliable results for the calculation of J of C-specimens.

Quantification of constraint effects in elastic-plastic crack front fields

In-plane and out-of-plane constraint effects on crack tip stress fields under both small-scale and large-scale yielding conditions are studied by means of three-dimensional numerical analyses of boundary layer models and of finite size specimens, M(T) and SE(B), respectively. It is shown that the ratio of the plastic zone size over the panel thickness, r p t , plays a key role in formation of the crack-tip fields, particularly the outof-plane stress components. For a vanishingly small plastic zone around the crack tip the stress fields are dominated by the plane strain solution. With increase of the applied loads, i.e. increasing the plastic zone size, the stress fields develop towards the plane stress state. Characterization of “constraint effects” in terms of Q-stress is investigated. The “second term” in the near tip stress field, which is defined as the difference between the full three-dimensional stress fields and the plane strain reference solution, appears to depend on the distance to the tip and to the free surface of the specimen. Hence, the whole three-dimensional crack front fields cannot be correctly described by a two-parameter formulation as the load increases. However, a unique linear relationship between Q and the hydrostatic stress was found in all three-dimensional crack front fields.

Enhanced elastic-plastic line-spring finite element

The elastic-plastic line-spring finite element of Parks and White (1982), as implemented in the ABAQUS finite element code (1988b), is modified in several ways for a better evaluation of crack-tip deformation parameters such as K1, J, crack-tip opening displacement and crack-tip stress triaxiality, the last of which is inferred or measured by the so-called T-stress and Q-stress parameters. An effective crack length formulation is introduced to capture the nonlinearity due to contained plane strain crack-tip plastic deformation, the size and orientation of which are known to be sensitive to the sign and magnitude (relative to yield strength) of the T-stress. More accurate yield surfaces, obtained from finite element limit analyses of plane strain single-edge cracked specimens, are employed to more sharply define the behavior of the line-spring model in the fully plastic region. More accurate relationships between incremental plastic crack-tip opening displacement and incremental load point displacement/rotation are also incorporated into the model for shallow crack configurations under fully plastic loading. The modified line-spring model is then applied to surface cracked plate problems having a wide range of crack-tip constraints, and the feasibility of implementing J-T(Q) based two-parameter characterizations of elastic-plastic crack front fields via simplified line-spring elements is examined.