Crack Tip Constraint Research Articles

Effects of crack depth and specimen size on ductile crack growth of SENT and SENB specimens for fracture mechanics evaluation of pipeline steels

Abstract A strong geometry dependence of ductile crack growth resistance emerges under large scale yielding. The geometry dependence is associated with different levels of crack tip constraint conditions. However, in a recent attempt to identify appropriate fracture mechanics specimens for pipeline steels, an “independent” relationship between the crack growth resistance curves and crack depths for SENT specimens has been observed experimentally. In this paper, we use the complete Gurson model to study the effects of crack depth and specimen size on ductile crack growth behavior. Crack growth resistance curves for plane strain, mode I crack growth under large scale yielding conditions have been computed. SENB and SENT specimens with three different specimen sizes, each specimen size with three different crack depths, have been selected. It has been found that crack tip constraint ( Q -parameter) has a weak dependence on the crack depth for specimens in the low constraint regime.

Stationary crack tip fields in elastic–plastic solids: an overview of recent numerical simulations

In this paper, an overview of some recent numerical simulations of stationary crack tip fields in elastic–plastic solids is presented. First, asymptotic analyses carried out within the framework of 2D plane strain or plane stress conditions in both pressure insensitive and pressure sensitive plastic solids are reviewed. This is followed by discussion of salient results obtained from recent computational studies. These pertain to 3D characteristics of elastic–plastic near-front fields under mixed mode loading, mechanics of fracture and simulation of near-tip shear banding process of amorphous alloys and influence of crack tip constraint on the structure of near-tip fields in ductile single crystals. These results serve to illustrate several important features associated with stress and strain distributions near the crack tip and provide the foundation for understanding the operative failure mechanisms. The paper concludes by highlighting some of the future prospects for this field of study.

J– T characterized stress fields of surface-cracked metallic liners bonded to a structural backing – I. Uniaxial tension

Surface crack-tip stress fields in a tensile loaded metallic liner bonded to a structural backing are developed using a two-parameter J–T characterization and elastic–plastic modified boundary layer (MBL) finite element solutions. The Ramberg–Osgood power law hardening material model with deformation plasticity theory is implemented for the metallic liner. In addition to an elastic plate backed surface crack liner model, elastic–plastic homogeneous surface crack models of various thicknesses were tested. The constraint effects that arise from the elastic backing on the thin metallic liner and the extent to which J–T two parameter solutions characterize the crack-tip fields are explored in detail. The increased elastic constraint imposed by the backing on the liner results in an enhanced range of validity of J–T characterization. The higher accuracy of MBL solutions in predicting the surface crack-tip fields in the bonded model is partially attributed to an increase in crack-tip triaxiality and a consequent increase in the effective liner thickness from a fracture standpoint. After isolating the effects of thickness, the constraint imposed by the continued elastic linearity of the backing significantly enhanced stress field characterization. In fact, J and T along with MBL solutions predicted stresses with remarkable accuracy for loads beyond full yielding. The effects of backing stiffness variation were also investigated and results indicate that the backing to liner modulus ratio does not significantly influence the crack tip constraint. Indeed, the most significant effect of the backing is its ability to impose an elastic constraint on the liner. Results from this study will facilitate the implementation of geometric limits in testing standards for surface cracked tension specimens bonded to a structural backing.

Effect of residual stresses on the crack-tip constraint in a modified boundary layer model

Residual stresses play a crucial role in structural integrity assessment. In this study, a large cracked cylinder with a weld in the center is applied to investigate the effect of residual stresses on the crack-tip constraint. A modified boundary layer model with a remote displacement-controlled elastic K-field and T-stress under small scale yielding has been used to simulate the problem. A two-dimensional tensile residual stress field due to the weld is introduced into the model by the so-called eigenstrain method. It has been shown that the residual stresses can significantly elevate the crack-tip constraint and thus increase the probability for cleavage fracture. The constraint parameter R introduced by the authors can be used to rank the crack-tip constraint induced by the bi-axial residual stresses. The R value decreases with the increase in the applied J-integral. The residual stress-induced constraint is also coupled with the T-stress. The R value becomes smaller with larger T-stress.

Experimental investigation on possible dependence of plastic zone size on specimen geometry

In this investigation the extent of the plastic zone size ahead of a crack-tip in single edge notched tension (SENT), compact tension (CT) specimens has been examined experimentally by micro-hardness technique and by elastic-plastic finite element analyses at different applied load levels. The magnitudes of the plastic zone size (PZS), rp ahead of crack-tip in the investigated specimens have been compared using normalized J-integral (J/a?y, where, a-crack length and ?y-yield stress of the material). The results show the dependence of PZS on specimen geometry due to varied in-plane crack-tip constraint. The results also demonstrate that the existing analytical models do not explain the experimental results of PZS satisfactorily.

Mixed-Mode Dynamic Crack Growth in a Functionally Graded Particulate Composite: Experimental Measurements and Finite Element Simulations

Mixed-mode dynamic crack growth behavior in a compositionally graded particle filled polymer is studied experimentally and computationally. Beams with single edge cracks initially aligned in the direction of the compositional gradient and subjected to one-point eccentric impact loading are examined. Optical interferometry along with high-speed photography is used to measure surface deformations around the crack tip. Two configurations, one with a crack on the stiffer side of a graded sheet and the second with a crack on the compliant side, are tested. The observed crack paths are distinctly different for these two configurations. Furthermore, the crack speed and stress intensity factor variations between the two configurations show significant differences. The optical measurements are examined with the aid of crack-tip fields, which incorporate local elastic modulus variations. To understand the role of material gradation on the observed crack paths, finite element models with cohesive elements are developed. A user-defined element subroutine for cohesive elements based on a bilinear traction-separation law is developed and implemented in a structural analysis environment. The necessary spatial variation of material properties is introduced into the continuum elements by first performing a thermal analysis and then by prescribing material properties as temperature dependent quantities. The simulated crack paths and crack speeds are found to be in qualitative agreement with the observed ones. The simulations also reveal differences in the energy dissipation in the two functionally graded material (FGM) cases. T-stresses and hence the crack-tip constraint are significantly different. Prior to crack initiation, larger negative T-stresses near the crack tip are seen when the crack is situated on the compliant side of the FGM.

A model on twinning-induced crack kinking out of a metal-ceramics interface

A continuum model is proposed to study the effects of deformation twinning on interface crack kinking in metal/ceramics layered materials. At the final stage of material failure, plastic work hardening exhausts and lattice rotation becomes main mechanism after competing with dislocation gliding. The crack-tip plasticity is established in terms of the second gradient of microrotation due to the coupling effect of the twins. The formed twinning structures not only shield the crack tip, but inhibit further dislocation emission by increasing the near-tip stress levels. A Dislocation-Free Zone (DFZ) can exist in the immediate vicinity of the tip. The model is based on the equivalence of the stresses derived from twin-based crack-tip plasticity, macroscopic plasticity and elasticity on the boundary. The two-parameter characterization of near-tip stress fields is used for the outer plastic zone to account for constraint effects. Crack kinking out of the interface follows the direction of the maximum flow stress from the crack-tip plasticity. The DFZ size and the crack-tip shielding ratio, as well as the kink angle, are obtained for various values of low hardening exponents and crack-tip constraints.

S94 Study on the Effect of Welding Residual Stresses on Crack-Tip Constraint

S94 Study on the Effect of Welding Residual Stresses on Crack-Tip Constraint

Residual stress induced crack tip constraint

This paper studies the effect of welding residual stresses on the near tip stress field in single edge notched bending and tensile specimens. A combined effect of mechanical stresses by the applied load and residual stress on the crack tip constraint is analyzed. Three initial residual stress distributions were considered. It has been shown that the crack tip stress field is strongly influenced by the residual stresses and a new parameter, R, is proposed to characterize the residual stress induced crack tip constraint. The results therefore suggest a three-parameter approach ( CTOD, Q and R) to characterize the crack tip stress field in the presence of residual stress where CTOD sets the size scale over which large stresses and large strains develop, and the geometry constraint parameter Q and the new residual stress induced constraint parameter R control the actual crack tip constraint level. For the cases analyzed, R is in general positive, which indicates that residual stress can enhance the crack tip constraint. However, the results also indicate that the R decreases towards zero and the effect of residual stress on crack tip constraint can be neglected when a full plastic condition is approached in the specimen.

Finite element formulation of a new nonlocal damage model

It is now widely recognized in literature that the results of the local damage model are mesh dependent. Regularization methods which use gradients of equivalent plastic strain in the material yield function are also popularly known as gradient plasticity models. Many times, these nonlocal forms of equivalent plastic strain have been used as a measure of material damage in the integral and gradient enhanced formulations. Regularization methods based on nonlocal forms of ductile void volume fraction are limited in literature, especially for the Rousselier's model. Moreover, the mesh independent nature of the nonlocal solutions are usually demonstrated with the help of 1D bar, shear band and notched tensile specimens, etc. Comparisons of the nonlocal solutions with those of experiment are hardly done, especially, for problems involving prediction of the fracture resistance behaviour of cracked specimens. In this work, the Rousselier's damage model has been extended to a nonlocal form using the nonlocal damage parameter ‘ d’ as an additional degree of freedom of the finite element (FE) model. The FE equations have been derived using the weak forms of the governing equations for both mechanical stress equilibrium and the damage equilibrium. The mesh independent nature of the model has been demonstrated through various examples, such as an axisymmetric tensile specimen and a standard fracture mechanics specimen (for which predicted results have been compared with those of experiment) using different mesh sizes. The ability of the new model to predict the effect of crack tip constraint on the fracture resistance behaviour has been demonstrated by analysing two different types of standard fracture mechanics specimens.

A numerical study of crack tip constraint in ductile single crystals

In this work, the effect of crack tip constraint on near-tip stress and deformation fields in a ductile FCC single crystal is studied under mode I, plane strain conditions. To this end, modified boundary layer simulations within crystal plasticity framework are performed, neglecting elastic anisotropy. The first and second terms of the isotropic elastic crack tip field, which are governed by the stress intensity factor K and T-stress, are prescribed as remote boundary conditions and solutions pertaining to different levels of T-stress are generated. It is found that the near-tip deformation field, especially, the development of kink or slip shear bands, is sensitive to the constraint level. The stress distribution and the size and shape of the plastic zone near the crack tip are also strongly influenced by the level of T-stress, with progressive loss of crack tip constraint occurring as T-stress becomes more negative. A family of near-tip fields is obtained which are characterized by two terms (such as K and T or J and a constraint parameter Q) as in isotropic plastic solids.

A continuum model of deformation-twin dominant crack growth in fcc metals

A continuum model is proposed to address the effects of deformation twinning on ductile versus brittle fracture behaviour of low strain-hardening fcc metals after exhaustion of work hardening. Instead of discrete twin nucleation, a number of partial dislocations ahead of the tip exhibit themselves as twins at the final stage of failure. The crack-tip plasticity is amended for deformation twinning and the constitutive form for the flow strength of arrays of twins of the same sign is expressed as a second gradient of microrotation for their coupling. The twins not only shield the crack tip but also inhibit further dislocation emission to form a dislocation-free zone (DFZ) in the immediate vicinity of the tip. The stress fields induced by deformation twinning lead to fracture branching under Mode I loading. The model is borrowed from the conceptual model presented by Beltz et al. [Acta Mater. 44 3943 (1996)], based on the equivalence of the stresses derived from twin-based crack-tip plasticity, macroscopic plasticity and elasticity on the DFZ boundary. The DFZ size and the crack-tip shielding ratio are obtained, as well as the branching angle. The branching angle is noteworthy for low strain-hardening metals. A strong dependence of the toughness on intrinsic surface energy and hardening index is examined. The toughness reduction due to crack-tip constraints and in the ductile-to-brittle transition (DBT) temperature region is revisited and found to be in agreement with experimental observations and available predictions.

Experimental and numerical analysis of in-plane and out-of-plane crack tip constraint characterization by secondary fracture parameters

In this study, several two-parameter- concepts are analyzed experimentally and numerically with respect to their capability of characterizing in-plane and out-of-plane crack tip constraint effects. Different approaches utilizing the second term Tstress of the linear-elastic crack tip stress field, a higher term A2 of the power-law hardening crack tip stress field, a hydrostatic correction term Q for a reference stress field or the local triaxiality parameter h are compared. Experimental results for a pressure vessel steel 22NiMoCr3-7 are investigated by means of the different approaches regarding their capability of constraint characterization for enhanced transferability. Theoretical aspects are investigated in a modified boundary layer analysis and in three-dimensional nonlinear elastic-plastic finite element analyses of the specimens. It is found that, with respect to their capability of quantifying combined in-plane and out-of-plane constraint effects, the investigated concepts differ significantly.

Ductile fracture behaviour of primary heat transport piping material

The fracture characteristics of pressure vessel materials must be understood well to implement leak-before-break concepts in the design of pressure vessels. For the construction of primary heat transport piping of Indian pressurised heavy water reactors, SA333 Grade 6 steel is employed, and it is therefore important to understand the fracture behaviour of this steel. The present paper presents the ductile fracture characteristics of SA333 steel at elevated temperatures encompassing the service temperature of the steel, the fracture behaviour under simulated seismic loading and the effect of variation of crack tip constraint on the fracture toughness of the material. Fractographic observations have been carried out to understand the origin of the high level of toughness of the material.

Effect of loading rate on dynamic fracture initiation toughness of brittle materials

Numerical simulation is carried out to investigate the effect of loading rate on dynamic fracture initiation toughness including the crack-tip constraint. Finite element analyses are performed for a single edge cracked plate whose crack surface is subjected to uniform pressure with various loading rate. The first three terms in the Williams’ asymptotic series solution is utilized to characterize the crack-tip stress field under dynamic loads. The coefficient of the third term in Williams’ solution, A3, was utilized as a crack tip constraint parameter. Numerical results demonstrate that (a) the dynamic crack tip opening stress field is well represented by the three term solution at various loading rate, (b) the loading rate can be reflected by the constraint, and (c) the constraint A3 decreases with increasing loading rate. To predict the dynamic fracture initiation toughness, a failure criterion based on the attainment of a critical opening stress at a critical distance ahead of the crack tip is assumed. Using this failure criterion with the constraint parameter, A3, fracture initiation toughness is determined and in agreement with available experimental data for Homalite-100 material at various loading rate.

Observation of Stress Field Around an Oscillating Crack Tip in a Quenched Thin Glass Plate

The variation of stress field around an oscillating crack tip in a quenched thin glass plate is observed using instantaneous phase-stepping photoelasticity. The successive images around the propagating crack are recorded by a CCD camera that is equipped with a pixelated micro-retarder array. Then, the phase maps of the principal stress difference and the principal direction are easily obtained even though the photoelastic fringes cannot be visualized. The path of the crack growth as well as the stress intensity factors and the crack tip constraint are obtained from these phase distributions. Results show that the mode I stress intensity factor and the crack tip constraint vary remarkably with the crack growth. In addition, the results show that the mode-II stress intensity factor exists even though the crack propagates smoothly.

Effect of plastic prestrain on the crack tip constraint of pipeline steels

Before and during operation, pipelines may suffer from plastic pre-deformation due to accidental loading, cold bending and ground movement. Plastic prestrain not only modifies steel's yield and flow properties but also influences its fracture performance. This paper focuses on the effect of prestrain history on crack driving force and crack tip constraint. A single-edge notched tension specimen has been selected for the study and the crack is assumed to exist before a prestrain history was applied. The results show that prestrain history has a strong effect on the crack tip stress field. A new parameter has been proposed to characterize the prestrain-induced crack tip constraint. For the same crack tip opening displacement level, prestrain history will elevate the crack tip stress field. The prestrain-induced constraint decreases with the increase of loading.

The effect of undermatching on crack tip constraint in a welded structure of nodular irons

Abstract The main aim of this paper is to investigate the effect of yield strength mismatch of parent and weld metal on the fracture behavior of plain and heat-treated welded nodular cast iron. For this, experimental and theoretical studies were performed. Nickel electrode, which has lower yield strength value than that of the parent material, was used to join nodular cast iron by cold arc welding method. In experimental study, fracture toughness (J-integral) values were determined for various crack locations including base, weld metal and heat affected zone. In theoretical study, finite element analyses were performed for the same crack locations with different crack lengths. Stress triaxiality and equivalent plastic strain values were determined for all crack locations and various crack lengths. Finally, fracture toughness values of the base metal were determined as lower than those of the other regions including the weld metal and the heat affected zones. Stress triaxiality and equivalent plastic strain values used to clarify the effect of yield strength mismatch on the constraint around crack tip increased with growing crack length in annealed and under-matched models. In annealed models, stress triaxiality values became slightly lower but equivalent plastic strain values appeared higher than those of under-matched models.

J-Q Characterization of Constraint Effects of a Three-Dimensional Cracked Specimen

Failure assessment of the integrity of a ductile flawed structural component is done currently by a one-parameter fracture mechanics approach. The J-integral is the one-parameter used; it has proven to be useful in order to predict ductile crack initiation. However, when tension loading dominates and/or a fully plastic condition develops around the crack, the J-integral alone does not describe completely the crack-tip stress field and a second parameter is needed. In this work, an accurate modeling of the elastic-plastic stress field around a deep crack in a three-dimensional three-point bend specimen is carried out. Numerical results for the crack-tip stress field are used to evaluate a crack-tip constraint parameter Q, in terms of applied loading, from contained plasticity to large-scale yielding. The parameter Q, measures the degree of stress triaxiality and constraint around the crack-tip. In order to obtain the stresses in the near-crack-tip field with high accuracy, a detailed mesh with higher order three-dimensional finite elements is located around the crack front. The modeling of crack-tip blunting deformation is performed by using a small notch radius in the crack-tip. Large-strain and finite-rotation nonlinear behavior effects around the crack-tip are included. The material, an ASTM A 516 steel, is modeled with incremental theory of plasticity. Numerical results of the Q triaxiality parameter are presented for increasing level loads to obtain an extended yield condition. Additional results of J-integral parameter and crack-tip opening displacement, for different load ratios and for different position across the specimen thickness are shown.

Constraint issues in cleavage fracture and matters arising from practical application

In the past 10 years much research has been carried out to deal with the question of how crack-tip constraint effects can be described and, moreover, how crack-tip constraint (stress tri-axiality in the vicinity of the crack tip) contributes to matters arising from practical application of structures and components containing postulated or real cracks and made of ferritic steel. In fracture mechanics, application crack-tip constraint can be influenced by loading (out of plane or multi-axial loading) or by the crack shape and crack depth to ligament ratio. Temperature loading of a crack in a structure is different compared to the loading condition of a fracture toughness specimen and a deep crack behaves differently compared to a short crack. In this paper a model for the prediction of cleavage fracture of ferritic steel is briefly described and summarized and the issues for practical application are pointed out. It turns out that crack-tip constraint, induced either by loading or geometry, can be described quantitatively by local approach models, but there is still a need to understand the micro structural features behind.