Modeling of ductile fracture: Significance of void coalescence

In this paper void coalescence is regarded as the result of localization of plastic flow between enlarged voids. We obtain the failure criterion for a representative material volume (RMV) in terms of the macroscopic equivalent strain (E_c) as a function of the stress triaxiality parameter (T) and the Lode angle (θ) by conducting systematic finite element analyses of the void-containing RMV subjected to different macroscopic stress states. A series of parameter studies are conducted to examine the effects of the initial shape and volume fraction of the primary void and nucleation, growth, and coalescence of secondary voids on the predicted failure surface E_c(T, θ). As an application, a numerical approach is proposed to predict ductile crack growth in thin panels of a 2024-T3 aluminum alloy, where a porous plasticity model is used to describe the void growth process and the expression for E_c is calibrated using experimental data. The calibrated computational model is applied to predict crack extension in fracture specimens having various initial crack configurations and the numerical predictions agree very well with experimental measurements.     

Modeling and simulation of large-scale ductile fracture in plates and shells

The work is concerned with the modeling and simulation of large scale ductile fracture in plate and shell structures. A meshfree method – the reproducing kernel particle method (RKPM) – is used in numerical computations in order to enact dynamic crack propagation without remeshing. There are several novelties in the present approach. First, we have developed a crack surface approximation and particle split algorithm for three-dimensional through-thickness cracks. Second, to represent evolving crack surface in 3D shell structures, a 3D parametric visibility condition algorithm is proposed, which re-constructs the local connectivity map for particles near the crack tip or crack surfaces, so that the meshfree interpolation field can represent physical material separation in the computational domain. Third, the constitutive update formulas in explicit time integration by different versions of Gurson models and the rate-dependent Johnson–Cook model are implemented for 3D computations. Finally, the performance of different Gurson-type models are investigated and compared with the experimental data of large scale in-plate tear process. Numerical simulations of crack propagation in stiffened plates and shells demonstrate that the proposed method provides an effective means to simulate ductile fracture in large scale plate/shell structures with engineering accuracy.     

Application of the strain energy density criterion to ductile fracture

The strain energy density criterion due to Sih is used to predict fracture loads of two thin plates subjected to large elastic-plastic deformation. The prediction is achieved with a finite element analysis which is based on Hill's variational principle for incremental deformations capable of solving gross yielding problems involving arbitrary amounts of deformation. The computed results are in excellent agreement with those obtained in Sih's earlier analysis and with an experimental observation.     

Mechanical modelling of ductile fracture

Mechanical models of material failure by void growth to coalescence are described to give a brief overview of methods applied in the analysis of ductile fracture. Approximate constitutive relations for porous ductile materials are discussed, modelling both the nucleation and growth of voids. The application of the material models is illustrated by numerical analyses for a tensile test specimen and for dynamic, ductile crack growth. Unstable void growth is a relevant mechanism in ductile materials subject to a high level of triaxial tension. The analysis of such cavitation instabilities in elastic-perfectly plastic materials is discussed for axisymmetric stress states, and the relevance to metal/ceramic components is emphasized.General Lecture presented at the 10th Italian National Congress of Theoretical and Applied Mechanics; AIMETA, Pisa, October 1990.     

The ductile fracture of polycarbonate

The fracture of a known ductile polymer (polycarbonate) is investigated. It is shown that polycarbonate obeys the Dugdale model of ductile yielding by comparing measured plastic-zone sizes and displacements to the theoretical predictions. Strain-energy release rates are calculated and the critical value is shown to be one or two orders of magnitude higher than critical values for brittle polymers. Photoelastic photographs of the fracture process are presented and it is shown that the photoelastic effect definitely enhances the definition of the yield zone. Microscopic photoelastic photographs are also presented which are used to give a new interpretation to the photoplastic effect. Finally, suggestions for future work are presented.     

Micromechanics of coalescence in ductile fracture

Significant progress has been recently made in modelling the onset of void coalescence by internal necking in ductile materials. The aim of this paper is to develop a micro-mechanical framework for the whole coalescence regime, suitable for finite-element implementation. The model is defined by a set of constitutive equations including a closed form of the yield surface along with appropriate evolution laws for void shape and ligament size. Normality is still obeyed during coalescence. The derivation of the evolution laws is carefully guided by coalescence phenomenology inferred from micromechanical unit-cell calculations. The major implication of the model is that the stress carrying capacity of the elementary volume vanishes as a natural outcome of ligament size reduction. Moreover, the drop in the macroscopic stress accompanying coalescence can be quantified for many initial microstructures provided that the microstructure state is known at incipient coalescence. The second part of the paper addresses a more practical issue, that is the prediction of the acceleration rate δ in the Tvergaard-Needleman phenomenological approach to coalescence. For that purpose, a Gurson-like model including void shape effects is used. Results are presented and discussed in the limiting case of a non-hardening material for different initial microstructures and various stress states. Predicted values of δ are extremely sensitive to stress triaxiality and initial spacing ratio. The effect of initial porosity is significant at low triaxiality whereas the effect of initial void shape is emphasized at high triaxiality.     

The ductile fracture of anisotropic materials

A theoretical solution is obtained which adapts the Dugdale model to anisotropic materials. The effect of anisotropy is shown to modify each isotropic field equation by amultiplicative constant which is a function of the anisotropic-material constants. A limit on the validity of a Dugdale-type solution is found using a von Mises' yield criterion which implies that the crack and plastic zone will extend along a direction other than the crack line. As long as the material is within pirescribed limits, the Dugdale finiteness condition is shown to be affected by material anisotropy only in the calculation of a yield stress. Experimental results on crack-opening displacements are presented which indicate that a large degree of anisotropy is necessary to cause significant deviations from isotropic theory. Results are presented which indicate that anisotropy does affect the direction of crack propagation.     

Energy dissipation mechanisms in ductile fracture

The objective is to investigate energy dissipation mechanisms that operate at different length scales during fracture in ductile materials. A dimensional analysis is performed to identify the sets of dimensionless parameters which contribute to energy dissipation via dislocation-mediated plastic deformation at a crack tip. However, rather than using phenomenological variables such as yield stress and hardening modulus in the analysis, physical variables such as dislocation density, Burgers vector and Peierls stress are used. It is then shown via elementary arguments that the resulting dimensionless parameters can be interpreted in terms of competitions between various energy dissipation mechanisms at different length scales from the crack tip; the energy dissipations mechanisms are cleavage, crack tip dislocation nucleation and also dislocation nucleation from a Frank-Read source. Therefore, the material behavior is classified into three groups. The first two groups are the well-known intrinsic brittle and intrinsic ductile behavior. The third group is designated to be extrinsic ductile behavior for which Frank-Read dislocation nucleation is the initial energy dissipation mechanism. It is shown that a material is predicted to exhibit extrinsic ductility if the dimensionless parameter bρ_disl^1/2 (b is Burgers vector, ρ_disl is dislocation density) is within a certain range defined by other dimensionless parameters, irrespective of the competition between cleavage and crack tip dislocation nucleation. The predictions compare favorably to the documented behavior of a number of different classes of materials.     

Modeling of plane strain ductile rupture

The formation of slanted fracture under plane strain conditions is studied using the finite Element (FE) method. Constitutive models proposed by Rousselier and by Gurson are used. Rice's condition for localization is checked at every point of the FE mesh for each time step. The role of mesh design (element size, element aspect ratio, symmetry) is first studied. The different constitutive models are then compared. It is in particular shown that the use of the f function in the Gurson model favors flat fracture.     

A multiresolution continuum simulation of the ductile fracture process

With the advancement in computational science that is stepping into the Exascale era and experimental techniques that enable rapid reconstruction of the 3D microstructure, quantitative microstructure simulations at an unprecedented fidelity level are giving rise to new possibilities for linking microstructure to property. This paper presents recent advances in 3D computational modeling of ductile fracture in high toughness steels. Ductile fracture involves several concurrent and mutually interactive mechanisms at multiple length scales of microstructure. With serial sectioning tomographic techniques, a digital dataset of microstructure features associated with the fracture process has been experimentally reconstructed. In this study, primary particles are accurately and explicitly modeled while the secondary particles are modeled by a two scale multiresolution continuum model. The present numerical simulation captures detailed characteristics of the fracture process, such as zigzag crack morphology, critical void growth ratios, local stress triaxiality variation, and intervoid ligament structure. For the first time, fracture toughness is linked to multiscale microstructures in a realistic large 3D model.     

Evaluating the time to ductile fracture under creep conditions

S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 30, No. 11, pp. 75–84, November, 1994.     

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:     

Impact fracture characterization of polymer with ductile behavior

The characterization of ductile polymers with ductile fracture behavior is still a controversial subject. Presently, two approaches based on fracture mechanics have been proposed for the evaluation of impact failure of plastics, i.e., the method using the concept of essential fracture work, and the crack initiation and propagation approach. This paper discusses the validity of the fracture parameters used in these approaches. Additional experimental results and evidence are presented; they indicate that the concept of essential work of fracture cannot be used to characterize the fracture property of plastics. At high loading rates, the fracture energy of plastics can decrease with crack extension, resulting in a variable essential work of fracture. It is also found that the work dissipated in the outer plastic zone as formulated in the concept does not only reflect the non-essential work but is also related to the fracture process.Instead, the approach based on two material parameters should be used to evaluate the impact fracture behavior. Crack initiation and propagation energies should be considered to account for the variation of material's fracture behavior during crack propagation so as to include time rate and size scale effects.     

The size dependence of micro-toughness in ductile fracture

Micro-toughness in ductile fracture is defined as the plastic work dissipated per unit fracture surface area in the material separation processes of void growth and coalescence. A micromechanics model for the estimation of the size dependence of micro-toughness in ductile fracture is presented. Size effects are incorporated in the model using the conventional mechanism-based strain gradient plasticity (CMSG) theory. A finite element model of an axisymmetric representative unit cell with an initial spherical void is used to validate model predictions. Two characteristic length scales emerge from the model. The initial void radius sets the scale for the initial spherical void growth. For the subsequent void coalescence, the scale is set by the width of the intervoid ligament. Energy dissipation in ductile fracture is found to be dominated by the mechanisms of coalescence, and the micro-toughness in ductile fracture is found to be size dependent for dimple sizes approximately one order of magnitude larger than the material length scale.     

On constructing the theory of ductile fracture near friction surfaces

A criterion of ductile fracture is proposed, which takes into account the singular character of theoretical solutions near the maximum friction surfaces and the emergence of a thin layer with intense plastic strains near surfaces with high friction stresses in real processes of metal forming. The equation for the thickness of the layer with intense plastic strains and the fracture criterion include the strain rate intensity factor, apparently, characterizing the intensity of physical processes that occur in a thin material layer near the friction surfaces. Some experimental data are used to determine the thickness of this layer. The ductile fracture criterion is analyzed by solving the problem of strip extrusion under conditions of plane strain deformation.     

A multiscale model for the ductile fracture of crystalline materials

In this paper, a multiscale model that combines both macroscopic and microscopic analyses is presented for describing the ductile fracture process of crystalline materials. In the macroscopic fracture analysis, the recently developed strain gradient plasticity theory is used to describe the fracture toughness, the shielding effects of plastic deformation on the crack growth, and the crack tip field through the use of an elastic core model. The crack tip field resulting from the macroscopic analysis using the strain gradient plasticity theory displayes the 1/2 singularity of stress within the strain gradient dominated region. In the microscopic fracture analysis, the discrete dislocation theory is used to describe the shielding effects of discrete dislocations on the crack growth. The result of the macroscopic analysis near the crack tip, i.e. a new K-field, is taken as the boundary condition for the microscopic fracture analysis. The equilibrium locations of the discrete dislocations around the crack and the shielding effects of the discrete dislocations on the crack growth at the microscale are calculated. The macroscopic fracture analysis and the microscopic fracture analysis are connected based on the elastic core model. Through a comparison of the shielding effects from plastic deformation and the discrete dislocations, the elastic core size is determined.     

Characterization of the fracture work for ductile film undergoing the micro-scratch

The interface adhesion strength (or interface toughness) of a thin film/substrate system is often assessed by the micro-scratch test. For a brittle film material, the interface adhesion strength is easily obtained through measuring the scratch driving forces. However, to measure the interface adhesion strength (or interface toughness) for a metal thin film material (the ductile material) by the micro-scratch test is very difficult, because intense plastic deformation is involved and the problem is a three-dimensional elastic-plastic one. In the present research, using a double-cohesive zone model, the failure characteristics of the thin film/substrate system can be described and further simulated. For a steady-state scratching process, a three-dimensional elastic-plastic finite element method based on the double cohesive zone model is developed and adopted, and the steady-state fracture work of the total system is calculated. The parameter relations between the horizontal driving forces (or energy release rate of the scratching process) and the separation strength of thin film/substrate interface, and the material shear strength, as well as the material parameters are developed. Furthermore, a scratch experiment for the Al/Si film/substrate system is carried out and the failure mechanisms are explored. Finally, the prediction results are applied to a scratch experiment for the Pt/NiO material system given in the literature. The project supported by the National Natural Science Foundation of China (19891180 and 19925211) and Bai Ren Plan of CAS