Constraint effects on multiple void interaction in pressure sensitive plastic solids

In this work, effects of pressure sensitive yielding and plastic dilatancy on void growth and void interaction mechanisms in fracture specimens displaying high and low constraint levels are investigated. To this end, large deformation finite element simulations are carried out with discrete voids ahead of the notch. It is observed that multiple void interaction mechanism which is favored by high initial porosity is further accelerated by pressure sensitive yielding, but is retarded by loss of constraint. The resistance curves predicted based on a simple void coalescence criterion show enhancement in fracture resistance when constraint level is low and when pressure sensitivity is suppressed.     

A finite element analysis of quasistatic crack growth in a pressure sensitive constrained ductile layer

Polymeric adhesive layers are employed for bonding two components in a wide variety of technological applications. It has been observed that, unlike in metals, the yield behavior of polymers is affected by the state of hydrostatic stress. In this work, the effect of pressure sensitivity of yielding and layer thickness on quasistatic interfacial crack growth in a ductile adhesive layer is investigated. To this end, finite deformation, finite element analyses of a cracked sandwiched layer are carried out under plane strain, small-scale yielding conditions for a wide range of mode mixities. The Drucker–Prager constitutive equations are employed to represent the behavior of the layer. Crack propagation is simulated through a cohesive zone model, in which the interface is assumed to follow a prescribed traction–separation law. The results show that for a given mode mixity, the steady state fracture toughness |K|_ss is enhanced as the degree of pressure sensitivity increases. Further, for a given level of pressure sensitivity, |K|_ss increases steeply as mode II loading is approached.     

Influence of crack tip constraint on void growth in ductile FCC single crystals

Effect of constraint (stress triaxiality) on void growth near a notch tip in a FCC single crystal is investigated. Finite element simulations within the modified boundary layer framework are conducted using crystal plasticity constitutive equations and neglecting elastic anisotropy. Displacement boundary conditions based on mode I, elastic, two term K-T field are applied on the outer boundary of a large circular domain. A pre-nucleated void is considered ahead of a stationary notch tip. The interaction between the notch tip and the void is studied under different constraints (T-stress levels) and crystal orientations. It is found that negative T-stress retards the mechanisms of ductile fracture. However, the extent of retardation depends on the crystal orientation. Further, it is found that there exists a particular orientation which delays the ductile fracture processes and hence can potentially improve ductility. This optimal orientation depends on the constraint level.     

Numerical simulations of crack tip fields in polycrystalline plastic solids

In this paper, modes I and II crack tip fields in polycrystalline plastic solids are studied under plane strain, small scale yielding conditions. Two different initial textures of an Al-Mg alloy, viz., continuous cast AA5754 sheets in the recrystallized and cold rolled conditions, are considered. The former is nearly-isotropic, while the latter displays distinct anisotropy. Finite element simulations are performed by employing crystal plasticity constitutive equations along with a Taylor-type homogenization as well as by using the Hill quadratic yield theory. It is found that significant texture evolution occurs close to the notch tip which profoundly influences the stress and plastic strain distributions. Also, the cold rolling texture gives rise to higher magnitude of plastic strain near the tip.     

Effect of constraint on void growth near a blunt crack tip

The growth of a single cylindrical hole ahead of a blunt crack tip was studied using large deformation finite element analysis in three-point bend specimens with different precrack depth. The effect of small second phase particles was taken into account by incorporating Gurson's constitutive equation. The effects of strain hardening and the initial distance from the hole to the crack tip were also investigated. The results show that the variation of crack tip opening displacement with load is not sensitive to constraint level. The effects of constraint on the growth of hole and ductile initiation toughness are diminished with decreasing initial distance from the hole to the blunt crack tip. This revised version was published online in August 2006 with corrections to the Cover Date.     

Three-dimensional modeling of ductile crack growth: Cohesive zone parameters and crack tip triaxiality

For 10 mm thick smooth-sided compact tension specimens made of a pressure vessel steel 20MnMoNi55, the interrelations between the cohesive zone parameters (the cohesive strength, T_max, and the separation energy, Γ) and the crack tip triaxiality are investigated. The slant shear-lip fracture near the side-surfaces is modeled as a normal fracture along the symmetry plane of the specimen. The cohesive zone parameters are determined by fitting the simulated crack extensions to the experimental data of a multi-specimen test. It is found that for constant cohesive zone parameters, the simulated crack extension curves show a strong tunneling effect. For a good fit between simulated and experimental crack growth, both the cohesive strength and the separation energy near the side-surface should be considerably lower than near the midsection. When the same cohesive zone parameters are applied to the 3D model and a plane strain model, the stress triaxiality in the midsection of the 3D model is much lower, the von-Mises equivalent stress is distinctly higher, and the crack growth rate is significantly lower than in the plane strain model. Therefore, the specimen must be considered as a thin specimen. The stress triaxiality varies dramatically during the initial stages of crack growth, but varies only smoothly during the subsequent stable crack growth. In the midsection region, the decrease of the cohesive strength results in a decrease of the stress triaxiality, while the decrease of the separation energy results in an increase of the triaxiality.     

Modelling of nucleation and void growth in dynamic pressure loading, application to spall test on tantalum

Dynamic ductile fracture is a three stages process controlled by nucleation, growth and finally coalescence of voids. In the present work, a theoretical model, dedicated to nucleation and growth of voids during dynamic pressure loading, is developed. Initially, the material is free of voids but has potential sites for nucleation. A void nucleates from an existing site when the cavitation pressure p _c is reached. A Weibull probability law is used to describe the distribution of the cavitation pressure among potential nucleation sites. During the initial growth, the effect of material properties is essentially appearing through the magnitude of p _c. In the later stages, the matrix softening due to the increase of porosity has to be taken into account. In a first step, the response of a sphere made of dense matrix but containing a unique potential site, is investigated. When the applied loading is a pressure ramp, a closed form solution is derived for the evolution of the void that has nucleated from the existing site. The solution appears to be valid up to a porosity of 0.5. In a second part, the dynamic ductile fracture of a high-purity grade tantalum is simulated using the proposed model. Spall stresses for this tantalum are calculated and are in close agreement with experimental levels measured by Roy (2003, Ph.D. Thesis, Ecole Nationale Supérieure de Mécanique et d’Aéronautique, Université de Poitiers, France). Finally, a parametric study is performed to capture the influence of different parameters (mass density of the material, mean spacing between neighboring sites, distribution of nucleation sites...) on the evolution of damage.     

Influence of statistical and constraint loss size effects on cleavage fracture toughness in the transition - A model based analysis

A database derived from tests on specimens with a large range of ligament (b) and thickness (B) dimensions was systematically analyzed to evaluate constraint loss and statistical size effects on cleavage fracture toughness. The objectives were to: (1) decouple size effects related to constraint loss, mediated by b and B, from those arising from statistical effects, primarily associated with B; and, (2) develop procedures to transfer toughness data to different conditions of constraint and B. The toughness database for a Shoreham pressure vessel steel plate, tested at a common set of conditions, was described in a companion paper. Quantification of constraint loss was based on an independently calibrated 3D finite-element critical stress-area, σ^∗-[K_Jm/K_Jc], model. The measured toughness data, K_Jm, were first adjusted using computed [K_Jm/K_Jc] constraint loss factors to the corresponding values for small scale yielding conditions, K_Jc=K_Jm/[K_Jm/K_Jc]. The K_Jc were then statistically adjusted to a K_Jr for a reference B_r = 25.4 mm. The B adjustment was based on a critically stressed volume criterion, modified to account for a minimum toughness, K_min, consistent with modest modifications of the ASTM E 1921 Standard procedure. The combined σ^∗-[K_Jm/K_Jc]-K_min adjustment procedure was applied to the Shoreham b − B database, producing a homogeneous population of K_Jr data, generally within the expected scatter. The analysis suggests that: (1) there may be a maximum B beyond which statistical size effects diminish, and (2) constraint loss in the three-point bend specimens begins at a relatively low deformation level. A corresponding analysis, based on a Weibull stress, σ_w-[K_Jm/K_Jc]-K_min, adjustment procedure, yielded similar, but somewhat less satisfactory, results. The optimized adjustment procedure was also applied to other K_Jm data for the Shoreham plate from this study, as well as a large database taken from the literature. The population of 489K_Jr data points, covering an enormous range of specimen sizes, geometries and test temperatures, was found to be consistent with the same master curve T₀ = −84 °C derived from the b − B database. Thus, calibrated micromechanical models can be used to treat size and geometry effects on K_Jm, facilitating using small specimens and data transfer to predict the fracture limits of structures.     

Effect of lattice orientation on crack tip constraint in ductile single crystals

In this work, the effect of lattice orientation on the fields prevailing near a notch tip is investigated pertaining to various constraint levels in FCC single crystals. A modified boundary layer formulation is employed and numerical solutions under mode I, plane strain conditions are generated by assuming an elastic–perfectly plastic FCC single crystal. The analysis is carried out corresponding to different lattice orientations with respect to the notch line. 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 notch tip are also strongly influenced by the level of T ‐stress. The present results clearly establish that ductile single crystal fracture geometries would progressively lose crack tip constraint as the T ‐stress becomes more negative irrespective of lattice orientation. Also, the near‐tip field for a range of constraint levels can be characterized by two‐parameters such as K–T or J–Q as in isotropic plastic solids.     

Numerical simulations of specimen size and mismatch effects in ductile crack growth - Part I: Tearing resistance and crack growth paths

The Gurson-Tvergaard-Needleman (GTN) model has been used for detailed numerical simulations of the effects of specimen size and yield stress mismatch on ductile crack growth behaviour in two different finite specimen geometries. For deep cracked bending specimens the crack growth resistance, expressed through the far-field J, increases as the specimen size is reduced, most strongly seen in case of low hardening. An opposite effect can be seen to some extent for shallow cracked specimens loaded in tension for low and intermediate hardening. For the yield stress mismatch cases low hardening and bend loading are found to promote crack growth deviation away from the initial crack plane.     

Elastic–plastic finite element analysis of the effect of compressive loading on crack tip parameters and its impact on fatigue crack propagation rate

The effects of applied compressive stress on the crack tip parameters and their implications on fatigue crack growth have been studied. Four center-cracked panel specimens with different crack lengths are analysed using finite element method. The results show that under tension–compression loading the local crack tip parameters are determined by two loading parameters. The two loading parameters are the maximum stress intensity and the maximum compressive stress in the applied stress cycle. Predictions of fatigue crack propagation behaviour based on the maximum stress intensity and maximum compressive stress agree well with experimental observations.     

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.     

T-stress effects on steady crack growth in a thin, ductile plate under small-scale yielding conditions: Three-dimensional modeling

The non-singular T-stress provides a first-order estimate of geometry and loading mode, e.g. tension vs. bending, effects on elastic–plastic, crack-front fields under mode I conditions. The T-stress has a pronounced effect on measured crack growth resistance curves for ductile metals – trends most computational models confirm using a two-dimensional setting. This work examines T-stress effects on three-dimensional (3D), elastic–plastic fields surrounding a steadily advancing crack for a moderately hardening material in the framework of a 3D, small-scale yielding boundary-layer model. A flat, straight crack front advances at a constant quasi-static rate under near invariant local and global mode I loading. The boundary-layer model has thickness B that defines the only geometric length-scale. The material flow properties and (local) toughness combine to limit the in-plane plastic-zone size during steady growth to at most a few multiples of the thickness (conditions obtainable, for example, in large, thin aluminum components). The computational model requires no crack growth criterion; rather, the crack front extends steadily at constant values of the plane-stress displacements imposed on the remote boundary for the specified far-field stress intensity factor and T-stress. The specific numerical results presented demonstrate similarity scaling of the 3D near-front stresses in terms of two non-dimensional loading parameters. The analyses reveal a strong effect of T-stress on key stress and strain quantities for low loading levels and less effect for higher loading levels, where much of the plastic zone experiences plane-stress conditions. To understand the combined effects of T-stress on stresses and plastic strain levels, normalized values from a simple void-growth model, computed over the crack plane for low loading, clearly reveal the tendency for crack-front tunneling, shear-lip formation near the outside surfaces, and a minimum steady-state fracture toughness for T = 0 loading.     

Numerical simulations of specimen size and mismatch effects in ductile crack growth - Part II: Near-tip stress fields

The effect of ductile crack growth on the near tip stress field in two different specimen geometries has been investigated. For homogeneous specimens it is observed that the peak stress level increases with ductile crack growth. The effect is most pronounced up to about 1 mm of crack growth. For low and intermediate hardening there is a significant effect of specimen size on the stress level. In case of mismatch in yield stress, the simulations show that the increase in stress level in the material with the lower yield stress is of a similar magnitude as is the case for stationary cracks. In case of ductile crack growth deviation from the original crack plane occurs, the highest stresses are still found close to the interface, and not in front of the current crack tip.     

The effect of T-stress on plane strain dynamic crack growth in elastic–plastic materials

In this paper, the effects of T‐stress on steady, dynamic crack growth in an elastic–plastic material are examined using a modified boundary layer formulation. The analyses are carried out under mode I, plane strain conditions by employing a special finite element procedure based on moving crack tip coordinates. The material is assumed to obey the J₂ flow theory of plasticity with isotropic power law hardening. The results show that the crack opening profile as well as the opening stress at a finite distance from the tip are strongly affected by the magnitude and sign of the T‐stress at any given crack speed. Further, it is found that the fracture toughness predicted by the analyses enhances significantly with negative T‐stress for both ductile and cleavage mode of crack growth.     

Incremental model for fatigue crack growth based on a displacement partitioning hypothesis of mode I elastic–plastic displacement fields

The mode I displacement field in the near crack tip region is assumed to be depicted by its partition into an elastic field and a plastic field. Then, each part of the displacement field is also assumed to be the product of a reference field, a function of space coordinates only, and of an intensity factor, function of the loading conditions. This assumption, classical in fracture mechanics, enables one to work at the global scale since fracture criteria can be formulated as a function of the stress intensity factors only. In the present case, the intensity factor of the plastic part of the displacement field measures crack tip plastic flow rate at the global scale. On the basis of these hypotheses, the energy balance equation and the second law of thermodynamics are written at the global scale, i.e. the scale of the K-dominance area. This enables one to establish a yield criterion and a plastic flow rule for the crack tip region. Then, assuming a relation between plastic flow in the crack tip region and fatigue crack growth allows an incremental model for fatigue crack growth to be built. A few examples are given to show the versatility of the model and its ability to reproduce memory effects associated with crack tip plasticity.     

Development of a new software for adaptive crack growth simulations in 3D structures

A new software system called ADAPCRACK3D has been developed by the authors to predict fatigue crack growth in arbitrary 3D geometries under complex loading by the use of the finite element method. The main focus of ADAPCRACK3D is on the determination of 3D crack paths and surfaces as well as on the evaluation of components' lifetimes as a part of the damage tolerant assessment. Throughout the simulation of crack propagation an automatic adaptive mesh adaption is carried out in the vicinity of the crack front nodes. The fracture mechanical evaluation is based on a new criterion recently developed by the authors.     

Correlation of fracture behavior in high pressure pipelines with axial flaws using constraint designed test specimens--Part I: Plane-strain analyses

This work presents a numerical investigation of crack-tip constraint for SE(T) specimens and axially surface cracked pipes using plane-strain, nonlinear computations. The primary objective is to gain some understanding of the potential applicability of constraint designed fracture specimens in defect assessments of pressurized pipelines and cylindrical vessels. The present study builds upon the J-Q approach using plane-strain solutions to characterize effects of constraint on cleavage fracture behavior for the analyzed fracture specimens and cracked pipes. Under increased loading, each cracked configuration follows a characteristic J-Q trajectory which enables comparison of the corresponding driving force curve in the present context. A key outcome of this investigation is that toughness data measured using SE(T) specimens appear more applicable for cleavage fracture predictions of pressurized pipelines and cylindrical vessels than standard, deep notch fracture specimens under bend loading. The results provide a strong support for use of constraint-designed SE(T) specimens in fracture assessments of pressurized pipes and cylindrical vessels.     

Influence of residual thermal stresses on fatigue crack growth life of discontinuous reinforcements in metal matrix composites

The fatigue life prediction model based on crack propagation from micro-structural features is derived and presented for planar and randomly oriented Discontinuous Reinforced Metal Matrix Composites (DRMMCs). The model contains the influence of micro-structural properties such as aspect ratio, volume fraction of particle/fibre and constraint between particle and the matrix. The effect of residual thermal stresses generated within the matrix during development of composite is considered. The particle/fibre plays a dominant role in the development of the cyclic plastic zone size ahead of the crack tip; moreover, it enhances the cyclic plastic deformation characteristics of DRMMC. The theoretical model-based evaluations for low cycle fatigue in DRMMCs are within the proximity of the experimental results.