Gurson Damage Model Research Articles

Ductile crack growth of high-graded pipeline steels in the presence of Lüders plateau

Strain-based engineering critical assessment methods allows certain amount of plastic strain during installation and in service, for pipelines crossing seismically-active areas. Most strain-based engineering critical assessment methods are established for materials with smooth stress-strain relationship, leaving the so-called Lüders plateau influence on ductile fracture response seldomly explored. This work studied the effect of the Lüders plateau on mode I ductile crack growth with the modified boundary layer (MBL) model under plane strain conditions. The “up-down-up” constitutive model was implemented and the Gurson damage model was selected to simulate crack propagation. Factors including the plateau length and softening modulus in the “up-down-up” constitutive model, strain hardening of the matrix material and the initial void volume fraction parameter were analyzed. Numerical results show that the Lüders plateau modifies the crack tip constraint and the damage evolution, and the plateau length plays the dominant role on ductile crack growth behaviour in the presence of Lüders plateau.

Creep damage constitutive model of rock based on the mechanisms of crack-initiated damage and extended damage

Since the classical element model cannot describe the nonlinear characteristics of rock during the entire compressive creep process, nonlinear elements and creep damage are generally introduced in the model to resolve this issue. However, several previous studies have reckoned that creep damage in rock only occurs in the accelerated creep stage and is only described by the Weibull distribution. Nevertheless, the creep damage mechanism of rocks is still not clearly understood. In this study, a reasonable representation of the damage variables of solid materials is presented. Specifically, based on the Gurson damage model, the damage state functions reflecting the constant creep stage and accelerated creep stage of rock are established. Further, the one-dimensional and three-dimensional creep damage constitutive equations of rock are derived by modifying the Nishihara model. Finally, the creep-acoustic emission tests of phyllite under different confining pressures are conducted to examine the creep damage characteristics of phyllite. And the proposed constitutive model is verified by analyzing the results of creep tests performed on saturated phyllite. Overall, this study reveals the relationship between the creep characteristics of rocks and the corresponding damage evolution pattern, which bridges the gap between the traditional theory and the quantitative analysis of rock creep and its damage pattern.

Prediction of Gurson Damage Model Parameters Coupled with Hardening Law Identification of Steel X70 Pipeline Using Neural Network

Prediction of Gurson Damage Model Parameters Coupled with Hardening Law Identification of Steel X70 Pipeline Using Neural Network

Investigation of Rousselier Model and Gurson-Tvergaard-Needleman Model in Ductile Fracture of API X65 Gas Pipeline Steel

In this research, the micromechanical Rousselier damage model, which is not available in commercial software is accomplished with a subroutine in Abaqus finite element analysis software. Ductile fracture behavior of API X65 steel is evaluated by simulation of tensile test of smooth and round notch bar specimens of base metal in hoop direction and weld metal. The Rousselier model and its parameters of this model are determined for API X65 steel based on experimental data. In this work, the Rousselier and Gurson damage model is compared for API X65 steel. Results of the tensile test and simulation for the Gurson model show inaccuracy in the final stage of the load-displacement plot. This is because in the Gurson model it is assumed that the fracture surface is flat and shear fracture does not occur in specimens, but in the Rousselier model, the shear fracture is considered. The Rousselier model shows more accurate results compared with experimental data in the final stage of loading. Furthermore, the Rousselier model shows little error comparing with the experiment around maximum load since the void growth due to nucleation is ignored in this model. Also, the Rousselier model shows better convergence when the grooving radius of tensile test specimen increasing but the Gurson model behaves differently.

Effect of the Lüders plateau on ductile fracture with MBL model

In this study, the effect of Lüders plateau on the ductile crack growth resistance has been investigated with the Gurson damage model and the modified boundary layer (MBL) model, under mode I plane strain condition. The Lüders plateau is modeled as horizontal by keeping the plateau stress equaling to the yield stress. A family of Lüders elongations ranging from 0 to 5% has been considered. The remote boundary condition of the MBL model is governed by the elastic K-field and T-stress. Numerical results show that the existence of the Lüders plateau on the stress-strain curve reduces the ductile crack growth resistance. The degree of reduction depends on the scale of the Lüders elongation. The crack tip stress field analysis indicates that the existence of the Lüders plateau varies the crack tip stress striaxiality distribution and the magnitude. It is also found that the size of plastic zone ahead of the crack tip is reduced, compared with the reference case for material without Lüders plateau. It is demonstrated that the effect of Lüders plateau on ductile crack growth is more significant at lower T-stress or for materials with higher toughness. The dependence of the initial void volume fraction and the T-stress on the ductile crack growth resistance are alleviated when the Lüders elongation is large.

Numerical study on the effect of the Lüders plateau on the ductile crack growth resistance of SENT specimens

The increasing demand of energy prompts the petroleum industry exploitation activities to the Arctic region where the low temperature is a strong challenge, both for structural design and material selection. For structural materials exhibiting the Luders plateau, it has been reported that lowering the temperature will increase the Luders plateau length. In order to obtain a deep understanding of the Luders plateau effect on ductile crack growth resistance, we performed numerical analyses with SENT specimens and the Gurson damage model. The Luders plateau was simplified by keeping the flow stress constant and varying the plateau length. The results show that the existence of the Luders plateau does not influence the initiation toughness, however, will alter the material’s fracture resistance significantly. It is found that the Luders plateau effect is in general controlled by the stress triaxiality level in front of the crack tip. Both the strain hardening and the crack depth effects on resistance curves are alleviated due to the Luders plateau. For materials with very small initial void volume fraction, the Luders plateau effect is more pronounced. Since the Luders plateau intensifies the crack driving force and may lower down crack resistance curve, special attention should be paid to the application of materials with the Luders plateau in the Arctic.

Determining critical CTOA from energy-load curves with DWTT specimen

Running ductile fracture is one of the most catastrophic accidents of pipelines for natural gas transportation. Crack arrest toughness is important for preventing crack extension to a long distance along pipeline. Critical crack tip opening angle (CTOAC) is a promising parameter for characterizing crack arrest toughness. In this study, a new method is proposed to calculate the CTOAC from the energy-load curves in an instrumented drop weight tearing test (DWTT). Numerical analyses with the Gurson damage model have been conducted to verify the proposed method. It shows that results calculated from the energy-load curves are slightly lower than the results measured from specimen surface. Results calculated from the proposed method also agree well with experimental results reported in the literature.

Research of the Gurson damage model of the different yield functions during the deep-drawing process

Based on the macroscopic constitutive models (MCCM), the Gurson damage model is introduced to build the mesoscopic constitutive models (MSCM) with anisotropy Gurson-Hill1948 and Gurson-Yld2003 damage models. The damage parameters of the Gurson-Hill1948 and Gurson-Yld2003 damage models using orthogonal analysis and inverse computed methods are discussed and compared with experimental and simulation results obtained using the user subroutine VUMAT implemented by Lin. The corresponding sensitivity of the damage parameters was obtained by orthogonal analysis, then these optimized damage parameters could describe the mechanical performance for 08Al sheet with 1 mm thickness. Basically, the simulation results are in accordance with the experiment results. The damage parameters of the Gurson-Hill1948 and Gurson-Yld2003 constitutive models are explored to describe the deep-drawing deforming process, failure performance and obtained equivalent stress, equivalent plastic strain, thickness, damage distribution, and the influence of the friction coefficient during the deep-drawing process.

Experimental and numerical investigation of fracture in fillet welds by cross joint specimens

The load capacity of fillet welds is investigated experimentally and numerically in cross joint specimens with the objective of calibrating multiple failure criteria for the ductile fracture of weld metal. The cross joint specimens are composed of mild shipbuilding steel with plate thicknesses of 20 mm and 30 mm respectively. The fillet welds are manually produced by flux-cored arc welding, using the filler metal Elgacore MXX100. To achieve different stress states in the weld joints, forces in two different directions and moments about two different axes are applied separately on various specimens. A uniquely designed specimen is employed for each load scenario. For the numerical investigations, an appropriate discretization of the weld joints is established by taking into account the distribution of the metallographic structure with the weld metal and the heat-affected zone. The distribution of the different materials is determined by a macrosection of a weld joint. The material behavior, in terms of true stress-strain curves for the weld metal and the material of the heat-affected zone, is identified by hardness measurements. With the established discretization of the weld joints and true stress-strain curves of the different materials, the experimentally determined force-displacement curves are reproduced in finite element analyses. Furthermore, the Gurson (1977) damage model are successfully calibrated for the weld metal.

Modified Gurson Model to Describe Non-linear Compressive Behaviour of Polyurethane Foam with Considering Density Effect

Polyurethane Foam(PUF), a outstanding thermal insulation material, is used for various structures as being composed with other materials. These days, PUF composed with glass fiber, Reinforced PUF(R-PUF), is used for a insulation system of LNG Carrier and performs function of not only the thermal insulation but also a structural member for compressive loads like a sloshing load. As PUF is a porous material made by mixing and foaming, mechanical properties depend on volume fraction of voids which is a dominant parameter on density. Thus, In this study, density is considered as the effect parameter on mechanical properties of Polyurethane Foam, and mechanical behavior for compression of the material is described by using modified Gurson damage model.

Microstructure Modelling of Dual-Phase Steel Using SEM Micrographs and Voronoi Polycrystal Models

The microstructure of dual-phase (DP) steels is composed of a matrix of ferrite reinforced by islands of martensite and the common interphase boundaries. To study the mechanical behavior of DP steels, steel with 45% ferrite and 55% martensite was fabricated and tested in the laboratory. Two types of finite element models were then created based on SEM images. The first model directly created the grains and boundaries from the SEM images, while the second model used a Voronoi type algorithm to construct geometries which are statistically similar to the SEM images. The models consider the measured morphology of ferrite, martensite, and their phase boundaries. The Gurson damage model was then used for the ferrite and boundary regions. The obtained results correctly predicted the failure mechanisms in a DP material. The results indicate that the deformation is localized due to microstructural inhomogeneities and the nucleation of voids in the boundaries between the ferrite and martensite grains. The good correlation between the numerical and experimental observations from SEM micrographs shows the efficiency of the proposed models in predicting the failure mechanism of DP steels.

Numerical integration of an advanced Gurson model for shear loading: Application to the blanking process

A new extension of the Gurson damage model has been proposed recently to predict ductile fracture under shear dominated loads. The aim of this work is to verify the ability of this approach to simulate, in an accurate way, the damage evolution in shearing processes. An implicit stress integration algorithm is then developed to implement the new model in a finite element code. The numerical procedure is checked through simulations of shear and uniaxial tension tests on a single elements. The extended Gurson damage model is tested and applied to the punching process to compare its predictive ability with the original approach. The obtained numerical results are in good agreement with experimental results of the punching process, showing better ductile fracture predictions compared to the original Gurson model.

Effect Analysis of Gurson Model Parameters on Crack Extension of Pipeline

Leakage-before-break technique is widely used in high energy pipeline of nuclear plant, for which crack stability of pipeline under complex loading condition is a key issue, and crack growth resistance curve of pipeline material is the important foundation for crack stability analysis. In this paper, ferritic steel A533B is studied, Gurson damage model is used to simulate crack process of contact tension specimen under unitension, and effect of Gurson model parameter on simulation result is discussed. The following results are found during simulation: initial porosity factor is the main parameter, when it increases gradually, unstable crack extension will be observed; however, only initial J toughness is affected by critical porosity factor; the minor parameter is load step control, when it increases, stable and convergent result is obtained. All results in this paper can be used to determine parameters in Gurson mode, which will be foundation for crack extension analysis of pipeline.

Design and identification of high performance steel alloys for structures subjected to underwater impulsive loading

Martensitic and austenitic steel alloys were designed to optimize the performance of structures subjected to impulsive loads. The deformation and fracture characteristics of the designed steel alloys were investigated experimentally and computationally. The experiments were based on an instrumented fluid–structure interaction apparatus, in which deflection profiles are recorded using a shadow Moiré technique combined with high speed imaging. Fractographic analysis and post-mortem thickness reduction measurements were also conducted in order to identify deformation and fracture modes. The computational study was based on a modified Gurson damage model able to accurately describe ductile failure under various loading paths. The model was calibrated for two high performance martensitic steels (HSLA-100 and BA-160) and an austenitic steel (TRIP-120). The martensitic steel (BA-160) was designed to maximize strength and fracture toughness while the austenitic steel (TRIP-120) was designed to maximize uniform ductility, in other words, to delay necking instability. The combined experimental–computational approach provided insight into the relationships between material properties (strength, uniform ductility, and post-necking ductility) and blast resistance of structures. In particular, the approach allowed identification of material/structure performances by identifying impulse-center deflection behavior and the impulse leading to panel fracture.

Implementation and Validation of a Gurson Damage Model Modified for Shear Loading: Effect of Void Growth Rate and Mesh Size on the Predicted Behavior

The optimization of automotive security components requires good knowledge of the material state after fabrication, particularly with respect to damage that may have been done to the material by the manufacturing process. To achieve this, numerical simulation of the fabrication process is often undertaken. However, classical continuum damage models, like the Gurson [3] model, are not appropriate for the simulation of the blanking by punching operation because the material damage is primarily the result of shear stresses. This work is focused on the use and validation of a modified Gurson type damage model capable of modeling this process, which has recently been proposed by Nahshan [7]. After a brief description of the modification, the implementation and the validation of the modified Gurson model is detailed. A comparison between the original Gurson model and the modified model is presented in order to highlight the importance of the modification for a pure shear stress state and to show that the two models are equivalent for a purely hydrostatic stress state. It is also shown that the results from the modified model are dependent on the finite element mesh size.

Left-Side of the Forming Limit Diagram (FLD) under Superimposed Double-Sided Pressure

Over the past decades, many kinds of double-sided pressure forming processes have been proposed to improve the formability of lightweight materials which exhibit distinctly poor forming capability. In the present study, the effects of double-sided pressure on the deformation behavior of AA5052-O aluminum alloy sheet metal under tension-compression deformation state are studied numerically using the finite element method based on the Gurson damage model. It is demonstrated that superimposed double-sided pressure significantly increases the left-side of the forming limit diagram and the formability increase value is sensitive to the strain path.

An Experimental and Numerical Assessment of Sheet-Bulk Formability of Mild Steel DC04

This paper presents investigations on development of a new way of teeth-forming, which is related to sheet-bulk metal forming, with application of incremental bulk forming process to sheets. For this purpose, a combined experimental-numerical study on damage assessment in sheet-bulk forming of DC04 is presented. Using scanning electron microscope (SEM) and glow discharge optical emission spectrometry (GDOS), a combined quantitative/qualitative metallurgical survey is carried out on undeformed specimens to illuminate microstructural aspects in the context of nonmetallic inclusion content, distribution and size which act as prime failure factors. These surveys are extended to monitor ductile damage accumulation with cavitation at different stages of the incremental sheet indentation process over certain sections. An anticipated failure mode is captured where formability is limited by severe macro-cracking preceded by localization with void sheeting. To this end, using a developed VUMAT subroutine for the micromechanically based Gurson damage model which is recently enhanced for shear fracture, the processes are simulated in ABAQUS/Explicit and comparisons with experiments are provided. The results support the requirement of integrating powerful coupled accumulative damage models in the virtual process design procedure for sheet-bulk metal forming. This requirement also arises from distinct features of these class of processes from conventional sheet metal forming processes which preclude use of forming limit curves.

Enhanced Ductility in Sheet Metals Produced by Cladding a Ductile Layer

The effect of cladding a ductile layer on necking and fracture in sheet metals under plane strain tension is studied numerically using the finite element method based on the Gurson damage model. It is demonstrated that the cladding increases both the necking and fracture strains. The increase in necking strain is due to the fact that cladding a ductile layer enhances the overall work hardening for the layered metal sheets according to the rule of mixtures. Furthermore, the increase in necking strain slows down the development of the triaxial tensile stress inside the neck, which delays the void nucleation and growth, and which, in turn, contributes to enhancement in ductility.

Experimental Engineering and Applications

This special issue of Experimental Mechanics contains selected papers presented at the 2nd International Conference on Advanced Computational Engineering and Experimenting (ACE-X 2008) held at Hotel Melia (Barcelona), Spain during the period 14th–15th July, 2008. During the conference, a special session related to Adhesive Bonding (organised by Prof. Lucas Filipe Martins da Silva and Prof. Juan Carlos Suarez Bermejo) was held. In addition, three short courses related to Modelling and Testing of Cellular Materials (organised by Prof. Andreas Ochsner), Structural Hybrid Materials: Biomimetism and Bioinspiration (organised by Prof. Juan Carlos Suarez Bermejo) and Structural Analysis in Vehicle Engineering (organised by Prof. Markus Merkel) were held. This issue contains full length manuscripts covering a wide range of topics in experimental engineering. The contribution by Shahani et al. is related to the fatigue crack growth in pipes under cyclic bending loads. In their work, experiments are compared to numerical results obtained from finite element simulation. Radnic and Matesan report the long-term behaviour of steel-reinforced concrete shells under static loading. The fracture evaluation in a dome port under shock impact is experimentally investigated by Kwon et al. and compared to numerical simulations. Dubois and co-workers report on the design of a testing rig to investigate the tag of carbon-epoxy prepregs. Johani and Nobari apply neural networks and modal data to investigate the dynamic behaviour of a structural adhesive. Shim et al. analyse the residual stresses in thick-walled cylinders considering the Bauschinger effect. Cardoso et al. present an inverse analysis to identify parameters of the Gurson damage model. Choi et al. investigate the nano-scale elastic modulus of thin Pt films based on the wrinkle pattern of buckled films whereas Lee et al. investigate thin Au films based on the microtensile test. Ren and co-workers analyse the elastic deformation of materials under distributed shear loads while the work by Lee et al. studies the biomechanical problem of dorsiflexion under eccentric exercise.

Enhanced ductility in round tensile bars produced by cladding a ductile ring

The effect of cladding a ductile ring on necking and fracture in round bars under tension is studied numerically using the finite element method based on the Gurson damage model. It is demonstrated that the cladding increases both the necking strain and the fracture strain. The effects of topological arrangement of cladding ring on necking and fracture are numerically investigated. It is indicated that while a topological arrangement of cladding has no noticeable effect on necking, it significantly influences the fracture strain. For a given volume fraction of cladding, the fracture strain could increase about 11% if the ductile ring is moved from the outmost to the innermost. It is also found that the subtle appearance of fracture surface due to cladding displays strong mesh sensitivity and may even be an artefact of the mesh.