Simulation Of Ductile Fracture Research Articles

Correlation of localized residual stresses with ductile fracture toughness using in situ neutron diffraction and finite element modelling

Localized residual stresses were correlated to ductile fracture toughness quantitatively in steel and aluminium alloys using in situ neutron diffraction method coupled with elastic-plastic finite element modelling. Local out-of-plane compression (LOPC) method generated compressive and tensile residual stresses in the vicinity of the fatigue pre-crack front in two compact tension (CT) specimens, respectively, and the evolution of the stress fields was simultaneously measured using in situ neutron diffraction technique under mode-I fracture loading. The results clearly showed that the localized tensile residual stress apparently accelerated stress transfer at the mid-thickness of the CT specimen compared to the specimen having compressive residual stress. The coupled quasi-static ductile fracture simulations and neutron diffraction results revealed a clear correspondence of fracture initiation toughness with localized residual stresses in both steel and aluminium alloys. In the aluminium case, tensile residual stress of 208 MPa was obviously detrimental to the fracture toughness resulting in a 43% reduction while compression of −220 MPa increases by up to 14%. On the other hand, localized residual stress in steel hardly affected fracture initiation toughness due to high plastic dissipation energy. This experiment-simulation coupled study quantitatively elucidates the distinctive role of plastic deformation and stress triaxiality in ductile fracture initiation between steel and aluminium alloy.

Computational investigation into the role of localisation on yield of a porous ductile solid

In ductile materials containing micro-voids, diffuse plasticity or localisation of plastic strain in narrow bands bridging the ligaments between voids can both occur as precursors to failure. In particular, localisation of plastic strain leads to coalescence through the formation of void sheets or plastic collapse of the ligament. If yielding is defined as the point in macro stress space at which the macroscopic plastic dissipation becomes large, either diffuse plasticity or localisation can cause yielding. Appropriate combinations of triaxiality T and Lode parameter L can cause localisation to occur earlier, and thereby modify the yield surface significantly. This is more likely to happen at high values of porosity. The competition between the two modes of yielding has been captured by a recently proposed multi-surface yield framework (Keralavarma, S. M., 2017, “A multi-surface plasticity model for ductile fracture simulations,” Journal of the Mechanics and Physics of Solids, 103, pp. 100–120), where the competition between the Gurson criterion for yielding by diffuse plastic flow and a criterion for localized yielding within discrete coalescence bands leads to a piecewise smooth yield locus with sharp vertices. In the present work, we generate yield surfaces computationally by using a voided, cuboidal unit cell and a computational homogenisation framework that allows for both macro deformation gradient and macro Cauchy stress control. The basic aim is to see how the multi-surface framework of yield compares with macro yield loci generated computationally using a formulation where both finite deformations and void shape changes are allowed. We show, for spherical, prolate and oblate initial voids, that localisation inevitably hastens macro yield and adds sharp vertices to the yield locus, for a wide range of L and T. The multi-surface framework, at least for spherical initial voids, is remarkably successful in capturing this competition.

A non-linear ductile damage growth law at elevated temperature

Continuum damage mechanics (CDM) model is commonly used for the prediction of ductile fracture. For numerical simulation of ductile fracture in impact or high-temperature problems, the damage growth law that incorporates the effect of high temperature is needed. Experimentally, it has been observed that damage growth decreases with temperature. However, the damage growth law at high temperature is not easily available in the literature. In the present work, a damage growth law at high temperature is proposed for steel, based on the experimental measurement of damage carried out at IIT Kanpur.

Numerical modelling of ductile fracture in steel plates with non-ordinary state-based peridynamics

This paper presents a methodology for the simulation of ductile fracture in steel plates based on non-ordinary state-based Peridynamics. A novel algorithm of crack approximation is proposed in this work, which makes it easier to track crack surface, measure crack length and implement damage criterion in constitutive model when crack propagates. To simulate the plastic behavior of steel and predict the occurrence of fracture, the Gurson-Tvergaard-Needleman (GTN) (Tvergaard and Needleman, 1984) constitutive model is adopted to take into account the effect of plasticity, void nucleation and coalescence during the propagation of crack. Two types of plate fracture tests that were conducted by Simonsen and To¨rnqvist (2004) provide sufficient experimental data, which could be used to calibrate the parameters of constitutive model and validate proposed method. After comparing the results between numerical simulation and experiments, a good agreement has been found and the numerical model developed here has exhibited a certain predictive capacity.

A fully coupled fluid-structure interaction simulation of three-dimensional dynamic ductile fracture in a steel pipeline

Long running fractures in high-pressure pipelines transporting hazardous fluid are catastrophic events resulting in pipeline damage and posing safety and environmental risks. Therefore, the ductile fracture propagation control is an essential element of the pipeline design. In this study, a coupled fluid-structure interaction modelling is used to simulate the dynamic ductile fractures in steel pipelines. The proposed model couples a fluid dynamics model describing the pipeline decompression and the fracture mechanics of the deforming pipeline exposed to internal and back-fill pressures. To simulate the state of the flow in a rupturing pipeline, a compressible one-dimensional computational fluid dynamics model is applied, where the fluid properties are evaluated using a rigorous thermodynamic model. The ductile failure of the steel pipeline is described as an extension of the modified Bai-Wierzbicki model implemented in a finite element code. The proposed methodology has successfully been applied to simulate a full-scale pipeline burst test performed by British Gas Company, which involved rupture of a buried X70 steel pipeline, initially filled with rich natural gas at 11.6 MPa and −5 °C.

Multi‐field formulation of large deformation ductile fracture

AbstractIn the present contribution we focus on a novel computational framework for the simulation of ductile fracture in elastoplastic solids. In particular, a fully non‐linear formulation of gradient plasticity is applied together with a higher order phase‐field approach to fracture to account for large elastic and plastic deformations along with three dimensional crack propagation. The proposed formulation is based on a multiplicative decomposition of the deformation gradient into elastic and plastic contributions and a subsequent multiplicative decomposition of the elastic part into a fracture sensitive and a fracture insensitive contribution, see [1]. Postulating that fracture requires a local state of tensile/shear deformation, the latter decomposition is used to formulate the isochoric and tensile contributions to the elastic strain energy, whereas the compressive contribution remains unaffected by the crack phase‐field and vice versa. The modification of the Griffith brittle fracture theory to ductile fracture is most crucial and has to be adjusted carefully. Within our framework, this adaptation is considered as dependency of the critical fracture energy density by the equivalent plastic strain. Concerning the elastic/plastic decomposition, we assume an isochoric plastic flow which requires special attention for the update procedure of the plastic deformation. To be specific, we apply an exponential time integration scheme such that we preserve the deviatoric state of the plastic deformation and obtain a correct evaluation of the phase‐field driving force. Eventually, a number of numerical examples will demonstrate the accuracy and capability of the proposed multi‐field approach to ductile fracture.

Simulation of ductile fracture of structural steels with void growth model and a continuum damage criterion based on it

Ductile fracture of single-edge U-notched and V-notched specimens under monotonic tension was investigated. Both experimental and numerical studies were conducted. In the tests on eight specimens, all ductile fracture initiated at mid-thickness of the notch tips and propagated all the way across the width of the specimens. Obvious plastic deformation was observed during both the fracture initiation and propagation procedures. Ductile fracture of these specimens was then simulated with void growth model (VGM) and a continuum damage criterion based on VGM. Extremely fine mesh and relatively coarse mesh were adopted in finite element analysis for the simulation. Load-displacement curves and the entire ductile fracture procedures obtained with the two fracture criteria for all the eight specimens agreed well with corresponding test results or with each other, by which the accuracy of both fracture criteria was verified. The efficiency of the two fracture criteria was also discussed. It was found that the computational cost of VGM is unacceptably high due to the request of extremely fine mesh along the fracture surface. With the continuum damage criterion, the ductile fracture of structural steels can be simulated accurately enough at acceptable computational cost even for steel components or connections with complicated configurations.

The effect of low stress triaxialities and deformation paths on ductile fracture simulations of large shell structures

In accidental limit state analysis of ship structures and their components, the common assumption is that failure takes place in the plate field under multi-axial tension, thus most advancements in developing fracture criteria have focused on that region. In contrast, failure in low stress triaxialities is relatively unexplored territory in the context of large-scale crash analysis. The probability of this failure mode increases with the decreasing ductility that is characteristic of high and extra high strength steels. Therefore, ductile fracture simulations are performed with large thin-walled steel structures employing four different fracture criteria that differently account low stress triaxialities and deformation history. Criteria are compared as to their capabilities to reproduce and predict experimentally measured behaviour. Analyses demonstrate that failure under lower stress triaxialities affects the response significantly especially when complex deformation history is considered. Suggestions are made for the further enhancement of fracture criteria as well as experimental configurations employed for benchmarking failure criteria.

Simulation of ductile fracture in pipeline steels under varying constraint conditions using cohesive zone modeling

In this study, the effect of non-singular T-stress (a measure of crack tip constraint) on crack growth resistance curves (R-curves) and crack tip opening angle (CTOA) was investigated. The investigation proceeded in two parts; first using a modified boundary layer (MBL) model to systematically assess the effect of T-stress on the R-curves and CTOA, and second comparing the CTOA under different loading modes, namely, bending and tension. Three steels were examined in this work; the first was a typical high strength steel referred to as TH, the second and third were pipeline steels referred to as X70 and X100. Surface-based cohesive zone models with four sets of bilinear traction-separation (TS) laws were used for TH steel. The models of X70 and X100 were computed using element-based cohesive zone modeling with a trapezoidal TS law. All simulations were conducted using the finite element (FE) program ABAQUS. It was assumed in these simulations that there was no effect of T-stress on the TS laws per se. With this assumption, it was found that the T-stress and loading mode have only a small effect (1–2°) on the CTOA for the materials studied.

Ductile Fracture Simulation of Constructional Steels Based on Yield-to-Fracture Stress–Strain Relationship and Micromechanism-Based Fracture Criterion

AbstractFracture is an important mode of failure in steel structures, whereas traditional fracture mechanics is difficult to apply in predicting ductile fracture in the presence of large-scale yiel...

Ductile fracture simulation under multi-axial loading

Ductile fracture simulation under multi-axial loading

Ductile and Brittle Fracture Simulation Combined with Cohesive Zone Model and Gurson Model Depending on Temperature

Ductile and Brittle Fracture Simulation Combined with Cohesive Zone Model and Gurson Model Depending on Temperature

Ductile Fracture Simulations for Through Wall Cracked Pipes by Work-Hardening Elastic-Plastic Ordinary State Based Peridynamics

Ductile Fracture Simulations for Through Wall Cracked Pipes by Work-Hardening Elastic-Plastic Ordinary State Based Peridynamics

Application of the GTN model to ductile crack growth simulation in through-wall cracked pipes

This paper presents ductile fracture simulation using the GTN (Gurson-Tvergaard-Needleman) model of through-wall cracked STPT410 carbon steel pipe test under pure bending. Three issues related to practical application are addressed; (i) how to determine the parameters in the GTN model from fracture toughness data, (ii) how to incorporate the element-size effect to the GTN model and (iii) the effect of the crack-tip mesh design on determination of the GTN model parameters. It is found that determined values of the parameters depend on the crack-tip mesh design and the finite element size used in simulation. The split of the crack tip element into two makes parameter determination easier and gives better simulation results, but is difficult to apply to three-dimensional surface crack problems.

A multi-surface plasticity model for ductile fracture simulations

The growth and coalescence of micro-voids in a material undergoing ductile fracture depends strongly on the loading path. Void growth occurs by diffuse plasticity in the material and is sensitive to the hydrostatic stress, while void coalescence occurs by the localization of plastic deformation in the inter-void ligaments under a combination of normal and shear stresses on the localization plane. In this paper, a micromechanics-based plasticity model is developed for an isotropic porous material, accounting for both diffuse and localized modes of plasticity at the micro-scale. A multi-surface approach is adopted, and two existing plasticity models that separately account for the two modes of yielding, above, are synthesized to propose an effective isotropic yield criterion and associated state evolution equations. The yield criterion is validated by comparison with quasi-exact numerical yield loci computed using a finite elements based limit analysis procedure. It is shown that the new criterion is in better agreement with the numerical loci than the Gurson model, particularly for large values of the porosity for which the loading path dependence of the yield stress is well predicted by the new model. Even at small porosities, it is shown that the new model predicts marginally lower yield stresses under low triaxiality shear dominated loadings compared to the Gurson model, in agreement with the numerical limit analysis data. Predictions for the strains to the onset of coalescence under proportional loading, obtained by numerically integrating the model, indicate that void coalescence tends to occur at relatively small plastic strain and porosity levels under shear dominated loadings. Implications on the prediction of ductility using the new model in fracture simulations are discussed.

A practical approach to modeling aluminum weld fracture for structural applications

This paper addresses the numerical simulation of plasticity and ductile fracture of large scale structures (e.g. ships, railcars, automobiles) fabricated with welds that exhibit appreciably lower strength than the plate material, often referred to as weld undermatching. It has been observed, both numerically and experimentally, that for such structures the weld undermatching often leads to plasticity and fracture being limited to the weld and heat affected zone (HAZ). While the large size of the structures of interest precludes the use of a refined three-dimensional element mesh capable of capturing the details of the weld/HAZ behavior, cohesive zones are ideal for capturing the overall effects of undermatched weld plasticity and fracture on a structural scale. This paper focuses on establishing a systematic calibration process for determining the cohesive zone constitutive behavior and examining the validity of this approach in the context of mode I tearing of a large welded two-layer AA6061-T6 sandwich panel. First, test data from a welded coupon is used to calibrate the cohesive law. Tearing fracture of this panel is examined using the established cohesive law to represent weld/HAZ along with elastic-plastic shell elements, with in-plane dimensions much greater than the layer thickness, to represent the parent metal. It was verified that, for this structure, plasticity was indeed confined to the welds and heat affected zones, and that the behavior of the panel was captured with reasonable fidelity.

Ductile fracture simulations by damage model based on continuous damage mechanics

Ductile fracture simulations by damage model based on continuous damage mechanics

Comparison of anisotropy evolution in BCC and FCC metals using crystal plasticity and texture analysis

Abstract The evolution of anisotropy in metals has been studied for many decades both experimentally and theoretically using computation. Although the experimental research on the evolution of anisotropy provided valuable data, there is lack of theories that can be used in macro-scale plasticity. Fracture of ductile metals occurs after going through a large amount of plastic deformation where anisotropy of the material changes significantly as manifested by texture development; processed metal slabs (such as rolled slabs) possess anisotropy due to texture produced by the metal forming process that the slabs went through and initially isotropic metals get to possess anisotropy as well due to the texture formation induced by the large amount of plastic deformation. Therefore, it is critical to take into account the effect of anisotropy evolution to accurately predict fracture characteristics and plastic flow behaviors in the simulation of ductile fracture and plastic flow of metals. The theory of anisotropy evolution of metals in macro-scale plasticity can be derived by quantifying the meso-scale grain-level physics through crystal plasticity simulations. Therefore, this paper investigates the evolution of anisotropy in BCC and FCC metals using crystal plasticity simulations and texture analysis to reveal the physics behind anisotropy evolution and provide comparison of anisotropy evolution between BCC and FCC metals, which can be used to propose the theory of anisotropy evolution in macro-scale plasticity.

Simulation of ductile fracture in welded tubular connections using a simplified damage plasticity model considering the effect of stress triaxiality and Lode angle

In the experiment of the welded CHS–RHS X-joint, ductile fracture initiated on the chord near the saddle position along the brace-to-chord intersection which led to punching shear failure mode. The initiation and extension of the ductile fracture reduces the punching shear resistance of the remaining intact material. In order to estimate the accurate strength and the failure mode of tubular connections, this paper proposes a new fracture model by extending the existing damage-mechanics based models to predict the ductile fracture failure in tubular connections. The proposed model considers not only the effect of the stress triaxiality but also the effect of the Lode angle on the fracture strain, so as to make an enhanced estimation on the “shear fracture mode”. To facilitate its engineering application, this paper proposes a simplified method to calibrate the material parameters solely from experimental results of common coupon tests. Besides, to examine the engineering application of the proposed fracture model to other types of welded tubular connections, this paper applies the proposed fracture model in analyzing the fracture failure in a welded CHS-plate X-joint, and further two I-beam-to-tubular-column connections reported by previous researchers. The numerical simulation predicts accurately the actual failure sequence observed in the experiment.

Numerical simulation of ductile fracture based on mean field homogenization method: Modeling and implementation

A mean filed homogenization method at large deformation is presented to describe the damage softening effects due to nucleation and growth of voids during ductile fracture. The developed homogenization frame is combined with the Nucleation-And-Growth model and the percolation theory based coalescence model for describing ductile damage evolution. A semi-implicit numerical algorithm is developed to solve the ductile damage model. Based on the model, we have carried out numerical simulations of the spall fracture of a Al 2024-T4 plate and a Ti–6Al alloy plate under impact loads. The simulated free surface velocity profiles show good agreement with experimental measures.