Simulation Of Ductile Fracture Research Articles

107 き裂を有するFCC単結晶板の延性破壊シミュレーション(材料力学II)

107 き裂を有するFCC単結晶板の延性破壊シミュレーション(材料力学II)

An Experimental Evaluation of Material Properties and Fracture Simulation of Cryorolled 7075 Al Alloy

This work presents an experimental evaluation of yield strength, tensile strength, and impact toughness of 7075 Al alloy. The extended finite element method (XFEM) has been chosen for quasi-static crack growth simulations using Charpy impact energy as the crack growth criterion for both Bulk and ultrafine-grained (UFG) 7075 Al alloy. The 7075 Al alloy is rolled for different thickness reductions (40 and 70%) at cryogenic (liquid nitrogen) temperature, and its mechanical properties are studied by performing the tensile and Charpy impact testing. The microstructural characterization of the alloy was carried out using field emission scanning electron microscopy (FE-SEM). The rolling of the Al alloy at cryogenic temperature suppresses dynamic recovery, and dislocation cells formed during processing, transformed into fully formed ultrafine-grains (600 nm) at 70% thickness reduction. The impact energy used as the crack growth criterion under quasi-static loading condition based on the Griffith energy concept. The elastic-plastic ductile fracture simulations are performed by XFEM using ABAQUS Software (Version 6.9). For crack modeling, two different types of functions are used to model a crack based on partition of unity concept. A discontinuous function is used to model the portion behind the crack tip, whereas crack tip is modeled by near-tip asymptotic functions. This permits the crack is to be represented explicitly without meshing the crack surfaces, thus crack propagation simulations can be carried out without a need of re-meshing. Strain energy release and stress distribution ahead of the crack tip is found for some practical crack problems. The numerical examples indicate a significant improvement in crack growth properties of UFG 7075 Al alloy as compared to its bulk form due to an effective grain refinement.

Experimental Testing and Computer Simulations of Ductile Fracture in Tool Steels

AbstractDuctility was determined in experimental four‐point bending tests of smooth specimens of tool steel. The tool steels had different contents of carbides and carbide sizes and with a hardness of approximately 60HRc. Two of the materials tested were produced powder metallurgically, one was spray formed and one was conventionally uphill ingot cast. Carbide size distribution analysis was performed on planar polished sections of each material. Correlation between carbide microstructure and ductility performance was obtained. The fracture mechanisms were investigated with fractography. A 3D FE‐model was used to simulate the four‐point bending tests and thereby analyse the matrix flow curve. Also the strain at failure was analysed for each material when simulations were performed based on experimental data. SEM‐images of the materials carbide microstructure were used to create 2D FE‐models. The models simulated crack initiation and propagation by removing elements in the steel matrix as the plastic strain reached a critical level. With three variants, simulations of crack initiation and propagation at carbides were investigated. That was carbides with no cohesion to matrix, carbides fixed to the matrix and carbides with internal cracks. Comparison of strains at failure for the 2D and the 3D FE‐models showed good correlation.

Ductile fracture locus of Ti–6Al–4V titanium alloy

The simulation of ductile fracture in real components is becoming a strategic issue in numerical simulations. Numerical simulations of crashes, forming processes, impacts and fractures are reliable only if carried out with an accurate material calibration. The topics involved in this kind of simulation require a complete calibration of both the true stress–strain curve and the failure. The focus of this work is the accurate calibration of the constitutive relations of the titanium alloy Ti–6Al–4V. The approach proposed is based on different experimental tests supported by numerical simulations performed by means of detailed FE models. The Bao–Wierzbicki ductile failure criterion is calibrated using a total of 11 specimens. These specimens are tested on a multiaxial test machine to investigate the failure at different stress triaxialities. Furthermore, the sensitivity to the mesh size and the assessment of the calibration accuracy are analysed in detail on different components in order to verify the geometry transferability.

Simulation of Ductile Fracture of Slabs Subjected to Dynamic Loading Using Cohesive Elements

Dynamic loading of elastic-plastic slabs is studied numerically using a finite element approach, where introduction of cohesive elements enables fracture. For the bulk material, J2-flow theory is chosen as constitutive model, whereas the behavior of the cohesive elements is described by an irreversible cohesive law. The fracture behavior is governed solely by the cohesive elements, which are incorporated in the original mesh after a certain deformation state is reached. It is found that cohesive elements that are introduced early in the simulation are able to sustain the shape of the slab, so that necking and specimen fracture may occur at a location that does not coincide with the position of the first developed cohesive zone. This is an important feature, especially in the case of multiple necking. The influence of introducing cohesive elements on the deformation behavior is studied by comparison of contour plots describing the time development of normalized strain rates. Numerical simulations where the insertion of cohesive elements is enabled are compared with corresponding results where the material model only consists of J2-flow theory. Differences in the simulated material response, such as delay in the onset of necking, indicate that depending on the aim of the study, introduction of cohesive elements will influence the observed results. In addition, the proportion of kinetic energy of the post-fracture fragment compared to the amount of input work as function of imposed loading velocity is studied along with the effect of changing specimen aspect ratio.

Numerical Simulation of Ductile Fracture in Cylindrical Tube Impacted Against a Rigid Surface

Impact of tubes has an extensive application in crashworthiness. Analytical and numerical studies on axial impact of tubes have been carried out mostly at low-to-moderate impact velocities at which only the buckling of tubes is observed. However, experimental observations show that tubes fracture when the impact velocity is high. The objective of this article is to study the fracture of cylindrical tubes impacted against a rigid surface by numerical simulation. First, through-the-thickness fracture at the impacted end is simulated at the impact velocity of 350 m/s. Then, a detailed parametric study is carried out with respect to various parameters like the friction coefficient, tube thickness, tube length, and impact velocity. With an increase in the friction coefficient, the spread of fracture is more toward the outer edge. Further, the spread of fracture toward the inner edge takes place in an inclined manner. At higher tube thickness, the spread of fracture ceases after some time without reaching the inner edge. The tube length is found to have no effect on the fracture. It is observed that the fracture spreads faster with the impact velocity.

112 ノッチを有するアルミ単結晶の延性破壊シミュレーションと検証(材料力学III)

112 ノッチを有するアルミ単結晶の延性破壊シミュレーションと検証(材料力学III)

Simulation of Ductile Fracture of Multiple Flaws

Interaction effect of multiple flaws on ductile fracture is studied numerically by Gurson's constitutive equation. Based on experiments, 2 parallel cracks problems and 3 parallel cracks problems are simulated. In some problems, crack coalescence does not occur, and it occurs in other cases. In all cases, ductile fracture processes are obtained, and results are compared with experimental ones. Fracture pattern and load-displacement curves agree well with experiments. It is shown that void growth term is dominant for the coalescence of cracks. Slanted crack problem and non-uniform length crack problem are simulated and evaluation method of multiple cracks problem is discussed.

Ductile Fracture Simulation of Pipe under Bending with Initial Defects

Crack propagating evaluation is needed to predict and prevent structural damages since many structure defects from numerous crack propagating. It is widely known that ductile fracture occurs when external load is exerted to the material, these load include strong and unpredictable load such as earthquakes and collision of objects. Ductile material fractures via nucleation of void, growth of void and coalescence of voids. Many studies have been conducted; Kikuchi and Sannoumaru have published papers on the studies of ductile fracture. In the first paper [1], the thickness effect on the microscopic fracture process and fracture toughness is studied experimentally. In the second paper [2], dimple fracture tests were performed using three point bending specimens. In the test, loading condition is changed from mode I to mixed mode condition to study the effect of the mixed mode loading. Numerical simulation is conducted using Gurson’s constitutive equation. It is found that crack growth direction is affected significantly by the loading condition. Ductile fracture of a pipe used in Light Water Reactor components is researched in this paper. Four point bending of a pipe experiment had been done by the Central Research Institute of Electric Power Industry [3]. They were experimented in two conditions; one at room temperature (23 ) and second at high temperature (300 ). As a result, crack propagation behavior differs largely form each other. At room temperature, crack propagates parallel from the pre crack, and at high temperature, crack propagates in a slanting direction from the pre crack. Results show that that difference from the two temperature distinction of a tensile test in a stress strain curve is very little. In this paper, this problem is studied at first by experiments, observation of fracture surface and numerical simulation.

Ductile Fracture Simulation of a Pipe under Bending

Ductile Fracture Simulation of a Pipe under Bending

Meshfree simulations of spall fracture

Shock wave induced spall fracture is a complex multiscale phenomenon, and it is a challenge to build a constitutive and computational model that can capture essential features of the spall fracture. In this work, we present a computational micro-mechanics model to simulate spall fracture by utilizing the multiscale micro-mechanics theory proposed by Wright and Ramesh [36] and a RKPM meshfree method. The focus of this work is to develop and demonstrate a simulation tool that is capable of simulations of spall fracture in engineering application. First, based on a well-known empirical formula, we relate the macroscale spall strength to the kinematics of micro void growth in a Representative Volume Element (RVE). The connection between micro void growth and overall kinematics of the RVE is made through the conservation of mass in the micro to macro transition process. Second, we develop a set of meshfree void growth algorithms that is tailored to represent kinematics of void nucleation, growth and coalescence, and these algorithms retain the conservation of mass, momentum, and energy during simulations of ductile spall fracture. Third, based on the Johnson–Cook model, we developed a meshfree computational formulation, and we have carried out simulations of the spall fracture of a Ti–6Al plate under impact loads to validate the model. From the simulation, we find that the interaction between the first two inelastic wave pulses plays an important role in the mechanism of spall fracture. The numerical results show that the proposed method can capture some features of the spall fracture, and it may be used to simulate the spall fracture in engineering applications.

Use of a modified Gurson model approach for the simulation of ductile fracture by growth and coalescence of microvoids under low, medium and high stress triaxiality loadings

Abstract In the paper the modified Gurson model is developed for the simulation of damage growth and ductile fracture under low, medium and high stress triaxiality loadings. A new coalescence criterion is introduced based on a simple assumption that singular value of the effective stress triggers the coalescence of microvoids in materials. According to the introduced approach the void coalescence described by means of the modified Gurson model is not only determined by the so-called critical, constant void volume fraction but also by the stress triaxiality ratio. Computational simulations have been carried out for Al 2024–T351 aluminum specimens. In order to find some improvements of micromechanical damage models, two different approaches have been compared for modeling the shear driven microvoid coalescence under low stress triaxiality loadings.

Simulation of critical behaviour on damage evolution

Based on a damage evolution equation and a critical damage function model, this paper has completed the numerical simulation of ductile spall fracture. The free-surface velocity and damage distribution have been used to determine jointly the physical parameters D1 (the critical linking damage), Df (the critical fracturing damage) and k (the softening rate of critical damage function model) of the critical damage function model, which are 0.11, 0.51 and 0.57 respectively. Results indicate that the parameters determined by any of shots could be applicable to the rest of other shots, which is convincing proof for the universal property of critical damage function. In our experiments, the shock pressure is about 1 GPa to 2.5 GPa. For the reason of limited pressure range, there are still some limitations in the methods of present analysis. Moreover, according to the damage evolution characteristic of pure aluminum obtained by experiments, two critical damages are obtained, which are 0.11 and 0.51 respectively. The results are coincident with the experimental ones, which indicate that the critical growth behaviour of damage occurs in the plastic metal under dynamic loading.

Ductile fracture simulation of hydropiercing process based on various criteria in 3D modeling

Hydropiercing has been used widely in the past decade in the automotive industry. So far, the ductile fracture of hydropiercing process considering the effect of hydroforming has not been studied in detail due to the complicated deformation process. In order to simulate hydropiercing process accurately, a 3D model considering the effect of hydroforming process has been developed in this study. Six ductile criteria were implemented to predict crack initiation and propagation by means of the user subroutine VUMAT of ABAQUS. The comparative study among the results obtained by the simulations using the different ductile criteria and the experiments was explored. The model using the Rice and Tracey Criterion shows good agreement with the experiment at loading pressure of 60–60 MPa, however the others could not. Moreover, the simulation errors using the Rice and Tracey Criterion at different loading pressure and hydropiercing type are small enough too compared with experiments so that this criterion could be used to simulate the hydropiercing process. Finally, the deformation mechanism of hydropiercing process has been discussed on the bases of simulations with the Rice and Tracey Criterion and experiments.

A non-local finite element based on volumetric strain gradient: Application to ductile fracture

The aim of this work is to propose a finite element formulation adapted to ductile fracture simulation using Continuum Damage Mechanics and unravelling two main encountered difficulties. First, as ductile damage represents voids nucleation and growth, constitutive behaviors constrain the plastic volumetric strain through damage evolution laws, leading to volumetric locking. A specific formulation is consequently needed. A three-field formulation is defined, in which volume change is treated as a new unknown; its relation to the displacement field is weakly enforced by mean of a Lagrange multiplier. Then, strain and damage localisation occurs due to softening, and leads to spurious mesh dependent solutions. A coupling between neighbouring material points is thus introduced through a volume change gradient term added in the three field formulation. First results show that this formulation permits to control localisation and to unravel mesh dependency.

Dimple Fracture Simulation under Mixed Mode Loading Condition

Dimple fracture under mixed mode loading condition is studied experimentally and numerically. By the mixed mode loading, it is found that fracture surface becomes much rougher than that of mode I fracture. It is also found that ductile fracture growth direction deviates from the original plane. It becomes clear that there are two factors affecting ductile fracture processes, one is mixed mode ratio and another is thickness effect. Three-dimensional finite element analyses are conducted to study effects of these factors. For the simulation of ductile fracture, Gurson’s constitutive equation is used with large deformation theory. These numerical results agree with experimental observation very well qualitatively.

A thermo-mechanical cohesive zone formulation for ductile fracture

The paper addresses the possibility to project both mechanical and thermal phenomena pertinent to the fracture process zone into a cohesive zone. A wider interpretation of the notion cohesive zone is thereby suggested to comprise not only stress degradation due to micro-cracking but also heat generation and energy transport. According to our experience, this widening of the cohesive zone concept allows for a more efficient finite element simulation of ductile fracture. The key feature of the formulation concerns the thermo-mechanical cohesive zone model, evolving within the thermo-hyperelastoplastic continuum, allowing for the concurrent modelling of both heat generation, due to the fracture process, and heat transfer across the fracture process zone. This is accomplished via thermodynamic arguments to obtain the coupled governing equation of motion, energy equation, and constitutive equations. The deformation map is thereby defined in terms of independent continuous and discontinuous portions of the displacement field. In addition, as an extension of the displacement kinematics, to represent the temperature field associated with the discontinuous heat flux across the fracture interface, a matching discontinuous temperature field involving the interface (or band) temperature is proposed. In the first numerical example, concerning dynamic quasi-brittle crack propagation in a thermo-hyperelastoplastic material, we capture the initial increase in temperature close to the crack surface due to the energy dissipating fracture process. In the second example, a novel application of ductile fracture simulation to the process of high velocity (adiabatic) cutting is considered, where some general trends are observed when varying the cutting velocity.

Numerical simulation of ductile fracture with the Rousselier constitutive law

This contribution aims at developing robust and reliable tools dedicated to predictive numerical simulation of ductile fracture. Description of damage mechanisms relies here on the Rousselier constitutive law. To achieve robustness and objectivity, several points need then to be addressed: reduction of the set of internal variables so as to recast the model into the framework of generalised standard materials; proper expression of the normal plastic flow rule at the vertex of the yield surface; finite strain formulation based on a multiplicative split of the deformation gradient; fully implicit integration of the constitutive equations leading to a single scalar equation that admits a unique root; use of mixed finite elements to avoid volumetric locking; strain gradient-based nonlocal model to control strain localisation and remedy spurious mesh dependency. The capabilities of the resulting numerical formulation are demonstrated through simulating the cup–cone fracture of a notched tensile specimen.

On some topics for the numerical simulation of ductile fracture

In this work, we analyze some aspects of the macroscopic Gurson–Tvergaard–Needleman (GTN) constitutive model when it is addressed to solve ductile fracture problems by means of numerical simulations: (i) The analytical solutions of the material discontinuous bifurcation problem is performed. Closed and exact formulas are obtained. The so determined critical conditions and the developed strain localization mode are afterward studied and compared in crack growth problems. Even when this methodology of analysis is rather standard at the present, the conclusions drawn from this study differ significantly from that obtained with a similar analysis in quasi-brittle fracture problems. (ii) A new very robust numerical integration method for the GTN model, namely the Impl–Ex Method, is proposed. It is a low computational cost algorithm, equivalent to a linear problem per each integration step, with a reasonable precision for engineering purposes. Its accuracy and convergence rate is assessed by means of an error study applied to a ductile fracture test simulation. (iii) A detailed analysis of a plane strain ductile crack growth problem is performed in a material containing two size-scale of voids. In the analysis, particular attention is given to the mesh size dependence and to the coalescence of the larger void.

Void coalescence processes quantified through atomistic and multiscale simulation

Simulation of ductile fracture at the atomic scale reveals many aspects of the fracture process including specific mechanisms associated with void nucleation and growth as a precursor to fracture and the plastic deformation of the material surrounding the voids and cracks. Recently we have studied void coalescence in ductile metals using large-scale atomistic and continuum simulations. Here we review that work and present some related investigations. The atomistic simulations involve three-dimensional strain-controlled multi-million atom molecular dynamics simulations of copper. The correlated growth of two voids during the coalescence process leading to fracture is investigated, both in terms of its onset and the ensuing dynamical interactions. Void interactions are quantified through the rate of reduction of the distance between the voids, through the correlated directional growth of the voids, and through correlated shape evolution of the voids. The critical inter-void ligament distance marking the onset of coalescence is shown to be approximately one void radius based on the quantification measurements used, independent of the initial separation distance between the voids and the strain-rate of the expansion of the system. No pronounced shear flow is found in the coalescence process. We also discuss a technique for optimizing the calculation of fine-scale information on the fly for use in a coarse-scale simulation, and discuss the specific case of a fine-scale model that calculates void growth explicitly feeding into a coarse-scale mechanics model to study damage localization.