Simulation Of Ductile Fracture Research Articles

Study on the PDDO-based meshfree method in numerical simulation of shell ductile fracture considering a non-local GTN model

A meshfree method is developed based on the peridynamic differential operator (PDDO) for ductile damage and fracture problems in metal shell structures. The kinematic equations coupled to classical continuum mechanics (CCM) are derived with the motion variables discretized by the PDDO. The elastoplastic and fracture behavior of the material are described by applying the Gurson-Tvergaard-Needleman (GTN) model with shear modification, and the non-local form of the model improves the computational convergence for different modeling scales. The zero-energy model in numerical computations is effectively controlled by introducing an hourglass force based on the average displacement state. The particles contact algorithm and multi-crack visualization algorithm are developed to simulate the fracture of shell structures under collision loads. By comparing with experiments, it is verified that the proposed PDDO-based meshfree method can accurately predict the ductile fracture of shell structures subjected to in-plane and out-of-plane loads.

Finite Element Ductile Fracture Simulation of Charpy and Drop Weight Tear Tests for API X52

This paper presents a systematic procedure for performing finite element (FE) impact ductile fracture simulation of Charpy (CVN) and Drop Weight Tear Tests (DWTT) with validation using test data of API X52. For deformation and fracture models, the Johnson-Cook (J-C) model is used, of which seven parameters are determined by analyzing (1) round bar tensile test data at three different temperatures (two parameters), (2) tensile test and fracture toughness test at room temperature (three parameters) and (3) instrumented Charpy test (load–displacement) data at room temperature (two parameters). FE impact fracture simulation results with the determined parameters show good agreement with instrumented CVN test data at three different temperatures (0 °C, −30 °C and −60 °C) and DWTT data at temperatures of RT and −30 °C. For DWTT simulation, an analysis of the pre-strain due to flattening is included. Additionally, sensitivity analyses for the effect of adiabatic heating and strain rate on simulation results show that, although both phenomena should be considered in simulation, the strain rate effect is more significant than the adiabatic heating effect.

Phase-field ductile fracture simulations of thermal cracking in additive manufacturing

We present a multiphysics phase-field fracture model for thermo-elasto-plastic solids in the context of finite deformation and apply it to simulate the hot cracking phenomenon during metal additive manufacturing. The model is derived in a thermodynamically consistent manner, with the intercoupling mechanisms among elastoplasticity, phase-field crack and heat transfer comprehensively considered. It involves particularly coupled parameters among these materials physics, e.g. plasticity-dependent degradation function and fracture toughness, damage-dependent yield surface and thermal properties, and temperature-dependent elastoplastic properties and fracture strength. The finite element implementation of the coupled phase-field model is benchmarked with simulation results of a tensile test of an I-shape specimen, encompassing elastoplasticity, hardening, necking, crack initiation and propagation, in contrast to the related experimental results. The validated model is further employed to simulate the multiphysics hot cracking phenomenon in additive manufacturing in the context of both the effective powder-bed model and the powder-resolved model thanks to prior non-isothermal phase-field powder-bed-fusion simulations. Simulation results reveal certain key features of the hot crack and its dependency on process parameters like beam power and scan speed, which are helpful for the fundamental understanding of crack formation mechanisms and process optimization.

A diffusive‐discrete crack transition scheme for ductile fracture at finite strain

SummaryThis study presents a diffusive‐discrete crack transition scheme for stably conducting ductile fracture simulations within a finite strain framework. In the developed scheme, the crack initiation and propagation processes are determined according to an energy minimization problem based on crack phase‐field theory, and the predicted diffusive path is transformed to a discrete representation using the finite cover method during the staggered iterative scheme. In particular, for stably conducting ductile fracture simulations, three computational techniques, the staggered iterative configuration update technique, the subincremental damage update technique, and the crack opening stabilization technique, are introduced. The first and second techniques can be used regardless of whether discrete cracks are considered, and the third technique is specialized for diffusive‐discrete crack transition schemes. Accordingly, ductile fracture simulations with the developed scheme rarely encounter troublesome problems such as oscillations in the displacement field and severe distortion of finite elements that can lead to divergence of calculations. After the crack phase‐field model for ductile fractures is formulated and discretized, the numerical algorithms for realizing the diffusive‐discrete crack transition while maintaining computational stability are explained. Several representative numerical examples are presented to demonstrate the performance and capabilities of the developed approach.

Elevated-temperature material properties and fracture behavior of fire-resistant steel FR355

Fire-resistant steel (FRS) has been increasingly used in engineering structures due to their advantages of excellent earthquake and fire resistance properties. Accurately characterization of material properties and limit states of steel material is very important for structural-safety design and finite element (FE) simulation. This paper presents the results of experimental and numerical investigations on the elevated-temperature performance of FRS in terms of material properties, full-range true stress-strain curve, ductile fracture behavior, which has not yet been reported. The experimental part of the present paper includes the steady-state tensile testing of conventional structural steel (CSS) and FRS at temperatures up to 800 °C. Hollomon law and weighted average method were adopted to derive full-range true stress-strain behavior of the investigated steels at elevated temperatures, which is required for ductile fracture simulation in ABAQUS. Ductile fracture of tensile coupon specimens was modelled using the stress-modified critical strain model (SMCS). To verify the accuracy and application of the proposed true stress-strain and fracture models, finite element (FE) simulations of tensile coupon tests were performed using ABAQUS/explicit. It shows that the FE simulation incorporating proposed material plastic behavior and ductile fracture model provides accurate predictions for fracture response of the tensile coupons.

Yield criterion for intergranular void coalescence under combined tension and shear

Intergranular ductile fracture is a failure mode that may arise in many metallic alloys used in industrial applications. It manifests as the successive nucleation, growth, and coalescence of cavities at grain boundaries. Thus, simulation of intergranular ductile fracture in polycrystals requires modeling those three different stages at the scale of grain boundaries, i.e. at the interface between two different crystals. In this study, a yield criterion for the coalescence of cavities at the interface between two isotropic materials obeying Mises plasticity is first developed by limit analysis in order to provide some insights into that phenomenon. This criterion is checked against numerical limit analysis under combined tension and shear and is found to agree with unit-cell simulations quantitatively. The model is then extended to crystals so as to account for the complex coupling between loading state, crystallographic orientations, and void microstructure in intergranular coalescence. This second criterion is also assessed through comparisons to numerical limit analysis for an FCC crystal lattice. The agreement is very good in the case of coalescence by internal necking and the trends displayed by coalescence under combined tension and shear are captured correctly. Some implications of the model on the competition between transgranular and intergranular ductile fracture are discussed. Finally, by combining this model with an existing criterion for void growth at grain boundaries, a multi-surface yield function relevant to intergranular ductile fracture is obtained and compared to unit-cell simulations.

Sensitivity analysis of GTN damage parameters: Application to notched plate ductile fracture simulation

The evolution of preexisting voids causes damage to metal structures with large plastic deformation. In the ABAQUS-Explicit computer code, the damage by the Gurson–Tvergaard–Needleman model (GTN model) is included in the porous failure criteria law. The numerical predictions using the GTN model are very sensitive to the calibrations of these parameters of the experimental results. This model describes until the damage, the mechanism of the evolution of the voids, which begins with their growth and their nucleation with the particles until the coalescence of these voids of a critical level, which causes the damage to the structure. This analysis uses Voce’s hardening model and von Mises’ equivalent stress flow theory. After validation with experimental results, this work aims to analyze the sensitivity of these GTN parameters to the response to damage and to the evolution of the gaps. This objective is applied on a plate notch.

Ductile fracture simulation on 10.9 HP bolts under composite loading at elevated temperatures

AbstractThe mechanical properties of the bolts deteriorate significantly at elevated temperatures; accurate prediction of the performance and fracture behaviour of steel bolted connections is essential for the fire safety assessment of steel structures and is a prerequisite for performance‐based fire safety design. Existing studies on the fracture mechanical properties of bolts at elevated temperatures are limited due to the difficulty and economics of testing. This paper presents the numerical analysis of combined loads on grade 10.9 high‐performance (HP) bolts. Based on the proven fracture analysis method, the fracture behaviour of HP bolts at high temperatures was investigated by fitting material parameters. Significant changes in the fracture shape of the bolts at high temperatures were found. The ultimate resistance, fracture deformation behaviour and strength reduction factors were analyzed. This study demonstrates the potential of using numerical analysis to reasonably predict the fracture behaviour of steel bolted joints at high temperatures and under complex loading conditions.

Finite element simulation method for combined Ductile-Brittle fracture of small punch test in hydrogen

This paper presents a simulation method for combined ductile–brittle fracture of small punch (SP) test in hydrogen and application to test data of API X70 steel. For ductile fracture simulation, the multi-axial fracture strain damage model determined from un-embrittled material with the hydrogen-embrittlement constant determined from SP test in hydrogen is used. To simulate brittle fracture, the critical stress method is proposed, where the critical stress is determined using the V notch round bar tensile test in hydrogen. The determined models are applied to simulate the SP test in hydrogen showing combined ductile and brittle fracture mode. Simulation can well reproduce not only the load–displacement curve but also the circumferential ductile cracking, followed by radial brittle cracking, observed in the test.

A gradient-based non-local GTN model: Explicit finite element simulation of ductile damage and fracture

Non-local models have over the years been established as an effective approach to solve the pathological mesh dependency problem observed in finite element simulation of strain-softening materials. This paper presents the formulation, implementation, and application of a gradient-based non-local Gurson–Tvergaard–Needleman (GTN) model for explicit finite element analysis. The porosity is taken as the non-local variable where the increment in porosity is averaged over the volume using an implicit gradient model. The gradient model is implemented in Abaqus/Explicit by utilising the coupled thermal–mechanical solver, which proves to be both a simple and computationally efficient approach. Due to the use of an explicit integration scheme, a transient term is introduced to the partial differential equation of the gradient formulation. The non-local GTN model is compared to the local counterpart for increasing mesh refinements using a plane strain shear band specimen, a plane strain tension specimen, and a plane strain compact tension specimen. The proposed approach can remedy the pathological mesh dependency problem. For the plane strain tension specimen, it is shown that the non-local GTN model will preserve the fracture mode (slant versus cup–cup fracture mode) when the mesh is refined. The non-local GTN model is also able to predict the same fracture mode as observed in ductile tearing experiments. However, non-local averaging can over-smooth the fields and exclude the slant fracture mode from occurring if the material length Lc is too large.

Effect of pre-crack non-uniformity for mini-CT geometry in ductile tearing regime

The mini-CT specimen attracts the attention from all over the world for application in fracture toughness measurement. However, one of the shortcomings of this geometry is related to the required tight accuracy of the specimen dimensions, in particular the fatigue pre-crack curvature which often violates the requirements of the ASTM standards. Given the limited thickness of mini-CT geometry, non-uniform pre-crack tends to develop during fatigue pre-cracking, resulting in a large proportion of mini-CT specimens being considered invalid.Previous investigations have demonstrated that mini-CT specimens with excessive crack front curvature can still provide meaningful fracture toughness results. In this paper, the effect of pre-crack front non-uniformity on ductile fracture is studied: first, the difference of macro parameters such as the applied load, J-integral and crack tip stress–strain field are investigated to illustrate the varying fracture behavior related to non-uniform pre-crack. Next, two micro-mechanics-based approaches, the Rice-Tracey void growth model and Thomason void coalescence model, are integrated to compare the ductile fracture initiation conditions associated with uniform and non-uniform fatigue pre-crack. Finally, the experimental verification of the ductile fracture simulations is performed for mini-CT specimens with uniform and 30° tilted initial cracks. The results indicate that the pre-crack non-uniformity plays a major role in the redistribution of local J-integral and stress–strain state, further affects the position of crack initiation and the early stages of crack propagation. Nevertheless, the pre-crack non-uniformity has limited effect on the global properties that are usually expected from fracture toughness tests, such as applied load, J-R curve and critical fracture toughness. The requirements in the ASTM E1820 regarding pre-crack front curvature need thus to be relaxed.

A new ductile fracture model for Q460C high-strength structural steel under monotonic loading: Experimental and numerical investigation

Tensile fracture static tests on nine specimens covering different stress states were performed to investigate the ductile fracture behavior of Chinese Q460C high-strength structural steel (HSS). Based on combining the Rice-Tracey model and Xue model, the new model considering the effect of stress triaxiality and Lode angle was proposed to predict ductile fracture of Q460C HSS. Furthermore, the stress softening criterion was incorporated into the new fracture model to simulate the fracture propagation of Q460C HSS better. The material parameters of the proposed fracture model for Q460C HSS were identified using MATLAB optimization code. The VUMAT subroutine was developed to perform ductile fracture simulations for each specimen, and the fracture simulation results show satisfactory agreement with the experimental results. In addition, the five existing ductile fracture models were also selected to compare the prediction accuracy of the new model. The comparative results show that the new model has better accuracy and is more suitable for predicting fracture initiation and propagation of Q460C HSS. Finally, the applicability of the new model in predicting the fracture of Q460 HSS was furtherly verified by successfully simulating the existing fracture tests of the notched round bar specimens and the bolted connections.

Ductile fracture simulation using phase field method with various damage models based on different degradation and geometric crack functions

For simulation of ductile fracture, plasticity and damage are two essential aspects. The phase field method emerged as an efficient mathematical tool to address the fracture processes involving crack initiation, merging, and branching. From the wide literature, it has been observed that the information on the suitability of the existing phase field models for simulation of ductile fracture is scanty. This paper proposes a phase field methodologies for simulation of ductile fracture considering the aspects like different degradation and crack geometric functions. The proposed formulation couples the damage model, constitutive behaviour of elasto-plastic solid and J2 plasticity. Numerical simulations are carried out using ABAQUS with user-defined element (UEL) subroutine codes, defining the displacement field and phase field variable. Several benchmark problems were analysed to investigate the (i) behaviour of the specimen (ii) the performance of various phase field damage models (PFDM) and (iii) the effect of non-dimensional parameters considered in the damage models. The maximum percentage difference between the numerically predicted maximum load and its corresponding displacement is in good agreement w.r.t experimental value under PFDM4 (±10% range). The output of the study provides an insight on the use of various damage models and other parameters for the simulation of ductile crack propagation. This proposed model can be further extended to the prediction of remaining life or residual strength of the structural component.

Void growth yield criteria for intergranular ductile fracture

Ductile fracture through growth and coalescence of intergranular cavities is a failure mode observed experimentally in many metallic alloys used in industrial applications. Simulation of this fracture process in polycrystalline aggregates requires modeling of the plastic yielding of porous boundaries. However, classical yield criteria for porous materials such as the Gurson–Tvergaard–Needleman model and its current extensions cannot account for the complex coupling between loading state, crystallographic orientations, void shape and material behavior at grain boundaries. In order to bridge this modeling gap, two yield criteria for intergranular ductile void growth are proposed. The first one is a GTN-like model derived from limit-analysis which, once calibrated, accounts for spherical voids at the interface of rate-independent crystals. The second one is developed from a variational approach and predicts yielding in viscoplastic crystals containing intergranular ellipsoidal cavities. Both models are validated against a wide database of numerical limit-analysis of porous bi-crystals using a FFT solver. Satisfying agreements are obtained, paving the way to microstructure-informed intergranular ductile fracture simulation. The interplay between plastic yielding inside grains and along grain boundaries is finally studied based on the proposed yield criteria.

Crack initiation and growth in 316LN stainless steel: Experiments and XFEM simulations

A methodology for computer simulation of ductile fracture in engineering structures using the eXtended Finite Element Method (XFEM) is presented. Crack initiation is modeled using an instability-based failure criterion derived from the micromechanics of void coalescence. The criterion depends on the state of stress at failure, strain hardening and the void volume fraction, whose evolution as a function of plastic strain is obtained using a physics-based void growth law. Material separation is modeled using the cohesive zone method, where cohesive surface elements are dynamically inserted into continuum elements that satisfy the failure criterion. The methodology is illustrated by comparing the model predictions with experimental data on uncracked and pre-cracked 316LN stainless steel specimens. It is shown that, using a set of parameters calibrated from standard tests, the model is able to quantitatively predict fracture in a variety of specimens. In contrast, widely used continuum damage models are unable to predict fracture in the different specimen types using a single set of material parameters.

Simulation of ductile fracture in aluminium alloys with random or strong texture using heuristic extensions of the Gurson model

Ductile fracture of two high-strength aluminium alloys in temper T6 is investigated using heuristic extensions of the Gurson model with non-quadratic yield criteria. Simulations of tensile tests on smooth and notched specimens made for each alloy either from cast billets with random texture or from extruded profiles with strong deformation texture are performed and compared with experiments from previous studies. The plastic anisotropy and its influence on the predicted fracture is investigated for the extruded profile materials through simulations in several tensile directions. In the heuristic extensions of the Gurson model, the Hershey–Hosford yield function is used for the materials with random texture and the anisotropic Yld2004-18p yield criterion is used for the materials with strong deformation texture. The two alloys have different fraction of constituent particles, and as a conservative assumption the initial porosity is taken equal to the particle fraction in the simulations. For each combination of alloy and processing condition (in total four combinations), the parameters governing the flow stress of the matrix material and the critical porosity at failure are determined using a single test, while the remaining tests are used for validation. Fracture is simulated by element erosion at the critical porosity. The results show that the heuristic extensions of the Gurson model give predictions of the tensile ductility with a satisfactory accuracy for the two alloys in both processing conditions.

Homogenized constitutive equations for porous single crystals plasticity

Ductile fracture through void growth to coalescence occurs at the grain scale in numerous metallic alloys encountered in engineering applications. Classical models used to perform numerical simulations of ductile fracture, as the Gurson–Tvergaard–Needleman model and its extensions, are relevant for the case of large voids compared to the grain size, in which a homogenization of the material behavior over a large number of grains is used. Such modeling prevents assessing the effects of microstructure on both crack path and crack propagation resistance. Therefore, homogenized constitutive equations for porous single crystals plasticity are proposed, featuring void growth and void coalescence stages, hardening and void shape evolution. An original numerical implementation based on the coupling of Newton–Raphson and fixed point algorithms is described. In order to assess the accuracy of the proposed model as well as another one described recently in the literature, an extended database of porous unit-cell simulation results is gathered, investigating the effect of crystallographic orientations and hardening behavior for a FCC material. Strengths and weaknesses of both models are detailed with respect to the reference simulations, leading to the definition of the validity domain of the current model and to pinpoint necessary refinements.

Evaluating the strength of grade 10.9 bolts subject to multiaxial loading using the micromechanical failure index: MCEPS

AbstractBolted joints in steel structures are generally subject to combined actions. The research on ultimate capacity of bolted joints under combined tension and shear actions, twin shear actions, and combined tension‐twin shear actions is relatively limited. The aim of this paper is to calibrate the fracture locus of grade 10.9 bolts using the mesoscale critical equivalent plastic strain (MCEPS). We use ductile fracture simulation to numerically evaluate the ultimate resistance of bolts subject to multiaxial loading and compare the results with the current design standards. The results show that predictions for grade 10.9 bolts subject to multiaxial loading in Chinese code GB 50017 and American code AISC‐360 are not on the safe side, while predictions in European code EN1993‐1‐8:2005 are slightly on the conservative side. We propose two modification factors to improve prediction of bolt strength subject to multiaxial loading; namely the multiaxial loading factor for shear resistance ξv and the multiaxial loading factor for tensile resistance ξt.

Hybrid experimental-numerical strategy for efficiently and accurately identifying post-necking hardening and ductility diagram parameters

Although various effective models for simulating ductile fracture in metallic materials have been established, the methods to identify the required parameters have scarcely been clarified. The difficulty for parameters identification of ductile fracture models is the actual bottleneck for accurate numerical predictions in ductile fracture simulation. In this paper, a strategy to efficiently identify the post-necking strain behaviour and the ductility diagram parameters is proposed by a hybrid experimental-numerical procedure. In the proposed strategy, only two types of experiments are required: a conventional tensile test and a crack growth test. All the parameters to simulate the post-necking strain hardening behaviour and the ductile fracture can be uniquely identified via numerical optimisations using load-displacement curves of the two tests. The proposed strategy was applied to an A2024T3 aluminium alloy and the post-necking hardening and ductility diagram parameters were identified by a flat tensile test and an Arcan test. Two types of plate specimens with a hole were then used to validate the proposed strategy. Good agreements between the experimental results and the numerical predictions clearly show the feasibility and accuracy of the proposed strategy. The results demonstrated that the proposed strategy is simple but effective. Therefore, it can be a general basis for characterising mechanical properties of various metallic materials.

Analyses of shearing mechanism during shear-cutting of 980 MPa dual-phase steel sheets using ductile fracture modeling and simulation

Analyses of shearing mechanism during shear-cutting of 980 MPa dual-phase steel sheets using ductile fracture modeling and simulation