A shear-coupled Gurson model incorporating out-of-plane constraint effects for three-dimensional ductile fractures

Lithium-ion batteries provide the power for portable electronics and found many other interesting applications. It is desirable to design batteries with high energy density and long cycle life. Silicon is among the highest Li-storing anode materials in batteries, but the large capacity is accompanied by significant volume expansion that causes mechanical failure and capacity fading after few charging/discharging cycles. There is evidence that the mechanical behavior of lithiated amorphous silicon depends on the history of charging and discharging. The goal of this thesis is to better understand the mechanical properties and behavior of lithiated silicon, specifically the dependence of its properties on the state of charging/discharging, through atomistic simulation, constitutive modelling and finite elements method calculations. Amorphous high-storage-capacity Li-Si flows at lower stresses than crystalline materials but the plastic flow stress decreases with charging and discharging, indicating important non-equilibrium aspects to the flow behavior. In this thesis, a mechanistically-based constitutive model for rate-dependent plastic flow in amorphous materials, during charging and discharging is developed based on two physical concepts: (i) excess energy is stored in the material during electrochemical charging and discharging due to the inability of the amorphous material to fully relax during the charging/discharging process and (ii) this excess energy reduces the barriers for plastic flow processes and thus reduces the flow stress. Plastic flow stress in our model is a result of a competition between the time scale of charging/discharging and the time scale of glassy relaxation. The two concepts, as well as other aspects of the model, are validated using molecular simulations on a model Li-Si system. Furthermore, I formulate and implement a finite element method based on the developed constitutive model to capture the full complexity of coupled chemical-mechanical evolution including plastic flow that arises in these amorphous battery materials. Fracture is the main cause of degradation and capacity fading in lithiated silicon during cycling, thus it is essential to develop mechanistic models for the fracture of Li-Si to interpret the experiments and facilitate the design. Here, I perform systematic atomistic simulations of crack propagation for different Li compositions discharged samples. I observe void nucleation and coalescence as the primary mechanism of crack growth in all samples. Discharging increases the structural disorder which results in decrease in the flow stresses but simultaneously facilitates void nucleation and growth. The fracture toughness and energy is increased by discharging, indicating that the flow and fracture of lithiated silicon depends on the history of charging/discharging. Because of the similarities between the fracture mechanism of Li-Si and ductile fracture, Gurson's model is used to help interpret the simulation results. Qualitative agreement between the trends predicted by Gurson's model based fracture simulations and MD simulations of cracks in Li-Si is demonstrated. Gurson-type models predict that the fracture energy scales with the yield stress and void spacing. In all tested cases the nucleated voids spaced within few nanometers of the crack tip, which explains the low fracture energy of Li-Si.

Numerical modeling of the fracture effects on the strength of steel circular hollow section joints has not been sufficiently addressed historically. The Gurson model simulates the plastic yield behavior of material with microvoids. It is found in the current study that we can offer an alternative approach in modeling the ductile fracture for the strength analysis of tubular joints. Two loading conditions are investigated on tubular bars with the Gurson model. The effects of void growth and nucleation are observed to be more prominent in the axial tensile mode than the shear mode. Two types of tubular joints are investigated: precracked tubular joints and intact tubular joints. The effect of ductile fracture is reflected by softening of material, which leads to reductions in load-deformation curves which are consistent with test observations. Due to the lack of material data, a sensitivity study is carried out on the Gurson's material properties.

103. Steroid binding components in human semen

The manufacturing of ductile materials generally inserts impurities into their microscopic composition. These impurities may detach from the surrounding matrix and even crack along progressive deformation. Due to the consequent incapacity of these undesirable particles of supporting any stress, these ductile materials are equivalently assumed to be porous. Porosity has been effectively shown to play a fundamental role in the mechanisms of ductile fracture. Many micromechanical models have been proposed since the 1970s with the aim of mathematically describing these mechanisms. Among them, the acclaimed Gurson model combines the averaging homogenization technique with the kinematic theorem of Limit Analysis to estimate the macroscopic yield criterion and porosity evolution law of porous ductile materials. However, the Gurson model and most of its extensions only account for isotropic ductile fracture. Thus, the purpose of the present work is to contribute to the conception of yield criteria for anisotropic porous ductile rupture. Three main contributions are hereby proposed by profiting from similar hypothesis to those of the Gurson model. The first contribution is the assessment of the influence of void morphology on overall yield criteria for those classes of materials. The second is the inclusion of an anisotropic yield criterion in the material matrix so that the macroscopic behavior presents matrix-induced anisotropy even for spherical cavities. The third and last advancement consists of generalizing the material matrix yield criterion of the Gurson model in order to include a linear transformation-based class of yield functions that has been widely used to represent specific high strength aluminum alloys. The results hereby presented highlight the consistency and robustness of the three formulations. Moreover, the role of the porosity on the modeling of yield behavior of aluminum alloys encourages further work regarding experimental parameter characterization.

Fracture experiments on TRIP‐assisted steel sheets covering a wide range of stress states (from shear to equibiaxial tension) are performed to create a comprehensive experimental database to calibrate and evaluate the shear‐modified Gurson model (Nielsen and Tvergaard, 2010) and the Modified Mohr‐Coulomb (MMC) fracture model (Bai and Wierzbicki, 2010). The experimental program includes notched tensile tests as well as fracture experiments on butterfly‐shaped specimens under combined tension and shear loading. Both phenomenological fracture models are physics‐inspired and take the effect of the first and third stress tensor invariants into account in predicting the onset of ductile fracture. The MMC model is based on the assumption that the initiation of fracture is determined by a critical stress state, while the shear‐modified Gurson model assumes void growth as the governing mechanism. The model accuracy is quantified based on the predictions of the displacements to fracture for experiments which have not been used for calibration. It is found that the MMC model predictions agree well with all experiments (less than 4% error), while less accurate predictions are observed for the shear‐modified Gurson model. A comparison of plots of the strain to fracture as a function of the stress triaxiality and the normalized third invariant reveals significant differences between the two models except within the vicinity of stress states that have been used for calibration.

A modified Gurson model and its application to punch-out experiments

The microscopic process of ductile fracture in the process zone is studied in this paper. First, the FRASTA (fracture surface topographic analysis) technique is used, and the ductile fracture processes of two kinds of aluminum alloys, 7075-T6 and 2017-T4, are observed. The nucleation, growth and coalescence of voids are observed in detail. The finite element analyses based on Gurson's model are then carried out. The element vanishing method is used with the finite deformation theory. Using the void volume percent as the fracture criterion, the nucleation and growth of voids and coalescence with the crack are simulated. It is shown that these phenomena occur in the process zone, and the numerical results agree qualitatively with the experimentalones.

Ductile fracture under extreme loading is different from fatigue under cyclic loading, it results from an excessive force applied to a metal such as aluminum, and the material undergoes large inelastic or plastic deformation before its final structural failure. The numerical simulation of ductile fracture has been a challenge in computational failure mechanics and materials science. In this paper, a meshfree method with the modified Gurson’s model is developed in the modeling and simulation of ductile fracture of thin shell structures under in-plane bending and stretching loading. The prediction of ductile crack growth agrees very well with experiment.

Numerical implementation and assessment of the GLPD micromorphic model of ductile rupture

The aim of this paper is to show, using an example, the finite element potential to simulate ductile fracture problems involving high number of degrees of freedom. The example consists of a model proposed by Gologanu, Leblond, Perrin and Devaux (GLPD model) to describe ductile fracture. This model is an extension of the famous Gurson's model to address the underlying unlimited lo- calization problem arising in the Gurson model. The GLPD model was derived from some refinement of Gurson's original homogenization procedure; the new model is of micromorphic nature, involving the second gradient of the macro- scopic velocity and generalized macroscopic stresses of moment type, together with some characteristic microstructural distance. The numerical implementa- tion of this model into finite element codes is quite involved, since its requires the use of finite element of class C 1 and the solution of a complex projection onto the yield locus problem. Enakoutsa and Leblond have proposed a numerical scheme that avoids these two difficulties. We present here some new assessments of this numerical scheme. First, we develop an analytical solution for the problem of an elastic hollow sphere, obeying the GLPD model and subjected to hydro- static tension; this solution agrees very well with the numerical predictions of the GLPD model. Also, comparisons between experimental and numerical load vs. displacement curves for an axisymmetric pre-cracked spcimen made of typical stainless steel are found to yield satisfatory results.

Numerical Approach to the Ductile Fracture of Steel Members

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

Mastering the art: Proficient finite element implementation and robust evaluation of a strain-hardening porous ductile material crack growth prediction model at finite strain

A complete Gurson model approach for ductile fracture

Modeling of scatter and size effect in ductile fracture: application to thermal embrittlement of duplex stainless steels